A Comprehensive Review of Load Frequency Control Technologies

Abstract

Load frequency control (LFC) is one of the most important tools in power system control. LFC is an auxiliary service related to the short-term balance of energy and frequency of power systems. As such, it allows the acquisition of a central role in enabling electricity exchanges and providing better conditions. The classification of LFC can be carried out from different angles: we can enumerate, among others, the type of control used. The following types of control are presented in this review: classical, optimal, and robust control. More advanced controls can also be used for classification: fuzzy logic control, ANN control, genetic algorithms, PSO control, etc. The influence of renewables and power control tools like FACTS is also considered as a category to be analyzed. The last classifications are related to two important subjects—the influence of DC links on LFC efficiency and the dangers of cyberattacks on the LFC.

1. Introduction

Properly operating interconnected power systems requires maintaining the balance between total electricity production and total load demand, also considering the losses associated with the system. This state of affairs causes the operating point of an electrical system to change over time and, as a result, deviations in the system’s nominal frequency and scheduled power exchanges with other areas may occur, which will adversely affect the operation of the system [1]. Load frequency control (LFC) is an auxiliary service related to the short-term balance of energy and frequency of power systems. It has a central role in enabling electricity exchanges and providing better conditions for electricity exchanges. First, the speed governor controls the speed of the main engine at the generating unit as the load on the generator changes. This function of controlling the rotational speed of the turbines is one of the system’s primary functions. The setting of the governor can be modified (and therefore adjusted) according to the load to maintain the speed of the prime mover as the load on the generator changes. This is the primary speed control function, paramount in keeping the frequency constant. Figure 1 depicts a basic diagram of a single-generation unit’s LFC [2]. The speed governor uses primary and supplementary control loops to sense the change in speed (frequency). The information is transmitted to a hydraulic amplifier, providing the mechanical forces necessary to position the main valve against the high steam (or hydraulic) pressure. The controller, therefore, provides a steady-state power output setting for the turbine. The control is much more complex for an accurate interconnected system than for the single unit shown in Figure 1 [3,4].

Two main parameters characterize studies of LFC. These are the frequency and power deviations of the connecting lines. Their variations are weighted and characterized by a linear combination in an area control error (ACE) variable. Over time, other research contributions, such as automatic generation control (AGC) regulator designs integrating excitation control and parallel AC/DC transmission links, load characteristics and parameter variations/uncertainties, effects of the introduction of the energy market system on the parameters of the LFC models, have been implemented. Models of adaptive AGC regulator models, microprocessor-based AGC, self-adjusting regulators, and new electrical energy supply systems based on renewable energy should also be considered when creating new LFC models.

The first authors who began an analysis of LFC problems were Concordia and Kirchmayer [5,6] and Concordia et al. [7]. These authors conducted an LFC analysis of two area hydrothermal systems. They also conducted a reasonably in-depth analysis of the effect of the regulator dead band [7] and the variation of several parameters on the system’s dynamic performance. Most articles devoted to LFC indicate that Cohn [5,6,7,8,9,10,11] was the first to propose a control scheme for overall power transfer in interconnected power systems based on a bond line polarization control strategy, particularly considerations for deciding frequency bias setting and time error techniques and inadvertent exchange correction for a sizeable multi-area power system. The work carried out during this period took into account the tie-line bias control strategy. Research carried out by Quazza [10] considers non-interactive control, during which the authors put forward a hypothesis whose main axis is the non-interaction between frequency and line power controls, which will result in handling load variations by each control area. In the 1950s and -60s of the 20th century, Aggarwal and Bergseth published research results on the dynamic behavior of LFC systems [11]. When work on optimal control systems could be applied to AGC regulator designs for interconnected power systems [12], a technique based on coordinated system-wide correction of timing error and involuntary exchanges was incorporated into an AGC study by Cohn [13]. Over time, more advanced controllers were designed, thus implementing additional controllers to effectively regulate the ACEs to zero [14,15,16,17,18,19]. The study of AGC for large and complex interconnected power networks involves dividing the entire system into different control areas [20,21,22]. Each control area consists of coherent generators operating at the same frequency.

FACTS and intelligent methods for completing the LFC action are presented in [23,24,25,26]. A control area is responsible for maintaining each area’s power demand and the system’s overall frequency during steady-state operation. The role of LFC in the electricity system with a certain degree of renewable energy penetration and the impact of power flow in LFC calculations are explored in [27,28,29,30,31,32,33,34,35]. When load disturbances occur, the role of each control area is to maintain its frequency and tie-line power by minimizing the ACE, composed, as said above, of deviations in frequency and tie-line power. The use of intelligent methods, the effect of deregulation in LFC analysis, and the impact of LFC analysis in microgrids are presented in [27,28,29,30,31,36]. The study of multi-area systems defined based on multi-control areas began a few decades ago [37,38,39]. This research is characterized by using intelligent methods [40] and considering electric vehicle models [41] in LFC analysis models.

Thus, a question arises: there have been so many reviews on LFC systems published so far. So, what is the point of doing another review? We are trying to give a response to this question. Indeed, there are a lot of comprehensive reviews on LFC [2,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59]. Although they indeed develop a fairly good presentation of state of the art with a fairly well-organized demonstration of LFC solutions for different scientific fields in which the different researchers carry out their activities, there are still quite a few areas that are missing articles. In our article, we found most of the articles on intelligent analysis techniques for LFC. We have even grouped together all the missing articles that we did not find in other journals or from which we extracted the analyses, in a section entitled “other intelligent techniques”, to perform our own analysis of the missing literature. In addition, we have introduced a significantly improved version of the “LFC and cybersecurity” section to insert articles that are relatively poorly known but interesting. Among other valuable comprehensive reviews, there are a few that tackle the problem of LFC in general [60,61,62,63], but most of them present specific research fields like the influence of deregulation on the LFC problem [64,65], LFC and diverse energy sources [66], LFC and renewables [67,68,69], LFC and smart grids [70], LFC, soft computing and optimization techniques [71,72], and LFC and the stabilization of signals in multiarea systems [62].

2. Evolution of the LFC Model Development

Several techniques for developing LFC mathematical models of interconnected power systems have become available thanks to developments in control system design. LFC designs are based on applying techniques developed in control system design. The following control systems can be listed among others. Before the 1950s, “classical“ control techniques were based on methods such as Root Locus, Bode, Nyquist, and Routh-Hurwitz. This period is considered the first era of classical control theory. All of these methods use transfer functions in the complex frequency domain. They also emphasize graphical techniques, the use of feedback, and the use of simplifying assumptions to approximate the temporal response. Unfortunately, these classic control methods were significantly limited in SISO (single-input, single-output) methods. The design of the transfer functions and the frequency domain limited the creation of models to time-invariant linear systems. In a multivariable system, control loops may interact since each single input/single output (SISO) transfer function may have acceptable properties regarding step response and robustness. In this case, the coordinated system control action may not be good. A relatively large number of articles are dedicated to applying classical control theory to LFC [12,73,74,75,76,77,78,79,80,81,82,83]. There are also a few papers in which the LFC system is studied using root locus techniques. In particular, we can list the works of J. E. Van Ness [76] and W. R. Barcelo [77]. The 1950s through the 1960s are considered the modern era of control systems. The adopted methods were based on state and space models developed during this period. The design allows system models to be written directly in the time domain. Analysis and design are also performed in the time domain. The limitations of classical control have been overcome by using methods based on a state space model. A lot of information about the structure and properties of the system could be obtained thanks to modern control. However, other essential feedback properties that could have been studied and manipulated using classical control were hidden. Modern power systems are much more complicated and include multiple inputs and outputs. Classical control theory, capable of handling single-input and single-output systems, is entirely useless for such systems. The design of more efficient AGC controllers for an interconnected power system through the application of modern control theory has been presented in numerous publications over the past four decades. More efficient LFC regulators for interconnected power systems have been designed and implemented by applying modern optimal linear control theory. Since then, a wide variety of articles containing research results on both the design and implementation of optimal LFC systems for power systems have been published [78,80,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104]. However, much of the work carried out so far concerns linearized models of two/multi-area power systems [12,13,97]. We can also cite literature positions in which the effect of generation rate constraint (GRC) has been included by considering both continuous and discrete power system models [105,106]. In reviewing the articles presented in the subsequent points, even more complex models will be presented where the non-linearities of the elements of the LFC control system will be considered.

During the last few years, many scientists have focused their research on considering the impact of time delays due to the usage of communication channels and how to incorporate renewable models in LFC analysis. The modeling and controller design for LFC and demand-side response in a deregulated environment, considering multiple time delays introduced by communication channels, are presented in [107]. The authors of [108] focused on a graphical method to calculate the stabilizing values of the PI controller parameters for a load frequency control (LFC) system consisting of a single area, taking into account the time delay. The authors of [109] showed the generalized extended state observer (GESO) and non-linear sliding mode control (SMC), which are merged to study the frequency deviation problem in multi-area power systems. The impact of an ultra-capacitor (UC) on the LFC of a restructured two-area multi-source system, incorporating a conventional thermal and solar thermal power plant (STPP), is the topic of [110]. The same authors also published an article analyzing the LFC of an unequal two-area system in a deregulated environment [111]. Area 1 comprises distribution generation (DG) and thermal units, and area 2 has gas and thermal units. The DG unit includes a wind turbine system (WTS), dish/Stirling solar thermal system (DSTS), aqua electrolyzer, fuel cell, diesel generator, and battery energy storage system. Finally, the authors of [112] designed an LFC model to analyze the effect of redox flow batteries (RFB) in multi-area restructured power systems.

3. LFC and Deregulation

Energy deregulation consists of selling electrical energy through reverse auctions, where each company offers the most attractive and, therefore, lowest possible price for its independent agencies. Independent agencies purchase the energy needed to meet their anticipated demand and set the best customer rate. Energy is thus supplied via existing utility infrastructure. Utility companies own the infrastructure and are responsible for transporting the energy rather than setting the rate that energy users pay. Retail energy providers compete to offer the best combination of rates and services. The deregulation of the electricity system plays an essential role in an electricity market context. The deregulated electricity system consists of GENCO, TRANSCO, and DISCO (entities responsible for generation, transmission and distribution), or the assessment policy is open. Depending on the leaders’ policy, the GENCOs may or may not have the opportunity to participate in the LDF task. The LFC system is made reliable thanks to the intervention of the independent network operator. Reference [113] details the effects of electricity sector deregulation on LFCs, as many regulated markets have moved towards a hybrid system. The vertically integrated utility that was transformed into many deregulated power systems began to disappear gradually and eventually ceased to exist. Nevertheless, restoring frequency and tie-line power to the desired values for each control area remains relevant as a goal of the LFC. It should also be considered that access to the deregulated electricity system is open. The contracts signed between GENCOS and DISCOS vary depending on the scenarios envisaged. Usually, independent system operators or other bodies are required to establish them. Donde and Pai simulated the LFC system optimization considering the deregulation [114]. The authors presented the concept of the DISCO participation matrix to facilitate the implementation of contracts. A few years later, a generalized dynamic model for an LFC system was developed in a deregulated environment by Shayeghi et al. [115]. A generalized LFC model in which the concept of an augmented generation participation matrix (AGPM) was integrated was developed in [115] to express the effect of possible contracts. The participation matrix is based on the concept of DISCO presented in [114]. The AGPM is an indicator showing the participation of a GENCO in the load according to the contract signed with a defined DISCO. The proposed generalized model helps visualize contracts and introduces new signals containing additional information on the dynamics of the generation distribution from GENCOs to the service of DISCOs carried out through the LFC control system. However, implementing an LFC strategy has always been carried out using linearized models, which only sometimes guarantee the stability of the systems. Already at the end of the 1980s, non-linear LFC models leading to the modification of the linear models used up to a certain period, taking into account the nonlinearities of the system, had been developed by teams from different research centers and published in articles [7,116,117,118]. Tripathy et al. [118] demonstrated the detrimental effect of the nonlinearity of the governor deadband on the stability of the conventional AGC system. The authors demonstrated that the nonlinearity of the governor dead band (GDB) could be the source of continuous oscillations in the transient response of the area frequency and tie-line power. Among recent publications, we can cite the paper [119], where a novel Firefly (FA) algorithm was used to optimize a hybrid fuzzy PID controller with derivative filter (PIDF) for load frequency control (LFC) of a multi-area, multi-source system. This model is further characterized by modeling the deregulated environment in which physical constraints such as GRC and GDB are considered nonlinear. LFC schemes for hydropower systems under deregulation are presented in [120]. The model presented in [121] also represents an interconnected power system with multi-source power generation for LFC in a deregulated electrical environment. The considered model is characterized by a combination of sources such as hydroelectric, thermal reheating and gas-generating units in each control area. A new AGC model with substantial modifications is presented in [122]. One principal modification concerns the turbines, creating aggregate turbines for each type. Another essential modification is the consideration of several types of turbines participating in the secondary control, and the final modification is the consideration of aggregate generation coefficient in forming the rotor angle input of the tie-line model.

Apart from the studies presented above, the LFC study on the deregulated structure of the three-area power system is shown in [123,124,125]. The AGC in a deregulated environment for a four-area interconnected power system is analyzed in [126,127]. In recent years, some authors have published more interesting articles dealing with the problem of LFC in a deregulated environment. We can cite, among others, the authors of [128], who have presented a distributed model predictive controller (MPC) by posing the LFC problem as a tracking control problem in the presence of external disturbances and constraints that represent GRC and load reference setpoint constraints. The distribution company participation matrix and area participation matrix are introduced to simulate the bilateral contracts found in the multi-area block diagram of an LFC model that considers market deregulation.

The penetration level of electric vehicles and renewable energy resources has rapidly increased with the evolution of conventional electricity systems towards the bright grid concept. With such growth in integrating renewable energy sources into the grid, controlling the load frequency is a significant operational challenge encountered in electric grids, requiring careful investigation. One proposed solution to this problem is designing a new fractional-order control system for interconnected power systems considering the deregulation environment [129]. Due to multiple bilateral transactions, a deregulated electricity system is considered complex and uncertain. The problematic nature of the operation and use of robust controllers makes the control of the load frequency in such a system of cardinal importance, hence its imperative nature. However, applications of conventional robust controllers in industry are limited due to their high order. In [130], a structured H-infinity controller has been designed for a deregulated power system with non-linear elements composed, among other things, of GRC and modeling the dead band of the regulator. The authors also considered the delay associated with the system’s communications network in the system from a practical point of view. The authors of [131] have presented a method based on optimal output feedback for LFC to simplify the feedback control by using only the measurable state variables within each control area. From a pragmatic point of view, we see an improvement in the dynamic response to the LFC problem in a deregulated environment. The main problem is limiting access to all system state variables, so it is impossible to measure them all. The optimal output feedback method is proposed in the paper [131] to solve this problem. A performance index under output feedback conditions leading to a coupled matrix equation is minimized to determine the optimal control law.

Open communication infrastructure is becoming an urgent need for the future power system due to the deregulation of the electricity market and the emergence of microgrids and smart grids. Usually, dedicated communication links are used for data exchange in LFC systems. Variable delay can lead to system instability when transferring data in the communication network. The authors of [132] investigate the stability of the LFC system in an islanded microgrid with a time delay. The authors of [133] propose to solve the problem of LFC in a restructured electrical system through a fuzzy controller based on bee mating optimization (HBMOF). In this process, it is essential to fine-tune the PID parameters to achieve the desired level of robust performance. PID parameters can be designed automatically by HBMO to reduce the design effort and find better fuzzy control of the system. Fast convergence of the algorithm and a more flexible controller can be achieved using this algorithm. A deregulated power system with a possible contract scenario under high load demand and area disturbance compared to fuzzy controllers PSO and GA via performance indices ITAE (∆p), ITAE (∆f), and Figure of Demerit (FD) was used to demonstrate the effectiveness of the proposed method.

In many works published on LFC and more area models, most control schemes are based on a centralized control strategy. Many of these strategies are published in [84,85,87,94,96,98,99,100,101,102,103,134]. There is, however, a specific limitation in all the works carried out so far—the centralized control strategy requires the exchange of data from areas of control spread across connected remote geographical territories, taking into account, of course, their complexities in terms of calculation and data storage in the intermediate process.

4. LFC According to the Topology of Power Systems

4.1. Single-Area LFC

The first works devoted to LFC were carried out on single-area models. One can list, among others, the LFC problem for single-area thermal energy systems [135,136,137,138,139]. The simplest models several hundred authors have subsequently referred to are presented in [135,136,137,138,139]. They were followed by models where the GRC is considered [135,139]. Other authors then worked on LFC models of single-area thermal systems with a single delay [137]. The LFC with multiple sources (thermal-hydro-gas) as a single area is proposed in [138]. Pan et al. [135] published a single-area LFC model where an adaptive controller performs the load frequency control of power systems. A PI adaptation was used by the authors for the creation of a new controller to achieve hyperstability and, therefore, to support changes in system parameters. A single-area LFC model using a robust controller, based on the Riccati equation approach, was designed by Wang et al. [136] to carry out power system load frequency control. As system uncertainties can have a significant influence on the accuracy of the developed model, another robust adaptive controller including system parametric uncertainties is proposed for power system LFC in [139]. A single-area model of LFC has also been used for the analysis. The authors of [137] analyzed the delay-dependent stability of the LFC scheme by using Lyapunov-theory-based delay-dependent criterion and linear matrix inequalities (LMIs) techniques. A model of single-area LFC was analyzed by [138]. According to the authors, the model represents a realistic single-area power system with multi-source power generation, including dynamic thermal power plants with reheat turbines, hydroelectric and gas power plants. There are a few newer papers where single-area LFC is still in use; we can enumerate, among others, the approach based on a two-degree-of-freedom, internal model control (IMC) scheme, which unifies the concept of model-order reduction like Routh and Padé approximations, and modified IMC filter design, recently developed by Liu and Gao [140,141]. The paper [140] is illustrates this method. A typical disturbance rejection and large-scale system control problem is presented in [140]. For this purpose, a simple approach to LFC design for power systems with parameter uncertainty and load disturbance is proposed. Two control schemes are used in [142]. The first is an adaptive supplementary control scheme for power system frequency regulation. An improved sliding mode control (SMC) is employed as the primary controller, where a new sliding mode variable is proposed explicitly for the LFC problem. An additional control signal beneficial to frequency regulation by adapting to real-time disturbances and uncertainties can be achieved through the use of an adaptive dynamic programming strategy. The authors of [143] analyzed the demand response (DR) impacts on the dynamic performance of power systems, specifically on the LFC problem. This is achieved by introducing a DR control loop in the traditional LFC model (called LFC-DR) for a single-area power system. The model has the feature of optimal operation through optimal power sharing between DR and supplementary control. Another LFC model that has uncertain parameters and time delays in communication networks but is robust and predictive is presented in [144]. According to the authors, the model is aimed at achieving good performance for the closed-loop system under practical problems of the network including uncertainties in the dynamic model, time delays in the system, and time-varying models. A graphical method to compute the stabilizing values of PI controller parameters for a single-area LFC system with time delay is presented in [108]. The method is based on the stability boundary locus. Finally, a model of LFC where the cybersecurity is taken into account is presented in [145]. A simple yet powerful type of attack, referred to as a resonance attack, on LFC power generation systems is presented in [145]. Specifically, in a resonance attack, an adversary craftily modifies the input of a power plant according to a resonance source (e.g., rate of change of frequency) to produce feedback in the LFC power generation system, such that the state of the power plant quickly becomes instable. We can, therefore, see that although the single zone LFC model seems too simple to be considered in LFC analysis, it provides sufficient understanding of the power system behavior, allowing the user to get an idea of the trend of parameter change in cases where additional control systems are sufficiently complicated.

4.2. Multi Area LFC Models

One of the oldest papers in which a two-area interconnected system is considered is [146]. The model included some novelties for the time, such as non-linearity and consideration of the stochastic nature of the load. The authors of [146] also used an optimal linear strategy, including a stability analysis. The authors of [146] concluded that the observer they used for the given nonlinear system performs well in monitoring the system’s security, and the coordinating control using cross feedback of accelerations gives good results. Nanda et al. [79] included models of steam plants in the LFC model and then investigated the stability and optimum settings of conventional automatic generation controllers for an interconnected power system. The authors concluded that in a reheat system, the optimum controller setting achieved without considering GRC becomes unacceptable in the presence of GRC. A method of designing discrete-type load frequency regulators of a two-area reheat-type thermal system with generation-rate constraints is presented in [82]. A systemic method of choosing the frequency bias parameter and the integrator gain of the supplementary control using the Lyapunov technique is presented in [147]. Moreover, in this case, the authors came to the conclusion that the nonlinearity of the deadband (backlash) of the regulator is a source of continuous oscillation in the transient response of the frequency area. The same phenomenon is observed in the case of the power of the connection line. The authors of [148] presented a new approach for controlling the load frequency of interconnected power systems. This approach is based on the use of variable structure systems theory and linear optimal control theory. A digital simulation of the modeled interconnected power system illustrated the proposed control scheme. A discrete-mode LFC model of an interconnected reheat thermal system, where a new ACE is calculated in the function of tie-power deviation, frequency deviation, time error, and inadvertent interchange, is presented in [149]. The authors stated that unlike a conventional ACE-based controller, they obtained results that show that the design they adopted guarantees zero steady-state timing errors and inadvertent interchange. The effectiveness of small-sized magnetic energy storage (MES) units (both superconducting and normal loss types) in improving the load frequency dynamics of large power areas is presented in [150]. The authors showed that the appropriate design of superconducting magnetic energy storage (SMES) devices can reduce the frequency and power oscillations of tie-lines following small, sudden load disturbances. An improved AGC employing self-tuning adaptive control for both the main AGC loop and SMES is presented in [151]. The results obtained by the authors of [34] showed that the self-tuning regulators significantly improve the system response. A new incremental model of a BES is presented and merged into the load frequency control of a power system [152]. Computer simulations show that the BES effectively dampens the oscillations caused by load disturbances. The frequency control concept and control design of an SMES coordinated with a phase shifter are presented in [153]. The obtained numerical results demonstrated the significant effects of LFC by the proposed control and the economic advantage of MJ capacity of SMES. The authors of [154] proposed a self-tuning fuzzy PID-type controller for solving the load frequency control (LFC) problem. A similar solution is proposed in [155], where fuzzy gain scheduling of PI controllers was applied in the area of load frequency control (LFC). The authors have shown that using variable values for the PI gains in the controller unit improves the dynamic performance of the system. Another example of fuzzy logic control is presented in [156]. The SMES device is controlled by FL to damp the frequency oscillations of interconnected two-area power systems due to load excursions.

A method based on a Type-2 Fuzzy System (T2FS) for LFC of power systems, including SMES units of a two-area interconnected reheat thermal system, is presented in [157]. A new robust PID controller for AGC of a hydro turbine power system, based on a maximum peak resonance specification graphically supported by the Nichols chart, is presented in [158]. Comparison of this new controller with a conventional PI controller and another PID controller used in a multi-machine power system showed remarkably improved system damping. According to the authors of [159], it is possible to conceive a method to consider the effects of nonlinearities in the design phase, even if most conventional linear design techniques can usually not find the sustaining oscillation simulation verifications needed to check the validations after design. When designing the model, it is sometimes necessary to use some nonlinear design techniques, during which parameter optimization methods by Lyapunov’s theorem or squared error integral (ISE) criteria are used. The frequency bias parameters and integrator gains of supplementary controllers can be selected so that oscillations do not occur or their amplitude is reduced. The generation of an optimal fuzzy rule base using the Fuzzy C-Means (FCM) clustering technique for charging frequency control is presented in [160]. The authors conducted a comparative analysis of the performance of the newly designed FCM controller with the conventional controller and the original Fuzzy controller in the presence of GRC. The analysis was carried out for two model cases: a two-area interconnected electrical system and a three-area system. The authors of [161] advocated for abandoning the use of a dedicated network in favor of an open communication network to manage the ACE signals and thereby solve the problem of area control design in LFC of the electrical system. The authors of [162] designed a sub-optimal AGC regulator of a two-area interconnected power system using an output feedback control strategy. The LFC system dynamic performance was investigated by implementing the sub-optimal AGC regulators in the wake of 1% load disturbance in one of the two areas. Another LFC model in which optimal AGC regulators were designed was also used to compare its results with the system dynamic response obtained with the proposed sub-optimal AGC regulators.

Among the newer articles on LFC analysis using a two-area model, the following papers can be considered: in the paper [163], a grid-connected electric vehicle supplies a distributed spinning reserve according to the frequency deviation at the plug-in terminal, which is a signal of supply-and-demand imbalance in the power grid. As a style of EV utilization, it is assumed that vehicle usage times are defined with the next plug-out timing determined in advance. A smart charging control is considered in the scheme considered. Satisfaction of vehicle user convenience and the effect on LFC are evaluated through a simulation. The paper [164] proposes an approach for analyzing the dynamic effects of virtual inertia in two-area AC/DC interconnected AGC power systems. A derivative control technique is used for higher-level control application of inertia emulation. Based on the proposed technique, the dynamic effect of inertia emulated by storage devices for frequency and active power control is evaluated. Further to the results reported by Jiang et al. [137], the paper [134] investigates LFC’s delay-dependent stability, emphasizing multi-area and deregulated environments. The authors used a new stability criterion to improve calculation accuracy and reduce the computation time, thanks to which the method is suitable for handling multi-area LFC schemes. This method is based on Lyapunov theory and the linear matrix inequality technique. The paper [165] studies the impacts of delays due to the use of open communication networks on the stability of single- and dual-area LFC. It proposes an analytical method for determining delay margins and upper bound delay for stability. While open communication infrastructures are embedded into smart grids to support vast amounts of data exchange, they are vulnerable to cyberattacks. The paper [166] investigates the effects of denial-of-service (DoS) attacks on LFC of smart grids. In contrast with existing works, the problem of how DoS attacks affect the dynamic performance of a power system is considered. In a highly penetrated wind farm power system, wind farms can collaborate to control the power system frequency as conventional units would. The paper [167] presents a novel model to control the frequency of the wind farm connected to conventional units. Throughout the proposed frequency control, the integral controller, washout filter, and PID controller could determine the active power variation value in different situations. The paper [168] aims at improving calculation accuracy and reducing the calculation burden of delay-dependent stability analysis for large-scale multi-area LFC schemes in traditional and deregulated environments. The paper [169] presents the automatic LFC of a two-area multisource hybrid power system (HPS). The interconnected HPS model consists of conventional and renewable energy sources operating in disparate combinations to balance the generation and load demand of the system. An Improved Ant Colony Optimization (IACO)-algorithm-optimized fuzzy PID (FPID) controller is proposed by the authors of [170]. The designed controller was used for LFC of multi-area systems. Moreover, the quality of the solution was improved by using the nonlinear incremental evaporation rate and pheromone increment updating. The authors of [171] propose an optimal coordinated control methodology based on multi-agent reinforcement learning (MARL) for multi-area smart generation control (SGC) under the control performance standards (CPS). A new MARL algorithm called correlated Q(λ) learning (CEQ(λ)) is presented to form an optimal joint equilibrium strategy for the coordinated LFC of interconnected control areas, and an SGC framework is proposed to facilitate information sharing and strategic interaction among multi-areas so as to enhance the overall long-run performance of the control areas. The authors of [172] presented cooperative control using differential games (DGs) as a possible solution to the problem of wear and tear of generating units, resulting from the integration of intermittent energy sources such as wind and solar power. The more the intermittent sources are present in the power system, the bigger the regulation burden of the control areas that lacks regulation capacity by providing the power supports via the tie-line. In [173], a new method is put forward for the closed-loop stability analysis of a PI-type LFC scheme with interval time-varying delay. Improved delay dependent conditions in terms of linear matrix inequalities for single-area and multi-area LFC systems are deduced by the proposed augmented Lyapunov–Krasovski (L-K) functional. The robust H_∞ sliding mode LFC (SMLFC) of a multi-area power system with time delay is investigated in [174]. The sufficiently robust frequency stabilization result for a multi-area power system with delay is presented in terms of linear matrix inequalities (LMI). Practical LFC is actually a sampled-data system, where the power commands sent to generation units are updated every few seconds. It is therefore desirable to analyze the delay-dependent stability of LFC when sampling is introduced. The authors of [175] undertook stability analysis of LFC with both sampling and transmission delay. The authors of [176] proposed an adaptive resilient LFC scheme for sub-systems of smart grids under DoS attacks with energy constraint. The method used has three stages—firstly, a resilient triggering communication scheme is introduced, where the triggering condition includes the uncertainty item induced by DoS attacks. Secondly, an adaptive resilient event-triggering LFC scheme is proposed to further reduce the communication burden and defeat the DoS attacks. Third, a stability criterion is derived for PI-based LFC systems by employing Lyapunov theory.

There are a large number of articles devoted to three or more area systems. Their analysis would require much more space; apart from that, the articles are relatively detailed and can be analyzed individually by those interested.

5. Decentralized Control

To be adequately implemented, LFC requires the availability of the state variables of the entire power system at one location (centralized control law). Therefore, implementing a centralized scheme will require complex data acquisition systems. The reliability of control systems involving extensive use of communication links is reduced. In contrast, system complexity is increased since redundancy and state estimation techniques must be employed to filter out the effects of data transmission errors. This centralized information structure does not match the distributed information structure of electric power systems, which are geographically dispersed, and distances between their interconnected components can be substantial. In the event of communications link failures, backup control systems are required because data transmission delays and data acquisition cycle times do not support the design of centralized control hardware and will undoubtedly increase the cost of the control system. Decentralized control strategies are therefore favored for economic and reliability reasons. These policies allow each area to be controlled separately using only the available information. In many research papers, continuous and discrete time system models are included in different LFC models using the concept of decentralized control [123,144,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193].

The authors of [192] presented the optimal decentralized LFC design for multi-area interconnected electric power systems. A fixed mode evaluation algorithm based on eigenvalue dynamics determines the proposed decentralized control scheme. The eigenvalue sensitivity expressions are also used to determine decentralized feedback gains, resulting in system transient performance similar to that obtained with a centralized optimal control law. The authors of [191] analyzed the structural properties of observability and controllability for a class of interconnected power system models. A state-space representation that is wholly observable and controllable is developed for a two-area interconnected power system. The area control feedback loops are completely decoupled thanks to the introduction of a complete decentralization of a global state-feedback control policy (e.g., pole assignment and optimal control). The authors of [190] presented a new LFC model based on a reduced-order observer and a PI controller in each area of the power system. The features of the decentralized scheme were designed to meet the requirements of the global system, a constraint-free structure for the feedback controller, and avoid the need for inter-area transfer of data for LFC. The authors of [189] presented systematic distributed control design methods suitable for large-scale interconnected power systems. The authors have adopted the following design methods: (i) a design method based on distributed implementations of centralized control systems, (ii) a design method based on model reduction in dynamical systems, and (iii) a design method based on modeling of the interactions between the subsystems understanding the global control system. The decentralized load frequency controller design problem has been transformed into an equivalent problem of MIMO-based decentralized controller design [188]. To this end, a multi-input multi-output (MIMO) control system has been designed. The authors have demonstrated that each local area load frequency controller can be designed independently, fulfilling a condition based on the structured singular values. Similarly to [188], the authors of [187] have also shown that although the design of decentralized robust LFC for interconnected multi-area power systems can be naturally formulated as a large-scale system decentralized control problem, it can also be transformed into an equivalent problem of decentralized controller design for a multi-input multi-output (MIMO) control system. The authors have proved that once the diagonal dominance is achieved in the multivariable system, simple controllers can be designed to achieve satisfactory performances. The authors have also proved that subject to a condition based on the structured singular values (SSVs), each local area load frequency controller can be designed independently even when diagonal dominance cannot be achieved. The authors of [186] presented a simple but easy-to-implement algorithm based on a variable-structure-system concept that could be applied to the problem of AGC of interconnected power systems. The authors also analyzed the effect of GRC nonlinearity on the system’s dynamic performance for reheat- and non-reheat-type steam turbines. The authors of [123] developed a new decentralized robust control strategy based on the mixed H₂/H_∞ control technique for solving the LFC problem in a deregulated power system. According to the authors, this newly developed design strategy combines the advantage of the H₂ and H_∞ control syntheses to achieve the desired level of robust performance against load disturbances, modeling uncertainties, and system nonlinearities. It gives a robust multi-objectives design addressed by the linear matrix inequality (LMI) techniques. The same authors have published a similar paper [193] where a new approach based on the µ-synthesis technique is presented for the robust decentralized load frequency controller design of a restructured multi-area power under the possible contracts. The LFC model has been designed so that in each control area, the connections were set so that the effects of potential agreements between areas are treated as a set of new disturbance signals to achieve decentralization between this area and the rest of the system. The authors of [193] have shown that, subject to a condition based on the structured singular values and H_∞ norm, each local area load frequency controller can be designed independently. The authors of [177] have published a paper on load frequency control of a multi-area power installation. The robust control theory can be used to decouple the areas for a decentralized complete load frequency controller. A new technique is included to exclude feedback from any immeasurable state. The product comprises a set of local load frequency controllers, one for each area. The design and operation of each local controller solely require the corresponding area’s parameters and state measurements. The proposed controller ensures that the overall multi-area power system is asymptotically stable. The authors of [178] have analyzed the LFC of large-scale power systems with unknown parameters using a new model reference-decentralized robust adaptive-output feedback controller. The control strategy used by the authors requires only local input–output data and can follow random changes in the operating conditions. The controller is designed so that each area’s trajectory errors and control gains remain uniformly delimited.

The authors of [179] proposed a new method for including a contribution from the demand side to primary frequency control. This type of technical solution has not been practiced in LFC because of problems dealing with many small loads rather than a limited number of generating units. The main difficulty is related to the cost and complexity of two-way communications between many loads and the control center. The authors of [179] proposed a method where this two-way communication is not essential, and the demand can respond to frequency error like the generators. The paper [180] presented a unified PID tuning method for power system LFC. The two-degree-of-freedom (TDF) internal model control (IMC) design method along with a PID approximation procedure was used by the tuning method. The time-domain performance and robustness of the resulting PID controller are related to two tuning parameters, and robust tuning of the two parameters is discussed. The author of [180] has shown that the presented method applies to power systems with non-reheated, reheated, and hydro turbines. The authors of [181] presented a method for tracking a secondary frequency control signal by groups of plug-in hybrid electric vehicles (PHEVs), controllable thermal household appliances under a duty-cycle coordination scheme, and a decentralized combined-heat-and-power generation unit. The LFC model presented by the authors of [181] consists of the following elements: groups of plug-in hybrid electric vehicles (PHEV), controllable thermal household appliances within the framework of a duty cycle coordination scheme, and a decentralized system with combined heat and power unit. Everything is managed simultaneously by tracking a secondary frequency control signal. The distribution of the control action on the participating units is performed by an aggregator utilizing a model predictive control (MPC) strategy, which allows the inclusion of unit and grid constraints. The design of a load frequency controller based on the decentralized sliding mode control is presented in [182]. The controller was tested in multi-area interconnected power systems with matching and unmatched uncertainties. The system’s dynamic performance in reaching intervals is improved by constructing PI switching surfaces in each area. An aggregated electric vehicle (EV)-based battery storage representing a V2G system is presented in [183]. The designed controller was used in long-term dynamic power system simulations. The analyzed cases concern typical days with high and low wind generation in the power system of Western Denmark. The paper [184] proposes a data-driven cooperative method for LFC of the multi-area power system based on multi-agent deep reinforcement learning (MADRL) in the continuous action domain. The proposed method can nonlinearly and adaptively derive the optimal coordinated control strategies for multiple LFC controllers through centralized learning and decentralized implementation. A robust predictive LFC for power systems with uncertain parameters and time delays in communication networks is presented in [144]. The proposed approach aims to achieve good performance for the closed-loop system under practical network problems, including uncertainties in the dynamic model, time delays in the system, and time-varying model. A robust decentralized PI control design for power system load frequency regulation with communication delays is proposed in [185]. The proposed methodology reduces the PI-based LFC problem to a static output feedback control synthesis for a multiple-delay system. The proposed control method gives a suboptimal solution using a developed iterative linear matrix inequality algorithm via the mixed H₂/H_∞ control technique.

6. Robust Control

In power systems, changes happen constantly in system parameters and characteristics, starting with load variations, modeling, and linearization errors and ending with environmental conditions. Therefore, each control area can appear in different uncertainties and disturbances. Consequently, it is typical for a power system’s operating points to change very randomly during a daily cycle. It is difficult and practically impossible to develop an optimal design of the LFC regulator based on the nominal values of the system parameters. This design is undoubtedly impractical in the case of LFC control. Therefore, implementing this type of regulator on the system would only be improved if one would like to ensure the desired operation of the system. This could lead to a degradation of the system’s dynamic performance or even a loss of system stability.

At the beginning of the 1970s, two main problems had to be overcome when creating models and solving the problem of LFC. The first one was the computation of an optimal controller, which became a challenging and time-consuming task as the order of the system went up, especially in a multiarea load frequency control system. The second problem was accessing the necessary data for the calculation because measuring some of the state variables could have been more feasible. Thus, it was impossible to implement the optimal controller that used all the state variables. Glover and Schweppe [194] have developed an advanced LFC law version based on an optimal control strategy. H.G. Kwatny et al. [105] have also proposed an optimal tracking approach for the design of an LFC system. The authors of [195] presented a method based on a theory of the construction of an observer. The closed-loop controller using a compatible observer responded almost identically to that obtained when all the state variables were measurable. Scientists have made considerable efforts to design LFC controllers with better performance to cope with changes in system parameters using various robust methodologies [136,139,195,196,197,198]. According to the robust control approach, in the case of LFC, the control objectives are linked to meeting the requirements of nominal stability and nominal performance and obtaining stability and robustness of the control from the performance point of view of LFC controllers of electrical systems. Wang et al. [136] have proposed a robust controller, based on the Riccati equation approach, for power system load frequency control. The design of the controller was quite simple, and it turned out that the controller is effective and can ensure that the entire system is asymptotically stable in the face of all probable uncertainties. A similar controller is proposed based on the robust control approach and an adaptive control technique [139]. The motivation for combining robust control with adaptive control is as follows: the full control approach aims to address minor parametric uncertainties and then use adaptive control for significant parametric uncertainties. The overall objective is to ensure the stability of the overall system and, at the same time, achieve good performance for all admissible uncertainties. After performing some simulations, the authors concluded that the proposed charge-frequency controller can work well even with the GRC. The authors of [139] have shown that loop-shaping methods, such as QFT, can significantly help design an effective, robust controller for LFC. A solid physical understanding of the system is necessary for creating this type of controller. A new method based on Lyapunov stability theory to implement a robust stabilizing controller is presented in [196]. The technique is combined with ‘matching conditions’ and tested for the load frequency controller of interconnected power systems with uncertain parameters. Another method for a robust decentralized load frequency controller, based on the Riccati equation approach, is proposed by some of the authors of [136,139] in [198] but for multi-area power systems with parametric uncertainties. The authors showed that the resulting controller needs neither remote communication nor feedback from other areas because it operates solely on its local measurements. The overall system is asymptotically stable for all admissible parametric uncertainties of the system. Enhancing inter-area mode damping is possible using multiple flexible AC transmission systems (FACTS) devices. Chauduri et al. have demonstrated an example of it in [199]. The paper [199] is not directly related to the LFC problem but could be an example of robust control in power systems. Two robust decentralized design methodologies for LFC are presented in [200]. The first one is based on control design using the linear matrix inequalities (LMI) technique. This method is aimed at obtaining robust control so that uncertainties have no effect on it. In contrast, the second controller is more appealing from an implementation point of view because it has a more straightforward structure. Moreover, its tuning is performed by a proposed novel robust control design algorithm to achieve the same strong performance as the first. The authors of [201] proposed a fuzzy system to adaptively decide on the appropriate PI gains of a PI controller based on the ACE and its change. Control is carried out by a Fuzzy-PI (FPI) controller. A strategy for solving the problem of non-accounting the non-linearities when creating the LFC model because of the distributed nature of a multi-area power system is presented in [202] by using a multi-agent reinforcement learning (MARL) approach. It consists of two agents in each power area; the estimator agent provides the ACE signal based on the frequency bias (b) estimation. The controller agent uses reinforcement learning to control the power system, and genetic algorithm optimization is used to tune its parameters. The problem of communication delays due to the system’s complexity and the open communication infrastructure is tackled in [203]. The authors showed that the possibility of communication signal delays and other problems must be carefully analyzed. A robust decentralized PI control design for power system load frequency regulation with communication delays is presented in [185]. The proposed control method gives a suboptimal solution using a developed iterative linear matrix inequalities algorithm via the mixed H₂/H_∞ control technique. The authors of [204] focused on the real-time detection of faults in the load frequency control loop of interconnected power systems. An algorithm for fault detection occurring under different operating conditions is presented. The model considers uncertainties, unknown changes in the load demand, and other external disturbances, such as plant and sensor noise. Although the approach applies to N-area systems, a two-area interconnected power system example is considered for simplicity [204]. As it was in the cases presented in [185,203], the usage of communication channels introduces time delays in LFC schemes. Those delays may degrade dynamic performance and even cause instability in a closed-loop LFC scheme. The authors of [205] presented a delay-dependent robust method for analysis/synthesis of a PID-type LFC scheme considering time delays. The authors of [206] presented the effects of introducing renewables and new power compensation technologies in the power systems. Higher penetration of wind generation and intermittency of its generation may cause a problem of significant frequency fluctuation when the load frequency control (LFC) capacity is not enough to compensate for the unbalance of generation and load demand. In the future, with V2G technology, plug-in hybrid electric vehicles (PHEV) are widely expected to be used for driving on the customer side. Generally, the power of a PHEV is charged by plugging into the home outlets as the battery energy storage is dispersed. The authors of [206] also presented a new coordinated V2G control and conventional frequency controller for robust LFC in the smart grid with large wind farms. The optimized SOC deviation control controls the battery state of charge (SOC). The structure of the frequency controller is a PI with a single input. The paper [207] again showed the impact of uncertain transmission delays, sampling periods, and parameter uncertainties regarding the power system. Other contingencies like load fluctuations and the intermittent generation of renewable energy sources (RESs) are also considered, including a robust delay-dependent PI-based LFC scheme for a power system based on sampled-data control. Another robust control design method for LFC is proposed in [208]. This time, the considered model includes distributed battery energy storage systems (BESSs) in LFC through BESS aggregators with sparse communication networks. A two-layer MPC is developed to provide more efficient control signals to improve the response of BESSs and make a more significant contribution to the LFC. The outer layer in the proposed structure produces the command signal for the aggregator based on signals produced by the inner layer and the signal provided by the actual system. Given various operational and physical constraints, these command signals are provided to achieve the lowest error value in ACE with a minimum control effort. Introducing electric vehicles for both the primary and secondary frequency controls may help rapidly suppress fluctuations in the system frequency due to load disturbances. Unfortunately, the wider the system is, the more complex the coordination of the overall control is. In networked control and wide-area communication infrastructures, multiple intervals of time-varying delays exist in the communication channels between the control center, power plant, and an aggregation of electric vehicles. Additionally, the coordination of the batteries’ state of charge control, the behaviors of the vehicle owners, and the uncertainties imposed by the changes in the batteries’ state of charge have to be considered. The authors of [209] first proposed a power system incorporating multiple time-varying delays and uncertainties. Then, they designed a robust static output feedback frequency controller to guarantee that the resulting closed-loop system is stable with an H_∞ attenuation level. The design conditions are formulated regarding tractable linear matrix inequalities that various computational tools can efficiently solve. One of the main obstacles to using DR in frequency regulation is communication delay, which exists when transferring data from the control center to appliances. To overcome this issue, an adaptive delay compensator (ADC) is used to compensate for the communication delay in the control loop. A modified frequency control model is proposed, where the demand response (DR) control loop is added to the traditional LFC model to improve the frequency regulation of the power system. An adaptive delay compensator (ADC) compensates for the communication delay in the control loop [210]. Another example of using MPC in LFC is presented in [211]. The model presented considers a gate-controlled series capacitor (GCSC) to contribute to LFC. The proposed control model consists of a two-layer MPC. A nominal MPC produces an initial control signal and predicts system frequency response in a little system without uncertainty. An ancillary MPC has a control command for the actual system with uncertainty based on measurements and signals provided by the nominal system. Optimization procedures are also conducted to attain optimal weighting coefficient values associated with the objective functions’ input and output. Due to the extensive practice of open communication links in the power system network, communication time delays are inevitable. They cause the deterioration of the performance of the LFC system, and in the worst conditions, the LFC system becomes unstable. A robust PI derivative double derivative (PIDD2) controller design for the perturbed LFC of the interconnected time-delayed power system is proposed in [212]. The PIDD2 controller is designed for the selected worst-case plant model of the original interval plant and is tuned using an internal model control (IMC) approach. The proposed control scheme is validated on a two-area time-delayed power system model in which parametric uncertainties in system parameters, CTD, nonlinearities, and step load demand disturbances are considered. An adaptive LFC model for interconnected power systems is presented in [213]. A novel control methodology using a robust UIO for dynamic state estimation and an interval type-2 fuzzy logic controller is presented in this paper. The considered power system is characterized by high penetration of renewable energy in a restructured power system environment. Regardless of unknown inputs or disturbances that impact the frequency stability, the proposed robust UIO can independently estimate the actual state of the power system in real-time. An interval type-2 fuzzy logic controller in the LFC loop of each interconnected system area is used to dampen frequency oscillations efficiently, thereby improving power system stability and resilience.

7. Optimal Control

One of the first papers discussing optimal control in LFC is [94]. The authors have presented a model in a mathematical form necessary for applying modem optimal control theorems. The authors have shown feasible ways to improve the megawatt-frequency control system’s dynamic response and stability margins. The authors of [88] proposed using a controller based on optimal stochastic system theory for solving the LFC problem of a classical two-area power system. Comparative studies have been conducted on the response of an interconnected power system using the new control algorithm to the response obtained using the conventional control strategy. A decentralized control method with a fixed mode evaluation algorithm based on eigenvalue dynamics is proposed in [92]. Decentralized feedback gains are determined using the eigenvalue sensitivity expressions. This will lead to the assessment of system transient performance similar to the one obtained with a centralized optimal control law. An optimal control algorithm for solving the LFC problem for a symmetrical two-area electric energy system is presented in [214]. The simulation conducted by the authors of [214] showed that the new formulation (1) is consistent with the operating policy in force during this period and (2) leads to improved system performance. In [195], a method of determining the suboptimal control of the system using the theory of aggregation of Aoki [215] was presented to overcome the difficulties of optimal controller computation in multiarea LFC. A bang-bang LFC policy based on Lyapunov’s second method is proposed in [216]. The proposed method is simple and practically feasible for implementation. A new method for process transfer function identification (TFI) and a new approach for developing a power unit’s dynamic model based on new applications for the presented TFI method are given in [217]. The power unit dynamic model, identified using three simple experiments, is applied to load frequency control. This dynamic model developed for the vicinity of the steady-state operation mode can be used for AGC purposes to tune load frequency control systems and build and set up a real-time simulator for dispatcher training. A suboptimum solution to the problem of sampled data optimum load frequency control with unknown deterministic incremental power demand is presented in [218]. The authors used a three-stage procedure to design a suboptimum stochastic controller. The first stage consists of determining the control gain for a deterministic optimum control, the second stage consists of creating a class of deterministic observers, and the third and final stage is adaptively choosing a scalar observer gain to minimize an instantaneous cost index. A dynamic optimization procedure used in the design of power systems’ LFC is presented in [219]. The LFC design is based on the optimal linear regulator theory, accommodated to satisfy the performance objectives of the LFC in extensive multiarea interconnections. According to the authors of [105], LFC can be considered a limited generation response capability problem. The problem is with the low-frequency domain associated with bulk generation change. The authors have proposed to formulate the LFC problem as a tracking one in which a tracking problem whereby energy source dynamics and load following play a central role. The derivation of output feedback and decentralized PI controllers suitable for controlling the frequency and tie-line powers in interconnected power systems is presented in [96]. The controller design method is based on the solution of a standard state feedback optimal control problem but with some constraints imposed on the structure of the feedback gain matrix. The structure of the controllers considered in [220] is much simpler and can be more readily implemented since, unlike methods presented in previous papers, where either an optimal state feedback law or a state estimator is used; the technique proposed in [220] uses only the directly measurable system state variables. A sub-optimal AGC regulator design for a two-area interconnected power system using a constrained feedback control strategy is presented in [221]. The power system dynamic performance is analyzed based on time response plots achieved with the implementation of designed optimal and sub-optimal AGC regulators in the wake of 1% load disturbance in one of the areas. Another version of the paper [221], which uses a sub-optimal AGC method, is presented in [162]. The authors used an output feedback control strategy, which has been applied in designing a regulator for a two-area interconnected power system. We can cite recent analyses concerning event-triggered control [222], where the authors present a system based on event-triggered fuzzy load frequency control. The controller was applied in a model containing wind power systems (WPSs) where the measurement outliers and transmission delays were also considered [222].

During the last few years, more modern methods have been used for optimal control of LFC systems. The authors of [223] presented a marine vessel power system with photovoltaic, WT, SWE, and ESS, which can be considered a specific mobile islanded microgrid. A new optimal fractional-order fuzzy PD+I LFC for islanded microgrids was designed for the microgrid model. The paper [224] proposes a data-driven, model-free method for LFC against renewable energy uncertainties based on deep reinforcement learning (DRL) in the continuous action domain. The authors of [225] proposed a novel frequency control method based on double sliding mode (SM) controllers for isolated microgrids with renewable sources. The controller was designed so that the SM pitch angle controller for the wind turbine generator (WTG) system has to smooth the wind power output. An SM load frequency controller (LFC) is also constructed for the diesel generator system to restore system frequency to normal through the secondary frequency regulation. In a typical renewable energy integrated micro-grid (REMG), micro-pumped storage units that rely on a tall building are built to convert energy by pumping water up to store energy and releasing the stored water to generate power. The authors of [226] proposed a novel energy storage method based on pumped hydropower (PHES) storage. The LFC controller optimization problem for the REMG is investigated, and the design of optimal controllers for multi-areas in the REMG is performed. A new approach employing an unknown input observer (UIO) for each power system area for tracking the dynamic states in real-time operation is proposed in [227]. Based on this approach, a novel, fully decentralized LFC approach was designed considering dynamic state estimation (DSE). The authors of [228] proposed a novel, unknown input functional observer-based optimal LFC approach for real-world complex nonlinear power systems. The control signal applied to each power plant is directly estimated via the well-designed functional observer. The proposed applicable dynamic estimator can handle parametric and nonparametric uncertainties, control loop and sensor faults, unknown inputs, and cyber-attacks. The paper [229] deals with a robust sliding mode control strategy based on the adaptive event-triggered mechanism against the frequency deviation caused by power imbalance or time delays. The control process is divided into four stages: first, a three-area power system attached to renewable energies and energy storage is considered, and the corresponding LFC model is established. Afterward, the networked control is introduced into the LFC scheme, and the adaptive trigger mechanism, which can adaptively adjust the event-triggered threshold, is designed to improve the data transmission efficiency; the LFC scheme with network-induced delays is formulated. The third stage is dedicated to the design of the Luenberger observer aimed at the estimation of the state errors and the design of the sliding surface; hereafter, the overall closed-loop system asymptotically stable and robust performance is analyzed by solving linear matrix inequalities. During the final stage of the control process, the control law proves that the system state trajectory can be driven into the designed sliding surface in a limited time. The utilization of wind turbines (WTs), solar generation, sea wave energy (SWE), and energy storage systems (ESSs) in marine vessel power systems is presented in [230]. A navigational vessel power system with photovoltaic (PV), WT, SWE, and ESS can be considered a mobile-islanded MG. An optimal modified model-free nonlinear sliding mode controller is introduced for the secondary LFC to balance consumption and power generation in shipboard MGs. The paper [231] is devoted to solving problems of fault estimation and fault-tolerant control for multiarea power systems with sensor failures. An integral-type sliding-mode control scheme against faults and disturbances is proposed to ensure that the resultant fault system is asymptotically stable, from which each subsystem state in the multiarea power system can be driven onto the designed sliding-mode surfaces in both the state estimation and error estimation spaces. The application of the increased integration of cyber and communication networks in microgrids for obtaining measurements and relaying controls results in a cyber–physical microgrid (CPM) is quite challenging in many applications. One example of such a complex application is LFC since the stochastic behavior of renewable generation makes this task more challenging. The participation of electric vehicle batteries in LFC is facilitated by the use of cyber–physical microgrids (CPM). Unfortunately, using information and communication technologies provides many advantages and leads to a close synergy between heterogeneous physical and cyber components, unlocking access points for cyber intrusions. An observer-based control strategy that can observe stochastic dynamic encumbrances and reimburse for them through a two-layer controller is presented in [232].

8. Intelligent Algorithms

8.1. Fuzzy Logic

Fundamental changes are occurring in LFC of interconnected power systems due to rapid growth in the number of RES, including wind turbines, PV, and other types of energy production/consumption technologies. Multi-objective regulatory optimization problems are characterized by a high degree of (1) policy diversification and (2) a wide distribution of demand and supply sources. Due to the complexity of the network structure, the infrastructure of modern LFC systems should be able to handle all these complex issues and ensure that the LFC systems can maintain the generation load balance after serious disturbances. For example, wind power fluctuations impose an additional power imbalance on the electrical system and cause a frequency deviation from the nominal value. Many studies have been reported in the literature on designing a fuzzy logic-based LFC regulator [155,233,234,235,236,237,238] to consider various aspects of the power system. Research on the LFC problem shows that among the intelligent controller tuning methods, fuzzy PI is among the most straightforward and most applicable to suppressing constant error [154,235]. On the other hand, the fuzzy PI controller is known to perform poorly in the system’s transient response.

The authors of [233] presented a new approach to studying the area LFC problem using fuzzy gain scheduling. The parameters of the PI controllers are optimized using the FL method, and zero steady-state time error and tie-line power exchange are guaranteed through optimal calculation of the area control error. The model considered in this paper includes control dead bands and GRC. Another method of fuzzy logic application for LFC is presented in [234]. A Sugeno-type fuzzy inference system was used for conventional PI and optimal load frequency controllers [236]. A smooth interpolation of the linear gains in the input space was performed, given that the system was well adapted. This takes place when the very non-linear system moves into its operating space. Fuzzy gain scheduling of PI controllers was used to solve the LFC problem. The system’s dynamic performance is improved by using variable values for the PI gains in the controller unit. The authors of [154] proposed a self-tuning fuzzy PID-type controller. The fuzzy PID type controller is constructed by establishing a set of rules, and then the control signal is directly deduced from the knowledge base and fuzzy inference. The problem of decomposition of multivariable systems for distributed fuzzy control is solved so that the power system is also decomposed regarding its load frequency control [237]. The authors concluded that their method suits multivariable systems with many state variables and efficiently implements distributed fuzzy control algorithms. The authors proposed two intelligent load frequency controllers [238] to regulate the power output and system frequency. The regulation is performed by controlling the speed of the generator with the help of fuel rack position control. The two controllers fulfill two very different roles—the first controller is obtained using fuzzy logic (FL) only, whereas the second one uses a combination of FL, genetic algorithms, and neural networks. As for any regular LFC control, whenever there is any change in the load demand, the controller strives to restore the frequency to its nominal value in the shortest time possible in a very smooth way. The authors of [235] have analyzed the problems associated with secondary frequency control and AGC. A fuzzy controller has been designed as part of the AGC system. The authors have worked on the design, implementation, and operational performance of the new regulator in Eskom’s National Control Centre. The difficulties associated with optimizing the original standard AGC controller are presented in detail in the article. A two-layered fuzzy controller for solving the LFC problem is presented in [239]. The first one is called the compensator, which generates and updates the reference value of ACE. In contrast, the second one, called the feedback fuzzy logic controller, makes the ACE decay to zero at a steady state. A comparative analysis of the power system frequency error responses using the conventional integral control system only and the proposed fuzzy controller is presented in the paper. Another application of the fuzzy logic controller in LFC is presented in [240]. The controller was applied to a two-area reheat thermal power system. Different types of inputs for the FLC and other numbers of triangular membership functions (MF) are considered to examine their effect on the dynamic responses of the AGC system. The performance of FLC has been compared with that of a conventional integral controller in the absence and presence of GRC.

Among the newer papers on using fuzzy logic controllers in LFC, the following can be listed: The direct-indirect adaptive fuzzy control technique is used to develop a novel LFC for multi-area power systems [241]. The authors have used the approximation capabilities of the fuzzy logic system to work on appropriate adaptive control laws and parameter-updating algorithms for unknown interconnected LFC areas. To minimize the approximation errors and the effects of external disturbances, a tracking performance criterion was introduced, and by the way, the stability of the closed-loop system is guaranteed. The system frequency deviation and power changes in tie-lines are minimized simultaneously using a new decentralized LFC scheme based on fuzzy logic [242]. This type of control is necessary for adequately functioning interconnected electrical systems in the presence of high-penetration wind energy. The particle swarm optimization (PSO) technique determines membership function parameters for optimal performance. The authors of [170] proposed a fuzzy PID controller (FPID) optimized by an improved ant colony optimization (IACO) algorithm for the LFC of multi-area systems. The quality of the solution could be improved by using the nonlinear incremental evaporation rate and updating the pheromone increment of the IACO algorithm. A modified objective function was proposed to improve the controller’s performance using parameters such as integral time multiplication absolute error (ITAE), overshoot, undershoot, and settling time with appropriate weighting coefficients. Moreover, sensitivity analysis is implemented under wide variations of operating conditions and system parameters to demonstrate the robustness of the proposed control method. Finally, the model was tested in a two-area, four-source hydrothermal power system with/without High Voltage Direct Current (HVDC) link. The authors of [243] propose a hybrid energy system with the application of a tidal power unit (TPU) and vehicle-to-grid (V2G) planned efficiently as an isolated MG. To adjust the uncertainty footprint (FOU) of the SIT2-FLC coefficient and thus improve the performance of the LFC, a new fractional gradient descent (FGD) based on a type 2 fuzzy logic controller with an interval of Single Input (SIT2-FLC) is suggested as the primary LFC controller. To generate the additional control action, which is useful for frequency stabilization by adapting to the randomness of load disturbances and RES, a deep deterministic policy gradient (DDPG) is generated, and the actor-critic framework is considered [243]. The increasing penetration of RES means that the adverse effects of specific sources are increasingly felt. Fluctuations in wind power can cause additional power imbalance to the electrical system and negatively affect frequency regulation performance. Faced with this challenge, the article [244] proposes a solution to simultaneously minimize the system frequency deviation and the tie-line power exchanges through an intelligent PI fuzzy logic scheme. This control is essential for properly functioning the LFC system with high wind energy penetration in interconnected electrical systems. The PSO technique determines the membership function parameters online to obtain optimal performance. In all analyses, the physical and technical aspects were fully considered. An adaptive multi-objective fractional-order PID controller improves the LFC of islanded microgrids (MGs) [245]. The MG is equipped with BESS in the form of electric vehicles (EVs). The unbalanced effects between the load and the supply of an isolated MG can be resolved by installing battery energy storage systems (BESS), one of the alternative solutions, electric vehicles. Electric vehicles can, therefore, be used as BESS according to the Vehicle-to-Grid (V2G) concept, significantly since the high costs and the tendency to degrade BESS are limiting factors. For the V2G controller to operate optimally under a wide range of operating conditions caused by the intermittent behavior of renewable energy resources, a novel fractional-order multiobjective control strategy for electric vehicles in V2G scenarios was designed [245]. A fuzzy adaptive model predictive approach for LFC of an isolated microgrid is presented in [246]. The authors implemented a centralized MPC with a single-input multi-output system model based on the distributed energy resources controlled in the microgrid. The parameter R_w of the MPC can be dynamically adjusted using a fuzzy controller, making MPC parameter-driven adaptable. The electricity network is the backbone of the main infrastructures that drive the country’s defense and economy. As a result, it is a prime target for cybercriminals and deserves special attention. As multi-area power systems can be subjected to multi-layer attacks, a novel distributed fuzzy-LFC approach is investigated for their defense. The system’s nonlinearities can be modeled and analyzed in the Takagi–Sugeno (T–S) interval type 2 (IT2) fuzzy framework. We know very well that this type of nonlinear factor does indeed exist in the dynamics of the turbine and the regulator. It should also take into account the uncertain parameters associated with it. The authors of [247] modeled multilayer attacks threatening the stability of power systems as an independent Bernoulli process. DoS attacks in the cyber layer and phasor measurement unit (PMU) in the physical layer can also be modeled similarly. An area-dependent Lyapunov function can be demonstrated, and sufficient conditions guaranteeing the asymptotic stability of the system with the ACE signals satisfying the H_∞ performance are deduced.

8.2. Artificial Neutral Networks (ANN)

During the LFC process, a compromise between fast transient recovery and low overshoot in the dynamic response of the overall system has to be made. The integrated controller of which most LFC systems are made has a gain which has to be set to this end. This type of regulation is nevertheless a great default—due to its slowness, the controller does not allow the controller designer to take into account possible changes in operating conditions and non-linearities of the generator, which is already related to its second primary defect, which is the need for more robustness. Scientists and engineers have conducted research to model controls on human neural network systems based on the human ability to control complex installations. Due to their excellent ability to model any nonlinear process, neural networks (NN) are used in different control problems. Neural networks are ideally suited to processes with various operating conditions. ANNs are appropriate to solve complex problems thanks to the following features: they possess massive parallelism and an ability to learn any nonlinearities, which are quite common in power system processes where nonlinear control problems occur, primarily when the system operates over the nonlinear range. The applications of ANNs for solving the LFC problem are reported in refs. [84,87,101,102,103,104].

LFC in renewable power systems with GRC can be improved using a terminal sliding mode control (T-SMC) method. The electrical system to be tested is interconnected and comprises two areas with wind turbines. Each area is equipped with a terminal sliding mode controller to facilitate achieving the LFC objective. Unfortunately, more and more RES increases the electrical system’s complexity, causing non-linearities and uncertainties. One of the practical tools to approximate the uncertainties is radial basis function neural networks (RBF NN). In the case of LFC systems, including renewable energy models, the parallel operation of terminal sliding mode controllers and RBF NNs helps to solve the LFC problem. [248].

The integrator’s gain is adjusted to keep a compromise between fast transient recovery and low overshoot in the dynamic response of the overall system. However, the integrated controller has some drawbacks that could be solved using other types of controllers. We can enumerate, for example, controllers based on simple neural networks that can overcome the disadvantages of the integrated controller, among others—slowness, no possibility of taking into account possible changes in operating conditions in the design of the controller, no possibility of managing non-linearities in the generator unit and finally lack robustness. PID controller parameters automatically adjust using the ANN. Simulation of self-tuning ANN-based PID controller is performed on a multi-area system. The neural network controller has much more satisfactory generalization ability, relevance, and reliability, as well as high operating precision in a multi-area system [249] compared to the integrated controller and PID controller.

A few summaries of new approaches of artificial intelligence (AI) techniques, such as fuzzy logic, artificial neural network (ANN), hybrid fuzzy neural network (HFNN), and genetic algorithm (GA) in frequency control load of the electrical power system are presented in [250]. As shown in [249], conventional controls such as P, I, D controls have defects that limit the possibility of their application in large power systems. Intelligent controllers should be used for LFC in a single-area or multi-area interconnected system. Careful analyses have been presented in [250] to compare intelligent controllers’ performance with conventional controllers.

The electrical system can be destabilized following a False Data Injection (FDI) attack on the LFC caused by an adversary. This type of attack could result in potential economic and fatal damage. Therefore, it is necessary to detect IDE attacks in real-time as well as to understand the possible adverse effects of these attacks. A neural network-based detection (NND) approach to estimate and detect FDI attacks injected into the detection loop (SL) of the system is presented in the paper [251].

To meet Poolco and bilateral transactions in the restructured electricity market, a neural network-based internal model control system (NN-IMC) was considered as a secondary controller for the load frequency control problem (LFC) [252]. The test system is divided into four areas to carry out the analyses. Several observations stand out from the analysis of the results—area frequency errors were eliminated to a steady state in all cases, and Gencos/Discos shared the increase in demand due to their involvement in the frequency regulation. Therefore, it was found that the NN-IMC control scheme performed well and effectively improved the system’s responses. After subsequently carrying out a comparative analysis of the performances of the NN-IMC control scheme with those of the fractional-order PID (FO-PID) control scheme, the authors of [252] also conclude that the performance of the FO-PID controller is higher than that of the NN-IMC [252].

The problem of controlling a hybrid energy storage system (HESS) for improved and optimized operation of load frequency control applications is presented in [253]. The supercapacitor is the primary power source, while the fuel cell is the auxiliary power source of the HESS. First, a HESS identification procedure is carried out using a Hammerstein-type neural network whose model of a nonlinear static gain is cascaded with a dynamic linear block. Secondly, a PID neural network used for adaptive control of HESS is used to design a feed-forward neural network based on a back-propagation training algorithm. At the same time, the operational constraint of the HESS is resolved via a dynamic anti-windup signal. Then, a suitable power reference signal for the HESS can be generated. Third, the stability and convergence of the whole system are proven based on the Lyapunov stability theory.

8.3. Particle Swarm Optimization—PSO

Particle swarm optimization (PSO) is a new population-based optimization technique. The friendly behavior of schools of fish or flocks of birds inspires it. As a powerful optimization technique, it has been widely used to solve the LFC problem in interconnected power systems. We can list some articles in which this technique is presented, and some analyses are detailed. The LFC problem in a single-area power system is solved using the PSO technique [254,255]. Another application of PSO, this time in electrical systems interconnecting several areas, is presented in [256]. The interconnected electricity systems in question are equipped, among other things, with multiple sources such as thermal, hydroelectric, and gas turbines. Additionally, hybrid PSO techniques with other soft computing techniques are proposed for LFC [257]. The system presented in the article [255] not only considers the deregulation of energy but also takes into account technical means, such as using a phase shifter controlled by thyristors (TCPS) in series with the tie-line near one area and SMES at the terminal of the other area. This, in conjunction with DFIG’s dynamic, active power support, achieves optimal transient performance for PoolCo transactions. Using craziness-based particle swarm optimization (CRPSO), the AGC loop’s integral gains and the TCPS and SMES parameters are optimized for optimal transient response of area frequencies and tie-line power deviation. Two modeling elements were selected in the mathematical modeling of a two-area system with interconnected thermal energy systems [256]: a state space model was created, and a known optimal control system technique under the name Linear Quadratic Regulator (LQR), as well as a PI controller, have been added. This design was adopted to improve the frequency response of the system. The optimal controller, known as Linear Quadratic Regulator (LQR), is tuned by a robust, intelligent PSO computing technique to improve the frequency response to load changes. In the case of LFC problems, it is essential to eliminate the disturbances by coordinating the regulation systems because the interconnections between certain areas are at the origin of the disturbances. In the case where TCPS is used in the tie-lines, a positive stabilization of the frequency oscillations of the system can be obtained thanks to the control of the energy flow of the connection lines by TCPS located between two areas and the interconnection, which is also expected to provide a new ancillary service for further electrical systems. The authors of [257] worked on an active frequency control function of the system provided by a control strategy using the phase angle control of TCPS. Following load demands and significant disturbances with and without TCPS, it is possible to optimally and robustly adjust the parameters of the PID controller in a bilateral contract scenario. This scenario is carried out by an algorithm based on PSO, which can find the most optimistic results. The results of the analysis conducted by the authors of [257] revealed that it is quite possible to effectively suppress frequency and line power oscillations compared to that obtained without TCPS for a wide range of parameter changes of central area, area load demands, and disturbances, even in the presence of system non-linearities. Changes in communication topology (CT) via multi-agent system (MAS) technology have been achieved in LFC through the use of an intelligent controller in a “smart grid (SG)” environment. The paper addressed network-induced effects, delay, and CT changes to examine the closed-loop system’s performance [258]. PSO is used to tune the parameters of a reinforcement learning-based intelligent controller composed of two levels: an estimator agent and a controller agent in each multi-area system. A trial to improve the AGC of the Multi-source Interconnected Power System (IPS) was carried out by including an improved structure of the PID controller called Integral Proportional Derivative (I-PD). The authors of [259] optimized the proposed controller parameters using a newly developed, robust, nature-inspired meta-heuristic technique called fitness-dependent optimizer (FDO). The proposed controller and technique were tested on three system models to show their effectiveness. An initial system established as follows has been proposed—two areas consisting of two diversified generation sources, including thermal reheating, gas, and hydroelectricity systems, are considered. The same system was adopted in the second scenario, but the composition is slightly modified by adding two nonlinearities: GRC and GDB. Finally, several non-linearities, notably the GDB, the Time Delay (TD), the GRC, and the Boiler Dynamics (BD), were also taken into account to make the system realistic and practical. Some recent meta-heuristic algorithms, such as learning optimization (TLBO), PSO, and Firefly Algorithm (FA), were used to compare the results. The results, such as overshoot (Osh), undershoot (Ush), and settling time (Ts) of the system frequency, demonstrated the superiority of the proposed technique over other meta-heuristic algorithms. The automatic LFC of a two-area multisource hybrid power system (HPS) is described in the paper [169]. To balance the generation and load demand of the system, an interconnected HPS model consisting of conventional and renewable energy sources operating in disparate combinations is used for analysis. The Hankel method of model order reduction using stability analysis of the nonlinear dynamic HPS model was conducted. The authors of [169] also tested integrating a cascaded PI-PD control for HPS. The controller gains were optimized by minimizing the area control error’s integral absolute error (IAE) using the PSO—Gravitational Search Algorithm (PSO-GSA) technique. As in several such cases, the effectiveness of the adopted approach was studied for different HPS model cases by evaluating the performance of the cascade control and comparing the results to those of other conventional controllers. In addition to virtual inertia control (VIC), a new approach to solve LFC in interconnected RES-penetrated power systems was proposed in [260]. This method is based on cooperative controllers using tilt and a hybrid modified particle testing optimization with a genetic algorithm (MPSOGA) as the main elements. SMES provides sufficient inertial energy for system stability as a VIC system. In each area considered, the LFC with control function is provided by two tilt-based controllers, including the tilt-derivative-integral (TID) controller for the SMES and the TID with filter (TIDF) for the LFC. Frequency stability in the studied two-area power systems is achieved through the optimal cooperative design of TID/TIDF controllers. Minimizing the frequency of nadir settling time during abrupt changes of RESs and/or load changes thanks to the formulated optimization process, considering the cooperative control of LFC and VIC, is the aim of the optimization process.

8.4. Genetic Algorithms (GAs)

Many papers published so far have demonstrated the superiority of standard PID control over integral control due to the advantages of each of the three individual control actions (P, I, and D). The PI controllers are designed using a linear model. One of the main disadvantages of linearized or linear systems is the failure to account for nonlinearities and their inability to achieve good dynamic performance for a wide range of operating conditions in a multi-area power system. Among all intelligent algorithms, GAs are the most popular and widely used genetic search algorithms based on the natural selection mechanism that works without knowledge of the task domain and uses only the physical fitness of the evaluated individuals. In the case of LFC problems, many examples of GA applications for nonlinear engineering optimization problem-solving have been presented so far. They can, therefore, be preferred as a general-purpose optimization method [125,126,127,128,129,130,131,132,133].

One of the applications of GAs to optimize the parameters of conventional AGC systems is presented in [261]. A numerical simulation of a two-area, no-reheat thermal system is used with the GA optimization process. In the search for the optimal parameters of the AGC, the integral of the square of the error and the integral of the absolute value multiplied by the time of the error performance indices are considered. The validity of GA in optimization, machine learning, and control applications has been established by many researchers [262]. The authors of [262] studied a new intelligent control system using the robust search function of GAs, integrating the basic idea of self-tuning regulators. The controller uses a GA-based algorithm to search for changes in system parameters and calculate the corresponding control law. The GA selection mechanism, which uses the square of the difference between the actual and estimated outputs as a fitness function, calculates the optimal parameters and the control law. The controller requires no prior knowledge or training data for learning and has an online parameter identification function. Another application of GA to optimize the parameters of conventional AGC systems is presented in [263]. The optimization process of the genetic algorithm is carried out in conjunction with a numerical simulation. The search for optimal AGC parameters considers several integral performance indices or cost functions. The analysis also includes more elaborate feedback control strategies, such as the PI type in the decentralized frame. The authors of [263] demonstrated the effectiveness of genetic algorithms in tuning AGC parameters. The application of fuzzy gain planning on PI LFC for a multi-area interconnected power system is described in [264]. An appropriate optimization method, namely the refined genetic algorithm (RGA), was used to adjust the membership functions and rule sets for fuzzy control to improve the performance of the power system. As in many cases listed so far, the authors demonstrated that the control methodology adopts a formulation for the area control error, whereby steady-state zero values for both time error and for inadvertent power, are always guaranteed. One of the main underlying problems associated with VSC reported in the literature is the trial-and-error selection of variable structure feedback gains. The authors of the article [265] tried to avoid this trap by selecting the variable structure controller (VSC) feedback gains by GA. The method proposed in this paper selects feedback gains optimally and systematically. The proposed design was applied to the load frequency problem of a single-area power system, where the system’s performance during staggered load variations was simulated and compared to some previous methods. The simulation results show that the system’s dynamic performance has improved, and the control effort has also been significantly reduced. The problem of LFC is solved using a GA algorithm based on a fuzzy gain scheduling approach. The authors of [266] propose a fuzzy system to adaptively decide the integral or PI controller gain according to the area control errors and their changes. The fuzzy system is designed automatically by genetic algorithms to reduce the fuzzy system design effort and the number of fuzzy rules. A new GA using an elitist strategy combined with similarity measures on relatives between individuals was used to improve the design performance.

Another method of solving the problem of AGC of multi-area power systems with nonlinear elements using a GA is presented in [267]. The method is aimed at optimizing the parameters of the PID sliding mode LFC. The advantages of PID control and sliding mode are present in the method. GA optimization technology is introduced in this paper to obtain the controller parameters instead of using a traditional analysis algorithm. The authors of [268] presented how a GA can be employed to optimize the PID sliding mode LFC parameters used in AGC of multi-area power systems with non-linear elements. GA optimization technology is introduced instead of traditional analysis algorithms to obtain controller parameters. The advantages of PID control and sliding mode are presented in detail. The authors of [269] show how the optimal gain settings of different types of controllers are obtained using the GA for a two-area hydropower system. After introducing the GA in a brief overview, its strategy as a control system design method is discussed. Analysis of test results for different types of controllers reveals that PID controllers give better dynamic responses for the two-area hydropower system. The paper proposes two robust decentralized control design methodologies for LFC [200]. The first aims to achieve robustness to uncertainties and is based on an H-infinity control design using the linear matrix inequalities (LMI) technique. The second methodology is based on a controller having a more straightforward structure, more attractive from an implementation point of view, and tuned by a new robust control design algorithm proposed to achieve the same strong performance as the first controller. The first controller is based on GA optimization and is aimed at tuning the control parameters of the PI controller subject to H-infinity constraints in terms of LMI. The second control design is called GALMI. The two proposed controllers are tested on a three-area power system with three load disturbance scenarios to demonstrate their robust performance. The authors of [254] demonstrate that the optimal PID gains of LFC systems determined by the hybrid GA-SA method are more globally optimal than those determined by the GA method. Concerning transient responses, they are also ideal for optimal integral gains. The authors of [270] also demonstrated that the optimal PID gains determined by the hybrid GA-SA technique are more globally optimal than those specified by the GA method. Regarding Sugeno fuzzy logic-based AGC for multi-area thermal power plants, various novel stochastic heuristic search techniques using PID gains optimization. These include classical particle swarm optimization, hybrid particle swarm optimization, and hybrid genetic algorithm simulated annealing. Regarding the optimal transient responses of area frequency and tie-line power flow deviations, the numerical results show that all optimization techniques are more or less effective. In any case, the authors of [271] demonstrated that the gains obtained by PSO are more optimal than those obtained by GA/hybrid GA-simulated annealing. PSO takes the least time to achieve the same optimal gains. System uncertainties are considered when developing a new robust design of decentralized frequency stabilizers of series synchronous static compensators (SSSC) [272]. The frequency of the system may be severely disturbed, and the interconnected system itself may be subject to oscillations whose frequency changes near the inter-area oscillation mode during the period when load disturbances appear since the interconnected electrical system is subject to changes in frequency near the inter-area oscillation mode. One can install an SSSC in series with a tie line between the interconnected systems to dynamically control the power flow to compensate for such load disturbances and stabilize frequency oscillations. SSSCs can be installed in a decentralized design as a multi-input, multi-output (MIMO) system in interconnected power systems. To extract the decoupled single-input, single-output (SISO) subsystem integrated into the inter-area mode of interest from a MIMO system, overlapping decompositions are used. To improve the inter-area mode damping in the decoupled subsystem, each frequency stabilizer of the SSSC can be designed in a modified manner. Additionally, the robust stability margin of the system against uncertainties such as various load changes, system parameter variations, etc., can be ensured in terms of Multiplicative Stability Margin (MSM) by incorporating the Multiplicative Uncertainty Model in the decoupled subsystem. The configuration of the frequency stabilizer is practically based on a second-order lead/lag compensator in the study presented in this article. A microgenetic algorithm automatically optimizes the frequency stabilizer control parameters without trial and error to acquire the desired damping ratio of inter-area mode and the best MSM. A new LFC model based on a fuzzy system is presented in [201]. The system adaptively decides a PI controller’s appropriate PI gains based on the ACE and its modification. A combination of GA and PSO, called FPI—HGAPSO, is proposed in the article to facilitate the design effort and improve the controller’s performance, a design of the FPI controller by hybridizing GA and PSO. The hybridization of the algorithm is carried out as follows—In FPI—HGAPSO, the elites of the GA population are improved by optimization of particle trials, and these improved elites are selected as parents for crossover operations and mutation. The PI controllers are designed using a linear model, then the non-linearities of the system are not accounted for, and they cannot gain any good dynamical performance for a wide range of operating conditions in a multi-area power system. A multi-agent reinforcement learning (MARL) approach is used in [202] to solve this problem. The method consists of two agents in each area; an estimator agent provides the ACE signal based on the estimate of the frequency bias (β), and another agent acts as a controller responsible for reinforcement learning whose task is to control the electrical system in which a genetic algorithm optimization is used to adjust its parameters. The method used in [202] allows excellent flexibility in defining the control objective and does not depend on system knowledge. The LFC problem can be optimized using several modern control theory designs, such as H-infinity. However, closed-loop poles may be caused by the importance and difficulties in selecting the weighting functions of the designs used and the associated zero pole cancellation phenomenon. Another problem lies in the order of the H-infinity controllers, which is as high as that of the optimized power plant or the model tested [273]. Another problem lies in the order of the H-infinity controllers, which is as high as that of the optimized installation [273]; therefore, the resulting controllers have a complex structure that reduces their applicability. Load frequency control of a two-area interconnected hydrothermal system by including a thyristor-controlled phase shifter (TCPS) in series with the tie line is presented in [274]. The proposed controller is tested in a two-area hydrothermal system, taking into account the realities that the controller has to face, among others, the practical aspects of the problem, such as dead zone and GRC, etc. After modeling the two-area hydrothermal system, a TCPS facility is incorporated into the tie-line model. After that, the TCPS control scheme is implemented in the two-area power system. The last step of the modeling is to consider the ISE (Integral Square Error) as an objective function that must be minimized. By using an optimization technique via genetic algorithms, we must, therefore, reduce the error of the system and the corresponding integral gain of the system to stabilize the frequency deviation of the system as well as the net power flow of the connecting lines of the two-area hydrothermal system kept within the normal operating range [274]. The authors of [275] introduced a state estimation method characterized by a rapid sampling of measured output variables such as frequency, active power flow exchange, and power generated by power plants engaged in the LFC of a given control area. The authors of [275] developed a novel discrete-time, full-feedback, sliding-mode controller for LFC in control areas (CAs) of a power system. The given controller can be applied for LFC in CAs with thermal and hydropower plants. A genetic algorithm designs the discrete-time sliding mode controller for LFC. A careful comparison of the implemented controller against the commonly used PI controller was conducted by extensive simulation experiments on a power system comprising four interconnected CAs. Simulation tests showed that the proposed controller provides better disturbance rejection, maintains the required control quality over a more comprehensive operating range, shortens the transient frequency response, avoids overshoot, and is more robust to system uncertainties. The authors of [238] developed two intelligent load frequency controllers to regulate the output power and frequency of the system by controlling the speed of the generator using the position control of the fuel rack. One of the controllers implemented was designed to study its performance and compare it to that of a conventional integral controller (CIC) and that of a conventional PI controller (CPIC). The first controller is obtained using only fuzzy logic (FL). The second controller’s role is to compare the performance of the control methods, which combine FL, genetic algorithms, and neural networks. The objective of the proposed controller(s) is to restore the frequency to its nominal value very smoothly in the shortest possible time whenever there is a change in load demand, etc. The AGC problem is solved by online implementing a fuzzy logic controller (FLC) with GA optimization [276]. SISO cascade loops were introduced to the LFC model to reorganize the multi-area AGC system. Hence, the complex AGC system problem can be solved using a simple FLC decision table algorithm. Nonlinear elements of AGC, such as GRC and saturation, are considered in this decision table search algorithm for FLC with GA optimization. The LFC problem is solved using an adaptive optimal gain planning approach in [277]. The integrated controller is widely used in the electrical industry. Hence, it is also used in this diagram. However, the GA is a much more robust method that could be used to optimize the integral gain for several power system operating conditions. A general mapping between operating conditions is achieved by conducting a process where optimal control gains are utilized by creating an Adaptive Network-based Fuzzy Inference System (ANFIS). The two approaches (GA and ANFIS) are compared to conventional integral control for a two-area power system. This time, a supervisory control system for improved and cost-effective operation of a small supercapacitor energy storage system (SCESS) is used to improve LFC [278]. The controller was developed based on Adaptive Generalized Predictive Control (AGPC). It has been designed to manage the operational constraints of the SCESS effectively while generating an appropriate power reference for the primary (inner) control loop of the SCESS. In response to a load disturbance, the direct control loop, in turn, reacts by forcing the SCESS to follow the power command received from the (outer) supervisory control loop. A genetic algorithm tunes the conventional tracking controller associated with the internal control loop in offline mode. The design of the overall primary control loop is done so that it behaves like a reference system whose model is used to calculate the dynamic inequality constraints in the optimization process of AGC [278]. The LFC in a multi-microgrid by a PDF+(1 + PI) controller with a GA is proposed in [279]. The challenges of controlling the load frequency in a multi-microgrid derive from variations in the sources and the load. It should be noted that various compensation techniques are applied if the MG operates in a grid-connected mode. Hence, there are fewer frequency control issues and, subsequently, less frequency deviation. On the contrary, if the MG operates in island mode, it faces enormous frequency control problems due to the dynamic nature of different renewable energy sources. The authors of [279] propose a PDF + (1 + PI) controller with GA to monitor the frequency change of microgrids and control the input of micro sources. Control strategies are developed based on the frequency deviation to regulate the micro-source output. The superiority of the designed method is demonstrated by comparing the developed method with conventional PID & PI controllers [279]. A recent metaheuristic optimization approach of the multi-verse optimizer (MVO) has been used for designing predictive control (MPC) based on LFC incorporated in a sizeable multi-interconnected system, is presented in [280]. The MVO was used to determine the optimal parameters of the MPC-LFC so that the desired output of the interconnected system under load disturbances is achieved. The tested system includes six renewable energy sources (RES) plants, including a thermal, hydroelectric, photovoltaic (PV) heating model with maximum power point tracking (MPPT), a wind turbine (WT), a diesel production (DG) and SMES. As usual in this type of analysis, the objective function is based on the absolute integral time error (ITAE) of the frequency and line power deviations. Nonlinearities in the effects of the regulator dead zone and the GRC of thermal power plants are also considered. The performance of the proposed MPC optimized via MVO is compared with that of other optimization methods, such as the method via intelligent water drops (IWD) and GA. By checking the effect of the variation of the system parameters on its behavior, we can evaluate the robustness of the proposed MPC-LFC-based MVO [280]. The next paper [281] described a method of fractional order based on the imperialist competition algorithm (ICA) with filter (IPDF), that is to say, a derivative of Integral tilt with filter controller (ITDF) in frequency control in two interconnected MG areas (isolation mode) with renewable penetration. As a first attempt of ICA, the absolute time integral error criterion is used to optimize the gains of the ITDF controller. After comparing the results of ICA-based control with two commonly used optimization strategies, namely genetic algorithm and particle testing optimization, the authors concluded that ICA is much superior to the previously listed strategies. Another test to show the effectiveness of the proposed controller is based on comparing the dynamic responses of multi-microgrid (MMG) controllers to those of PI drift with filter (PIDF) and tilt critical drift with filter (TIDF). A PI Fractional-Order PI Derivative (PI-FOPID) cascade controller is proposed in [282] to improve the performance of the LFC controller by enhancing the frequency response of a hybrid microgrid system. The authors of [282] refined the optimal gains of the proposed controller using Gorilla Troops Optimizer (GTO), a recent metaheuristic optimization algorithm. The developed algorithm was tested on a two-area microgrid system containing diesel generators, various renewable energy sources such as photovoltaic and wind generation systems, and different energy storage devices. The actual wind speed measurements and solar irradiation were collected to design a suitable system model. The authors subsequently adopted a typical flow of the analysis. Firstly, the performance of the proposed cascaded PI-FOPID developed controller is compared with the GTO-based single-structure fractional-order PID (FOPID) controller and many other optimization techniques presented in previous literature, such as GA and PSO after a robustness study of the proposed cascaded PI-FOPID controller is carried out by testing it in different scenarios such as different step load disturbances, random load disturbances and variation of renewable energy sources. So far, several LFC models have been designed in different scientific articles. Most of these models are simplified to keep the calculation process manageable. However, it is necessary to consider other parameters to create the models as precisely as possible. For this purpose, physical constraints such as the GDB, the GRC, and the delay in the communication links must be imposed to demonstrate these constraints’ effect on the AGC performance [283]. Using this procedure, one can evaluate the model most accurately. Unfortunately, precise modeling of LFC systems leads to the introduction of physical constraints and an increase in the number of areas to control, therefore increasing the complexity of the final model obtained. Thus, one must use intelligent data-driven methods such as GAs, fuzzy logic controllers, and neural networks to solve optimization problems. Therefore, the authors of [283] used GA as an optimization technique to tune the controller gains in this paper. The results showed that to stabilize the performance of LFC, using GA as an additional tool to optimize LFC parameters is a valuable method [283].

8.5. Other Intelligent Methods

The article [23] presents one of the new methods that fits outside the commonly used categories. It consists of adjusting the controller’s parameters of the differential evolution (DE) algorithm and its application to the LFC of a multi-source electrical system with different energy production sources. As the method is relatively new, the authors first tested it on a single-area multi-source power system with integrated controllers for each unit considered, and the DE technique was applied to obtain the controller parameters. Then, the study was extended to a multi-area and multi-source electrical system comprising an HVDC connection in parallel with the AC connection line used to interconnect two areas. Finally, the DE algorithm was used to optimize the I, PI, and PID controller parameters.

The paper [284] also presents the design and performance analysis of a PI controller based on the differential evolution (DE) algorithm for AGC of an interconnected electrical system. The authors searched for a solution to the optimization problem, and DE was used to find optimal controller parameters. The LFC model comprises a two-area, no-reheat thermal system with PI controllers for design and analysis. To increase the performance of the controller, three different objective functions are derived, including (1) the absolute integral time multiplication error (ITAE), (2) the damping ratio of the dominant eigenvalues, and (3) the stabilization time with appropriate weight coefficients. A comparative analysis of the performance of the proposed DE-optimized PI controller with some recently published modern heuristic optimization techniques, such as Bacteria Foraging Optimization (BFOA) and Genetic-Algorithm-Based PI Controller (GA-PIC) for the same interconnected electrical system, was carried out. The obtained results demonstrate the superiority of the DE algorithm.

Load disturbances cause the main problem in controlling the load frequency of electrical systems due to continuous and rapid changes in small loads. LFC can be achieved using a new PID controller for resilient differential control against load disturbances [285]. The Imperialist Competitive Algorithm (ICA) can be used to specify controller parameters. The paper [285] presents a new method to solve this problem based on a filtering technique that eliminates the effect of this type of disturbance. The objective of regulation is to return the frequency of each area of the electrical system to its nominal level and reduce the power transfer between the control area. The ICA is, therefore, used to obtain the best dynamic frequency response for a wide range of load changes by regulating the controller parameters.

The paper [286] proposes a novel fuzzy PID controller for AGC of interconnected power systems. A hybrid differentially evolving particle swarm optimization (DEPSO) technique is used to optimize the gains of the fuzzy PID controller using a time integral multiplied by the absolute value of the error criterion. The authors of [286] demonstrated the superiority of the hybrid DEPSO algorithm over the differential evolution and PSO algorithm.

As in the case of [286], the authors of [287] also proposed a fuzzy PID controller optimized for differential evolution with derivative filter (PIDF) for the LFC of a system deregulated electric with multi-source energy production and interconnected via parallel AC/DC transmission link. The LFC model developed by the authors of [287] was extended by considering significant physical constraints such as delay and GRC to have a precise idea of the LFC problem. The authors of [287] also proposed a fuzzy PID controller optimized for differential evolution (DE) with a derivative filter (PIDF) for the LFC of a deregulated electric system with multi-source energy production and interconnected via parallel AC/DC transmission link. The controller’s assessment was conducted in such a way that all possible electricity transactions that take place in a deregulated electricity market were taken into account.

Another example of using FLC to improve the performance of the LFC system is presented in [288]. Since the effectiveness of the action of a logic controller depends on a sufficient and precise knowledge base, as the number of rules in a knowledge base increases, its complexity increases, which affects the calculation time and memory requirements. A Polar Fuzzy logic controller is then proposed to overcome these problems. The Polar Fuzzy Controller (PFC) aims to restore frequency and line power smoothly to its nominal value in the shortest possible time if a load disturbance is applied to any area of the electrical system. The PFC is made adaptive using a genetic algorithm fuzzy system (GAF) approach. The performances of simple PFC and adaptive PFC using GAF were evaluated by comparing them with those of fuzzy and conventional PI controllers in a three-area system.

The AGC of an unequal three-area gas–thermal–thermal system is presented in [289]. The thermal systems are equipped with single reheat turbines and have GRCs of 3% per minute. A GRC of 20%/minute is provided in a gas plant. The FA was used in the LFC model of [289] to simultaneously optimize the secondary controller gains and other parameters. To achieve effective AGC control, a maiden attempt was made to examine and highlight the application of a filter-coupled integral derivative (IDF) controller. The performances of the implemented IDF controller were evaluated and compared to those of several conventional controllers. The superiority of the IDF over the commonly used supplementary controllers is revealed.

Another example of using the FA is presented in the article [290]. This time, the algorithm is used with an online wavelet filter on the AGC model for a reheating thermal energy system interconnected with three unequal areas. The model used for the tests described in [290] is quite complex and includes time delay, dead zone, boiler, GRC, and high-frequency noise components. Therefore, the authors of [290] specially included noise in the model to test the effectiveness of the new filtering technique based on wavelet transform, which is introduced to remove the noise(s) from the ACE signal. A signal integrity index was used to measure filter performance. The results of simulations conducted by the authors of [290] show that FA can outperform PSO in obtaining the minimum objective function based on the integral of time-weighted squared error (ITSE).

An application of the new artificial intelligence search technique to find the optimization of nonlinear LFC parameters by considering the PID controller for a power system is presented in [291]. The Bacterial Foraging Optimization (BFOA) algorithm is used to search for the optimal controller parameters to minimize the time domain objective function for a two-area no-reheat thermal system equipped with a PID controller. By comparing the performance of the proposed technique with the performance of conventional Ziegler Nichols (ZN) and genetic (GA) algorithms, it has been demonstrated that the proposed BFOA-based algorithm in PID controller tuning is superior to other known algorithms. Tests were conducted under different operating conditions and system parameter variations to check the effectiveness and robustness of the proposed BFOA algorithm.

The authors of [292] studied the sophisticated application of redox flow batteries (RFB) coordinated with a unified power flow controller (UPFC) to improve the LFC of a multi-area power system containing multiple sources. As in the case of complex LFC models, GDB and GRC are also considered in the performed analyses. The power transfer capacity of the tie-line can be improved using UPFC, the main application of which is to stabilize the frequency oscillations of the inter-area mode of the interconnected power system. This can be achieved by dynamic control of the energy flow of the tie-line. Redox flow batteries have a fast response and exceptional operation under overcharge conditions and, most importantly, do not age despite frequent charging and discharging. Apart from performing a load leveling function, the battery is handy for secondary electrical system control and maintaining the power quality of distributed electrical resources. Besides proposing new devices like UPFC and redox flow batteries, the authors also use the Artificial Bee Colony (ABC) algorithm, optimizing the parameters of the cost functions with the integrated controller.

Solving the problem of real-time small-scale load (SLP) disturbances of the interconnected power system is one of the main tasks of LFC. Any control tool created is designed to achieve this, but in the most efficient way possible, so that the system can acquire resistance to random and rapid changes in these disturbances [293]. On the one hand, the continuous nature of the load profile is designed for its implementation in a real-time AGC application. Still, regarding optimal AGC performance, rapid load changes over a constant period are always a source of problems. In this case, it is, therefore, a question of closely examining the frequency difference and the behavior of the energy flow profiles of the tie-lines within the control areas. A novel quasi-oppositional harmony search (QOHS) algorithm based on a PID controller and a filtering technique is proposed in [293] to overcome the consequences of the listed problems. The authors of [293] performed performance verification tests of the proposed QOHS algorithm by comparing its dynamic responses to those offered by the imperialist competitive algorithm for the same test system.

The quasi-oppositional harmony search (QOHS) algorithm is proposed in the article [24] as an optimization tool for solving the AGC problem in a deregulated regime. The tested LFC is the AGC of a realistic power system with a distinct combination of multi-area and multi-source generation units in each control area in a deregulated framework. Modeling, simulating, optimizing, and correlating interdependent dynamic performances for AGC study are the highlighting features of the present analysis.

The article [294] also relates to modeling LFC in a deregulated environment. A novel swarm optimization algorithm, i.e., fruit fly optimization algorithm, is proposed to regulate multiple conventional controllers of a multi-area, multi-source interconnected power system in a deregulated environment. The analyzed LFC model is quite complex. It consists of a multi-source combination of thermal, hydroelectric, and nuclear reheat generation units in each control area with an appropriate production rate constraint and an AC/DC link, all in a deregulated environment. Performance comparison of several controllers such as I, PI, PID, integral-double derivative (IDD), and PI-double derivative (PIDD) is carried out in different working scenarios of the power system. It turned out that the PIDD controller operated better than other controllers.

The authors of [295] analyzed new control techniques in an LFC model. A two-degree-of-freedom (2DOF) controller called 2DOF-integral plus double derivative (2DOF-IDD) was proposed for the first time in AGC as a secondary controller. Secondary controller gains and other parameters were simultaneously optimized using a newer scalable computing technique called the cuckoo search (CS) algorithm. The authors first compared the dynamic system responses for various 2DOF controllers such as 2DOF-PI, 2DOF-PID, and 2DOF-DD. Preliminary analyses revealed that responses with 2DOF-IDD are better than others. Apart from testing new control techniques, the performances of several FACTS devices such as Static Synchronous Series Compensator (SSSC), Thyristor Controlled Series Capacitor (TCSC), Thyristor Controlled Phase Shifter (TCPS), and Flux Controller interline power (IPFC) in the presence of a 2DOF-IDD controller were also analyzed and compared. Ultimately, it turned out that dynamic responses with IPFC are better than others.

The following article [296] was published two years before the previous article [295] and analyzed the same type of two-degree-of-freedom (2DOF) controller called the 2DOF-integral plus double derivative (2DOF-IDD) proposed in AGC as a secondary controller. The only difference is that FACTS devices are not considered in the analyzed LFC model. Apart from the comparison of dynamic performances of the developed controllers, the authors of [296] also performed a sensitivity analysis, which revealed that the optimized 2DOF–IDD CS controller parameters obtained under nominal loading conditions and nominal stepped load disturbance (SLP) size are robust and need not be reset in case of significant changes in system load and SLP.

A cascade aggregate of integral-order and fractional-order controllers named integral derivatives and secondary filter and PD controllers (IDN-FOPD) is proposed in [297] to solve the LFC problem in a power system with multiple areas. Multi-area automatic control is considered uneven regarding power generation in a restructured environment. The LFC model is structured as follows: each location has two production (GENCO) and distribution (DISCO) companies. The GENCOs in area 1 are wind power plants and thermal units; in area 2, they are split into two categories—shaft gas turbines and thermal units. A comparative analysis of the performance of the IDN-FOPD controller compared to that of commonly used conventional controllers is presented in the article [297]. The comparison revealed the superiority of the IDN-FOPD controller. The whale optimization algorithm was used to obtain the controller gains, along with other parameters. In the final part of the paper, the authors of [297] proposed to compare the performance of different flexible devices of AC transmission systems, such as static synchronous series compensators, thyristor-controlled series capacitors, and power flow controllers interline (IPFC), incorporating them one at a time into the LFC model using an IDN-FOPD controller. They conclude that the IPFC presents the best performance.

A new LFC scheme based on an indirect adaptive fuzzy control technique is implemented for multi-area power systems [298]. As in any LFC model, the local load frequency controller is designed using each area’s frequency and line power deviations. The electrical systems studied in this article are on unknown parameters. Therefore, fuzzy systems’ approximation capabilities are used to identify unknown functions in controller design, formulate appropriate adaptive control law, and update algorithms for controller parameters. Moreover, an auxiliary control signal is introduced into the proposed controller to mitigate the effect of fuzzy approximation error and the impact of external disturbances on the tracking performance. Simulation results of a three-area power system demonstrated the effectiveness of the proposed LFC compared to a conventional PID controller.

An LFC system composed of reheat turbines and equipped with the appropriate GRC was modeled in order to test the performance of a fractional-order PID (FOPID) controller [125]. Thermal-type systems are distributed into several areas in a deregulated environment. Several integer order (IO) controllers were performed and compared with the FOPID controller. The conducted analyses confirmed that the FOPID controller provides better dynamic performance than IO controllers in equal and unequal area systems.

A new optimization technique called the Cuckoo Search (CS) algorithm for optimal tuning of PI controllers for the LFC of a three-area interconnected system is presented in the paper [299]. The LFC system is subjected to various loading conditions where the nonlinearities of the system are analyzed to confirm the effectiveness of the suggested algorithm. The PI-based LFC parameters are robustly adjusted and solved by the CS algorithm to obtain the most optimistic results using a time domain-based objective function. The authors of [299] compared the CS algorithm for optimal tuning of PI controllers to GA, PSO, and conventional integrated controllers. They conclude that CS-based controllers have improved the performance of LFC in general.

The AGC of a three-area thermal system integrating a solar thermal power plant (STPP) in one of the areas is presented in the article [300]. The conventional thermal system model includes a single reheat turbine and appropriate GRCs. Two variations of the system—with and without STPP integration—are evaluated to determine the performance of I, PI, and PID controllers. A new evolutionary computational technique, considered innovative then and called the Gray Wolf Optimization (GWO) algorithm, is first used in AGC to optimize the secondary controller gains.

The design procedure and numerical validation of a robust fuzzy-logic-based fine-tuning approach designed to improve LFC capabilities in multi-area power systems are presented in the paper [301]. Judicial parameter tuning of a PI controller encountering fault occurrences or significant changes in system load conditions can be improved through a robust fine-tuning approach based on fuzzy logic. Unlike conventional PI controllers typically designed for fixed operating conditions, the described approach demonstrates strong performance in the face of power system uncertainties and disturbances.

The LFC problem of a multi-area interconnected power system in the presence of wind turbines (WTs) can be solved through a distributed MPC (DMPC) scheme [302]. The external disturbances and constraints represent the load reference set point, GRC, and control input constraints of the WT. These are formulated to obtain an LFC model in which the controller predictive distributed model is designed. The main goal is to attenuate the disturbances.

The authors of [303] analyzed another MPC for LFC of an interconnected power system. The limits of the power flow of connection lines, production capacity, and production change rate are considered in the MPC model based on a simplified Nordic electricity system. The analyzed model considers participation factors for each generator as optimization variables. The authors also suggested that power transfer margins of connection lines should be guaranteed through margin variables and price information via a defined objective function. A Kalman filter used for state estimation is included in the model to complement the MPC solution for LFC. Finally, a comparison of the presented MPC to a conventional LFC/AGC scheme with PI controllers is included.

Yet another distributed MPC (DMPC) model for the LFC of a power system, including inherently variable wind power generations, is presented in the paper [304]. Information from other controllers for their local purpose to achieve effective coordination is collected by the DMPC, which subsequently communicates the power system measurement and forecast data. The controllers also consider the given constraints, such as GRCs, wind speed, pitch angle, and load input constraints for each area, to solve the optimization problem.

Among the most popular techniques used to optimally tune controllers are evolutionary algorithms. The authors of [305] presented how to use the wind-driven optimization (WDO) algorithm, a newly developed evolutionary algorithm, to tune load frequency controllers. The impact of different objective functions on the performance of evolutionary algorithms in controller tuning was studied based on simulation studies. A comparative analysis was also conducted to evaluate the effectiveness of the proposed optimization algorithm compared to other evolutionary algorithms. Finally, by changing the parameters of the electrical system and varying its configuration, the robustness of the proposed method is confirmed.

Simultaneous optimization of the controller gains of an LFC system is performed using a nature-inspired optimization technique called the Ant Lion Optimizer (ALO) algorithm [306]. The authors of the article [306] demonstrated that the best performance was obtained using the PID + DD controller in terms of reduced settling time, peak overshoots, and decreasing oscillations compared to other techniques, such as those applied to using I, PI, and PID controllers. The comparison was made based on the dynamic frequency responses and the corresponding tie-line powers. Furthermore, a sensitivity analysis was conducted to demonstrate the robustness of the optimal gains of the best controller obtained under nominal conditions.

An LFC scheme based on distributed MPC (MPC-LFC) is presented in [307]. This algorithm effectively improves the control performance in frequency regulation of the power system. Laguerre orthonormal functions approximate the predicted control trajectory to reduce the computational burden in continuous optimization with a sufficiently large prediction horizon. By adding a terminal equality constraint to the online quadratic optimization and taking the cost function as a Lyapunov function, we can obtain the closed-loop stability of the proposed MPC scheme. Treatments of some typical constraints in LFC have additionally been studied based on the specific Laguerre-based formulations. The models of two interconnected power systems were analyzed to validate the effectiveness of distributed MPC-LFC and its superiority over comparative methods.

A three-area interconnected power system model is presented in [308]. LFC analysis uses a novel, robust, decentralized LFC algorithm design that considers system uncertainties and external disturbances. The concept of active disturbance rejection control (ADRC) is used to design the LFC model analysis presented in the paper. ADRC is effective against various parameter variations, model uncertainties, and significant disturbances. It is, therefore, very effective in estimating and mitigating the total effect of multiple uncertainties in real time. Different types of turbines, such as non-reheat turbines, reheat turbines, and hydraulics, were used to test the ADRC-based LFC solution. The effectiveness of ADRC against an existing PI-type controller tuned via genetic algorithm linear matrix inequalities (GALMIs) was demonstrated.

Modern wind turbines are connected to the primary grid via power electronics (e.g., Type 3 or Type 4 wind turbines) to maximize available wind energy. So, unlike conventional synchronous generators, which are synchronously connected to the grid and operate synchronously with each other, wind turbines are electromagnetically disconnected from the rest of the power system and offer little or no inertia. The reduction in synchronous power reserves after frequency disturbances further intensifies this problem, particularly the ability of the system to maintain the frequency within a permissible range, mainly because the reduction in the system’s inertia imposes severe technical challenges for preserving the stability of the system frequency. Grid operators are therefore obliged to require that renewable energy sources, also called non-synchronous generators, behave in a certain way like synchronous generators and participate in (rapid) frequency control in the event of need. A review of the latest research results and developed mechanisms for frequency control using wind energy conversion systems as the most frequently deployed renewable energy sources in modern power systems is presented in [308,309].

The design and simulation of an adaptive neuro-fuzzy inference system (ANFIS) controller for a power network with non-linearities such as boiler dynamics, GRC, regulator dead-band, and time delay are presented in [310]. The Bode plot approach was used to tune a PI controller to obtain the training dataset for the proposed controller. A comparison of the dynamic performance of the ANFIS controller to that of a conventional controller led to the conclusion that, concerning peak overshoot and settling time, the ANFIS controller is significantly better than the classic one.

Another rather complex algorithm at first glance, consisting of the Bat-Inspired Algorithm (BIA) and Gravitational Search Algorithm (GSA) as new artificial intelligence (AI) techniques, is presented in [311]. The two algorithms combined are used to design the MPC with SMES and capacitive energy storage (CES) for LFC. Lately, designers tend to use the technique of trial and error and their expertise to define the parameters of the MPC with the SMES and CES units. In this paper, the parameters of MPC are adjusted simultaneously with SMES and CES units using BIA and GSA to solve this problem.

The paper [312] presents the possibility of using sliding mode to control LFC models. In the traditional sliding mode control method, singularity always exists due to the reduced order of the control method. A new full-order sliding mode control method first applied to LFC is presented in the article [312]. Two types of sliding mode control—the complete order sliding mode control method including terminal sliding mode control (TSM) and linear sliding mode control (LSM) are introduced.

The paper [313] presents another example of controlling an LFC model where WT models are included. For the first time, a resilient hybrid fractional-order controller (hy-FOC) consisting of a fractional-order PID controller (FOPID) and fractional-order sliding mode controller (FOSMC) is used for frequency regulation of an island hybrid power system (HPS) integrated with a generator wind power driven by a doubly fed induction generator (DFIG). The slime mold algorithm can obtain near-optimal hy-FOC gains by minimizing an integral error criterion. Apart from that, to estimate the uncertain disturbances of the plant and integrate the estimated output into control law, a Luenberger disturbance observer (Dob) is designed, the final objective being to alleviate chattering in the production of the sliding mode controller (SMC). An in-depth comparative study with the results of the PI derivatives (PID), SMC, FOPID, and FOSMC under various operating conditions, such as the consideration of model uncertainties and uncertain external disturbances, was carried out to be able to establish the acceptability and superiority of the proposed hy-FOC.

A method for solving the LFC problem in an interconnected power system network is proposed in [314]. The controller is a conventional PI/PID using the gray wolf optimization (GWO) technique. The proposed algorithm was used in a two-area interconnected no-reheat thermal energy system, and then a three-area system was studied. The LFC model includes the steam turbine’s GRC. The dynamic stability of the evoked systems is explored in the presence of GRC.

The differential search algorithm (DSA) is inserted into the paper [315] to solve the problem of LFC in the power system. The classic PI/PIDF controller optimized using DSA is implemented on an identical two-area thermal–thermal power system in two more realistic power systems widely used in the literature. The authors of [315] evaluated the usefulness of DSA, studying three innovative, improved algorithms, namely Comprehensive Learning Particle Trial Optimization (CLPSO), Mutation and Crossover Strategy and Parameter Set in differential evolution (EPSDE) and success history-based DE (SHADE). Finally, validation of the superiority of the DSA-optimized PI/PID/PIDF controller is confirmed by an in-depth comparative analysis with some recently used meta-heuristic algorithms such as the FA, BFOA, GA, Craziness-based PSO (CRPSO), Differential Evolution (DE), Teaching–Learning-Based Optimization (TLBO), PSO, and Quasi-oppositional Harmony Search Algorithm (QOHSA).

The design and performance analysis of the DE algorithm based on a parallel two-degree-of-freedom PID (2-DOF PID) controller for LFC of the interconnected electricity system is presented in [316]. Conventional and modified objective functions are used for design purposes. The design problem is formulated as an optimization problem, and DE is used to find the optimal controller parameters.

A fractional-order PID (FOPID) controller based on Gases Brownian Motion Optimization (GBMO) is used to mitigate frequency and power exchange deviations in a two-area power system, taking into account the governor saturation limit [313,317]. The designer must determine which derivative and integrator parts have non-integer orders in an FOPID controller. The FOPID controller has more flexibility than the PID controller.

An opposition-based harmonic search (OHS) technique is used to optimize an LFC model composed of two areas, demarcated as Area I and Area II, consisting of thermal, hydroelectric, and gas units [318]. The designed model considers the stability of small signals via a participating factor to determine the oscillation state of the system, i.e., the frequency deviation in the two areas. A suitable controller is required to reduce system oscillations. This design also includes the economical load-sharing mechanism in the LFC for economical load division during load diversion. The optimal value of the integral gain of the integral controller must be selected to achieve the objective. Due to the slow response of the governor mechanism, both the primary and secondary controllers are insufficient to reduce the tie-line deviation and power oscillations of the significant disturbances in the areas. An energy storage system, the redox flow battery (RFB), is used to improve the system’s dynamic response, which has a meager time constant and rapid response.

The LFC of a two-area interconnected multiple-unit thermal reheat power system in a restructured environment is presented in [319]. If adequate damping is not available, system frequency oscillation may persist and increase to the point of causing a series frequency stability problem. Additionally, the movement of the control valve may be delayed, resulting in a delay in the storage of steam in the steam trunk and the heater of the thermal power plant. Finally, compensation of the mechanical power output after the load disturbance may not arrive on time. An interline power flow controller (IPFC) can, therefore, be used in series with the link and redox flow batteries (RFBs) in one of the areas to stabilize the system. The authors used the Bacterial Foraging Optimization (BFO) algorithm [319] to optimize the integral gains of the load frequency controller under different transactions in the competitive electricity market.

The authors of [320] also present the design and performance analysis of the Bacterial Foraging Optimization Algorithm (BFOA)—Fuzzy Optimized PI/PID (FPI/FPID) controller for solving the AGC of traditional/re-engineered multi-area interconnected power systems. A traditional two-area thermal system without reheating is first considered. Then, using the integral of the squared error objective function, the gains of the fuzzy controller are adjusted using BFOA. Finally, the authors demonstrated the superiority of the designed controller compared to other known solutions by juxtaposing the results with PSO, FA, BFOA, hybrid PI based on BFOA–PSO, and fuzzy PI controllers based on pattern searching (PS) and PSO algorithms for the same power system structure.

Intelligent control strategies are required to achieve satisfactory power system operation in real time. This is due to the ever-increasing size, complexity, non-linearity, structural variations of modern power systems, and increasing energy demand. To ensure good performance of AGC in a two-area interconnected power system, a novel fuzzy PID controller with a filter and double integral (FPIDF-II) is proposed in [321].

The paper [322] aims to design a cascaded fuzzy fractional-order (FO) PI-FOPID (CFFOPI—FOPID) controller as a new control strategy for the solution of the AGC problem in a power system. A stochastic imperialist concurrency algorithm is used to determine the controller parameters. The controller has been designed to ensure convergence of the area frequency and line power deviation under load disturbances to zero within a defined minimum time.

A novel hybrid fuzzy PID controller based on local unimodal sampling (LUS) and teaching–learning-based optimization (TLBO) is proposed in [323] for LFC of a power system multisource interconnected to two areas, with and without HVDC connection. The proposed hybrid LUS and TLBO (LUS–TLBO) algorithm is used to optimize the scale factors of fuzzy PID controllers and the gains of conventional PID controllers. The authors of [323] demonstrate the superiority of the fuzzy PID controller optimized by the LUS—TLBO algorithm proposed for the two electrical systems (with and without HVDC connection) compared to the results of tests on the differential evolution algorithm (DE) optimized for a conventional PID controller for the same electrical systems.

The BAT algorithm is proposed in paper [324] for optimal tuning of PI controllers for the design of a load frequency controller (LFC). The BAT algorithm was used to find the most optimistic results to solve the problem of robust PI-based LFC design tuning and was formulated as an optimization problem based on an objective function in the time domain.

The LFC model in the paper [325] comprises conventional generators and various renewable sources with a modified cascade controller. The controller parameters are optimized using a new hybrid scheme of the Improved Teaching–Learning-Based Optimization Differential Evolution (hITLBO-DE) algorithm. Finally, the performance of the hITLBO-DE tuned cascade controller with dynamic load change is compared with other techniques, such as TLBO applied to PID, double integral derivative (IDD), and PIDD.

Due to the effectiveness of the Improved Grey Wolf Optimizer (I-GWO) Algorithm in solving complex engineering problems, especially those related to power systems, this optimization technique is becoming very popular among researchers. An AGC based on IGWO is presented in the article [326]. The objective of the control is to eliminate the frequency and power exchange deviation in an interconnected electrical system.

The authors of [327] have worked out a maiden attempt to propose a new hybrid-peak-area-based performance index criteria (PICs) for the optimal tuning of supplementary controller gains. So far, no significant efforts have been made to formulate effective PICs to acquire additional control and improve AGC dynamic performance. A sensitivity analysis was carried out to demonstrate the superiority of the proposed PIC and determine significant changes in the parameters of the AGC power system model.

The authors of the paper [328] presented a first approach to the hybrid adaptive guided gravitational search and pattern search (hGGSA-PS) optimization method “gbest” for LFC of a multi-area interconnected power system. The developed model considers the non-linear effect of the GRC. The considered LFC model is a single-stage dual-area thermal–thermal type with a PID controller whose PID parameters are optimized by the proposed technique. Initially, the integral time absolute error (ITAE) fitness function is used to guide the “gbest” gravitational search algorithm (GGSA). Then, the best solution obtained from the GGSA is refined using the pattern searching (PS) technique. Comparing the optimization results using hGGSA-PS with other modern computing techniques, we conclude that this method performs much better optimization than others.

Among the latest methods of intelligent tuning of LFC, we can list the positions [329,330,331,332]. The authors of [329] have implemented a new technique of control called Tilted Integral Fractional Derivative with Filter plus Fractional Derivative controller (TI Dμ1N Dμ2), the acronym of which is TIFDNFD. This new technique aims to achieve the LFC of two area-multi-source power systems. The performance of the proposed controller has been compared with other recent controllers. The same authors of [329] have proposed another technique called the “Levy flight and Fitness Distance Balance (FDB)-based coyote optimization algorithm (LRFDBCOA)” to improve the performance of AGC, or, more precisely, the LFC because the economic dispatch of the system is not considered [330]. The LFC system comprises three different PV-based interconnected power systems in a two-area PV-reheat thermal power system with a PI controller. A few intelligent methods such as the GA, FA, and modified whale optimization algorithm (M-WOA) have been used for the analysis. As for [329] and [330], another paper [331] has been published by one of the authors of [329,330]. The method used was, this time, an improved version of GA, more precisely, a hybrid simulated annealing-genetic algorithm (hSA-GA). As outlined in the paper, the method was first tested on nine benchmark functions, and then the control parameters of the LFC controller, which a PID-type controller, were tuned. After conducting a comparative analysis with other tuning methods, the authors concluded that hSA-GA exhibits better control performance on power systems than the compared studies. Finally, the first author of [329,330,331] has published another paper [332], in which another modern control method was presented. This method is called fractional-order PID. Due to its superior performance over conventional PID controllers, they have been applied in different scientific areas. The authors of [332] have proposed a method called MOGOA-FOPID in which both the frequency deviation and the control signal are minimized together for the frequency control in the microgrid.

9. LFC, Renewables and FACTS Devices

In the event of low load disturbances in the presence of suitable additional controllers, and due to the persistence of system frequency and tie-line deviations for an extended period, the system regulator may no longer be able to absorb frequency fluctuations due to its slow response. In recent decades, FACTS devices have become standard practice in utilizing existing transmission capacities entirely instead of adding new transmission lines. A new AGC regulator design technique based on static var compensators (SVC) was presented by El-Emary and El-Shibina [333] in the 1990s. A design for controlling power flow in link lines in an interconnected power system using thyristor-controlled phase shifters (TCPS) was also presented in [334]. This device allows the injection of a variable series voltage to affect the power flow by modifying the phase angle. The authors of [334] also considered the design of a decentralized controller based on GA with and without redox flow batteries, including TCPS. Using power electronic systems in power system control systems is becoming increasingly common.

In the beginning, static VAR compensation systems were used to dampen oscillations in the dynamic responses of the power system. Reference [333] presents how to use the SVC device as a new basic AGC regulator design technique. The SVC helps create a feedback signal consisting of frequency deviation and reactive power variation to stabilize the electrical power system. It is well known that the coefficient of these deviations depends on the system and controller parameters. Another device whose influence on LFC has also been studied is photovoltaic systems (reference [335]). In addition to other previous observations, it was revealed that a power system containing a 10% contribution from PV stations would require a 2.5% increase in LFC capacity compared to a conventional system. Other units, such as storage systems such as BES, SMES, and CES, or fuel cells, also contribute favorably to the dynamic performance of the power system [331].

A few authors of [257,336,337] also presented the design of using TCPS to provide an active control function for the LFC problem in the power system. As for the previously analyzed cases, TCPS is used to regulate the flux of electrical power. When TCPS is equipped with a power regulator and frequency-based stabilizer, it can also significantly influence power flow in the transient states after power disturbances [336]. In the case of a simple interconnected power system consisting of two power systems, the control of TCPS can force good damping of both power swings and oscillations of local frequency. In the case of a more extensive interconnected power system consisting of more than two power systems, the influence of the control of TCPS on damping can be more complicated. Firm damping of local frequency oscillations and power swings in one tie-line may cause more significant oscillations in remote tie-lines and other systems. Hence, using devices like TCPS to dampen power swings and frequency oscillations in an extensive interconnected power system must be justified by a detailed analysis of power system dynamics.

The authors of [272] contributed a robust decentralized frequency stabilizer design based on synchronous static compensators while considering system uncertainties. The LFC of a two-area interconnected system, of which one area is composed of power systems with several hydroelectric units and the second is composed of mixed thermal/thermal-hydroelectric units, is presented in [338]. Coordinated control between TCPS and SMES, whose gains of the controller are integrated into the AGC loop, and the parameters of TCPS/SMES are optimized by a craziness-based PSO, as presented in [338].

Apart from this, system operators are facing more and more challenges to meet the AGC system requirements, which aim to maintain the target network frequency and scheduled connection flows, especially with the ever-increasing penetration of intermittent generation resources that are not dispatchable in electrical grids. On the other hand, through fast-acting energy storage devices, effective damping of electromechanical oscillations of a power system is possible since additional energy storage capacity is provided in addition to the kinetic energy storage provided by the moving mass of the generator rotor. Thus, in a power system, the instantaneous mismatch between actual power supply and demand under sudden load changes can be reduced by adding fast-response active energy sources such as BES devices, SMEs, and CES. Energy storage devices share sudden power changes required in the load. In the recent literature, several authors have demonstrated that battery energy storage systems (BESSs) are an effective tool thanks to their regulatory capacity in the context of system operation. With the constant expansion of renewable energy sources (RES), the provision of ancillary services is becoming an increasingly difficult task. Some researchers [82,146,147] have studied improving the LFC performance of power systems and include a BES unit. As more renewables participate in AGC, real-time AGC dispatching has become a more complex nonlinear optimization. Meanwhile, it should be solved in a calculation time shorter than the time cycle of the AGC (e.g., 4 s). For this problem, most existing optimization techniques must be revised to balance optimization speed and optimal quality.

Energy storage facilities using batteries and thyristor power converters can operate as pumped hydro storage units. In [339], controlling the load frequency of the steam storage and the operation of the instantaneous reserve can be regulated through a battery energy storage facility, which promises operational and economic benefits. The article [340] presents an example of this regulation type. The LFC of an interconnected thermal reheating system is studied by integrating the intervention of the battery energy storage system (BES), which is controlled using the ACE. The authors of [341] have shown the control performance of RF battery systems. Dynamic simulation results showed that the LFC capacities of RF battery systems are ten times higher than fossil fuel systems due to their fast response characteristics. Wind power plants (WPPs) are also considered devices that can provide frequency auxiliary services (FASs). However, ensuring that variable wind generation can reliably provide these ancillary services is a challenge. This gap can be partially overcome by combining the possibilities of ESS to compensate for the intermittent energy production of wind turbines. WPP’s commitment to FAS is through the use of the battery energy storage system (BESS). An example of this type of solution is presented in [342]. The authors of this paper use a BESS to support the mandatory FAS of a WPP (including primary and secondary frequency control) by developing a coordinated state machine-based control strategy. Using this method, a reliable FAS is obtained in which the operational constraints of the WPP (e.g., real-time reserve) and BESS (e.g., state of charge [SOC], charge, and discharge rate) are taken into account.

As with wind turbines, the intermittent and uncertain nature of photovoltaic systems leads to frequency regulation problems as the penetration rate of photovoltaics increases. The system requires fast response regulation to recover the frequency quickly when rapid fluctuations occur; however, in the case of traditional power plants with slow dynamics, the ability to keep up with the rapidly changing regulatory signal must be evident. Therefore, as in all of the cases analyzed so far, a BESS is an effective source of regulation to respond to frequency deviations immediately. A study in the article [343] addresses the issue of sizing an aggregated BESS through a series of system-level performance tests with different BESS penetration rates.

In addition to issues related to the broad penetration of renewable energy, one can also consider issues related to the dynamics of AGC itself. The authors of [344] investigated how dynamically available AGC (DAA) could be used in conjunction with a BESS, focusing on AGC signal distribution strategies prioritized and proportionally. An approach to using BESS for coordinated frequency regulation is proposed in [345] to improve the AGC performance of generators whose parameters cannot fulfill the conditions of stricter AGC criteria established by grid operators to regulate generators. The effectiveness and use of BESS in the context of network regulation and integration is examined in [346]. The operation of a 1 MW/2 MWh grid-tied battery energy storage system (BESS) in a 10 MW R&D wind farm for AGC for 29 days is analyzed. Studies carried out by the authors of [346] established a BESS response time of just one second, which is faster than the currently accepted practice of a conventional generator with governor control. The article [347] is in the same series as article [345]. A new BESS control strategy is presented to improve the dynamic performance of the AGC system. The regulation response accuracy margins are used to evaluate the performance of the AGC. These parameters define the slowest and fastest permitted power response to a regulation signal. One of the main objectives of this operation is to improve the regulation service by minimizing the non-compliance rate with the corresponding dynamic performance criteria and its defined precision margins. Indeed, a complete state of charge control (SoC control) is included in the strategy. The strategy is carried out so that extreme load levels are avoided. BESS is therefore used only during designated regulatory assistance periods, identifying and involving unnecessary regulatory efforts. With this strategy, BESS degradation is minimized.

Some intelligent methods are also used to improve the performance of the LFC in cooperation with the ESS. A fully optimized PID fuzzy load frequency controller (LFC) with filter (FPIDF) is presented in [348] to improve the performance of a hybrid microgrid system. A recent optimization algorithm, the Marine Predator Algorithm (MPA), is used to optimize the gains and input scaling factors and membership functions of the proposed fuzzy PIDF controller. The authors of [348] tested the controller’s performance on a two-area hybrid microgrid system model containing various renewable energy sources and storage devices. Another aspect of the use of ESS is the control of the SOC of these devices. The paper [349] proposes a state control algorithm for multiple distributed BESS with their state of charge (SOC) feedback. This type of control has proven effective in providing network services while managing the SOC of the ESS. The authors of [349] explain how one should integrate multiple ESSs into LFC, thus helping to increase the functional roles of legacy generators effectively. In this way, to extend the mathematical links between the ESS SOC and the power dynamics for frequency regulation, the paper’s authors study a simple and improved adaptive BESS controller based on a hybrid Fuzzy-ANFIS algorithm [350]. The controller emulates virtual inertia by controlling the active power flow to improve frequency stability, i.e., frequency nadir and rate of change of frequency (ROCOF). The controller was modeled and analyzed by the authors of [350]. The results obtained made it possible to conclude the performance of the controller. An FR auxiliary energy storage battery simulation model was built in MATLAB/Simulink [351]. The created model analyzes the system’s response characteristics during regular operation and verifies the system operation strategy during failures. The authors of [351] concluded that an energy storage battery reduces the grid frequency offset by 38.1% and increases the power response speed by at least 25 times in regular running. Another example related to the control strategy for the use of battery energy storage systems (BESS) and demand response (DR) in the LFC task is presented in [352]. First, considering the presence of wind farms, reactive loads, and the constraints of BESS, the unit commitment problem is solved. The best location and optimal size of the BESS and the regulating power of the reactive loads are also determined. Finally, the improvement of frequency regulation, considering the participation of wind farms, is envisaged based on an applied plan of defined rules. Different states associated with the frequency response of the power system, as well as the state of charge (SOC) of the BESS, are considered in the above plan. Another alternative solution to improve frequency regulation is based on the demand response (DR) program. A handicap in the form of communication delay is a rather severe obstacle to realizing this strategy.

Electromechanical oscillations of a power system can be effectively damped using fast-acting energy storage devices. The storage devices in question can provide, in addition to the kinetic energy of the generator rotor, a storage capacity that can respond to sudden changes in energy requirements. SMES devices are characterized by a few properties, such as low discharge rate, fast acting, increased time required for power flow reversal, and maintenance requirements. They are, therefore, used as load frequency stabilizers [150,151,152,353,354,355,356,357,358,359,360,361,362,363,364]. ESSs, in general, and BESs, in particular, can be used to provide rapid active power compensation, so they can also be used to improve the performance of LFC. The authors of [151] studied a proposal for enhancing AGC by using self-tuning adaptive control for the main AGC loop and adding SMES for oscillation damping. Simulations conducted by the authors of [151] showed that the proposed adaptive control system is very effective in damping oscillations caused by load disturbances and that its performance is relatively insensitive to changes in the gain parameters of the SMES controller. A new incremental model of a BES is presented in [152]. The BES model is merged into the LFC of a power system. The authors of [152] developed a complete numerical model of a two-area interconnected power system, including the regulator dead zone and the GRC. The model can be used in cases close to absolute power systems. The controller gains of the LFC model were optimized using the second Lyapunov method. The BES integrated into the LFC model can intervene during charge and discharge mode operations. Simulation tests conducted by the authors of [152] demonstrated the effectiveness of BES in damping oscillations caused by load disturbances. The authors of [150] show the efficacy of SMES units (both superconducting and normal loss) in meeting sudden electrical energy needs. The authors of [150] also proposed the best ways to utilize these units’ small energy storage capacity to improve the load frequency dynamics of large power areas. The authors of [358] developed an LFC model of the two-area interconnected power system, including the nonlinearity of the regulator dead zone, steam reheat constraints, and boiler dynamics. This LFC model also included a small-capacity SMES model. They noted a clear improvement in LFC performance through the interaction of the primary and secondary control systems and through the influence of the SMES, as well as by optimizing the gain parameters and carrying out stability studies using the second Lyapunov method. Another two-area interconnected LFC model with a reheat steam turbine, governor dead-band nonlinearity, and SMES is presented in [359]. The developed model is of the discrete state-space type. The effect of sudden power delivery on an actual power load, in combination with the impact of a small-capacity SMES, is studied based on the obtained LFC model. Besides considering the different elements of the model, the authors also analyzed the possibility of using an IGBT converter instead of a thyristor converter as a power conditioning system with the SMES.

Instead of modeling a two-area system as usual, the authors of [360] presented the possibility of applying a layered ANN controller to study the problem of AGC of four-way interconnected power system areas. The first three areas include steam turbines, while the last consists of a hydroelectric turbine. All areas are equipped with SMES units. The study also considers the system’s non-linearities by including a back-propagation through time algorithm. Some critical observations resulted from the preliminary analysis of the developed model. First, the system equations were satisfactory, so no ANN emulator was used. Then, the simulation of the power system performance using conventional integrated controllers and an ANN controller led to the conclusion that the performance of the ANN controller is better than traditional controllers. The authors of [361] studied a method based on fuzzy logic controllers (FLC) for AGC of power systems, including SMES units. The simplest methods of frequency regulation aim to minimize frequency transients. The process is based on conventional PI controllers, reacting to the secondary control of the AGC, whose objective is to make the balance error zero after a sufficient delay time. Instead of this simple conventional method, the authors of [361] propose a technique based on FLC configurations. The results obtained using FLCs are superior to those of traditional controllers regarding settling and overshoot times. The article [362] analyzes AGC models equipped with SMES devices. The model presented in [362] shows the AGC analysis of an interconnected hydrothermal energy system consisting of two areas in the presence of GRC. The addition of a small-capacity SMES unit in both regions is studied in the paper. We obtain the optimal values of the required gain parameters using an integral squared error (ISE) technique to minimize a quadratic performance index. The analyses carried out by the authors of [362] lead to the conclusion that SMES units installed in one or the other areas are as efficient as SMES units installed in both regions and considerably improve dynamic performances following a load disturbance in one or more areas. A small-sized CES unit is proposed in the papers [364] to improve the dynamic performance of a power system with LFC. A model of a two-area interconnected power system, which includes the nonlinearity of the regulator dead-band, the steam reheat turbine, the boiler dynamics, and the generator flow constraint, is developed for the analysis. The paper [363] proposes a method based on phase shifters to stabilize frequency oscillations of a two-area LFC system and another three-area LFC system. After using a system reduction method, the developed design can be extended to the general design applicable to multi-area LFC systems. The idea is based on the classic design of stabilizing an inter-area oscillation mode between interconnected areas. The LFC model developed in [272] considers the system’s uncertainties. A new robust design of decentralized frequency stabilizers based on static series synchronous compensators (SSSC) is also included. The dynamic power flow control by an SSSC installed in series with a tie line between interconnected systems can be applied to compensate for load disturbances with changing frequency in the vicinity of the inter-area oscillation mode and stabilize frequency oscillations. The problem of power oscillations due to reduced system damping has become increasingly severe with the increase in the size and capacity of power systems, the growth of widespread interconnections, and the high presence of power sources in the form of renewable energies. With the increasing attention to power system stabilization through SMES control, as this SMES unit has a self-commutated converter and is capable of simultaneously and quickly controlling the active and reactive powers for the improvement of the LFC, an additional SMES controller programmed with fuzzy gain is associated with the AGC. The authors of [353] demonstrated that SMES with the additional gain-programmed controller could perform more effective primary frequency control for a multi-area power system. The paper [354] presents a new LFC scheme that integrates the energy storage aggregator (ESA) and its associated disturbance observer. The authors of [354] also proposed a finite-time leader–follower consensus algorithm to control small-scale ESSs via sparse communication networks. Through this tracking mechanism, the algorithm ensures that the ESA is suitable for frequency control signals while the state of charge between each ESS is balanced in finite time. A method for coordinating LFC and SMES technology is presented in [355]. The proposed method uses a novel Mite Testing Algorithm (MSA) to obtain an optimal PID controller in the Egyptian power system (EPS). The AGC model represents planning for the Egyptian electricity system of the future, where high wind power penetration (HWPP) is considered. The developed strategy aims to compensate for the EPS frequency deviation, notably conventional generators, by keeping them from exceeding their rated power during load disturbances and mitigating power fluctuations of wind power plants. A simple interconnected power system consisting of two power systems showed that controlling TCPS can force good damping of power fluctuations and local frequency oscillations. Firm damping of local frequency oscillations and power variations in a tie-line can cause more significant oscillations in distant tie-lines and other systems. A detailed analysis of power system dynamics was conducted in [365] to justify using TCPS to dampen power variations and frequency oscillations in an extensive interconnected power system. A novel Tilt-Integral Derivative Controller with Filter (TIDF) is proposed in [366] for the LFC of multi-area power systems. The authors of [366] performed a comparative analysis of the results with some recently published heuristic approaches, such as the FA, GA, and PID controllers optimized for PSO for the same interconnected power system. The results obtained confirmed the superiority of the proposed approach. A mathematical model of the AGC of an interconnected hydrothermal energy system with the coordinated operation of a SMES unit in the thermal area and a Thyristor Controlled Phase Shifter (TCPS) in series with the tie-line is presented in [367]. The model also considers the GRCs for the thermal and hydro systems. A quadratic performance index obtained using the integral squared error technique is optimized to calculate the gain parameters of the integral controller. A comparative analysis of the dynamic responses demonstrates the effectiveness and efficiency of the proposed SMES-TCPS combination in suppressing and stabilizing frequency oscillations and tie-power deviations and reducing the stabilization time. The paper [368] presents a new dynamic model and control approach for a static synchronous series compensator (SSSC) to participate effectively in the AGC of an interconnected deregulated power system. A new mathematical formulation is extracted to present the participation of SSSC in the exchange of energy flows on the tie-lines. Furthermore, fractional-order controllers (FOCs) are used to design an efficient SC damping controller. The impact of integrating FACTS devices, namely TCPS and TCSC, on the AGC of a two-area thermally deregulated power system was studied in [369] to improve the performance of responses such as frequency deviation and oscillation damping and the deviation of the power of the tie-line between the areas and the energy generated by the GENCOs. A method based on a type 2 fuzzy system (T2FS) is studied in [157] for the LFC of power systems. The analysis model includes SMES units and the two-area interconnected thermal reheat system. The model also considers GRC and boiler dynamics (BD). The main advantage of the implemented controller is its incredible insensitivity to significant load changes and variations in plant parameters, even in the presence of nonlinearities. A PDF plus (1 + PI) controller optimized using the Grasshopper Optimization Algorithm (GOA) is used for solving the AGC of a power system with flexible AC transmission system (FACTS) devices [370]. The AGC system comprises three reheat turbine-driven thermal units of different power levels with appropriate GRCs and other FACTS devices. The FACTS-device-equipped AGC system is also boosted by a new multi-stage controller design structure of a PDF plus (1 + PI) while the GOA adjusts the controller gains. The authors of [370] demonstrated that the proposed algorithm is the best compared to other algorithms, including the GA and the PSO algorithm. A comparative analysis of AGC performance with different FACTS devices on three thermal control areas equipped with a reheat turbine and appropriate GRC is presented in the paper [371]. A Gray Wolf Optimization (GWO) algorithm for tuning controller gain parameters is used to optimize the parameters of a new dual-stage controller based on a PD filter plus a PI (PDF more (1 + PI)), introduced with a relatively recent scalable calculation technique. The dynamic responses of the system with the controller (PDF plus (1 + PI)) and GWO are compared to the traditional PI and PID controller with the GWO technique. The tests reveal that the controller responses (PDF plus (1 + PI)) are superior to the PI and PID responses. The paper [372] demonstrates the effectiveness of FACTS devices such as the SSSC and thyristor controller series compensator (TCSC) in maintaining system stability with an interconnected power system (IPS). A secondary regulator was initially proposed, including a fractional order (FO)-type PID (FOPID) optimized with the water cycle algorithm (WCA). The research paper [373] proposes a fuzzy-based PID controller to create the control loop required for the AGC of the multi-source power system. A new Advanced-Whale Optimization Algorithm (A-WOA) was also used to provide the parameters of the fuzzy PID controller. Various comparative studies have been carried out at the controller level from the perspective of the technique used to justify the superiority of the proposed Fuzzy PID controller and the new A-WOA technique. The authors concluded that the proposed A-WOA designed Fuzzy PID controller was the most improved method to achieve AGC in the multi-source power system under different operating conditions. Deploying additional devices, such as FACTS, and replacing the governor controller with a PID controller can benefit the system. The paper [374] proposes a control of the load frequency using a PID controller and a series synchronous static compensator (SC). PSO is used as an optimization method to find the best parameter. A novel sliding mode control (SMC) strategy for controlling the frequency and voltage in a complex power system under electrical fault conditions is proposed in [375]. The LFC is achieved by modifying the position of the generator valves, while the bus voltage is controlled using a FACTS device such as the Static Var Controller. The inter-area connection lines also transmit power, which is taken into account in the LFC since the obligations of import/export of active power from/to the connection areas must be respected. The SMC used by the authors is characterized by inherent fluctuations. An improvement has been introduced to the SMC system to provide superior performance in regulating frequencies and busbar voltage magnitudes. The AGC model of three unequal area thermal systems with a single reheat turbine and including the appropriate GRC in each area is presented in [376]. Various 2DOF type controllers such as 2DOF-PI and 2DOF-PID are compared to analyze the dynamic responses of the system. After conducting investigations, it turned out that responses with 2DOF-PID were better than others. In addition to using a two-degree-of-freedom (2DOF) PID controller, FACTS devices such as the SSSC and the interline power flow controller (IPFC) have also been used to evaluate their performance. The secondary controller gain and other parameters of the 2DOF controllers were optimized simultaneously using the FA. The dynamic responses of the system with 2DOF PID were compared with those of 2DOF PID controllers equipped with SSSC and IPFC. The authors came to the conclusion that the dynamic responses of AGC systems equipped with IPFC were better than those of others. Decentralized controllers equipped with flexible AC transmission system (FACTS) devices to achieve AGC in power networks are proposed in [377]. The FACTS functionality of redirecting energy flows by controlling the physical parameters of the connection lines is used in the additional control of the AGC. The procedure for synthesizing a controller for a generation area uses information from neighboring areas only; hence, the control design is decentralized. Moreover, the method used in [377] is termed plug-and-play because if a generation area is plugged in or out, most neighboring areas must update their controllers, leaving the rest of the network unaffected. A multi-area system is presented in [378]. The effect of various FACTS devices and HVDC links on the operation of power systems is analyzed. Hybrid production units such as hydrothermal and wind (WTS) are incorporated into the analyzed system. The considered multi-area AGC system is equipped with a contemporary controller called 2DOF-TIDN. The optimal values of the controller parameters were successfully determined using the BSA algorithm. Comparative analysis of the use of 2DOF-TIDN, PID and TID controllers revealed that the system with 2DOFTIDN provides better dynamics. Additionally, integrating an HVDC link parallel to the AC link line and using WTS revealed significantly improved system dynamics. Furthermore, the study of integrating various FACTS devices on a three-area AGC system showed that, among the FACTS devices used, among others, TCPS, SSSC and GCSC, the latter presents the best dynamic properties for stabilization of frequency signals. An in-depth overview of LFC of thermal, hydroelectric, and gas turbine power plants using RFB and SSSC technologies is presented in [379]. The analyzed LFC system consists of thermal and hydroelectric units, a gas power plant with a GDB, and a diesel engine generator in a two-area network for power generation. The parameters of a PI controller are optimized to mitigate the frequency and tie-line deviations that occur in the system due to load change. Gray Wolf optimization techniques are used to optimize controller parameters. There is also a possibility of storing energy using an RFB battery. The effectiveness of this battery on frequency deviation stability is also studied. Different cases of system operating regimes—without RFB or SSSC and with RFB and SSSC—are analyzed from the point of view of steady-state stability. An LFC model for three area systems, including a unified power flow controller (UPFC), is analyzed in [380]. The system has been designed so that a deeper understanding of how the power system works is obtained. Apart from the action of the UPFC, frequency deviations obtained using various controllers, such as PID and Fuzzy, are compared to better understand the operation of these controllers. The authors of [381] present a study of the compound power system’s LFC under deregulated conditions. The LFC test system is divided into two areas: a thermal system, a biogas plant, distributed generation (DG), and an electric vehicle (EV). The system is additionally equipped with an HVDC line to improve the power transfer capacity of the connecting lines. The stored energy is sent through the HVDC line for frequency regulation. The EV is used to manage the uncontracted load. A Quasi Opposition Lion Optimization Algorithm (QOLOA) is applied to improve the controller gain. Additionally, a static series synchronous compiler (SSSC) is used to enhance the transfer capability of the AC tie-line.

The imbalance between electricity load and generation can be significant when high penetration of renewable energy sources is present in the power system, resulting in large amounts of renewable generation integrated into power systems. Power fluctuations in the interconnection line and high system frequency may appear due to the interconnection of renewable energy systems, which are complex nonlinear systems. This situation often leads to the appearance of insufficiently damped oscillations, especially during extreme and dynamic load situations. Control of the load frequency guarantees the nominal operating frequency and the orderly fluctuation of the network interconnection power, which contributes, in most cases, to solving the problem formulated in the previous point. Thanks to efficient and intelligent control systems, such as LFC in particular, the electrical system provides high-quality electrical energy to consumers. The recent trend is to configure a hybrid generation system combining diversified types of renewable energy sources to ensure higher reliability of electricity generation from renewable energy sources. Thanks to hybrid electricity production, renewable energy sources have become more accessible. Due to the intermittent nature of renewable energy sources, LFC is vital to avoid partial or complete system collapse. In some of the articles presented below, some authors attempt to study examples of diversified, integrated renewable energy sources focusing on LFC, as shown in all articles listed in this work. In conventional power systems, LFC is usually achieved via AGC. Communication plays a vital role in integrating intelligence into the interconnected power system. However, historical records prove that data transfer has always been vulnerable to cyberattacks. An entire chapter will be devoted to the different types of possible cyberattacks on LFC systems. These cyberattacks could lead to a blackout and cause national security concerns if not identified and contained. Future AGC systems must be capable of handling complex interactions between control areas with HVDC links and distributed generation equipment. In such a scenario, the effects of extended interconnections, Phase Locked Loop (PLL), and frequency measurements cannot be ignored. The dynamic impact of PLL and frequency measurements are significant for HVDC operation. To achieve acceptable AC/DC system performance, dynamic PLL models and measurements should also be considered in LFC model analyses.

Photovoltaic (PV) generators are considered an indispensable choice in the current design schemes of virtual power plants (VPPs). Coordinating start–stop and continuously adjustable PV units poses a notable challenge in VPPs with high-level PV penetration due to significant differences in unit capacity and operating characteristics. A proposed solution to this problem is presented in the article [356], where the authors suggested an AGC instruction allocation algorithm using mixed integer line programming (MILP) with a controller special PV inverter. The simulation results showed that this algorithm can facilitate effective coordination between on–off PV units and continuously adjustable PV units within VPP. The effects that small wind turbine (WT) output can have on the LFC process are presented in the article [357]. A simulation model of a utility’s AGC process, using system load data recorded in real time and modified to account for the overall output of small WTs through the use of synthesized data, is presented in the article. Various WT penetrations of the total system load are defined by including a series of WT output scenarios. An assessment of how the system performs compared to the base case is conducted using ACE values; the time between zero crossings, inadvertent accumulation, and control pulses sent to the regulating units are determined to evaluate the evolution of system performance compared to the base scenario. The uncertainties that arise on the power generation side due to the large-scale integration of the doubly fed induction generator (DFIG) mean that higher requirements are imposed on the performance of frequency regulators. The paper [382] studies the AGC strategy, based on a predictive control model with the participation of DFIG, to improve their secondary frequency regulation support capacity. The created LFC model combines control and optimization: an AGC controller is designed based on distributed MPC and can adapt to system uncertainties through continuous optimization and correction feedback. The optimization problem and constraint conditions are transformed into standard quadratic forms to facilitate the solution. A three-area LFC system is used to test the frequency support capability of the proposed AGC controller. A novel graph convolution network (GCN) with feasible output correction is proposed in [383] to quickly create a high-quality AGC dispatch control scheme for renewable energy and conventional power plants. Due to the increasing number of renewable energy sources participating in AGC, real-time AGC dispatching has become a more complex nonlinear optimization. This problem should be solved in a calculation time shorter than the time cycle of the AGC (for example, 4 s). A proposed solution to this problem is based on a novel graph convolution network (GCN) with feasible output correction [383]. This could lead to the rapid acquisition of high-quality AGC dispatch control schemes for renewable energy and conventional power plants. High data quality can be guaranteed by generating training data from offline optimization by a genetic algorithm with multiple runs. Another example of a multisource LFC model is presented in [384]. The LFC model comprises four-area interconnected power systems containing integrated renewable energy sources of photovoltaic and wind power. Considering the increased penetration levels of photovoltaic and wind and a thermal hydroelectric system, the designed model constitutes quite a complex challenge. Adding a hydroelectric system as the fourth type results in the open-loop system pole of the hydroelectric system being located on the right half of the S-plane. The stability of the modeled electrical system will, therefore, strongly depend on the robustness of the controller. The author of the article [384], therefore, proposed a new MPC-(1 + PIDN) designed for high-order interconnected areas (HOIA) to stabilize the frequency robustly. The salp swarm algorithm is adopted to optimize the parameters of the PIDN controller. An LFC model of a two-area power system integrating hybrid energy storage (HES) for enhanced frequency regulation services is presented in [385]. The authors focused on a mixed hierarchical control method, including inherent communication delays, as the generalized LFC model. The cascaded integral-tilt derivative (TI-TD) controller coefficients are optimized using the quasi-oppositional Harris Hawks optimization (QOHHO) algorithm. The dynamic performance of the HES system used is compared with two other systems—a battery energy storage system (BES) and a system without energy storage (WES). The comparison is made from the perspective of real-time charging and the intermittency of renewable energies. Finally, real-time analysis using the OPAL-RT simulator was carried out to demonstrate the effectiveness of the proposed HES-based hybrid LFC model. Clear improvement in the frequency regulation capabilities of the tested power system was noted. Combining different electrical energy sources with electrochemical energy storage to improve frequency regulation (FR) performance can significantly improve the auxiliary service revenue of FR thermal power units and provide flexible resources for an increased proportion of new energy supply systems. Several factors can influence the optimal allocation of energy storage capacity in the thermal energy system for FR. Not only is it related to the characteristics of thermal power units, frequency control characteristics, and type of energy storage technology, but the performance index, market rules, etc., also influence the effectiveness of FR. The paper [386] presents a method for evaluating the equivalent life of battery storage using the rain flow method, establishes the optimal configuration model of thermal storage combined with maximum net benefit based on the index comprehensive FR performance evaluation of the Guangdong power grid, and finally combines the battery storage multi-layer state-of-charge control (SOC) strategy. Suppose the imbalance between load and generation during the production of large quantities of renewable energy integrated into the conventional system is not managed effectively. In that case, the resulting uncertainty can lead to excessive deviations in frequency and tie-line power flows. To minimize the system frequency and tie-line power deviations in conventional AGC, an MPC method called feedforward frequency control is used, considering the disturbances resulting from renewable energy sources such as wind turbines or PV generators [387]. Compared to conventional control methods, the implemented controller reduces frequency and tie-line deviations much better over time in a multi-area test power system. A new Fractional-Order Integral-Tilt Derivative with Filter (FOI-TDN) controller control technique powered by the current software computing technique of hybrid sine-cosine algorithm with Fitness Dependent Optimizer (hSC-FDO) is presented in [388]. This technique is used to improve the frequency control of power systems. Practical constraints with non-linear characteristics, such as controller dead-band, communication delay, boiler dynamics, and generator rate constraint, are integrated into the given system model, making the analysis more realistic. Suppose, in general, that LFC is often used via AGC in conventional electricity systems based on renewable energy sources. In that case, AGC is generally avoided to reduce costs. Instead, we prefer to use the concept of ballast load at the output of renewable energy sources. This option is cheaper and easier to achieve when having a functional LFC. As in the case of LFC in the conventional system, the ballast load must be powered so that the power output matches the total power consumption of the load and the power dissipation in the ballast load. The authors of [389] studied an LFC model by controlling a ballast load through the classic controllers: I, PI, and PID. The PSO technique optimized the controller parameters. A new proposal for frequency variation stabilization using a tilted integral derivative (TID) controller in AGC is presented in [390]. A two-area interconnected power system has been implemented to study the output power variation according to the load demand and the technique for LFC. A distributed generation represented by a wind energy system, whose output power varies in a high range, is used in area 1. By varying the wind load demand, changes in power output can be effectively controlled. Here, the Differential Evolution (DE) algorithm is considered to improve the gain of a tilted integral derivative (TID) controller. The AGC of the future Egyptian multi-source electricity systems is presented in [391]. The study considers high penetrations of RES and electric vehicles (EVs). The considered RES include photovoltaic power plants, wind power plants, concentrated solar power plants, and hydroelectric power plants. The analysis proposed a fractional-order PID (FOPID) controller for LFC and its parameters were tuned using the Runge Kutta optimizer (RUN), which is a new optimization algorithm. The FOPID controller performance was compared with that of a PID, PI, and I controller to assess the FOPID controller performance. A modern power grid model including conventional generators considering nonlinearities, in addition to RES and energy storage (ES) units, is presented in [392] for studying the LFC problem. Three types of RES are involved in the study: wind, photovoltaic, and solar thermal. Furthermore, the model was designed to consider the action of two types of ES units: SMES and battery energy storage (BES). An optimal control design is established via a novel optimization approach based on a Marine Predator Algorithm (MPA). The controllers optimized in the analysis of the LFC system model are PID controllers. An improved form of chaotic atom search optimization (IASO) algorithm by adapting a one-dimensional (1D) chaotic map (tent, sinusoidal, and logistic) is proposed in [393] to improve the search capability by intensifying the exploitation stage. A novel parameter design of a fractional-order integrally PD controller for automatic LFC is implemented based on this new technique. A multi-area, multi-source hybrid power system (HPS) is subsequently analyzed and optimized by minimizing the absolute integral time error. A coordination control strategy for wind farms with line-commutated converter (LCC)-based HVDC delivery is presented in [394] to participate in LFC. The role of the HVDC rectifier is to detect the network frequency to achieve the control coordination strategy. This detection is based on controlling the active power by detecting the frequency level. A droop signal is introduced at the level of the rectifier control loop as a function of the frequency deviation. If the grid frequency is too high or too low, the active power flow through the HVDC link will be reduced or increased. Wind generation pitch controllers, in turn, will vary wind production, increasing or decreasing the blades’ angles to reduce or increase the captured wind energy. Another reliable optimization tool, Harris Hawks (HHO), is proposed in [395]. This optimizer is based on an approach to evaluate the optimal parameters of the PI controller simulating LFC. A multi-interconnected system model with renewable energy sources (RES) is used to test the optimizer. Two interconnected power systems were analyzed to demonstrate the robustness of the proposed HHO-based controller compared to other optimizers and the traditional controller. Another variation of using the Leader Harris Hawks optimization algorithm is presented in [396]. A predictive controller model is associated with it to assist the HHO, hence the acronym (MPC-LHHO). The new optimizer is tested in a frequency and voltage regulation model with high RES penetration.

Some aspects of energy generation, such as the modification of unit commitment controls, economic dispatch, regulation, and frequency regulation when the level of wind generation capacity is significant, are discussed in the article [397]. First, a constraint in the form of the penetration level of the wind farm is determined, which limits the worst-case change in wind production from a network due to, e.g., a storm to being less than the worst first loss resource emergency or conventional generation commitment. The WF penetration constraint acts only as an indicator that additional spinning reserve, load tracking, and unloadable generation capacity are required via adjustment of unit commitment and AGC controls if the penetration constraint of WF is violated. Then, a discussion relating to the methodology, costs, and advantages of modifying the unit commitment when WECS production is significant is conducted (i.e., the WTG penetration constraint is satisfied or violated). The contribution of a doubly fed induction generator (DFIG) to system frequency responses is presented in [398]. The impact of different governor settings and system inertia is investigated. This is performed by DFIG, which provides an inertial response via artificial velocity coupling. The effects of the inertial response on the machine’s behavior and its importance for frequency regulation are also discussed. A new control algorithm is developed to extract maximum energy from the turbine in a stable manner after establishing the influence of converter current limits and auxiliary loop parameters on the inertial response. A control scheme that allows doubly fed induction wind generators (DFIWGs) to participate effectively in system frequency regulation is studied in [399]. This control approach is achieved in the following way—the wind turbines operate according to an optimal deloaded power extraction curve such that the active power supplied by each wind turbine increases or decreases during changes in system frequency. The control strategy, therefore, consists of defining a combination of static converter control and pitch control, adjusting the rotor speed and active power according to the optimal deloaded power extraction curve, and providing a primary frequency regulation capability. The design and implementation of a new control system for a DFIG of the type used with wind turbines is presented in the paper [400] to support the operation of the power system. Some aspects of this control system are presented in the article. Firstly, this controller provides a DFIG-based wind farm with operational and control compatibility with conventional power plants and can contribute to voltage maintenance and recovery following grid outages. In addition, the system ensures the ability to provide a stabilization capacity of the power system, which improves the overall damping of the system. Finally, the control system contributes to short-term frequency support following a loss of network generation. The power output of wind turbines is usually fluctuating. It affects the system’s frequency, whereas a hybrid electric system uses many wind generators on small, isolated islands. This problem can be solved using a new renewable energy system on small, remote islands. The system proposed in [401] can provide high-quality energy using an aqua electrolyzer, fuel cell, renewable energy, and diesel generator. Hydrogen generated by an aqua electrolyzer is fuel for a fuel cell. Simplified frequency control models and extensive simulations of wind penetration scenarios over an extended multi-year period are used to determine changing trends in the frequency behavior of a power system following the loss of the largest generator [402]. The frequency change rate and frequency nadir characterize the system’s frequency response. A novel control strategy for frequency control in a standalone application based on the coordination control of fuel cells (FCs) and a double-layer capacitor bank (DLC) in a power-to-energy system renewable hybrid autonomous hybrid is implemented in [403]. The implemented system comprises renewable energy production subsystems, including a wind turbine generator (WTG), photovoltaic (PV) system, FC system, and DLC bank as an energy storage system. The next paper [404] presents a method for efficiently operating a BESS associated with a frequency control problem. The operation of the BESS is simulated using a control system model and a purpose-built controller. System constraints are considered in the strategy based on a predictive control model intended to ensure the optimal operation of the BESS. The predictive controller performance is also optimized using a frequency prediction model based on Gray’s theory. Frequency deviations in a small power system can be reduced through an integrated control method for a WF, as presented in the paper [405]. WWF uses two control schemes to achieve frequency control: load estimation and short-term wind speed forecasting. A minimum-order observer is used as a disturbance observer to estimate the load in the small power system. The short-term forward wind speed is predicted using the least squares method to regulate the output power control of the WF according to the changing wind speed. The expected wind speed adjusts the output power command of the WF as a multiplying factor with fuzzy reasoning. An LFC design using the MPC technique in a multi-area power system in the presence of wind turbines is presented in the paper [406]. In the proposed model, each local controller is designed in such a way as to guarantee the stability of the entire closed-loop system. The considered frequency response model also includes wind turbines and the physical constraints of the governors and turbines.

The dynamic participation of DFIG for frequency control of a two-area interconnected power system in a competitive and restructured electricity market is analyzed in the article [407]. The authors of [407] propose a frequency control assistance function responding proportionally to the frequency deviation. This action aims to extract kinetic energy from the wind turbine to improve the system’s frequency response. Optimal transient performance for PoolCo transactions can be achieved through the presence of a TCPS in series with the bonding line and SMES at the terminal of an area, in conjunction with DFIG’s dynamic, active power support. The craziness-based particle swarm (CRPSO) method is used to optimize the integral gains of the AGC loop and the parameters of the integrated TCPS and SMES. The dynamic participation of a wind turbine based on a doubly fed induction generator in the frequency regulation of the system is presented in [408]. The authors proposed a modified inertial control scheme for a DFIG that uses frequency deviations instead of frequency derivatives to rapidly inject active power, which arrests frequency drops during transient conditions. The integral square error technique was used to obtain optimal values of the speed control parameters of a doubly fed induction generator-based wind turbine. The BESS is one of the practical solutions to the problems of rising distribution voltage and frequency fluctuation due to the extensive integration of renewable energy sources. In the article [409], the authors present a solution to the high cost of BESS based on an application of controllable loads such as electric vehicles (EVs) and heat pump water heaters (HPWHs) to control the power system. This trick helps reduce the required BESS capacity. A new supplementary LFC method using several EVs and HPWHs as controllable loads is proposed in this paper. The article [410] discusses and corrects the significant drawbacks of turbine deloading methods, which are necessary for a wind generator (WG) to participate in primary or secondary LFC. Two main deloading techniques are used: overspeed deloading and pitch-controlled deloading. A wind farm based on a DFIG can provide short-term frequency regulation. A control strategy that allows this park to give this power is studied in [411]. The controller can dynamically manipulate the position of the DFIG rotor flux vector to slow down the generator, thereby providing a temporary increase in output power and reducing the frequency drop following the transient period, resulting, for example, in loss of network generation. The authors of [411] conducted case studies of DFIG operating under different speed and power output conditions. In the doubly fed induction generator, it is possible to use adaptive adjustment of the hang and the inertia control loop gains using a new method presented in [412]. Data-driven methods, which only operate based on the system’s input and output, eliminate the defects and problems of the power system and wind turbine modeling. Adaptive adjustment of the statism and inertia control loop gains is provided using the second derivative of the error, thanks to which the control is faster and a drop in frequency is avoided. The output of the next moment is proposed by implementing the nearest neighborhood of the K vector in the proposed control method. Using the Hessian matrix, the coefficients of the frequency control loops are then adaptively adjusted. The authors of [413] present an AGC model to analyze and simulate the production of renewable energy for two area power systems in the presence of a wind farm with high penetration of renewable energy. The combination of automatic production control and automatic voltage regulation of thermal units is taken into account in the analyzed model. Due to the unpredictable structure and intermittent fluctuation of the RES, the operation of an isolated microgrid is more complex due to the low inertia of the system. The rate of change of frequency (RoCoF) is high in isolated microgrids compared to the conventional power system. It is therefore necessary to provide fast frequency response from existing distributed energy resources, which are technologies connected to inverters.

The authors of [395] demonstrated that renewable energy resources such as diesel engine generators (DEGs), fuel cells (FCs), flywheel energy storage systems (FESS), and wind turbine generators (WTGs) can improve the frequency excursion under various operating conditions if dynamic signal models for RES are introduced into isolated microgrids and their appropriate contribution in LFC studies is considered. A fractional-order (FO) PI minus FO derivative with filter coefficient (FOPI-FODF) controller was used as a secondary controller in the AGC of a multi-area system incorporating various sources [414]. The crow search algorithm was used to optimize controller gains. After conducting a comparative analysis of the system’s dynamic response with and without renewable energy sources for FOPI-FODF and for some commonly used integer order and FO controllers, it was found that the FOPI-FODF controller had the best performance. A new secondary controller with a cascaded combination of the proportionally fractional-order derivative (FO) with filter coefficient (N) and proportionally FO integral derivative with filter coefficient (N) (FOPDN-FOPIDN) is proposed for the first time in [415]. The simulated AGC model contains a high-voltage direct current (RHVDC) tie-line and realistic Stirling solar thermal system (RDSTS) models in multi-area LFC studies in a deregulated scenario. After carrying out exhaustive tests, it turned out that the performance indices (peak amplitude, stabilization time, and oscillation amplitude) of the controller show dominance compared to existing FOPI, PIDN, and FOPIDN controllers in policy schemes such as poolco, bilaterals, and contract violations. A new fractional-order cascade controller called Cascade Fractional-Order PI with Fractional-Order Integral Derivative with Filter (FOPIFOIDN) is used as a secondary controller in an AGC model presented in [416]. The model is a precise high-voltage direct-current (AHVDC) type using a transmission line’s inertia emulation control strategy in the AGC of a multi-area composed of different source systems. The regulator dead-band and appropriate GRCs are considered for thermal systems. Comparing the system dynamics with various fractional-order controllers and the proposed FOPI-FOIDN controller while comparing one at a time reveals a better dynamic performance of the latter. A novel combination of particle foraging-oriented (BFO-PSO) test optimization techniques for a hydro-dominant energy system model was used in the LFC model presented in [417]. This technique was used to optimize the design of an LFC system based on PID. The controller was implemented against classical PID, Pessen’s integral rule, some overshoot, and no overshoot, as well as the recently published BFOA algorithm regarding calculated gains and absolute error multiplied by inverse time (ITAE). As the performance of the hydroelectric system is slow and oscillating, it was decided to implement additional improvements to the proposed design by comparing the combination of Unified Power Flow Control (UPFC) in series with the tie-line and hydrogen aqua electrolyzer installed at the area 2 terminal. An optimal and efficient solution to an AGC problem in hybrid power systems, with the addition of a deregulated scenario, can be obtained through the implementation of the grasshopper optimization algorithm (GOA) using a PID (3DOF-PID) controller with three degrees of freedom [418]. A high-voltage direct-current (HVDC) link was used to evaluate the performance of the PID controllers, and 3DOF-PID was tested with it. The study found that the GOA-optimized 3DOF-PID controller is better than any conventional technique, such as the Mite Test Algorithm (MSA) optimization technique.

10. LFC Scheme with DC Links

To meet the needs of energy transfer over large distances, since the end of the 1960s, HVDC transmission has established itself as an alternative link in the electricity system scenario due to its numerous technical and economic advantages. One of the oldest papers on a method of automatic frequency ratio control (AFC) by a DC system is presented in [419]. LFC control also includes tie-line bias control (TBC) action in AC/DC systems and can cooperate with AFC and TBC in AC systems. The working principle is that the frequency deviations of two AC systems are detected, and its controller adjusts the DC power to achieve constant frequency control. Another model of AC/DC transmission system is studied in detail in [420]. The control effects of an AFRC system on random load disturbances in a steady state are analyzed. The authors of [421] analyzed an optimal three-level controller for controlling the load frequency of a power system, which minimizes frequency deviations resulting from a sudden disturbance. A new control variable resulting from the consideration of DC power is considered in the system model. The three levels of control defined by the authors of [421] are as follows: the first control level is DC power control, local control represents the second control level, and coordination of controls stands for the third control level. Each local controller in the control hierarchy is responsible for controlling a subsystem based on interaction variables provided by the coordinator. The Santo Tomé HVDC converter is the second DC link asynchronously dependent on the power systems of Argentina and Brazil. The Santo Tomé back-to-back high-voltage DC (HVDC) link control design is presented in the paper [422]. Besides HVDC control functions, the Santo Tomé converter station also has an LFC function. The article [423] describes two power system models, in which model 1 consists of two power system areas with hydroelectric plants, while model 2 has one power system area with hydroelectric plants and the other with thermal heating plants. A DC link is the system interconnection parallel to the AC tie line. The authors of [423] showed that the dynamic response of interconnected hydropower system areas is slow and degraded in all aspects of response quality. This degradation in system dynamic performance can be effectively compensated by using a DC link parallel to an active bonding line as the system interconnection between two areas of the power system. A comprehensive study on the dynamic performance of a two-area power system interconnected via parallel AC/DC transmission links subject to parametric uncertainties is presented in [424]. The frequency deviation at the rectifier end is used to obtain the dynamic model of the incremental power flow through the DC transmission link. Stability fluctuated by load demands can be improved using an LFC scheme using electric vehicles (EVs) [425]. The LFC model developed by the authors of [425] is composed of a four-area electrical system integrating intelligent and renewable electric vehicles. A combination of high-voltage alternating current/direct current links and thyristor-controlled phase shifters interconnect the areas within the system. A comprehensive study on the dynamic performance of a more realistic power system with various sources in each area and interconnected via parallel AC/DC transmission links is presented in the paper [426]. Each area uses various sources such as thermal power, hydropower, and gas for electricity generation. Testing is performed using optimal AGC regulators designed and implemented to handle load disturbances in 1% increments within each control area, considering that the electrical system comprises two areas. Eigenvalue analysis is also conducted to evaluate the improvement of the stability of this realistic electrical system, which is equipped with a DC tie-line in parallel with another AC tie-line as an interconnection. It has been shown that in the presence of hydropower as one of the various sources in the power system, the transient response of the power system under step load disturbance is sluggish/poor. On the other hand, if we consider parallel AC/DC links as an interconnection between areas rather than using only AC connection lines, an appreciable dynamic performance of the system is obtained. Facilitating rapid control of primary frequency and system inertia in an AC network can be helped by combining the advantages of DC-link energy storage systems with a high-voltage DC link converter-based voltage source (VSC-HVDC) and kinetic energy storage devices of wind turbines. The authors of [427] proposed a method that combines the energy stored in the HVDC link with the power control capabilities of the wind turbines to provide a fast frequency response without being forced to use excessive capacity or impose exceptional performance on wind turbines. One of the concepts that has been widely used recently is the concept of virtual synchronous power (VSP). This power is used most of the time to simulate the dynamic effects of virtual inertia emulations by HVDC links, particularly in AGC systems. A multi-area AGC system is presented in [428], where higher-level control applications are studied. Using this concept in AGC contributed to a clear improvement in the system’s dynamic performance. The authors of [170] proposed a fuzzy PID controller (FPID) optimized by an improved ant colony optimization (IACO) algorithm for the LFC of multi-area systems. The quality of the solution could be improved by using the nonlinear incremental evaporation rate and updating the pheromone increment of the IACO algorithm. A modified objective function was proposed to improve the controller’s performance using parameters such as integral time multiplication absolute error (ITAE), overshoot, undershoot, and settling time with appropriate weighting coefficients. Moreover, sensitivity analysis is implemented under wide variations of operating conditions and system parameters to demonstrate the robustness of the proposed control method. Finally, the model was tested in a two-area, four-source hydrothermal power system with/without a high-voltage direct current (HVDC) link. Modeling of HVDC links in an accurate manner for dynamic studies of AGC/LFC of multi-area interconnected power systems is presented in [429] to demonstrate the accumulated error due to the conventional HVDC link model. Finally, a control strategy based on inertia emulation in AGC to exploit the stored energy from the capacity of HVDC links for AGC operations is also implemented in this paper. One of the technologies enabling the development of large-scale international networks, such as the European super grid, can be based on multi-terminal high-voltage direct current (MTDC) networks. This kind of network could play an essential role in regulating the frequencies of the AC system. Frequency regulation in MTDC AC-connected grids has focused on many techniques based on a PI controller. MPC is proposed in [430] as a new way to implement automatic production control while minimizing DC grid power losses. A flexible frequency operation strategy with significant renewable energy penetration to achieve power grid flexibility is proposed in [431]. Customized frequency via BTB HVDC is accomplished through flexible frequency operation, and ultimately, the whole system operates with extended frequency regulation.

The authors of [432] propose a high-order differential feedback controller (HODFC) and a high fractional-order differential feedback controller (FHODFC) developed for solving the LFC problem in multi-area power systems. The PSO algorithm is used to optimize the gains of the HODFC and FHODFC, with the end goal being to minimize the integral of the time-weighted absolute error performance index (ITAE). Comparing the controller structures reported in recent state-of-the-art literature and the HODFC for two identical no-reheat thermal power systems, a two-area multi-source power system consisting of gas, thermal, and hydro generation units, with/without taking into account the HVDC link, it has been demonstrated that the controller based on the FHODFC method has superior performance to the conventional controllers used until now. Different system parameters and loading conditions are studied to demonstrate the robustness of the designed controllers. As in the case of other LFC systems, the limitations of GDB and GRC are also considered for the system under study to examine the handling success of the non-linearity of the proposed controllers. A VSC-HVDC link should be able to balance the frequencies of the interconnected networks under tolerable disturbances to share the spinning reserves. The article [433] presents a communication-free scheme for frequency regulation of interlinked networks with a VSC-HVDC link. The method is based on the synchronous generator emulation control (SGEC) strategy. The programmed powers of the rectifier and the inverter are replaced by their actual powers if the disturbance is tolerable. A new VSC-HVDC control system called “INEC” (INertia Emulation Control), which allows a VSC-HVDC system to provide support emulating the inertia of a synchronous generator (SG), is studied in [434]. The energy required for this comes from the capacity of the HVDC connection, adjusted upwards by inserting additional capacity. A VSC-HVDC system has, through this method, a fixed ability to emulate a wide range of inertia constants (H) by specifying the amount of allowed DC voltage variation. Simulations were carried out to test the INEC scheme, during which the scheme’s performance was carried out for transitions, which included faults and load changes. The authors of [435] introduce a decentralized robust load frequency controller (DRLFC) in coordination with auxiliary frequency controllers (AFC). The power system for which the controller is designed includes areas interconnected by normal tie-lines and variable-frequency high-voltage direct-current (HVDC) transmission links where AFCs are present. The robustness of the solution is tested, taking into account the limits of the uncertainties of the system parameters. The DRLFC includes local load frequency controllers, one for each area, which operate on its local measurements. Regardless of the nature of the admissible uncertainties, as well as the operation of the DRLFCs and AFCs, the system is designed to ensure the overall stability of the system. The paper [436] is focused on the effects of PLL and frequency measurements in the frequency carriers of the HVDC interconnected system. The dynamic impact of HVDC links considering PLL effects during coordination with the AC system is presented and discussed in [86]. A second-order function is introduced to consider the implications of PLL. The impact of communication delays on AGC operation and state space models is evaluated using a Pade approximation method.

11. LFC and Cybersecurity

The power grid is the backbone of the main infrastructures that drive the country’s defense and economy. As a result, it is a prime target for cybercriminals and deserves particular attention. The power grid is physically dispersed and interacts dynamically with the associated cyberinfrastructure that controls its operation, making developing security measures to ensure cybersecurity a tough challenge. The integration of today’s electrical systems with communications infrastructure makes them particularly vulnerable to cyberattacks, some of which can disrupt their regular operation in an undetectable way. Among the control systems that are difficult to master in the event of the emergence of cybersecurity threats is the AGC. The AGC uses large-scale communication systems to send/receive measurements/control actions on frequency and power deviation in the power system. Minor errors in the AGC can cause the frequency to go out of the allowed range, and power outages can occur. FDI attacks are one of the types of attacks that can have a particularly harmful consequence on the operation of control systems and the LFC in particular. AGC systems are particularly vulnerable to FDI attacks, given their reliance on communications links to send/receive measurements/control actions on frequency and power deviations in the electrical system; AGC is highly vulnerable to malicious attacks and therefore requires urgent investigations as it is the only automatic feedback loop between cyber and physical infrastructures. By falsifying sensor measurements for AGC operation, attackers can cause service outages and infrastructure damage. An attack caused by the adversary through destabilizing the LFC can destabilize the electrical system. Potential economic and fatal damage could result from this type of attack. Therefore, real-time detection of FDI attacks is necessary to prevent and avoid the adverse effects of this kind of attack. FDI attacks (FDIAs) against AGC systems can also lead to unstable or non-optimal power grid operation. The effect of cyberattacks on AGC systems and the numerous approaches proposed to detect IDE attacks are the subject of several research studies. However, none of the previous works considered the non-linearity of the AGC system, and all the proposed solutions are only effective under the assumption of linearity of the AGC model. Among the adverse effects of intelligent injection of false data on load measurements, we can cite, among others, the possibility of triggering false relay operation (FRO) of frequency-based protection relays, thus affecting the frequency of the electrical system and threatening the safety of electrical systems. Cyber systems are essential to the efficiency and reliability of power system operation. They also guarantee the security of the system’s operating margins. An attacker can cause severe damage to the underlying physical system by compromising control and monitoring applications facilitated by the cyber layer. Critical assets of the power system must be protected against electronic threats. This protection has traditionally been accomplished using conventional cybersecurity measures involving host- and network-based security technologies. In recent years, there has been an increase in highly skilled attacks capable of bypassing these security mechanisms. These attacks can cause significant disruption to the proper functioning of control systems. The main articles analyzing the effects of cyberattacks on AGC are presented below.

The authors of [437] analyzed the impact of data integrity attacks on AGC, the power system’s frequency, and the electricity market’s operations. A general framework for applying attack-resilient control to power systems as an intelligent attack detection and mitigation composition has been proposed in [437]. A model-based anomaly detection and attack mitigation algorithm for AGC has been developed and presented in [437]. Finally, the authors evaluated the detection ability of the proposed anomaly detection algorithm by performing some simulation analyses. Smart grid infrastructures are becoming increasingly vulnerable to cyberattacks due to the integration of open communication systems. These communications systems are increasingly involved in supporting vast amounts of data exchange. The effects of DoS attacks on the LFC of intelligent grids are analyzed in the article [166]. Unlike the works published so far, the problem was analyzed from the perspective of the effect of DoS attacks on the dynamic performance of the power system. A switched system was developed based on the state space model of power systems subject to DoS attacks. The dynamics of a power system become unstable due to DoS attacks, which have been proven through switched systems theories. Several DoS attack scenarios were carried out to compare the different dynamic performances of the power system, such as convergence and steady-state errors; a time-switched attack (TDS) introducing delays in the dynamics of power systems can have devastating consequences on smart grids if no preventative measures are considered during the design of these systems. The authors of [438] analyzed how a TDS attack affects the dynamic performance of a power system. First, a spatial state model of an intelligent grid system subjected to a TDS attack was formulated using a hybrid systems approach. Afterward, simulation examples were conducted and analyzed to demonstrate how a TDS attack can be used to sabotage and destabilize an intelligent grid. Another aspect of the effect of time-delay (TD) attacks on AGC performance in a multi-area power system is presented in [439]. In this study, the authors analyzed a three-area power system. Then, they conducted a simulation of delay attacks to evaluate the performance of the AGC scheme during disruptions resulting from these attacks. The authors of [440] present an attempt to apply game theory to the security of intelligent networks. This study combines quantitative risk management techniques with decision-making on protective measures. A risk assessment process in which the well-known measure of conditional value at risk (CVaR) is used to quantify the consequences of data injection attacks. This analysis makes it possible to evaluate the loss of the defender due to load shedding in simulated scenarios. A stochastic security game model will subsequently use the calculated risks as input parameters. Dynamic programming techniques that consider resource constraints are ultimately used to resolve the game to make appropriate decisions on defensive measures. The paper [346] studies the impact of a cyberattack on a power station from the angle of frequency disturbances during sudden changes in system load. A solution method is proposed to maintain the stability of the system. The system characteristic equations are presented to derive the stable limit of the speed regulation for the LFC and the gain of the integrated controller of the AGC. Simulations are carried out to show the frequency deviations and oscillations of the power system depending on the nature of the cyberattack (positively biased or negatively biased attack). FDI attacks against AGC are presented in [441]. AGC measurement sensors may be subject to attacks that may result in frequency excursion, triggering corrective actions such as disconnection of customer loads or generators, power outages, and potentially costly equipment damage. An attack impact model was derived, followed by an optimal attack analysis consisting of a series of FDIs, minimizing the time remaining until the start of corrective actions and leaving the shortest time for the grid to carry out a counterattack. The authors showed that the attacker can learn the impact pattern of the attack and achieve the optimal attack in practice by eavesdropping on data via sensors and capturing some system constants. The paper [442] presents a mathematical framework for studying the stability of a two-area system in the event of data attacks on the AGC system. Analysis and simulation results are presented to identify attack levels that could make the AGC system unstable. A neural network-based detection (NND) approach to estimate and detect FDI attacks injected into the detection loop (SL) of the system is presented in [251]. A two-area distributed system is considered for carrying out case studies and thus demonstrating the effectiveness of the NND strategy. AGC systems in modern smart grids become particularly vulnerable to FDI attacks as cyber attackers target the communication links of modern intelligent grids. The paper [443] investigates the impact of cyberattacks on AGC and how attacks can be carried out. A method for detecting cyberattacks using a Kalman-filter-based technique is proposed. The journal version of the paper [444] is presented in [445]. The paper [445] studies the impact of FDI attacks on AGC.

A resilient event-triggering H_∞ LFC for multi-area power systems with energy-constrained DoS attacks is presented in the paper [446]. The presence of DoS attacks is considered in the design of the LFC. First, multi-area closed-loop power systems include a delay model as a function of area control errors. Then, a resilient event-triggering communication RETC scheme is simulated, which results in a loss of a particular portion of induced packets caused by DoS attacks. This simulation will improve the efficiency of transactions. Finally, two stability and stabilization criteria based on Lyapunov theory are used for multi-area power systems considering energy-limited DoS attacks. A simple but powerful type of attack called resonance attack is presented in [145]. In a resonance attack in an AGC system, an attack can manifest itself by cleverly changing the input to a power plant based on a resonance source (e.g., rate of change of frequency) to produce feedback on the LFC energy production system. This attack can cause a change in the state of the power plant, quickly leading to its instability. An LFC system composed of linear, non-linear, and high-order elements was designed to simulate in-depth resonance attacks, clearly showing the effectiveness of organized attacks. A cyberattack detection algorithm based on the dynamic watermarking approach is developed in [447]. An online framework has been implemented to detect cyberattacks on AGC. Suppose we deal with attackers who have in-depth knowledge of the physical and statistical models of the targeted power systems. In that case, we can use a detection algorithm offering a theoretical guarantee of detection of cyberattacks. The authors of [447] claimed the proposed framework is practically implementable, as it needs no hardware update on generation units.

Other articles cited show that FDI attacks (FDIAs) can be carried out stealthily with destructive results. The article [448] presents this same logic by proposing a method for detecting and identifying attacks based on anomalies to protect the AGC system against cyber vulnerabilities. To detect attacks, the proposed method [448] estimates the states of the LFC system using an unknown input observer (UIO) and calculates the residual function of the UIO. A stochastic estimator of unknown input (SUIE) is used by the authors of [449] as a method of detecting FDIA targeting the AGC system. The SUIE estimates the states of the load frequency control system, which contains the AGC as the control loop. An FDIA appears when an increase in the residual function (RF) of SOOT beyond a defined threshold is certified. In addition, the optimal gain of the SUIE can also be adjusted so that the effect of process and measurement noise on the estimated states is minimized. Therefore, SUIE can be designed to operate in a modified manner, using some or all of the system state space model inputs. Therefore, SUIE collects the need for real-time load change information across the entire network and maximizes state estimation accuracy. We can see that several works have examined the effect of cyberattacks on AGC systems. Many approaches have been proposed to detect IDE attacks against them. However, AGC systems are non-linear, and none of the previous works considered this non-linearity. As a result, all the solutions proposed so far are only effective under the AGC model’s linearity assumption. The paper [450] attempts to include non-linearity in the analysis model by inserting a particle filter to detect FDI attacks in AGC systems. The communication delay and non-linearities of the governor’s deadband are also considered. The authors of [451] studied the state estimation on LFC of multi-area power systems subject to delayed input attack. Firstly, a model of the LFC system subjected to a timed switch attack is modeled. Attacks are formulated so that a timeout is included. Then, an observer is included to estimate the state of the system. Guaranteeing asymptotic stability of the LFC system is considered by constructing sliding surfaces with a discontinuous controller. Finally, a sliding mode controller is built to ensure the reachability of the system trajectories. The paper [452] presents optimal attack schemes against LFC by converging a coordinated attack. The attacks are carried out in such a way that the measurement (load) of the sensor is disrupted along with the regular operation of the LFC, thereby causing excessive frequency/generation excursions of the system. To design this type of attack properly, it is essential to have information from the available LFC system. A few types of cyberattacks on LFC are studied in [453]. A detection scheme considering specific attack strategies is presented by unifying attack and detection. Regarding the design of attack schemes, four attack strategies are systematically analyzed based on their mechanism and influence on the performance of the LFC so that the most effective one is selected as the adopted attack scheme from the hackers’ point of view. Compromised signals are distinguished from standard signals. Using a multi-layer perceptron classifier makes extracting the differences in ACE under attack and everyday situations possible. An attack-resilient control scheme for the AGC system based on attack detection using state estimation is presented in [454]. The proposed approach requires redundancy of sensors available at the transmission level in the electrical network. Mixed-integer linear programming (MILP) exploits recent results on attack detection. The sensors under attack are detected and identified in the presence of noise using the proposed algorithm. It is possible to differentiate the non-attacked sensors, which will then be averaged and made available to the feedback controller. Another algorithm related to the state estimation attack is presented in the article [455]. FDI attacks against AGC system measurements are analyzed using an algorithm based on simultaneous input and state estimation to simultaneously detect and compensate for attacks against AGC system measurements. The algorithm treats the FDI attack signal as an unknown input whose value is estimated accordingly. Then, the estimated value of the IDE is used to compensate for the attack effect. This information allows the control center to decide based on the signals from the corrected sensors, not those manipulated. An adaptive and resilient LFC scheme for intelligent grid subsystems subject to energy-constrained DoS attacks is proposed in [176]. First, the authors introduce a resilient trigger communication scheme. An element of uncertainty induced by DoS attacks, including the trigger condition, is considered in this scheme. Then, to further reduce the communication load and defeat DoS attacks, an adaptive and resilient event-triggering LFC scheme is proposed. The proposed schema has an event trigger parameter that can be dynamically adjusted. Finally, the authors of [176] derived a stability criterion for LFC systems based on the PI control using the Lyapunov theory.

The authors of [456] present a method to detect and mitigate possible cyberattack patterns, such as FDIs and DoS attacks targeting AGC systems. The proposed method, called the Cyber Attack Detection and Attack Platform (CDMP), uses the predicted ACE data for attack identification and attack. The CDMP suggested in this article involves three steps for optimal operation and identifying all false arbitrary data injected into the network. A load-altering attack is studied in the article [457]. This attack is carried out to control the power system’s frequency. Related defense strategies are proposed to improve frequency control performance. A novel model-free defense framework is presented for the first time, considering the difficulty of applying a model-based controller in large-scale power systems. Active and passive defense mechanisms are designed for the power system defense strategy. As part of the first defense mechanism, it is assumed that the defender has the initiative to learn different attack scenarios. Adaptive defense strategies are implemented using online attack credentials and a pool of offline trained strategies. Regarding the second mechanism, the defender is assumed to tolerate various attack scenarios passively via the pre-trained offline strategy. The authors of [457] concluded that both approaches prove effective through validation based on IEEE reference systems. This article [458] proposes a memory-based event-triggering H_∞ LFC method for power systems through a bandwidth-constrained open network. To overcome the bandwidth constraint, a memory-based event-triggered scheme (METS) is first proposed to reduce the number of transmitted packets. Compared with the existing memoryless event-triggered schemes, the proposed METS can utilize a series of the latest released signals. To deal with the random deception attacks induced by open networks, a networked power system model is well established, which couples the effects of METS and random deception attacks in a unified framework. Then, a sufficient stabilization criterion is derived to obtain the memory H_∞ LFC controller gains and event-triggered parameters simultaneously. A novel resilient control system for LFC systems subject to FDI attacks is presented in the paper [459]. Typically, encryption is used in data transfer links as the first layer of defense. The authors of [459] propose a second layer of defense capable of detecting and mitigating IDE attacks on power systems. A new anomaly detection technique consisting of a Luenberger observer and an artificial neural network (ANN) is presented in the article [459]. The extended Kalman filter enhances the observer structure to improve the ANN’s ability to detect and estimate online since FDI attacks can occur quickly. A resilient controller was designed based on attack estimation. Hence, the need for control reconfiguration proves futile. A cyber–physical model of LFC is presented in [460]. Based on the model, the authors proposed an FDIA detection and defense mechanism based on the GAN network. The proposed method can detect and defend against FDIAs that aim to calculate, contrast, and replace control signals. A cyber–physical microgrid (CPM) is the culmination of the increasing integration of cyber and communications networks into microgrids to obtain measurements and relay controls. CPM opens the way to many essential applications. The participation of electric vehicle batteries in the LFC [232] is also facilitated through CPM. Like any technology, these new information and communication possibilities not only offer a multitude of advantages but also lead to a close synergy between heterogeneous physical and cyber components, at the same time opening access points to cyber intrusions. Faulty controls and corrective measures can result from a cyber intrusion, which can activate in the background and camouflage itself as uncertainty, hence the need for an observer-based control strategy capable of observing stochastic dynamic loads and compensating them via a two-layer controller. The paper [461] proposes an optimal two-stage Kalman filter (OTS-KF) to simultaneously estimate the state and cyberattacks in an AGC system. The AGC dynamic model includes bias/cyberattack modeling as unknown inputs. Five types of cyberattacks, i.e., FDI, data replay attack, DoS, scaling, and ramp attacks, are injected into the measurements and estimated using OTS-KF. As the load variations of each area are seldom available, outliers and system load variations are assessed by reformulating the OTS-KF. An optimization-based formal model for finding the optimal FDI attack (OFDIA) with the minimum required time leading to a false relay operation (FRO) is presented in the paper [462]. The dynamic behavior of the power system in an optimization framework is considered to find the optimal size of attacks on the dispatch cycles of several generators to minimize the attack launch time. The impact of power system parameters, including inertia, regulator sag, time constant, and attacker accessibility to loads, on attack success and launch time is analyzed in [462]. The more we are in the peripheral areas of the network, the fewer cybersecurity protections there are. The widespread deployment of distributed energy resources (DERs) further expands the risk of cyberattacks as the threat landscape extends to the network edge. A systematic demonstration of cyber–physical events, made possible by an integrated transmission, distribution, and communication co-simulation framework, is carried out in the article [463]. Cyber risks for the power grid under DER-enabled AGC can be analyzed from different angles. The demonstrator can capture the dynamic passage of frequency and voltage in milliseconds to minutes on the scale of an interregional system. One of the newest papers related to the cybersecurity of LFC systems is [464]. The authors present a new attack strategy that exploits the learning capabilities of a convolutional neural network and long short-term memory on encrypted data to predict the imminent operating state of a power system. Attackers can orchestrate timely DoS attacks on AGC systems, accurately predicting vulnerable operational conditions through encrypted traffic analysis, thereby significantly amplifying the physical impact of their cyberattacks. Thanks to the use of the IPsec/ESP protocol, which offers encryption at the network layer, it is possible to guarantee the confidentiality of the contents of the original packet and improve the complexity of traffic analysis. However, despite implementing this type of network traffic protection measure, the research presented by the authors of [464] demonstrates that attackers can still extract spatio-temporal characteristics from high-entropy encrypted synchrophasor data packets. The finding described in [464] highlights the inherent limitations of IPsec/ESP protocols to block malicious network traffic analysis completely and achieve absolute prevention of these harmful activities. Consequently, the confidentiality of the operational state of the power system remains compromised.

A table containing an exhaustive list of methods and technologies used in LFC analysis is presented in

Table 1. Methods and technologies used in the LFC literature presented in this article.

Methods and Technologies Used in LFC Analysis		References
LFC Reviews		[2,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59]
Classical control and LFC		[12,73,74,75,76,77,78,79,80,81,82,83,190]
Optimal LFC systems		[80,82,84,85,86,87,88,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,162,219,223,224,225,226,227,228,229]
Consideration of GRC or GDB in LFC models		[105,106,161,288,290,368,377]
Models of LFC with Time Delay consideration		[107,108,144,166,169,174,175,176,178,204,205,206,207,208,209,210,213,288,291]
LFC and Deregulation		[107,111,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,165,189,253,295,298,358,408]
LFC and Renewables		[110,111,168,173,207,231,245,309,310,314,326,344,349,361,362,363,369,377,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,407,408,409,410,411,412,413,414,417,418,419]
LFC and Centralized Control		[86,88,90,94,96,98,99,100,134]
LFC in Single-Area model		[108,135,136,137,138,139,140,141,142,143,144,145]
LFC in Multiple-Area Models		[74,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176]
LFC, BESS and FACTS devices		[74,146,147,148,149,150,151,152,153,154,157,258,273,275,281,295,298,312,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,386,387,393,396,405,408,409,410,411,412,413,414,453]
LFC and Fuzzy Logic Controllers (FLC)		[154,155,156,157,158,159]
LFC and Electrical Vehicles		[163,191,193,207,233,244,246,410,426]
LFC and DC Networks		[99,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437]
LFC and Cyberattacks		[145,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,248,249,250,251,252,347,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464]
LFC and Multisource systems		[24,170,254,281,319,324,395,415]
LFC and Model Predictive Control		[209,212,281,303,304,305,308,407]
LFC and Decentralized Control		[88,123,144,187,188,189,190,191,192,193,194,229,309]
LFC and Robust Control		[105,136,139,178,195,196,197,198,199,200,201,202,203,204,205]
LFC and Intelligent Methods	Fuzzy Logic (FL)	[154,155,156,157,158,159,171,202,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,288,289,299,303,355]
	Artificial Neutral Networks (ANN)	[93,94,95,96,97,100,250,251,252,253,354]
	Particle swarm optimization (PSO)	[170,255,256,257,258,259,260,390]
	Genetic Algorithms (GAs)	[239,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,289]
	Other intelligent methods	[23,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,385,386,387,388,389,390,391,392,393,394,414,415,416,417,418,419,433]

.

12. Conclusions

To provide sufficient, reliable, and good-quality electrical energy, reasonable LFC is achieved after finding solutions to one of the critical problems in the operation and control of electrical systems. Specific LFC methods also help maintain tie-line power exchanges at specified values. Over the past few years, several problems have been discovered related to achieving the objectives of the LFC, i.e., frequency regulation and monitoring of load demands maintaining power exchanges of connection lines to precise values. Many research activities on LFC focus on the issues of modeling uncertainties, system nonlinearities, complexity, and multi-variable power system conditions, which soon become factors determining the synthesis of LFC for multi-objective optimization control. Among the most valuable methods in research on optimizing LFC models are optimal control, multi-level and decentralized control, and adaptive control. The importance of these methods was established after deregulation using recent research findings. The articles analyzed in this literature review showed that among the discussed categories of LFC strategies, robust and AI-based control methods showed the ability to perform better, particularly in dealing with system nonlinearities, modeling uncertainties, and area load disturbances under different operating conditions. Regarding the unique aspect of the deregulated electricity market, it will serve as an auxiliary service and acquire a central role in enabling electricity trading and providing better conditions for electricity trading. Unfortunately, deregulation has changed the structure of the electricity system, making most of the old LFC systems unsuitable for the new regime, which has worsened the situation for researchers in power systems, forcing them to work on a system that involves many uncertainties and disturbances. Among the popular ancillary services in recent years is electricity demand, considered a reliable source of ancillary services in modern power systems with high penetration of renewable energy sources. Many articles also analyze AGC schemes based on the concepts of neural networks and fuzzy logic and the incorporation of parallel AC/HVDC links in the design of AGC regulators. As for the resilience of LFC systems to cyberattacks, nowadays, smart grids are becoming more vulnerable to malicious attacks, such as injecting false data into electronic surveillance systems. This results from their continuous evolution, which increases their operational efficiency. There is a growing need for cyber-resilient control techniques that go beyond traditional cyber defense mechanisms to detect highly skilled attacks. Many authors have analyzed the impact of data integrity attacks on AGC on power system frequency and electricity market operation. A notion of attack-resilient control, combining intelligent detection and attack mitigation, has also emerged in recent years. In communication systems, open communication architecture is increasingly used, making it vulnerable to cyberattacks with potentially catastrophic consequences. Attacks such as DoS attacks, time switch attacks (TDS) (by introducing delays in the dynamics of power systems), and FDIs minimize the time remaining until disruptive corrective actions begin, allowing the shortest time for the network to thwart or attack by resonance for as long as possible. Resonance attacks are becoming increasingly common when an adversary cleverly modifies the input to a power plant based on a resonance source to produce feedback on the LFC power generation system. Several counterattack measures are presented in more than thirty articles, the review of which is shown in the last chapter of this article. One issue that needs to be presented here is inertia. It is well-known that large-scale penetration of RES decreases the inertia of a power system, which causes high ROCOF and frequency deviations. To address this issue, virtual inertia injection is becoming more popular as a new standard to combat LFC stability issues. A few papers dealing with this issue were published lately but have yet to be included in this review. Good reviews on the state of the art can be found [45,48]. This review of articles concerning the LFC has yet to exhaust the subject. Similar state-of-the-art methods have previously been published [2,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59]. However, the papers presented in this review will help the researchers bridge the gap between current and future LFC trends by obtaining the necessary knowledge to research large-area hybrid power systems.