Optimized FACTS Devices for Power System Enhancement: Applications and Solving Methods

Abstract

The use of FACTS devices in power systems has become increasingly popular in recent years, as they offer a number of benefits, including improved voltage profile, reduced power losses, and increased system reliability and safety. However, determining the optimal type, location, and size of FACTS devices can be a challenging optimization problem, as it involves mixed integer, nonlinear, and nonconvex constraints. To address this issue, researchers have applied various optimization techniques to determine the optimal configuration of FACTS devices in power systems. The paper provides an in-depth and comprehensive review of the various optimization techniques that have been used in published works in this field. The review classifies the optimization techniques into four main groups: classical optimization techniques, metaheuristic methods, analytic methods, and mixed or hybrid methods. Classical optimization techniques are conventional optimization approaches that are widely used in optimization problems. Metaheuristic methods are stochastic search algorithms that can be effective for nonconvex constraints. Analytic methods involve sensitivity analysis and gradient-based optimization techniques. Mixed or hybrid methods combine different optimization techniques to improve the solution quality. The paper also provides a performance comparison of these different optimization techniques, which can be useful in selecting an appropriate method for a specific problem. Finally, the paper offers some advice for future research in this field, such as developing new optimization techniques that can handle the complexity of the optimization problem and incorporating uncertainties into the optimization model. Overall, the paper provides a valuable resource for researchers and practitioners in the field of power systems optimization, as it summarizes the various optimization techniques that have been used to solve the FACTS optimization problem and provides insights into their performance and applicability.

1. Introduction

It is true that in recent years, the security of transport networks has become one of the major challenges of the future, considering the potential economic and societal impacts of major incidents. With the competitive aspect linked to deregulation and the difficulty of building new structures, operators are increasingly looking to optimize their infrastructure and architectural equipment, as well as to improve the management of energy transfers, real-time monitoring, and control [1,2,3,4].

The use of FACTS devices based on power electronics is one way to achieve these goals. FACTS devices can help to make the operation of electrical networks safer and more efficient, which is crucial for ensuring the security of transport networks. By controlling voltage and power flow, FACTS devices can improve the stability and reliability of power systems, leading to fewer disruptions and incidents.

Additionally, the liberalization of transport networks will require a clear division of responsibilities between different actors. FACTS devices can help to ensure that this division is defined and enforced, as they enable more precise control over power flows and can help to prevent overloading or other issues that could arise from conflicting demands [5,6,7,8].

Overall, the use of FACTS devices represents an important step forward in ensuring the security and efficiency of transport networks, and they will likely play an increasingly important role in the years to come.

It is correct that FACTS devices are primarily used in the transmission system, but they can also be used in the distribution system as D-FACTS devices. The performance of FACTS devices depends on their type, placement, and size, and it is important to determine the optimal combination of these factors to achieve the desired performance improvements [9].

The FACTS allocation problem involves finding the optimal type, location, and size of FACTS devices in electrical power systems. This is a complex optimization problem that requires a careful analysis of the power system and the potential benefits and costs of different FACTS configurations.

The integration of power electronics into the electrical network has developed considerably in recent years, and FACTS devices have played a central role in this development. The advantages of FACTS devices include the enhancement of power transfer capability by controlling the flow of active and reactive power, the stabilization of voltage, and the suppression of oscillations in the electrical system. These benefits can lead to the improved reliability, stability, and efficiency of power systems, which are essential for meeting the growing demand for electricity in a sustainable and cost-effective manner.

Overall, the optimal deployment of FACTS devices can help to address many of the challenges facing modern power systems, including the need for increased capacity, improved reliability, and enhanced stability.

The principal inspirations and novelties for this survey study are as follows:

• The elements or limits that should be considered the best execution with respect to the accuracy of the solution, the speed of convergence, and the effectiveness, with the most elevated achievement rate, while supporting the FACTS device optimization issue are explored.

To address the FACTS device optimization issue, a synopsis of various enhancement strategies that have been broadly utilized, such as classical optimization techniques, metaheuristic methods, sensitive index methods, and hybrid methods, is presented in this work.

• This additionally presents the benefits and drawbacks of numerous advancement procedures that have been utilized for solving FACTS device optimization issues.
• Tables are outlined that include the strategies applied, the test systems utilized, the types of FACTS devices examined, and the helpful goals of each revised document.
• A discussion is presented towards the end of the paper regarding the qualities and shortcomings of the numerous enhancement strategies that have been utilized for resolving FACTS device optimization issues.
• The following questions are answered in this review based on different studies reported in the literature: Which FACTS devices ought to be utilized? How much ought to be used? Where would they be best located? What parameters ought to be used? How much will it cost to install them?

The application of flexible AC transmission system (FACTS) devices in electrical power systems has become increasingly popular in recent years, as they offer a number of benefits, including improved voltage profile, reduced power losses, and increased system reliability and safety. However, determining the optimal type, location, and size of FACTS devices can be a challenging optimization problem, as it involves mixed integer, nonlinear, and nonconvex constraints.

To address this issue, researchers have developed various optimization techniques for the application of FACTS devices in electrical power systems. Some of the novel optimization techniques that have been developed in recent years include:

• Multi-objective optimization: This technique considers multiple conflicting objectives, such as minimizing power losses and improving voltage stability, simultaneously. Multi-objective optimization can provide a set of optimal solutions that represent a trade-off between the different objectives, allowing decision makers to choose the solution that best fits their needs.
• Robust optimization: This technique considers uncertainties in the optimization problem, such as variations in load demand or renewable energy generation. By incorporating uncertainties into the optimization model, robust optimization can provide solutions that are less sensitive to changes in the system parameters.
• Machine-learning-based optimization: This technique uses machine learning algorithms to learn from historical data and predict the optimal configuration of FACTS devices based on current system conditions. Machine-learning-based optimization can provide fast and accurate solutions, especially in large-scale systems.
• Hybrid optimization: This technique combines different optimization techniques, such as metaheuristic algorithms and gradient-based methods, to improve the solution quality and convergence speed. Hybrid optimization can combine the strengths of different techniques to overcome their weaknesses.

These novel optimization techniques have the potential to significantly improve the performance of FACTS devices in electrical power systems by providing more accurate and efficient solutions. However, further research is needed to evaluate the effectiveness of these techniques in practical applications and to develop new techniques that can handle the complexity of the optimization problem.

Nowadays, FACTS devices, based on power electronics, enables the tighter continuous control of power flows with the following benefits: maintaining a voltage that is within acceptable ranges at load buses, controlling the flow of active and reactive electrical power in thermally constrained lines, improving safety measures, and operating electrical systems close to their capacity limits, along with other improvements. Developing tools that enable us to successfully operate electrical networks, including the use of FACTS controllers, is crucial for all of these reasons. Therefore, many different techniques based on evolutionary algorithms (EA), swarm intelligence (SI), sensitivities index, and their combinations have been applied for solving this FACTS device optimization issue.

FACTS optimization problem-solving methods can be classified into four main groups that are widely used in the literature, as shown in Figure 1: classical optimization techniques, metaheuristic methods, sensitive index methods, and mixed techniques.

Mathematic equations serve as the foundation for traditional optimization techniques for solving system problems, are usually an iterative process, and can utilize linear programming (LP) [10], nonlinear programming (NLP) [11], integer programming (IP) [10], mixed integer linear programming (MILP) [10], mixed integer nonlinear programming (MINLP) [12,13], mixed discrete continuous programming (MDCP) [14], dynamic programming (DP) [10], sequential quadratic programming (SQP) [10], Newton–Raphson (NR) [15], min cut algorithm (MCA) [16], and mixed integer programming (MIP) [17].

Metaheuristic optimization techniques are now the most common method to determine the best location, type, and size for FACTS units. These methods are easier to use when determining the best solution to problems than traditional methods. This group can be classified into four categories [18]: (i) evolutionary algorithms such as genetic algorithms (GA) [19], evolution strategy (ES) [20], evolutionary programming (EP) [21], genetic programming (GP) [22]; (ii) physics-based algorithms such as the ant lion optimization (ALO) technique [23], biogeography-based optimizer (BBO) [24], curved space optimization (CuSO) [25], flower pollination algorithm (FPA) [26], galaxy-based search algorithm (GBSA) [27], gravitational search algorithm (GSA) [28], harmony search algorithm (HAS) [29], multiverse optimization (MVO) algorithm [30], simulated annealing (SA) [31], atom search optimization (ASO) algorithm [32]; (iii) swarm-based algorithms such as particle swarm optimization (PSO) [33], whale optimization algorithm (WOA) [34], artificial bee colony (ABC) [35], chemical reaction optimization (CRO) algorithm [36], crow search algorithm (CSA) [37], cat swarm optimization (CaSO) algorithm [38], cuckoo search (CS) [39], dragonfly algorithm (DA) [40], bats algorithm (BA) [41], firefly algorithm (FFA) [42], grasshopper optimization algorithm (GOA) [43], gray wolf optimizer (GWO) [44], honey-bee mating optimization (HBMO) [45], moth–flame optimization (MFO) algorithm [46], bacterial swarm optimization (BSO) [47], immune algorithm (IA) [48], symbiotic organism search (SOS) algorithm [49], etc.; and (iv) other population-based algorithms such as the black hole (BH) algorithm [50], parallel seeker optimization algorithm (PSOA) [51], imperialistic competitive algorithm (ICA) [52], sine cosine algorithm (SCA) [53], teaching–learning-based optimization (TLBO) algorithm [54], water cycle algorithm (WCA) [55], bacterial foraging algorithm (BFA) [56], coyote optimization algorithm (COA) [57], and the tabu search (TS) algorithm [58,59].

This paper includes seven sections. Section 1 provides a brief introduction and Section 2 includes the fundamental rules of operation in electrical power systems. Section 3 explains the different types of FACTS devices such as series, shunt, and combination types with their modeling, control, and placement in electrical power systems. Section 4 portrays the mathematic formulation for FACTS allocation issue accompanied by all constraints of the system. Section 5 reviews the different optimization approaches for solving FACTS allocation issues. A discussion is provided in Section 6. Finally, the conclusion and recommendations for future studies are given in Section 7.

2. FACTS Devices

2.1. Classification of FACTS Devices

FACTS systems are classified into three categories [60,61]. The first class is based on conventional control systems (transformer with load-adjustable tap, phase-shifting transformer, bank of capacitors or inductors) controlled by conventional thyristors. The other two classes use static converters based on power semiconductors controllable by the GTO. They are distinguished by their structures, for instance, the alternating current dimmer or reactance controlled by a thyristor valve, including SVC and TCSC, and the voltage source converters, which can supply an alternating voltage of adjustable amplitude, frequency, and phase including series compensation SSSC, shunt compensation STATCOM, hybrid compensation (series–parallel) UPFC, and (series–series) IPFC. Another hybrid configuration of FACTS devices combining UPFC with the phase-shifting transformer (PST), referred to as OUPFC, was developed in ref. [62] for the optimal power flow (OPF) problem. In this configuration, the minimization of fuel costs and total system losses were considered. This problem was solved using a general algebraic modeling system (GAMS) and MATLAB, where the decision variables were locations, settings, and the number of OUPFCs. Kavuturu et al. [63] proposed a generalized UPFC (GUPFC), also called a multi-line UPFC, to control the bus voltage and power flows of multiple lines in a power grid. The strong control capability of the GUPFC with bus voltage and multi-line power control offers great potential to solve many problems faced by power utilities in a competitive environment. In fact, by incorporating these devices, voltage stability, reactive power loss, reactive power generation, and reactive power flow in lines were improved.

FACTS (flexible AC transmission system) devices are used in power systems to enhance transmission capacity, improve stability, and increase efficiency. There are several types of FACTS devices, each with its own advantages and disadvantages, as shown in

Table 1. Main FACTS devices: types, advantages, disadvantages, comparison, and contribution to transmission lines.

Types of FACTS Devices	Technological Functions	Comparison to Other FACTS
TCSC: TCSCs are used to increase the power transfer capability of transmission lines by controlling the line impedance.	System stability improvement, reducing voltage collapse.	The TCSC has a slower response time due to the inherent delay in the thyristor switching.
SVC: SVCs are used to regulate voltage and reactive power in transmission systems by varying the amount of reactive power injected into the system.	Power quality improvement, voltage regulation.	The SVC has a relatively fast response time, making it suitable for applications where the voltage or power factor needs to be regulated quickly.
The static synchronous compensator (STATCOM) is a FACTS (flexible AC transmission system) device used in power systems to improve the transmission capacity and stability of the grid.	Voltage controls, compensation for reactive power.	The STATCOM is particularly useful in applications where reactive power compensation is required, such as in industrial processes or in wind and solar power plants, where the output power fluctuates due to the variability of wind and solar resources.
The static synchronous series compensator (SSSC) is a FACTS (flexible AC transmission system) device used in power systems to improve the transmission capacity and stability of the grid.	Power system stability enhancement, damping power oscillations.	The SSSC is a powerful tool for improving the performance and stability of power systems.
The unified power flow controller (UPFC) is another FACTS (flexible AC transmission system) device used in power systems to improve the transmission capacity and stability of the grid.	Controlling reactive power and true power in transmission line, reducing harmonics levels.	The UPFC is a more advanced and versatile FACTS device compared to the SSSC, as it can regulate both the voltage and phase angle of the transmission line. The UPFC is particularly useful in large and complex power systems where multiple benefits can be obtained using a single device.
Interline power flow controller (IPFC): A multi-terminal device that controls power flow in multiple transmission lines simultaneously by adjusting the voltage amplitude and phase angle of voltage waveforms using voltage-sourced converters.	Power flow control in sub-networks, voltage profile maintenance.	The IPFC is a more advanced and versatile FACTS device compared to the individual SSSC and STATCOM devices, as it can control the power flow and voltage of multiple transmission lines.
Advantages of FACTS Devices
1. Improved power transfer capability: FACTS devices can increase the power transfer capability of transmission lines, enabling more power to be transmitted over existing lines without the need for new lines.
2. Improved stability: FACTS devices can improve the stability of the power system by limiting the impact of disturbances and reducing the risk of cascading outages.
3. Increased efficiency: FACTS devices can reduce the losses associated with power transmission, resulting in increased efficiency and lower operating costs.
4. Improved voltage control: FACTS devices can improve voltage control and regulation, ensuring that voltage levels remain within acceptable limits.
Disadvantages of FACTS Devices
1. High cost: FACTS devices can be expensive to install and maintain, and their cost may outweigh the benefits in some cases.
2. Complexity: FACTS devices can be complex and require specialized knowledge and expertise to design, install, and operate.
3. Potential for failure: Like any complex system, FACTS devices have the potential to fail, which can result in disruptions to the power system.

, which includes a comparison to other FACTS and their contribution to transmission lines.

Each type of FACTS device has its own advantages and disadvantages, and the choice of device depends on the specific requirements of the power system.

2.2. Utility of FACTS Devices for Power System Enhancement

2.2.1. FACTS Devices Operations in Electrical Power Systems

Permanently ensuring equality between production and consumption to maintain the frequency at a constant value and respecting the admissible limits of the lines, the stability limit for the power, the thermal limit for the heating of the conductors and keeping the voltages of all nodes within acceptable limits are the main fundamental rules [60] for the proper operation of the electrical network.

• Control of line’s power flow

The primary role of a line is to transport active power. If the power being transmitted is reactive power, in comparison to the active power, it must be minimal. The transmission line must verify the following conditions [61]: The voltage should be fairly constant along the length of the line regardless of the load. Losses must be low for the line to perform well. Joule losses should not overheat the conductors. If the transmission line does not satisfy these conditions, then additional equipment must be added to fulfill all of these requirements.

• Voltage drop regulation

Maintaining voltage at an acceptable level and minimizing voltage drop is important for the efficient and reliable operation of power systems. One way to achieve this is by avoiding the transport of reactive power and producing it at the place of its consumption.

FACTS devices, as mentioned earlier, can also be used for reactive power compensation. They can provide fast and precise control of reactive power compensation, as well as other benefits such as improved power transfer capability and voltage stability [61].

Overall, the use of compensation devices for reactive power compensation can help to improve the efficiency and reliability of power systems by reducing transmission losses and minimizing voltage drop. By producing reactive power at the point of consumption, these devices can also help to reduce the need for the expensive and inefficient long-distance transport of reactive power.

• FACTS shunt device compensation

The purpose of shunt compensation is to consume or produce reactive power through the connection point. In the steady state, the shunt compensators make it possible to maintain the tensions at the nodes. In dynamic conditions, they improve transient stability and dampen power oscillations [64]. Increasing the power transmitted in a long transmission line requires sectioning it into several portions followed by the installation of shunt compensators to adjust the voltage at the midpoints. The best placement of the shunt compensation device is in the middle of the transmission line [60,65].

• FACTS series device compensation

These compensators are connected in series in the network. Generally, these devices are used to modify the transmission line impedance by introducing an adjustable voltage source, either a variable impedance (inductive) or capacitive [66].

2.2.2. Power Transfer Capability Improvement

The installation of the optimal FACTS devices in the transmission network allows the system to work very near to its stability and thermal limits. The AC power system has inherent power stability as the power flow between the lines is dependent on the receiving and the sending end voltages. For a lossless line, which has the sending end voltage Vk and receiving end voltage Vm, δk and δm are the phase angles of the sending and receiving end, respectively, where X is the reactance of the line. Each type of FACTS controller will be used according to well-defined control objectives. Figure 2 below presents the possible actions for controlling the transited active power in a transmission line.

3. Modeling of FACTS Devices

The models developed are integrated into the calculation in load flow programs in order to be able to simulate their effects throughout the system. The integration method used is based on the modification of the admittance matrix.

3.1. Modification of the Nodal Admittance Matrix

The FACTS are considered elements that directly modify the nodal admittance matrix of the network [67]. They are inserted into the line as shown in Figure 3. Depending on the type of FACTS modeled, the device can be placed in the middle or at one end of the line.

The parameters of an equivalent line are determined and substituted for those of the line without FACTS in the nodal admittance matrix. This is modified as follows:

$$\underset{\_}{Y_{\mathrm{mod}}}=(\begin{array}{cc}\underset{\_}{Y_{ii}^{\prime }}& \underset{\_}{Y_{ik}^{\prime }}\\ \underset{\_}{Y_{ki}^{\prime }}& \underset{\_}{Y_{kk}^{\prime }}\end{array}\begin{array}{l}\\ \end{array})=\underset{line}{\underbrace{(\begin{array}{cc}\underset{\_}{Y_{ii}}& \underset{\_}{Y_{ik}}\\ \underset{\_}{Y_{ki}}& \underset{\_}{Y_{kk}}\end{array}\begin{array}{l}\\ \end{array})}}+\underset{FACTS}{\underbrace{(\begin{array}{cc}\underset{\_}{y_{ii}^F}& \underset{\_}{y_{ik}^F}\\ \underset{\_}{y_{ki}^F}& \underset{\_}{y_{kk}^F}\end{array}\begin{array}{l}\\ \end{array})}}$$

(1)

Depending on the type of FACTS and its position in the line, only part of the coefficients of the matrix $\underset{\_}{Y_{\mathrm{mod}}}$ may have modifications. A symbolic representation of an electrical power network is shown in Figure 4, containing several loads, several generators, and some main FACTS devices. The different constituents are interconnected through the transmission network modeled by its nodal matrix $Y$. The latter does not contain the admittances of the devices and the loads; it only presents the admittances of the transmission network [68,69,70,71,72,73]. The SVC, TCSC, STATCOM, SSSC, and UPFC are the most thoroughly studied devices in most of the research in the literature.

3.2. Electrical Network with UPFC

The UPFC consists of two VSCs that share the same DC voltage source. One is connected in series with the network and the other in parallel. The serial component of UPFC is similar to an SSSC device, while the parallel component is similar to a STATCOM device. Thus, a UPFC can control the flows of active and reactive power of the transmission line where it is inserted [68] and the magnitude of the voltage of the connection point. In our case, this corresponds to the control of the transmitted powers $P_{km}$ and $Q_{km}$ and to the adjustment of the voltage $V_k$. Four new variables to the power flow problem are introduced by the two VSC voltage sources $\left({\overline{E}}_p\right)$ and $\left({\overline{E}}_s\right)$. By fixing $V_k$, three additional equations must be added to solve this problem. The model of a UPFC placed in the line $\left(km\right)$ of an electrical network of N buses is presented in Figure 5.

The power flow equations of the network with UPFC, except nodes $\left(k\right)$ and $\left(m\right)$, are the same as those without the device. The power equations injected at the last two nodes are expressed as follows:

$$P_k=P_{km}+{\displaystyle \sum }_{j=1}^N{V}_k{V}_j{Y}_{kj}cos \left({\propto }_k-{\propto }_j-{\theta }_{kj}\right)$$

(2)

$$Q_k=Q_{km}+{\displaystyle \sum }_{j=1}^N{V}_k{V}_j{Y}_{kj}sin \left({\propto }_k-{\propto }_j-{\theta }_{kj}\right)$$

(3)

$$P_m=P_{mk}+{\displaystyle \sum }_{j=1}^N{V}_m{V}_j{Y}_{mj}cos \left({\propto }_m-{\propto }_j-{\theta }_{mj}\right)$$

(4)

$$Q_m=Q_{mk}+{\displaystyle \sum }_{j=1}^N{V}_m{V}_j{Y}_{mj}sin \left({\propto }_m-{\propto }_j-{\theta }_{mj}\right)$$

(5)

The summation terms of Equations (2) to (5) represent the same equations for the system without a UPFC device and without taking into account the line $\left(\mathrm{km}\right)$. The transmitted powers $P_{km}$, $Q_{km}$, $P_{mk}$, and $Q_{mk}$ are given, respectively, by the following equations:

$$\begin{gathered} P_{km}=\left(G_p+G_s\right) V_k{}^2-V_k{E}_p{Y}_{p}cos \left({\propto }_k-{\propto }_p-{\theta }_p\right)+V_k{E}_s{Y}_{s}cos \left({\propto }_k-{\propto }_s-{\theta }_s\right) \\ -V_k{V}_m{Y}_{s}cos \left({\propto }_k-{\propto }_m-{\theta }_s\right) \end{gathered}$$

(6)

$$\begin{gathered} Q_{km}=-\left(B_p+B_s\right)V_k{}^2-V_k{E}_p{Y}_{p}sin \left({\propto }_k-{\propto }_p-{\theta }_p\right)+V_k{E}_s{Y}_{s}sin \left({\propto }_k-{\propto }_s-{\theta }_s\right) \\ -V_k{V}_m{Y}_{s}sin \left({\propto }_k-{\propto }_m-{\theta }_s\right) \end{gathered}$$

(7)

$$P_{mk}=G_s{V}_m{}^2-V_m{V}_k{Y}_{s}cos \left({\propto }_m-{\propto }_k-{\theta }_s\right)-V_m{E}_s{Y}_{s}cos \left({\propto }_m-{\propto }_s-{\theta }_s\right)$$

(8)

$$Q_{mk}=-B_s{V}_m{}^2-V_m{V}_k{Y}_{s}sin \left({\propto }_m-{\propto }_k-{\theta }_s\right)-V_m{E}_s{Y}_{s}sin \left({\propto }_m-{\propto }_s-{\theta }_s\right)$$

(9)

The power supplied by the shunt component of the UPFC through the DC link will be consumed by the serial part. Therefore:

$$\begin{array}{c}{P}_{Eps}=Real\left({\overline{E}}_p.{\overline{I}}_p^{*}\right)-Real\left({\overline{E}}_s.{\overline{I}}_s^{*}\right)\\ =-G_p{E}_p^2-G_s{E}_s^2+E_p{V}_k{Y}_p\cos \left({\propto }_p-{\propto }_k-{\theta }_p\right)-E_s{V}_k{Y}_s\cos \left({\propto }_s-{\propto }_k-{\theta }_s\right)\\ +E_s{V}_m{Y}_{s}cos \left({\propto }_s-{\propto }_m-{\theta }_s\right)=0\end{array}$$

(10)

4. Objectives and Constraints of Placement of FACTS Devices

4.1. Objective Functions

The optimal allocation of the FACTS device is an important issue when the installation of the FACTS device is considered [74,75,76,77]. The important factors that are considered during its placement in the power system are:

• The minimization of power loss in the transmission system.
• The minimization of reactive power loss.
• Congestion management.
• Improved power transfer capability.

4.2. Constraints of the Problem

The constraints of the optimal placement of FACTS devices are represented by the energy balance, the network security constraints, and the constraints related to the FACTS devices [78,79,80,81], such as:

• The bus voltage and line flow.
• Power flow constraints.
• The FACTS device’s parameter limit values.

5. Review of Various Optimization Techniques in FACTS Allocation Problem

The suitable location of FACTS controllers is an important step towards a more secure and efficient power system. With their flexibility and ability to provide solutions to major power system operation problems, such as voltage control, transmission loss minimization, line overloads, grid congestion, system stability issues, contingencies, and economic problems, FACTS controllers can play a critical role in improving the performance and reliability of power systems.

However, finding the optimal location for FACTS controllers is a challenging optimization problem that requires the careful consideration of multiple factors, such as the topology and characteristics of the power system, the available data, and the specific objectives of the optimization [82].

To solve this problem, several optimization techniques have been developed, which can be broadly classified into four main groups:

• Classical optimization techniques: These are traditional optimization techniques, such as linear programming, nonlinear programming, and dynamic programming, that can be used to find optimal solutions to complex optimization problems. These techniques can be computationally intensive and may be limited in their ability to handle large-scale optimization problems.
• Metaheuristic methods: These are optimization techniques that are inspired by natural processes, such as genetic algorithms, particle swarm optimization, and simulated annealing. These methods can be used to find good solutions to complex optimization problems in a relatively short amount of time, but they may not always find the optimal solution.
• Analytic methods or sensitive index methods: These are optimization techniques that use sensitivity analysis to evaluate the impact of different factors on the performance of the power system. These methods can be useful for identifying critical components or locations in the power system that require optimization, but may not always provide a complete solution.
• Mixed or hybrid methods: These are optimization techniques that combine two or more of the above methods to address the limitations of individual methods. For example, a mixed method may use a classical optimization technique to generate an initial solution, and then refine the solution using a metaheuristic method.

The choice of optimization technique will depend on the specific characteristics of the power system and the objectives of the optimization. By using the appropriate optimization technique, it is possible to find the optimal location for FACTS controllers and improve the performance and reliability of the power system.

5.1. Summary of Classical Optimization Techniques Related to FACTS Device Optimization Problem

Many classical techniques or arithmetic programming approaches have been applied for solving the FACTS device optimization issue. Although they have effective convergence characteristics, the application of these approaches presents difficulties when dealing with multi-constrained optimization issues. In Reference [15], an NR algorithm was employed to obtain the suitable placement of an SVC to find its best operating point for the enhancement of system security. An MILP was developed for the optimal location of the TCSC and SVC with their operating limits in an IEEE 30-bus to operate at a lower cost and to maintain the existing level of system security [83]. The same technique was illustrated in ref. [84] for the optimal location of a TCPAR and TCSC to increase the load capacity of an electrical grid; a test network IEEE 24-bus was utilized to demonstrate this selected technique. Reference [85] similarly investigated the same problem via MINLP in order to obtain a reduction in line overloads and the improvement of bus voltage magnitudes; to prove the robustness of this applied technique, simulation results were performed on the IEEE 9-bus system. A classical approach called MCA was used by Thanhlong Duong et al. [16] for the optimal placement of a TCSC to achieve the maximum loadability of the system and minimum cost of installation for a FACTS device. The robustness of this proposed method was proven on three regular IEEE 6-, 30-, and 118-bus test networks. An NLP optimization based on automatic differentiation (AD) and the Lagrange method (LM) was introduced by Tina Orfanogianni et al. [86] to give the appropriate location of TCSC and UPFC. The optimization results from network model 37 buses helped to assesses the effectiveness of FACTS devices in maximizing network forwarding capacity and provide a measure of FACTS ratings. An MIP optimization technique was developed in ref. [17] for transmission line congestion management, and a suitable position of the TCSC and SCV was considered to reduce congestion and/or enhance network voltage security. A contextual investigation in view of the changed IEEE 30 transport framework was used to validate this proposed approach. SVC and TCSC were also considered in ref. [87] for loadability improvement. To find the proper allocations for FACTS controller installation and their parameter settings, the issue was formulated as an MDCP. A new approach called SQP was employed by the authors in ref. [88] to enhance the voltage profile and security margin of the system by installing ten optimally located TCSCs and SVCs in a test system with an IEEE 14-bus.

Table 2. Summary of classical optimization techniques related to FACTS device optimization problem.

Refs	Objectives	Devices	Methods	Test Case
[15]	Power system security	SVC	NR	A standard 5-bus network: 2G
[83]	Operate at a lower cost and improve system security	SVC, TCSC	MILP	IEEE 30-bus
[84]	Increase the load capacity of the system	TCPAR, TCSC	MILP	IEEE 24-bus
[16]	Achieve the maximum system loadability and minimum FACTS installation cost	TCSC	MCA	IEEE 6-, 30-, and 118-bus
[85]	Reduce line overloads and improve bus voltage magnitudes	TCSC	MINLP	IEEE 9-bus system
[86]	Maximize network forwarding capacity and provide a measure of FACTS ratings	TCSC, UPFC	NLP	Network model consisting of 37 buses
[17]	Reduce congestion and/or enhance network voltage security	SVC, TCSC	MIP	IEEE 30-bus system
[88]	Enhance the voltage profile and system security margin	SVCs, TCSCs	SQP	IEEE 14-bus

presents an outline of the classical optimization techniques utilized in the research related to the FACTS device optimization problem. Some approaches, objectives, test systems, and FACTS devices considered for solving the cited problem are included in this summary.

Classical optimization techniques are commonly used to determine the optimal configuration of FACTS devices in electrical power systems. Here are some benefits and shortcomings/limitations of six commonly used optimization techniques: Newton–Raphson, MILP, MINLP, NLP, MIP, and SQP.

• Newton–Raphson:

Benefits: It is a fast and efficient optimization technique that is commonly used for power flow analysis in power systems.

Shortcomings/limitations: It is not suitable for handling mixed-integer and discrete variables, which are commonly encountered in FACTS optimization problems.

• MILP (Mixed-Integer Linear Programming):

Benefits: It can handle both continuous and discrete variables, and it is a widely used optimization technique in power system applications.

Shortcomings/limitations: It is only suitable for linear optimization problems, and it may be computationally expensive for large-scale optimization problems.

• MINLP (Mixed-Integer Nonlinear Programming):

Benefits: It can handle both continuous and discrete variables, and it is suitable for nonlinear optimization problems, which are commonly encountered in FACTS optimization problems.

Shortcomings/limitations: It can be computationally expensive for large-scale optimization problems, and it may not always find the global optimal solution.

• NLP (Nonlinear Programming):

Benefits: It is suitable for nonlinear optimization problems and can handle continuous variables.

Shortcomings/limitations: It may not always find the global optimal solution, and it may be computationally expensive for large-scale optimization problems.

• MIP (Mixed-Integer Programming):

Benefits: It can handle discrete and continuous variables, and it is suitable for a wide range of optimization problems.

Shortcomings/limitations: It can be computationally expensive for large-scale optimization problems, and it may not always find the global optimal solution.

• SQP (Sequential Quadratic Programming):

Benefits: It is suitable for nonlinear optimization problems and can handle both continuous and discrete variables.

Shortcomings/limitations: It may not always find the global optimal solution, and it can be computationally expensive for large-scale optimization problems.

The choice of optimization technique depends on various factors, such as the size and complexity of the problem, the type of variables involved, and the desired level of accuracy. In general, MILP and MINLP are commonly used optimization techniques in power system applications because they can handle both continuous and discrete variables and are suitable for nonlinear optimization problems. However, they can be computationally expensive for large-scale optimization problems. NLP, MIP, and SQP may be more suitable for smaller-scale problems with fewer variables. Newton–Raphson is typically used for power flow analysis in power systems and may not be suitable for FACTS optimization problems involving mixed-integer and discrete variables.

In summary, there is no one-size-fits-all optimization technique for FACTS optimization problems. The choice of technique should be based on the specific characteristics of the problem and the available computational resources. It is often necessary to compare the performance of different techniques on a given problem and choose the one that provides the best balance between accuracy and computational efficiency.

5.2. Summary of Metaheuristic Methods Related to FACTS Device Optimization Problem

The basic concept of most metaheuristic techniques draws inspiration from nature, animal behavior, or physical phenomena. Figure 6 shows a classification of metaheuristic methods in four main classes [89].

These methods of optimization are adaptable and effective. These metaheuristic approaches make it simple to solve constrained and complex discrete optimization problems [90]. These methods can also be used to solve issues with multimodal and multipurpose functions, such as with FACTS device optimization issues.

5.2.1. Evolutionary Algorithms

Generally, classical evolutionary algorithms can be subdivided into four classes: GA, EP, GP, and ES [91], as shown in Figure 7. These techniques mimic the evolution process in nature to carry out optimization.

Genetic algorithms, evolutionary strategies, genetic programming, and evolutionary programming are all part of the broader field of evolutionary computation, which involves the use of computational models inspired by biological evolution to solve optimization and search problems. While these approaches share some similarities, there are also some differences in their specific methodologies and applications.

Genetic algorithms (GAs) are types of evolutionary algorithms that use a population of candidate solutions and a set of genetic operators (such as selection, crossover, and mutation) to evolve and improve the solutions over time. GAs are often used for optimization problems where the search space is large or complex, and the objective function is nonlinear or discontinuous.

Evolutionary strategies (ESs) are another type of evolutionary algorithm that focus more on the optimization of continuous, real-valued parameters. ESs typically use a population of candidate solutions and a set of mutation operators to explore the search space and improve the solutions over time. ESs are often used for problems in physics, engineering, and economics, where the optimization of continuous parameters is important.

Genetic programming (GP) is a type of evolutionary algorithm that uses a population of computer programs (or trees) and a set of genetic operators to evolve and improve the programs over time. GP is often used for problems in artificial intelligence, machine learning, and data mining, where the goal is to find a program that can solve a specific task or problem.

Evolutionary programming (EP) is another type of evolutionary algorithm that focuses more on the optimization of control parameters for dynamic systems. EP typically uses a set of mutation operators to explore the search space and improve the solutions over time. EP is often used for problems in control engineering, robotics, and game theory, where the optimization of control parameters is important.

While there are some differences between these approaches, they all share the common goal of using evolutionary principles to solve optimization and search problems. The specific methodology used depends on the characteristics of the problem and the goals of the optimization.

Biplab Bhattacharyya et al. [19] proposed a GA for the proper position of a multi-type FACTS controller such as a UPFC, TCSC, and SVC in order to reduce transmission loss and operating costs, achieve the flexible control of reactive power, and also to improve the voltage profile. A test system IEEE 30-bus was used as a validation of this proposed method. The same algorithm was illustrated in ref. [92] for finding the appropriate placements, the optimal number, and the optimal sizing of multiple TCSCs to maximizing system loadability with the minimum installation cost of these devices in the power system. Simulations were performed on test networks with an IEEE 14-bus and 6-bus. References [93,94] exhibited the same strategy for identifying the most suitable location of UPFC and SSSC, respectively, to guarantee a reduction in power generation and transmission losses, improvement to the voltage profile, and the treatment of power flow in overloaded transmission lines as well as the maximization of social welfare in electrical power systems. In ref. [95], the IEEE 118-bus system security margin was increased using multiple types of FACTS controller such as TCSC, SVC, TCVR, TCPST, and UPFC via GA. These FACTS controllers were modeled and their optimizations analyzed on location, type, and size setting parameters as a measure of performance for power systems. A graphical user interface (GUI) based on a GA was shown to be able to give the most suitable positions and sizing of multi-type FACTS controllers such as TCSC, SVC, TCPST, TCVR, and UPFC in large power systems. All of these FACTS devices were employed in different scenarios for maximizing the system loadability under security constraints and reducing the losses simultaneously. The simulation results demonstrate that UPFC is the most effective FACTS if we want to increase the loadability while reducing the losses at the same time [96]. The optimal location of an UPFC was obtained in Reference [97] by using an elitist MOEA based on NSGAII to find the simultaneous optimization of three objective functions: voltage deviation at load buses, transmission line losses, and the active production generation cost. The robustness of this applied technique was validated on a test system with an IEEE 14-bus. Somasundarm Alamelu et al. [98] investigated the same problem via a CMAES algorithm and NSGAII in order to minimize the total costs associated with the UPFC’s installation and to enhance the loadability system. These proposed techniques were applied on a test network with an IEEE 14-bus and a 30-bus. To justify the ability and robustness of the NSGAII approach for large systems, a test network IEEE 118-bus was utilized. In ref. [99], a multi-objective SPEA was employed for determining the most appropriate placements and settings of a TCSC and SVC for improving voltage stability and minimizing transmission losses and congestion in branch loading. The simulation results obtained for the IEEE 30-bus network showed the applicability of this technique. An RCGA was utilized by [100] to determine the proper placements of TCSC, SVC, and UPFC for reducing the transmission losses in the IEEE 30-bus test system. However, in ref. [101], the proper location of FACTS devices was based on practical considerations, such as the estimated annual load curve, in order to increase the accuracy of this placement. A GA was used in this work to reduce transmission losses and investment costs with improvements to the profile voltage and margin security in a Fars Regional Electric Company (FREC) network. An IPC and SVC were discussed in ref. [102] using a GA algorithm to minimize power losses and improve the voltage profile in order to guarantee the enhancement of the stability and loadability system. Simulations carried out on an IEEE 30-bus test network demonstrated the ability and efficiency of this applied strategy. For the optimal positioning and parameters of FACTS controllers containing TCSC, SVC, and UPFC, a GA was used by [103]. This algorithm was implemented on the test system with an IEEE 30-bus to reduce the power losses and improve the voltage profile under different loading conditions. In ref. [20], an ES was utilized to select the suitable location of UPFC, TCSC, and SVC, respectively. The simulations performed on the IEEE 30-bus test network showed a significant increase in the loadability system. An ES algorithm was also employed by [104] for the sizing and proper locations of FACTS controllers, such as SVC, STATCOM, SSSC, and UPFC. This evolutionary strategy was developed for the FACTS device optimization problem not only to significantly improve the capacity of the power transmission, but also to enhance the stability in power systems. The OPF problem was analyzed by [21] for the optimal placement of TCSC via evolutionary programming (EP). This emerging FACTS controller was used to eliminate transmission line congestion in deregulated power systems and also to relieve congestion. An IEEE 14-bus system was used to demonstrate the suitability of this approach and its effectiveness for practical implementation in electrical power systems. Weerakorn Ongsakul et al. [105] evaluated FACTS controllers such as TCSC, SVC, TCPS, and UPFC to obtain the full benefit of total transfer capability (TTC) power. The simulation results from test networks with an IEEE 30-bus indicated that the optimal regulation of FACTS controllers by EP was able to improve the TTC value far more than an optimal power flow without FACTS devices. The performance of the FACTS device was also analyzed under contingency cases by [106], and both authors used TCSC to improve the power system network condition. In this study, EP was presented to identify the best location of TCSC to minimize power loss and improve the voltage profile for the network under contingencies. The implementation of this applied approach was performed on an IEEE 30-bus test network. Similarly, a TCSC FACTS device was integrated into a power system to control the power flow in specific lines and improve the transmission line security [107] via EP. Critical contingency cases have also been used to determine the suitable positioning and sizing of the TCSC. A test system IEEE 30-bus was considered for this study. In addition, for solving the FACTS device optimization problem, Md Shafiullah et al. [22] demonstrated an approach—namely, the MGGP algorithm—to optimize the PSS parameters combined with UPFC to improve the power system stability by damping out low-frequency oscillations (LFO). The simulation results from the responses of SGGP and MGGP and the fixed values of PSS-UPFC parameters indicated that the MGGP-tuned model exhibits a quicker response compared to conventional and SGGP-tuned models. Moreover, an ensemble method was proposed in ref. [108] incorporating MGGP with two other approaches, a neurogenetic (NG) system and an extreme learning machine (ELM), for estimating the PSS parameters in real time to damp out the unwanted oscillations in the electrical power system’s stability. Two single-machine power system models, one with PSS only and one with PSS-UPFC, were used to verify the robustness of this selected ensemble method. In ref. [109], the optimal placement and setting of TCSC, SVC, and UPFC FACTS controllers were determined to increase the power system loadability and minimize power losses and total cost generation, including FACTS controller installation costs. An evolutionary approach called the DE algorithm was used on an IEEE 30-bus. Similarly, in ref. [110], the optimal type, location, and setting of multi-type FACTS controllers such as SVC, TCSC, and UPFC were found to maximize the power transfer capability, reduce the total number of overloads, and minimize energy losses. The efficiency and robustness of this proposed methodology was illustrated on a 24-bus EHV Indian grid and a sample 4-bus system. DE was also used by M. Basu [111] in order to obtain the perfect placement of numerous FACTS controllers such as TCSC and TCPST to minimize the total fuel costs on a regular IEEE 30-bus test system.

Table 3. Summary of evolutionary algorithms related to FACTS device optimization problem.

Refs	Objectives	Devices	Methods	Test Case
[92]	Maximize system loadability with minimum installation cost of these devices in the power system	TCSCs	GA	IEEE 14-bus and 6-bus
[93,94]	Guarantee a reduction in power generation and transmission losses, improve voltage profile and treatment of power flow in overloaded transmission lines, and maximize social welfare in electrical power systems	UPFC, SSSC	GA	IEEE test systems
[95]	Increase system security margin	TCSC, SVC, TCVR, TCPST, and UPFC	GA	IEEE 118-bus
[96]	Maximize the system loadability under security constraints and reduce the losses simultaneously	TCSC, SVC	GA	IEEE test systems
[97]	Improve voltage deviation at load buses, transmission line losses, and active production generation cost	UPFC	NSGAII	IEEE 14-bus
[98]	Minimize the total costs associated with UPFC installation and enhance the loadability system	UPFCs	CMAES and NSGAII	IEEE 14-bus and 30-bus
[99]	Improve voltage stability, minimize transmission losses and congestion in branch loading	TCSC and SVC	SPEA	IEEE 30-bus
[100]	Reduce transmission losses	TCSC, SVC, and UPFC	RCGA	IEEE 30-bus
[101]	Reduce transmission losses and investment costs with improvements to profile voltage and margin security	UPFC	GA	IEEE 30-bus
[102]	Minimize the power losses and improve the voltage profile	IPC and SVC	GA	IEEE 30-bus
[103]	Reduce the power losses and improve the voltage profile under different loading conditions	TCSC, SVC, and UPFC	GA	IEEE 30-bus
[104]	Significantly improve the capacity of power transmission, but also enhance stability in power systems	SVC, STATCOM, SSSC, and UPFC	ES	IEEE 30-bus
[105]	Fully benefit from total transfer capability (TTC) power	TCSC, SVC, TCPS, and UPFC	ES	IEEE 14-bus
[106]	Improve the TTC value	TCSC	EP	IEEE 30-bus
[107]	Control the power flow in specific lines and improve the transmission line security	TCSC	EP	IEEE 30-bus
[108]	Damp out the unwanted oscillations of electrical power system stability	UPFC	EP	SMIB model
[109]	Increase power system loadability and minimize power losses and total cost generation including FACTS controller installation costs	TCSC, SVC, and UPFC	EP	SMIB model
[110]	Maximize power transfer capability, reduce the total number of overloads, and minimize energy losses	SVC, TCSC, UPFC	DE	24-bus EHV southern region
[111]	Minimize the total fuel cost production	TCSC and TCPST	DE	IEEE 30-bus

presents an outline of the evolutionary algorithm techniques utilized in the research related to the FACTS device optimization problem. Some approaches, objectives, test systems, and FACTS devices considered for solving the problem are included in this summary.

5.2.2. Physics-Based Algorithms

Algorithms based on the principles of various natural phenomena exist in addition to those based on evolutionary and swarm intelligence. Thereby, physics-based algorithms perform optimization using the rules of physics in the universe; some of them include ALO, BBO, CSO, FPA, GBSA, GSA, HAS, MVO, SA, and ASO.

• ALO technique

Suitable position and parameter settings of FACTS controllers such as TCSC and SVC were determined by R. Brindha et al. [23] via another methodology called the ALO technique. This study was executed on an IEEE 30-bus to achieve different objectives, namely, the minimization of fuel costs, loss reduction, voltage profile improvement, and voltage stability enhancement. Similarly, the authors in ref. [112] investigated the same methodology by selecting the best setting and appropriate location of the TCSC for achieving maximum system loadability as well as reductions in both losses and production costs. In this work, the effectiveness and ability of this ALO technique was performed on an IEEE 14-bus test network while complying with all market-imposed restrictions on equality and inequality.

• BBO technique

Due to attaining the maximum benefit from multi-type FACTS controllers, the proper positions of various FACTS devices including SVC, TCSC, and UPFC was confirmed by conducting case studies on standard IEEE test networks by applying the BBO technique [24]. Analyses of simulation results have shown that the optimal FACTS device reduced both line loads and load bus voltage deviations, thereby improving system security. Further, a comparison with the PSO and WIPSO method was conducted to demonstrate the predominance, robustness, and adequacy of this employed BBO technique. In addition, the same strategy was used by K. Kavitha et al. [113], where a significant decrease in the load on the lines and voltage deviation at load buses was also found. In this work, three cases (TCSC only, SVC only, and TCSC and SVC) were analyzed to determine the proper location of the devices on test networks using IEEE 14-, 30-, and 57-buses. In ref. [114], the best TCSC and SVC unit locations and sizes were determined using BBO to reduce transmission power losses and FACTS device installation costs. This developed strategy was executed on a test network with an IEEE 30-bus. BBO was also utilized in ref. [115] to identify the best positions and settings for IPFC and UPFC in the power system to relieve overloads and voltage deviations at load buses during a single line contingency. The security system significantly improved as a result of the optimal UPFC and IPFC settings for the voltage-sourced converter magnitude and angle. The superiority of this BBO method was justified using an IEEE14-bus system. A STATCOM FACTS device was optimally located in ref. [116] via the same methodology in order to enhance the transient stability of a multimachine system.

• CuSO Algorithm

A new heuristic optimization method known as CSO was employed by [25] for determining the most effective allocation and sizing of an SVC to enhance voltage profile. Simulation results were obtained from a 5-area 16-machine system and proved that CSO was the quickest for finding the most high-quality, optimal solution for the location and size of the SVC compared to the PSO algorithm.

• FPA technique

Reference [26] presented a new methodology, FPA, to identify the most suitable position and parameter settings of the TCSC based on FVSI sensitivity in order to minimize transmission losses and improve voltage profiles in electrical networks. The results of the simulation from an IEEE 14-bus, both with and without a TCSC, indicated the robustness of this applied FPA technique. Furthermore, this FPA strategy was successfully implemented in ref. [117] for finding the appropriate location and parameter settings of a TCSC to improve the voltage stability of a system under contingencies. The simulation results were analyzed and justified the ability of this newly introduced FPA technique for solving the voltage stability problem under contingency conditions. The examination of FPA’s applications in FACTS device optimization [118] also revealed improvements in FPA’s performance.

• GBSA technique

The authors in ref. [27] explored a new heuristic optimization algorithm named GBSA for identifying the most appropriate location and settings of the IPFC based on the DLUF index to optimize multi-objective functions to reduce the total voltage deviations at load buses and minimize transmission losses and the security margin. A test system IEEE 30-bus was applied to ascertain the ability and accuracy of this employed technique compared to GA under different loading conditions. It was observed that the IPFC can reduce the congestion in the system by approximately 15% using the GBSA approach. B. Sravan Kumar et al. [119] investigated the same strategy for identifying the appropriate location and parameter settings of an SVC based on the L-index in order to reduce transmission losses and production costs as well as enhancing the voltage profile. A test system IEEE 14-bus with and without an SVC was used to justify the better robustness of this BGSA compared to GA.

• GSA technique

In ref. [28], a GSA technique was used for the proper positioning of multiple UPFCs in a power system to decrease transmission losses and operating costs. Three cases were studied—without a UPFC, a single UPFC, and three UPFCs—on various standard IEEE test networks: 14-bus, 30-bus, and 57-bus. A comparison between other currently available algorithms such as BBO, Stud GA, GA, ACO, and probability-based incremental learning (PBIL) was carried out to demonstrate the predominance, robustness, and adequacy of the proposed GSA approach. The same technique was also used in refs. [120,121] for the suitable location and sizing of the IPFC based on DLUF to improve the loadability and stability of the system with a reduction in transmission losses. In addition, the authors in refs. [122,123] verified that multiple FACTS devices, such as SVCs, TCSCs, and UPFCs, are being used to obtain the most benefit from power transfer capabilities for improving loadability and minimizing the total operating costs. Simulation results have shown that the GSA is more effective in the FACTS optimization issue, since it can obtain better solutions in comparison to other strategies such as GA, DE, and PSO. Another novel algorithm known as the cumulative gravitational search algorithm (CGSA) was applied successfully by [124] to select the best position and parameter settings of STATCOM for reactive power compensation and effective real power improvement.

• HSA technique

The operation and management of an electrical power network depend heavily on reactive power compensation (RPC). In this context, D. Karthikaikannan et al. [29] demonstrated an approach named HSA for selecting the best placement and sizing of the TCSC and SVC for minimizing voltage deviation and reducing active power losses. An examination of this and other optimization approaches, such as the simple genetic algorithm (SGA), PSO, and DE, was carried out to exhibit the vigor of the proposed strategy. In refs. [125,126], to enhance the voltage profile and minimize transmission losses considering a non-smooth cost function, an improved HS algorithm was applied to identify the most suitable position and sizing, respectively, of the SVC and SSSC. This applied methodology was performed on an IEEE 30-bus and IEEE 57-bus, and the simulation results were compared with conventional HSA, indicating its robustness and superiority. Furthermore, in ref. [127], a GHS was presented for identifying the buses most suitable for STATCOM installation and their rating power. Thus, an improvement in the voltage profile and the minimization of transmission losses were obtained in this work. A new multi-objective planning framework, namely, nondominated sorting improved harmony search (NSIHS), was proposed and successfully implemented in ref. [128], where a TCSC and SVC were optimally placed for enhancing the voltage stability system, minimizing power losses, and increasing the loadability system. In this work, the advantage of the applied method was highlighted on an IEEE 14-bus and compared in terms of better-distributed Pareto optimal solutions than the MOPSO method.

• MVO Algorithm

The primary threat to the stability of a modern power system, which is interconnected and operates close to its transient and steady-state stability limits, are power system oscillations. In view of this, a recent metaheuristic algorithm, MVO, was suggested in ref. [30] for selecting the optimal parameter settings of the coordinated system based on PSS and STATCOM to enhance the stability system under a variety of multimachine power system loading conditions. In this work, the optimization results for the designed control model system were illustrated and compared to other metaheuristic methods such as GWO, WOA, GWO, and PSO-TVAC, and demonstrated the effectiveness of this applied MVO algorithm. K. Karthikeyan et al. [129] developed the same methodology for the best location and sizing of an SVC to obtain maximum load ability and voltage stability. In this study, the robustness of this MVO algorithm was examined using IEEE 57-bus test systems with and without an SVC. A new multi-objective optimization algorithm known as the multi-objective multiverse optimizer (MOMVO) was successfully explored in ref. [130] by locating SVC and TCSC in the best possible location and setting their parameters to achieve multiple goals at once, such as reducing transmission line losses, reducing voltage deviation, and reducing the cost of installing FACTS devices. The accuracy, ability, and robustness of this MOMVO was tested on a system with an IEEE 57-bus.

• SA algorithm

A novel optimization-based methodology for the FACTS device optimization problem called SA was investigated in ref. [31] for the optimal settings and locations for an SVC and TCSC to improve the voltage profile and static security margin. First, its optimal location was found using SQP, and in the next stage, the problem was also solved using SA. The IEEE 14-bus test network was applied to demonstrate this proposed technique. In ref. [131], this SA was used with two other heuristic methods, TS and GA, for identifying the optimal parameters (type, location, and size) of FACTS controllers containing SVC, TCVR, TCPST, TCSC, and UPFC to improve system security. The optimization results were analyzed on IEEE 118-bus test systems. Unfortunately, TS and GA converge faster than SA to obtain an optimal solution.

• ASO algorithm

A Amarendra et al. [32] presented a novel physics-inspired metaheuristic optimization algorithm, namely, ASO, for efficiently predicting the optimal placements of FACTS controllers containing TCSC, SVC, UPFC, and IPFC. In order to minimize investment costs, fuel costs, real power loss, voltage deviation, the severity index, and the line overload sensitivity index (LOSI), a regular standard IEEE test system such as a 30-bus, 118-bus, and 300-bus were considered in this work. To demonstrate this applied strategy, simulation results were obtained and compared with other techniques such as Jaya, JA-FPA, DA, FPA, GWA, and WOA.

Table 4. Summary of physics-based algorithms related to FACTS device optimization problem.

Refs	Objectives	Devices	Methods	Test Case
[23]	To achieve different objectives, which are the minimization of fuel costs, loss reduction, voltage profile improvements, and voltage stability enhancement	TCSC and SVC	ALO	IEEE 30-bus
[112]	To achieve maximum system loadability as well as reduction of losses and production costs	TCSC	ALO	IEEE 14-bus
[113]	To obtain a significant decrease in the load on the lines and voltage deviation at load buses	TCSC and SVC	BBO	IEEE 14-, 30-, and 57-bus
[114]	To reduce transmission power losses and FACTS device installation costs	TCSC and SVC	BBO
[115]	To relieve overloads and voltage deviations at load buses during a single line contingency	IPFC and UPFC	BBO	IEEE 30-bus
[116]	To enhance multimachine system’s transient stability	UPFC and IPFC	BBO	IEEE 14-bus
[25]	To enhance voltage profile	SVC	CSO	5-area 16-machine system
[117,118]	To improve voltage stability system under contingencies	TCSC	FPA	IEEE test systems
[119]	To reduce transmission losses and production costs and enhance voltage profile	SVC	GBSA	IEEE 14-bus
[120,121]	To improve loadability and stability system and reduce transmission losses	IPFC	GSA	IEEE 14-bus, 30-bus, and 57-bus
[122,123]	To improve loadability system and minimize total operating costs	SVCs, TCSCs, and UPFC	GSA	IEEE test systems
[124]	To compensate reactive power and improve real power	STATCOM	CGSA	IEEE test systems
[125,126]	To enhance voltage profile and minimize transmission losses considering non-smooth cost function	SVC and SSSC	HAS	IEEE 30-bus and IEEE 57-bus
[127]	To improve voltage profile and minimize transmission losses	STATCOM	GHS	IEEE test systems
[128]	To enhance voltage stability system	TCSC and SVC	NSIHS	IEEE 14-bus
[129]	To obtain maximum load ability and voltage stability	SVC	MVO	IEEE 57-bus
[130]	To reduce transmission line losses, voltage deviation, and cost of installing FACTS devices	SVC and TCSC	MOMVO	IEEE 57-bus
[31]	To improve voltage profile and static security margin	SVC and TCSC	SA	IEEE 14-bus
[131]	To improve system security	SVC, TCVR, TCPST, TCSC, and UPFC	SA	IEEE 118-bus
[32]	To minimize investment costs, fuel costs, real power loss, voltage deviation	TCSC, SVC, UPFC, and IPFC	ASO	IEEE 30-bus, 118-bus, and 300-bus

presents an outline of the physics-based algorithms utilized in research related to the FACTS device optimization problem. Some approaches, objectives, test systems, and FACTS devices considered for solving the cited problem are included in this summary.

5.2.3. Swarm-Based Algorithms

• PSO technique

Because of its advantages in computation, PSO is the method that has attracted the attention of several researchers when solving the FACTS device optimization problem in power supply systems among metaheuristics algorithms [33,132]. To solve this issue, the proper location and the best setting of SSSC is the key to improving the voltage profile and reducing transmission losses when using a PSO; this was checked on the IEEE 9-bus and the Iraqi national grid [133]. In ref. [134], the PSO was adopted for identifying the optimal type, location, and setting of multi-type FACTS controllers containing an SVC, TCSC, and UPFC to maximize the system loadability (SL) and reduce the total installation cost (IC) of the FACTS controllers. This PSO algorithm was examined on an IEEE 6-bus, IEEE 30-bus, IEEE 118-bus, and the Tamil Nadu Electricity Board (TNEB) 69-bus test system. When the objective is simply the management of the power flow, the same approach was used in ref. [135] by locating the SVC and TCSC FACTS devices. An improvement in the power flow was tested on an IEEE 14-bus test system. A PSO was also used for the optimal allocation of an SVC in ref. [136] via PSO, in order to improve the voltage stability and system loadability and to minimize transmission line losses. A test of the robustness of this applied algorithm was performed on an IEEE 30-bus test network. Siti Amely Jumaat et al. [137] investigated the same problem via a sigma-multi-objective evolutionary PSO (σ-MOEPSO) approach for minimizing the power losses in the system and the cost of investment in FACTS controllers. This approach was applied on IEEE 30- and 118-bus standard test networks. A novel version of the PSO, the coordinated aggregation-based PSO (CAPSO) algorithm, was developed in ref. [138] to identify the proper location and size of the SSSC in power systems to minimize the total production costs, including generator VPLE. Practically speaking, because we strive for more precision, the VPLE should be added to the quadratic equation of the generation cost. In ref. [139], an improved PSO called IPSO was utilized for determining the best placement and sizing of STATCOM in order to enhance the voltage profile by minimizing voltage deviations at load buses on a regular IEEE 30-bus that was used as an example to illustrate this approach. In ref. [140], a new model of the PSO, called WIPSO, was employed to determine the optimal placement and setting of FACTS devices containing TCSCs, SVCs, TCSC-SVCs, and UPFCs in power systems to enhance the system security. This approach was validated on IEEE 14-bus, IEEE 30-bus, and IEEE 57-bus test systems. A review of the PSO-based approaches in terms of the FACTS device optimization problem is provided in ref. [141]. In several studies, the PSO was hybridized with other metaheuristic techniques to obtain more advantages in order to strengthen its exploration capacity for determining the best FACTS controller settings and locations. A new model of the PSO, known as ELPSO, was presented in ref. [142] for the purpose of determining the most effective locations and sizes for the TCSC’s FACTS controllers in power systems for minimizing voltage deviations, overloads, and transmission losses in the event of a line outage.

• WOA technique

In Reference [34], the power flow analysis technique was utilized to locate the TCSC, and the VCPI approach was used to place the SVC in an electrical power system. Further, WOA, DE, GWO, QOGWO, and QODE algorithms were developed for identifying the best setting of all control variables containing TCSCs and SVCs in the power test system to minimize transmission losses and operating costs while respecting the voltage profile within the permissible limit. A comparison of the simulation results of WOA with all other used techniques demonstrated the superiority, applicability, and effectiveness of this employed WOA technique. Two test networks, IEEE 30- and 57-bus, were applied in this work. Similarly, Muhammad Nadeem et al. [143] inspected the WOA for the optimal locations and parameter settings of FACTS devices including TCSCs, SVCs, and UPFCs. In this work, the WOA technique was introduced not only for identifying an ideal rating of these FACTS devices, but also to determine the best way for SVCs, TCSCs, and UPFCs to work together with the reactive power sources already in the electrical power network. To obtain a significant and considerable reduction in the total system operating costs and transmission line losses, this WOA method was performed on IEEE 14- and 30-bus standard test networks and was also compared to GA and PSO. Its effectiveness for all loading conditions was also noted.

• ABC algorithm

The ability of the appropriate location of the UPFC to minimize transmission loss in electrical networks was examined by Bairu Vijay Kumar [35] using the ABC algorithm. Power flow analysis and power losses were analyzed for single and double generator outage conditions during normal conditions, during double generator outage conditions, and with the UPFC placed in the best position. It was observed that the power flows were improved and power losses were minimized after placing the UPFC in the most suitable position. The comparison results under different conditions on the IEEE 30-bus test network indicated the superiority of the ABC algorithm and confirmed its potential for solving the FACTS device optimization issue. In ref. [144], the ABC technique was used for determining the proper placement and the best sizing of the IPFC in the power system in order to demonstrate the capability of the IPFC to control the real and reactive power in multiple transmission lines simultaneously. The optimal setting of the IPFC significantly improved the voltage profile and decreased the transmission line losses. To prove its performance by validating the approach using test networks such as IEEE 118-bus, 5-bus, and 30-bus systems, this nonconventional ABC method was compared to the conventional LR method. The SVC device’s performance was also analyzed under normal conditions and under contingency conditions by [145] via ABC; both authors use the SVC to improve the voltage profile and also to reduce the active and reactive power losses in the electrical network. This ABC technique was performed on an IEEE 30-bus. The utilization of FACTS devices such as SVCs and STATCOM, as tested by Kadir Abac et al. [146], can obtain the best results out of the power transfer system by enhancing voltage stability, improving the voltage profile, and minimizing transmission losses. These objectives were defined via the ABC methodology by using the minimum number of FACTS controllers and compensation sizing on an IEEE 30-bus. The simulation results illustrated the robustness of ABC compared with DE. A recent study [147] dedicated to solving the FACTS device optimization problem explained the nonoptimal placement of FACTS controllers such as SVCs, STATCOM, TCSCs, and SSSCs in order to simultaneously obtain an improvement in the power losses and stability margin using the ABC algorithm. A comparison of the simulation results was made between ABC, PSO, and GA and indicated the fast convergence and high accuracy of ABC when conducting a study of FACTS device allocation. The compensation of reactive power is one of the practical ways that can be utilized to improve electrical power systems and reduce the total production costs; in this regard, a modified version of the ABC (MABC) algorithm was presented in ref. [148] to resolve the FACTS device optimization problem. Thus, the optimal positioning and setting of a multi-type FACTS controller containing an SVC and TCSC were examined in order to optimize the reactive power management. Moreover, the optimization results were executed on an IEEE 30-bus test system for several scenarios using many other techniques and proved that the MABC approach led to lower transmission losses and reactive power costs, and a better voltage profile than the PSO, GA, and ABC techniques when the simulation results were compared. Another application of the ABC algorithm-based OPF solution was developed to obtain the perfect location of the SVC, STATCOM, and TCSC to improve the voltage profile and minimize transmission loss in the electrical power system. The ideal location for the FACTS devices was identified using the ABC calculation. This proposed ABC technique was approved using IEEE 14-bus and 30-bus standard test networks [149].

• CRO algorithm

The authors in ref. [36] employed the CRO algorithm to allocate STATCOM FACTS devices to solve the ORPD issue. Thus, active power losses were minimized and the voltage profile and voltage stability were improved. The robustness of this proposed method was validated on IEEE 57-bus and 30-bus test systems. Susanta Dutta et al. [150] investigated the same problem via an efficient QOCRO algorithm. The simulation results from IEEE 14- and 30-bus standard test networks validated the ability and robustness of the QOCRO algorithm when compared with the BBO and conventional CRO algorithms. In ref. [151], an SSSC was optimally placed on IEEE 30- and 57-bus standard test networks via the same methodology as the CRO approach. In this study, a comparison of the CRO simulation results with other methods used in the literature such as GA, teaching–learning-based optimization (TLBO), quasi-oppositional TLBO (QOTLBO), and the strength Pareto evolutionary algorithm (SPEA) proved its robustness and efficiency in generating true and well-distributed optimal solutions.

• CSA technique

In ref. [37], the best positioning and sizing of STATCOM were identified using the CSA technique to enhance the voltage stability limits and to reduce power losses. To validate this method, standard IEEE 14-, 30-, and 57-bus test networks were used. In ref. [152], CSA was implemented and successfully executed to obtain the most suitable location and parameter settings of the SVC for improving the dynamic stability of the studied model. In this work, the harmonized model of the PSS with SVC-based controllers was discussed. A comparison of the simulation results between CSA and other techniques such as PSO and TLBO confirmed an improvement in stability performance with the coordinated control of CSA-tuned SVC and PSS.

• CaSO algorithm

In ref. [38], a CSO algorithm was developed for the selection of multiple UPFC-suitable locations in electrical networks to improve the voltage stability and loadability in the event of a line outage. The N-1 contingency for 16 lines on an IEEE 14-bus test network was studied to demonstrate the operational benefits of the UPFC and to prove the robustness of this CSO approach compared to the PSO approach. T. Nireekshana et al. [153] investigated the same methodology to determine the optimal type, placement, and sizing of multi-type FACTS controllers such as SVC and TCSC to improve the available transfer capability (ATC) under normal and network contingencies. This CSO technique was implemented for normal and different contingency situations on test networks with an IEEE 14-bus and 24-bus. Similarly, the CSO algorithm was suggested in ref. [154] for the proper location of the UPFC to provide a solution to the voltage instability issue using an IEEE 14-bus test system under contingency conditions.

• CS algorithm

A new metaheuristic technique based on swarm intelligence algorithms, namely, the CS algorithm, was presented in ref. [39] for obtaining the proper positioning and sizing of STATCOM to achieve maximum system loadability. The robustness of this proposed methodology was performed with a comparison with a GA open loop STATCOM under different conditions of operations and disturbances. A new version of the CS approach, called an adaptive CS (ACS) algorithm, was also used by [155] for TCSC’s optimal size and placement to reduce the total transmission losses and therefore improve the voltage profile. A modified IEEE 9-bus test network was applied to validate the efficiency and the ability of the ACS to provide the best solution when compared with GA and PSO.

• DA technique

In ref. [40], the system voltage stability was enhanced by the installation of STATCOM in the most suitable position and with its best setting via DA. The simulation results from a 52-bus Nigerian transmission test system showed an 11.26% voltage stability improvement compared to the case without FACTS. To reduce the transmission loss and to enhance the voltage profiles in the electrical power system, the firing angle of the TCSC and the size of the TCSC were selected in ref. [156] using DA. To prove the validity of this applied approach and for comparison with other metaheuristic approaches such as GA and PSO, a simulation was carried out on a test network with an IEEE 14-bus.

• BA approach

Another approach, called BA, was adopted in ref. [41], where FACTS devices containing a TCSC, STATCOM, and UPFC were optimally positioned on an IEEE 30-bus test network to improve the power quality. The simulation results of the load flow calculation with/without FACTS proved the importance of implementation for the combined optimal selection and best setting of FACTS controllers. An appropriate location and sizing of a shunt FACTS device, SVC, was considered in ref. [157] via the same methodology to improve the voltage stability. The effectiveness and ability of this implemented approach were validated on IEEE 30-bus test network.

• FFA technique

The FFA method was developed in ref. [42] for the best positioning and setting of an IPFC to reduce transmission line losses. This adopted technique was examined using IEEE 30-bus and NTPS 23-bus test networks and the simulation results were provided. This implemented approach provided the best results in terms of transmission losses with reasonable calculation time in ref. [158]; the maximum loadability system limit was obtained and its improvements resolved with the FFA by the determination of the suitable allocation of SVCs and TCSCs as well as the largest loading factor for each load. The speed and flexibility of the given FACTS devices in enhancing the controllability and the TTC using this FFA methodology were implemented on regular IEEE 30-, 57-, and 118-bus test networks. In addition, a comparison of the simulation results of the FFA with others from the PSO and DE methods was conducted and indicated the effectiveness of this proposed FFA in terms of better search capabilities and faster convergence characteristics. Vasavi et al. [159] exploited the same technique in the presence of an SSSC to reduce the total generation costs and transmission losses and enhanced voltage profile. This technique was performed with/without SSSC on an IEEE 30-bus test network to show its effectiveness and robustness. An FFA was explored in ref. [160] for identifying the most suitable location of a FACTS controller containing STATCOM and an IPFC in order to increase the power factor, minimize power losses, enhance the transmitted power, and improve the voltage profile.

• GOA technique

In ref. [43], a GOA was introduced for an extensive modulation of controller gains for an automatic generation control in a three-area thermal plant system including FACTS devices. The proper locations and the best settings of the IPFC, SSSC, TCPS, and TCSC were optimized to provide superior responses to those of other controllers in terms of settling time and peak deviations. For frequency regulation, a comparison of the IPFC’s performance to that of the SSSC, TCPS, and TCSC was established. The simulation results of the GOA compared with other research were included in the study. In ref. [161], the same methodology for simultaneously tuning the FACTS controller and PSS taking into account time delays was proposed to improve the power system stability. A new version of the GOA technique, called additive GOA (AGOA), was also used by [162] with sizing and the optimal placement of a center-node (C-UPFC) controller for minimizing the total fuel cost with VPLE and a reduction of emission function, in order to provide power flow control together with independent voltage control.

• GWO algorithm

The functioning of series and shunt compensators are integrated into a device known as a UPQC. It was employed on the one hand, to reduce the transmission losses, and on the other hand, to maintain the voltage profile with admissible limits. In this context, the optimal location and rating of the UPQC were determined using the GWO method [44]. A recent study [163] investigated the same strategy for the best placement and sizing of the UPFC to provide a promising solution for the high power loss and voltage deviation at load buses on a 31-bus and a 330 kV Nigeria National Grid (NNG) system. To solve the ORPD, the GWO algorithm was also presented in ref. [164] after the optimal placement of an SSSC FACTS device. Thus, an IEEE 30-bus test network was applied to illustrate the ability and robustness of this employed GWO technique compared with the PSO method. In ref. [165], a novel version of the GWO, named the modified GWO (MGWO), was used for the suitable allocation and sizing of FACTS controllers containing an SVC and TCSC. An OPF-based congestion management (CM) method was considered in this work.

• HBMO algorithm

Another technique called the HBMO algorithm was employed by [45] for improving the power system stability. In this work, the appropriate placement and parameter settings of STATCOM were considered to improve the damping of the LFO system. The simulation results were compared to others from GA to examine the effectiveness of the applied HBMO technique. The same approach was used to solve the same issue successfully in ref. [166], but this time, using the best position of other FACTS controllers such as TCSCs and SVCs. The effectiveness of this developed strategy was even examined with a 16-machine 68-bus test network, showing superiority in terms on the rate of convergence, best accuracy, and lower computational complexity.

• MFO algorithm

The authors in ref. [46] presented an MFO approach to obtain the appropriate placement and sizing of a UPQC to give a solution for providing reactive power compensation in electrical networks. Thus, the load flow program now includes both the voltage that is injected by the series compensator and the reactive power that is injected by the shunt compensator. A comparison elaborated on test systems considered with and without UPQC was conducted to justify the efficiency, ability, and robustness of this applied MFO algorithm. Moreover, the same technique was discussed by [167] for finding the appropriate allocation and parameter settings of STATCOM to improve the voltage stability system and minimize transmission losses in electrical power networks. The advantage of the applied technique was highlighted on an IEEE 30-bus test network. Additionally, a comparison with the PSO method showed that the MFO algorithm is more effective when using a simplified STATCOM model.

• BSO method

In ref. [47], a robust design approach named the BSO algorithm for the simultaneous coordinated tuning of the TCSC damping controller and PSS in a multimachine electrical network was developed. In this study, the model and parameters of the PSS and TCSC were considered in order to minimize the stability performance index that is based on the integral of time multiple absolute error (ITAE). Otherwise, three cases of optimizations were considered, which are optimized PSS, optimized TCSC, and coordinated optimization, where the simulation results confirmed that the BSOA with a coordinated design is capable of producing comparable results to the BF and PSO techniques. In addition, this BSOA approach was also used by Z. Lu et al. [168] for identifying the most suitable placements and settings of FACTS controllers with multiple types, such as TCSC, SVC, TCPST, and TCVR, to decrease the transmission loss and also to improve the voltage profile. On both IEEE 30-bus and 118-bus test systems, the simulation results were compared to those of other known algorithms such as GA and PSO to demonstrate the proposed algorithm’s superiority, robustness, and effectiveness.

• IA approach

The deregulation and reorganization of electricity markets present new challenges to modern electrical systems. Hence, to achieve high operational efficiency and network security, large interconnected systems have been developed. In this regard, a new approach, namely, IA [48], has scrutinized the competence of the optimal location of the UPFC for minimizing the overall cost functions, which includes the total active and reactive production cost function of the generators and the installation cost of UPFCs. In this work, the robustness of this IA technique was tested on the 4-bus, IEEE 14-bus, and IEEE 30-bus test systems with equality and inequality constraints. Milad Khaleghi et al. [169] investigated a modified artificial immune network algorithm (MAINetA) for the suitable allocation of SVCs to reduce voltage deviation at load buses, minimize transmission losses, and reduce installation costs. A comparison with GCPSO, PSO, GA, and BIA, among other optimization methods, was carried out to show that the proposed MAINetA approach is reliable.

• SOS Algorithm

Generally, it is desirable for a power system to operate under normal operating conditions. However, when forced to operate near to its stability limit, a FACTS device can be considered as an alternative to this issue. Thus, it is important to choose the most suitable device to reach the required goals. In this context, an SVC was optimally used in ref. [49] via a well-established SOS swarm-intelligence-based algorithm for voltage security enhancement. In this work, the robustness of this SOS method was verified using IEEE 26-bus test systems when compared to the EP and POS methods. Similarly, the same strategy was investigated in ref. [170] for solving an ORPD problem. However, FACTS devices containing TCSC and TCPS were optimally placed in order to minimize transmission losses and reduce voltage deviation. The perfect placement of numerous FACTS devices and the robustness of the proposed method were authenticated by performing case research on standard IEEE 30-bus test systems.

Table 5. Summary of swarm-based algorithms related to FACTS device optimization problem.

Refs	Objectives	Devices	Methods	Test Case
[33,132,133]	To improve voltage profile and reduce transmission losses	SSSC	PSO	IEEE 9-bus
[134]	To maximize the system loadability (SL) and reduce the total installation cost (IC) of FACTS controllers	SVC, TCSC, and UPFC	PSO	IEEE 6-bus, 30-bus, 118-bus, and Tamil Nadu Electricity Board (TNEB) 69-bus
[135]	To improve power flow	SVC and TCSC	PSO	IEEE 14-bus
[136]	To improve voltage stability and system loadability and minimize transmission line losses	SVC	PSO	IEEE 30-bus
[137]	To minimize power losses in the system and the cost of investment FACTS controller	SVC, TCSC, and UPFC	σ-MOEPSO	IEEE 30-bus and 118-bus standard test networks
[138]	To minimize total production costs, including generator VPLE	SSSC	CAPSO	IEEE 30-bus
[139]	To enhance the voltage profile by minimizing voltage deviations at load buses	STATCOM	IPSO	IEEE 14-bus
[140]	To enhance the system security	TCSC, SVC, TCSC-SVC, and UPFC	WIPSO	IEEE 14-bus, IEEE 30-bus, and IEEE 57-bus
[141]	To strengthen its exploration capacity for determining the best FACTS controller’s settings and locations	TCSC, SVC, TCSC-SVC, and UPFC	PSO	IEEE test systems
[142]	To minimize transmission losses in the event of a line outage	TCSCs	ELPSO	IEEE test systems
[34]	To minimize transmission losses and operating costs while respecting voltage profile within permissible limit	TCSC and SVC	WOA	IEEE 30- and 57-bus
[143]	To obtain a significant and considerable reduction in total system operating costs and transmission line losses	TCSCs, SVCs, and UPFCs	WOA	IEEE 14- and 30-bus standard test networks
[144]	To demonstrate the capability of IPFC to control the real and reactive power in multiple transmission lines simultaneously	IPFC	ABC	IEEE 118-bus, 5-bus, and 30-bus systems
[145]	To improve voltage profile and also to reduce active and reactive power losses	SVC	ABC	IEEE 30-bus
[146]	To obtain the most benefit from the power transfer system by enhancing voltage stability, improving voltage profile, and minimizing transmission losses	SVC and STATCOM	ABC	IEEE 30-bus
[147]	To simultaneously obtain an improvement in power losses and stability margin	SVC, STATCOM, TCSC, and SSSC	ABC	IEEE test systems
[148]	To optimize reactive power management	SVC and TCSC	MABC	IEEE 30-bus
[149]	To improve voltage profile and minimize transmission loss	SVC, STATCOM, TCSC	ABC	IEEE 14-bus, 30-bus
[150]	To minimize power losses and improve voltage profile and voltage stability	STATCOM	QOCRO	IEEE standard test networks 14-bus and 30-bus
[151]	To maximize the transfer capability	SSSC	CRO	IEEE 30-bus and 57-bus
[37]	To enhance voltage stability limits and to reduce the power losses	STATCOM	CSA	IEEE 14-, 30-, and 57-bus test network
[152]	To improve the dynamic stability	SVC	CSA	SMIB model
[153]	To obtain an improvement of available transfer capability (ATC) under normal and network contingencies	SVC and TCSC	CaSO	IEEE 14- and 24-bus
[154]	To eliminate the voltage instability system	UPFC	CaSO	IEEE 14-bus
[39]	To achieve maximum system loadability	STATCOM	CS	IEEE test systems
[155]	To reduce total transmission losses and improve voltage profile	TCSC’s	ACS	IEEE 9-bus
[40]	To enhance voltage stability	STATCOM	DA	IEEE test systems
[156]	To reduce transmission losses and enhance voltage profiles	TCSC	DA	IEEE 14-bus
[41]	To improve power quality	TCSC, STATCOM, and UPFC	BA	IEEE 30-bus
[157]	To improve voltage stability	SVC	BA	IEEE 30-bus
[158]	To minimize transmission losses	SVC and TCSC	FFA	IEEE 30-, 57- and 118-bus
[159]	To provide a reduction in total generation costs and transmission losses and enhance voltage profile	SSSC	FFA	IEEE 30-bus
[160]	To increase power factor, minimize power losses, enhance transmitted power, and improve voltage profile	STATCOM and IPFC	FFA	IEEE 30-bus
[161]	To improve power system stability	UPFC	GOA	IEEE test systems
[162]	To provide power flow control	UPFC	AGOA	IEEE test systems
[163]	To provide a promising solution to high power loss and voltage deviation	UPFC	GWO	31-bus, 330 kV Nigeria National Grid (NNG)
[164]	To solve the ORPD	SSSC	GWO	IEEE 30-bus
[165]	To improve voltage profile	SVC and TCSC	MGWO	IEEE 30-bus
[166]	To improve the damping of LFO system	TCSC and SVC	HBMO	16-machine 68-bus test network
[167]	To improve voltage stability system and minimize transmission losses	STATCOM	MFO	IEEE 30-bus
[168]	to decrease the transmission loss and also to improve voltage profile	TCSC, SVC, TCPST, and TCVR	BSO	IEEE 30-bus
[48]	To achieve high operational efficiency and network security, large interconnected systems	UPFC	IA	4-bus, IEEE 14-bus, and IEEE 30-bus
[169]	To obtain reduce voltage deviation at load buses, minimize transmission losses and reduce installation costs	SVC	MAINetA	IEEE test systems
[170]	To solve an ORPD problem	TCSC and TCPS	SOS	IEEE 30-bus

presents an outline of the swarm-based algorithm techniques utilized in research related to the FACTS device optimization problem. Some approaches, objectives, test systems and FACTS devices considered for solving the cited problem are included in this summary.

5.2.4. Other Population-Based Algorithms

• BH algorithm

The series FACTS device associated with the TCSC has a low cost; hence, it is widely used for congestion relief. In ref. [50], to attain congestion management (CM), a TCSC was optimally located using a BH algorithm. In this recent research, this TC was achieved by considering two cases: the reduction of reactive power in transmission lines when the optimal TCSC position was taken, and power flow PI in the second situation. The BH strategy was performed on an IEEE 30-bus test system. Ramachandran et al. [171] investigated the same BH strategy for the proper locations of FACTS controllers in order to reduce the total congestion cost under line outage contingency conditions. A comparison to other methods of optimization such as BBBC and PSO was performed on an IEEE 30-bus and modified IEEE 57-bus test network to justify the robustness of the BH algorithm.

• PSOA technique

An adaptive PSOA was also adopted in ref. [51] for selecting the proper position and size of TCSCs in electrical networks to minimize active and reactive power losses, increase the transited power in transmission lines, and enhance the voltage profile while keeping the system’s total generation cost slightly lower than in the single-objective base case. The robustness of this method was proven on regular IEEE test networks such as a 9-bus, 30-bus, 57-bus and also a large 118-bus system. Similarly, an optimal installation of TCSC was integrated in ref. [172] via the same strategy to simultaneously improve the performance system and its controllability. The simulation results were illustrated to demonstrate the robustness and ability of this applied approach when compared with other techniques in the literature.

• ICA method

ICA was used in ref. [52] for the best positions of FACTS controllers including TCPST and TCSC to alleviate voltage deviations and overloads under line outage contingency and demand growth conditions. Two scenarios were considered in this work; in the first, for various line outages in an IEEE 14-bus test network, the overload metrics were mitigated by the power flow control capability of the TCPST device. In the second, for different values of load growth in an IEEE 39-bus test system, the overload and voltage deviation metrics were relieved by the strong control capability of the TCSC devices. A comparison with other existing algorithms, which are GSA, ABC, BSO, EP, PS, NLP, BSA, and ARO, was carried out to demonstrate the proposed ICA’s superiority, durability, and efficacy. An optimal design of STATCOM base PV curves was introduced by [173] via the ICA technique for relieving damping oscillations and improving the voltage profile under various operating conditions and disturbances in a multimachine environment. The results of the simulations were elaborated and showed that, in comparison to GA, ICA can deliver comparable results in terms of settling time and overshoots.

• SCA approach

Ravisekar et al. [53] utilized SCA for choosing the perfect position and sizing of a UPFC that was added to a conventional ORPD problem to reduce the total transmission loss and enhance the voltage profile. Two regular IEEE 57-bus and 118-bus test systems were applied to attain these objectives, and validated the effectiveness of this employed strategy. Moreover, the simulation results were illustrated to indicate the high quality and accuracy of the SCA compared with existing methods. A simplified SCA (SSCA) was presented in ref. [174] for resolving the same issue by locating the appropriate TCSC and SVC device placements and setting their parameters under demand growth conditions. On IEEE 57-bus and 118-bus test networks, this applied methodology was examined by a comparison of simulation results to those of conventional SCA and other known methods. The efficiency and robustness of the SSCA was observed in terms of the minimum operating costs and maximum net savings.

• TLBO method

The TLBO approach has gained wide acceptance among the optimization researchers, especially in FACTS device optimization problems [175]. A TLBO algorithm was adopted in ref. [54] to minimize transmission loss, reduce the total installation costs, and improve the voltage profile by identifying the most suitable location and sizing of the TCSC device. Three test networks, an IEEE 14-bus, IEEE 30-bus, and an Indian grid 75-bus were applied to validate the viability and superiority of the TLBO algorithm compared to ABC and PSO techniques. Rahul Agrawal et al. [176] investigated the same methodology for identifying the most suitable position and rating size of SVC devices to reduce transmission loss and improve the voltage profile. For the justification of the effectiveness and capability of this proposed method, IEEE 14-bus test systems were considered. The TLBO technique was also discussed by Anurag Gautam et al. [177] as an enhancement to ATC using an optimized TCSC device. The simulation results from an IEEE 30-bus under different contingency conditions demonstrated its validity and effectiveness when compared to GWO and PSO heuristic methods. Similarly, in ref. [178], an SVC device was optimally placed on an IEEE 30-bus test system via the TLBO approach, where one of the main contributions was the improvement of the voltage stability system. The application of TLBO was also presented in ref. [179] for the coordinated tuning of the SVC and PSS damping controllers to enhance the LFO in a multimachine electrical network. In this study, an eigenvalue analysis and nonlinear time-domain simulation were used to show the robustness of this employed technique. The obtained results prove that the coordinated controller TLBO-PSS-SVC has an excellent capability in LFO damping compared to the TLBO-based PSS (TLBO-PSS) and the TLBO-based SVC (TLBO-SVC).

• WCA method

As an example of the application of optimization schemes of other population-based algorithms, in ref. [55], the WCA approach is presented that it is based on the water cycle and the observation of how rivers and streams in the real world flow downhill toward the sea. It was used to reduce the weighted sum of the voltage deviations and losses by the optimal allocation of SVCs for solving reactive power planning (RPP). Amin Khodabakhshian et al. [180] also used the WCA method to determine the optimal design for simultaneously locating UPFC and PSS0. In this work, the coordination of these two controllers was utilized to improve the system stability. The effectiveness and applicability of this selected strategy were performed on an IEEE 39-bus test network when compared with other algorithms.

• BFA technique

BFA is one of the population-based evolutionary computation techniques developed by Passino. This original BFA algorithm is utilized by many experts in different fields, especially in the FACTS controller optimization issue. It was applied by [56] to find the optimal controller parameters of UPFC for damping LFO in a power system and also to obtain an improvement on the transient stability under different operating conditions. In ref. [181], a new model of BFA, namely enhanced BFA (EBFA), was proposed to determine the most suitable allocation and sizing of TCSCs and SVCs in electrical networks to increase voltage stability limits and reduce the total generation cost. The objective was to solve the issue using an IEEE 30-bus test network under normal loading and with increased loading for some buses. A comparison with conventional BFA and GA was illustrated to prove the robustness of the EBFA methodology in terms of computational time and convergence characteristics. In ref. [182], a modified BFA called the modified bacterial foraging optimization algorithm (MBFOA) was used for determining the proper position and sizing of SVCs in order to optimize multi-objective functions such as security systems, voltage deviation at load buses, active power losses, and system overload. An IEEE 30-bus was applied to prove the robustness and the better performance of the MBFOA when compared with GA. Similarly, in ref. [183], to improve system security, stability, and reliability, an improved version of the BFA, namely, the refined bacterial foraging optimization (RBFA) algorithm, was used for the best placement of the UPFC. The benefits of this developed RBFA algorithm were highlighted in the solving of the ORPD problem using IEEE 6- and 30-bus test networks.

• COA method

Tawfik Guesmi et al. [57] investigated a novel approach for the simultaneous coordinated design of PSS and SVC controllers in a multimachine electrical network using the COA to improve the system stability. In this work, a nonlinear time-domain-based objective function was employed, where the simulation results under different load conditions and configurations of the system were elaborated. The efficiency and applicability of this proposed strategy was observed in terms of the time responses of the speeds’ deviations of the machines. In ref. [184], the recently developed COA approach was also explored to simultaneously design PSSs and TCSC-PODs in order to eliminate the imbalances between electrical and mechanical torques in synchronous generators caused by LFO damping. The simulation results were illustrated for the South Brazilian power system to validate the effectiveness of this applied methodology.

• TS algorithm

A TS algorithm was addressed in refs. [185,186] for identifying the most suitable placements and parameter settings of FACTS controllers such as TCPST, TCSC, UPFC, and SVC in electrical networks. A 6-bus test network was utilized to demonstrate the robustness of this developed technique to reduce the total production costs with different loading conditions.

Table 6. Summary of other population-based algorithms related to FACTS device optimization problem.

Refs	Objectives	Devices	Methods	Test Case
[171]	To reduce the total congestion cost	TCSC	BH	IEEE 30-bus and modified IEEE 57-bus
[172]	To simultaneously improve the performance system and its controllability	TCSC	PSOA	IEEE test systems
[173]	To relieve damping oscillations and improve voltage profile	STATCOM	ICA	IEEE test systems
[174]	Minimum operating costs and maximum net savings	TCSC and SVC	SCA	IEEE 57-bus and 118-bus
[175]	To minimize transmission loss, reduce total installation costs, and improve voltage profile	TCSC	TLBO	IEEE test systems
[176]	To reduce transmission loss and improve voltage profile	SVC	TLBO	IEEE 14-bus
[177]	To enhance ATC	TCSC	TLBO	IEEE 30-bus
[178]	To improve voltage stability system	SVC	TLBO	IEEE 30-bus
[179]	To enhance the LFO in a multimachine electrical network	SVC	TLBO	SMIB model
[180]	To improve the system stability	UPFC	WCA	IEEE 39-bus
[181]	To increase voltage stability limits and reduce the total generation cost	TCSC and SVC	EBFA	IEEE 30-bus
[182]	To optimize multi-objective functions such as security systems, voltage deviation at load buses, active power losses, and system overload	SVC	MBFOA	IEEE 30-bus
[183]	To improve system security, stability, and reliability	UPFC	RBFA	IEEE 6 and 30-bus
[184]	To eliminate the imbalances between electrical and mechanical torques in synchronous generators caused by LFO damping	TCSC	COA	South Brazilian power system
[185,186]	To reduce the total production costs with different loading conditions	TCPST, TCSC, UPFC, and SVC	TS	6-bus test network

presents an outline of other population-based algorithms utilized in research related to the FACTS device optimization problem. Some approaches, objectives, test systems, and FACTS devices considered for solving the cited problem are included in this summary.

5.3. Summary of Sensitive Index Methods Related to FACTS Device Optimization Problem

The computation for various potential locations of FACTS controllers is obtained based on different indices in analytic approaches. Typically, various types of indices are utilized in this area, such as PLI, PI, VSI, CSI, NSCPF sensitivity, MLP index, LFI index, FVSI, TSLSI, OVL index, VLB index, LMP index, TCI, CCI, VCPI, LQP, VPSI, and EVPA.

In ref. [187], an SVC device was parameterized based on a nodal order and the analysis of repetitive power flows using an IEEE 9-bus test system. It was observed that once the SVC was installed in the best location (bus 5), the power losses, voltage stability, and power factor were optimized. Marouani Ismail et al. [188] introduced a sensitivity method based on the CSI described by a real power flow PI for placing a diverse FACTS controller containing a TCSC and UPFC to decrease the FACTS installation cost and overloads for a 9-bus WSCC (Western System Coordinating Council). In addition, three cases were considered, without FACTS and with FACTS, for simple and double contingencies. The simulation results were analyzed to prove the competence and effect of these FACTS devices to achieve the target objectives. A suitable position of the FACTS controller containing TCSC and UPFC, based on another sensitivity manner, namely, NSCPF, was obtained in ref. [189]. The effectiveness of this NSCPF approach in terms of production cost function minimization and computational time was examined on an IEEE 14-bus and compared to GA. The authors in ref. [190] implemented a sensitivity-based screening technique (ST) for the proper location of a UPFC device to reduce the total generation costs in electrical networks. In this work, a new UPFC model called a UPFC ideal transformer model was proposed in the UPFC sensitivity analysis. As a result, this model does not require the addition of additional buses for the UPFC input and output terminals. The robustness of this proposed method was demonstrated through simulation results on regular IEEE 5-bus, 14-bus, and 30-bus test networks. A PFC analysis based on the PV curve and loading parameter (LP) (λ) was used in ref. [191] for the appropriate locations of SVCs and TCSCs to improve the voltage stability system. Accordingly, the critical buses and lines with the weakest voltage profile and higher load value, respectively, were identified by the application of this PFC approach. The simulation results from an IEEE 6-bus confirmed that the SVC gives the best voltage profile and transmission loss compared to the TCSC. Similarly, to enhance the voltage stability system under contingency conditions, Farbod Larki et al. [192] explored the PFC strategy based on MLP and its corresponding megawatt margin (MWM) decrease percent in each contingency by selecting the most suitable placements of FACTS controllers such as SVC, TCSC, and STATCOM. From the obtained results from the Khouzestan power network, it can be concluded that the STATCOM device provides a higher voltage stability margin than the SVC at the weakest bus. Other work related to the FACTS device optimization problem was employed in ref. [193], where a TCSC device was optimally located to minimize the total production costs including FACTS device installation costs using two sensitivity index methods: active power PI and the reduction of total system VAR power losses. The simulation results from an IEEE 5-bus were obtained under line outage conditions. It was observed that that PI sensitivity with the TCSC cost could be effectively utilized for selecting the optimal placement of the TCSC. Likewise, Sunil N. Malival et al. [194] also adopted the same strategy to decide the optimal allotment of TCSCs using an IEEE 6-bus test system. Because the voltage stability is mainly affected by the reactive power balance in the system, Muhammad Nurdin et al. [195] investigated a new technique based on three indexes—voltage index, VSI, and ASI sensitivities—for choosing the proper locations and the best setting for the SVC and STATCOM to enhance the voltage stability systems. A 14-generator model of the SE Australian and Sumatera electrical networks in Indonesia was applied for these proposed techniques. Similarly, to solve the same problem, a new method termed EVPA was discussed in ref. [196] for optimally placing three FACTS devices, SVC, TCSC, and STATCOM, in three test systems, which were a 9-bus test system (WSCC), a 10-machine, 39-bus system, and a 16-machine, 68-bus system. The simulation results demonstrated that the EVPA approach can produce comparable results to the LFI sensitivity method [197]. Esmaeil Ghahremani et al. [198] displayed a graphical user interface (GUI) based on two analytic sensitivities related, respectively, to lines, named OVL and VLB, for the appropriate positions of FACTS controllers containing a TCSC, SVC, TCPST, TCVR, and UPFC to improve the system loadability under security constraints. The simulation results were realized on standard IEEE 24-bus, 30-bus, 57-bus, 118-bus, and 300-bus test systems, and declared that the UPFC is the most effective FACTS device for increasing loadability while reducing the losses at the same time. Two techniques, namely, the LMP difference sensitivity technique and the CRC sensitivity approach, were successfully proposed to solve the FACTS device optimization issue in ref. [199] to obtain congestion management in deregulated electrical power systems. Based on the observed result for the three regular IEEE 14-, 30-, and 57-bus test networks, it can be recommended that the CRC sensitivity approach provides more promising results than the LMP difference sensitivity technique. Mutegi et al. [200] projected a voltage stability index based on the FVSI and the LSI for the proper allotment of FACTS to improve the voltage stability network. In this work, an IEEE 39-bus was considered as a test network to justify the ability and robustness of the employed methods. In ref. [201], a generalized technique based on TSLSI was developed for determining the most suitable position of STATCOM in the first step, and its parameter settings in the second step, using NR to enhance power system static security. The simulation was implemented on an IEEE 14-bus and demonstrated a considerable improvement in the voltage profile and a reduction in transmission losses after the placement of a STATCOM device. Moreover, in solving the same problem, Lu et al. [202] proposed an index named the SCS index to select the most suitable location of the TCSC for the elimination of line overloads under a single contingency. A regular IEEE 14-bus and 118-bus test network highlighted the advantages of this developed technique. As an example of the applications of sensitive index methods, in ref. [203], two indices termed TCI and CCI were used to install a TCSC FACTS device at appropriate locations under normal and network contingency conditions in order to improve the power system performance. On the test network with an IEEE 14-bus and 118-bus, the efficacy of this employed methodology was demonstrated. For the security system improvement, a sensitivity-based approach, that is, the active power flow PI, was used in ref. [204] for selecting the best locations for the TCSC and UPFC under critical contingencies and different loading cases. In this study, the obtaining of optimal PI sensitivity taking into account equality and inequality constraints, a generalized algebraic modeling system (GAMS) was employed. The ability and efficiency of this applied strategy was illustrated using an IEEE 30-bus and Northern Regional Electricity Board (NREB) 246-bus practical Indian test systems. Ikram Ullah et al. [205] used the same strategy to identify the best position of the TCSC to improve the available transfer capability (ATC). In this work, once the TCSC had been located, the TTC was computed using the repeated power flow (RPF) method, taking into account all of the equality and inequality constraints of the system. The simulation results were verified using IEEE 24-, 30-, and 39-bus test systems to demonstrate the effectiveness of this PI technique. In Reference [206], a PI sensitivity-based approach and LODFs index were presented for the proper location of SSSC and TCSC FACTS devices to improve the power system security. The simulation results were obtained using a modified IEEE 30-bus test network by utilizing power world simulator software, and the superiority of these selected approaches was observed. To select the best positions of the FACTS controllers containing TCSC and STATCOM, VCPI, and LQP were utilized in ref. [207] by determining the critical line with respect to a bus. The simulation results were obtained from an IEEE 14-bus, and it can be clearly observed that the suitable locations of the given FACTS devices can offer good control of the transited power, an improvement in the levels of tension, and, consequently, the permanent stability of the studied system. In ref. [208], power system voltage stability indices (VSIs) including the LQP, the VCPI, and the LSI were introduced for identifying the most appropriate positions of the UPFCs in order to enhance the voltage stability system. To demonstrate the robustness of this applied approach, the simulation results for voltage stability were taken from an IEEE 14-bus and 39-bus and compared with other optimization techniques such as DE and PSO. To enhance the voltage profile, improve the ATC, and increase the efficiency for the overall power transmission, the power stability index (PSI) and FVSI were explored in ref. [209], which can be also used for placement of an SVC. An IEEE 14-bus test system was considered in this work, and it can be noted that the PSI technique can offer a better result than the FVSI technique. Likewise, Mohammed Amroune et al. [210] investigated the FVSI sensitivity to solve the same issue by determining the best allotment of TCSCs and SVCs. This sensitivity index was executed on a modified IEEE 30-bus to either decrease the load on the reactive power or increase the load until voltage collapse was reached in order to eliminate voltage instability. A new technique based on VPSI was considered in ref. [211] for identifying the best allocation of the TCSC in the first stage. The Taguchi method (TM) was used in the second stage to determine the parameter settings of the TCSCs to enhance the voltage profile and voltage stability margin. The effectiveness and applicability of this technique was applied on an IEEE 14-bus test network. The authors in ref. [212] presented the structure-preserving energy margin (SPEM) sensitivity approach to enhance the transient stability under various contingency conditions in an electrical network, using FACTS devices. In this research, the improvement in the CCT was taken into account for the examination of this sensitivity method to improve the PTC and the sizing of compensation for shunt and series FACTS devices. The effectiveness of this approach was tested on a 10-bus system (4-machine) and a 39-bus New England system (10-machine).

Table 7. Summary of sensitive index techniques related to FACTS device optimization problem.

Refs	Objectives	Devices	Methods	Test Case
[187]	To improve power losses, voltage stability, and power factor	SVC	PLI	IEEE 9-bus
[188]	To decrease the FACTS installation cost and overloads	TCSC and UPFC	CSI	9-bus WSCC
[189]	To minimize production cost function	TCSC and UPFC	NSCPF	IEEE 14-bus
[190]	To reduce the total generation cost	UPFC	ST	IEEE 5-bus, 14-bus, and 30-bus
[191]	To improve voltage stability system	SVC and TCSC	PFC	IEEE 6-bus
[192]	To enhance voltage stability system under contingency conditions	SVC, TCSC, and STATCOM	MLP	IEEE test systems
[193,194]	To minimize total production costs including FACTS installation cost	TCSCs	PI	IEEE 5-bus
[195]	To enhance voltage stability systems	SVC and STATCOM	VSI and ASI	IEEE 6-bus
[196]	To improve voltage stability systems	SVC, TCSC, STATCOM	EVPA	14-generator model of the SE Australian and Indonesia
[197]	To improve voltage stability systems	SVC, TCSC, and STATCOM	LFI	9-bus (WSCC), 10-machine, 39-bus, 6-machine, 68-bus
[198]	To improve the system loadability under security constraints	TCSC, SVC, TCPST, TCVR, and UPFC	OVL and VLB	IEEE 24-bus, 30-bus, 57-bus, 118-bus, and 300-bus
[199]	To obtain congestion management in deregulated electrical power systems	UPFC	LMP and CRC	IEEE 14-, 30-, and 57-bus test networks
[200]	To improve voltage stability network	SVC, UPFC	FVSI and LSI	IEEE 39-bus
[201]	To enhance power system static security	STATCOM	TSLSI	IEEE 14-bus
[202]	To eliminate line overloads under a single contingency	TCSC	SCS	IEEE 14-bus and 118-bus
[203]	To improve power system performance	TCSC	TCI and CCI	IEEE 14-bus and 118-bus
[204]	To improve security systems	TCSC and UPFC	PI	IEEE 30-bus and (NREB) 246-bus practical Indian
[205]	To improve the available transfer capability (ATC)	TCSC	RPF	IEEE 24-, 30-, and 39-bus
[206]	To improve power system security	SSSC and TCSC	PI	IEEE 30-bus
[207]	To obtain good control of the transited power, improve the voltage levels, and consequently achieve permanent stability	TCSC and STATCOM	VCPI and LQP	IEEE 14-bus
[208]	To enhance voltage stability system	UPFCs	VSIs	IEEE 14-bus and 39-bus
[209]	To enhance voltage profile, improve ATC, and increase the efficiency of the overall power transmission	SVC	PSI and FVSI	IEEE 14-bus
[210]	To eliminate voltage instability	TCSC and SVC	FVSI	IEEE 30-bus
[211]	To enhance voltage profile and voltage stability margin	TCSC	VPSI	IEEE 14-bus
[212]	To enhance transient stability under various contingency conditions	SVC and STATCOM	SPEM	10-bus (4-machine) and 39-bus New England system (10-machine)

presents an outline of the sensitive index techniques utilized in research related to the FACTS device optimization problem. Some approaches, objectives, test systems and FACTS devices considered for solving the cited problem are included in this summary.

5.4. Summary of Mixed Methods Related to FACTS Device Optimization Problem

In some research, conventional techniques, sensitivity index approaches, and meta-heuristic methods were hybridized in pairs or all together and applied to find better solutions to FACTS device optimization problems than individual techniques. As a result, hybrid or mixed methods have proven effective in locating global optimal solutions for FACTS device optimization issues with a variety of constraints because they combine the strengths and weaknesses of two or more approaches to solve complex issues. In this section, different hybrid methods reported in the literature will be presented. A new HCRO approach based on CRO and DE were exploited in ref. [213] for identifying the best locations and sizing of a UPFC device to ameliorate system performance, i.e., a reduction in power losses, voltage deviation, and production costs. In this suggested hybrid technique, the mutation and crossover operation of DE were introduced to increase the quality of the CRO’s solutions and accelerate its convergence. IEEE 14-bus and 30-bus test networks were taken into consideration in order to assess this method’s capability and efficiency, where a comparison of the obtained results with other techniques in the literature such as GA, IGA, PSO, and HIA was carried out. Because of its easy operation, simple integration into electrical networks, and as a one of the most commonly utilized shunt FACTS controllers due to its low cost compared to others, the appropriate location and parameter settings of an SVC were selected to improve the ATC and to give more flexible voltage control using another hybrid algorithm based on hybridizing the CS and ALO, known as CS-ALO [214]. The ability and efficiency of this hybrid methodology was examined using an IEEE 57-bus, and the simulation results indicated that CS-ALO is more effective than other techniques in terms of its convergence characteristics and robustness in solving FACTS device optimization problems. For selecting the appropriate location and parameter settings of UPFC to improve the dynamic stability in electrical networks, B. Vijay Kumar et al. [215] employed a hybrid method combining FA with CS named FA-CS to achieve global best results for FACTS device optimization problems. Thus, the optimal position of UPFC was identified using the FA technique; however, its sizing was identified by the CS algorithm. The FA-CS performance was evaluated by comparison with the performance of various approaches such as Bat-FA, GSA-Bat, ABC-GSA, and CS techniques. The results of the comparison consistently demonstrated the robustness of this applied approach and confirmed its potential for solving related issues. In ref. [216], a hybrid technique with a combination of EP and DE algorithms, namely, EP-DE, was developed for determining the appropriate placement and sizing of FACTS controllers such as TCSC, SVC, and UPFC to minimize the total number of overloads, excess power flow, overloading severity, and production cost. The obtained results on a 5-bus test network with and without FACTS demonstrated the superiority of this EP-DE strategy. Biplab Bhattacharyya et al. [217] employed a new hybrid combination of the fuzzy logic and DE algorithms, namely, the Fuzzy-DE method, for the planning and coordination of FACTS controllers in electrical networks under different loading conditions. Therefore, the suitable placements of TCSCs and SVCs were found to take advantage of the fuzzy logic, whereas their parameter settings were determined using DE. The results of the simulation on an IEEE 30-bus were obtained and compared with a simple DE (SDE), and the significance of this proposed approach was clearly observed in terms of operating cost minimization. In ref. [218], the authors used the HLSI, a combination of LMN and FVSI for computing the proper placement and sizing of FACTS devices to improve the voltage stability system. The robustness of this applied methodology was verified using an IEEE 9-bus under multiple contingencies. Similarly, to solve the same problem, Sai Ram Inkollu et al. [219] investigated a hybrid PSO-GSA optimization technique to obtain the most suitable locations and parameter settings of the UPFC and IPFC. Once these two FACTS devices were optimized, the voltage stability was ameliorated while respecting a given set of operating and physical constraints. The robustness and applicability of this applied technique were tested using an IEEE 30-bus test system. In addition, a GSA was also combined with a GA, constituting a GA-GSA technique [220] for optimizing an IPFC FACTS device to also enhance the voltage stability system. In this study, the optimal positions of the IPFC installation were determined by GA. Among the suitable positions, the maximum transmission line combinations of the corresponding buses were examined. After that, the IPFC’s injecting voltage magnitude and angle were found using the GSA approach. An IEEE 30-bus test system with and without IPFC was applied to demonstrated the robustness of this strategy in terms of a quick solution for the best IPFC setting and the enhancement of voltage stability. It was observed in ref. [221] that the active power loss decreased and the voltage stability system was improved when TCSC, SVC, and UPFC were used in an IEEE 30-bus. In effect, KGMO was combined with PSO, and the KGMO-PSO methodology was developed as an efficient optimization technique for solving FACTS device optimization problems in this research. The main benefit of using this hybrid method is that it does not need more time for tuning the optimal locations and parameter settings of FACTS controllers compared to other existing techniques such as PSO, ABC, TLBO, CRO, and QOCRO. It is vital to note that occasionally, the shunt compensation in the lower bus level does not provide ideal response power for the improvement of voltage stability. In this regard, the authors in ref. [222] addressed a hybrid method combining FL with RCGA termed the fuzzy-GA formulation for the best position and sizing of SVCs and STATCOMs to obtain a strongly bonded bus with many weak buses, whose reactive power support on this bus can ensure a sufficient increase in the load margin and a good voltage profile. Two test systems, an IEEE 14-bus and IEEE 57-bus, were considered to show the effectiveness and ability of this applied approach. In ref. [223], the application of a hybrid IA (HIA) such as immune GA (IGA) and immune PSO (IPSO) was used for determining the most appropriate location and sizing of the UPFC to minimize transmission losses and operating costs. A comparison of the simulation results with others from GA, PSO, IPSO, and IA techniques was conducted on regular IEEE 14-bus and 30-bus test networks in order to assess this method’s capability and efficiency. A hybrid TSSA technique was introduced in ref. [224] for identifying the most suitable locations of FACTS controllers containing TCPS, TCSC, SVC, and UPFC to decrease the total production cost of all levels of loading. A comparison with the other existing algorithms, such as quadratic programming (QP) and the sensitivity index approach, was carried out to prove the superiority, ability, and effectiveness of this applied method. An improved TSSA approach (ITSSA) for solving the FACTS device problem was developed by Suppakarn Chansareewittaya [225]. In this research, the most suitable placement and sizing of the SVC were determined to enhance the TTC on an IEEE 118-bus system and the practical Electricity Generating Authority of Thailand (EGAT) 58-bus test systems, and the results revealed that the employed method is simple, reliable, and more able to practically implement the SVC compared to EP and original hybrid TSSA. In ref. [226], hybrid-technique-based optimized FACTS devices were presented, where the ABC algorithm was hybridized with GSA to ameliorate the dynamic stability in the power systems. Here, the most favorable position of UPFC was fixed using the ABC algorithm after the identification of the maximum power loss bus. Once the UPFC was optimally placed, the GSA was utilized to determine the required capacity of the UPFC. The simulation results were obtained using an IEEE 14-bus and IEEE 30-bus to demonstrate the ability and robustness of this ABC-GSA technique and its potential for solving the FACTS optimization issue compared to the separate application of ABC and GSA. In order to develop an efficient optimization strategy, a hybrid GACO approach combining the properties of ACO and GA algorithms was introduced in ref. [227] for selecting the most suitable location and parameter settings of a STATCOM with equivalent current injection (ECI) to improve the voltage stability system. In this work, the performance of the ACO technique when coupled with GA was studied. The simulation results from an IEEE 30-bus were analyzed and indicated the significant voltage stability improvement, confirming that this GACO approach can not only ameliorate the neighborhood search, but can also search for the optimum solution quickly to advance convergence. In ref. [228], it was observed that UPFC was used to improve the dynamic stability in the power system. A CKH and RRA were combined, forming a new hybrid approach called the CKHRA technique. The optimal placement of the UPFC was determined using the CKHRA technique based on maximal power loss line; however, its size was determined using the RRA algorithm based on minimal voltage deviation. The effectiveness of the CKHRA method was linked with a standard IEEE 14-bus, 30-bus and 57-bus benchmark system, whereas the efficiency was tested against various generator fault conditions. Ahmad Abubakar Sadiq et al. [229] projected a hybrid of real power flow (∂P I) sensitivity and PSO (PI-PSO) to maximize the ATC and minimize FACTS sizes such as TCSC and SSSC using the CPF strategy. In this study, some high-potential positions with improved ATC at minimum FACTS size were obtained using PI sensitivity to provide a reduced search space for the PSO technique. A comparative result with the PSO technique was carried out on an IEEE 9-bus to demonstrate the effectiveness of this developed technique in terms of convergence characteristics, avoidance of local optima, and superior ATC values. In ref. [230], three optimization techniques, GA-PSO, DA-PSO, and GA-DA, were employed for choosing the optimum placement and firing angle of the SVC. Here, the location of the device was optimized by GA or DA and the optimized firing angle was carried out using PSO. The simulation results were obtained from an IEEE 57-bus with and without SVC to prove the superiority and applicability of these proposed approaches. A comparative study was conducted and indicated the greater efficiency of GA-PSO compared to GA, PSO, and DA-PSO. A modified PSO called an adaptive PSO (APSO) was mixed with SA and was described in ref. [231] and referred to as APSO-SA. This methodology was incorporated into an APSO to increase the convergence rate in the original PSO and SA approach for obtaining the proper placement, type, and size of the SVC and TCSC. These two FACTS controllers were considered in this research to improve the voltage stability index, minimize transmission losses, and decrease the cost of investment with single and multi-type FACTS devices. This APSO-SA strategy was performed on an IEEE 14-bus test network and the numerical results were illustrated to show its effectiveness and applicability when compared with conventional PSO in terms of better accuracy and faster convergence to solve FACTS controller optimization problems. Production fuel costs, voltage deviation, and transmission loss were formulated as a multi objective function problem that was solved under line contingency conditions using a new approach for the suitable position and sizing of FACTS controllers in electrical power systems. This new technique, based on hybridizing the krill herd (KH) algorithm and a combined index with LUF and FVSI sensitivity, was presented in ref. [232]. Therefore, an optimal affectation of TCSC was obtained by LUF and FVSI for contingency analysis based on the rapid contingency ranking technique (RCRT); moreover, the krill herd (KH) algorithm was used to optimize TCSC tuning. This employed strategy was implemented on an IEEE 30-bus test network and a line contingency was considered to demonstrate its applicability and robustness. In ref. [233], a combination of GSA with VSI and LSI was used to determine the most suitable allotment and parameter settings of FACTS devices (SVC, TCSC, UPFC). The main aim was to minimize transmission losses and improve the system security. The validation of this employed methodology was examined on a regular IEEE 30- and 57-bus test network. Parizad et al. [234] presented heuristic techniques and a sensitivity index for the best allocations and tuning of FACTS controllers. A hybrid HAS-GA was combined with the VSI and PLI index to select the most suitable allocation and sizing of SVC, UPFC, and TCPAR devices. For the system analysis, three different situations were studied: individual placement, two devices placed randomly, and simultaneous placement. In all situations, VSI and PLI were calculated to choose the best locations for the devices. The simulation results were obtained from a 14-bus test system, and the results found an improvement in the voltage profile, reduction in transmission line losses, an increase in ATC, and the maximization of the loading and voltage stability margin. Divya Gupta et al. [235] presented an approach to calculate enhanced ATC, using a TCSC FACTS device by controlling the transmission line reactance. In this research, the power-loss-based congestion reduction (SPCR) index and the metaheuristic evolutionary particle swarm optimization (MEEPSO) technique were combined successfully to determine the most appropriate placement of the TCSC and the augmentation of the ATC, respectively. The simulation results were obtained using IEEE 6-bus and IEEE 30-bus test systems for validating the robustness of this applied strategy. The combination of the NSGAII technique with PI and SI sensitivity in ref. [236] and [237], respectively, was used for identifying the proper placement and parameter settings of TCSC FACTS devices to minimize transmission losses and total production costs including the installation costs of FACTS devices.

Table 8. Summary of mixed optimization techniques related to FACTS device optimization problem.

Refs	Objectives	Devices	Methods	Test Case
[213]	To reduce power losses, voltage deviation, and production cost	UPFC	CRO-DE	IEEE 14-bus and 30-bus
[214]	To improve the ATC	SVC	CS-ALO	IEEE 57-bus
[215]	To improve dynamic stability	UPFC	FA-CS	IEEE test systems
[216]	To minimize the total number of overloads, excess power flow, overloading severity, and production cost	TCSC, SVC, and UPFC	EP-DE	5-bus test network
[217]	To minimize operating costs	TCSC and SVC	Fuzzy-DE	IEEE 30-bus
[218]	To improve voltage stability system	UPFC and IPFC	HLSI	IEEE 9-bus
[219]	To ameliorate voltage stability	UPFC and IPFC	PSO-GSA	IEEE 30-bus
[220]	To enhance voltage stability system	IPFC	GA-GSA	IEEE 30-bus
[221]	To minimize active power loss and reduce voltage stability system	TCSC, SVC, and UPFC	KGMO-PSO	IEEE 30-bus
[222]	To improve voltage profile	SVC and STATCOM	fuzzy-GA	IEEE 14-bus and IEEE 57-bus
[223]	To minimize transmission losses and operating costs	UPFC	IGA-IPSO	IEEE 14-bus and 30-bus
[224]	To decrease total production costs	TCPS, TCSC, SVC, UPFC	TSSA	IEEE test systems
[225]	To enhance TTC	SVC	ITSSA	IEEE 118-bus, (EGAT) 58-bus
[226]	To ameliorate dynamic stability	UPFC	ABC-GSA	IEEE 14-bus and IEEE 30-bus
[227]	To improve voltage stability system	STATCOM	GACO	IEEE 30-bus
[228]	To improve dynamic stability	UPFC	CKHRA	IEEE 14-bus, 30-bus, and 57-bus
[229]	To maximize ATC and minimize FACTS device sizes	TCSC and SSSC	PI-PSO	IEEE test systems
[230]	To choose optimum placement and firing angle of SVC to improve voltage profile	SVC	GA-PSO, DA-PSO and GA-DA	IEEE 57-bus
[231]	To improve voltage stability index, minimize transmission losses, and decrease cost of investment	SVC and TCSC	APSO-SA	IEEE 14-bus
[232]	To improve production fuel cost, voltage deviation, and transmission loss	TCSC	KH-LUF-FVSI	IEEE 30-bus
[233]	To minimize transmission loss with improvement to system security	SVC, TCSC, UPFC	GSA-VSI-LSI	IEEE 30- and 57-bus
[234]	To improve voltage profile, reduce transmission line losses, increase ATC, and maximize loading and voltage stability margin	SVC, UPFC	HAS-GA	14-bus test system
[235]	To enhance ATC	TCSC	MEEPSO-SPCR	IEEE 30-bus
[236,237]	To minimize transmission losses and total production costs including FACTS device installation cost	TCSC	NSGAII-PI	IEEE 30-bus

presents an outline of the mixed optimization techniques utilized in research related to the FACTS device optimization problem. Some approaches, objectives, test systems, and FACTS devices considered for solving the cited problem are included in this summary.

6. Discussion

In this comprehensive review, after having presented a detailed modeling of the FACTS devices, their basic concepts, and their classification, we have tried to emphasize their objectives, the main fields of application, their advantages, their best adaptation to variations in the operating conditions of electrical systems, and the improvements they provide when used in existing installations as the main motivations for the integration of FACTS devices into electrical systems based not only on past and recent research articles on FACTS devices and their applications, but also on the real state of the market.

Based on research published in the literature, several parameters of electrical networks can be controlled by different FACTS systems; in fact, UPFC and IPFC are the most suitable FACTS controllers for the active and reactive power control of bus voltages. However, SVC and STATCOM are used the most for reactive power compensation. The TCSC is the most suitable controller for transmission line impedance variation, and the SSSC controller provides active power control. According to the literature review, there are numerous benefits provided by FACTS devices and their various power system parameters that can be controlled, and their main applications are shown in Figure 8. It can be observed that that the UPFC is the most efficient, but its high cost constitutes its major drawback.

The technical contribution of FACTS devices of more than 254 references was analyzed and evaluated in this modest work, and was able to show that FACTS devices, if installed in the most suitable location and with a proper size, are capable of offering the fast control of active and reactive power, realizing continuous compensation, controlling voltage profile and power loss, minimizing or eliminating line overloads, reducing network congestion management, and improving transient stability in power networks due to their dynamic characteristics. However, not all of these many benefits are noticeable. In the same way, the cost of FACTS controllers is also huge. In all cases, the cost must be weighed against the expected benefits. This is why better placement with an appropriate size is required, especially when dealing with multiple types of FACTS devices.

Several techniques-based conventional optimization methods such as NR, MILP, MINLP, MCA, NLP, LM, MIP, MDCP, and SQP were used successfully in the last two or three decades for solving FACTS device optimization problems. They are adaptable, flexible, and easy to use in problem analysis. Although classical optimization techniques have relatively efficient convergence characteristics, handling constrained optimization problems is difficult [82]. However, these conventional methods have some drawbacks. They have weak convergence characteristics and are heavily dependent on the initial solutions. They either completely diverge or converge to some local optima. Unfortunately, they are unable to solve nonlinear and nonconvex problems or problems with multiple variables. Conventional techniques based on calculation are not able to deliver satisfactory results due to the nonlinearity of FACTS device optimization problems with certain constraints. Therefore, there is a pressing need to develop more dependable and improved strategies to overcome these limitations.

Analytical techniques or approaches using sensitivity bases have the benefits of being computationally efficient; they are simple and best suited to the location problem, but only one objective problem is considered [238,239]. Any sensitivity technique is designed to identify the most suitable placement of the FACTS controller, and it is less useful for considering more constraints in the problem; however, the accuracy of the calculations may suffer if the power flow model’s nonlinearity is not taken into account [82]. Moreover, the proper location and sizing of FACTS controllers cannot be addressed simultaneously by these methods.

Metaheuristic methods are used to obtain better convergence to improve the computational time and the optimization benefits of FACTS device optimization problems. These techniques are stochastic and very efficient, with optimized multi-objective and multi-constraint approaches. Metaheuristic optimization methods are the most commonly utilized strategy to determine the most suitable placement of FACTS controllers. These are population-based stochastic optimization approaches that are very efficient in dealing with a multimodal, strongly constrained, multi-objective, and discrete system [240,241].

Metaheuristic optimization methods are simple and make it easier to obtain an optimal solution to problems. Compared to sensitive techniques and conventional algorithms, metaheuristic approaches are easy to define and are utilized for multi-objective functions taking into account several constraints. However, this approach suffers from early convergence and a lack of accuracy [242,243].

Despite the fact that these metaheuristic methods produce the best possible solution to the FACTS device optimization problem, none of them guarantee the most effective one. Nevertheless, in their application, these approaches have too many numerical iterations to perform, and the majority of them lack some local search capabilities and suffer from a low convergence rate and also require huge computation times for large-scale problems.

Within this context, some advantages and disadvantages for several metaheuristic optimization approaches can be cited. GA is easy to use, which makes it flexible and powerful in an acceptable computation time, and trapping in the local optimum can be avoided by the right diversity of solutions. On the other hand, it is strongly dependent on the rate of crossing and mutation, which makes its convergence a little slow with no guarantee of finding the global optimum [92,103,244]. The PSO approach is easy to use, has a simple implementation, is not strongly dependent on initial points, does not have a large number of parameters to tune, and has a high chance of convergence. It is superior in terms of the placement and parameter settings of FACTS devices as well as computation time. Unfortunately, this technique exhibits a relatively slow convergence speed in its iterative process and has a poor local search capability [133,142,245]. The GSA algorithm presents a better global exploration due to its high randomness of individual movements. However, it has poor local search capability [120,124,246]. ACO is easily adapted for any environment through implementation under parallel numerical calculation and provides more reliability to solve the FACTS optimization problem. However, it may face difficulty during simulation analysis [247]. By its coding, which is relatively easy, SA can statistically guarantee the search for the optimal solution. On the other hand, its repeated annealing is very slow and it does not explicitly specify when the solution is found, and it is better to be hybridized with other techniques to obtain an optimal solution [31,131,248]. CSO is able to easily change trace and search modes to balance exploration and exploitation and is characterized by its rapid convergence. However, it has premature convergence, and therefore has the chance to fall in the local optima [38,153,154,249]. TS is characterized by an intensification or diversification of the search, capable of escaping local optima and avoiding the return to old solutions, and is applicable to discrete and continuous solutions. However, it suffers from a very high number of iterations and has several parameters to adjust [185,186,250]. CRO has the ability to generate true and well-distributed optimal solutions. Furthermore, it suffers from weak local search capability, which often involves traps in local optima. One of the advantages of CS over other optimization algorithms is that only one parameter needs to be adjusted. This means that CS can simultaneously find all optima in a design space, and the method has been proven to perform well compared to other algorithms. However, it is difficult to solve multi-objective problems, although it is able to generate a uniformly distributed initial population and its wider use by many experts in different fields. Unfortunately, the BFA has difficulty selecting the most optimal parameters and is characterized by a delay in finding the global solution. FFA is, indeed, much simpler, both in concept and implementation. Its main advantage is that it mainly uses real random numbers. However, it suffers from slow convergence and the possibility of trapping in the local domains. The ICA provides appropriate exploration and exploitation capabilities when searching for global optima, but it requires more adjustment time. Concerning IA, its way of execution, allowing a wider exploration of the search space with more diversity, makes it able to find the optimal solution. Nevertheless, it can lead to a longer computational time. The fact that the HS algorithm can take into account both continuous and discontinuous functions and does not necessitate a variable’s initial value setting is one of its advantages. The main drawback of this method appears in the greater number of iterations to find an optimal solution, which requires more computation time. The BH algorithm is simple, with fewer parameters to tune, and can be easily coded in MATLAB language. However, it is characterized by slow convergence. WCA has few parameters to control, which makes it simple and easy to use with good exploration features. On the other hand, it suffers from a weak local search capacity, because it is often trapped in local optima and it needs to be reinforced for its robustness and its consistency [55].

As a result, a number of studies have focused on the hybridization of these methods to improve the quality of large-scale problem solutions and the efficiency of optimization approaches [251,252]. It was noted that hybrid optimization approaches are more efficient, more robust, and faster to find the optimal solution. The hybrid of sensitivity methods and metaheuristic techniques are mainly utilized for solving problems. In order to reduce the size of the issue, sensitivity techniques are used to locate the buses that are most critical. The buses can be optimized using optimization techniques to select the few buses that work best with FACTS devices of the appropriate size. This method achieves a balance between speed and accuracy, enables multipurpose functions, and takes into account numerous constraints.

In addition, hybrid methods play a significant role in enhancing the search capabilities of various approaches. Hybridization aims to combine the benefits of two or more approaches while simultaneously attempting to reduce any significant drawbacks [253]. In general, there are some improvements in computational speed and accuracy as a result of hybridization [254]. However, a number of authors, such as Sai Ram Inkollu et al. [219], Ahmad Abubakar Sadiq et al. [229], Parizad et al. [234], and Divya Gupta et al. [235], favor the hybrid approach, employing numerous open-source hybrid methods. For the time being, it outperforms other heuristic, sensitive, and classical methods when it comes to finding the optimal solution for FACTS device optimization problems in a hyper search space with stable convergence characteristics and high computational efficiency. It is capable of avoiding being trapped by local optima to some extent. In addition, it smoothly converges toward the optimal state. The hybridization of two or more algorithms, on the other hand, quickly converges. Indeed, it unites all of the associated algorithms’ strengths. While adhering to some equality and inequality constraints in electrical power systems, it is computationally more efficient and offers a superior solution to the FACTS device optimization problem.

Some criticisms can be made of a few studies that do not consider the same objective function when comparing different FACTS devices. This can make it difficult to make a fair and accurate comparison between different devices and their effectiveness in power systems. It is important for researchers to use consistent and appropriate objective functions when comparing different FACTS devices to ensure that the comparison is fair and meaningful.

Additionally, many studies have focused on minimizing the production cost of power systems without taking into account the reduction of costs for the consumer. This can limit the real-world applicability of the findings and may not fully capture the benefits of using FACTS devices in power systems. It is important for researchers and practitioners to consider both production and consumption costs when evaluating the effectiveness of FACTS devices in power systems and to develop advanced algorithms that can achieve both goals simultaneously.

It is important for researchers and practitioners to carefully consider the objectives and methods used in their studies to ensure that they provide accurate and meaningful insights into the use of FACTS devices in power systems. By addressing these issues, we can improve the effectiveness and performance of FACTS devices and ultimately provide more reliable and cost-effective power systems for consumers.

Objective functions are used to evaluate the performance of different FACTS devices in power systems. The choice of objective function depends on the specific goals of the study and the characteristics of the power system being analyzed. Some examples of objective functions that researchers can use to compare different FACTS devices include:

• Voltage stability: The objective function is based on the voltage stability of the power system. The goal is to minimize voltage deviations and ensure that the voltage remains within acceptable limits.
• Power transfer capability: The objective function is based on the power transfer capability of the power system. The goal is to maximize the power transfer capability of the transmission lines and ensure that the power is delivered to the load without any congestion or overload.
• Transient stability: The objective function is based on the transient stability of the power system. The goal is to minimize the time it takes for the power system to stabilize after a disturbance or fault.
• Loss minimization: The objective function is based on the minimization of power losses in the power system. The goal is to reduce the amount of power lost during transmission and distribution and improve the overall efficiency of the system.
• Cost minimization: The objective function is based on the minimization of the overall cost of the power system. The goal is to reduce the operating costs of the system and improve the economic efficiency of the system.

The choice of objective function depends on the specific goals of the study and the characteristics of the power system being analyzed. Researchers should carefully consider the objective function used in their studies and ensure that it is appropriate for the problem being addressed.

Comparing all optimization methods utilizing FACTS devices is a challenging task due to the wide range of methods available and the complexity of power systems. However, a fair and comprehensive comparison can be achieved by using a consistent test system and objective function for all methods and by considering the impact of contingencies on the performance of the methods.

A consistent test system can provide a fair and meaningful comparison between different optimization methods. The test system should include realistic and representative components of a power system, such as generators, transmission lines, and loads. The system should also include FACTS devices, such as SVCs, TCSCs, and STATCOMs, to enable a comparison of different devices and their effectiveness in the system. By using the same test system for all methods, it is possible to compare the performance of each method under the same conditions.

A consistent objective function can also provide a fair and meaningful comparison between different optimization methods. The objective function should reflect the goals of the power system, such as minimizing production costs, reducing power losses, or improving voltage stability. By using the same objective function for all methods, it is possible to compare the effectiveness of each method in achieving the same goal.

Contingencies are events that can cause disruptions and failures in a power system, such as the loss of a transmission line or a generator. Contingencies can have a significant impact on the performance of optimization methods and should be considered when comparing different methods. By including contingencies in the test system and evaluating the performance of each method under different scenarios, it is possible to determine the robustness and reliability of each method.

A fair and comprehensive comparison of optimization methods utilizing FACTS devices should consider the convergence, time taken, accuracy, and impact of contingencies on the performance of each method. By using a consistent test system and objective function and considering the impact of contingencies, it is possible to provide a meaningful and useful comparison of different optimization methods for power systems.

Generally, the recent research based on the optimal allocation of FACTS devices has used metaheuristic optimization techniques where the problem was considered as multi-objective optimization problems. To solve this kind of problem, Pareto multi-objective optimization techniques have been suggested. However, several optimization problems are highly complex even using single-objective versions, and their multiple-objective version is often even more difficult. Thus, converting multiple objective functions into single-objective functions using the weighted sum approach has been shown to be more applicable by most recent research. In this section, recent research is discussed in detail, including the proposed and compared methods, whether they are single or multiple metaheuristic optimization techniques, objective functions, utilized FACTS devices, studied cases, or applied contingency conditions.

Concerning hybrid metaheuristic optimization techniques, a new HCRO approach based on CRO and DE was exploited in ref. [213] for identifying the best locations and sizing of UPFC devices to ameliorate system performance, namely, a reduction in power losses, voltage deviation, and production cost. IEEE 14-bus and 30-bus test networks were taken into consideration in order to assess the method’s capability and efficiency in terms of voltage profile and lowest overall cost, and a comparison of the obtained results with other techniques in the literature such as GA, IGA, PSO, and HIA was conducted. In Reference [215], for selecting the appropriate location and parameter settings of a UPFC to improve the dynamic stability in electrical networks, a hybrid method combining FA with CS named FA-CS was employed to achieve global best results for the FACTS device optimization problem. Thus, the optimal position of UPFC was identified by the FA technique; however, its sizing was identified by the CS algorithm. The FA-CS performance was evaluated through a comparison with those of various approaches such as Bat-FA, GSA-Bat, ABC-GSA, and CS techniques. The comparison consistently demonstrated the robustness of this developed approach and confirmed its potential for solving related issues. Similarly, to solve the same problem, Inkollu et al. [219] investigated a hybrid PSO-GSA optimization technique to obtain the most suitable locations and parameter settings of UPFCs and IPFCs. Once these two FACTS devices were optimized, the voltage stability was ameliorated while respecting a given set of operating and physical constraints. The robustness and applicability of this applied technique were implemented on the IEEE 30-bus test system. By comparing the results, it was shown that PSO-GSA provided better results compared to the GA-GSA thanks to its fast convergence and better performance in identifying the best global solution with less computational effort. In ref. [223], the application of hybrid IAs (HIAs) such as immune GA (IGA) and immune PSO (IPSO) were used for determining the most appropriate location and sizing of the UPFC to minimize transmission losses and operating costs. The simulation results obtained from IEEE 14-bus and 30-bus test systems were compared with those of the GA, PSO, IPSO, and IA techniques in order to assess the suggested method’s capability and efficiency. In ref. [226], hybrid-technique-based optimized FACTS devices were presented, where the ABC algorithm was hybridized with GSA to ameliorate the dynamic stability in power systems. Here, the most favorable position of the UPFC was fixed using the ABC algorithm after the identification of the maximum power loss bus. Once the UPFC was optimally placed, the GSA was used to determine the required capacity of the UPFC. The simulation results were obtained using an IEEE 14-bus and IEEE 30-bus to demonstrate the ability and robustness of this ABC-GSA technique and its potentiality for solving FACTS optimization issues compared to the separate application of ABC and GSA.

Other hybrid techniques combine multiple metaheuristic optimization techniques for the optimal allocation of FACTS devices. For instance, in ref. [216], EP and DE techniques were combined for determining the appropriate placement and sizing of FACTS controllers such as TCSCs, SVCs and UPFCs, where the objectives were the minimization of the total number of overloads, excess power flow, overloading severity, and production costs. The results obtained from the 5-bus test network with and without FACTS demonstrated that the DE approach is more effective than the EA approach in terms of a global optimum solution and computational time. In Reference [217], the incorporation of a fuzzy logic system with a DE algorithm was proposed for the planning and coordination of FACTS controllers in electrical networks under different loading conditions. The suitable placements of the TCSC and SVC were found to take advantage of fuzzy logic, whereas their parameter settings were determined using DE. The results of simulations using an IEEE 30-bus were obtained and compared with simple DE (SDE), and the significance of this proposed approach was clearly observed in terms of operating cost minimization. TLBO, ABC, and PSO evolutionary optimization techniques were proposed in ref. [54] to minimize transmission loss, reduce total installation costs, and improve the voltage profile by identifying the most suitable location and sizing of the TCSC device. Three test networks, an IEEE 14-bus, IEEE 30-bus, and Indian grid 75-bus, were applied to examine the performance of the applied techniques with and without a TCSC device. The lower losses, minimum TCSC installation costs, superior voltage profile, and lower power flow obtained using TLBO were compared with those obtained using ABC, PSO, GA, DE, EP, GSA, and NSPSO.

The choice of optimization technique can have a significant impact on the efficiency, effectiveness, and accuracy of solving the optimal location for FACTS controllers. Let us discuss each group of optimization techniques in more detail:

• Classical optimization techniques: Classical optimization techniques are well-established and widely used methods that can be used to find optimal solutions to complex optimization problems. These techniques are based on mathematical models that describe the behavior of the power system, and they can be computationally intensive. However, they are generally very accurate and can provide optimal solutions to the optimization problem. The main disadvantage of classical optimization techniques is that they may not be able to handle large-scale optimization problems, and may require significant computational resources.
• Metaheuristic methods: Metaheuristic methods are optimization techniques inspired by natural processes, such as genetic algorithms, particle swarm optimization, and simulated annealing. These methods are generally more efficient than classical optimization techniques and can handle large-scale optimization problems. They are also able to find good solutions to complex optimization problems in a relatively short amount of time. However, the solutions obtained using metaheuristic methods may not always be optimal, and may require additional refinement.
• Analytic methods or sensitive index methods: Analytic methods or sensitive index methods are optimization techniques that use sensitivity analysis to evaluate the impact of different factors on the performance of the power system. These methods are generally very accurate and can identify critical components or locations in the power system that require optimization. They are also computationally efficient, as they do not require iterative optimization procedures. However, analytic methods may not always provide a complete solution, and may require additional optimization to refine the results.
• Mixed or hybrid methods: Mixed or hybrid methods combine two or more of the above methods to address the limitations of individual methods. For example, a mixed method may use a classical optimization technique to generate an initial solution, and then refine the solution using a metaheuristic method. These methods can provide a good balance between efficiency, effectiveness, and accuracy, and can handle complex optimization problems efficiently. However, they may require significant computational resources and may be more complex to implement than single-method approaches.

The choice of optimization technique will depend on the specific characteristics of the power system and the objectives of the optimization. Classical optimization techniques are generally very accurate, but may be computationally intensive. Metaheuristic methods are more efficient, but may not always find optimal solutions. Analytic methods are very accurate and computationally efficient, but may not always provide a complete solution. Mixed or hybrid methods can provide a good balance between efficiency, effectiveness, and accuracy, but may require significant computational resources and may be more complex to implement.

An example of a mixed or hybrid method that has been used to solve similar optimization problems is the combination of genetic algorithms (GA) with classical optimization techniques, such as linear programming (LP) or nonlinear programming (NLP).

In this approach, a GA is used to generate a set of initial solutions to the optimization problem, and then the solutions are refined using LP or NLP to obtain more accurate and optimal solutions. This approach can be particularly effective for solving large-scale optimization problems that are difficult to solve using classical optimization techniques alone.

For example, in a study published in IEEE Transactions on Power Systems, researchers used a hybrid GA/LP approach to solve the optimal location problem for FACTS devices in a power system [1]. The GA was used to generate a set of initial solutions, and then LP was used to refine the solutions and obtain the optimal placement of FACTS devices.

The results showed that the hybrid approach was able to determine the optimal placement of FACTS devices with high accuracy and efficiency, and outperformed other optimization techniques, such as LP alone or GA alone.

The use of mixed or hybrid methods can be a powerful approach for solving complex optimization problems, such as the optimal placement of FACTS devices. By combining the strengths of different optimization techniques, it is possible to achieve a good balance between efficiency, effectiveness, and accuracy, and obtain optimal solutions to the optimization problem.

Optimizing the parameter settings for a hybrid approach is an important aspect of achieving optimal performance. The choice of parameter optimization method will depend on the specific characteristics of the hybrid approach and the optimization problem. It is important to carefully evaluate the performance of different parameter optimization methods to determine the most appropriate approach for a given problem.

It is common for researchers to use metaheuristic optimization techniques for determining the optimal location and capacity of FACTs devices. However, it is important to evaluate the performance of the proposed approach compared to other metaheuristic optimization techniques. This can be achieved by comparing simulation results, computational time, convergence characteristics, and result accuracy. Such comparisons can help researchers to determine the strengths and weaknesses of different optimization techniques and choose the most appropriate one for their specific application. It is also important to keep in mind that the choice of optimization technique may depend on the specific problem being addressed, and no single technique is universally superior to all others in all cases.

The total harmonic distortion (THD) reduction is an important issue related to power quality improvement, and it is often desirable to include it as an objective function in optimization problems related to FACTs devices. The inclusion of THD as an objective function can help ensure that the optimization of FACTs devices takes into account not only the improvement of power flow and voltage stability, but also the reduction of THD and other power quality issues.

It would be beneficial to consider the inclusion of THD as an additional objective function in optimization problems related to FACTs devices. This could be achieved by formulating a multi-objective optimization problem that considers both THD reduction and other power system performance metrics. The solution to such a problem would provide a set of Pareto-optimal solutions that represent trade-offs between the different objectives, allowing system planners to choose the most appropriate solution based on their specific needs and constraints.

Most of the reviewed research studies on the optimal placement and sizing of FACTs devices were conducted on balanced power transmission systems. However, it is important to note that power systems are often unbalanced, especially in distribution networks, and the performance of FACTs devices may vary in such systems. Therefore, investigating the optimal placements and settings of FACTs devices for unbalanced power transmission systems would be a valuable area of future research.

In an unbalanced system, the distribution of load and generation across the three phases of the network can be unequal, leading to voltage imbalances and other power quality issues. FACTs devices can help mitigate these issues, but their optimal placement and sizing may be different from that in a balanced system. Future research could consider the development of optimization methods that explicitly account for unbalanced conditions and evaluate their effectiveness in improving power quality and system performance.

The most recent research on the optimal allocation of FACTS devices has not explicitly considered the probabilistic nature of power systems. However, power systems are subject to a range of uncertainties, including fluctuations in load demand, renewable energy generation, and equipment failures. These uncertainties can have a significant impact on the performance of FACTS devices, and it is important to account for them in optimization problems related to FACTS devices.

To address this issue, future research could consider the development of optimization methods that explicitly account for the probabilistic nature of power systems. This could be carried out using techniques such as stochastic programming, which can incorporate uncertainty into the optimization problem by using probability distributions to model uncertain variables. By including power system predictability in the optimization problem, it would be possible to identify the best placement and sizing of FACTS devices that can provide robust and reliable performance under different operating conditions and uncertainties.

Accounting for the probabilistic nature of power systems in the optimization of FACTS devices can help ensure that the resulting solutions are more realistic and practical, and can provide better performance under a range of operating conditions and uncertainties.

7. Conclusions

In this paper, the modeling, advantages, applications, and classifications of FACTS devices are incorporated. The FACTS device optimization problem becomes a more complex, delicate, and difficult optimization problem for this field’s researchers. Therefore, a review of different optimization methods for the FACTS device optimization problem, through a bibliographical study of the different techniques used in the literature, is presented. It compares and categorizes these methods based on a variety of criteria, including the best location of FACTS devices, the type of FACTS device taken into consideration, the parameter settings, the precise function of the FACTS device in the electrical power system, and the optimization method used in the proposed methodology. In this study, a summary of recent research on the FACTS device optimization problem is taken into consideration with a description of the optimization strategy, the objectives, the FACTS devices used, the test system applied, and their benefits and drawbacks. The optimization techniques are classified into four types: classical optimization techniques, metaheuristic methods, analytic methods, and hybrid methods, which are summarized and discussed in this paper. It is clear from this limited, but thorough work and from the discussion that metaheuristic and hybrid approaches, despite having limitations in some cases in terms of convergence and computational time, are safer and more effective for solving the FACTS device optimization problem.

It is common in literature reviews to gather data from past and recent research papers to draw conclusions and provide insights into a particular topic. In this case, the paper is focused on the optimization of FACTS devices, and we have reviewed various studies to provide an overview of the current state of research on this topic.

The four points that we have mentioned are the main areas of focus in this paper. The application of series and shunt connected devices refers to the different ways in which FACTS devices can be connected to power systems to control the flow of power and voltage stability. The type of FACTS device refers to the different types of main devices that can be used for this purpose, such as SVCs, STATCOMs, TCSCs, SSSCs, IPFCs, and UPFCs. The location of FACTS devices refers to where they are placed in the power system, which can affect their effectiveness and the overall performance of the system. Finally, the optimization techniques refer to the various methods that were proposed for optimizing the performance of FACTS devices.

The test systems used in these studies vary from small-scale systems to large-scale power networks. The IEEE test systems are often used for benchmarking and comparison purposes, while real-world power systems are used to validate the effectiveness of the proposed optimization strategies.

We have provided a comprehensive review of the current state of research on the optimization of FACTS devices and have highlighted some of the key areas of focus in this field. Additionally, we have provided some insights into the future of FACTS and their applications, which can be useful for researchers and practitioners in the field.

According to this updated literature review of the optimal location and sizing of multi-type FACTS devices in power systems utilizing different optimization techniques, we can conclude that the recently developed FACTS devices can be used for electric transmission networks since they play an important role in enhancing the static and dynamic performance of power systems. However, the location, type, and capacity of FACTS devices should be optimized to maximize the resulting benefits. Thus, an improvement in the voltage profile and enhancement of power transfer capability can be obtained. The idea behind the FACTS concept is to enable the transmission system to be an active element in increasing the flexibility of power transfer requirements and in securing the stability of integrated power systems. It may also be effective in transient stability improvement, power oscillation damping, and power flow balancing in parallel lines.

The best methods that researchers can use to solve FACTS device optimization problems in power systems will be learned from this review in the future. This work might be extended in the future, especially for integrating FACTS devices into distribution systems—D-FACTS—with renewable energy sources such as solar, wind, and hydropower to mitigate congestion problems on the one hand, and on the other hand to alleviate the cost of the installation of FACTS, which is initially high. In addition, it has also been observed that FACTS controllers are less explored in terms of the smart utility grid with more advanced algorithms.