Search Results (198)

The coupling of power and natural gas infrastructures introduces gas-side constraints and cyberattack risks into load frequency control (LFC). This paper proposes an auxiliary Kalman filter (AKF)-based tube-based MPC (TMPC) framework for gas–electricity coupling systems under gas pressure false data injection attacks (FDIAs). A pressure-dependent gas turbine (GT) power limit is incorporated into the frequency control constraint, and an auxiliary pressure model is identified from attack-free data as a virtual pressure sensor. Residuals, normalized innovation squared statistics (NIS), and cumulative sum (CUSUM) statistics are used for attack detection, while compromised pressure measurements are reconstructed using the AKF estimates. Simulations on a two-area power system coupled with an 11-node gas network show that under attack-free operations, the integral absolute error (IAE) values of TMPC, conventional MPC, and PI control are 0.7040, 1.9626, and 2.9834 Hz·s, respectively. Thus, TMPC reduces the accumulated frequency deviation by approximately 64% and 76%, compared with conventional MPC and PI control, respectively. Under FDIAs, the IAE decreases from 1.1645 to 0.7039 Hz·s after AKF-based pressure reconstruction, corresponding to an approximately 40% reduction. Meanwhile, the mean absolute error (MAE) of gas pressure reconstruction decreases from 0.1714 to 0.0157 bar, corresponding to an approximately 91% reduction in pressure reconstruction error. Compared with the denoising autoencoder (DAE) and graph signal recovery approaches, the proposed method achieves the highest detection rate of 98.39%, effectively limiting FDIA propagation to GT constraints and frequency regulation. Full article

This paper studies performance analysis and load frequency control (LFC) for a Takagi–Sugeno (T-S) fuzzy power system equipped with an energy storage unit. A corresponding T-S fuzzy representation of the system is constructed. Subsequently, a new lemma of slack Lyapunov function is constructed, which relaxes the conventional positive-definiteness requirement on the quadratic form, provides additional flexibility in the LMI formulation, and yields less conservative stability conditions. In addition, a genetic-algorithm-based outer search is employed to optimize the scalar parameter $\varrho$, while the associated LMIs are solved using the LMI solver, thereby reducing the conservatism of the stability conditions and enlarging the maximum allowable delay bound. Simulation cases are finally presented to confirm the feasibility and effectiveness of the proposed methods. The proposed method increases the maximum allowable delay bound by $2.6920\%$, $4.0220\%$ and $4.0528\%$ compared with the reference method for the tested controller parameters. Full article

Recently, microgrid (MG) structures include a mix of renewable energy sources (RES) and conventional sources. At high levels of RES penetration, reduced inertia and frequency stability have been confirmed in several studies. Properly designed and structured load frequency control (LFC) and virtual inertia control (VIC) are feasible solutions to these problems. In this paper, a new hybridized two-degree-of-freedom (2DOF) non-integer controller is proposed for multi-generation, multi-area MGs’ frequency regulation. The proposed new LFC is based on a 2DOF tilt-integral/tilt-derivative-double-derivative controller with a filter (TI-TD²F²). Meanwhile, the proposed design process considers coordinating capacitive energy storage (CES) to help regulate frequency deviation, as well as the high penetration of RESs (wind and PV). The incorporation of CES participation in frequency regulation helps provide fast VIC for the studied multi-MG system. Furthermore, an Enhanced Escape Algorithm (EESC) optimization algorithm is proposed to simultaneously optimize the control parameter set of the two-area MG system. The proposed EESC optimization algorithm identifies appropriate parameters for controller design, yielding better overall dynamic performance. An enhanced Escape Algorithm (EESC) is based on boosting the searching mechanism of the conventional Escape Algorithm by the integration of three modifications, including the Chaos map logistic mutation mechanism, the Fitness distance balance mechanism, and the Sorted Quasi-oppositional based learning (SQOBL). The proposed 2DOF TI-TD²F² controller demonstrates improved frequency stability and sustainable operation under load changes, variation in RESs, and other uncertainties of system parameters. The obtained results showed that the proposed EESC optimization algorithm adjusts the parameters of the TI-TD²F² controller, which significantly improves the dynamic performance in load frequency and tie-line power control. Compared to traditional TID and FOPID controllers, TI-TD²F² achieves up to a 70–80% reduction in tie-line power deviation and up to 60% faster settling time in many scenarios, demonstrating better robustness, faster response, and better overall system stability. Full article

Load Frequency Control (LFC) is critical for maintaining stability in smart grids (SGs) against complex hybrid (deterministic and/or stochastic) cyber-deception attacks. This paper presents a new approach to handle such a complicated problem via trajectory tracking of the response of a pre-designed ideal attack-free model. This method guarantees robust tracking in LFC and desired transient behavior (e.g., rising time, settling time). More precisely, the optimal attack-free model’s response is controlled by the chosen control strategy as a result of load variations. The output of such a model is used online to clean up the cyber-deception attacked output of the system. The cleaned output is then used to estimate the states of the system using the recently developed Regularized Least Squares (RLS) observer. Then, a control strategy is proposed to ensure a trajectory tracking mechanism where the cyber-attacked system is forced to follow the trajectories of an ideal attack-free reference model. Unlike other approaches, which attenuate the effect of cyber-attacks, the present approach eliminates the distortions created by these attacks completely. The stability of the proposed scheme is rigorously analyzed, and its efficacy is validated through the application of an isolated power system. Full article

The problem of load frequency control (LFC) becomes more severe with the extensive integration of photovoltaic (PV) generation owing to the intermittent nature of the source. In this study, a machine learning approach is developed to design the proportional–integral–derivative (PID) controller of a two-area PV–thermal LFC system, extending a prior proportional–integral (PI) benchmark to full PID action. A Random Forest model is trained to predict the relationship between the six PID gains and the closed-loop integral of time-multiplied absolute error (ITAE), yielding an accurate performance model (test R² = 0.933) that is subsequently searched by a metaheuristic optimizer to determine the controller gains; the resulting controller is termed ML-PID. The novelty of the approach lies in employing the learned model not as a controller or a physical-quantity predictor, as in existing ML-based LFC studies, but as a reusable performance model that maps the controller gains directly to the closed-loop index and guides the PID design. To isolate and quantify the contribution of the learned model, the same three optimizers, namely the Cheetah Optimizer (CO), the Grey Wolf Optimizer (GWO), and Particle Swarm Optimization (PSO), are also applied directly to the plant, yielding purely metaheuristic controllers (CO-PID, GWO-PID, and PSO-PID) that are compared against the machine learning-assisted designs under identical algorithms and computational budget, with CO selected on the basis of the Friedman and Wilcoxon tests. The proposed ML-PID-CO controller attains the minimum ITAE under a step-load disturbance, approximately 70% lower than that of the reference SCHO-PI controller and comparable to the directly optimized controllers, with reduced control effort. Under a simultaneous variation in the plant time constants, it is the most robust of all controllers, exhibiting the smallest Δf₁ undershoot and a performance that degrades about 4.2 times less than that of the reference. The results show that a learned performance model provides a good and reusable basis for PID design. It can be searched over repeatedly once built and reduces the per-design simulation burden relative to direct metaheuristic tuning, while the design is largely independent of the optimizer used. Full article

Load frequency control (LFC) plays a critical role in maintaining frequency stability and regulating power transfer between interconnected areas subjected to continuous load variations. In multi-area systems, disturbances tend to propagate through interconnected tie-lines rather than remaining restricted locally, often leading to slower responses and weak coordination when conventional controllers are employed. In this paper, a two-degrees-of-freedom fractional-order differential integration (2DOF FO-TID) controller is proposed to improve both frequency regulation and dynamic interaction. The structure enables independent tuning of tracking and disturbance rejection, allowing greater flexibility in shaping system response. The controller parameters are optimally tuned by the Artificial Ecosystem Optimization (AEO) algorithm. The proposed approach is evaluated on a two-area hybrid thermal power system incorporating an SMES unit within the MATLAB/Simulink (R2022b) environment and compared with PID, FOPID, and TID controllers under identical conditions. The results indicate that, although some conventional controllers provide faster stabilization in one area, their performance in the interconnected area remains slower. In contrast, the proposed controller achieves more robust behavior across both areas, with the settling time of the second area reduced from about 25 s to nearly 11 s without degrading the response of the first area. These results highlight the importance of coordination in multi-area systems and demonstrate that the proposed approach enhances overall system performance and damping compared to conventional methods. Full article

This paper presents an adaptive and flexible Automatic Generation Control (AGC) scheme designed for power system splitting and reconnection. The proposed AGC remains fully operational throughout grid splitting, maintaining independent control over each separated area and supporting the transition toward reconnection through improved Area Control Error (ACE) and frequency recovery. It detects splitting by analyzing the frequency coherency of generating units and then autonomously configures the operational mode of each area in accordance with ENTSO-E rules. It applies an adaptive PI controller whose integral gain ($I_{\mathrm{GAIN}}$) is dynamically selected from a lookup table developed through offline tuning and correlation analysis to accommodate various grid configurations. Additionally, during splitting, the AGC performs adaptive reserve activation in each area, rather than relying on predetermined market-based reserve activation. The proposed AGC scheme is validated within a software-in-the-loop (SIL) environment using a representative model of the Turkish Transmission System. The results show that the proposed AGC maintains continuous and adaptive load frequency control (LFC) and improves reserve deployment in both interconnected and isolated operating modes of multi-area power systems. The proposed scheme reduces ACE recovery time by up to 87%, mitigates overshoots, and accelerates frequency recovery. These results demonstrate the scheme’s ability to maintain continuous AGC operation, improve frequency and ACE recovery, and satisfy the adopted ENTSO-E operational performance criteria under splitting conditions. Full article

To achieve optimal performance of load frequency control (LFC), a data-driven scheme is proposed for renewable power systems in this paper. A multi-agent Actor-Double-Critic deep reinforcement learning approach is developed to ensure real-time scheduling that complies with system safety operation constraints within the multi-area LFC power system. For implementation, each individual controller only needs local information in its control area to deliver optimal control signals. A Self-Critic and Cons-Critic network is employed to improve the convergence speed during the multi-agent training process. Simulations on two-area and three-area LFC power systems are performed to verify and validate the analytical results. Comparisons with conventional PI and fuzzy PI controllers demonstrate that the presented approach effectively reduces training difficulties, guarantees the satisfaction of system safety constraints, and significantly improves the dynamic frequency regulation performance of the power system. Full article

The increasing penetration of renewable energy sources introduces significant variability, low-inertia behaviour, and operational uncertainty into modern power systems, resulting in frequent frequency deviations and degraded dynamic stability. Conventional Load Frequency Control (LFC) approaches based on fixed-parameter PID controllers often exhibit limited disturbance rejection capability under nonlinear and stochastic operating conditions. This study proposes an enhanced LFC framework that integrates a PID controller optimised using the Flower Pollination Algorithm (FPA) with support from a Unified Power Flow Controller (UPFC) and a Redox Flow Battery (RFB) to improve frequency regulation, damping, and robustness in renewable-integrated low-inertia power systems. This study developed a MATLAB/Simulink single-area power system model comprising governor, turbine, and generator-load dynamics to evaluate controller performance under a 0.01 pu step disturbance, stochastic load variations, renewable energy fluctuations, and ±20% parameter uncertainty conditions. The FPA optimally tuned the PID controller gains using the Integral Time Absolute Error criterion to enhance transient response and disturbance rejection capability. Comparative analyses were conducted against conventional PID and fuzzy-based controllers using settling time, overshoot, RMS deviation, ITAE, and mean frequency deviation indices. Simulation results demonstrate that the proposed FPA–PID + UPFC framework significantly outperforms the conventional PID controller by achieving approximately 66.6% settling-time reduction, 72.1% RMS reduction, and 75.5% ITAE reduction. The proposed framework reduced settling time from 18.46 s to 6.16 s and substantially improved damping performance under stochastic disturbances. The coordinated integration of the UPFC and RFB further enhanced transient stability through dynamic power-flow regulation and rapid active-power compensation during disturbances. Sensitivity analysis under parameter uncertainty and stochastic operating conditions confirmed stable and reliable operation under stochastic disturbances and parameter uncertainty conditions. The proposed architecture, therefore, provides an effective, practically applicable solution for secondary frequency regulation in renewable-rich smart grids, low-inertia transmission systems, microgrids, and future distributed power networks. Full article

The increasing integration of renewable energy sources into interconnected multi-area power systems (IMAPSs) has led to a significant reduction in synchronous inertia, making frequency regulation considerably more challenging. While existing studies have explored the use of integral sliding mode load frequency control (ISMLFC) schemes to stabilize area frequency and tie-line power flows in IMAPSs, these approaches predominantly rely on conventional two-phase sliding mode control. Such methods, however, have demonstrated notable limitations in maintaining the stability of IMAPSs under increasingly complex operating conditions. In addition, all the IMAPS state variables must be measured, which can cause difficulty in real IMAPS applications. Therefore, this study proposes a novel load frequency control (LFC) strategy that coordinates the single-phase sliding mode control and state observer methods to solve these above limitations. First, a dynamic IMAPS model with single phase sliding mode control based on state observer scheme is established under renewable resource uncertainties and load disturbances. Then, a novel linear matrix inequality (LMI) based on Lyapunov functional is constructed to analyze the stability of the IMAPS. Furthermore, the decentralized single-phase sliding mode load frequency control (DSPSMLFC) method is developed for the LFC of the ISMLFC. Finally, three testing scenarios are employed to verify the efficiency and advantage of the proposed DSPSMLFC approach in MATLAB/Simulink R2023a. The simulation results confirm that the proposed DSPSMLFC scheme can improve the LFC of the IMAPS under renewable resource uncertainties and load disturbances. Full article

In modern power-system load frequency control (LFC), proportional–integral–derivative (PID) controllers are widely used because of their simple structure and ease of implementation. However, the combined effects of communication delay and nonlinear constraints can degrade control performance. To address this issue, this paper proposes a model-constraint-aware optimal PID tuning method based on a Hybrid Differential Evolution–Chaotic Grey Wolf Optimizer (HDE-CGWO). First, a nonlinear LFC model incorporating data sampling, communication delay, governor deadband (GDB), and generation rate constraint (GRC) is established, and a PID-based LFC model is formulated. Next, an objective function based on the integral of time-weighted absolute area control error (ACE), namely ACE-based integral of time-weighted absolute error (ITAE), is constructed. Accordingly, quasi-opposition-based learning (QOBL), chaotic warm-up, Lévy flight, and differential evolution (DE) are incorporated into the standard Grey Wolf Optimizer (GWO) to develop an HDE-CGWO-based PID design scheme for LFC under sampled-data delay and nonlinear unit constraints. Finally, simulation studies are carried out on a multi-area LFC system. The resulting time-domain responses and statistical results show that, compared with standard GWO in the single-area test, HDE-CGWO reduces the ACE-based ITAE by about 43.3%. In the three-area system, the ACE-based ITAE is reduced by about 3.0% under step disturbances and about 1.4% under random disturbances compared with the warm-up Grey Wolf Optimizer (WGWO), indicating that the proposed method can reduce frequency deviations, attenuate post-disturbance oscillations, and accelerate the dynamic recovery process under the considered disturbance conditions. Full article

Reliable load frequency control (LFC) in interconnected hybrid power systems remains challenging in the presence of nonlinear operating conditions, random demand variations, and parametric uncertainty. This study proposes a PSO-based LFC framework for a two-area hybrid power system and examines its performance through two successive stages. In the first stage, a Particle Swarm Optimization (PSO)-tuned Fuzzy PID controller is developed and benchmarked against reported Fuzzy-PIDF schemes optimized by MPA and COR. In the second stage, three PSO-tuned hybrid fuzzy structures, namely Fuzzy PI-PD + PID, Fuzzy (PI + PD) + PID, and Fuzzy PI + Fuzzy PD + PID, are formulated and comparatively assessed under identical operating conditions. The examined cases include nominal linear operation, Governor Dead Band (GDB) and Generation Rate Constraint (GRC) nonlinearities, random load disturbance, and seven parametric uncertainty scenarios. In the first stage, the PSO-tuned Fuzzy PID controller attains an ITAE of 0.00003433 under linear conditions and 0.00003822 under GDB/GRC nonlinearities, while yielding lower cumulative error than the benchmark controllers. In the second stage, the Fuzzy PI-PD + PID structure records the lowest ITAE and the shortest settling time, with ITAE = 0.000003655 and ST = 0.4234 s under nominal conditions, and ITAE = 0.000004063 and ST = 0.4519 s under nonlinear conditions. Under parametric uncertainty, its ITAE ranges from 2.482 × 10⁻⁶ to 4.833 × 10⁻⁶ with the nominal gains retained. Overall, the results indicate that the proposed PSO-based framework provides improved LFC performance within the examined linear, nonlinear, random-disturbance, and parametric-uncertainty scenarios for the studied two-area hybrid power system. Full article

Wind power uncertainty can significantly deteriorate the frequency regulation performance and robustness of load frequency control (LFC) systems, particularly in the presence of communication delays. However, most existing studies rely on simplified wind power fluctuation models, which cannot adequately capture the segmented and stochastic characteristics of wind speed variations. As a result, the resulting robustness analysis may deviate from practical operating conditions, leading to controller designs that are less reliable and less effective in real-world scenarios. To address this issue, this paper develops a robust controller co-design framework for delayed LFC systems under wind power uncertainty. First, a probabilistic wind power model with wind speed segmentation characteristics is established, and electric vehicles are incorporated into frequency regulation to construct a multi-area delayed LFC model. Then, a robust performance index is introduced to quantify disturbance rejection capability, and a genetic algorithm–particle swarm optimization-based collaborative optimization strategy is employed to determine controller parameters efficiently. Simulation results on both single-area and two-area LFC systems demonstrate that the proposed method achieves superior frequency regulation performance and stronger robustness against wind disturbances and time delays compared with designs that neglect wind uncertainty. Quantitatively, compared with controllers designed based on simplified wind power modeling, the proposed design framework reduces the normalized integral of time multiplied absolute value of the error (ITAE), integral of squared error (ISE), and integral of absolute error (IAE) indices by approximately 17.4% and 9% on average in the single-area and two-area cases, respectively. Full article

The increasing integration of intermittent renewable energy sources (RESs) into islanded Hybrid Power Systems (HPSs) is a critical step towards global energy sustainability; however, it poses significant challenges to frequency stability owing to low system inertia and stochastic power fluctuations. To address these challenges and enable higher penetration of green energy, this study proposes a novel and robust Load Frequency Control (LFC) strategy based on the Crested Porcupine Optimizer (CPO). A customized Mode-Dependent Adaptive Balloon (MDAB) controller is developed, wherein the virtual control gain is dynamically tuned based on the real-time operating modes and disturbance severity. Furthermore, to optimize communication resources and mitigate actuator wear in networked microgrids, an intelligent event-triggered (ET) mechanism is seamlessly integrated into the adaptive logic. The proposed control framework is rigorously validated through comprehensive nonlinear simulations and comparative analyses with state-of-the-art metaheuristic algorithms (GTO, GWO, JAYA, and GO). The evaluation encompasses step load disturbances, severe parametric uncertainties (+25%), realistic 24-h diurnal cycles with solar cloud shading and wind turbulence, and extended practical constraints, including Battery Energy Storage System (BESS) integration and Internet of Things (IoT) communication delays. The results demonstrate the superiority of the CPO-tuned framework, which achieved the fastest transient recovery (settling time of 3.4367 s) and the lowest absolute Integral Absolute Error (IAE). Additionally, the proposed ET-based strategy not only reduced the communication burden but also improved the overall control performance by 37% in terms of IAE compared with continuous approaches. By inherently filtering measurement noise, mitigating control signal chattering, and maintaining resilience under nonideal latency, the proposed architecture offers a highly robust and resource-efficient solution that directly guarantees the operational sustainability and reliability of modern smart microgrids. Full article

Synchronous Alternating Current (AC) power systems are increasingly supported by embedded High-Voltage Direct Current (HVDC) links to enhance operational flexibility and ensure security of supply. However, the loss of High-Voltage Alternating Current (HVAC) interconnections in these synchronous areas may lead to transmission network splitting, posing serious challenges to frequency stability due to the reduction in overall system inertia and stiffness. In this paper, a supplementary control layer is proposed to enable embedded HVDC systems, particularly those based on modern Voltage Source Converters (VSCs), to support frequency stability under post-splitting conditions. The proposed control strategy combines Angle-Difference Control (ADC), Frequency-Difference Control (FDC), and feedforward action, enabling fast and coordinated active-power modulation. A single-bus, dynamic multi-area Load Frequency Control (LFC) model is developed, combining the regulation of thermal units, Renewable Energy Sources’ (RESs’) Fast Frequency Response (FFR) with Synthetic Inertia (SI), and VSC-HVDC modulation. The effectiveness of the proposed control layer is demonstrated by applying it to the East Tyrrhenian Link (ETL), an embedded VSC-HVDC interconnection connecting Sicily with the mainland of Italy, under a post-splitting low-inertia condition in which Sicily operates as an islanded synchronous system, i.e., after losing synchronism with the mainland of Italy, in a 2030 scenario condition. The simulation results demonstrate that the proposed controller enables embedded VSC-HVDC systems to actively participate in post-splitting frequency containment and damping, as well as coordinated active power reallocation, thereby enhancing overall system stability and resilience. Full article