A Fully Distributed Observer Consensus Protocol for Nonlinear Multi‐Area Power Systems With Dynamic Event‐Triggered Transmission Strategy

A memory output sliding mode load frequency control (MOSMLFC) strategy is proposed for multi-area interconnected power systems under historical-frequency-triggered denial-of-service (DoS) attacks. Due to the use of the open network, the multi-area power system is prone to cyber-attacks. Different types of attack models have been built to describe the actual attack behavior, so that effective strategies can be quickly formulated in the event of an attack. Therefore, a historical-frequency-triggered DoS attacks model is presented from the perspective of attackers, with the aim of destroying the stable state of the multi-area power system. It is assumed that attackers determine the timing of DoS attacks by monitoring the operational status of multi-area power systems and designing the triggering condition with historical frequency. A MOSMLFC strategy is investigated to ensure the security performance of multi-area power systems under historical-frequency-triggered DoS attacks, which applies the memory output information of the power system to realize the controller design. The security condition of multi-area power systems under historical-frequency-triggered DoS attacks is obtained by Lyapunov’s theorem and linear matrix inequality (LMI). Numerical examples are tested over the IEEE 10-generator 39-bus system and the results prove the usefulness and superiority of the proposed method. Note to Practitioners—Load frequency control is widely applied in multi-area power systems to achieve a balance between the load demand and generation. Frequent cyber-attacks are a threat to the normal operation of the power system. It is therefore necessary to develop appropriate strategies to defend against cyber-attacks. So far, there have been many different forms of cyber-attacks. This has prompted defenders to build different types of attack models to describe the actual attack behavior in order to preemptively formulate appropriate defensive strategies. Smart attacker may notice that certain characteristics of the target system are important, such as the power system frequency. This motivates us to propose a historical frequency-triggered DoS attack model that contributes to a deep understanding of the impact of cyber-attacks on the power system. We propose a unique sliding mode control approach to ensure the stable performance of power system state and output simultaneously.

This paper presents a new decomposition and coordination algorithm based on Ward equivalent to solve distributed reactive-power optimization problem in multi-area power system. At first, multi-area interconnected power system is partitioned into master and slaver areas, boundary buses are defined as different bus types respectively corresponding to different areas, and hence the transfer method of phase angles from master area to slaver areas is determined. Secondly the initial value of equivalent injection power is obtained according to power-flow calculation at basic operating state. Then computational efficiency of the equivalent admittance matrix of external network due to change of transformer ratios is highly enhanced during optimization process by means of the inverse matrix modification lemma, and also the equivalent accuracy of external network is improved greatly. Moreover a kind of external coordination strategy which is suitable for reactive-power optimization calculation is introduced and better coordination effects with less coordination communications are obtained. Finally testing results on 538-bus practical systems is used to validate the correctness and effectiveness of the proposed algorithm in comparison with the centralized optimization method.

AIn this paper, impact of communication delay on distributed load frequency control (dis-LFC) of multi-area interconnected power system (MAIPS) is investigated. Load frequency control (LFC), as one of ancillary services, is aimed at maintaining system frequency and inter-area tie-line power close to the scheduled values, by load reference set-point manipulation and consideration of the system constraints. Centralized LFC (cen-LFC) requires inherent communication bandwidth limitations, stability and computational complexity, as such, it is not a good technique for the control of large-scale and geographically wide power systems. To decrease the system dimensionality and increase performance efficiency, distributed and decentralized control techniques are adopted. In distributed LFC (dis-LFC) of MAIPS, each control area (CA) is equipped with a local controller and are made to exchange their control actions by communication with controllers in the neighboring areas. The delay in this communication can affect the performance of the LFC scheme and in a worst case deteriorates power system stability. To investigate the impact of this delay, model predictive controller (MPC) is employed in the presence of constraints and external disturbances to serve as LFC tracking control. The scheme discretizes the system and solves an on-line optimization at each time sample. The system is subjected to communication delay between the CAs, and the response to the step load perturbation with and without the delay. Time-based simulations were used on a three-area MAIPS in MATLAB/SIMULINK environment to verify the investigations. The overshoot and settling time in the results reveals deterioration of the control performance with delay. Also, the dis-LFC led to zero steady states errors for frequency deviations and enhanced the MAIPS’ performance. With this achievement, MPC proved its constraints handling capability, online rolling optimization and ability to predict future behavior of systems.

In this paper, an optimizedType-2 fuzzy logic controller (T2FLC) is developed for load-frequency control (LFC) of multi-area interconnected power systems. In particular, theproposed controller employs the Hybrid Big Bang-Big Crunch (HBB-BC) algorithm to optimize the membership functions, which considers system uncertainties and nonlinearities. Thecomparison results under two different load disturbances using simulation show that the optimized T2FLC is superior in frequency oscillation and transmission line poweras compared to conventional PI, PID, and Type-1 fuzzy controllers. The settling time is reduced by 40% and the frequency fluctuation amplitude is decreased by 70% compared to the PI controller; the ITAE is the lowest, indicating that the T2FLC is the bestin terms of damping oscillations and guaranteeing system stability.

Maintaining frequency stability in modern multi-area interconnected power systems has become increasingly challenging due to the stochastic nature of wind power and reduced effective system inertia. Under these dynamic conditions, traditional fixed-gain PID controllers frequently fail to provide robust regulation. To address this limitation, this study proposes and evaluates a practical model-free secondary control strategy for multi-area Load Frequency Control (LFC). The proposed hybrid MFAC–PID framework integrates an incremental model-free adaptive control (MFAC) law with a low-gain incremental PID damping term. This combination leverages real-time input–output data to determine primary control actions without relying on an explicit plant model, while the PID component supplies supplementary damping based on recent control errors. Furthermore, the controller utilizes online pseudo-gradient estimation to dynamically adapt to stochastic wind fluctuations and ±5% parametric uncertainty. Simulation results demonstrate that the hybrid design substantially enhances Area Control Error (ACE) regulation. Under wind-disturbed conditions, it reduces the aggregated Integral Absolute Error (IAEtotal) from 92.76 to 41.10, representing an improvement of over 50% compared with the fixed-gain PID baseline. Additionally, the controller maintains a low computational overhead of 0.306 milliseconds per control cycle. These findings indicate that the hybrid MFAC–PID structure provides a robust, computationally efficient solution for real-time Automatic Generation Control (AGC) in renewable-integrated multi-area power grids.

Electric vehicles (EVs) can be employed intelligently in Vehicle-to-Grid (V2G) and Grid-to-Vehicle (G2V) modes for Load Frequency Control (LFC) in the power grid. Due to the rapid variation of charging or discharging power, EVs can perform frequency regulation tasks and serve as distributed energy storage devices. In this paper, a linearized model of an interconnected multi-area power system is formulated in the restructured environment to include Electric Vehicle Aggregators (EVA). The DISCO Participation Matrix (DPM) is used to model Poolco and bilateral contracts in restructured multi-area power systems along with the participation of EVs. The faster dynamic response of EVs can effectively control the deviations in area frequencies imposed by the DISCOs load demand. The gains of the integral controller employed in each area are tuned by Real Coded Genetic Algorithm (RGA) by minimizing the integral square error function for area frequency deviations. The efficacy of power support from the EVs for load frequency control is validated by simulating different Poolco and bilateral transactions. It is shown that the EVs have a significant impact on obtaining optimal transient response for area frequencies, tie-line powers and power generation of conventional thermal generating units for any type of transaction in a restructured environment.

Load frequency control is one of the most important issues in multi area power systems. In this context, due to growing development of wind turbines in power systems, this type of renewable power sources can be used efficiently in frequency control. This paper applies doubly-fed induction generators (DFIGs) along with other conventional generation units for frequency performance enhancement after disturbances in multi-area power systems. Proportional integral (PI) controller is the conventional controller which is used in DFIGs to contribute in frequency control. The parameters of PI controller for DFIG are optimized by improved particle swarm optimization (IPSO) method. Simulation results in a three-area power system illustrate the efficiency of the DFIGs for frequency and tie-line power oscillations improvement.

In this paper a new bilinear and nonlinear second-order state observer which is globally asymptotically stable is constructed to estimate the unmeasurable state variables. Then an unstable controlled current induction motor drive system which cannot be stabilized by a linear state observer is successfully stabilized by feeding the reconstructed state variables from the nonlinear observer to the frequency control channel. This scheme is easily implementable, resulting in an asymptotically stable overall closed-loop system. These results are numerically verified by simulation.

A nonlinear state observer can be used as a resolver-to-digital converter (RDC); however, when the speed is not constant, its performance deteriorates. In this paper, a composite state observer is presented. The estimation speed from the nonlinear state observer is compensated by the estimation speed from the arctangent method in the feed-forward form. Compared with the arctangent method, this method has a strong ability to suppress random disturbances. Compared with an RDC based on a nonlinear state observer, the accuracy of the angle and speed is improved as the appearance of phase delay is weakened. Experiments demonstrate the effectiveness of the observers.

Adaptive event-triggered PID load frequency control for multi-area interconnected wind power systems under aperiodic DoS attacks

The state of charge (SOC) estimation of lithium‐ion batteries is complex due to the various nonlinear uncertainties present in the battery. However, in this paper, a new nonlinear state observer (NSO) is proposed to be designed for the estimation of accurate and robust SOC. This proposed observer is suitable for both continuous and discrete‐time nonlinear systems. To design the nonlinear observer, two‐RC equivalent circuit model state equations are simulated for the dynamic behavior of the lithium‐ion battery. The seventh‐order polynomial fitting approach is assumed for the nonlinear relationship between open‐circuit voltage (OCV) and SOC, and the exponential fitting method is used to estimate the battery's offline parameters. Lyapunov's stability criterion achieves the stability and convergence capability of the proposed method. An urban dynamometer driving schedule (UDDS) cycle was adopted to estimate the performance of the proposed observer by comparing it with the well‐established methods like unscented Kalman filter (UKF) and sliding mode observer (SMO) algorithms, and it was found that the proposed observer achieved better performance like accurate SOC, high convergence capability, and less SOC error.

A new mechanism for remedial action schemes design in a multi-area power system considering competitive participation of multiple electricity market players

The integration of electric vehicles (EVs) into power systems via vehicle-to-grid (V2G) technology offers new opportunities for bidirectional energy exchange and resource allocation. However, time delays and adversarial attacks in communication networks can undermine the coordination of EV aggregators and power systems. To address this challenge, this paper presents a hybrid counterfactual learning approach for control of EV aggregators in the multi-area power systems V2G and load frequency control (LFC) framework. The proposed hybrid approach integrates counterfactual multi-agent learning, adversarial training, and monotonic neural network (CMA-HMNN). The multi-agent counterfactual learning marginalizes the impact of individual actions on the overall reward, thereby better coordinating controllable resources and reducing variances in adversarial multi-agent training. By enforcing deviation-command monotonicity constraints within the neural network architecture, the proposed approach can satisfy Lyapunov stability conditions and improve the stability of power systems with integrated EVs. Adversarial training based on the fast gradient sign method (FGSM) is applied to enhance the robustness of the networks against perturbations. Even under concurrent time-varying communication delays and malicious threats from communication networks, the method effectively coordinates multiple generation resources and EV aggregators. Compared with four DRL-based control methods, the superiority of the proposed method is verified on the three-area power system and IEEE 39-bus power system with wide EVs integrations.

The voltage stability of large scale renewable energy grid-connected system plays a major role in a power system environment. Nowadays, Integration of large scale wind power may have severe impacts on the power system operation. Stable, reliable and economic operation of the power system under the massive integration of wind power is a big challenge to power system operators. This paper seeks to study the voltage stability problems for the integration of wind power and Photovoltaic (PV) to the IEEE-14 bus network. Modern analytical tools are demonstrated to study voltage stability analysis by using PV analysis and dynamic analysis. Comparative study is developed to present the behavior of voltage stability of the system that employs PV and different types of wind farms. These analyses define the amount of reactive power required to enhance voltage stability. Simulation of 14-IEEE network with integrated renewable energy sources is developed using PSS/E.

Information and communication technology tremendously facilitates the operation efficiency and economy of modern power systems in recent years. However, risks such as bandwidth constraints and malicious attacks threaten the secure load frequency control (LFC) of power systems. To mitigate such risks, this paper proposes distributed observer-based event-triggered LFC schemes for multi-area power systems under cyber attacks. Considering the practical situation that only local system output information may be available, distributed observer-based LFC schemes are designed. Meanwhile, to reduce the communication burden, an event-triggered mechanism is adopted to design control laws, where both static and dynamic event-triggered approaches are taken and the dynamic one is proved to be more economical in terms of control cost. Verifiable sufficient conditions are established to guarantee the stability of the closed-loop system in the presence of cyber attacks and the controller gains are explicitly derived. Finally, validation studies on a three-area interconnected power system are carried out to demonstrate the proposed control schemes. Note to Practitioners—Load frequency is a crucial index for evaluating the quality of electric energy and thus LFC has brought considerable attention in the area of power systems control. Although many achievements have been made on the LFC of multi-area power systems, the risks such as bandwidth constraints and malicious attacks affect the normal operation of LFC due to the interconnection between different power systems. To deal with these risks, this paper focuses on designing event-triggered LFC to guarantee the stability of the frequency deviation while reducing the communication burden and mitigating cyber attacks. More importantly, the proposed event-triggered LFC is designed based on an observer and can be implemented in a distributed manner, which is relatively practical in real applications. The results presented in this paper aim to provide a helpful reference for stable and secure LFC design of multi-area power systems, such that the corresponding application research can be promoted.