Load Frequency Control System Research Articles

Design of control systems with multiple memoryless nonlinearities for inputs restricted in magnitude and slope

This paper develops a methodology for designing a control system composed of a linear time-invariant system interconnecting with multiple decoupled time-invariant memoryless nonlinearities. The design problem is to determine parameters of the system such that its outputs and the nonlinearity inputs always remain within prescribed bounds for all exogenous inputs whose magnitude and slope satisfy certain bounding conditions. By using Schauder fixed point theorem, we show that a design associated with a linear system is also a solution of the problem. Based on this, we further develop surrogate design criteria in the form of the inequalities that can readily be solved in practice. Sufficient conditions for the solvability of such inequalities are given for deadzone and saturation. To show the usefulness and the effectiveness of the methodology, a design example of a load frequency control system with time delay is carried out where deadzone and saturation are taken into account.

Renewable Energy‐Based Load Frequency Controller and Model with a Reduced Order for a Large‐Scale Power System

Power system stability relies heavily on load frequency control (LFC) because it ensures that the power generated in a grid matches the load demand. The conventional LFC methods are no longer adequate with the rising use of renewable energy sources like wind and solar power. These resources are intermittent, and their power output varies depending on weather conditions. As a result, incorporating renewable energy resources (RERs) into the LFC system necessitates a different approach. One method is to use advanced control algorithms that can respond quickly to changes in power output. Hence, this article proposes an autoencoder‐based jellyfish optimization developed in this framework to reduce the power outage and control voltage and frequency fluctuations. The LFC system can be optimized by combining autoencoder and jellyfish optimization techniques to effectively handle the variability and unpredictability of RERs while maintaining the power system's stability and reliability. This approach may also result in more efficient and cost‐effective power system operation by reducing the need for conventional power generation and minimizing the impact of RERs on the system.

Resilient Event-Triggered Load Frequency Control for Cyber-Physical Power Systems Under DoS Attacks

In cyber-physical power systems (CPPSs), additional control as the compensating control plays a very important part in load frequency control (LFC) systems. The additional control in the LFC system is constrained by limited communication resources and cyber-attacks, which may cause performance degradation or destabilize the system. Accordingly, this paper proposes resilient event-triggered LFC for CPPSs with an additional control loop under denial-of-service (DoS) attacks. Firstly, a resilient event-triggered communication scheme is presented to reduce the occupation of communication resources under DoS attacks in the additional control loop. Then, different from existing event-triggered LFC systems, this paper establishes a novel switched LFC system model, where the resilient event generator is integrated into an additional control loop when suffering from DoS attacks. It is the first time that the additional control loop of the LFC system simultaneously considers communication resources and cyber-security. Furthermore, we derive exponential stabilization criteria by applying the Lyapunov stability theory based on the established model. Criteria are derived to obtain the weighting matrix and controller gain simultaneously by applying the linear matrix inequality technique. Finally, a one-area and two multi-area CPPSs with the additional control loop under DoS attacks are used to testify the availability of the proposed resilient event-triggered LFC scheme.

Black Widow Optimization for Power System Load Frequency Control: A Comparative Study

This research paper mainly engrossed on developing a suitable novel tuning methodology named Black Widow Optimization (BWO) Algorithm for power system optimization problems. Load Frequency Control (LFC) and Automatic Voltage Regulator (AVR), two of the most important control systems in the power system arena, are employed as test systems to assess the efficiency of the suggested BWO approach. Various analyses, such as transient analysis, are employed to evaluate the efficiency of the suggested BWO approach in LFC and AVR systems. robustness analysis and convergence analysis. The significant performance measures of test system such as output power of each generating unit, maximum peak, settling time, steady state error, rise time and voltage/frequency deviations of the frequency and voltage responses are considered for the comparison purposes. The comparative analysis clearly demonstrates that the proposed novel tuning methodology provides better transient performances subjected to Step Load Perturbations (SLP), Variable Load Perturbations (VLP), and robustness performances under a wide range of load and parameter changes ranging from -50% to +50%. The convergence analysis of BWO algorithm also performed in LFC and AVR test systems and results better convergence characteristics with minimal convergence time as well as least fitness value is obtained with the BWO algorithm.

Optimization of Load Frequency Control Gain Parameters for Stochastic Microgrid Power System

Interconnected multi-area microgrids are vital for the future of sustainable and reliable power systems. Effective load frequency control (LFC) is indispensable for ensuring their stable operation. This paper introduces a PID-based LFC system tailored for a stochastic microgrid with diverse power sources, including solar, wind, diesel engine generators, and electrical batteries. The gain parameters of the proposed microgrid PID LFC controller are optimized using genetic algorithms (GA), teaching learning-based optimization (TLBO), and cohort intelligence algorithms. Integral time-multiplied absolute error (ITAE) and integral time-squared error (ITSE) serve as the cost functions for all optimization algorithms. The study evaluated the performance of these optimized microgrid PID LFC configurations under random step load disruptions. Our primary findings reveal that the cohort intelligence-optimized PID LFC controller excels in minimizing computation time (upto 76% and 94% lesser than GA and TLBO respectively) and exhibits superior robust response characteristics. Moreover, the cohort intelligence algorithm requires fewer iterations (upto 66% and 90% lesser than GA and TLBO respectively) and enhances power supply quality within the multi-power microgrid electrical framework, specifically in terms of effective load frequency control.

Optimizing the Load Frequency of a Two-Area Interlinked Power System using Artificial Intelligence Techniques

Power costs are increasing on a daily basis, generating changes in system frequency and causing serious concerns with system stability. It has become a major problem to offer customers with uninterrupted and high-quality power. To mitigate these issues, a linked power system's load distribution and network frequency should be constantly reviewed. Load frequency control adjusts the generator's energy output and tie line power between prescribed limits. As well as regulating generator output power, load frequency control also adjusts tie line power. The disturbance in the frequency due to different load changes is regulated using the proposed scheme. In this article, a two-area load frequency control system is constructed and evaluated using various control approaches, including a proportional integral derivative (PID) controller, a proportional integral (PI) controller, a fuzzy logic-based controller, and an Artificial Neural Network (ANN). The goal is to assess the power system's resilience under different loading conditions with these control schemes. The performance of the controllers is compared based on peak-undershoot, peak-overshoot, and settling time, focusing on tie line power and frequency response. To achieve this, the design is implemented using MATLAB/SIMULINK software.

Data-driven load frequency cooperative control for multi-area power system integrated with VSCs and EV aggregators under cyber-attacks

This paper proposes a cooperative load frequency control (LFC) strategy based on a multi-agent deep reinforcement learning (MADRL) framework for the multi-area power system in the presence of voltage source converters (VSCs) and electric vehicle (EV) aggregators under cyber-attacks. Different from the existing LFC model, a novel transfer function of VSCs is first improved by the space-vector technique and integrated with EV aggregators to develop a multi-area training environment. By installing the agent in different control areas and interacting state transition information between agents and the new environment, the MADRL-based control strategy is achieved for centralized training and decentralized execution. Thus, the proposed MADRL method can coordinate thermal turbines, VSCs, as well as EV aggregators in the different control areas. Furthermore, a suitable cyber-attack model that can circumvent bad data detection (BDD) is reconstructed according to the perspective of adversaries for the LFC system. Then the double critic networks and parameter updating policy are designed to eliminate and mitigate the fluctuations caused by cyber-attacks. The comparative simulation with other control strategies on a three-area test power system demonstrates the superior performance of the proposed MADRL-based approach.

Robust stability region analysis of time‐delayed load frequency control systems with EVs aggregator using Kharitonov theorem

AbstractThis study focuses on analyzing the robust stability regions and robustness margin of a time‐delayed load frequency control (LFC) system with Electric Vehicles (EVs) using the Kharitonov Theorem. Communication time delays in LFC systems can jeopardize stability and reliability, leading to suboptimal controller performance. Integrating EVs into LFC systems enhances dynamical stability but introduces additional complexity. Therefore, it is crucial to employ robust analysis and controller design techniques to ensure system stability. In this study, we utilize the Kharitonov Theorem to determine the robust stability regions and stability boundaries in the parameter plane of the Proportional‐Integral (PI) controller. By considering communication time delays and parametric uncertainties in the LFC system with EVs (LFC‐EVs), the robust PI controller gains using these methods are efficiently computed. To evaluate the performance of the theoretically computed robust controller parameters, time‐domain simulations are conducted.

Adaptive Event-Triggered Model Predictive Load Frequency Control for Power Systems

This paper investigates the adaptive event-triggered (AET) output feedback model predictive control (MPC) method for the load frequency control (LFC) problem of hybrid power system involving the thermal power and the photovoltaic power. First, an AET communication mechanism, which possesses the ability to dynamically adjust the trigger threshold parameter according to an adaptive law, is addressed to reducing the communication overhead, while keeping the required control performance; Second, the output feedback model predictive controller which is composed of an off-line designed state observer and an on-line solved optimization problem, is proposed using the techniques of quadratic boundedness and S-procedure. The state observer gain is obtained by off-line maximizing the trace of a matrix which is closely related to minimal positively invariant set; While the output feedback MPC strategy is acquired by expressing the infinite horizon control moves as a free control move and a linear feedback law based on the estimated state; Third, the recursive feasibility of the on-line optimization problem and the stability of the closed-loop system are analyzed by the fact that the estimated state and estimation error will converge to the presented minimal positively invariant set. Finally, MATLAB and its linear matrix inequality (LMI) toolbox are used to solve the optimization problem, and the LFC system with load disturbance is simulated and analyzed. The simulation results show that the proposed method is feasible and effective.

Impact of virtual inertia and damping control on stability delay margins of load frequency control systems with renewable energy sources

Impact of virtual inertia and damping control on stability delay margins of load frequency control systems with renewable energy sources

Load frequency control of power system based on improved AFSA-PSO event-triggering scheme

Aiming at the impact of redundant information transmission on network resource utilization in current power systems, an improved event-triggered scheme based on particle swarm optimization and artificial fish swarm algorithm for power system load frequency control (LFC) with renewable energy is proposed. First of all, to keep the stability and security of power systems with renewable energy, the load frequency control scheme is investigated in this paper. Then, to relieve the communication burden and increase network utilization, an improved event-triggered scheme based on the particle swarm algorithm and artificial fish swarm algorithm is explored for the power system load frequency control. Then, by utilizing improved Lyapunov functional and the linear matrix inequality method, sufficient condition for the H∞ stability of the load frequency control system is established. Finally, a two-area load frequency control system and IEEE-39 node simulation models are constructed to verify the effectiveness and applicability of the proposed method.

Load Frequency Control Using the Particle Swarm Optimisation Algorithm and PID Controller for Effective Monitoring of Transmission Line

Load frequency control (LFC) plays a critical role in maintaining the stability and reliability of the power system. With the increasing integration of renewable energy sources and the growth of complex interconnected grids, efficient and robust LFC strategies are in high demand. In recent years, the combination of particle swarm optimisation (PSO) and proportional-integral-derivative (PID) controllers, known as PSP-PID, has been used as a promising approach to enhance the performance of LFC systems. This article focuses on modelling, simulation, optimisation, advanced control techniques, expert knowledge, and iterative refinement of the power system to help achieve suitable PID settings that provide reliable control of the load frequency in the transmission line. The performance indices of the proposed algorithm are measured by the integral time absolute error (ITAE), which is 0.0005757 with 0.9994 Ki, 0.7741 Kp, and 0.1850 Kd. The model system dynamics are tested by varying the load frequency from 300 MW to 350 MW at a load variation of 0.2. The suggested controller algorithm is relatively reliable and accurate in power system management and protection load frequency control compared to conventional methods. This work can be improved by including more generating stations synchronised into a single network.

Adaptive H∞ event-triggered load frequency control in islanded microgirds with limited spinning reserve constraints

Using an islanded microgrid (MG) with large-scale integration of renewable energy is the most popular way of solving the reliable power supply problem for remote areas and critical electrical users. However, compared with traditional power systems, the limited spinning reserves and network communication bandwidth may cause weak frequency stability in the presence of stochastic renewable active outputs and load demand fluctuations. In this paper, an adaptive event-triggered control (ETC) strategy for a load frequency control (LFC) system in an islanded MG is proposed. First, a bounded adaptive event-triggered communication scheme is designed. This not only saves on network resources, but also ensures that the control center has a sensitive monitoring ability for the MG operating status when the frequency deviations have been effectively damped. Secondly, by fully considering the spinning reserve constraints and uncertain communication delays, the LFC system is described as a nonlinear model with saturation terms. Design criteria for ETC parameters are strictly deduced based on Lyapunov stability theory. Finally, an ETC parameter optimization algorithm based on random direction search is developed to reconcile the bandwidth occupancy and control performance. The effectiveness of the proposed method is verified in an MG test system.

Adaptive event‐triggering mechanism‐based N‐step predictive load frequency control for power systems with cyber attack

AbstractAlthough there have already been many works on the model predictive control (MPC) for load frequency control (LFC) of modern power systems, limited works can be found in the literature related to the output feedback MPC. This article studies an N‐step synthesis approach of output feedback MPC for LFC systems considering the problems of communication efficiency and network security. First, to improve the communication efficiency, an adaptive event‐triggering (AET) scheme involving two adaptive laws is designed to reduce the number of transmitted data packages which offers more flexible compared with existing event‐triggering schemes; Second, to handle the network security, a new model of LFC power system combining the AET scheme and random deception attack under an unified framework is established; Moreover, a synthesis approach of output feedback MPC with N‐step strategy is addressed for LFC of power system by parameterizing the infinite control moves into a series of output feedback laws. Compared with the existing predictive load frequency control methods, the present technique is shown as an useful way to improve the control performance since more degrees freedom is introduced by the N‐step strategy. Finally, the simulation experiment is carried out to verify our technique.

Frequency Domain Analysis of Load Frequency Control Using PIDTune Model Standard

The load frequency control system aims to regulate the frequency in the electric power system at a normal value with a predetermined tolerance limit. In practice, the load frequency control system does not always operate optimally, therefore a controller is needed to be added to the load frequency control system. The controller designed is a variation of the combination of Proportional-Integral-Differential (PID) controllers with the standard model PIDTune method consisting of proportional (P) controller, proportional integral (PI) controller, proportional differential (PD) controller, Proportional Integral Differential (PID) controller, Proportional Differential controller with first-order filter on differential section (PDF), and Proportional Integral Differential controller with first-order filter on differential section (PIDF). This study is aiming to carry out simulation and analysis in the frequency domain and then analyze the robustness of the reheat type power frequency control system and then design a PID controller for the reheat type power frequency control system in basic configuration, filter configuration, feedback configuration, feedforward configuration, and cascade configuration using PIDtune Model Standard on Matlab software. From the results of simulation and analysis, the controller that complies the design criteria and can make the reheat type of load frequency control system work optimally based on frequency domain analysis and robustness analysis is a proportional-integral (PI) controller in a feedback configuration with gain margin (Kg) equals to 38.11 dB, phase margin equals to 59.6°, infinity bandwidth, peak resonance value (Mr) equals to 1.19, maximum sensitivity peak value (MS) equals to 1.24, and complementary maximum sensitivity peak value (MT) equals to 1,17.

Comparative analysis of various energy storage systems in a conventional LFC system considering RDSTS, PWTS and AHVDC models

This article examines the performance of various energy storage systems (ESS) in a traditional load frequency control (LFC) interconnected system. ESS like capacitive systems (CS), battery systems (BS), ultra-capacitors (UC), redox flow batteries (RFB) and their combinations are explored. The explored system comprises of conventional three-area thermal with realistic dish-striling solar thermal system (RDSTS) in area-1, precise wind turbine system (PWTS) in area-2 and RDTS-PWTS in area-3. The performance of cascaded PI with PIDN as a secondary controller is employed for the first time. The controller values are simultaneously optimized by hybrid crow search algorithm (HCSA). The effect of introducing RES like RDSTS and PWTS have been studied, and the results shows that RES leads to superior dynamics over thermal. A novel performance index namely HPA-ISE is anticipated and shows improves responses over ISE. Also, investigations are carried on optimal AHVDC and ESS locations. Moreover, the responses with AC-AHVDC and ESS highlights the predominance of ESS over AC-AHVDC and thermal systems. Further, studies comparing other ESS reveal that RFB performs them. Furthermore, when RFB is combined with UC and CS, it is discovered that RFB-UC produces better results.

Formula omitted] Load frequency control of power systems with multiple time-varying delays via improved reciprocally convex inequality

This paper focuses on the stability problem and the design method of PI-type H∞ controller for load frequency control (LFC) of power systems with multiple time-varying delays (MTD). In the existing researches, the model of LFC system with time delays is not accurate enough since it is established based on the assumption that the time delays are all the same. This paper proposes a novel model of multi-area LFC system with MTD. Both the stability analysis and controller design in this paper are based on the improved model to ensure the applicability of the proposed method in general. First, a novel Lyapunov-Krasovskii functional (LKF) containing delay-product-type term (DPT) is constructed and auxiliary function-based integral inequality (AFBII) is utilized to handle the integral term of the derivative of LKF. Then, an improved reciprocally convex inequality is proposed to obtain the less conservative stability criteria in terms of linear matrix inequalities (LMIs). Next, an effective H∞ controller design method is developed based on the proposed stability criteria. Finally, simulation experiments are done to illustrate the superiority of proposed criteria and effectiveness of proposed design method.

Delay-Dependent Stability Analysis of Multi-Area LFC-EVs System

In this study, the delay-dependent stability of a multi-area Load Frequency Control (LFC) system with Electric Vehicle (EV) aggregators is investigated with the help of the Advanced Clustering with Frequency Sweeping (ACFS) method for incommensurate time delays. Both Integer-Order (IO) and Fractional-Order Proportional Integral (FOPI) controllers are utilized as a controller. The communication infrastructure used in LFC systems induces time delays resulting in deteriorations in the system stability. Even if the maximum allowable delay margin limits are not exceeded, these inevitable time delays could cause undesired frequency deviations and tie-line power fluctuations. The ACFS method is employed in this study to investigate impacts of time delays and to ensure better controller performance objectives taking into account the effects of time delays. Firstly, 2-dimensional (2D) stability delay maps are obtained for various LFC-EVs system parameters. The stability regions are then verified by the Quasi-Polynomial Mapping Root (QPmR) finder algorithm and MATLAB/Simulink-based time-domain simulations. The results clearly show that the participation of the EV aggregators in traditional LFC systems improves the frequency regulation and tie-line power-sharing in the system. Finally, it is concluded that the stability regions are enhanced as the fractional order of the FOPI decreases.

Resilient Load Frequency Control of Power Systems to Compensate Random Time Delays and Time-Delay Attacks

Load frequency control (LFC) of modern power systems tends to employ open communication networks to transmit measurement/control signals, which makes the LFC scheme more vulnerable to random time delays and time delay attacks. In this paper, a resilient and active time-delay-compensation-based LFC scheme is proposed to compensate the random time delays and time delay attacks. At first, a state observer is employed to estimate the state of the LFC system. Then a networked predictive control method is used to predict the control signals of the system at the future moments. Next, an evaluation and compensation scheme for random time delays and time delay attacks is constructed in the actuator side of the LFC scheme based on the updating period of the actuator and the timestamp technique. Due to the stochastic characteristics of the random time delays or TDAs, the stability condition of the proposed scheme is developed with the aid of the mean square stability theory. Moreover, a dual-loop open communication is employed in the proposed scheme to improve the reliability and resilience. At last, simulation and experiment tests are undertaken to demonstrate the effectiveness of the proposed scheme.

Optimized Non-Integer Load Frequency Control Scheme for Interconnected Microgrids in Remote Areas with High Renewable Energy and Electric Vehicle Penetrations

Renewable energy systems (RESs) have introduced themselves as vital solutions for energy supply in remote regions, wherein main utility supply systems are not available. The construction of microgrid (MG) systems is useful candidate for proper control and management with hybrid RESs. However, RESs-based MGs face reduced power system inertia due to the dependency of RESs on power electronic converter systems. Accordingly, preserving nominal operating frequency and reduced deviations in tie-line power are crucial elements for proper operation of interconnected MGs in remote areas. To overcome this problem, load frequency control (LFC) systems have proven featured solutions. Therefore, this paper proposes a new non-integer LFC method based on the fractional order (FO) control theory for LFC in interconnected MGs in remote areas. The proposed control is based on the three degree of freedom (3DoF) cascaded 1+proportional-integral-derivative-accelerated (PIDA) controller with FOPI controller, namely 3DoF 1+PIDA/FOPI LFC scheme. The proposed 3DoF 1+PIDA/FOPItakes the advantages of the accelerated term of PIDA control to improve power system transients, regarding maximum overshoot/undershoot and settling times. Additionally, it employs outer loop to reduce errors and faster inner loop to mitigate disturbances effects. The contribution of plug-in controlled electric vehicles (EVs) are considered to enhance the frequency regulation functions. An optimized design of the proposed 3DoF 1+PIDA/FOPI LFC scheme is proposed using the newly developed hybrid equilibrium optimizer (EO)-slime mould optimization (SMA) algorithm (namely EOSMA optimizer). The EOSMA combines the features of the EO and SMA powerful optimization algorithms. A two interconnected MGs in remote areas with RESs and EVs inclusions with high penetration levels is selected to verify the proposed 3DoF 1+PIDA/FOPI LFC scheme and the EOSMA optimizer. The results show high ability of the proposed controller and design scheme to minimize MGs’ frequency and tie-line power fluctuations and to preserve frequency stability and security.