Distributed model predictive load frequency control of multi-area interconnected power system

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.

BackgroundAutomatic generation control (AGC) of multi-area interconnected power system (IPS) is often designed with negligible cross-coupling between the load frequency control (LFC) and automatic voltage regulation (AVR) loops. This is because the AVR loop is considerably faster than that of LFC. However, with the introduction of slow optimal control action on the AVR, positive damping effect can be achieved on the LFC loop thereby improving the frequency control. In this paper, LFC synchronized with AVR in three-area IPS is proposed. Model predictive controller (MPC) configured in a dense distributed pattern, due to its online set-point tacking is used as the supplementary controller. The dynamics of the IPS subjected to multi-area step and random load disturbances are studied. The efficacy of the developed scheme is ascertained by simulating the disturbed system in MATLAB/Simulink.ResultsBased on the comparative analysis on the system responses, it is established that by cross-coupling the LFC loop with AVR, reductions of 66.45% and 59.09% in the frequency and tie-line power maximum deviations respectively are observed, while the respective settling times are found to be reduced by 29.68% and 22.77% when compared with the uncoordinated control scheme. In addition, the standard deviation and variance of the integral time absolute error of the system’s responses have reduced by 23.21% and 20.83% respectively compared to those obtained in a similar study.ConclusionsThe reduction in the maximum deviations and settling times in the system states indicates that introducing the voltage control via AVR loop has improved the frequency control significantly. While the lower standard deviation and variance of the integral time absolute error signify improvement in the robustness of the developed algorithm. However, this improvement is at the detriment of the controller size and computational complexity. In the uncoordinated control scheme, the control vector is one-dimensional, while in the coordinated scheme, the control vector is two-dimensional for each CA.

In power system automatic generation control, the existence of the generation rate constraints (GRC) and the valve limit on the governor can greatly influence the dynamic responses of the power system. Model predictive control is a popular control strategy which takes systematic account of process input, state and output constraints, thereby is employed to load frequency control to cope with the GRC. The valve limit on the governor is modeled by a fuzzy model so that the local predictive controllers are incorporated into the nonlinear control system. The proposed methodology is tested with an interconnected power system. Simulation results demonstrate the effectiveness of the proposed nonlinear constraint predictive control algorithm.

A Tilt Integral Derivative (TID) controller is designed in this paper for the Load Frequency Control (LFC) issue of a multi-area interconnected restructured power system. The suggested TID controller settings are fine-tuned using a novel optimization technique known as Hunger Games Search (HGS) algorithm. A multi-area interconnected power system with various generating units is used to test the performance of the proposed TID controller based on HGS. The suggested controller also takes into account system non-linearities such as Generation Rate Constraints (GRCs) and Governor Dead Band (GDB). The superiority of HGS's optimization over a range of other significant optimization techniques, such as the grey-wolf optimization algorithm, has been confirmed. The simulation results show that the proposed TID controller based on HGS improves system frequency stability significantly under a variety of load perturbation scenarios.

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

The stability control of nominal frequency and terminal voltage in an interconnected power system (IPS) is always a challenging task for researchers. The load variation or any disturbance affects the active and reactive power demands, which badly influence the normal working of IPS. In order to maintain frequency and terminal voltage at rated values, controllers are installed at generating stations to keep these parameters within the prescribed limits by varying the active and reactive power demands. This is accomplished by load frequency control (LFC) and automatic voltage regulator (AVR) loops, which are coupled to each other. Due to the complexity of the combined AVR-LFC model, the simultaneous control of frequency and terminal voltage in an IPS requires an intelligent control strategy. The performance of IPS solely depends upon the working of the controllers. This work presents the exploration of control methodology based on a proportional integral–proportional derivative (PI-PD) controller with combined LFC-AVR in a multi-area IPS. The PI-PD controller was tuned with recently developed nature-inspired computation algorithms including the Archimedes optimization algorithm (AOA), learner performance-based behavior optimization (LPBO), and modified particle swarm optimization (MPSO). In the earlier part of this work, the proposed methodology was applied to a two-area IPS, and the output responses of LPBO-PI-PD, AOA-PI-PD, and MPSO-PI-PD control schemes were compared with an existing nonlinear threshold-accepting algorithm-based PID (NLTA-PID) controller. After achieving satisfactory results in the two-area IPS, the proposed scheme was examined in a three-area IPS with combined AVR and LFC. Finally, the reliability and efficacy of the proposed methodology was investigated on a three-area IPS with LFC-AVR with variations in the system parameters over a range of  ± 50%. The simulation results and a comprehensive comparison between the controllers clearly demonstrates that the proposed control schemes including LPBO-PI-PD, AOA-PI-PD, and MPSO-PI-PD are very reliable, and they can effectively stabilize the frequency and terminal voltage in a multi-area IPS with combined LFC and AVR.

Higher Order Degree of Freedom Controller for Load Frequency Control of Multi Area Interconnected Power System with Time Delays

Self-tuning algorithm for automatic generation control in an interconnected power system

This paper integrates the wind turbines (WTs) into the interconnected power system and designs a distributed model predictive control (DMPC) controller for the primary frequency regulation problem. The WTs have been treated as a part of the power system to take part in primary frequency regulation with load disturbances. A frequency response model of multi-area power system including WTs is introduced, in which the physical constraints of the governors and turbines are considered. The distributed model predictive controller is designed by posing the primary frequency regulation problem as disturbance rejection problem of large system with state and input constraints. Analysis and simulation results for a two-area interconnected power system with WTs show possible improvements on closed-loop performance, while respecting physical hard constraints. Comparisons have been made made between the DMPC controller with and without WTs. The results confirm the superiority of the proposed DMPC scheme with the participation of the wind turbines in the primary frequency regulation.

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.

This study focuses on designing an effective intelligent control method to stabilize the net frequency against load variations in multi-control-area interconnected power systems. Conventional controllers (e.g. Integral, PI, and PID) achieve only poor control performance with high overshoots and long settling times. They could be replaced with intelligent regulators that can update controller parameters for better control quality. The control strategy is based on fuzzy logic, which is one of the most effective intelligent strategies and can be a perfect substitute for such conventional controllers when dealing with network frequency stability problems. This paper proposes a kind of fuzzy logic controller based on the PID principle with a 49-rule set suitable to completely solve the problem of load frequency control in a two-area thermal power system. Such a novel PID-like fuzzy logic controller with modified scaling factors can be applied in various practical scenarios of an interconnected power system, namely varying load change conditions, changing system parameters in the range of ±50%, and considering Governor Dead-Band (GDB) along with Generation Rate Constraint (GRC) nonlinearities and time delay. Through the simulation results implemented in Matlab/Simulink software, this study demonstrates the effectiveness and feasibility of the proposed fuzzy logic controller over several counterparts in dealing with the load-frequency control of a practical interconnected power system considering the aforesaid conditions.

In this paper, Proportional Integral Derivative (PID) controller is designed using Differential Evolution (DE) algorithm to Load Frequency Control (LFC) in three areas of an interconnected power system. The proposed controller has appropriate dynamic response, so it increases damping in transient state in unhealthy conditions. Different generators have been used in three areas. Area 1 includes thermal non-reheat generator and two thermal reheat generators; area 2 includes hydro and thermal non-reheat generators, and area 3 includes hydro and thermal reheat generators. In order to evaluate the performance of the controller, Sim/Matlab software is used. Simulation results show that the controller designed using DE algorithm is not affected by load changes, disturbance, or system parameters changes. Comparing the results of proposed algorithm with other load frequency control algorithms, such as PSO and GA, it has been found that this method has a more appropriate response and satisfactory performance

Load frequency control (LFC) is vital for balancing power generation with fluctuating power demand. It ensures that the system frequency and tie-line power are maintained at their desired levels. The design of an LFC system is crucial for the automation of power systems. This article introduces a Fuzzy Proportional-Integral-Derivative (FPID) control approach for LFC in an interconnected reheat thermal power system, utilizing a Particle Swarm Optimization (PSO) method and incorporating the Generation Rate Constraint (GRC) as nonlinearities. The proposed controller offers the advantage of effectively managing system nonlinearities while being better than classical controllers. The response of the FPID controller is contrasted with both the conventional Proportional-Integral (PI) controller and the Fractional Order PID (FOPID) controller, in scenarios both including and excluding the Generation Rate Constraint (GRC). The response of the system is analyzed by considering load disturbances in each region of the integrated power network.

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.

This paper deals with the importance of load frequency control (LFC) for single and interconnected power system. It is important to keep the frequency of the system and the inter area tie power stable. The goal of LFC is to maintain the frequency, the desired power output and to control the change in tie line power between control areas in an interconnected power system. Two different techniques have been implemented in this paper which are model predictive controller MPC and conventional proportional plus integral controller PI for LFC of single area power system as well as two area system. To investigate the powerful and robustness of model predictive control (MPC) technique for LFC problems in electric power system, time simulations is performed. The obtained results indicate that the MPC provide better damping to the single area system as well as two-area system in case of load disturbance compared with conventional PI controller. The studied single-area and two-area systems are modelled and simulated using Simulink/Matlab software.