Load Frequency Control Problem Research Articles

Novel tuning rules for IMC-high-order PID load frequency controller of power systems

The problem of load frequency control (LFC) for power grids has received widespread attention in power industrial control. Ensuring the stability of the frequency is the primary concern that constrains the development of the electric power system. This paper presents a novel internal model control (IMC)- proportional-integral-derivative (PID) controller design method for LFC control systems, centered on pole-zero conversion. This method aims to simplify the system model's complexity and improve the system's performance. The IMC controller is approximated as a PID series compensator (high-order PID), with exact tuning formulas provided for various scenarios. These include single-area without or with reheat turbines, hydro turbines with transient droop compensators, wind turbines, and gas turbines. The tuning formulas are characterized by a single parameter, determined under robustness constraints and integrated time absolute error (ITAE). The proposed tuning method considers the generator rate constraint (GRC) and applies to multi-area single-source and multi-area multi-source power systems. The results of the simulation confirm that the controller tuning method presented in this paper has significant advantages over the existing design methods concerning robustness and anti-interference performance.

Event-based [formula omitted] load frequency control for fuzzy Markov-jump IPS with wind power under hybrid attacks

This paper addresses the H∞ load frequency control problem of interconnected power systems that incorporate high-permeability wind power and face a mixed attack of deception and denial of service. The interconnected power system is modeled as a Takagi–Sugeno (T-S) fuzzy Markov jump system. Given the involvement of wind power, optimizing the utilization of already in-demand communication resources becomes imperative. Thus, a new event-triggering mechanism is adopted to reduce data transmission traffic. Simultaneously, in response to the general network’s vulnerability to network attacks in power systems, a closed-loop system with Markov jump, modeled using the T-S fuzzy approach, is studied. A novel multi-agent Event-Triggering Strategy (ETS) composed of membership functions is proposed to address the mismatch between the membership functions of fuzzy systems and fuzzy controllers, and ensure the consistency of multi-agent systems. Subsequently, employing Lyapunov-Krasovskii theory and stochastic analysis techniques, conditions sufficient to ensure the asymptotic stability of interconnected power systems are derived from linear matrix inequalities. Finally, simulation verification is provided to ensure the accuracy and feasibility of the obtained theory.

A Novel Failure-Distribution-Dependent Non-Fragile $H_\infty$ Fault-Tolerant Load Frequency Control for Faulty Multi-Area Power Systems

This paper studies the non-fragile <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> fault-tolerant load frequency control problem for multi-area power systems with actuator failures. At first, considering the distribution characteristics of partial failures, a stochastic distribution model is established for actuator partial failures. Next, for the perturbations of controller gains, not only the additive uncertainties but also the multiplicative uncertainties are incorporated into the fault-tolerant controller design. The coupling items which hardly directly solved have turned into a W-problem in fault-tolerant load frequency control. Furthermore, a novel failure-distribution-dependent non-fragile <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> fault-tolerant load frequency control algorithm is given by using linear matrix inequalities technology and Lyapunov-Krasovskii functional method. Finally, a numerical example with a three-area power system are given to show the effectiveness of the proposed methods.

Adaptive distributed MPC based load frequency control with dynamic virtual inertia of offshore wind farms

AbstractThe penetration of offshore wind farms (OWFs) in city‐close power systems is rapidly increasing. System inertia will be further reduced. Active frequency support of wind power is essential to solve the load frequency control (LFC) problem. Here, the dynamic virtual inertia control (VIC) method is employed to enhance frequency stability within the permitted operating states of OWFs. An adaptive distributed model predictive control (DMPC) method is proposed and applied to an interconnected power system. The dynamic VIC‐based LFC model is derived and used to construct the predictive model of DMPC. To expand the adaptation of the analytical linearized model of OWFs in different operating points, the adaptive law is further designed to dynamically adjust the parameters of DMPC. The simulation results demonstrate the effectiveness of the proposed control method. The frequency fluctuations can be well‐restrained under different disturbances.

Switched Observer-Based Adaptive Event-Triggered Load Frequency Control for Networked Power Systems Under Aperiodic DoS Attacks

This paper is concerned with a resilient load frequency control (LFC) problem for networked power systems against the aperiodic denial-of-service (DoS) attack. First, considering the intermittent nature of the aperiodic DoS attack and the unavailability of the partial system states simultaneously, a switched observer-based time-delay networked power model is established. Second, to save network bandwidth resources, a novel adaptive event-triggering mechanism is designed by applying a switch-adjusting threshold parameter scheme. Then, a switched observer-based PI controller is designed and a piecewise Lyapunov functional analysis approach is developed such that the exponential stability of closed-loop augmented power systems is derived with desired H∞ performance in forms of linear matrix inequality (LMI). Finally, a power system example with IEEE 39-bus is provided to illustrate the effectiveness of the designed schemes.

Optimizing Artificial Neural Networks for Multi Area Network : A Metaheuristic Perspective

Regression, data classification and function approximation are among the most common applications that make use of machine learning models. However, due to the vast range of applications for machine learning, comprehensive understanding of how to choose a model based on machine learning, as well as how to choose its structure, training method, and performance analysis criterion, is frequently lacking. This key issue is addressed using a well-known load frequency control (LFC) problem which is instrumental in maintaining balance between power generation and load demand. The study relates to developing and contrasting the performance of the Meta heuristic optimization based approach to the artificial neural network (ANN) based machine learning topology for the LFC control against the optimized ANN controller. The selected performance indices are peak time and settling time of the frequency deviation. It is observed that Linear Neural Network (LNN) outperforms Feedforward Neural Network (FNN) and Recurrent Neural Network (RNN). The performance is enhanced when its parameters are optimized by the metaheuristic algorithms.

Adaptive Active Disturbance Rejection Load Frequency Control for Power System with Renewable Energies Using the Lyapunov Reward-Based Twin Delayed Deep Deterministic Policy Gradient Algorithm

The substitution of renewable energy sources (RESs) for conventional fossil fuels in electricity generation is essential in addressing environmental pollution and resource depletion. However, the integration of RESs in the load frequency control (LFC) of power systems can have a negative impact on frequency deviation response, resulting in a decline in power quality. Moreover, load disturbances can also affect the stability of frequency deviation. Hence, this paper presents an LFC method that utilizes the Lyapunov reward-based twin delayed deep deterministic policy gradient (LTD3) algorithm to optimize the linear active disturbance rejection control (LADRC). With the advantages of being model-free and mitigating unknown disturbances, LADRC can regulate load disturbances and renewable energy deviations. Additionally, the LTD3 algorithm, based on the Lyapunov reward function, is employed to optimize controller parameters in real-time, resulting in enhanced control performance. Finally, the LADRC-LTD3 is evaluated using a power system containing two areas, comprising thermal, hydro, and gas power plants in each area, as well as RESs such as a noise-based wind turbine and photovoltaic (PV) system. A comparative analysis is conducted between the performance of the proposed controller and other control techniques, such as integral controller (IC), fractional-order proportional integral derivative (FOPID) controller, I-TD, ID-T, and TD3-optimized LADRC. The results indicate that the proposed method effectively addresses the LFC problem.

Reliable Event-Triggered Load Frequency Control of Uncertain Multiarea Power Systems With Actuator Failures

Load frequency control (LFC) is crucial for the economic operation and safety of power systems. Therefore this paper addresses the LFC problem for uncertain multi-area power systems with actuator failures. Specifically, actuator failures, uncertainties and communication bandwidth constraints appearing in multi-area power systems are taken into account simultaneously, and novel reliable event-triggered LFC schemes are proposed to cope with these troubles. The proposed schemes can ensure the asymptotical stability of the closed-loop system when only matched uncertainty exists. For the case of coexisting matched and mismatched uncertainties, the state trajectories of the closed-loop system can be controlled within a bounded set, where the size of the bounded set is only related to the mismatched uncertainty. To illustrate the theoretical results, a numerical example of three-area interconnected power system is presented. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Load frequency directly affects the quality of electric energy and is one of the main observation states of power systems, hence LFC has been widely investigated in the literature. For multi-area power systems, the system model to be controlled may be subjected to multiple unfavorable factors in practical situations, such as limited bandwidths, model uncertainties and actuator failures. To cope with these unfavorable factors, this paper is devoted to developing a unified control framework to guarantee the stability of the frequency deviation based on the event-triggered mechanism. Considering both matched and unmatched system uncertainties may exist as well as the bound of system uncertainties can be unknown, event-triggered control schemes including static event-triggered LFC and adaptive event-triggered LFC are accordingly designed to deal with aforementioned situations such that the closed-loop system is asymptotically or boundedly stable. The research outcome of this paper provides simple but effective LFC approaches that can be used to maintain the reliable and stable operation of multi-area power systems.

Distributed fault-tolerant PI load frequency control for power system under stochastic event-triggered scheme

This article investigates the load frequency control problem of interconnected power systems by proposing a distributed fault-tolerant proportional integral (PI) control strategy. Firstly, a unified actuator fault model is established, and a distributed fault-tolerant PI control strategy is proposed on the basis of the actuator fault model. Then, a stochastic event-triggered scheme (SETS) based on stochastic sampling period is developed to relieve the redundant occupation of network communication resources. Further, an asymptotical stability criterion with H∞ performance is established by means of the Lyapunov method. Finally, illustrative examples are presented from two cases, isolated power system and interconnected power systems, to demonstrate the effectiveness of the designed control approach and the superiority of SETS compared with periodic event-triggered scheme.

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.

Multi-area load frequency regulation of a stochastic renewable energy-based power system with SMES using enhanced-WOA-tuned PID controller

This paper presents a novel nature-inspired meta-heuristic optimization algorithm known as the Enhanced Whale Optimization Algorithm (EWOA), which imitates humpback whales' social behavior to solve the optimization of multi-area automatic load frequency control (LFC) problems of a stochastic renewable energy-based power system with superconducting magnetic energy storage (SMES). An EWOA algorithm is presented in response to the limitations of the conventional WOA algorithm, including its sluggish convergence time, low accuracy, and propensity to easily enter local optimum. The system model investigated includes some physical constraints such as the time delay (TD), generation rate constraint (GRC), reheat turbine (RT), and the dead band (DB). The impacts of these physical constraints on the dynamic performance of the proposed controller were investigated. The EWOA algorithm is utilized to dynamically optimize the parameters of the PID controller for optimal system performance. The effectiveness and dynamic performance of the proposed controller are compared with the conventional WOA using some performance metrics. The system model also includes superconducting magnetic energy storage (SMES) units in both areas and their impacts on the system performances are also investigated. The effects of the changes of two different parameters of the system (frequency bias parameter, B, and the governor speed regulation, R) on the frequency deviation responses and the controller's robustness are examined. It is evident from the results that the dynamic performance of the proposed controller is better than that of the conventional WOA and it is more robust and stable to changes in system loading, parameters, and step load perturbation.

Harris hawks optimization algorithm for load frequency control of isolated multi-source power generating systems

Abstract This paper presents a recent bio-inspired optimization algorithm for the critical topic of load frequency control (LFC) in an isolated multi-source power generating system. A specific model that emerges from the scientific literature and consists of reheated thermal, hydro and gas-turbine power sources is examined. The main goal is to tune the controller of each generating source i.e. find their optimal gains through bio-inspired optimization algorithms. Namely, the algorithms applied are the Whale Optimization Algorithm (WOA), Grey Wolf Optimizer (GWO), Particle Swarm Optimization (PSO), and the newly proposed Harris Hawks Optimization (HHO). It was observed that all optimization algorithms succeeded in obtaining controllers’ gain values which ensure stable system operation. Also, the simulation results indicated the superiority of the proposed HHO algorithm over the other algorithms for all the considered scenarios. In this article, for the first time to the authors’ knowledge extend an attempt has been made to optimize an isolated multi-source system using the bio-inspired HHO algorithm. The present study considered the LFC problem with a variety of different scenarios, taking into account both sub-cases of nonlinearities (e.g., generation rate constraint, boiler dynamics, etc.) and their combinations, as well as combinations of different controllers and load disturbances, which are not found in the literature. Last but not least, the robustness of the selected controller was further evaluated. The obtained results clearly demonstrated that the controller’s gains established in normal conditions do not require retuning when critical system parameters undergo a significant variation.

Maiden application of TIDμ1NDμ2 controller for effective load frequency control of non‐linear two‐area power system

AbstractIn the paper, the maiden application of Tilted Integral Fractional Derivative with Filter plus Fractional Derivative controller (), called TIFDNFD controller, is proposed to achieve load frequency control (LFC) of two area‐multi source power system. In the study, both areas include thermal power, hydropower, and gas turbine power systems. In this study, generation rate constraint and governor dead‐band are integrated into the power system to evaluate the performance of the controller in a non‐linear environment. The wild horse optimizer (WHO) is used for controller parameter tuning in the LFC problem for the first time. The performance of the proposed controller is demonstrated by comparing it with the recently published studies including different controllers. In this study, to obtain more realistic results, solar photovoltaic (PV) power, wind power, and load demand with stochastic form have been added to the power system. In addition, the dynamic effect of the hydrogen storage system, consisting of an electrolyser and a fuel cell, is considered a grid supporter. The superiority of the WHO algorithm in optimization has been verified by comparing it with three optimization algorithms recently proposed. Finally, the resilience and robustness of the power system are evaluated in perturbed system parameters.

Tunicate Swarm Algorithm based Optimized PID controller for automatic generation control of two area hybrid power system

In the modern power system, the use of renewable energy sources is increasing rapidly, which makes the system more sensitive. Therefore, it requires effective controllers to operate within the allowable ranges. The existing techniques based on cascaded controllers implemented so far for load frequency control have the advantage of improving the system response. However, this makes the system a more complex and time-consuming process. This makes the system more straightforward, makes it easy to optimize PID parameters, and provides results in acceptable ranges. This paper attempts to solve the load frequency control (LFC) problem in an interconnected hybrid power system with a classical PID controller employing the tunicate swarm algorithm (TSA). This algorithm is used for two areas of an interconnected hybrid power system: thermal, hydro, nuclear, and wind. The PID controller parameters are optimized by tunicate swarm algorithm using integral time absolute error (ITAE) based objective function. To show the robustness of the proposed TSA algorithm, a sensitivity analysis is performed for four case studies ranging from 20% to 30% load increments and decrements. The performance of the proposed TSA algorithm has been compared with the well-known optimization algorithms, particle swarm optimization (PSO), artificial bee colony (ABC), and arithmetic optimization algorithm (AOA) in terms of overshoot, undershoot, and settling time. The simulation results show that the proposed TSA has better optimization capability than PSO, ABC, and AOA in terms of overshoot, undershoot, and settling time.

Influence of ultra‐capacitor on AGC of five-area hybrid power system with multi-type generations utilizing sine cosine adopted dingo optimization algorithm

In this article, the load frequency control (LFC) problem of a five-area automatic generation control (AGC) power system with multi-type generations is addressed by utilising a technique that considers the changing of the dingo optimisation algorithm known as sine cosine adopted dingo optimisation algorithm (SCaDOA) based tilt integral derivative (TID) regulator. AGC needs an energy storage system (ESS) and some intelligent adaptable control techniques to guarantee the balance in the system's stability. Consequently, this paper utilizes the TID regulator alongside ultra‐capacitor (UC) ESS to settle the AGC issue. At first, the execution of the sine cosine adopted calculation is tried by contrasting it and the standard DOA calculation by considering different standard benchmark functions. Further, the proposed plan strategy is likewise applied to a five-area system comprising different conventional and non-conventional/renewable energy sources along with UC. The execution of the controller has been finished for different stacking conditions of the power system. It is seen that the said UC with TID controller is more viable contrasted with the other standard controllers.

Novel Fractional-Order Proportional-Integral Controller for Hybrid Power System with Solar Grid and Reheated Thermal Generator

This paper presents a new fractional-order proportional-integral, (PI)λ (FO[PI]) type structure to investigate the load frequency control (LFC) problem. In the literature, some controllers’ extensive tuning options may slow or complicate the optimization process. Due to the intricacy of the tuning, even if there are fewer tuning parameters, a robust structure can be obtained. The (PI)λ structure deviates from the standard FOPI, integer PID, or PI-PD controllers with the same or fewer tuning parameters. The efficacy of a tri-parametric fractional-order controller is examined on a two-area interconnected hybrid power system comprising a photovoltaic (PV) grid and a Reheated Thermal Generator (RTG). In order to obtain optimal performance with lower control efforts, a novel dual-performance index is developed for the LFC problem. Various analyses are also proven to perform better than other optimized controllers from the recent literature. The presented scheme is significantly robust to disturbance interruptions, non-linearities, and parameter perturbations. It is also observed that there are no stability issues due to communication time delays. It is highlighted that the improvement can be obtained without adding complex structure or controller parameters.

Event-Triggered Sliding Mode Load Frequency Control of Multiarea Power Systems Under Periodic Denial-of-Service Attacks

A sliding mode load frequency control (SMLFC) problem is committed for interconnected power systems under periodic denial-of-service (DoS) attacks. A suitable sliding surface is designed to deduce the state space equation in the multiarea power systems. An event-triggered device is used to determine whether the sampling state should be transmitted, and a new event-triggered condition is provided to match periodic DoS attacks. By utilizing the multiple Lyapunov–Krasovskii function approach, the globally exponential stability is proved based on matrix inequalities and the exponential stability criterion is subsequently obtained in terms of linear matrix inequalities. A suitable control law is established to ensure the reachability of power system. The feasibility and superiority of the proposed SMLFC are illustrated by numerical examples.

Optimal Load Frequency Control of a Hybrid Electric Shipboard Microgrid Using Jellyfish Search Optimization Algorithm

This paper examines the critical topic of load frequency control (LFC) in shipboard microgrids (SMGs), which face challenges due to low system inertia and the intermittent power injection of renewable energy sources. To maintain a constant frequency (even under system uncertainties), a robust and well-tuned controller is required. In this paper, a study was conducted first by examining the performance of three different controller architectures, in order to determine which is the most-appropriate for the multi-energy SMG system. The time delays that occur due to communication links between the sensors and the controller were also considered in the analysis. The controllers were tuned using a very recent bio-inspired optimization algorithm called the jellyfish search optimizer (JSO), which has not been used until recently in LFC problems. To assess the tuning efficiency of the proposed optimization algorithm, the SMG’s frequency response results were comprehensively compared to the results obtained with other bio-inspired optimization algorithms. The results showed that the controllers with gains provided by the JSO outperformed those tuned with other bio-inspired optimization counterparts, with improvements in performance ranging from 19.13% to 93.49%. Furthermore, the robustness of the selected controller was evaluated under various SMG operational scenarios. The obtained results clearly demonstrated that the controller’s gains established in normal conditions do not require retuning when critical system parameters undergo a significant variation.

Event-triggered model-free adaptive predictive control for multi-area power systems under deception attacks

This paper focuses on the event-triggered model-free adaptive predictive load frequency control (LFC) problem for multi-area power systems under false data injection (FDI) attacks. First, the power system model is assumed to be unknown, and the nonlinear power system is converted into an equivalent linear data model using the input and output data of the powerline system. The FDI attacks on the power system is also modeled, and a Bernoulli stochastic process is used to represent whether the data is transmitted successfully or not. Second, the equivalent linear data model to predicts upcoming events, and a new event-triggered model-free adaptive predictive control scheme is designed via the predictions. And a RBF neural network disturbance estimator is designed to estimate and compensate for the effects caused by disturbances, and then power system stability is analyzed. An event-triggered scheme is also developed in the design of the LFC in order to save communication and computational burden. The results show that the designed control algorithm is data-driven independent of the power system structure and does not require the measurement of any system state signals. Finally, the effectiveness and correctness of the scheme is verified by a three-area numerical example and simulation results.

Blockchain-assisted spent electric vehicle battery participation for load frequency control problems in interconnected power systems is resilient, low-carbon, and offers revenues to the operators

Parked electric vehicles (EVs) participation is thought to be a low-carbon and resilient solution in addressing the load frequency control (LFC) problems in interconnected power systems (IPS). But this participation results in multiple issues such as trust, traceability, and transparency (3Ts) for EV owners in terms of financial compensation, battery effects, and range anxiety; early EV batteries end-of-life (EoL) management by recyclers; and burden on critical materials for new EV batteries manufacturing. Hence, to avoid the highlighted issues while addressing LFC, we propose a product life-extension circular business model and blockchainification of non-digital assets inspired spent EV battery (SEVB) buffer storage system. Two area IPS where areas 1 and 2 having a tie-line power agreement, SEVB storage system, particle swarm optimization (PSO)-based controller, and blockchain-based participatory smart contracts (BC-PSC) are modeled. Resilience Performance, Life Cycle Analysis, and Techno-Economic (RePLiCATE) approach is used for realizing the feasibility. Results showed BC-PSC protocols and PSO effectively obtained the controller's optimal parameters under disruptive scenarios ranging from 5 to 20%. The recovery times went from 18.60 to 46.43 sec. SEVB in LFC produces 18.71% less global warming potential than parked EVs. Revenues for SEVB owners were 122.27%, 100.22%, and 66.67% higher than cash spent on charging at off-peak, mid-peak, and on-peak, respectively.