A novel hybrid gravitational search and pattern search algorithm for load frequency control of nonlinear power system

In this paper, a hybrid gravitational search algorithm (GSA) and pattern search (PS) technique is proposed for load frequency control (LFC) of multi-area power system. Initially, various conventional error criterions are considered, the PI controller parameters for a two-area power system are optimized employing GSA and the effect of objective function on system performance is analyzed. Then GSA control parameters are tuned by carrying out multiple runs of algorithm for each control parameter variation. After that PS is employed to fine tune the best solution provided by GSA. Further, modifications in the objective function and controller structure are introduced and the controller parameters are optimized employing the proposed hybrid GSA and PS (hGSA-PS) approach. The superiority of the proposed approach is demonstrated by comparing the results with some recently published modern heuristic optimization techniques such as firefly algorithm (FA), differential evolution (DE), bacteria foraging optimization algorithm (BFOA), particle swarm optimization (PSO), hybrid BFOA-PSO, NSGA-II and genetic algorithm (GA) for the same interconnected power system. Additionally, sensitivity analysis is performed by varying the system parameters and operating load conditions from their nominal values. Also, the proposed approach is extended to two-area reheat thermal power system by considering the physical constraints such as reheat turbine, generation rate constraint (GRC) and governor dead band (GDB) nonlinearity. Finally, to demonstrate the ability of the proposed algorithm to cope with nonlinear and unequal interconnected areas with different controller coefficients, the study is extended to a nonlinear three unequal area power system and the controller parameters of each area are optimized using proposed hGSA-PS technique.     

计及时滞的互联电网负荷频率控制最优分数阶PID控制器设计

分数阶PID控制器相比于传统整数阶PID控制器,具有控制性能好、鲁棒性强等诸多优势,可应用于电网的负荷频率控制(load frequency control,LFC)中.针对网络化时滞互联电网的LFC问题,提出了一种基于计算智能的分数阶PID控制器参数优化整定方案.该方案选择时滞LFC系统时域输出响应构建优化目标函数,采用最近提出的灰狼优化算法获得最优的分数阶PID控制器参数,所设计的控制器能确保一定时滞区间内LFC系统的稳定性.仿真算例表明,所设计的LFC最优分数阶PID控制器比传统整数阶PID控制器的控制性能更优,时滞鲁棒性更强.     

Simulation based neuro-fuzzy hybrid intelligent PI control approach in four-area load frequency control of interconnected power system

This paper presents a novel control approach of hybrid neuro-fuzzy (HNF) for load frequency control (LFC) of four-area power system. The advantage of this controller is that it can handle the non-linearities, and at the same time it is faster than other existing controllers. The effectiveness of proposed controller in increasing the damping of local and inter area modes of oscillation is demonstrated in four area interconnected power system. Area-1 and area-2 consist of thermal reheat power plant whereas area-3 and area-4 consist of hydro power plant. Performance evaluation is carried out by using fuzzy, ANN, ANFIS and conventional PI and PID control approaches. The performances of the controllers are simulated using MATLAB/Simulink package. The result shows that intelligent HNF controller is having improved dynamic response and at the same time faster than ANN, fuzzy and conventional PI and PID controllers.     

Designing an adaptive type-2 fuzzy logic system load frequency control for a nonlinear time-delay power system

In this paper, a combination of type-2 fuzzy logic system (T2FLS) and a conventional feedback controller (CFC) has been designed for the load frequency control (LFC) of a nonlinear time-delay power system. In this approach, the T2FLS controller which is designed to overcome the uncertainties and nonlinearites of the controlled system is in the feedforward path and the CFC which plays an important role in the transient state is in the feedback path. A Lyapunov–Krasovskii functional has been used to ensure the stability of the system and the parameter adjustment laws for the T2FLS controller are derived using this functional. In this training method, the effect of delay has been considered in tuning the T2FLS controller parameters and thus the performance of the system has been improved. The T2FLS controller is used due to its ability to effectively model uncertainties, which may exist in the rules and data measured by the sensors. To illustrate the effectiveness of the proposed method, a two-area nonlinear time-delay power system has been used and compared with the controller that uses the gradient-descend (GD) algorithm to tune the T2FLS controller parameters.     

改进的粒子群算法在电力系统AGC中的应用

针对自动发电控制(AGC)中的负荷频率控制(LFC),对粒子群算法的计算过程进行了改进,提出了一种能有效的协调粒子群算法的优化精度和优化速度的方法,即动态改变粒子数目。该方法基于粒子群算法对于粒子数目的相对不敏感,可以在不影响精度的前提下大幅度提高优化速度,节约计算时间,适应予优化对象较复杂的情况。并针对单区域和两区域互联电力系统的不同指标要求,给出了用改进的粒子群优化算法优化PI控制器参数的方法,分别进行优化设计。仿真结果显示,其性能明显优于遗传算法优化的PI控制器。     

Study of differential search algorithm based automatic generation control of an interconnected thermal-thermal system with governor dead-band

An attempt has been made to the effective application of a recently introduced, powerful optimization technique called differential search algorithm (DSA), for the first time to solve load frequency control (LFC) problem in power system. In this paper, initially, DSA optimized classical PI/PIDF controller is implemented to an identical two-area thermal-thermal power system and then the study is extended to two more realistic power systems which are widely used in the literature. To assess the usefulness of DSA, three enhanced competitive algorithms namely comprehensive learning particle swarm optimization (CLPSO), ensemble of mutation and crossover strategies and parameters in differential evolution (EPSDE), and success history based DE (SHADE) are studied in this paper. Moreover, the superiority of proposed DSA optimized PI/PID/PIDF controller is validated by an extensive comparative analysis with some recently published meta-heuristic algorithms such as firefly algorithm (FA), bacteria foraging optimization algorithm (BFOA), genetic algorithm (GA), craziness based particle swarm optimization (CRPSO), differential evolution (DE), teaching-learning based optimization (TLBO), particle swarm optimization (PSO), and quasi-oppositional harmony search algorithm (QOHSA). A case of robustness and sensitivity analysis has been performed for the concerned test system under parametric uncertainty and random load perturbation. Furthermore, to demonstrate the efficacy of proposed DSA, the system nonlinearities like reheater of the steam turbine and governor dead band are included in the system modeling. The extensive results presented in this article demonstrate that proposed DSA can effectively improve system dynamics and may be applied to real-time LFC problem.     

An intelligent coordinator design for GCSC and AGC in a two-area hybrid power system

This study addresses the design procedure of an optimized fuzzy fine-tuning (OFFT) approach as an intelligent coordinator for gate controlled series capacitors (GCSC) and automatic generation control (AGC) in hybrid multi-area power system. To do so, a detailed mathematical formulation for the participation of GCSC in tie-line power flow exchange is presented. The proposed OFFT approach is intended for valid adjustment of proportional–integral controller gains in GCSC structure and integral gain of secondary control loop in the AGC structure. Unlike the conventional classic controllers with constant gains that are generally designed for fixed operating conditions, the outlined approach demonstrates robust performance in load disturbances with adapting the gains of classic controllers. The parameters are adjusted in an online manner via the fuzzy logic method in which the sine cosine algorithm subjoined to optimize the fuzzy logic. To prove the scalability of the proposed approach, the design has also been implemented on a hybrid interconnected two-area power system with nonlinearity effect of governor dead band and generation rate constraint. Success of the proposed OFFT approach is established in three scenarios by comparing the dynamic performance of concerned power system with several optimization algorithms including artificial bee colony algorithm, genetic algorithm, improved particle swarm optimization algorithm, ant colony optimization algorithm and sine cosine algorithm.     

Load Frequency Control of Multi-interconnected Renewable Energy Plants Using Multi-Verse Optimizer

A reliable approach based on a multi-verse optimization algorithm (MVO) for designing load frequency control incorporated in multi-interconnected power system comprising wind power and photovoltaic (PV) plants is presented in this paper. It has been applied for optimizing the control parameters of the load frequency controller (LFC) of the multi-source power system (MSPS). The MSPS includes thermal, gas, and hydro power plants for energy generation. Moreover, the MSPS is integrated with renewable energy sources (RES). The MVO algorithm is applied to acquire the ideal parameters of the controller for controlling a single area and a multi-area MSPS integrated with RES. HVDC link is utilized in shunt with AC multi-areas interconnection tie line. The proposed scheme has achieved robust performance against the disturbance in loading conditions, variation of system parameters, and size of step load perturbation (SLP). Meanwhile, the simulation outcomes showed a good dynamic performance of the proposed controller.     

Delay-discretization-based sliding mode $$H_{\infty }$$ load frequency control scheme considering actuator saturation of wind-integrated power system

This paper investigates the combined effect of actuator saturation and time-delay on load frequency control (LFC) of a wind-integrated power system (WIPS). Actuator saturation is represented in two different approaches such as polytopic and sector bounding. Delay-discretization-based sliding mode \(H_{\infty }\) control approach is proposed to design a novel LFC scheme. The proposed control scheme requires present as well as delayed states information as input to the controller. This requirement of control scheme is fulfilled by adopting a finite known delay. This finite known delay used in controller design is discretized into delay intervals. Lyapunov–Krasovskii functional is defined for each delay interval, and \(H_{\infty }\) stabilization criteria for the closed loop WIPS are derived in linear matrix inequality framework using Wirtinger-based inequality. The proposed control scheme is tested by considering a numerical example of two-area WIPS.

     

A novel hybrid DEPS optimized fuzzy PI/PID controller for load frequency control of multi-area interconnected power systems

In this paper, a novel hybrid Differential Evolution (DE) and Pattern Search (PS) optimized fuzzy PI/PID controller is proposed for Load Frequency Control (LFC) of multi-area power system. Initially a two-area non-reheat thermal system is considered and the optimum gains of the fuzzy PI/PID controller are optimized employing a hybrid DE and PS (hDEPS) optimization technique. The superiority of the proposed controller is demonstrated by comparing the results with some recently published modern heuristic optimization techniques such as DE, Bacteria Foraging Optimization Algorithm (BFOA), Genetic Algorithm (GA) and conventional Ziegler Nichols (ZN) based PI controllers for the same interconnected power system. Furthermore, robustness analysis is performed by varying the system parameters and operating load conditions from their nominal values. It is observed that the optimum gains of the proposed controller need not be reset even if the system is subjected to wide variation in loading condition and system parameters. Additionally, the proposed approach is further extended to multi-area multi-source power system with/without HVDC link and the gains of fuzzy PID controllers are optimized using hDEPS algorithm. The superiority of the proposed approach is shown by comparing the results with recently published DE optimized PID controller and conventional optimal output feedback controller for the same power systems. Finally, Reheat turbine, Generation Rate Constraint (GRC) and time delay are included in the system model to demonstrate the ability of the proposed approach to handle nonlinearity and physical constraints in the system model.     

PSO-scaled fuzzy logic to load frequency control in hydrothermal power system

This paper, presents the particle swarm optimization-based fuzzy logic controller (PSO FLC) design for load frequency control in a two-area interconnected hydrothermal power system. Flexible alternating current transmission system devices and energy storage devices are being installed to improve the reliability and stability of the system under dynamic conditions. One such devices namely thyristor-controlled phase shifter (TCPS) is connected in series with the tie-line to damp out the power swings and frequency oscillations. Similarly at the terminal of one control area, a fast acting energy storage device of superconducting magnetic energy storage (SMES) is connected to meet the sudden changes in demand. The existing conventional controllers are unable to provide the satisfactory performance over a wide range of operating conditions due to system nonlinearity and plant parameter variations. To improve the dynamic performance of the system, this work proposes an intelligent tuning approach using a combination of particle swarm optimization (PSO) and fuzzy logic technique. In this work, PSO algorithm is employed for the optimal selection of membership function parameters of the proposed fuzzy PI, TCPS and SMES controllers by minimizing the time domain objective function. The simulation study is performed by the proposed PSO FLC in a two-area interconnected power system. To show the effective performance of the proposed controller, a comparative study has been made with the conventional, genetic algorithm and fuzzy logic-based optimized controller under varying load conditions.     

Application of flower pollination algorithm in load frequency control of multi-area interconnected power system with nonlinearity

This work presents an application of bio-inspired flower pollination algorithm (FPA) for tuning proportional–integral–derivative (PID) controller in load frequency control (LFC) of multi-area interconnected power system. The investigated power system comprises of three equal thermal power systems with appropriate PID controller. The controller gain [proportional gain (K _p), integral gain (K _i) and derivative gain (K _d)] values are tuned by using the FPA algorithm with one percent step load perturbation in area 1 (1 % SLP). The integral square error (ISE) is considered the objective function for the FPA. The supremacy performance of proposed algorithm for optimized PID controller is proved by comparing the results with genetic algorithm (GA) and particle swarm optimization (PSO)-based PID controller under the same investigated power system. In addition, the controller robustness is studied by considering appropriate generate rate constraint with nonlinearity in all areas. The result cumulative performance comparisons established that FPA-PID controller exhibit better performance compared to performances of GA-PID and PSO-PID controller-based power system with and without nonlinearity effect.

     

风电介入下的多区域互联电力系统分布式经济模型预测负荷频率控制

针对风电介入下的多区域互联电力系统,提出一种分布式经济模型预测负荷频率控制策略.通过将大规模互联电力系统分解成若干个动态耦合的子系统,这些子系统能够利用网络交流并共享信息,使得各区域的控制器实现各自优化问题的求解.同时,在满足状态约束和控制输入约束的前提下,遵循传统火力发电优先、风力发电配合的原则,通过在线求解优化问题,实现风电介入下的多区域互联电力系统的负荷频率控制.为了提高系统整体运行经济性,所提出的分布式经济模型预测控制器将负荷调频成本、燃料消耗成本以及风力发电成本等经济性指标考虑在内.仿真结果表明,在阶跃负荷扰动下,所设计的控制器不仅可以满足调频要求,在降低计算负担和提高经济性能方面也具有一定优势.     

Multi area AGC scheme using imperialist competition algorithm in restructured power system

This paper is focused on optimization based design methodology and application of PID controller in restructured, competitive electricity market environment, for AGC problem. The paper compares two search algorithms for designing of PID controller used for AGC in multiarea power system. The optimal parameters of PID controller have been determined with the use of Imperialist Competitive Algorithm (ICA). A deregulated scenario has been considered to develop the model of the multiarea AGC scheme. This paper presents that the ICA tuned PID (ICA-PID) controller can optimally regulate the generators output and can provide the best dynamic response of frequency and tie-line power on a load perturbation. The performance of proposed controller has been checked on 2-area thermal power system and 3-area thermal-hydro power system with the consideration of generation rate constraint (GRC). The results obtained by ICA-PID controller and genetic algorithm tuned (GA-PID) controller have been compared on the basis of performance parameters (settling time and oscillations). It is seen that ICA-PID controller shows the better performance as compared to GA-PID controller.     

Distributed Model Predictive Load Frequency Control of Multi-area Power System with DFIGs

Reliable load frequency control (LFC) is crucial to the operation and design of modern electric power systems. Considering the LFC problem of a four-area interconnected power system with wind turbines, this paper presents a distributed model predictive control (DMPC) based on coordination scheme. The proposed algorithm solves a series of local optimization problems to minimize a performance objective for each control area. The generation rate constraints (GRCs), load disturbance changes, and the wind speed constraints are considered. Furthermore, the DMPC algorithm may reduce the impact of the randomness and intermittence of wind turbine effectively. A performance comparison between the proposed controller with and without the participation of the wind turbines is carried out. Analysis and simulation results show possible improvements on closed-loop performance, and computational burden with the physical constraints.      

Performance investigation of ABC algorithm in multi-area power system with multiple interconnected generators

This paper presents an extensive study on the application of Artificial Bee Colony (ABC) algorithm for load frequency control (LFC) in multi-area power system with multiple interconnected generators. The LFC model incorporates various possible physical constraints and non-linearities such as generation rate constraint, time delay, dead zone and boiler. The ABC algorithm is used to find the optimum PID controller parameters. The tuning performance of the algorithm is comparatively investigated against different optimization technique such as evolutionary programming (EP), genetic algorithm (GA), gravitational search algorithm (GSA) and particle swarm optimization (PSO). The robustness analysis of the system is also evaluated by investigating the dynamic response of the controller with load demand at varying time step, tuning based on different performance criterion and by varying the load demand. The performance of the system is evaluated based on the settling time and maximum overshoot value of the frequency deviation response. The performance of ABC is also verified against an exhaustive search based on interval halving method. Despite employing a single controller for multiple interconnected generators, the optimized controller is able to successfully damp oscillations in the system response and regulate the area control error back to zero in minimal amount of time. The results indicate the superiority of the ABC algorithm’s search mechanism in finding the optimum set of PID controller’s gain.     

Robust distributed MPC for load frequency control of uncertain power systems

Reliable Load frequency control (LFC) is crucial to the operation and design of modern electric power systems. However, the power systems are always subject to uncertainties and external disturbances. Considering the LFC problem of a multi-area interconnected power system, this paper presents a robust distributed model predictive control (RDMPC) based on linear matrix inequalities. The proposed algorithm solves a series of local convex optimization problems to minimize an attractive range for a robust performance objective by using a time-varying state-feedback controller for each control area. The scheme incorporates the two critical nonlinear constraints, e.g., the generation rate constraint (GRC) and the valve limit, into convex optimization problems. Furthermore, the algorithm explores the use of an expanded group of adjustable parameters in LMI to transform an upper bound into an attractive range for reducing conservativeness. Good performance and robustness are obtained in the presence of power system dynamic uncertainties.     

Non-linear sliding mode load frequency control in multi-area power system

This paper addresses non-linear sliding mode controller (SMC) with matched and unmatched uncertainties for load frequency control (LFC) application in three-area interconnected power system. In conventional LFC scheme, as the nominal operating point varies due to system uncertainties, frequency deviations cannot be minimized. These lead to degradation in the dynamic performance or even system instability. In this paper, an effective control law is proposed against matched and unmatched uncertainties.. The proposed controller has ability to vary closed-loop system damping characteristics according to uncertainties and load disturbances present in the system. The frequency deviation converges to zero with minimum undershoot/overshoot, fast settling time, significantly reduced chattering and ensures asymptotic stability. In addition, the controller is robust in the presence of parameter uncertainties and different disturbance patterns. It also guarantees high dynamic performance in the presence of governor dead band (GDB) and generation rate constraint (GRC). Simulations are performed to compare the proposed controller with linear SMC. Using proposed control strategy, undershoot/overshoot and settling time gets reduced by approximately 30% with respect to linear SMC. The computed performance indices and qualitative results establish the superiority as well as applicability of the proposed design for the LFC problem. Further, the proposed controller scheme is validated on IEEE 39 bus large power system.     

考虑通信时滞和采样周期的电力系统负荷频率控制

针对电力系统负荷频率稳定控制问题,本文提出了一种时滞/采样相关的离散负荷频率控制(LFC)方案.首先,考虑通信网络传输时滞和反馈信号采样周期对系统的影响,建立闭环电力系统LFC模型.然后,基于建立的LFC模型,利用双边闭环Lyapunov泛函和LMI技术,提出了低保守性的时滞/采样相关稳定准则和控制器设计方法,确保所提控制方案能在一个较大的通信时滞和采样周期条件下保持电力系统稳定运行.最后,通过单区域和三区域电力系统验证所提方法的有效性.仿真结果表明,所设计LFC方案比现有其他LFC方案的控制性能更佳,鲁棒性更强,并且能在一定大小的通信时滞条件下提升电力系统的动态性能.     

Teaching–learning based optimization algorithm based fuzzy-PID controller for automatic generation control of multi-area power system

This paper deals with the design of a novel fuzzy proportional–integral–derivative (PID) controller for automatic generation control (AGC) of a two unequal area interconnected thermal system. For the first time teaching–learning based optimization (TLBO) algorithm is applied in this area to obtain the parameters of the proposed fuzzy-PID controller. The design problem is formulated as an optimization problem and TLBO is employed to optimize the parameters of the fuzzy-PID controller. The superiority of proposed approach is demonstrated by comparing the results with some of the recently published approaches such as Lozi map based chaotic optimization algorithm (LCOA), genetic algorithm (GA), pattern search (PS) and simulated algorithm (SA) based PID controller for the same system under study employing the same objective function. It is observed that TLBO optimized fuzzy-PID controller gives better dynamic performance in terms of settling time, overshoot and undershoot in frequency and tie-line power deviation as compared to LCOA, GA, PS and SA based PID controllers. Further, robustness of the system is studied by varying all the system parameters from −50% to +50% in step of 25%. Analysis also reveals that TLBO optimized fuzzy-PID controller gains are quite robust and need not be reset for wide variation in system parameters.