Tuning and Assessment of Proportional–Integral–Derivative Controller for an Automatic Voltage Regulator System Employing Local Unimodal Sampling Algorithm

Abstract—This article presents an approach for obtaining proportional–integral–derivative controller parameters for an automatic voltage regulator system based on a local unimodal sampling optimization algorithm. A conventional integral time of squared error objective function and modified objective functions in terms of integral time of absolute error, integral of absolute error, integral of squared error, peak overshoot, and settling time with appropriate weighting factors are employed to tune the controller parameters. Different objective functions are employed to obtain optimized proportional–integral–derivative controller gains. Superiority of proposed technique over some recently published modern heuristic optimization techniques, such as artificial bee colony algorithm, particle swarm optimization algorithm, and differential evolution algorithm, for the same automatic voltage regulator system is demonstrated. Simulation results reveal that the proposed proportional–integral–derivative controlled automatic voltage regulator system tuned by the local unimodal sampling algorithm with modified objective function exhibits better performance in terms of settling time, peak overshoot, and stability. The robustness of the system tuned by the proposed algorithm is also studied satisfactorily by varying the time constants of the automatic voltage regulator system in the range of –50% to +50% in steps of 25%.     

TLBO optimized sliding mode controller for multi-area multi-source nonlinear interconnected AGC system

This paper represents design of output feedback sliding mode controller (SMC) for multi area multi-source interconnected power system. After designing output feedback SMC, teaching and learning based optimization (TLBO) technique is utilized to optimize feedback gain and switching vector of the controller. The superiority of the proposed approach is shown by comparing the result with output feedback tuned SMC with differential evolution and particle swarm optimization and state feedback SMC tuned with genetic algorithm for a two area thermal interconnected power system. Further, the proposed approach is extended to multi-area multi-source non linear automatic generation control (AGC) system with/without HVDC link. First area consists up thermal, hydro and gas; second area consists up thermal, hydro and nuclear as generating unit. Additionally, the superiority of proposed approach is shown by sensitivity analysis, which is carried out with wide changes in system parameters.     

Automatic generation control application with craziness based particle swarm optimization in a thermal power system

In this study, a novel gain scheduling Proportional-plus-Integral (PI) control strategy is suggested for automatic generation control (AGC) of the two area thermal power system with governor dead-band nonlinearity. In this strategy, the control is evaluated as an optimization problem, and two different cost functions with tuned weight coefficients are derived in order to increase the performance of convergence to the global optima. One of the cost functions is derived through the frequency deviations of the control areas and tie-line power changes. On the other hand, the other one includes the rate of changes which can be variable depends on the time in these deviations. These weight coefficients of the cost functions are also optimized as the controller gains have been done. The craziness based particle swarm optimization (CRAZYPSO) algorithm is preferred to optimize the parameters, because of convergence superiority. At the end of the study, the performance of the control system is compared with the performance which is obtained with classical integral of the squared error (ISE) and the integral of time weighted squared error (ITSE) cost functions through transient response analysis method. The results show that the obtained optimal PI-controller improves the dynamic performance of the power system as expected as mentioned in literature.     

Antlion Algorithm Optimized Fuzzy PID Supervised On-line Recurrent Fuzzy Neural Network Based Controller for Brushless DC Motor

In this paper, Antlion algorithm optimized Fuzzy PID supervised on-line Recurrent Fuzzy Neural Network based controller is proposed for the speed control of Brushless DC motor. Learning parameters of the supervised on-line recurrent fuzzy neural network controller, i.e., learning rate (η), dynamic factor (α), and number nodes (N_i) are optimized using Genetic algorithm, Particle Swarm optimization, Ant colony optimization, Bat algorithm, and Antlion algorithm. The proposed controller is tested with different operating conditions of the Brushless DC motor, such as varying load conditions and varying set speed conditions. The time domain specifications such as rise time, overshoot, undershoot, settling time, recovery time, and steady state error and also integral performance indices such as root mean square error, integral of absolute error, integral of squared error, and integral of time multiplied absolute error are measured and compared for above optimized controller. Simulation results show Antlion algorithm optimized Fuzzy PID supervised on-line recurrent fuzzy neural network based controller has proved to be superior than other considered controllers in all aspects. In addition, the experimental verification of proposed control system is presented to test the effectiveness of the proposed controller with different operating conditions of the Brushless DC motor.     

Effective oscillation damping of an interconnected multi-source power system with automatic generation control and TCSC

Stabilizing area frequency and tie-line power oscillations in interconnected power systems are main concerns that have received significant attention in automatic generation control (AGC) studies. This paper deals with modeling and simulation of thyristor controlled series capacitor (TCSC) based damping controller in coordination with AGC to damp the oscillations and thereby, improve the dynamic stability. The contribution of TCSC in tie-line power exchange is formulated analytically for small perturbation and a systematic method based on the Taylor series expansion is proposed for modeling of TCSC based damping controller. The integral gains of AGC and TCSC parameters are optimized simultaneously using an improved particle swarm optimization (IPSO) algorithm through minimizing integral of time multiplied squared error (ITSE) performance index. The performance of the proposed TCSC–AGC coordinated controller is compared with case of AGC alone. A two-area interconnected multi-source power system, including TCSC located in series with the tie-line, is studied considering nonlinearity effects of generation rate constraint (GRC) and governor dead band (GDB). Simulation results show that proposed controller shows greater performance in damping of the oscillations and enhancing the frequency stability. Furthermore, sensitivity analyses are carried out against system loading condition, parametric uncertainties, and different perturbation patterns to show the robustness of TCSC–AGC.     

Comparative performance analysis of Artificial Bee Colony algorithm in automatic generation control for interconnected reheat thermal power system

This study extensively presents the Automatic Generation Control (AGC) application of Artificial Bee Colony (ABC) algorithm. This algorithm is one of the new population based optimization algorithms which have been developed since 2005. In this study, the algorithm is applied to the interconnected reheat thermal power system in order to tune the parameters of PI and PID controllers which are used for AGC. The tuning performance of the algorithm is compared with that of Particle Swarm Optimization (PSO) algorithm through transient response analysis method. In addition to these, the robustness analysis is applied to the power system which is optimized by ABC algorithm so as to determine its response towards changing in the load and the system parameters, varied in the range of ±50%. The behavior of the system is also investigated with this analysis towards the different cost functions such as integral of absolute error (IAE), integral of squared error (ISE), integral of time weighted squared error (ITSE) and integral of time multiplied absolute error (ITAE). At the end of the study, it is seen that the ABC algorithm is successfully applied to the AGC in the application of interconnected reheat thermal power system, and it shows better tuning capability than the other similar population based optimization algorithm. Furthermore, it is also seen that the proposed system is robust and is not affected by changing in the load, the power system parameters and the cost functions.     

基于鲁棒方差优化的电力系统频率控制研究

随着新能源发电大规模并网,随机负荷扰动给电力系统稳定优化运行提出了新的挑战。针对自动发电控制过程中存在的随机扰动和参数摄动的问题,提出了一种基于鲁棒方差约束的状态反馈控制器的参数优化方法。根据鲁棒方差控制(Robust Variance Control,RVC)中不等式约束条件,分析了闭环系统在抑制随机扰动和提高阶跃扰动响应动态性能之间的博弈关系。构造了融合稳态状态方差和控制能量输出约束的优化问题,利用线性矩阵不等式(Linear Matrix Inequality,LMI)获得了鲁棒方差控制器参数。在此基础上,对配置的区域极点圆心坐标值和正标量两个参数进行遗传优化,得到性能指标最优的控制策略。以两区域电力系统模型为例,表明该方法能够有效抑制随机扰动并保持良好的控制性能和鲁棒性能。     

基于MVO算法与改进目标函数的电力系统负荷频率控制

针对风电并网时的随机波动功率、负荷频率控制(load frequency control, LFC)系统参数变化所引起的电力系统频率稳定问题,提出了一种基于智能优化算法与改进目标函数的互联电网LFC系统最优PID控制器设计方法。首先,分析了基于PID控制的含风电互联电力系统LFC闭环模型。其次,在时间乘误差绝对值积分(integral of time multiplied absolute error, ITAE)性能指标的目标函数中考虑了区域控制器的输出信号偏差,对优化目标函数进行改进。采用性能优良的多元宇宙优化(multi-verse optimizer, MVO)算法先计算后验证的思路,寻优获得最优PID控制器参数。最后,以两区域4机组互联电力LFC系统为例,仿真验证了基于MVO算法结合改进目标函数所获得的PID控制器,比基于MVO算法所获得的PID控制器,对阶跃负荷扰动、随机负荷扰动、风电功率偏差扰动以及系统的参数变化,具有相对较好的鲁棒性能。并且,对控制器参数也具有相对较好的非脆弱性指标。     

Power-Frequency Balance in Multi-generation System Using Optimized Fuzzy Logic Controller

This paper emphasizes the development of control strategy for inter-area oscillation suppression for a unified two-area hydro–thermal deregulated power system. A proportional derivative-type fuzzy logic controller with integral (PDFLC+I) controller was proposed for automatic generation control. Further comparisons among conventional integral controller, proportional integral derivative controller, and PDFLC+I are carried out, where the PDFLC+I controller is optimized by four different optimization techniques namely, algorithm, ant colony optimization, classical particle swarm optimization, and adaptive particle swarm optimization. In PDFLC+I controller optimization, scaling parameters of controllers are optimized. A comparative study shows that the proposed PDFLC+I controller has a better dynamic response following a step load change for the combination of PoolCo and bilateral contract-type transaction in deregulated environment. Proposed controller performance has also been examined for ±30% variation in system parameters. Non-linearity in the form of governor dead band is taken into account during simulation.     

Bat inspired algorithm based optimal design of model predictive load frequency control

Bat inspired algorithm (BIA) has recently been explored to develop a novel algorithm for distributed optimization and control. In this paper, BIA-based design of model predictive controllers (MPCs) is proposed for load frequency control (LFC) to enhance the damping of oscillations in power systems. The proposed model predictive load frequency controllers are termed as MPLFCs. Two-area hydro-thermal system, equipped with MPLFCs, is considered to accomplish this study. The suggested power system model considers generation rate constraint (GRC) and governor dead band (GDB). Time delays imposed to the power system by governor-turbine, thermodynamic process, and communication channels are accounted for as well. BIA is utilized to search for optimal controller parameters by minimizing a candidate time-domain based objective function. The performance of the proposed controller has been compared to those of the conventional PI controller based on integral square error (ISE) technique and the PI controller optimized by genetic algorithms (GA), in order to demonstrate the superior efficiency of the BIA-based MPLFCs. Simulation results emphasis on the better performance of the proposed MPLFCs compared to conventional and GA-based PI controllers over a wide range of operating conditions and system parameters uncertainties.     

考虑饱和环节的自动发电控制时滞系统串级控制

自动发电控制(AGC)调节过程中存在发电机变化率约束、时延等约束条件,使得基于线性模型的AGC控制策略不能反映真实电力系统的频率调节特性。针对AGC时滞系统同时存在饱和与时延的问题,提出了一种基于内外环比例—积分(PI)稳定域的串级控制系统遗传优化策略。基于AGC系统的负荷频率控制与机组控制组成的串级控制回路,采用Hopf分岔代数判据和时滞系统稳定域理论,分别求取了内外回路的PI稳定域,证明了饱和及时延参数会影响到PI稳定域的变化。通过将稳定域转化为控制器参数优化的约束条件后,对内环优化采用不同指标进行对比,证明了绝对误差积分(IAE)指标对于扰动具有更好的抑制能力;而对外环的对比表明采用时间乘平方误差积分(ITSE)指标具有更小的波动量。遗传优化结果表明所提控制策略能够有效抑制饱和及时延环节对系统性能的影响。     

Comparative performance evaluation of SMES-SMES, TCPS-SMES and SSSC-SMES controllers in automatic generation control for a two-area hydro-hydro system

This paper presents the automatic generation control (AGC) of an interconnected two-area multiple-unit hydro-hydro system. As an interconnected power system is subjected to load disturbances with changing frequency in the vicinity of the inter-area oscillation mode, system frequency may be severely disturbed and oscillating. To compensate for such load disturbances and stabilize the area frequency oscillations, the dynamic power flow control of static synchronous series compensator (SSSC) or Thyristor Controlled Phase Shifters (TCPS) in coordination with superconducting magnetic energy storage (SMES) are proposed. SMES-SMES coordination is also studied for the same. The effectiveness of proposed frequency controllers are guaranteed by analyzing the transient performance of the system with varying load patterns, different system parameters and in the event of temporary/permanent tie-line outage. Gains of the integral controllers and parameters of SSSC, TCPS and SMES are optimized with an improved version of particle swarm optimization, called as craziness-based particle swarm optimization (CRPSO) developed by the authors. The performance of CRPSO is compared to that of real coded genetic algorithm (RGA) to establish its optimization superiority.     

Automatic generation control of power system using a novel quasi-oppositional harmony search algorithm

The present work approaches a novel quasi-oppositional harmony search (QOHS) algorithm, as an optimization technique, for its optimum performance in the subject area of automatic generation control (AGC) of power system. The proposed QOHS algorithm is applied with an aim to converge rapidly towards the optimal solution(s) that houses both the characters of two guesses, i.e. opposite-point and quasi-opposite point. The area of concern of this study is to discuss the multi-objective problems of an interconnected power system for the benefits of AGC. The proposed QOHS algorithm is, individually, applied to single-area, precede to two-area considering the non-linearity effects of governor dead band and generation rate constraint and, finally, extended to four-area power system showing the consequences of multiple load disturbances. A case of robustness and stability analysis are also investigated for the studied two-area power system model. The control strategy, for the dynamic power system model, is based on area control error. The simplicity of the structure and acceptability responses of the well-known proportional–integral–derivative controller enforces to implement as a controller in this work. The comparative evaluation of the proposed QOHS algorithm is carried out by the way of comparing the dynamic performances of the studied power system model with those offered by other algorithms reported in the recent state-of-the-art literature. The simulation works, presented in the paper, reveal that the proposed QOHS algorithm may be effectively utilized for the purpose of AGC study of power system having varying degrees of complexities and non-linearities. Moreover, the proposed QOHS based control strategy adopted in this work provides a robust and stable speed control mechanism.     

Application of Firefly Algorithm for Load Frequency Control of Multi-area Interconnected Power System

Abstract—In this article, a firefly algorithm is proposed for load frequency control of multi-area power systems. Initially a two equal area non-reheat thermal system is considered and the optimum gains of the proportional integral/proportional integral derivative controller are optimized employing the firefly algorithm technique. The superiority of the proposed approach is demonstrated by comparing the results with some recently published techniques such as genetic algorithm, bacteria foraging optimization algorithm, differential evolution, particle swarm optimization, hybrid bacteria foraging optimization algorithm-particle swarm optimization, and Ziegler–Nichols-based controllers for the same interconnected power system. Further, the proposed approach is extended to a three-unequal-area thermal system considering generation rate constraint and governor dead-band. Investigations reveal on comparison that proportional integral derivative controller provides much better response compared to integral and proportional integral controllers. Additionally, robustness analysis is carried out by varying the operating load condition and time constants of speed governor, turbine, and inertia constant in the range of +50 to –50% from their nominal values as well as the size and position of step load perturbation to demonstrate the robustness of the proposed firefly algorithm optimized proportional integral derivative controller.     

Load frequency control of a realistic power system with multi-source power generation

In this paper, load frequency control (LFC) of a realistic power system with multi-source power generation is presented. The single area power system includes dynamics of thermal with reheat turbine, hydro and gas power plants. Appropriate generation rate constraints (GRCs) are considered for the thermal and hydro plants. In practice, access to all the state variables of a system is not possible and also their measurement is costly and difficult. Usually only a reduced number of state variables or linear combinations thereof, are available. To resolve this difficulty, optimal output feedback controller which uses only the output state variables is proposed. The performances of the proposed controller are compared with the full state feedback controller. The action of this proposed controller provides satisfactory balance between frequency overshoot and transient oscillations with zero steady state error in the multi-source power system environment. The effect of regulation parameter (R) on the frequency deviation response is examined. The sensitivity analysis reveals that the proposed controller is quite robust and optimum controller gains once set for nominal condition need not to be changed for ±25% variations in the system parameters and operating load condition from their nominal values. To show the effectiveness of the proposed controller on the actual power system, the LFC of hydro power plants operational in KHOZESTAN (a province in southwest of Iran) has also been presented.     

AGC of a multi-area multi-source hydrothermal power system interconnected via AC/DC parallel links under deregulated environment

This paper proposes the automatic generation control (AGC) of an interconnected multi-area multi-source hydrothermal power system under deregulated environment. The two equal control areas with hydro and thermal generating power sources are interconnected via AC/DC parallel links. The optimal proportional integral (PI) regulators are designed for the proposed power system to simulate all power market transactions which are possible in a restructured power system. The concept of DISCO participation matrix (DPM) is harnessed to simulate the transactions. Eigenvalue study is conducted to assess the effect of AC/DC parallel links on system performance. The study is also conducted, considering appropriate generation rate constraints (GRCs) for thermal and hydro generating sources. Further, the dynamic responses of the proposed multi-source hydrothermal power system are compared with single-source thermal–thermal power system and it has been ascertained that the responses of proposed power system are sluggish with large overshoots and settling times. Finally, the study is extended to frame and implement optimal PI regulators for the first time for the AGC of a conventional two-area non-reheat thermal power system with governor dead-band nonlinearity. The superiority of the optimal PI regulators has been established by comparing the results with recently published best claimed craziness based particle swarm optimization (CRAZYPSO) and hybrid bacterial foraging optimization algorithm-particle swarm optimization (hBFOA-PSO) algorithms based PI controller tuned for the same interconnected power system.     

Ant Colony Optimized Fuzzy Control Solution for Frequency Oscillation Suppression

This paper presents a novel approach in addressing a critical power system issue, i.e., automatic generation control (AGC) in a smart grid scenario. It proposes the design and implementation of an optimized fuzzy logic controller (FLC) for AGC of interconnected power network. There are three different sources of power generation considered in the two-area interconnected model of power system network. First area is equipped with a single reheat thermal unit and a superconducting magnetic energy storage (SMES) unit, while another area has a hydro-unit with SMES. A multi-stage optimization strategy for the optimal solution of FLC for tie-line and frequency oscillation suppression is proposed in this paper using an ant colony optimization technique. The optimization of FLC is carried out in four different stages. The first stage is the optimization of range of input and output variables; the second stage is the optimization of membership function; the third and fourth stages are the optimization for rule base and rule weight optimization, respectively. The performance of the proposed controller is also compared with another control approaches to stabilize P_tie-line and Δf oscillations; these are the Ziegler–Nichols-tuned proportional–integral–derivative (PID) controller and genetic algorithm optimized PID controller. A comprehensive analysis of the traditional techniques and proposed techniques is presented on the basis of major dynamic performance parameters, i.e., settling time and peak overshoot.     

考虑风机虚拟惯性的预测优化PIDD2自动发电控制方法

风电的大规模渗透,使分布式发电系统的自动发电控制(automatic generation control, AGC)必须应对自然环境不确定性所带来的影响,构建了风电机组参与频率调节的区域互联电网AGC模型;然后,对风机虚拟惯性的控制特性进行了分析,将其应用于短时负荷波动的快速响应;在此基础上,提出一种对带有二阶微分的比例积分微分控制器(proportional integral differential plus second order derivative, PIDD2)进行预测优化的控制策略。通过建立含PIDD2控制器的AGC模型,采用预测算法计算该系统的最优预测序列,并据此调整PIDD2控制器的参考信号,从而获取最优的AGC效果。仿真结果表明:在大规模风电渗透的AGC系统中,所提方法能有效解决传统固定参数PID控制器对系统动态变化所表现的不适应性问题。     

蚁群优化PI控制器在静止无功补偿器电压控制中的应用

静止无功补偿器(static var compensator,SVC)通常用来进行负荷补偿或系统补偿,在系统补偿时往往用于电压稳定控制,针对电压稳定控制的工况,文中提出一种采用蚁群算法优化PI控制器参数的方法,克服了常规PI控制对被控对象数学模型的依赖性,简单易于实现。蚁群优化算法中,以时间与误差绝对值乘积积分(integral of time-weighted absolute error,ITAE)准则作为寻优目标函数,对PI控制器的比例、积分参数进行调整、寻优,使SVC系统的响应过程达到最优。仿真和实验结果表明,该最优PI控制器能快速跟踪SVC系统的电压设定值,基于该PI控制器的SVC能迅速进行无功补偿,具有较强的适应性和较高的补偿精度。     

基于深度强化学习的孤立多微电网系统频率和电压综合控制

分布式电源出力不确定性和负荷功率扰动给孤立多微电网系统稳定带来较大威胁。提出基于多智能体柔性动作评价(MA-SAC)算法的孤立多微电网负荷频率控制器(LFC),同时采用柔性动作评价(SAC)算法对自动电压调节器(AVR)的比例积分(PI)控制参数进行优化调整。建立了多微电网LFC和AVR组合模型。对于电压和频率控制器的设计,分别根据SAC算法和多智能体深度强化学习(MA-DRL)框架建立各自的状态、动作空间与奖励函数。选择合适的神经网络与训练参数经过预学习生成深度强化学习控制器。最后通过仿真分析,基于SAC算法优化的PI控制器能更快跟踪电压参考值;多微电网系统遭遇功率扰动时,MA-SAC控制器可以快速维持频率稳定。