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.     

Age-of-information-aware PI controller for load frequency control

Open communication system in modern power systems brings concern about information staleness which may cause power system frequency instability. The information staleness is often characterized by communication delay. However, communication delay is a packet-centered metric and cannot refect the requirement of information freshness for load frequency control (LFC). This paper introduces the age of information (AoI), which is more compre-hensive and informative than the conventional communication delay modeling method. An LFC controller and com-munication are integrated into the design for LFC performance improvement. An AoI-aware LFC model is formulated frst, and considering each allowable update period of the smart sensor, diferent AoI-aware PI controllers are then designed according to the exponential decay rate. The right AoI-aware controller and update period are selected according to the degree of frequency fuctuation of the power system. Case studies are carried out on one-area and two-area power systems. The results show the superior performance of the AoI-aware controllers in comparison to the delay-dependent controllers.     

Load frequency control and automatic generation control using fractional-order controllers

Recently, fractional calculus has received extensive attention and research. Accordingly, there is an increasing interest in fractional-order (FO) dynamic systems and controllers. The widely used classical integer-order proportional-integral controller and proportional-integral-derivative controller are usually adopted in the load frequency control (LFC) and automatic generation control (AGC) to improve the dynamic response and to eliminate or reduce steady-state errors. This paper utilizes the FO controllers to improve stability and response of LFC and AGC system. The paper uses the integral of the time-weighted absolute error performance index for optimal controller design. The paper investigates LFC and AGC for both isolated and interconnected power systems and shows that FO controllers perform better than classical integer-order controllers in theses systems.     

Two-level optimal load–frequency control for multi-area power systems

In large-scale power systems, classical centralized control approaches may fail due to geographically distribution of information and decentralized controllers result in sub-optimal solution for load–frequency control (LFC) problems. In this paper, a two-level structure is presented to obtain optimal solution for LFC problems and also reduce the computational complexity of centralized controllers. In this approach, an interconnected multi-area power system is decomposed into several sub-systems (areas) at the first-level. Then an optimization problem in each area is solved separately, with respect to its local information and interaction signals coming from other areas. At the second-level, by updating the interaction signals and using an iterative procedure, the local controllers will converge to the overall optimal solution. By parallel solving of areas, the computational time of the algorithm is reduced in contrast to centralized controllers. This approach is applicable to any interconnected large-scale power system. However, for simulation purposes, a three-are power system is presented to show advantages and optimality of the proposed algorithm.     

Load frequency control of an autonomous hybrid power system by quasi-oppositional harmony search algorithm

This paper deals with a novel quasi-oppositional harmony search algorithm (QOHSA) based design of load frequency controller for an autonomous hybrid power system model (HPSM) consisting of multiple power generating units and energy storage units. QOHSA is a novel improved version of music inspired harmony search algorithm for obtaining the best solution vectors and faster convergence rate. In this paper, the efficacy of the proposed QOHSA is adjudged for optimized load frequency control (LFC) of an autonomous HPSM. The studied HPSM consists of renewable/non-renewable energy based generating units such as wind turbine generator, solar photovoltaic, solar thermal power generator, diesel engine generator, fuel cell with aqua-electrolyzer while energy storage units consists of battery energy storage system, flywheel energy storage system and ultra-capacitor. Gains of the conventional controllers such as integral (I) controller, proportional–integral (PI) controller and proportional–integral–derivative (PID) controller (installed as frequency controller one at a time in the proposed HPSM) is optimized using QOHSA to mitigate any frequency deviation owing to sudden generation/load change. In order to corroborate the efficacy of QOHSA, performance of QOHSA to design optimal LFC is compared with that of other well-established technique such as teaching learning based optimization algorithm (TLBOA). The comparative performances of the HPSM under the action of QOHSA/TLBOA based optimized conventional controllers (I or PI or PID) are investigated and compared in the present work. It is found that the QOHSA tuned frequency controllers improves the overall dynamic response in terms of settling time, overshoot and undershoot in the profile of frequency deviation and power deviation of the studied HPSM.     

Design of integral controller for Load Frequency Control of Static Synchronous Series Compensator and Capacitive Energy Source based multi area system consisting of diverse sources of generation employing Imperialistic Competition Algorithm

This paper presents the design of integral controller for Load Frequency Control (LFC) under deregulated environment having diverse sources of power generation employing Imperialistic Competition Algorithm (ICA). Static Synchronous Series Compensator (SSSC) along with Capacitive Energy Storage (CES) has also been proposed to further increase the dynamic performance of the system in terms of peak time, overshoot and settling time. The concept of soft computing techniques greatly helps in overcoming the disadvantages posed by the conventional controllers. Open transmission access and the evolving of more socialized companies for generation, transmission and distribution affects the formulation of LFC problem. So the traditional LFC system is modified to take into account the effect of bilateral contracts on the dynamics. Simulation results show that the Imperialistic Competition Algorithm based system employing Static Synchronous Series Compensator and Capacitive Energy Source has better dynamic performance over the system without these parameters.     

Robust decentralized load frequency control of interconnected power system with Generation Rate Constraint using Type-2 fuzzy approach

The Load Frequency Control (LFC) problem has been a major subject in electrical power system design/operation. LFC is becoming more significant recently with increasing size, changing structure and complexity in interconnected power systems. In practice LFC systems use simple Proportional Integral (PI) controllers. As the PI control parameters are usually tuned, based on classical approaches. Moreover, they have fixed gains; hence are incapable of obtaining good dynamic performance for a wide range of operating conditions and various load changes, in multi-area power system. Literature shows that fuzzy logic controller, one of the most useful approaches, for utilizing expert knowledge, is adaptive in nature and is applied successfully for power system stabilization control. This paper proposes a Type-2 (T2) fuzzy approach for load frequency control of two-area interconnected reheat thermal power system with the consideration of Generation Rate Constraint (GRC). The performance of the Type-2 (T2) controller is compared with conventional controller and Type-1 (T1) fuzzy controller with regard to Generation Rate Constraint (GRC). The system parametric uncertainties are verified by changing parameters by 40% simultaneously from their typical values.     

Bacteria foraging optimization algorithm based load frequency controller for interconnected power system

Social foraging behavior of Escherichia coli bacteria has recently been explored to develop a novel algorithm for distributed optimization and control. The Bacterial Foraging Optimization Algorithm (BFOA), as it is called now, is currently gaining popularity in the community of researchers, for its effectiveness in solving certain difficult real world optimization problems. This paper proposes BFOA based Load Frequency Control (LFC) for the suppression of oscillations in power system. A two area non-reheat thermal system is considered to be equipped with proportional plus integral (PI) controllers. BFOA is employed to search for optimal controller parameters by minimizing the time domain objective function. The performance of the proposed controller has been evaluated with the performance of the conventional PI controller and PI controller tuned by genetic algorithm (GA) in order to demonstrate the superior efficiency of the proposed BFOA in tuning PI controller. Simulation results emphasis on the better performance of the optimized PI controller based on BFOA in compare to optimized PI controller based on GA and conventional one over wide range of operating conditions, and system parameters variations.     

Robust Load Frequency Control with Dynamic Demand Response for Deregulated Power Systems Considering Communication Delays

Communication networks are used in load frequency control (LFC) for transmitting remote measurements and control commands, and in demand side response (DSR) for aggregating small-scale controllable loads. This paper investigates modeling and controller design for LFC together DSR in a deregulated environment, considering multiple time delays introduced by the usage of communication channels. Time delay model of the deregulated multi-area LFC with dynamic demand control (DDC) is obtained at first, in which a typical thermostatically controlled appliance, air conditioner, is used for DDC. A robust proportional integral derivative (PID) load frequency controller is designed, through the H_∞ performance analysis and the particle swarm optimization (PSO) searching algorithm, to deal with the load disturbances and multiple delays in the LFC loop and the DDC loop. Case studies based on a three-area deregulated LFC system demonstrate the effectiveness of the proposed load frequency controller and the performance improvement from the DDC. Simulation results show that the DDC can increase the delay margin of the LFC scheme. Moreover, several delay stable regions are revealed via simulation method.     

Quasi oppositional harmony search algorithm based controller tuning for load frequency control of multi-source multi-area power system

This paper deals with the load frequency control (LFC) study of single-area and interconnected two-area power system having diversified power sources. The two areas considered in the present study are identical. Each area is having thermal, hydro and gas based power plants. Split-shaft model of gas turbine is used in the present work as one of the diversified generating unit for the purpose of LFC study. Optimal gains of the classical controllers (like integral controller, proportional–integral controller and proportional–integral–derivative (PID) controller, one installed at a time in the studied models) are obtained by using a novel music-inspired metaheuristic harmony search algorithm (HSA) which incorporates quasi opposition based learning technique for memory initialization and also for generation jumping. Single-area power system with diverse power sources is considered and its optimal transient performances are obtained and compared for step load perturbation. The same approach is further extended to two-area interconnected power system consisting of diverse power sources with nominal values of area input parameters. The performance of PID controller is found to be the best one for the studied power system models. It is also revealed that the performance of the interconnected two-area power system with AC–DC tie line is better in comparison to AC tie line.     

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。     

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。     

Sliding mode based load-frequency control in power systems

The paper presents a new discrete-time sliding mode controller for load-frequency control (LFC) in control areas (CAs) of a power system. As it uses full-state feedback it can be applied for LFC not only in CAs with thermal power plants but also in CAs with hydro power plants, in spite of their non-minimum phase behaviors. To enable full-state feedback we have proposed a state estimation method based on fast sampling of measured output variables, which are frequency, active power flow interchange and generated power from power plants engaged in LFC in the CA. The same estimation method is also used for the estimation of external disturbances in the CA, what additionally improves the overall system behavior. Design of the discrete-time sliding mode controller for LFC with desired behavior is accomplished by using a genetic algorithm. To the best of our knowledge, proposed controller outperforms any of the existing controllers in fulfilling the requirements of LFC. It was thoroughly compared to the commonly used PI controller by extensive simulation experiments on a power system with four interconnected CAs. These experiments show that the proposed controller ensures better disturbance rejection, maintains required control quality in the wider operating range, shortens the frequency’s transient response avoiding the overshoot and is more robust to uncertainties in the system.     

Robust coordinated design of multiple and multi-type damping controller using differential evolution algorithm

A robust coordination scheme to improve the stability of a power system by optimal design of multiple and multi-type damping controllers is presented in this paper. The controllers considered are power system stabilizer (PSS) and static synchronous series compensator (SSSC)-based controller. Local measurements are provided as input signals to all the controllers. The coordinated design problem is formulated as an optimization problem and differential evolution (DE) algorithm is employed to search for the optimal controller parameters. The performance of the proposed controllers is evaluated for both single-machine infinite-bus power system and multi-machine power system. Nonlinear simulation results are presented over a wide range of loading conditions and system configurations to show the effectiveness and robustness of the proposed coordinated design approach. It is observed that the proposed controllers provide efficient damping to power system oscillations under a wide range of operating conditions and under various disturbances. Further, simulation results show that, in a multi-machine power system, the modal oscillations are effectively damped by the proposed approach.     

A Framework for Economic Load Frequency Control Design Using Modified Multi-objective Genetic Algorithm

This article deals with the coordination of security-constrained economic dispatch and load frequency control in an interconnected power system. The realistic and performance optimization inherent of the load frequency control (LFC) and security-constrained economic dispatch are fully considered without simplifying assumptions. For this purpose, modeling security-constrained economic dispatch as a discontinuous control action in the continuous frequency response model of a power system is well addressed. Considering conflict behavior of LFC and security-constrained economic dispatch beside the powerfulness of the multi-objective genetic algorithm (GA) to solve high-dimensional problems with conflicted objective functions makes it attractive for the automatic generation control coordination problem. The employed security-constrained economic dispatch utilizes the advantages of dynamic economic dispatch to achieve more realistic results. The GA is used to compute the decentralized control parameters and centralized generation levels of the on-line units to achieve an acceptable operating point. A significant modification in convergence speed has been performed by using LFC model properties in corporation with the genetic algorithm, so the proposed method gives considerable promise for implementation in multi-area power systems. The efficiency of the proposed algorithm and modification is demonstrated on a three control area power system.     

Load frequency control of power system under deregulated environment using optimal firefly algorithm

In this paper, a novel Firefly Algorithm (FA) optimized hybrid fuzzy PID controller with derivative Filter (PIDF) is proposed for Load Frequency Control (LFC) of multi area multi source system under deregulated environment by considering the physical constraints such as Generation Rate Constraint (GRC) and Governor Dead Band (GDB) nonlinearity. As the effectiveness of FA depends on algorithm control parameters such as randomization, attractiveness, absorption coefficient and number of fireflies are systematically investigated, the control parameters of FA are tuned by carrying out multiple runs of algorithm for each control parameter variation then the best FA control parameters are suggested. Additionally, the superiority of the FA is demonstrated by comparing the results with tuned Genetic Algorithm (GA). To investigate the effectiveness of the proposed approach, time domain simulations are carried out considering different contracted scenarios and the comparative results are presented. Further, sensitivity analysis is performed by varying the system parameters and operating load conditions. It is observed from the simulation results that the designed controllers are robust and the optimum gains of proposed controller need not be reset even if the system is subjected to wide variation in loading condition and system parameters. Finally, the effectiveness of the proposed control scheme is evaluated under random step load disturbance.     

Impact of communication time delays on combined LFC and AVR of a multi-area hybrid system with IPFC-RFBs coordinated control strategy

In this paper, the impact of communication time delays (CTDs) on combined load frequency control (LFC) and automatic voltage regulation (AVR) of a multi-area system with hybrid generation units is addressed. Investigation reveals that CTDs have significant effect on system performance. A classical PID controller is employed as a secondary regulator and its parametric gains are optimized with a differential evolution - artificial electric field algorithm (DE-AEFA). The superior performance of the presented algorithm is established by comparing with various optimization algorithms reported in the literature. The investigation is further extended to integration of redox flow batteries (RFBs) and interline power flow controller (IPFC) with tie-lines. Analysis reveals that IPFC and RFBs coordinated control enhances system dynamic performance. Finally, the robustness of the proposed control methodology is validated by sensitivity analysis during wide variations of system parameters and load.     

基于事件触发控制的时滞电力系统负荷频率控制

区域电网间存在较高的数据传输,使有限的通信和计算资源变得拥塞。为降低区域电网间的通信负担,提出基于事件触发控制的时滞电力系统负荷频率控制(LFC)方法。针对具有通信延迟的LFC系统,建立基于事件触发控制的时滞LFC动态模型。进而采用多求和不等式,提出具有事件触发控制器的时滞相关LFC系统Lyapunov稳定分析判据;在此基础上,推导了基于事件触发通信和输出反馈的负荷频率控制器协同设计方案,以保证电力系统频率稳定性的同时提高数据传输效率。仿真结果表明,所提方法能够有效减小互联系统频率和联络线功率振荡,保证系统的时滞稳定性并减少网络通信的冗余传输。     

Robust decentralized neural networks based LFC in a deregulated power system

In this paper, a decentralized radial basis function neural network (RBFNN) based controller for load frequency control (LFC) in a deregulated power system is presented using the generalized model for LFC scheme according to the possible contracts. To achieve decentralization, the connections between each control area with the rest of system and effects of possible contracted scenarios are treated as a set of input disturbance signals. The idea of mixed H₂/H_∞ control technique is used for the training of the proposed controller. The motivation for using this control strategy for training the RBFNN based controller is to take large modeling uncertainties into account, cover physical constraints on control action and minimize the effects of area load disturbances. This newly developed design strategy combines the advantage of the neural networks and mixed H₂/H_∞ control techniques to provide robust performance and leads to a flexible controller with simple structure that is easy to implement. The effectiveness of the proposed method is demonstrated on a three-area restructured power system. The results of the proposed controllers are compared with the mixed H₂/H_∞ controllers for three scenarios of the possible contracts under large load demands and disturbances. The resulting controller is shown to minimize the effects of area load disturbances and maintain robust performance in the presence of plant parameter changes and system nonlinearities.     

Robust analysis and design of power system load frequency control using the Kharitonov's theorem

This paper presents a robust decentralized proportional-integral (PI) control design as a solution of the load frequency control (LFC) in a multi-area power system. In the proposed methodology, the system robustness margin and transient performance are optimized simultaneously to achieve the optimum PI controller parameters. The Kharitonov’s theorem is used to determine the robustness margin, i.e., the maximal uncertainty bounds under which the stable performance of the power system is guaranteed. The integral time square error (ITSE) is applied to quantify the transient performance of the LFC system. In order to tune the PI gains, the control objective function is optimized using the genetic algorithm (GA). To validate the effectiveness of the proposed approach, some time based simulations are performed on a three-area power system and the results are then compared with an optimal PI controller. The comparisons show that the proposed control strategy provides the satisfactory robust performance for the wide range of system parameters and load changes in the presence of system nonlinearities and is superior to the other methods.