Decentralized robust adaptive-output feedback controller for power system load frequency control

In this paper, a new model reference-decentralized robust adaptive-output feedback controller is proposed for the load frequency control (LFC) of large-scale power systems with unknown parameters. This control strategy requires only local input–output data and can follow random changes in the operating conditions. The controller is designed such that the trajectory errors and the control gains of each area remain uniformly bounded. In the proposed method, firstly an adaptive observer is designed to estimate the state variables and system parameters using local data only. Then a locally linear combination of the estimated states and the model reference states are used to design a robust adaptive-output feedback controller for each area. Simulation results for a three-area power system show that the proposed controller achieves good performance even in the presence of plant parameter changes and system non-linearities. Received: 18 October 2001/Accepted: 24 October 2001     

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。     

Adaptive fuzzy logic load frequency control of multi-area power system

Based on indirect adaptive fuzzy control technique, a new load frequency control (LFC) scheme for multi-area power system is proposed. The power systems under study have the characterization of unknown parameters. Local load frequency controller is designed using the frequency and tie-line power deviations of each area. In the controller design, the approximation capabilities of fuzzy systems are employed to identify the unknown functions, formulate suitable adaptive control law and updating algorithms for the controller parameters. It is proved that the proposed controller ensures the boundedness of all variables of the closed-loop system and the tracking error. Moreover, in the proposed controller an auxiliary control signal is introduced to attenuate the effect of fuzzy approximation error and to mitigate the effect of external disturbance on the tracking performance. Simulation results of a three-area power system are presented to validate the effectiveness of the proposed LFC and show its superiority over a classical PID controller.     

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.     

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.     

Decentralized load frequency controller for a multi-area interconnected power system

This paper proposes a control scheme for the load frequency control (LFC) problem of multi-area power systems. These systems are treated as interconnected dynamical systems. In the design of the proposed controller, each local area network is overlapped with states representing the interconnections with the other local area networks in the global system. Then, a decentralized control scheme is developed as function of the local area state variables and those resulting from the overlapped states which represent an approximation of the interconnection variables. The proposed controller guarantees the asymptotic stability of the overall closed loop system.The simulation results indicate that the proposed control scheme works well. In addition, they show that the controlled system is robust to changes in the parameters of the power system and to bounded input disturbances acting on the system. Moreover, the simulation results show that the controlled system behaves well even when there is a maximum limit on the rate of change in power generation.     

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.     

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.     

Comparative performance analysis of teaching learning based optimization for automatic load frequency control of multi-source power systems

This paper presents a new population based parameter free optimization algorithm as teaching learning based optimization (TLBO) and its application to automatic load frequency control (ALFC) of multi-source power system having thermal, hydro and gas power plants. The proposed method is based on the effect of the influence of teacher on the output of learners and the learners can enhance their knowledge by interactions among themselves in a class. In this extensive study, the algorithm is applied in multi area and multi-source realistic power system without and with DC link between two areas in order to tune the PID controller which is used for automatic generation control (AGC). The potential and effectiveness of the proposed algorithm is compared with that of differential evolution algorithm (DE) and optimal output feedback controller tuning performance for the same power systems. The dynamic performance of proposed controller is investigated by different cost functions like 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) and the robustness of the optimized controller is verified by its response toward changing in load and system parameters. It is found that the dynamic performance of the proposed controller is better than that of recently published DE optimized controller and optimal output feedback controller and also the proposed system is more robust and stable to wide changes in system loading, parameters, size and locations of step load perturbation and different cost functions.     

An adaptive controller for power system load-frequency control

An adaptive controller is presented for load-frequency control of power systems. It uses a PI (proportional-integral) adaptation to satisfy the hyperstability condition for taking care of the parameter changes of the system. Only the available information on the states and output are required for the control. No explicit parameter identification is needed. The controller can be designed by using a reduced plant model to simplify the design without degrading the performance much, so it is very easy to implement practically. The simulation results indicate that good control performance can be obtained and that the performance is sensitive to the plant parameter changes. The control remains effective in the presence of generation rate constraints     

基于控制系统四元组形式的发电机非线性分散鲁棒控制

分析了仅包含状态变量、输出变量、控制变量的控制系统常规三元组形式应用到发电机分散鲁棒控制时遇到的困难，为克服这些困难提出了包含状态变量、输出变量、控制变量、量测变量的控制系统四元组形式的概念。量测变量的引入使得发电机综合控制模型本身变为各机解耦、与外部系统网络参数及动态无关，在此模型下设计出分散鲁棒控制器是自然的。此模型可以考虑系统包含各种动态元件如FACTS元件、HVDC系统等情况，在此四元组模型下，通过直接寻求控制量与控制目标之间关系的关联度方法将发电机控制的四元组模型完全线性化，通过励磁控制使发电机端电压具有良好的动态特性，通过汽门控制提高发电机功角暂态稳定性。数字仿真表明，所设计的基于控制系统四元组形式的发电机非线性分散鲁棒综合控制器是有效的。     

Robust multivariable predictive based load frequency control considering generation rate constraint

In this paper, a robust multivariable Model based Predictive Control (MPC) is proposed for the solution of load frequency control (LFC) in a multi-area power system. The proposed control scheme is designed to consider multivariable nature of LFC, system uncertainty and generation rate constraint, simultaneously. A constrained MPC is employed to calculate optimal control input including generation rate constraints. Economic allocation of generation is further ensured by modification of the predictive control objective function. To achieve robustness against system uncertainty and variation of parameters, a linear matrix inequality (LMI) based approach is employed. To validate the effectiveness of the proposed controller, time-based simulations on a three-area power system are performed and the results are then compared with PI controller. The results evaluation reveals that the proposed control strategy offers satisfactory performance in the presence of system constraint and provides robust performance for an extensive range of system uncertainty.     

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.     

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。     

负荷频率系统的LFC模糊监控器设计

应用在LFC控制中常规的模糊调整增益PI控制器和I控制器,只针对单一区域的负荷频率进行控制,并不考虑实际模型中的互相扰动.其中最突出的问题是由于不限制联络线上的功率流动,电能总是从频率高区域流向频率低区域,加剧了频率高区域的控制负担,再加上各区域控制动作的不协调,使得当扰动在不同的时间和幅值时引起系统调节过程的急剧恶化,导致整个系统不稳定.提出一种基于模糊MAMDANI推理算法的模糊监督控制器,采用各个区域的频率偏差作为控制器的输入,监督控制器作为一种前馈补偿,设计输出为一个ACE的倍数,加快调节过程,到达稳态.经过实验仿真数据对比,说明提出的监督控制器能有效提高系统的稳定性.     

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.     

Design of biogeography optimization based dual mode gain scheduling of fractional order PI load frequency controllers for multi source interconnected power systems

This paper presents the effect on application of biogeography optimization (BBODMFOPI) based dual mode gain scheduling of fractional order proportional integral controllers for load frequency control (LFC) of a multi source multi area interconnected power systems. This controller has three parameters to be tuned. Thus, it provided one more degree of freedom in comparison with the conventional proportional integral (PI) controller. For proper tuning of the controller parameters, Biogeography-Based Optimization (BBO) was applied. BBO is a novel evolutionary algorithm which involves the methodology of making the system effectively by using mathematical techniques. The dual mode concept is also incorporated in this work, because it can improve the system performance. In this work, simulation investigations were taken out on a two-area power system with different generating units. The simulation results show that the proposed biogeography optimization based dual mode gain scheduling of fractional order PI controllers, provide better transient as well as steady state response. It is also found that the proposed controller is less sensitive to the changes in system parameters and robust under different operating condition of the power systems.     

Decentralized load frequency based on H∞ control

This paper presents a decentralized load frequency control (LFC) based on H_∞ optimal control theory with an observer. A few LFC schemes have been proposed based on the optimal control theory, but they have not considered the change of system parameters in operation and the characteristics of load disturbances in a target system. In this paper, H_∞ robust control is introduced to address such problems. Owing to its practical merit, the proposed control scheme is a decentralized LFC. Employing observer theory, the proposed method requires only frequency and tie‐line power deviation in each area. Numerical simulations are shown to demonstrate the effectiveness of the proposed method. H_∞ control was proven to show greater effectiveness of damping disturbance over the conventional optimal control by the design of control systems aimed at restricting the H_∞ norm of its transfer function. In particular, when a decentralized LFC is applied, by reducing the system size, H_∞ norm is easier to dampen; thus H_∞ control is more effective in the decentralized control. Future research topics include the design of H_∞ control system with a weight on frequency response. © 2001 Scripta Technica, Electr Eng Jpn, 136(3): 28–38, 2001     

基于尼科尔斯PID设计方法的负荷频率控制

为解决互联水电系统负荷频率控制(load frequencycontrol,LFC)问题,及保持互联电网系统频率、联络线功率及区域控制误差(area control error,ACE)的稳定,根据闭环系统谐振峰值与系统响应最大峰值之间的关系,构建一个与系统参数及控制器参数都相关的优化问题,通过该问题的求解获得控制器参数与系统参数之间的数学关系,针对水轮发电系统非最小相位特性,通过串加比例–微分(proportional-derivative,PD)控制方式降低系统阶次,设计尼科尔斯(Nichols)曲线的比例–积分–微分(proportional-integral-derivative,PID)控制器。基于模型参数扰动和负荷干扰的仿真结果表明:尼科尔斯PID控制器能快速调整系统频率偏差、联络线功率偏差及ACE为0,具有良好的鲁棒性能和抗负荷干扰性能,系统过渡过程性能明显优于传统PID调节器结果。     

On the eigenvalue control of electromechanical oscillations byadaptive power system stabilizer

The eigenvalue control strategy, which utilizes an adaptive power system stabilizer, is presented for the decentralized control of damping and frequency of electromechanical oscillations in power systems. The control procedure includes the complete identification of the decoupled subsystem model in real-time from local measurements only and the assignment of its estimated electromechanical eigenvalue by the change of stabilizer parameters. The robustness and efficiency of the proposed adaptive controller to enhance overall system stability are illustrated by several examples, including the three-machine power system model