Neural-Network-Based Terminal Sliding Mode Control for Frequency Stabilization of Renewable Power Systems

This paper addresses a terminal sliding mode control (T-SMC) method for load frequency control (LFC) in renewable power systems with generation rate constraints (GRC). A two-area interconnected power system with wind turbines is taken into account for simulation studies. The terminal sliding mode controllers are assigned in each area to achieve the LFC goal. The increasing complexity of the nonlinear power system aggravates the effects of system uncertainties. Radial basis function neural networks (RBF NNs) are designed to approximate the entire uncertainties. The terminal sliding mode controllers and the RBF NNs work in parallel to solve the LFC problem for the renewable power system. Some simulation results illustrate the feasibility and validity of the presented scheme.      

Neural sliding-mode load frequency controller design of power systems

Load frequency control (LFC) is one of the most profitable ancillary services of power systems. Governor dead band (GDB) nonlinearity is able to deteriorate the LFC performance. In this paper, controller design via a neural sliding-mode method is investigated for the LFC problem of power systems with GDB. Power systems are made up of areas. In each area, a sliding-mode LFC controller is designed by introducing an additional sate, and a RBF neural network is utilized to compensate the GDB nonlinearity of the area. Weight update formula of the RBF network is derived from Lyapunov direct method. By this scheme, not only the update formula is obtained, but also the control system possesses the asymptotic stability. Simulation results illustrate the feasibility and robustness of the presented approach for the LFC problems of single-area and multi-area power systems.     

Grasshopper optimization algorithm for optimal load frequency control considering Predictive Functional Modified PID controller in restructured multi-resource multi-area power system with Redox Flow Battery units

Load frequency control (LFC) is a well-established issue in design and operation of power systems considering to the extension, restructuring, and complexity of the interconnected power systems and also the emergence utilization of renewable energy resources. This paper studies the frequency control of multi-area multi-source power system based on the importance of the LFC in the stability of the power system which includes various generation units of thermal, hydroelectric, wind, natural gas and diesel under the restructured environment. In this system, non-linear physical constraints, governor dead band (GDB) and generation rate constraint (GRC) are considered. In this paper, a new Predictive Functional Modified PID (PFMPID) controller is proposed that the effectiveness of this controller is verified compared to the traditional one. In order to optimize and demonstrate the superiority of the proposed control method, Grasshopper Optimization Algorithm (GOA) is proposed as a suitable solution. To further improve the performance of the under study system, the use of the Redox Flow Battery (RFB) energy storage unit has also been proposed. Since the operation evaluation of the proposed process is necessary in different system conditions, the performance of the proposed method is studied under various disturbances and simulation results are presented.     

奇异摄动型卡尔曼滤波算法及其在互联电力系统负荷频率控制中的应用

本文讨论了一种大系统实时随机最优控制算法--奇异摄动型卡尔曼滤波的设计问题. 建立了线性定常离散互联电力系统的奇异摄动模型.奇异摄动型卡尔曼滤波每循环一步所需 要的计算时间和内存量会大大减小.文中还考虑了控制增益的计算问题.通过对华北互联电 力系统LFC的仿真证明了其控制效果和奇异摄动型卡尔曼滤波算法的有效性.     

Design of decentralized robust load-frequency controller based on SVD method

A decentralized robust control scheme is presented for the load-frequency control of interconnected power systems with uncertain parameters. A singular value decomposition (SVD) technique and Lyapunov stability theory are adopted to implement a decentralized robust controller. The stability analysis of the closed-loop interconnected systems for all admissible uncertainties is discussed. The performance robustness of the proposed decentralized robust control scheme has been verified through simulation studies on a two-area power system model. The effectiveness of the decentralized control algorithm is compared to that of a centralized robust one. It has been found that both control schemes have almost the same performance with integral control action in the presence of parametric uncertainty in the plant.     

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.     

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.      

含混合储能的互联电力系统传感器容错负荷频率控制

为了改善多区域互联系统电能质量的问题,在原有负荷频率控制系统(LFC)的基础上引入由超级电容和蓄电池两者组成的混合储能系统(HESS),并针对电力系统中难以避免的传感器故障问题设计传感器主动容错策略.首先,建立含HESS的LFC系统模型用以减少负荷扰动对系统频率带来的影响;其次,针对带HESS的互联电力系统设计传感器主动容错策略,避免因传感器故障而引发的系统故障;最后,通过对一个三区域带HESS的互联系统进行仿真实验,验证HESS对改善互联系统电能质量的可行性和所提出的容错控制(FTC)的有效性.     

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.     

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.     

网络稳定性与控制的小增益原理:回顾与近期进展

小增益定理是现代控制理论中极为重要的基本工具之一,它在关联系统和不确定系统的鲁棒稳定性分析以及鲁棒控制器设计的许多工作中都发挥着极大的作用.基于输入到状态稳定性的概念,笔者于1994年首次提出了广义非线性小增益定理.与之前的小增益定理不同,这一结果为同时刻画关联系统的内部稳定性和外部稳定性提供了一个统一的框架.从镇定与鲁棒自适应控制到分散式或分布式控制以及输出调节(抗干扰渐近跟踪),基于非线性小增益定理已经发展出一系列的鲁棒非线性控制器设计新工具.在过去10年间,复杂非线性大系统已成为研究热点,驱动着小增益定理向更加完备的网络小增益定理方向发展,以期解决网络稳定性与控制中的新问题.对此,针对非线性小增益理论的一些最新研究进展及其在通讯和计算约束下的网络化控制和事件驱动控制应用结果进行综述,并对该理论的未来研究方向给出一些建议.     

多区域互联电力系统的自适应滑模负载频率控制

本文研究了一类计及电动汽车的电力系统中的负荷频率控制问题, 首先, 将电动汽车模型与传统的负载频率控制模型相结合,在未知扰动波动范围的条件下设计了自适应滑模控制律. 其次, 分别考虑了电网调频中的匹配扰动和不匹配扰动问题, 并利用李亚普诺夫稳定性理论导出了匹配和不匹配条件下的系统稳定的充分条件. 最后, 两个区域电力系统的仿真结果表明, 电动汽车作为电源和负载都可以提高电网的频率稳定性, 所设计的控制器可以有效地调节电网的频率波动.     

Robust load-frequency control for uncertain nonlinear power systems: A fuzzy logic approach

A new robust load-frequency control (LFC) methodology is proposed for controlling uncertain nonlinear power systems. Critical nonlinearity in the power system—the valve position limit on the governor, and the parametric uncertainty are concerned. The Takagi-Sugeno fuzzy model of the power system under consideration is first constructed to design the robust fuzzy-model-based LFC. Sufficient conditions for the robust asymptotic convergence of the frequency deviation are then provided in terms of linear matrix inequalities. Boundedness of the other system variables is also studied to ensure justifiable grounds for use of the proposed LFC method. Simulation results convincingly validate the effectiveness of the novel LFC design scheme and the theoretical discussions, which give a positive answer to the quality control of the electric energy.     

Frequency Regulation of Power Systems With a Wind Farm by Sliding-Mode-Based Design

Load frequency regulation is an essential auxiliary service used in dealing with the challenge of frequency stability in power systems that utilize an increasing proportion of wind power. We investigate a load frequency control method for multi-area interconnected power systems integrated with wind farms, aimed to eliminate the frequency deviation in each area and the tie-line power deviation between different areas. The method explores the derivative and integral terminal sliding mode control technology to solve the problem of load frequency regulation. Such technology employs the concept of relative degrees. However, the subsystems of wind-integrated interconnected power systems have different relative degrees, complicating the control design. This study develops the derivative and integral terminal sliding-mode-based controllers for these subsystems, realizing the load frequency regulation. Meanwhile, closed-loop stability is guaranteed with the theory of Lyapunov stability. Moreover, both a thermal power system and a wind power system are applied to provide frequency support in this study. Considering both constant and variable external disturbances, several numerical simulations were carried out in a two-area thermal power system with a wind farm. The results demonstrate the validity and feasibility of the developed method.      

Observer based robust integral sliding mode load frequency control for wind power systems

This paper investigates the load frequency control (LFC) for wind power systems with modeling uncertainties and variant loads. Since the system state is difficult to be accurately measured due to perturbation of nonlinear load, an observer is designed for reconstructing a substitution system state. Afterwards, an integral sliding surface is designed and a sliding mode LFC (SMLFC) strategy is proposed for reducing frequency deviations of the overall power system. Remarkably, it has been pointed out that a larger convergence rate of the observer error system has positive influences on the SMLFC performances, while the larger observer gain deteriorates the dynamic behavior. For seeking an acceptable balance so as to determine the optimal controller parameters, a collaborative design algorithm is proposed. The proposed method not only guarantees the asymptotical stability of overall power systems but also capable of improving the system robustness. Numerical examples are provided to demonstrate the effectiveness of the proposed methods.     

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.     

互联电力系统鲁棒分布式模型预测负荷频率控制

负荷频率控制是现代互联电力系统运行的重要保障.本文针对含有不确定因素和负荷扰动的多区域互联电力系统提出了一种基于线性矩阵不等式参数可调节的鲁棒分布式预测控制算法.设计各个区域控制器目标函数引入相邻区域的状态变量和输入变量,同时考虑发电机变化速率约束和阀门位置约束,将求解一组凸优化问题转化成线性矩阵不等式求解,得到各个区域的控制律,在线性矩阵不等式中引入一组可调参数,将优化一个上限值转化成优化吸引区,降低算法的保守性.仿真结果验证了该算法在负荷扰动、系统参数不确定和结构不确定性情况下具有鲁棒性.     

Active disturbance rejection based load frequency control and voltage regulation in power systems

An active disturbance rejection controller (ADRC) is developed for load frequency control (LFC) and voltage regulation respectively in a power system. For LFC, the ADRC is constructed on a three area interconnected power system. The control goal is to maintain the frequency at nominal value (60Hz in North America) and keep tie line power flow at scheduled value. For voltage regulation, the ADRC is applied to a static var compensator (SVC) as a supplementary controller. It is utilized to maintain the voltages at nearby buses within the ANSI C84.1 limits (or ±5% tolerance). Particularly, an alternative ADRC with smaller controller gains than classic ADRC is originally designed on the SVC system. From power generation and transmission to its distribution, both voltage and frequency regulating systems are subject to large and small disturbances caused by sudden load changes, transmission faults, and equipment loss/malfunction etc. The simulation results and theoretical analyses demonstrate the effectiveness of the ADRCs in compensating the disturbances and achieving the control goals.     

Small-gain theory for stability and control of dynamical networks: A Survey

This paper provides a personal account of the small-gain theory as a tool for stability analysis, control synthesis, and robustness analysis for interconnected uncertain systems. A milestone in modern control theory is the development of a transformative stability criterion known as the classical small-gain theorem proposed by George Zames in 1966, that surpasses Lyapunov theory in that there is no need to construct Lyapunov functions for the finite-gain stability of feedback systems. Under the small-gain framework, a feedback system composed of two finite-gain stable subsystems remains finite-gain stable if the loop gain is less than one. Despite its apparent simplicity at first sight, Zames’s small-gain theorem plays a crucial role in the development of linear robust control theory. Borrowing techniques in modern nonlinear control, especially Sontag’s notion of input-to-state stability (ISS), the first generalized, nonlinear ISS small-gain theorem proposed by one of the authors in 1994 overcomes the two shortcomings of Zames’s small-gain theorem. First, the use of nonlinear gains allows to consider strongly nonlinear, interconnected systems. Second, the role of initial conditions is made explicit so that both internal Lyapunov stability and external input-output stability can be studied in a unified framework. In this survey paper, we first review early developments in the nonlinear small-gain theory for interconnected systems of various types such as continuous-time systems, discrete-time systems, hybrid systems and time-delay systems, along with applications in robust nonlinear control. Then, we describe how to obtain a network small-gain theory for large-scale dynamical networks that are comprised of more than two interacting nonlinear systems. Constructive methods for the generation of Lyapunov functions for the total network are presented as well. Finally, this paper discusses how the network/nonlinear small-gain theory can be applied to obtain innovative solutions to quantized and event-based nonlinear control problems, that are important for the development of a complete theory of controlling cyber-physical systems subject to communications and computation constraints.     

Multi machine power system excitation control design via theories of feedback linearization control and nonlinear robust control

The dynamics of a large-scale power system are both nonlinear and interconnected. The equilibrium of such a system is typically unknown and uncertain, and the controllers within are also subject to physical limitations. In this paper, a new application of nonlinear robust control is presented for power system control design. It is assumed that the controllers are designed as a part of generator excitation system design. First, a customized exact feedback linearization scheme is developed for the power system under investigation. This new linearization scheme allows one to transform the power system with a single-axis system model into a linear uncertain system with an unknown equilibrium. Based on the latest development of nonlinear robust control theory, a novel control design is then applied to stabilize the resulting linearized uncertain system. Finally, a nonlinear decentralized excitation control is obtained by the inverse transformation. Compared with existing control schemes, the proposed control is free from such common deficiencies of power system nonlinear controllers as network dependence and equilibrium dependence. Detailed stability analysis and engineering judgment in the control design are provided. The results of simulation studies are presented.