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.     

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.     

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.     

基于滑模控制的含风储多域电力系统负荷频率控制

建立含风储多域互联电力系统负荷频率控制(LFC)模型,同时考虑系统参数不确定性、储能系统和传统机组控制信道延时问题.为提高系统鲁棒性,降低储能系统的容量配置,针对含风储的LFC模型,设计滑模负荷频率控制器,并提出滑模负荷频率控制器和储能协调的控制策略.算例分析表明,所提出的协调控制策略在新能源大规模渗透和系统负荷波动情况下能够有效减小系统频率偏差和区域控制偏差,同时降低储能系统的配置容量,提高电力系统安全稳定运行的经济性.     

A nonlinear sliding surface to improve performance of a discrete-time input-delay system

A sliding mode controller is proposed for an uncertain input-delay system to enhance performance. A nonlinear sliding surface is proposed to achieve better transient response for general uncertain discrete SISO linear systems with input delay. Both matched and unmatched perturbations are considered and ultimate boundedness of motion is proved. The step tracking problem is analysed. The proposed surface increases the damping ratio of the transformed system (delay free) as the output moves nearer to the setpoint. To simplify the surface design, a linear matrix inequality based tuning procedure is proposed. The control law is designed based on an equivalent control approach which guarantees one step reaching. The scheme is able to achieve low overshoot and low settling time simultaneously which is not possible with a linear sliding surface. Simulation results verify the effectiveness of the proposed nonlinear surface over different linear surfaces.     

Maiden application of colliding bodies optimizer for load frequency control of two-area nonreheated thermal and hydrothermal power systems

This article presents a novel load frequency control (LFC) approach using colliding bodies optimizer (CBO) for frequency stabilization of interlinked multiarea electric power systems. The optimal parameters of the suggested CBO-based proportional–integral–derivative-filter controller ascertain an effective LFC solution. First, a well-known and widely used linearized two-area nonreheated thermal power system is examined to demonstrate the efficacy of the proposed approach. The effectiveness of the proposed method is analyzed by comparing the outcomes of several recently presented LFC schemes. The performance analysis shows a settling time improvement of 3.10%, 14.29%, and 18.66% in the case of area-1 and area-2 frequencies and tie-line power deviations compared with an imperialist competitive algorithm (ICA)-based controller. The robustness of the proposed scheme is also evaluated in the presence of various operating scenarios. Additionally, the work is extended to a two-area nonreheated hydrothermal power system. The proposed method shows an improvement of over 60% in the performance index compared with several existing techniques-based controllers such as optics-inspired optimization, gray-wolf optimization, quasi-oppositional differential search algorithm, bacterial foraging optimization algorithm, and ICA.     

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.     

Mini-max integral sliding-mode control for multimodel linear uncertain systems

An original linear time-varying system with matched and unmatched disturbances and uncertainties is replaced by a finite set of dynamic models such that each one describes a particular uncertain case including exact realizations of possible dynamic equations as well as external unmatched bounded disturbances. Such a tradeoff between an original uncertain linear time varying dynamic system and a corresponding higher order multimodel system containing only matched uncertainties leads to a linear multi-model system with known unmatched bounded disturbances and unknown matched disturbances as well. Each model from a given finite set is characterized by a quadratic performance index. The developed minimax integral sliding mode control strategy gives an optimal minimax linear quadratic (LQ)-control with additional integral sliding mode term. The design of this controller is reduced to a solution of an equivalent mini-max LQ problem that corresponds to the weighted performance indices with weights from a finite dimensional simplex. The additional integral sliding mode controller part completely dismisses the influence of matched uncertainties from the initial time instant. Two numerical examples illustrate this study.     

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.     

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.     

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.     

基于非线性PID的非最小相位系统控制

提出一种新型非线性PID控制器简单结构，利用非线性PID控制器的非线性特性，抑制非最小相位系统的右半平面零点所造成的负调问题，克服非最小相位系统的超凋、负调和调整时间之间的矛盾。数值仿真结果表明，由非线性PID控制器构成的非最小相位系统具有良好的动静态性能、高的控制精度和较强的鲁棒性。数值结果说明方法有效，算法简单，易于实时实现。     

Stabilization of perturbed system via IMC: An application to load frequency control

This paper proposes a robust controller for a parametric uncertain system of order three. The scheme conceptualizes the approach of selecting the worst-case plant and then the controller is designed using the internal model control principle which constitutes the reduced model of worst-case plant. The beauty of the proposed approach is that even though the plant is uncertain, the complete robust stability analysis and controller design is carried out by a single linear model. As an illustrative example, a load frequency control (LFC) problem is considered for single- and multi-area power systems in presence of unexpected disturbances, parametric uncertainties and physical constraints. The proposed controller is also applied to the network topology similar to standard IEEE 39 bus system (New England 10 machine test system) to validate the more realistic LFC application. Simulation studies show that the proposed controller brings robust and fast disturbance rejection attributes.     

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.     

Design of a Proportional-Integral-Derivative Controller for an Automatic Generation Control of Multi-area Power Thermal Systems Using Firefly Algorithm

Essentially, it is significant to supply the consumer with reliable and sufficient power. Since, power quality is mea sured by the consistency in frequency and power flow between control areas. Thus, in a power system operation and control, automatic generation control (AGC) plays a crucial role. In this paper, multi-area (Five areas: area 1, area 2, area 3, area 4 and area 5) reheat thermal power systems are considered with proportional-integral-derivative (PID) controller as a supplemen tary controller. Each area in the investigated power system is equipped with appropriate governor unit, turbine with reheater unit, generator and speed regulator unit. The PID controller parameters are optimized by considering nature bio-inspired firefly algorithm (FFA). The experimental results demonstrated the comparison of the proposed system performance (FFA-PID) with optimized PID controller based genetic algorithm (GA PID) and particle swarm optimization (PSO) technique (PSO PID) for the same investigated power system. The results proved the efficiency of employing the integral time absolute error (ITAE) cost function with one percent step load perturbation (1% SLP) in area 1. The proposed system based FFA achieved the least settling time compared to using the GA or the PSO algorithms, while, it attained good results with respect to the peak overshoot/undershoot. In addition, the FFA performance is improved with the increased number of iterations which outperformed the other optimization algorithms based controller.      

Dynamic output feedback sliding mode design for a class of linear unmatched uncertain systems

This paper investigates the output feedback stabilization problem for a class of multi-input/multi-output (MIMO) systems with matched/unmatched uncertainties by the variable structure system (VSS) with a new sliding mode control. In dynamic systems, a new idea of a sliding sector that consists of two sets of switching surfaces is proposed. A new invariance condition is derived such that the reduced-order system in the new sliding mode is completely invariant to both matched and unmatched uncertainties. Additionally, to demonstrate the effectiveness of the proposed scheme and to reduce the drawbacks of conventional VSS design, a modified dynamic variable structure controller using only the output variables is applied to perform the sliding mode. Furthermore, a stability analysis of the overall system is also provided. Finally, an example is given to illustrate the effectiveness of the control scheme.     

Multi-objective voltage and frequency regulation in autonomous microgrids using Pareto-based Big Bang-Big Crunch algorithm

Voltage and frequency regulation is one of the most vital issues in autonomous microgrids to ensure an acceptable electric power quality supply to customers. In this paper, a real-time control structure including power, voltage, and current control loops is proposed for microgrid inverters to restore voltage and frequency of the system after the initiation and load changes. The Proportional-Integral (PI) gains of the voltage controller are optimized in a real-time basis after a perturbation in the microgrid to have a fast and smooth response and a more stable system. The current controller produces Space Vector Pulse Width Modulation command signals to be fed into the three-leg inverter. The multi-objective optimization problem has objective functions of voltage overshoot/undershoot, rise time, settling time, and Integral Time Absolute Error (ITAE). The modified Multi-Objective Hybrid Big Bang-Bing Crunch (MOHBB-BC) algorithm is employed as one of efficient evolutionary algorithms in order to solve the optimization problem. The MOHBB-BC method obtains a set of Pareto optimal solutions; a fuzzy decision maker is used to pick up the most preferred Pareto solution as the final solution of the problem. Results from testing the control strategy on a case study are discussed and compared with previous works; according to them, the proposed method is able to obtain dynamic PI regulator gains to have a more appropriate response.     

带有非线性不确定奇异系统的积分滑模控制

针对一类含有非线性不确定的奇异系统, 提出了一种面向性能的鲁棒控制器. 控制器由3部分组成: 积分滑模控制、附加的非线性控制及复合非线性反馈控制. 积分滑模控制可将匹配不确定完全抵消并使系统轨迹进入理想滑模; 附加的非线性控制用来抑制理想滑动模态上非匹配不确定对系统稳定性和性能的影响; 复合非线性反馈控制则保证闭环系统输出按性能要求渐近地跟踪参考输入信号. 最后通过算例说明所提算法的有效性.     

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.      

A neuro-genetic controller for nonminimum phase systems.

This paper investigates a neurocontroller for nonminimum phase systems which is trained off-line with genetic algorithm (GA) and is combined in parallel with a conventional linear controller of proportional plus integral plus derivative (PID) type. Training of this kind of a neuro-genetic controller provides a solution under a given global evaluation function, which is devised based on the desired control performance during the whole training time interval. Empirical simulation results illustrate the efficacy of the proposed controller compared with a conventional linear controller in point of learning capability of adaptation and improvement of performances of a step response like fast settling time, small undershoot, and small overshoot.