# 北京28最稳定规律: 基于遗传算法的短期无功优化

华中科技大学 硕士学位论文 基于遗传算法的短期无功优化 姓名：Husam Shaheen 申请学位级别：硕士 专业：电力系统及其自动化 指导教师：程时杰 20050429 II 摘 要 本文研究了电力网络短期无功优化问题为解决这一问题必须对电力系统运 行的经济性和安全性问题进行分析包括电力系统物理条件约束如电力系统功 率平衡约束发电机发电能力的约束和线路传输能力的约束等分析为了解决该优 化问题本论文提出了一种目标函数可以在进行无功优化的同时考虑电力系统 中的各种运行条件约束安全性约束物理条件约束以及无功控制器出力限制约 束 论文的研究目标在于根据当天进行的次日 24 小时负荷预测曲线确定次日 24 小时内每一小时无功控制装置包括补偿电容和变压器抽头的正确设置使电 力系统在不超出所有无功控制装置全天允许动作次数的条件下达到系统的有功功 率损耗达到最小并在所有可能的运行条件下保持令人满意的节点电压值 对于论文中提出的目标函数采用遗传算法进行优化遗传算法GA是一种 新型的优化算法和其他的优化算法相比较具有有计算量较少能优化复杂函数 的优点全天多时段的无功优化问题实际上是一个多步优化决策问题为此论文 提出了一种新的优化算法即两层遗传算法其中的第一层遗传算法用来确定一天 中每一运行小时内的最优无功分布也即无功控制器最优设置第二层遗传算法 用来最终求解全天最优无功功率分布 将所提出的算法用于 IEEE30 节点系统的无功优化问题实验结果证明了该算法 的可行性和有效性 关键词: 遗传算法无功控制器 短期规划 电力系统潮流 I ABSTRACT The aim of this work is to develop an optimal short-term scheduling of reactive power in electric distribution systems. To do this, some decision analysis needs to undertake regarding to economic and security aspects. These decision analysis need to consider the physical constraints existing within power systems, such as the generation and transmission limits. An objective function is used that takes into account the security aspects, as well as the physical constraints, and the probabilistic nature of reactive power controllers. The target of this research is to determine the proper settings of the control devices (capacitor banks and transformer taps) for the 24 hours in the next day, which minimize the active power losses (reducing the cost) without exceeding the allowable number of movements of the control devices per day, and maintaining satisfactory voltage profile under various loading conditions. The objective function is then optimized (economically) by use of the Genetic Algorithm - a new-age tool that is relatively less computationally intensive than other optimization techniques, and is capable of optimizing complicated functions. The GA algorithm is implemented in two levels. At the first level, a GA is implemented to determine the optimal reactive power dispatch (optimal settings of control devices) for each operating hour in the day, and then at the second level, another GA is implemented again to find the final optimal reactive power dispatch for the whole day. The proposed method was applied to a modified IEEE 30-bus power system to show the feasibility and the capability of the proposed method. The experiment was carried out and the results are presented in this thesis. Keywords: Genetic Algorithm, Reactive power controllers, Short-term scheduling, Power System Load Flow. 1 Introduction In the last few decades, with the advances in communication and data processing technologies, electric utilities have become very interested in distribution automation. With the increasing complexity of power distribution systems, it is becoming essential to automate some tasks that have always been done manually. It has also been estimated that utilities could save as much as 10% of their annual maintenance and operating expenses by taking the advantages of these technologies [1]. One important area in which distribution automation being applied is the area of reactive power management-reactive power dispatch and control. Effective reactive power dispatch and control is able to minimize the total power system losses by adjusting parameters in the power system while staying within equipment limits. A reactive power dispatch assumes that real power has been dispatched and will be remained fixed throughout the optimization procedure. The slack bus real power will decrease due to a reduction in total system losses. Therefore, the system operation costs will be decreased. Over the years, many algorithms based on the classical techniques for solving reactive power dispatch and control problem have appeared in the technical literature [2, 16]. More specifically, nonlinear programming (NLP), successive linear programming, mixed integer programming, Newton and quadratic techniques have found applications to power system operational problems. Most of these approaches can be broadly categorized as constrained optimization techniques. More recently, expert systems, evolved around artificial intelligence (AI) concept, have also been applied [17, 22]. Notwithstanding that these techniques have been successfully applied to sample power systems, some implemental difficulties still remain unresolved because the reactive power dispatch and control problem is, by nature, a global optimization with several local minima. The first obvious problem is where a local minimum is returned instead of a unique global minimum. The second difficulty is the inherent integer nature of the problem. Most control devices (transformer tap positions, switchable shunt capacitor and reactor banks) have pre-specified discrete values. Thus, no matter how accuracy of the continuous 2 solution is, it is impossible, without making engineering approximations, to assign these values directly to the physical control devices. In an attempt to circumvent the extant computational complexity and other limiting mathematical assumptions, some new stochastic search techniques developed to solve global optimization problems have also appeared in the last two decades [23, 32]. These search techniques including Genetic Algorithms, tabu search, simulated annealing, and particle swarm optimization, etc, and the most popular among these search techniques is the application of GAs to power system operational optimization problems. However, the applicability of these algorithms to a practical system is limited because of the constant load model they adopt. In fact, the load demands in power systems are vary from time to time. The optimal control scheme should be changed also due to the time- varying load demands. Thus, the optimal dispatch scheme considering constant load data cannot be put into practice in the real time applications. Only the optimization with time varying load demand could get the feasible dispatch scheme. It determines when and how to operate the electric devices to minimize the total daily energy loss. This is a very complex nonlinear optimization both temporally and spatially. Some attempts for solving this problem have been done [33, 35]. In reference [33], Hong and Liao tried to solve the short-term (one day) scheduling of the reactive power controllers by decomposing the entire problem into two levels: the master and the slave levels. The master level deals with the minimization of the depreciation cost of compensators and EHV transformers taps in order to reduce the control action for compensators and EHV transformer taps while satisfying operating constrains. The slave level treats the minimization of capitalized MW losses while satisfying security constraints. The slave level also treats OLTCs and determines scheduling of the generator voltages. These two levels interact through linear constraints in the iteration process. In reference [34], You, Xiao, Chang, and Da, have tried to solve the problem by using a heuristic and algorithmic combined approach. The objective is to determine the proper setting values of capacitor banks and transformer taps for the 24 h in the next day. The approach simplifies the mathematical model of the daily setting values of reactive power/voltage control devices, solves the temporal optimization of each control devices by heuristic rules, and then converts the optimization model with time-varying load into the 3 same one as conventional optimization model with constant load. Therefore, the algorithms applied to the conventional optimization model can be easily used to solve the optimization model with time varying load demand. Ruey and Yung in reference [35] introduced a fuzzy-based approach in solving the problem. The main purpose of this method is to find out the combination of main transformer load tap changer (LTC) positions and capacitors on/off switching operations in a day, such that the voltage deviations at the secondary bus of main transformer become as small as possible, while the reactive power flows through the main transformer and the real power losses at feeders become as little as possible. To minimize system repairing cost, the total number of switching operations of LTC and capacitors in a day must be kept as few as possible. From the descriptions given above, it can be seen that the linguistic expressions such as “as small as possible,” “as little as possible,” and “as few as possible” are not clear. For this reason, the reactive power and voltage control problem is first formulated with fuzzy sets, and then a simulated annealing searching technique is used to find out a proper combination of LTC positions and capacitors on/off switching operations in a day. However, in references [33, 34] the problem was solved by a decomposition theory and successive linear integer-programming algorithm respectively, but these methods can t guarantee that the optimal obtained solutions are a global solutions, in addition to their time consuming properties. In reference [35] the problem was solved by a simulated annealing method, which is a time consuming method. In addition to this, it is applied only for single transformer. To overcome such difficulties a GA-based approach was proposed in this thesis. This thesis presents a new method based on the genetic algorithm (GA) to solve the short-term scheduling of reactive power dispatch and control problem. The main objective is to determine the proper settings of the control devices for the 24 hours in the next day, which minimizing the active power losses without exceeding the allowable number of movements of the control devices per day while maintaining satisfactory voltage profile under various loading conditions. The admissible control devices in the reactive power dispatch and control problem include generating unit reactive power capability, transformers equipped with on-load-tap changing facilities, discrete shunt capacitors. 4 The task, therefore, is to employ the GA to search the optimal settings of the foregoing control devices, within the specified feasible boundaries in the parameter space for one operational day. This thesis was organized as follows: Chapter 1 gives an overview of the reactive power dispatch and control, while in Chapter 2 the problem is formulated as a single objective optimization problem with equality and inequality constraints. The power flow calculations, the major tool for the reactive power dispatch and control, are presented in a general formulation in Chapter 3 along with a brief discussion of solution techniques. Chapter 4 describes genetic algorithms in a general context as a tool for solving combinatorial optimization problems. Chapter 5 gives a description of how genetic algorithm can be applied to the problem of short-term scheduling of reactive power controllers. Based on the solution methodology presented in Chapter 5, a program was written in MATLAB programming package implementing the algorithm for solving the optimal short-term scheduling of reactive power controllers. This program was implemented on a modified IEEE 30-bus system and the results of this simulation are presented in Chapter 6. The last chapter discusses some of the conclusions drawn from this study and presents some ideas for extending the work covered in this thesis. 5 Chapter 1 Overview of Reactive Power Dispatch and Control 1.1 Introduction In recent years, increasing attention has been given to improving power system operation by reducing the fuel consumption, and by better utilizing of the existing equipment to defer new equipment purchases. Other related factors influencing utilities are inflation, fuel shortages and price increases, and increased pressure to borrow less money .One approach addressing these concerns is reactive power management [36,38]. Normally, there are two basic types of reactive power flows of concern in a power system: 1. Reactive power consumed by loads. 2. Reactive power consumed within the network. The components, which absorb reactive power, are generators and synchronous condensers operated with a lagging angle; shunt reactors, line and transformer inductances, static reactive power compensators, and loads. Reactive power is generated by generators and synchronous condensers operated with leading angle, static capacitors, static compensators, and the capacitance of lines and cables. Reactive power management can be defined as the control of generator voltages, variable transformer tap settings, compensation, and switchable shunt capacitor and reactor banks plus the allocation of new shunt capacitor and reactor banks in a manner that best achieves a reduction in system losses and/or voltage control. Reactive power management by electric utilities, under steady state and dynamic system conditions, can be subdivided into the following categories: 1.1.1 Reactive Power Planning This deals with the installation or removal of the reactive power equipment in a power system. Typically, this effort is directed at system conditions from several months to several years in the future. 6 1.1.2 System Operation Planning This concerns with the improvement of operating practices utilizing existing reactive power equipment. It performs for system conditions anticipated to occur a few days to a year in the future. 1.13 Reactive Power Dispatch and Control This determines the actual equipment operations. The associated analysis is performed seconds to hours prior to its implementation. The term equipment refers to the reactive power compensating devices, as well as the monitoring, control, and communication equipment required to carry out the real-term dispatching function. Reactive power compensating equipment that may be installed, removed, or controlled, includes: switched shunt capacitors, shunt reactors, series capacitors, static compensators, synchronous condensers, generators, and load tap-changing transformers. The ancillary equipment includes: measuring devices for reactive power, relays, automatic controls (e.g. substation automation), switches and circuit breakers, and communication equipment (e.g. power line carrier). This thesis mainly concerns with the third category, which is the reactive power dispatch and control. 1.2 Importance of Reactive Power Dispatch and Control Reactive power dispatch and control, has grown in importance for a number of reasons which are briefly as follows: 1. The requirement for more efficient operation of power systems has increased with the price of fuels. For a given distribution of power, minimizing the total flow of reactive power can reduce the losses in the system 2. The extension of transmission networks has been curtailed in general by high interest rates, and in particular cases by the difficulty of acquiring right-of- way. 7 3. The exploitation of hydropower resources has proceeded spectacularly to the point where remote, hostile generation sites have been developed. In spite of the parallel development of DC t