改进遗传算法在无功优化中的应用研究

【作者】 蒲永红；

【导师】 张明军；

【作者基本信息】 山东大学 ， 电力系统及其自动化， 2007， 硕士

【摘要】 电力系统的无功优化控制，不仅能有效地降低系统的有功功率损耗，而且还可以改善电网的电压质量，对系统的安全稳定、经济运行具有非常重要意义。无功优化问题是一个含有连续变量和离散变量的混合优化问题，求解过程相当复杂。传统的非线性规划、线性规划、混合整数等优化算法依赖于精确的数学模型，一般要求所处理问题的目标函数连续、可导。算法所求最终解和选取的初始值密切相关，只有初始点离全局最优点较近时，才可能达到真正的最优。此外，不能实现对离散变量的精确处理，因而用于含有离散变量的无功优化问题时，其结果会有较大误差。为克服这些缺点，研究人员逐渐把人工智能方法运用于无功优化这一领域。在全面掌握当前电力系统无功优化研究进展的基础上，本文系统探讨了求解无功优化的经典算法和现代人工智能算法，总结分析了它们各自的特点及使用情况。为提高解的质量与计算效率，本课题对无功优化的数学模型、求解算法进行了较为深入研究，进而提出了一种用于无功优化的改进遗传算法。为满足电力系统的经济性要求，本文以有功损耗最小为目标函数。同时，考虑到电网的安全运行，采用罚函数的方式来处理电压及发电机无功出力的约束条件，建立以三者综合最优为目标的数学模型。此外，为了提高遗传算法无功优化的计算速度，本文综合比较了三种常用的罚系数取值方式，选用了按指数规律变化的罚系数。简单遗传算法用于无功优化时存在“早熟”、容易陷入局部最优、计算速度慢，对控制变量的处理存在较大误差等缺点。针对于此，本文对简单遗传算法进行了改进：采用混合编码方式精确处理离散变量，分阶段设计了不同的适应度函数，在进化前后期采用不同选择方式的遗传操作，以及针对编码方式，使用算术交叉和小变异操作等。改进后的算法除保留了简单遗传算法的多点搜索、鲁棒性强的优点之外，收敛速度得到提高，算法的适用性及全局搜索能力增强。遗传算法应用于无功优化问题时计算速度比较慢，除了算法自身的原因之外，另外一个重要的因素就是要反复的求解潮流方程。潮流计算的快慢直接影响到整个算法的计算速度。本文在研究常用潮流算法之后，采用其中计算速度快的X-B型快速解耦法，并进一步从两方面对其在遗传算法无功优化程序中的应用做了改进。一方面，根据快速解耦法中X′的构成与遗传算法中的个体无关，将以往程序计算过程中反复形成X′改为一次构成，在之后的计算中，直接调用即可。另一方面，考虑到潮流计算收敛精度对计算速度及遗传算法群体更新的影响，本文在遗传进化前期，采用收敛精度低的潮流计算，后期采用收敛精度高的计算。通过以上两方面的改进，可以有效地提高无功优化的计算速度，减少计算时间。本文最后使用MATLAB语言分别编写了简单遗传算法和改进遗传算法的无功优化程序，结合IEEE14节点和IEEE30节点无功优化仿真对两种算法进行对比分析。结果表明，与简单遗传算法相比，改进算法具有更好的全局收敛能力和更高的计算速度。更多还原

【Abstract】 Reactive power optimization in power system can not only reduce power loss, but also improve voltage quality. So it is of great importance to security and economic operation of power system.Reactive optimization of power systems is a mixed optimizing question, which its operating variables include the continual and the separate, its solved process is quite complex. Conventional algorithms such as nonlinear programming, linear programming, mix integer rely on the precise mathematical model, in general, and request the objective function of solved problem to be continual, differential. The final result obtained by the algorithm closely correlates with the initialization, only this initialization approaches optimal solution, the algorithm could acquire the optimal result. In addition, these traditional optimizing algorithms can not precisely dispose of the separate variable, when applied to the reactive power optimization, its result would have a biggish error. For the sake of mending the deficiency, researchers gradually make use of artificial intelligence method to solve reactive optimization. On the base of comprehensively grasping the current reactive optimization of power system ,This paper systematically discusses the classical and the modern artificial intelligence algorithms that applied to reactive optimization problem , Analyze and summarize their respective characteristics and their application. In order to improve result and increase computational speed, this thesis deep studies the mathematical model and algorithms of reactive optimization, so, proposes a kind of modified genetic algorithm.For the economic need of power system operation ,therefore, this paper take power loss minimum as objective function, simultaneously, considering the security operation of electrical network, deal the restriction of voltage and reactive power produced by generator with the penalty function , establishes mathematical model that makes three aspects integrative optimization., moreover, for the increasing the computing speed of reactive power optimization by genetic algorithm ,this paper synthetically compared three kinds to the penalty coefficient and take the exponential variation rule .The simple genetic algorithm is constrained by its poor converging performance , readily leads to local optimization, its computing speed is slow ,and can not precisely deal with separate variable, in view of the deficiency of simple genetic algorithm, this paper make some improvement, employing hybrid-coding to handle separate variable and different fitness functions at different stage, using the dissimilar reproducing in the evolutional process, according as coding ,still make use of arithmetic crossover and small mutation. Except the improved algorithm retained performances of multi-spots search and the strong robust, its convergent rate obtains the enhancement, the algorithm’s applicability and global searching ability increase.When applied to reactive power optimization, the genetic algorithm’s computing speed is quite slow, besides algorithm self reason, another important factor is of repeatedly solving the power flow equation. Calculating speed of power flow directly influence entire algorithm’s speed. Based on comparing power flow algorithms, the paper adopts the fast decouple method, and has made the improvement to it in genetic algorithm reactive power optimization procedure application from the two sides, one side , because matrix X’ is foreign to the individual of genetic population ,so making matrix X’ is once ,or not repetitive, in course of computing, the calculating program directly use this matrix. On the other hand, convergent precision is also influence computing speed and population’s updating, thus power flow which its convergent precision is low is employed in prophase of evolution, however which its convergent precision is high in anaphase. By means of the improvement, speed of the reactive power optimization may availably enhanced , the computing time can be saved.The paper finally used the MATLAB language to compile the simple genetic algorithm and the improvement genetic algorithm reactive power optimization program, the IEEE14-bus and the IEEE30-bus system simulation result indicated, when the improvement algorithm applied to the reactive power optimization, compared with the simple genetic algorithm, it had a better ability of the global research and the higher convergence rate.更多还原