无功优化进化计算的局部搜索策略及多目标处理方法
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摘要
近年来,电力系统无功优化进化计算以其高灵活性、高鲁棒性、强适应性等特征,在电力系统优化领域受到了广泛的关注。这类无功优化算法不需要使用任何梯度信息,对函数性态的依赖性较小,能够方便地同时处理连续与离散无功电压控制设备,是当前研究的热点问题之一。但作为一类随机型的不确定优化方法,进化计算在求解无功优化这类电力系统复杂问题时,仍存在一些不够完善的地方,如容易出现早熟现象,收敛速度较慢,局部搜索能力不高等。目前虽然已经提出了很多相应的改进措施,但算法性能仍有较大的提升空间,且还存在较多问题亟待解决,如在引入局部搜索策略时如何获得收敛性的全面提升,协同进化中如何对控制变量进行分组,考虑多目标优化模型时如何在目标函数间权衡等等。鉴于此,本文以无功优化进化计算的改进策略为研究对象,内容涉及采用多局部搜索策略的无功优化进化计算、多目标无功优化进化计算及其两阶段优化策略、鲁棒性无功优化模型及优化策略、无功优化协同进化中的控制变量分组方法等四部分内容。所做的工作和所取得的主要成果归纳如下：
提出了一种采用多局部搜索策略的无功优化模因算法。该算法在现有局部搜索策略的基础上,提出了修正型、定向型和随机型等3类无功优化模因,并由此构造出无功优化模因池,以达到结合多局部搜索策略的目的。在IEEE 30节点上的系统仿真表明,新算法可以发挥各类局部搜索策略的优势,具有更全面的收敛特性,寻优效率较高。此外,算例中还分析了参与局部搜索的个体的比例对算法性能的影响,得出了比例过高将影响算法性能的结论。
提出了无功优化多目标模型转换方法的一种等值线分析法。该方法借助于地理学中等值线的概念,能够从几何意义的角度,描绘出各类无功优化多目标模型转换方法在目标空间的寻优方向,并挖掘出各种模型转换方法中最优解的几何意义。在这基础上,探讨了各种模型转换方法之间的联系,并据此对模型转换方法进行了比较和归类。
比较研究了五种经典多目标进化算法在无功优化计算中的性能特点。从帕累托前沿、外部解、C指标等角度对五种算法进行了详细的比较,并分析了各算法在求解无功优化问题时所表现出的不同性能等级。结果表明,改进强度帕累托进化算法(Strength Pareto Evolutionary algorithm 2,SPEA2)与改进非支配解排序遗传算法(Nondominated Sorting Genetic Algorithm-Ⅱ,NSGAⅡ)表现出了最优异的性能特点,能获得质量较高的帕累托最优解集。
提出了多目标无功优化进化计算的一种分阶段优化策略。该优化策略将优化过程分为全局搜索和集中搜索两个阶段。第一阶段采用NSGAⅡ搜索到粗略的帕累托解集后,决策者从中获取目标函数的近似分布范围、目标函数间的近似关系等粗略信息,分析并制定对最优解的要求,简单直观的表达偏好信息；在此基础上,第二阶段利用等值线分析的相关结论,获取决策者对最优解的要求后设定偏好参数,并采用权值法、目标规划法、ε约束法等方法,有针对性的在重点区域和方向上进行集中寻优,获得满足要求的最优解。仿真分析表明,分阶段策略能够综合NSGAⅡ与模型转换方法的优势,灵活实用,具有较高的寻优效率。
提出了基于蒙特卡洛积分的鲁棒性无功优化模型。该模型采用了蒙特卡洛积分形式的目标函数,近似地替代了在负荷水平波动下电压偏移、系统网损的期望值,搜索能够抵御负荷波动的无功优化鲁棒解。为降低蒙特卡洛积分的误差,提出了一种鲁棒性无功优化的样本解选择方法。该方法将样本解表示为系统负荷增加比例与功率增长方向两个参数,并根据负荷的增减情况选择恰当的样本解。算例分析中分别采用遗传算法及NSGAⅡ,计算了IEEE118节点系统的单目标与多目标鲁棒性无功优化问题。结果表明,对于负荷水平的波动,无功优化鲁棒解更能保持解的质量,性能较优。
提出了基于自动分区遗传算法的一种无功优化协同进化的分组方法。该方法将控制变量分组问题转换为降阶电网分区问题,并构造了降阶电网分区优化模型。新模型不仅采用了典型的聚类有效性指标,而且考虑了控制变量分组的均匀性。在此基础上,引入了自动分区遗传算法用于求解新分区模型。该算法采用了种子分区编码方法,能够自适应地选择分区数目,具有较高的灵活性。在IEEE 118节点的算例表明,新分区算法能够自动确定分区数目,快速合理地对系统控制变量进行分组,能够进一步提高无功优化协同进化计算的并行效率。
In recent years, evolutionary computation (EC) for reactive power optimization (RPO) has drawn extensive attention due to its features of high flexibility, high robustness, and strong adaptability. Such reactive power optimization algorithm is a hot topic of current research because it does not need any gradient-based information, does not depend on the functional state of the objectives, and does not has any trouble to handle both continuous and discrete reactive power and voltage control equipments. As a class of stochastic optimization methods, however, EC still has some disadvantage when solving complex problems such as RPO, i.e., premature, slow convergence, low local search ability. Although many modification strategies have been proposed, there is still large margin for improvement, and many issues need further discussion, i.e., how to obtain overall upgrade of convergence when applying local search strategies (LSSs), how to group the control variables in coevolutionary computaion, how to balance between the objectives in multiobjective optimization, etc. To solve these problems, the strategies of improvement for EC in RPO is chosen to be the research topic, including four aspects, say, EC with multiple LSSs for RPO, multiobjective reactive power optimization and its two-stage optimization strategy, robust reactive power optimization model and optimization strategy, and grouping methods of control variables in coevolutionary computation for RPO. The outputs of the thesis are listed as follows.
Memetic algorithm based on multiple LSSs for RPO is proposed. Based on the existing LSSs, correcting memes, directed memes and stochastic memes are proposed to form the meme pool for RPO, by which the multiple LSSs can be combined together. The algorithm is applied in IEEE 30 bus system and numerical simulations demonstrate that the algorithm combines all the advantages of LSSs and shows the best performance of convergence. In addition, simulation results with different percentage of population participating in LSSs process are compared and relationship between percentage of population and efficiency of the algorithm is analyzed.
A contour-line analysis approach for objective-converting methods (OCMs) in RPO is proposed. With the contour line concept in geography area, contour analysis can obtain the search directions of various OCMs in the objective space, and uncover geometric meaning of their optimal solutions. According the the observations, the intrinsic link between OCMs are studied, and OCMs are compared and classified.
Five state-of-the-art multiobjective evolutionary algorithms (MOEAs) are compared for RPO. Pareto front, the outer solutions, and C measure are used to analyze the performance of the five MOEAs in RPO, which are classified into five performance levels. Strength Pareto Evolutionary algorithm 2 (SPEA2) and Nondominated Sorting Genetic Algorithm-II (NSGAII) are demonstrated to be the best algorithms that can obtain Pareto front with higher quality.
A two-stage optimization strategy is proposed for MOEAs to solve multiobjective RPO. The strategy divides the search process into two phases, global search and focused search. The first stage uses NSGAII to search for a rough Pareto set, from which the decision maker (DM) obtain the information of the approximate distribution range of the objective functions, their approximated relationships, and then draw the requirements and preferences of the optimal solution in a simple and visualized way. On this basis, the second phase set preference parameters, and then adopts weighted method, goal attainment method,ε-constraint method, to focus on the key areas and directions in the optimization. Simulation analysis showed that the new strategay can combine the advantages of NSGAII and OCMs and it is a flexible and practical approach with high optimization efficiency.
Robust RPO based on Monte Carlo integration is proposed. It adopts a Monte Carlo integral form of the objective functions, calculating the approximate expectations of system loss and voltage deviation in the presense of load fluctuations and searching for robust solution that is immune with load perturbations. To reduce the error of Monte Carlo integration, a samplingetechnique is proposed for RPO.It expresses a sample solution as two parameters, the percentage of the system load increase and the direction of power growth, and then select the appropriate sample solution in accordance with load changes. Genetic algorithms and NSGAII is used to solve robust RPO on IEEE-118 test system and the results show that during the fluctuations of the system load, the robust solutions can better maintain their quality with higher performance.
A genetic-algorithm-based approach is proposed for the grouping of control variables in the coevolutionary computation for RPO.In this approach, the control variable grouping problem is converted to a reduced network partition problem, and a mathematic model is formulated. The new model not only adopted the typical cluster validity index, and taken the uniformity of group size of control variables into account. On this basis, a genetic-algorithm-based partition method is introduced to solve the new model. This method employs a seed encoding scheme that can adaptively choose the partition number with high flexibility. The simulation result on IEEE 118-bus system demonstrates that the new partition approach can automatically determine the partition number, grouping the control variables fast in a reasonably way. It can further improve the parallel efficiency of coevolutionary computation for RPO.
提出了一种采用多局部搜索策略的无功优化模因算法。该算法在现有局部搜索策略的基础上,提出了修正型、定向型和随机型等3类无功优化模因,并由此构造出无功优化模因池,以达到结合多局部搜索策略的目的。在IEEE 30节点上的系统仿真表明,新算法可以发挥各类局部搜索策略的优势,具有更全面的收敛特性,寻优效率较高。此外,算例中还分析了参与局部搜索的个体的比例对算法性能的影响,得出了比例过高将影响算法性能的结论。
提出了无功优化多目标模型转换方法的一种等值线分析法。该方法借助于地理学中等值线的概念,能够从几何意义的角度,描绘出各类无功优化多目标模型转换方法在目标空间的寻优方向,并挖掘出各种模型转换方法中最优解的几何意义。在这基础上,探讨了各种模型转换方法之间的联系,并据此对模型转换方法进行了比较和归类。
比较研究了五种经典多目标进化算法在无功优化计算中的性能特点。从帕累托前沿、外部解、C指标等角度对五种算法进行了详细的比较,并分析了各算法在求解无功优化问题时所表现出的不同性能等级。结果表明,改进强度帕累托进化算法(Strength Pareto Evolutionary algorithm 2,SPEA2)与改进非支配解排序遗传算法(Nondominated Sorting Genetic Algorithm-Ⅱ,NSGAⅡ)表现出了最优异的性能特点,能获得质量较高的帕累托最优解集。
提出了多目标无功优化进化计算的一种分阶段优化策略。该优化策略将优化过程分为全局搜索和集中搜索两个阶段。第一阶段采用NSGAⅡ搜索到粗略的帕累托解集后,决策者从中获取目标函数的近似分布范围、目标函数间的近似关系等粗略信息,分析并制定对最优解的要求,简单直观的表达偏好信息；在此基础上,第二阶段利用等值线分析的相关结论,获取决策者对最优解的要求后设定偏好参数,并采用权值法、目标规划法、ε约束法等方法,有针对性的在重点区域和方向上进行集中寻优,获得满足要求的最优解。仿真分析表明,分阶段策略能够综合NSGAⅡ与模型转换方法的优势,灵活实用,具有较高的寻优效率。
提出了基于蒙特卡洛积分的鲁棒性无功优化模型。该模型采用了蒙特卡洛积分形式的目标函数,近似地替代了在负荷水平波动下电压偏移、系统网损的期望值,搜索能够抵御负荷波动的无功优化鲁棒解。为降低蒙特卡洛积分的误差,提出了一种鲁棒性无功优化的样本解选择方法。该方法将样本解表示为系统负荷增加比例与功率增长方向两个参数,并根据负荷的增减情况选择恰当的样本解。算例分析中分别采用遗传算法及NSGAⅡ,计算了IEEE118节点系统的单目标与多目标鲁棒性无功优化问题。结果表明,对于负荷水平的波动,无功优化鲁棒解更能保持解的质量,性能较优。
提出了基于自动分区遗传算法的一种无功优化协同进化的分组方法。该方法将控制变量分组问题转换为降阶电网分区问题,并构造了降阶电网分区优化模型。新模型不仅采用了典型的聚类有效性指标,而且考虑了控制变量分组的均匀性。在此基础上,引入了自动分区遗传算法用于求解新分区模型。该算法采用了种子分区编码方法,能够自适应地选择分区数目,具有较高的灵活性。在IEEE 118节点的算例表明,新分区算法能够自动确定分区数目,快速合理地对系统控制变量进行分组,能够进一步提高无功优化协同进化计算的并行效率。
In recent years, evolutionary computation (EC) for reactive power optimization (RPO) has drawn extensive attention due to its features of high flexibility, high robustness, and strong adaptability. Such reactive power optimization algorithm is a hot topic of current research because it does not need any gradient-based information, does not depend on the functional state of the objectives, and does not has any trouble to handle both continuous and discrete reactive power and voltage control equipments. As a class of stochastic optimization methods, however, EC still has some disadvantage when solving complex problems such as RPO, i.e., premature, slow convergence, low local search ability. Although many modification strategies have been proposed, there is still large margin for improvement, and many issues need further discussion, i.e., how to obtain overall upgrade of convergence when applying local search strategies (LSSs), how to group the control variables in coevolutionary computaion, how to balance between the objectives in multiobjective optimization, etc. To solve these problems, the strategies of improvement for EC in RPO is chosen to be the research topic, including four aspects, say, EC with multiple LSSs for RPO, multiobjective reactive power optimization and its two-stage optimization strategy, robust reactive power optimization model and optimization strategy, and grouping methods of control variables in coevolutionary computation for RPO. The outputs of the thesis are listed as follows.
Memetic algorithm based on multiple LSSs for RPO is proposed. Based on the existing LSSs, correcting memes, directed memes and stochastic memes are proposed to form the meme pool for RPO, by which the multiple LSSs can be combined together. The algorithm is applied in IEEE 30 bus system and numerical simulations demonstrate that the algorithm combines all the advantages of LSSs and shows the best performance of convergence. In addition, simulation results with different percentage of population participating in LSSs process are compared and relationship between percentage of population and efficiency of the algorithm is analyzed.
A contour-line analysis approach for objective-converting methods (OCMs) in RPO is proposed. With the contour line concept in geography area, contour analysis can obtain the search directions of various OCMs in the objective space, and uncover geometric meaning of their optimal solutions. According the the observations, the intrinsic link between OCMs are studied, and OCMs are compared and classified.
Five state-of-the-art multiobjective evolutionary algorithms (MOEAs) are compared for RPO. Pareto front, the outer solutions, and C measure are used to analyze the performance of the five MOEAs in RPO, which are classified into five performance levels. Strength Pareto Evolutionary algorithm 2 (SPEA2) and Nondominated Sorting Genetic Algorithm-II (NSGAII) are demonstrated to be the best algorithms that can obtain Pareto front with higher quality.
A two-stage optimization strategy is proposed for MOEAs to solve multiobjective RPO. The strategy divides the search process into two phases, global search and focused search. The first stage uses NSGAII to search for a rough Pareto set, from which the decision maker (DM) obtain the information of the approximate distribution range of the objective functions, their approximated relationships, and then draw the requirements and preferences of the optimal solution in a simple and visualized way. On this basis, the second phase set preference parameters, and then adopts weighted method, goal attainment method,ε-constraint method, to focus on the key areas and directions in the optimization. Simulation analysis showed that the new strategay can combine the advantages of NSGAII and OCMs and it is a flexible and practical approach with high optimization efficiency.
Robust RPO based on Monte Carlo integration is proposed. It adopts a Monte Carlo integral form of the objective functions, calculating the approximate expectations of system loss and voltage deviation in the presense of load fluctuations and searching for robust solution that is immune with load perturbations. To reduce the error of Monte Carlo integration, a samplingetechnique is proposed for RPO.It expresses a sample solution as two parameters, the percentage of the system load increase and the direction of power growth, and then select the appropriate sample solution in accordance with load changes. Genetic algorithms and NSGAII is used to solve robust RPO on IEEE-118 test system and the results show that during the fluctuations of the system load, the robust solutions can better maintain their quality with higher performance.
A genetic-algorithm-based approach is proposed for the grouping of control variables in the coevolutionary computation for RPO.In this approach, the control variable grouping problem is converted to a reduced network partition problem, and a mathematic model is formulated. The new model not only adopted the typical cluster validity index, and taken the uniformity of group size of control variables into account. On this basis, a genetic-algorithm-based partition method is introduced to solve the new model. This method employs a seed encoding scheme that can adaptively choose the partition number with high flexibility. The simulation result on IEEE 118-bus system demonstrates that the new partition approach can automatically determine the partition number, grouping the control variables fast in a reasonably way. It can further improve the parallel efficiency of coevolutionary computation for RPO.
引文
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