考虑不确定性因素的电力系统电压稳定与无功优化问题研究
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摘要
作为电力系统分析领域两个重要的问题，电压稳定与无功优化的研究经历了多年的发展，分别取得了丰硕的成果。传统研究中所采用的数学模型和求解方法大多属于确定性分析的范畴，所获得的结论对于提高系统电压稳定性与优化无功资源配置均具有重要的指导意义。然而，电力系统本质上是一个含有诸多不确定性因素的大型系统。当前可再生能源发电大规模并网的新形势下，越来越多的随机因素不断涌现，电压稳定与无功优化研究中更为深入地考察电网不确定性因素带来的影响显得尤为必要。针对不确定性因素的分析思路、建模方法及求解策略将进一步完善电压稳定与无功优化研究的理论体系，产生更多具有参考价值和实用意义的成果。鉴于此，本文以考虑不确定性因素的电压稳定与无功优化问题为研究重点，内容涉及风速相关性对电压失稳鞍结分岔的影响分析、计及注入功率不确定性的电压稳定概率评估、多目标进化算法求解无功优化的比较分析与改进方法、计及负荷不确定性的鲁棒多目标无功优化策略等四个部分。本文工作和取得的主要成果归纳如下：
分析了邻近风电场风速相关性对电压失稳鞍结分岔的影响。采用Nataf变换技术建立多风电场相关风速随机变量概率分布模型，结合鞍结分岔特征方程和蒙特卡罗仿真，获得不同相关强度的风速下电压稳定裕度的概率分布。此外，通过定义两种风险指标，对风速相关性引起电压失稳的风险予以量化分析，为精确判断系统电压稳定性提供了一种辅助手段。算例分析表明，风速强相关引起系统在较低的负荷增长水平下发生鞍结分岔的概率明显增加，不利于电网的安全稳定。
提出了一种可以处理风速、负荷等输入随机变量相关性的电压稳定概率评估方法。根据输入随机变量的边缘累积分布，通过拉丁超立方采样生成风速和负荷样本用于蒙特卡罗仿真，在保证计算精度的前提下有效地提高了计算效率；将其和Nataf变换结合，使得所提出的方法能够方便地计及临近风电场风速之间及节点负荷之间的相关性因素。在考虑风电和负荷注入功率不确定性的条件下，通过IEEE118节点标准系统的仿真计算，验证了所提出方法的有效性和准确性。
比较研究了基于不同算法框架的典型多目标进化算法应用于无功优化的性能特点。以IEEE30节点标准系统的多目标无功优化计算为例，从非支配解集质量和多样性、帕累托前沿分布广阔性和均匀性及收敛速度等多个方面，比较算法的寻优性能，分析其优势或不足，在评估各种算法计算性能的基础上提出了进一步改进的思路。
提出了一种基于多种进化算法自适应选择(multiple evolutionary algorithms withadaptive selection strategies，MEAASS)的多目标无功优化方法。根据该领域研究现状，分析已有算法全局搜索能力、局部搜索能力、收敛速度、计算结果一致性及跳出局部最优能力等方面的特征；在考虑协调性与互补性的基础上，建立包含4类算法的备选池；在进化过程不同阶段根据寻优性能自适应地确定备选算法的使用比例，鼓励寻优性能更高的算法产生更多子代个体；所提出的方法综合了多种算法的性能优势，提高整体寻优效率。
提出了能够计及节点负荷随机性及其相关性的鲁棒多目标无功优化策略。基于蒙特卡罗积分形式的鲁棒优化模型，以系统有功损耗和电压偏移的均值近似地替代负荷波动邻域内的期望值，并同时考虑各种负荷扰动条件下系统运行约束，搜索无功优化鲁棒解。算例分析中采用本文提出的新方法MEAASS求解IEEE30节点标准系统的鲁棒多目标无功优化问题，结果表明鲁棒性优化改善了无功调控方案在负荷不确定性环境下的稳定性和适应性，提高了无功优化的工程实用价值。
Voltage stability and optimal reactive power dispatch (ORPD) are two important andhot topics in power engineering field, in which many researches have been done andabundant achievements have been achieved. Conventional investigations in these twotopics, including mathematical models and solution methods, belong to the category ofdeterministic analysis, and their conclusions have significant instructive effect on voltagestability enhancement and reactive power resources optimal utilization. However, powersystem is in nature a large one with various uncertain factors. With the heavy integration ofrenewable energy sources, more and more random factors continue to emerge in currentpower system. Thorough consideration of these uncertain characteristics in these two topicsis particularly significant. Investigations on modeling methods and solving strategy foruncertain characteristics can make contribution to the amendment of academic theory ofvoltage stability as well as ORPD research, and obtain more achievements with referencevalue and practical significance. To this reason, research on the two topics under uncertainenvironments is chosen to be the theme of this thesis, with the following four aspectsincluded: impact of wind speed correlation (WSC) on voltage instability saddle-nodebifurcation (SNB), voltage stability probabilistic evaluation considering uncertainty inpower injection, comparison and improvement of multi-objective evolutionary algorithms(MOEAs) for multi-objective ORPD, and robust optimal strategy for multi-objectiveORPD with consideration of load uncertainty. The investigations and achievements of thisthesis are listed as follows.
Impact of correlated wind speeds on voltage instability SNB is comprehensivelyinvestigated. Nataf transformation is adopted to establish WSC model for wind farms withclose locations. Based on SNB transversality condition equations and Monte Carlosimulation technique, probability distribution of voltage stability margin under differentWSC coefficients is obtained. Moreover, two risk indexes are presented and the voltage stability deterioration caused by WSC is evaluated from the viewpoint of risk analysis.Experimental results demonstrate that the probability of SNB under relative lower loadgrowth level increases with the strengthening of WSC, implying strong correlated windspeeds bring negative effect in safe and stable operation of power system as far as voltagestability is concerned.
A probabilistic evaluation method of voltage stability accounting for uncertainties inwind speeds and load levels is proposed. Based on Latin hypercube sampling (LHS) MonteCarlo simulation technique, this method can maintain a high degree of accuracy and reducecomputational burden when compared with the simple random sampling Monte Carlomethod. In addition, by combining LHS with Nataf transformation, the presented methodcan deal with correlated wind speeds of different wind farms and correlated load levels ofdifferent buses. Interior point method is used to solve nonlinear programming problems forvoltage stability critical point on the sampling points, and the probability distribution ofvoltage stability margin is obtained. The effectiveness and accuracy of the proposedmethod is validated by case study on the IEEE118bus system.
Five current typical MOEAs are selected and from an overall perspective theapplication of them in multi-objective ORPD is comparatively researched. Different fromtraditional approach that combines multiple objective functions into a single one by settingpreference parameters, the multi-objective model, in which the system network loss andvoltage deviation are taken into account, is directly utilized. Based on the test case of IEEE30bus system, the optimal performances of five MOEAs are compared and thesuperiorities and defects of them are analyzed in the viewpoints of quality and diversity ofnon-dominated solution set, extensity and uniformity of final Pareto front and convergencespeed. On the basis of evaluating computing performances of five MOEAs the prospect offurther research is put forward.
A new optimal method based on multiple evolutionary algorithms with adaptiveselection strategies (MEAASS) for multi-objective ORPD is proposed. Based on analysisof characteristics of state-of-the-art MOEAs, and considering the rules of consistency andcomplementation, candidate algorithm pool containing four different algorithms is presented. By means of adaptively favoring individual algorithms that exhibit higherreproductive success during the search, MEAASS simultaneously merges the strengths ofmultiple algorithms for population evolution. Based on the test case of IEEE30bus system,the computing performance of MEAASS is compared with existing popular algorithms.The numerical simulations demonstrate that MEAASS can obtain better performance ofconvergence during the entire optimization process.
A robust optimal strategy for multi-objective ORPD with consideration of loadrandomness and correlation is proposed. Based on Monte Carlo integral form of objectivefunctions, the expectations of system network loss and voltage deviation in presence ofload fluctuations are approximately calculated, meanwhile the operational constraints undervarious load perturbations are taken into account, finally robust non-dominated solutionswhich are insensitive to load uncertainty are achieved. To reduce the error of Monte Carlointegration, LHS combinated with Nataf transformation is adopted to generate load levelsample. MEAASS is utilized to solve the robust multi-objective ORPD on IEEE30bussystem, and the results demonstrate that control schemes obtained by robust optimalstrategy can maintain their performance and consistency with existence of load uncertainty.
分析了邻近风电场风速相关性对电压失稳鞍结分岔的影响。采用Nataf变换技术建立多风电场相关风速随机变量概率分布模型，结合鞍结分岔特征方程和蒙特卡罗仿真，获得不同相关强度的风速下电压稳定裕度的概率分布。此外，通过定义两种风险指标，对风速相关性引起电压失稳的风险予以量化分析，为精确判断系统电压稳定性提供了一种辅助手段。算例分析表明，风速强相关引起系统在较低的负荷增长水平下发生鞍结分岔的概率明显增加，不利于电网的安全稳定。
提出了一种可以处理风速、负荷等输入随机变量相关性的电压稳定概率评估方法。根据输入随机变量的边缘累积分布，通过拉丁超立方采样生成风速和负荷样本用于蒙特卡罗仿真，在保证计算精度的前提下有效地提高了计算效率；将其和Nataf变换结合，使得所提出的方法能够方便地计及临近风电场风速之间及节点负荷之间的相关性因素。在考虑风电和负荷注入功率不确定性的条件下，通过IEEE118节点标准系统的仿真计算，验证了所提出方法的有效性和准确性。
比较研究了基于不同算法框架的典型多目标进化算法应用于无功优化的性能特点。以IEEE30节点标准系统的多目标无功优化计算为例，从非支配解集质量和多样性、帕累托前沿分布广阔性和均匀性及收敛速度等多个方面，比较算法的寻优性能，分析其优势或不足，在评估各种算法计算性能的基础上提出了进一步改进的思路。
提出了一种基于多种进化算法自适应选择(multiple evolutionary algorithms withadaptive selection strategies，MEAASS)的多目标无功优化方法。根据该领域研究现状，分析已有算法全局搜索能力、局部搜索能力、收敛速度、计算结果一致性及跳出局部最优能力等方面的特征；在考虑协调性与互补性的基础上，建立包含4类算法的备选池；在进化过程不同阶段根据寻优性能自适应地确定备选算法的使用比例，鼓励寻优性能更高的算法产生更多子代个体；所提出的方法综合了多种算法的性能优势，提高整体寻优效率。
提出了能够计及节点负荷随机性及其相关性的鲁棒多目标无功优化策略。基于蒙特卡罗积分形式的鲁棒优化模型，以系统有功损耗和电压偏移的均值近似地替代负荷波动邻域内的期望值，并同时考虑各种负荷扰动条件下系统运行约束，搜索无功优化鲁棒解。算例分析中采用本文提出的新方法MEAASS求解IEEE30节点标准系统的鲁棒多目标无功优化问题，结果表明鲁棒性优化改善了无功调控方案在负荷不确定性环境下的稳定性和适应性，提高了无功优化的工程实用价值。
Voltage stability and optimal reactive power dispatch (ORPD) are two important andhot topics in power engineering field, in which many researches have been done andabundant achievements have been achieved. Conventional investigations in these twotopics, including mathematical models and solution methods, belong to the category ofdeterministic analysis, and their conclusions have significant instructive effect on voltagestability enhancement and reactive power resources optimal utilization. However, powersystem is in nature a large one with various uncertain factors. With the heavy integration ofrenewable energy sources, more and more random factors continue to emerge in currentpower system. Thorough consideration of these uncertain characteristics in these two topicsis particularly significant. Investigations on modeling methods and solving strategy foruncertain characteristics can make contribution to the amendment of academic theory ofvoltage stability as well as ORPD research, and obtain more achievements with referencevalue and practical significance. To this reason, research on the two topics under uncertainenvironments is chosen to be the theme of this thesis, with the following four aspectsincluded: impact of wind speed correlation (WSC) on voltage instability saddle-nodebifurcation (SNB), voltage stability probabilistic evaluation considering uncertainty inpower injection, comparison and improvement of multi-objective evolutionary algorithms(MOEAs) for multi-objective ORPD, and robust optimal strategy for multi-objectiveORPD with consideration of load uncertainty. The investigations and achievements of thisthesis are listed as follows.
Impact of correlated wind speeds on voltage instability SNB is comprehensivelyinvestigated. Nataf transformation is adopted to establish WSC model for wind farms withclose locations. Based on SNB transversality condition equations and Monte Carlosimulation technique, probability distribution of voltage stability margin under differentWSC coefficients is obtained. Moreover, two risk indexes are presented and the voltage stability deterioration caused by WSC is evaluated from the viewpoint of risk analysis.Experimental results demonstrate that the probability of SNB under relative lower loadgrowth level increases with the strengthening of WSC, implying strong correlated windspeeds bring negative effect in safe and stable operation of power system as far as voltagestability is concerned.
A probabilistic evaluation method of voltage stability accounting for uncertainties inwind speeds and load levels is proposed. Based on Latin hypercube sampling (LHS) MonteCarlo simulation technique, this method can maintain a high degree of accuracy and reducecomputational burden when compared with the simple random sampling Monte Carlomethod. In addition, by combining LHS with Nataf transformation, the presented methodcan deal with correlated wind speeds of different wind farms and correlated load levels ofdifferent buses. Interior point method is used to solve nonlinear programming problems forvoltage stability critical point on the sampling points, and the probability distribution ofvoltage stability margin is obtained. The effectiveness and accuracy of the proposedmethod is validated by case study on the IEEE118bus system.
Five current typical MOEAs are selected and from an overall perspective theapplication of them in multi-objective ORPD is comparatively researched. Different fromtraditional approach that combines multiple objective functions into a single one by settingpreference parameters, the multi-objective model, in which the system network loss andvoltage deviation are taken into account, is directly utilized. Based on the test case of IEEE30bus system, the optimal performances of five MOEAs are compared and thesuperiorities and defects of them are analyzed in the viewpoints of quality and diversity ofnon-dominated solution set, extensity and uniformity of final Pareto front and convergencespeed. On the basis of evaluating computing performances of five MOEAs the prospect offurther research is put forward.
A new optimal method based on multiple evolutionary algorithms with adaptiveselection strategies (MEAASS) for multi-objective ORPD is proposed. Based on analysisof characteristics of state-of-the-art MOEAs, and considering the rules of consistency andcomplementation, candidate algorithm pool containing four different algorithms is presented. By means of adaptively favoring individual algorithms that exhibit higherreproductive success during the search, MEAASS simultaneously merges the strengths ofmultiple algorithms for population evolution. Based on the test case of IEEE30bus system,the computing performance of MEAASS is compared with existing popular algorithms.The numerical simulations demonstrate that MEAASS can obtain better performance ofconvergence during the entire optimization process.
A robust optimal strategy for multi-objective ORPD with consideration of loadrandomness and correlation is proposed. Based on Monte Carlo integral form of objectivefunctions, the expectations of system network loss and voltage deviation in presence ofload fluctuations are approximately calculated, meanwhile the operational constraints undervarious load perturbations are taken into account, finally robust non-dominated solutionswhich are insensitive to load uncertainty are achieved. To reduce the error of Monte Carlointegration, LHS combinated with Nataf transformation is adopted to generate load levelsample. MEAASS is utilized to solve the robust multi-objective ORPD on IEEE30bussystem, and the results demonstrate that control schemes obtained by robust optimalstrategy can maintain their performance and consistency with existence of load uncertainty.
引文
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