基于相量量测单元的电力系统状态估计性能改进研究
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摘要
电力系统状态估计的理论研究已经比较成熟,但以加权最小二乘法(WeightedLeast Square,WLS)为主的状态估计器在实际应用中性能表现并不理想。对于特定状态估计器,提高其状态估计性能表现除了要排除遥测和遥信中的不良数据之外,主要依赖于(1)量测设备精度的提高及其优化配置;(2)量测方程模型(主要指线路参数)的准确程度的提高。本文即从以上两个方面入手,进行探讨性研究。
第二章中对近三十年来电力系统状态估计相关主要工作进行了详尽的综述和分析,并结合作者自身理解,给出了电力系统WLS状态估计理论的关键要点和步骤,为此后各章节奠定基础。
第三章、第四章着重讨论PMU优化配置问题。其中,第三章以SCADA/PMU量测混合配置为基本框架,针对PMU多目标优化配置问题,以使系统满足可观测性、降低成本和提高状态估计性能等为目标,归纳出两个常用的优化问题模型。针对模型Ⅰ,提出压缩编码方法,引入标准遗传算法(SGA)予以求解;针对模型Ⅱ,提出先进行目标分类优化再依照Pareto规则优化的思想,并提出分步变异遗传算法(SMGA)。仿真算例表明,本文所提两个通用目标函数模型恰当,算法稳定可靠。
以第三章所提模型为基础,第四章提出适用于工程应用的估计准确度加权估算公式;深入分析了第Ⅱ类OPP问题二层规划的本质和分段目标函数的多峰特性;在引入克隆算法(CLONALG)及其重组和高频变异算子之后,根据免疫记忆原理,提出基于PMU数目记忆的加速算子,在抗体进化过程中(而非成熟后)加以应用,并根据种群中抗体所含PMU的数目的接近程度,分段调整循环补充规模、重组概率和高频变异概率。基于IEEE 14/57节点潮流数据的两个算例表明,该改进CLONALG算法能快速稳定地依次求出全局最优解和次优解组。
将SMGA算法与改进CLONALG算法对比可知,两算法各有所长。SMGA能够简单快速收敛到全局最优解;改进CLONALG则能以较快速度稳定地达到全局最优解和次优解组,为设计提供多样选择。综合而言,改进CLONALG算法更优。
第五章、第六章着重讨论了准确估计线路参数的方法。第五章分析了电力系统状态估计和参数估计的理论依据并指出传统解法的不足,提出基于经验知识的参数估计目标函数修正项,推导了状态估计和参数估计目标函数极值点的关系,由此提出并证明了新的基于垂直投影的估计策略。针对目标函数投影的局部单峰特性,提出分段适应粒子群优化(SPSO)算法。补充证明了以多次估计的均值作无偏估计的正确性。仿真算例表明:修正目标函数和SPSO算法能快速准确地估计线路参数,且可提高估计准确度和降低对量测系统参数可估计性的要求;取连续多次估计的均值,则可减小量测误差导致的参数估计偏差。
第六章则基于全PMU量测系统,提出新的基于动态滤波的电力系统线路参数估计完整策略:静态线性状态估计和误差处理、虚拟量测(Pseudo Measurement)转换、虚拟量测误差转换、系统动态状态向量降维处理、以变比自动调整的变压器为原型的随机化线路参数运动模型以及基于KF的动态滤波等。仿真算例分别模拟了线路中不包含/包含变比可调变压器的两种情况,结果表明,线路参数估计滤波过程稳定可靠,有效抑制了单轮参数的大估计误差,显著改善了估计准确度。对比试验表明,该策略优于多轮估计平均法。文中还就单个时间断面上参数估计大误差的成因、参数滤波估计与静态状态估计结合的必要性和动态状态向量降维处理的合理性等进行了进一步讨论。
综上所述,本文从改进量测系统配置和提高线路参数估计准确度两个角度,分别探讨了提高电力系统状态估计性能的方法:提出SMGA和改进CLONALG算法等,解决了PMU优化配置这一多目标优化问题;提出SPSO算法,求解基于经验知识的参数估计改进目标函数;引入线路参数随机化模型,提出基于动态滤波的完整参数估计方案。上述诸方法都能够针对性的解决各问题,效率、效果良好。下一步工作将侧重于整合上述两组思路,提出综合考虑量测系统配置改进和线路参数准确度改进的能付诸实际应用的方案。
Although the main theories of power system state estimation have been well developed,but in practice,state estimators,such as these based on weighted least square(WLS) criterion,can't provide with good performance as expected.To a specific state estimator,its performance is determined mainly by the possible occurrence of bad data,the measurement capacity and precision,and the accuracy of the model(measurement function).In this paper,attention is paid mainly to making use of the measurement capacity optimally and improving the accuracy of the model.
In chapter 1,the main work of power system state estimation in the recent 30 years is surveyed and analyzed.And the main knowledge points and procedures of WLS state estimation are listed in chapter 2,which will serve the following chapters as a theoreticl base.
In chapter 3 and 4,the optimal PMU placement problems are discussed.In chapter 3,under the framework of using the hybrid measurement systems of SCADA and PMU,the multi-objective optimal PMU placement(OPP) problems,which include objects as the observability of the measurement sets,the equipment cost and the performance of the corresponding state estimator,are classified into two types.The typeⅠproblem is solved with a standard genetic algorithm(GA) when all the schemes are collated and coded properly.And for the typeⅡproblem,a strategy of sorting all these obects first and then applying the Pareto rule is proposed,from which a stepwise mutation GA arises.Combined examples support the above methods well.
As a continuing part of chapter 3,in chapter 4,a weighted formula of calculating the estimation accuracy is proposed.It is pointed out that the objective function of the typeⅡproblem is a multi-modal function.The improved clonal algorithm(CLONALG) with recombination and hypermutation operators is introduced to search the optimal and sub-optimal solutions.And an accelerating operator based on memory is proposed and the number of cycle supplement population and the probabilities of hypermutation and recombination are stepwisely adjusted.The modifications can quicken and stabilize the optimizing process and prevent the search from locally optimal traps.The examples based on IEEE 14-bus/57-bus indicate that the proposed algorithm is more applicable than the original CLONALG.
The SMGA method is relatively simpler and can reach the globally optimal solution faster than the improved CLONALG,while the latter can provide both the globally and the locally optimal solutions and offer much more options to the designerns.In this sense,the improved CLONALG is better than the SMGA algorithm.
The following work is about improving the model accuracy of transmission lines. In chapter 5,a knowledge-based correction term for the objective function of parameter estimation is proposed.The relationship between the function extreme points of state estimatin and parameter estimation is deduced.A strategy of projecting the parameter objective function from the augmented solution space to the parameter space is proposed and proved.Corresponding to the unimodality of the vertical projection,a heuristic algorithm called as staged particle swarm optimization(SPSO) is proposed.The estimation errors are analyzed and the mean values are proposed as unbiased estimators of the parameters.The examples indicate that the unkown line parameters can be estimated faster and more accurately with the proposed objective function and SPSO and the solving procedure relies less on the augmented jacobian matrix.It is also shown that the mean estimated values of the parameters are close to the truth values.
In chapter 6,a novel and complete strategy of estimating transmission line parameters based on dynamic filtering is proposed,which includes static linear estimation,pseudo-measurement conversion,measurement error conversion,deducing the dimension of the state vector,parameter dynamic models based on ratio adjustable transformer,and the dynamic filtering based on Kalman filter.The examples simulate two different cases of equiping and not equiping with transformers in a line.The results show that the proposed strategy is much better than the method of taking average over estimates from multiple shots.Further discussions proceed then.
In brief,all the proposed motheds above can solve the specific problems efficiently.Futhure work will be focused on how to improve both the configuration of the measurement system and the accuracy of the line parameters at the same time and integrate these methods into practice.
第二章中对近三十年来电力系统状态估计相关主要工作进行了详尽的综述和分析,并结合作者自身理解,给出了电力系统WLS状态估计理论的关键要点和步骤,为此后各章节奠定基础。
第三章、第四章着重讨论PMU优化配置问题。其中,第三章以SCADA/PMU量测混合配置为基本框架,针对PMU多目标优化配置问题,以使系统满足可观测性、降低成本和提高状态估计性能等为目标,归纳出两个常用的优化问题模型。针对模型Ⅰ,提出压缩编码方法,引入标准遗传算法(SGA)予以求解;针对模型Ⅱ,提出先进行目标分类优化再依照Pareto规则优化的思想,并提出分步变异遗传算法(SMGA)。仿真算例表明,本文所提两个通用目标函数模型恰当,算法稳定可靠。
以第三章所提模型为基础,第四章提出适用于工程应用的估计准确度加权估算公式;深入分析了第Ⅱ类OPP问题二层规划的本质和分段目标函数的多峰特性;在引入克隆算法(CLONALG)及其重组和高频变异算子之后,根据免疫记忆原理,提出基于PMU数目记忆的加速算子,在抗体进化过程中(而非成熟后)加以应用,并根据种群中抗体所含PMU的数目的接近程度,分段调整循环补充规模、重组概率和高频变异概率。基于IEEE 14/57节点潮流数据的两个算例表明,该改进CLONALG算法能快速稳定地依次求出全局最优解和次优解组。
将SMGA算法与改进CLONALG算法对比可知,两算法各有所长。SMGA能够简单快速收敛到全局最优解;改进CLONALG则能以较快速度稳定地达到全局最优解和次优解组,为设计提供多样选择。综合而言,改进CLONALG算法更优。
第五章、第六章着重讨论了准确估计线路参数的方法。第五章分析了电力系统状态估计和参数估计的理论依据并指出传统解法的不足,提出基于经验知识的参数估计目标函数修正项,推导了状态估计和参数估计目标函数极值点的关系,由此提出并证明了新的基于垂直投影的估计策略。针对目标函数投影的局部单峰特性,提出分段适应粒子群优化(SPSO)算法。补充证明了以多次估计的均值作无偏估计的正确性。仿真算例表明:修正目标函数和SPSO算法能快速准确地估计线路参数,且可提高估计准确度和降低对量测系统参数可估计性的要求;取连续多次估计的均值,则可减小量测误差导致的参数估计偏差。
第六章则基于全PMU量测系统,提出新的基于动态滤波的电力系统线路参数估计完整策略:静态线性状态估计和误差处理、虚拟量测(Pseudo Measurement)转换、虚拟量测误差转换、系统动态状态向量降维处理、以变比自动调整的变压器为原型的随机化线路参数运动模型以及基于KF的动态滤波等。仿真算例分别模拟了线路中不包含/包含变比可调变压器的两种情况,结果表明,线路参数估计滤波过程稳定可靠,有效抑制了单轮参数的大估计误差,显著改善了估计准确度。对比试验表明,该策略优于多轮估计平均法。文中还就单个时间断面上参数估计大误差的成因、参数滤波估计与静态状态估计结合的必要性和动态状态向量降维处理的合理性等进行了进一步讨论。
综上所述,本文从改进量测系统配置和提高线路参数估计准确度两个角度,分别探讨了提高电力系统状态估计性能的方法:提出SMGA和改进CLONALG算法等,解决了PMU优化配置这一多目标优化问题;提出SPSO算法,求解基于经验知识的参数估计改进目标函数;引入线路参数随机化模型,提出基于动态滤波的完整参数估计方案。上述诸方法都能够针对性的解决各问题,效率、效果良好。下一步工作将侧重于整合上述两组思路,提出综合考虑量测系统配置改进和线路参数准确度改进的能付诸实际应用的方案。
Although the main theories of power system state estimation have been well developed,but in practice,state estimators,such as these based on weighted least square(WLS) criterion,can't provide with good performance as expected.To a specific state estimator,its performance is determined mainly by the possible occurrence of bad data,the measurement capacity and precision,and the accuracy of the model(measurement function).In this paper,attention is paid mainly to making use of the measurement capacity optimally and improving the accuracy of the model.
In chapter 1,the main work of power system state estimation in the recent 30 years is surveyed and analyzed.And the main knowledge points and procedures of WLS state estimation are listed in chapter 2,which will serve the following chapters as a theoreticl base.
In chapter 3 and 4,the optimal PMU placement problems are discussed.In chapter 3,under the framework of using the hybrid measurement systems of SCADA and PMU,the multi-objective optimal PMU placement(OPP) problems,which include objects as the observability of the measurement sets,the equipment cost and the performance of the corresponding state estimator,are classified into two types.The typeⅠproblem is solved with a standard genetic algorithm(GA) when all the schemes are collated and coded properly.And for the typeⅡproblem,a strategy of sorting all these obects first and then applying the Pareto rule is proposed,from which a stepwise mutation GA arises.Combined examples support the above methods well.
As a continuing part of chapter 3,in chapter 4,a weighted formula of calculating the estimation accuracy is proposed.It is pointed out that the objective function of the typeⅡproblem is a multi-modal function.The improved clonal algorithm(CLONALG) with recombination and hypermutation operators is introduced to search the optimal and sub-optimal solutions.And an accelerating operator based on memory is proposed and the number of cycle supplement population and the probabilities of hypermutation and recombination are stepwisely adjusted.The modifications can quicken and stabilize the optimizing process and prevent the search from locally optimal traps.The examples based on IEEE 14-bus/57-bus indicate that the proposed algorithm is more applicable than the original CLONALG.
The SMGA method is relatively simpler and can reach the globally optimal solution faster than the improved CLONALG,while the latter can provide both the globally and the locally optimal solutions and offer much more options to the designerns.In this sense,the improved CLONALG is better than the SMGA algorithm.
The following work is about improving the model accuracy of transmission lines. In chapter 5,a knowledge-based correction term for the objective function of parameter estimation is proposed.The relationship between the function extreme points of state estimatin and parameter estimation is deduced.A strategy of projecting the parameter objective function from the augmented solution space to the parameter space is proposed and proved.Corresponding to the unimodality of the vertical projection,a heuristic algorithm called as staged particle swarm optimization(SPSO) is proposed.The estimation errors are analyzed and the mean values are proposed as unbiased estimators of the parameters.The examples indicate that the unkown line parameters can be estimated faster and more accurately with the proposed objective function and SPSO and the solving procedure relies less on the augmented jacobian matrix.It is also shown that the mean estimated values of the parameters are close to the truth values.
In chapter 6,a novel and complete strategy of estimating transmission line parameters based on dynamic filtering is proposed,which includes static linear estimation,pseudo-measurement conversion,measurement error conversion,deducing the dimension of the state vector,parameter dynamic models based on ratio adjustable transformer,and the dynamic filtering based on Kalman filter.The examples simulate two different cases of equiping and not equiping with transformers in a line.The results show that the proposed strategy is much better than the method of taking average over estimates from multiple shots.Further discussions proceed then.
In brief,all the proposed motheds above can solve the specific problems efficiently.Futhure work will be focused on how to improve both the configuration of the measurement system and the accuracy of the line parameters at the same time and integrate these methods into practice.
引文
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