大规模电力系统动态等值方法及相关问题研究
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摘要
随着电力系统的发展，现代电力系统逐渐形成了巨大的互联模式，以求提高电能质量和供电可靠性。如何保证大系统的安全稳定运行是一个重大而迫切的问题。一方面，由于系统元件众多，对其详细建模进行暂态稳定分析是很困难的；另一方面，受到软件资源规模的限制（如RTDS、EMTDC等软件），不可能对系统中所有元件进行详细建模。采用动态等值技术化简系统是解决这个问题的有效措施。本文针对大规模电力系统的动态等值方法及相关问题进行了较为深入的探讨，主要工作成果包括：
1、提出用于发电机同调识别的粒子群-模糊c均值聚类算法（PSO-FCM）。该算法把聚类中心数作为粒子进行编码，利用粒子群优化的并行性和全局搜索能力，通过不断更新粒子的速度和位置实现寻优，并克服了模糊c均值聚类对初值的依赖和易陷入局部极值的缺点。文中还构造了3个聚类有效性函数进行聚类效果的评价。IEEE10机39节点系统仿真表明，该算法具有快速、准确、简单、易实现的特点，有效解决了同调发电机的识别问题，可用于电力系统不同运行方式下的发电机同调识别。
2、提出用于发电机同调识别的改进PSO-FCM算法。为提高PSO-FCM算法的收敛性能，在PSO速度公式中增加收敛因子和随机选取粒子的某个个体极值为扰动量，目的是增加粒子的多样性、避免粒子产生聚集而出现早熟，从而使算法收敛到全局最优。仿真表明，改进的PSO-FCM算法除保留了PSO-FCM的优点外，还改善了算法的收敛性，改进的PSO-FCM算法适用于同调发电机的识别。
3、基于电力系统大型分析工具PSD-BPA和等值软件PSDEP，以海南电网为背景对同调等值法进行工程应用研究。首先，给出等值的总体原则。其次，为弥补PSDEP中等值机Powell优化聚合算法的不足，用加权法作为等值机参数聚合的补充，并提出用于等值机加权聚合参数优化的自适应差分进化算法。其中，差分进化算法（DE）中的缩放因子和交叉概率因子采用自适应策略。最后仿真表明，海南电网数据规模被压缩近6倍，等值前后系统的潮流分布基本相同、动态特性基本一致。DE的自适应设计改善了算法的收敛性，提高了等值机参数聚合的精度。基于改进加权法的同调等值方法可用于大规模电力系统的动态等值化简。
4、基于小扰动分析程序PSD-SSAP，提取系统特征值分析的相关因子为特征量，并提出基于大型统计软件SPSS的k均值聚类和系统聚类相结合的发电机同调分群方法。根据同调分群结果，可把同调发电机组进行聚合从而化简系统，亦可作为安装PSS机组的选择依据。本文提出强相关同调机组安装PSS的策略，并给出多机PSS参数整体协调优化的混沌粒子群算法（CPSO）。CPSO克服了粒子群早熟和混沌搜索对初值敏感的缺点，具有不依赖初值、搜索快速、遍历性的特点。海南电网SSAP仿真表明，基于发电机同调分群的PSS协调优化配置有效提高了系统的阻尼。该方法不但解决了小扰动时发电机同调分群问题，且对多机PSS的合理配置提出了解决方案，提高了系统的小干扰稳定性，具有较好的工程应用前景。
5、提出新的在线估计等值方法。该方法首先给出等值发电机+综合负荷的等值系统模型。其中，发电机采用较精细的六阶模型，综合负荷模型包括静态ZIP负荷和三阶动态感应电动机负荷。其次，提出基于差分进化算法（DE）的等值系统参数辨识策略。为解决DE存在的早熟收敛问题，构造变异方式不同的两个差分进化群，两群并行进化，且定时交换信息，目的是增加种群的多样性、改善算法的收敛性。仿真表明，改进的双群体差分进化算法有效解决了等值系统的参数辨识问题，算法简单、收敛快、鲁棒性好，辨识的参数精度较高。建立的等值系统模型更符合电网实际，等值后外部系统的动态特性基本被保留。所提新的估计等值法可用于在线大规模系统外部系统的等值化简。
6、提出感应电动机负荷的同调分群和聚合方法。首先，根据提取的反映电动机动态特性的特征量，提出用于同调电动机负荷分群的混沌粒子群-模糊c均值聚类算法（CPSO-FCM）。用CPSO的快速性、随机初始化和并行寻优能力，克服FCM依赖于初值和易陷入局部最优的缺点，并用有效性函数对聚类结果进行评价。其次，提出同调感应电动机负荷聚合的辨识策略，并提出等值负荷参数辨识的改进双群体差分进化算法。仿真表明：分群算法收敛快、鲁棒性好，辨识的负荷参数精度高，等值系统完全保留了原始系统的动态特性。该方法可用于在线估计等值中大量感应电动机负荷的等值化简。
本文研究工作得到了国家高技术研究发展计划（863计划）（No.2011AA05A102）的资助。
With power system development, modern power system is gradually grown up towardsinterconnection of large scale so as to enhance the quality of electric energy and the reliabilityof power supply. Thus, how to guarantee safe and stable operation for large scale powersystems becomes a significant and urgent issue. Major challenges include the difficulty toanalyze transient stability for such large scale power systems with numerous elements modeledin detail on one hand, and the limited professional software capability on the other hand, suchas Real Time Digital Simulator (RTDS), Electro Magnetic Transient in DC System (EMTDC),etc. Using dynamic equivalence technology to reduce power systems is considered to be aneffective measure to solve this problem. In order to improve dynamic equivalence method andits related technology for large scale power systems, some research has been done in thedissertation, and main key points as follows:
1. An algorithm marked as PSO-FCM, namely, the Fuzzy c-means Clustering (FCM)based on the Particle Swarm Optimization (PSO), is presented to solve the partition problem ofcoherent generators. In this algorithm, the cluster center is taken as a particle for encoding, andthe parallel property and the global searching capacity of the PSO algorithm are applied to theoptimization through continuously renewing the velocity and position of the particles. Thus,the dependency of the FCM algorithm upon the initial value and the risk of falling into localoptimum are largely reduced. Moreover, in order to evaluate the clustering validity, threevalidity functions are constructed. Simulated results on IEEE10-generator39-bus system showthat the PSO-FCM algorithm is suitable for the partition of coherent generators of powersystems in various operation modes because it is of simplicity, easy realization, high accuracyand high speed.
2. An algorithm marked as modified PSO-FCM is presented to solve the partitionproblem of coherent generators. In order to improve PSO-FCM convergence performance, twoways are presented: convergence factor and disturbance introduced to the formula ofPSO velocity by randomly selecting optimal position of particle, which can increase diversityof particle swarm and avoid premature on account of aggregation of particle. The modifiedalgorithm can easily converge to global optimum. Simulated results show that the MPSO-FCM algorithm is suitable for the partition of coherent generators due to the improved convergenceperformance the original advantages of PSO-FCM.
3. The dynamic equivalent based on coherency is studied on Hainan Power Grid by thePower System Dynamic Equivalence Program (PSDEP) and large simulation tool PSD-BPAfor power systems. First, the overall principle of dynamic equivalence is presented. Second, inorder to remedy the deficiency of Powell optimization algorithm in PSDEP which is used toaggregate equivalent generators, weighting method is presented as supplement to aggregateparameter of coherent generators, and then Differential Evolution (DE) algorithm which hasexcellent property is presented to optimize parameter of equivalent generators acquired byweighting method. Self-adaptive strategy is adopted for zoom factor and crossover probabilityfactor in DE. Finally, simulated results show that the data scale of Hainan Power Grid isreduced six times approximately, and the power flow of equivalent system is almost identicalwith original system, and the main dynamic characteristics of original system retain well. Thealgorithm convergence and precision of equivalent generators’ parameters are improved byself-adaptive strategy in DE. The coherency-based dynamic equivalent method by modifiedweighting method is suitable for reducing large scale power systems.
4. Based on small signal analysis procedure SSAP, correlation factor of eigenvalueanalysis for systems is selected as characteristic quantity, and a method combining k-meansclustering and hierarchical clustering is proposed to identify generators with large-scalestatistical software-Statistical Package for Social Sciences (SPSS). On the basis of result ofcoherent generators’ identification, it can aggregate coherent generators to simplify powersystems, and also serve as selecting principle of generators with PSS installed. It proposes thatPSS is installed in strongly correlated generators, and Chaotic Particle Swarm Optimization(CPSO) algorithm for PSS parameters optimization is presented. The disadvantage of PSO,leading into local optimum, and that of chaotic search, sensitive to initial value, are overcomein CPSO. CPSO is independent on initial value, high speed and good ergodic property. Bytesting on Hainan Power Grid based on SSAP, it is concluded that the damp of system isimproved after coordinated optimization of PSS parameters based on coherent identificationresult of generators. The method is effective to solve the problem of identification coherentgenerators in small signal analysis, and also presents a solution of reasonable allocation of multi-generator’ PSS. The small signal stability is enhanced for power systems with themethod, which has a better prospect in engineering application.
5. A new method of estimation dynamic equivalence used for online is presented. First,the model of external equivalent system which comprised equivalent generator and compositeload is given. In equivalent system model, refined six-order model of generator is adopted, andstatic state ZIP load combining three-order dynamic inductive motor are included in compositeload model. Then, it is presented the identification strategy based on Differential Evolution(DE) algorithm. In order to solve premature problem of DE, double differential evolutionswarms with different variation are formed, and considering double swarms parallel evolution,and exchange message at regular time. The aim is to increase diversity of swarms and improveconvergence of DE. Simulated result shows that the method is effective to parameteridentification problem of equivalent system. The algorithm is simple and rapid, and it is higheraccuracy and better robustness for identified parameter. Equivalent system model obtained isbetter accord with practical power system, and equivalent system can preserve main dynamiccharacteristics of external system well. The new estimation equivalent method can be used toreduce external system of large scale power systems online.
6. A method for identification and aggregation coherent inductive motor loads is proposed.Firstly, it is presented the algorithm of Fuzzy c-means Clustering by Chaotic Particle SwarmOptimization (CPSO-FCM) to identify coherent motors, on the basis of the characteristicswhich reflect the dynamic performance of motor. The merits of CPSO algorithm areconvergence to optimal value rapidly, independence initial value, and parallel search so as toovercome FCM’ disadvantage which is upon the initial value and has the risk of falling intolocal optimum. A validity function is constructed so as to evaluate the clustering validity.Secondly, identification strategy is employed to aggregate coherent inductive motor loads, andthe parameter of equivalent motor load is acquired by using modified double swarms DE. Bytesting on IEEE10-generators39-bus system, the conclusion is presented that CPSO-FCMalgorithm is rapid convergence and robust. It has high accuracy of identified load parameter,and equivalent system can preserve the main dynamic characteristics of original system well.The method can be used to simplify mass inductive motor loads in online estimationequivalence.
This dissertation is supported by the National High Technology Research andDevelopment Program of China (863Program)(2011AA05A102).
1、提出用于发电机同调识别的粒子群-模糊c均值聚类算法（PSO-FCM）。该算法把聚类中心数作为粒子进行编码，利用粒子群优化的并行性和全局搜索能力，通过不断更新粒子的速度和位置实现寻优，并克服了模糊c均值聚类对初值的依赖和易陷入局部极值的缺点。文中还构造了3个聚类有效性函数进行聚类效果的评价。IEEE10机39节点系统仿真表明，该算法具有快速、准确、简单、易实现的特点，有效解决了同调发电机的识别问题，可用于电力系统不同运行方式下的发电机同调识别。
2、提出用于发电机同调识别的改进PSO-FCM算法。为提高PSO-FCM算法的收敛性能，在PSO速度公式中增加收敛因子和随机选取粒子的某个个体极值为扰动量，目的是增加粒子的多样性、避免粒子产生聚集而出现早熟，从而使算法收敛到全局最优。仿真表明，改进的PSO-FCM算法除保留了PSO-FCM的优点外，还改善了算法的收敛性，改进的PSO-FCM算法适用于同调发电机的识别。
3、基于电力系统大型分析工具PSD-BPA和等值软件PSDEP，以海南电网为背景对同调等值法进行工程应用研究。首先，给出等值的总体原则。其次，为弥补PSDEP中等值机Powell优化聚合算法的不足，用加权法作为等值机参数聚合的补充，并提出用于等值机加权聚合参数优化的自适应差分进化算法。其中，差分进化算法（DE）中的缩放因子和交叉概率因子采用自适应策略。最后仿真表明，海南电网数据规模被压缩近6倍，等值前后系统的潮流分布基本相同、动态特性基本一致。DE的自适应设计改善了算法的收敛性，提高了等值机参数聚合的精度。基于改进加权法的同调等值方法可用于大规模电力系统的动态等值化简。
4、基于小扰动分析程序PSD-SSAP，提取系统特征值分析的相关因子为特征量，并提出基于大型统计软件SPSS的k均值聚类和系统聚类相结合的发电机同调分群方法。根据同调分群结果，可把同调发电机组进行聚合从而化简系统，亦可作为安装PSS机组的选择依据。本文提出强相关同调机组安装PSS的策略，并给出多机PSS参数整体协调优化的混沌粒子群算法（CPSO）。CPSO克服了粒子群早熟和混沌搜索对初值敏感的缺点，具有不依赖初值、搜索快速、遍历性的特点。海南电网SSAP仿真表明，基于发电机同调分群的PSS协调优化配置有效提高了系统的阻尼。该方法不但解决了小扰动时发电机同调分群问题，且对多机PSS的合理配置提出了解决方案，提高了系统的小干扰稳定性，具有较好的工程应用前景。
5、提出新的在线估计等值方法。该方法首先给出等值发电机+综合负荷的等值系统模型。其中，发电机采用较精细的六阶模型，综合负荷模型包括静态ZIP负荷和三阶动态感应电动机负荷。其次，提出基于差分进化算法（DE）的等值系统参数辨识策略。为解决DE存在的早熟收敛问题，构造变异方式不同的两个差分进化群，两群并行进化，且定时交换信息，目的是增加种群的多样性、改善算法的收敛性。仿真表明，改进的双群体差分进化算法有效解决了等值系统的参数辨识问题，算法简单、收敛快、鲁棒性好，辨识的参数精度较高。建立的等值系统模型更符合电网实际，等值后外部系统的动态特性基本被保留。所提新的估计等值法可用于在线大规模系统外部系统的等值化简。
6、提出感应电动机负荷的同调分群和聚合方法。首先，根据提取的反映电动机动态特性的特征量，提出用于同调电动机负荷分群的混沌粒子群-模糊c均值聚类算法（CPSO-FCM）。用CPSO的快速性、随机初始化和并行寻优能力，克服FCM依赖于初值和易陷入局部最优的缺点，并用有效性函数对聚类结果进行评价。其次，提出同调感应电动机负荷聚合的辨识策略，并提出等值负荷参数辨识的改进双群体差分进化算法。仿真表明：分群算法收敛快、鲁棒性好，辨识的负荷参数精度高，等值系统完全保留了原始系统的动态特性。该方法可用于在线估计等值中大量感应电动机负荷的等值化简。
本文研究工作得到了国家高技术研究发展计划（863计划）（No.2011AA05A102）的资助。
With power system development, modern power system is gradually grown up towardsinterconnection of large scale so as to enhance the quality of electric energy and the reliabilityof power supply. Thus, how to guarantee safe and stable operation for large scale powersystems becomes a significant and urgent issue. Major challenges include the difficulty toanalyze transient stability for such large scale power systems with numerous elements modeledin detail on one hand, and the limited professional software capability on the other hand, suchas Real Time Digital Simulator (RTDS), Electro Magnetic Transient in DC System (EMTDC),etc. Using dynamic equivalence technology to reduce power systems is considered to be aneffective measure to solve this problem. In order to improve dynamic equivalence method andits related technology for large scale power systems, some research has been done in thedissertation, and main key points as follows:
1. An algorithm marked as PSO-FCM, namely, the Fuzzy c-means Clustering (FCM)based on the Particle Swarm Optimization (PSO), is presented to solve the partition problem ofcoherent generators. In this algorithm, the cluster center is taken as a particle for encoding, andthe parallel property and the global searching capacity of the PSO algorithm are applied to theoptimization through continuously renewing the velocity and position of the particles. Thus,the dependency of the FCM algorithm upon the initial value and the risk of falling into localoptimum are largely reduced. Moreover, in order to evaluate the clustering validity, threevalidity functions are constructed. Simulated results on IEEE10-generator39-bus system showthat the PSO-FCM algorithm is suitable for the partition of coherent generators of powersystems in various operation modes because it is of simplicity, easy realization, high accuracyand high speed.
2. An algorithm marked as modified PSO-FCM is presented to solve the partitionproblem of coherent generators. In order to improve PSO-FCM convergence performance, twoways are presented: convergence factor and disturbance introduced to the formula ofPSO velocity by randomly selecting optimal position of particle, which can increase diversityof particle swarm and avoid premature on account of aggregation of particle. The modifiedalgorithm can easily converge to global optimum. Simulated results show that the MPSO-FCM algorithm is suitable for the partition of coherent generators due to the improved convergenceperformance the original advantages of PSO-FCM.
3. The dynamic equivalent based on coherency is studied on Hainan Power Grid by thePower System Dynamic Equivalence Program (PSDEP) and large simulation tool PSD-BPAfor power systems. First, the overall principle of dynamic equivalence is presented. Second, inorder to remedy the deficiency of Powell optimization algorithm in PSDEP which is used toaggregate equivalent generators, weighting method is presented as supplement to aggregateparameter of coherent generators, and then Differential Evolution (DE) algorithm which hasexcellent property is presented to optimize parameter of equivalent generators acquired byweighting method. Self-adaptive strategy is adopted for zoom factor and crossover probabilityfactor in DE. Finally, simulated results show that the data scale of Hainan Power Grid isreduced six times approximately, and the power flow of equivalent system is almost identicalwith original system, and the main dynamic characteristics of original system retain well. Thealgorithm convergence and precision of equivalent generators’ parameters are improved byself-adaptive strategy in DE. The coherency-based dynamic equivalent method by modifiedweighting method is suitable for reducing large scale power systems.
4. Based on small signal analysis procedure SSAP, correlation factor of eigenvalueanalysis for systems is selected as characteristic quantity, and a method combining k-meansclustering and hierarchical clustering is proposed to identify generators with large-scalestatistical software-Statistical Package for Social Sciences (SPSS). On the basis of result ofcoherent generators’ identification, it can aggregate coherent generators to simplify powersystems, and also serve as selecting principle of generators with PSS installed. It proposes thatPSS is installed in strongly correlated generators, and Chaotic Particle Swarm Optimization(CPSO) algorithm for PSS parameters optimization is presented. The disadvantage of PSO,leading into local optimum, and that of chaotic search, sensitive to initial value, are overcomein CPSO. CPSO is independent on initial value, high speed and good ergodic property. Bytesting on Hainan Power Grid based on SSAP, it is concluded that the damp of system isimproved after coordinated optimization of PSS parameters based on coherent identificationresult of generators. The method is effective to solve the problem of identification coherentgenerators in small signal analysis, and also presents a solution of reasonable allocation of multi-generator’ PSS. The small signal stability is enhanced for power systems with themethod, which has a better prospect in engineering application.
5. A new method of estimation dynamic equivalence used for online is presented. First,the model of external equivalent system which comprised equivalent generator and compositeload is given. In equivalent system model, refined six-order model of generator is adopted, andstatic state ZIP load combining three-order dynamic inductive motor are included in compositeload model. Then, it is presented the identification strategy based on Differential Evolution(DE) algorithm. In order to solve premature problem of DE, double differential evolutionswarms with different variation are formed, and considering double swarms parallel evolution,and exchange message at regular time. The aim is to increase diversity of swarms and improveconvergence of DE. Simulated result shows that the method is effective to parameteridentification problem of equivalent system. The algorithm is simple and rapid, and it is higheraccuracy and better robustness for identified parameter. Equivalent system model obtained isbetter accord with practical power system, and equivalent system can preserve main dynamiccharacteristics of external system well. The new estimation equivalent method can be used toreduce external system of large scale power systems online.
6. A method for identification and aggregation coherent inductive motor loads is proposed.Firstly, it is presented the algorithm of Fuzzy c-means Clustering by Chaotic Particle SwarmOptimization (CPSO-FCM) to identify coherent motors, on the basis of the characteristicswhich reflect the dynamic performance of motor. The merits of CPSO algorithm areconvergence to optimal value rapidly, independence initial value, and parallel search so as toovercome FCM’ disadvantage which is upon the initial value and has the risk of falling intolocal optimum. A validity function is constructed so as to evaluate the clustering validity.Secondly, identification strategy is employed to aggregate coherent inductive motor loads, andthe parameter of equivalent motor load is acquired by using modified double swarms DE. Bytesting on IEEE10-generators39-bus system, the conclusion is presented that CPSO-FCMalgorithm is rapid convergence and robust. It has high accuracy of identified load parameter,and equivalent system can preserve the main dynamic characteristics of original system well.The method can be used to simplify mass inductive motor loads in online estimationequivalence.
This dissertation is supported by the National High Technology Research andDevelopment Program of China (863Program)(2011AA05A102).
引文
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