多维导数阶数控制的多步Taylor级数暂态稳定计算方法
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摘要
为提高电力系统暂态稳定分析效率,本文提出了多维阶数控制的多步Taylor级数暂态稳定快速计算方法。该方法基于多步Taylor级数展开理论,针对不同时间常数的机组及不同积分时刻的机组转角状态量,根据时域仿真计算精度建立了转角状态量的高阶导数阶数差异化控制策略,并从理论上分析了忽略部分高阶导数对转角轨迹的影响。所提方法可实现状态变量时间和空间上的动态多维导数阶数控制,消除常规Taylor级数法暂态稳定分析的计算冗余。New England 10机39节点算例仿真验证了所提方法可灵活方便地实现Taylor级数法的时空多维阶数控制,能有效提高暂态稳定分析效率。
To enhance the efficiency of transient stability analysis of power system,a transient stability calculation method using multi-step Taylor series controlled by multi-dimensional derivative order was proposed in this paper. This method was based on the multi-step Taylor series expansion theory,and for generating sets with different time-constants and angle states at different integration moments,the corresponding differentiated strategies with high-order derivative order control were established for the angle states according to the calculation accuracy of time-domain simulation. Moreover,the effect of ignoring part of the high-order derivatives on angle tracks was analyzed theoretically. The proposed method could realize a dynamical multi-dimensional derivative order control of state variables in both time and space,and also eliminate the computation redundancy of conventional Taylor series method for transient stability analysis. Simulation results of a 10-generator 39-bus New England system verified that the proposed method could realize the spatialtemporal multi-dimensional derivative order control of Taylor series method with flexibility and convenience,and could significantly improve the efficiency of transient stability analysis.
To enhance the efficiency of transient stability analysis of power system,a transient stability calculation method using multi-step Taylor series controlled by multi-dimensional derivative order was proposed in this paper. This method was based on the multi-step Taylor series expansion theory,and for generating sets with different time-constants and angle states at different integration moments,the corresponding differentiated strategies with high-order derivative order control were established for the angle states according to the calculation accuracy of time-domain simulation. Moreover,the effect of ignoring part of the high-order derivatives on angle tracks was analyzed theoretically. The proposed method could realize a dynamical multi-dimensional derivative order control of state variables in both time and space,and also eliminate the computation redundancy of conventional Taylor series method for transient stability analysis. Simulation results of a 10-generator 39-bus New England system verified that the proposed method could realize the spatialtemporal multi-dimensional derivative order control of Taylor series method with flexibility and convenience,and could significantly improve the efficiency of transient stability analysis.
引文
[1]李朋,李欣然,韦肖燕,等(Li Peng,Li Xinran,Wei Xiaoyan,et al).泰勒级数在电力系统暂态稳定性分析中的应用(Research on improving transient stability by energy storage system based on transient potential energy control)[J].电力系统及其自动化学报(Proceedings of the CSUEPSA),2017,29(5):41-47.
[2]付强,杜文娟,王海风,等(Fu Qiang,Du Wenjuan,Wang Haifeng,et al).交直流混联电力系统小干扰稳定性分析综述(Small signal stability analysis of AC/DC hybrid power system:an overview)[J].中国电机工程学报(Pro?ceedings of the CSEE),2018,38(10):2829-2840.
[3]袁小明,程时杰,胡家兵(Yuan Xiaoming,Cheng Shijie,Hu Jiabing).电力电子化电力系统多尺度电压功角动态稳定问题(Multi-time scale voltage and power angle dy?namics in power electronics dominated large power sys?tems)[J].中国电机工程学报(Proceedings of the CSEE),2016,36(19):5145-5154.
[4]朱蜀,刘开培,秦亮,等(Zhu Shu,Liu Kaipei,Qin Liang,et al).电力电子化电力系统暂态稳定性分析综述(Analysis of transient stability of power electronics domi?nated power system:an overview)[J].中国电机工程学报(Proceedings of the CSEE),2017,37(14):3948-3962.
[5]周挺辉,严正,唐聪,等(Zhou Tinghui,Yan Zheng,Tang Cong,et al).基于多核处理器技术的暂态稳定并行算法(A parallel algorithm for the transient stability comput?ing based on multi-core processor technology)[J].电力系统自动化(Automation of Electric Power Systems),2013,37(8):70-75.
[6]汪芳宗,张磊(Wang Fangzong,Zhang Lei).基于辛Ra?dau方法的暂态稳定性并行计算方法(Parallel algo?rithm based on symplectic Radau method for transient sta?bility simulation)[J].电力系统保护与控制(Power Sys?tem Protection and Control),2011,39(23):34-38.
[7]江涵,江全元(Jiang Han,Jiang Quanyuan).基于GPU的交直流电力系统暂态稳定双层并行仿真(A two-level parallel transient stability algorithm for AC/DC power sys?tem based on GPU platform)[J].电力系统保护与控制(Power System Protection and Control),2012,40(21):102-108.
[8]戴远航,陈磊,张玮灵,等(Dai Yuanhang,Chen Lei,Zhang Weiling,et al).基于多支持向量机综合的电力系统暂态稳定评估(Power system transient stability assess?ment based on multi-support vector machines)[J].中国电机工程学报(Proceedings of the CSEE),2016,36(5):1173-1180.
[9]郑焕坤,常鲜戎,王正辉(Zheng Huankun,Chang Xian?rong,Wang Zhenghui).高精度A稳定隐式调谐Taylor级数法在电力系统中的应用(Application of high preci?sion and A-stability implicit tuned Taylor series method in power system)[J].电工技术学报(Transactions of Elec?trotechnical Society),2012,27(1):217-223,280.
[10]郭志忠,柳焯(Guo Zhizhong,Liu Zhuo).快速高阶Tay?lor级数法暂态稳定计算(Fast transient stability simula?tion by higher order Taylor series expansions)[J].中国电机工程学报(ProceedingsoftheCSEE),1991,11(3):7-16.
[11]郭志忠(Guo Zhizhong).发电机功角的二项式导数递推规律(The binomial derivative recursion laws of generator’s power and angle)[J].中国电机工程学报(Proceedings of the CSEE),2005,25(16):147-152.
[12]刘建楠,白雪峰,徐英,等(Liu Jiannan,Bai Xuefeng,Xu Ying,et al).多步高阶Taylor级数暂态稳定最优积分格式(Optimal integral scheme of multi-step high-order Tay?lor series method for transient stability calculation)[J].电力自动化设备(Electric Power Automation Equipment),2012,32(10):121-126.
[13]房大中,张尧,宋文南,等(Fang Dazhong,Zhang Yao,Song Wennan,et al).泰勒级数在电力系统暂态稳定性分析中的应用(Application of Taylor series in power sys?tem transient stability assessment)[J].天津大学学报(Journal of Tianjin University),1998,31(6):772-777.
[14] Wang Zongyi,Guo Zhizhong. A fast method for transient stability assessment based on Taylor series expansion[C]//IEEE/PES Transmission and Distribution Conference and Exhibition. Dalian,China,2005.
[15]白雪峰,郭志忠(Bai Xuefeng,Guo Zhizhong). Taylor级数法暂态稳定计算中阶数的动态控制(The dynamic control of order selection in fast transient stability simula?tion by higher order Taylor series expansions)[J].电力系统自动化(Automation of Electric Power Systems),1999,23(22):5-7.
[16]王宇宾,常鲜戎,罗艳,等(Wang Yubin,Chang Xian?rong,Luo Yan,et al).基于隐式Taylor级数法的电力系统暂态稳定计算(An implicit Taylor series method for simulation of power system transient)[J].华北电力大学学报(Journal of North China Electric Power University),2005,32(2):1-6.
[17]夏世威,白雪峰,陈士麟,等(Xia Shiwei,Bai Xuefeng,Chen Shilin,et al).多群模式Taylor级数法暂态稳定计算(Transient stability calculation by multi-machine equiv?alent Taylor series method)[J].电力系统自动化(Auto?mation of Electric Power Systems),2010,34(10):24-28.
[18]徐英,白雪峰,郭志忠(Xu Ying,Bai Xuefeng,Guo Zhi?zhong).采用动态多维阶数控制的暂态稳定计算方法(Transient stability calculation method using dynamic multi-dimension order control)[J].中国电机工程学报(Proceedings of the CSEE),2008,28(19):81-85.
[19]徐英,白雪峰,郭志忠(Xu Ying,Bai Xuefeng,Guo Zhi?zhong).多步高阶暂态稳定计算方法(Transient stabili?ty calculation based on explicit multi-step multi-deriva?tive integration method)[J].电力系统自动化(Automa?tion of Electric Power Systems),2009,33(15):33-37.
[20]徐英,郭志忠(Xu Ying,Guo Zhizhong).多步高阶隐式泰勒级数法暂态稳定计算(Transient stability calculation by implicit multi-step Taylor series method)[J].电力系统保护与控制(Power System Protection and Control),2011,39(23):11-15,20.
[21]夏世威,郭志忠,陈士麟,等(Xia Shiwei,Guo Zhizhong,Chen Shilin,et al).变阶多步Taylor级数法暂态稳定并行计算(Parallel transient stability calculation by multistep dynamic-order Taylor method)[J].电力系统保护与控制(Power System Protection and Control),2012,40(22):25-31.
[22]倪以信,陈寿孙,张宝霖.动态电力系统的理论和分析[M].北京:清华大学出版社,2002.
[2]付强,杜文娟,王海风,等(Fu Qiang,Du Wenjuan,Wang Haifeng,et al).交直流混联电力系统小干扰稳定性分析综述(Small signal stability analysis of AC/DC hybrid power system:an overview)[J].中国电机工程学报(Pro?ceedings of the CSEE),2018,38(10):2829-2840.
[3]袁小明,程时杰,胡家兵(Yuan Xiaoming,Cheng Shijie,Hu Jiabing).电力电子化电力系统多尺度电压功角动态稳定问题(Multi-time scale voltage and power angle dy?namics in power electronics dominated large power sys?tems)[J].中国电机工程学报(Proceedings of the CSEE),2016,36(19):5145-5154.
[4]朱蜀,刘开培,秦亮,等(Zhu Shu,Liu Kaipei,Qin Liang,et al).电力电子化电力系统暂态稳定性分析综述(Analysis of transient stability of power electronics domi?nated power system:an overview)[J].中国电机工程学报(Proceedings of the CSEE),2017,37(14):3948-3962.
[5]周挺辉,严正,唐聪,等(Zhou Tinghui,Yan Zheng,Tang Cong,et al).基于多核处理器技术的暂态稳定并行算法(A parallel algorithm for the transient stability comput?ing based on multi-core processor technology)[J].电力系统自动化(Automation of Electric Power Systems),2013,37(8):70-75.
[6]汪芳宗,张磊(Wang Fangzong,Zhang Lei).基于辛Ra?dau方法的暂态稳定性并行计算方法(Parallel algo?rithm based on symplectic Radau method for transient sta?bility simulation)[J].电力系统保护与控制(Power Sys?tem Protection and Control),2011,39(23):34-38.
[7]江涵,江全元(Jiang Han,Jiang Quanyuan).基于GPU的交直流电力系统暂态稳定双层并行仿真(A two-level parallel transient stability algorithm for AC/DC power sys?tem based on GPU platform)[J].电力系统保护与控制(Power System Protection and Control),2012,40(21):102-108.
[8]戴远航,陈磊,张玮灵,等(Dai Yuanhang,Chen Lei,Zhang Weiling,et al).基于多支持向量机综合的电力系统暂态稳定评估(Power system transient stability assess?ment based on multi-support vector machines)[J].中国电机工程学报(Proceedings of the CSEE),2016,36(5):1173-1180.
[9]郑焕坤,常鲜戎,王正辉(Zheng Huankun,Chang Xian?rong,Wang Zhenghui).高精度A稳定隐式调谐Taylor级数法在电力系统中的应用(Application of high preci?sion and A-stability implicit tuned Taylor series method in power system)[J].电工技术学报(Transactions of Elec?trotechnical Society),2012,27(1):217-223,280.
[10]郭志忠,柳焯(Guo Zhizhong,Liu Zhuo).快速高阶Tay?lor级数法暂态稳定计算(Fast transient stability simula?tion by higher order Taylor series expansions)[J].中国电机工程学报(ProceedingsoftheCSEE),1991,11(3):7-16.
[11]郭志忠(Guo Zhizhong).发电机功角的二项式导数递推规律(The binomial derivative recursion laws of generator’s power and angle)[J].中国电机工程学报(Proceedings of the CSEE),2005,25(16):147-152.
[12]刘建楠,白雪峰,徐英,等(Liu Jiannan,Bai Xuefeng,Xu Ying,et al).多步高阶Taylor级数暂态稳定最优积分格式(Optimal integral scheme of multi-step high-order Tay?lor series method for transient stability calculation)[J].电力自动化设备(Electric Power Automation Equipment),2012,32(10):121-126.
[13]房大中,张尧,宋文南,等(Fang Dazhong,Zhang Yao,Song Wennan,et al).泰勒级数在电力系统暂态稳定性分析中的应用(Application of Taylor series in power sys?tem transient stability assessment)[J].天津大学学报(Journal of Tianjin University),1998,31(6):772-777.
[14] Wang Zongyi,Guo Zhizhong. A fast method for transient stability assessment based on Taylor series expansion[C]//IEEE/PES Transmission and Distribution Conference and Exhibition. Dalian,China,2005.
[15]白雪峰,郭志忠(Bai Xuefeng,Guo Zhizhong). Taylor级数法暂态稳定计算中阶数的动态控制(The dynamic control of order selection in fast transient stability simula?tion by higher order Taylor series expansions)[J].电力系统自动化(Automation of Electric Power Systems),1999,23(22):5-7.
[16]王宇宾,常鲜戎,罗艳,等(Wang Yubin,Chang Xian?rong,Luo Yan,et al).基于隐式Taylor级数法的电力系统暂态稳定计算(An implicit Taylor series method for simulation of power system transient)[J].华北电力大学学报(Journal of North China Electric Power University),2005,32(2):1-6.
[17]夏世威,白雪峰,陈士麟,等(Xia Shiwei,Bai Xuefeng,Chen Shilin,et al).多群模式Taylor级数法暂态稳定计算(Transient stability calculation by multi-machine equiv?alent Taylor series method)[J].电力系统自动化(Auto?mation of Electric Power Systems),2010,34(10):24-28.
[18]徐英,白雪峰,郭志忠(Xu Ying,Bai Xuefeng,Guo Zhi?zhong).采用动态多维阶数控制的暂态稳定计算方法(Transient stability calculation method using dynamic multi-dimension order control)[J].中国电机工程学报(Proceedings of the CSEE),2008,28(19):81-85.
[19]徐英,白雪峰,郭志忠(Xu Ying,Bai Xuefeng,Guo Zhi?zhong).多步高阶暂态稳定计算方法(Transient stabili?ty calculation based on explicit multi-step multi-deriva?tive integration method)[J].电力系统自动化(Automa?tion of Electric Power Systems),2009,33(15):33-37.
[20]徐英,郭志忠(Xu Ying,Guo Zhizhong).多步高阶隐式泰勒级数法暂态稳定计算(Transient stability calculation by implicit multi-step Taylor series method)[J].电力系统保护与控制(Power System Protection and Control),2011,39(23):11-15,20.
[21]夏世威,郭志忠,陈士麟,等(Xia Shiwei,Guo Zhizhong,Chen Shilin,et al).变阶多步Taylor级数法暂态稳定并行计算(Parallel transient stability calculation by multistep dynamic-order Taylor method)[J].电力系统保护与控制(Power System Protection and Control),2012,40(22):25-31.
[22]倪以信,陈寿孙,张宝霖.动态电力系统的理论和分析[M].北京:清华大学出版社,2002.