基于状态空间法的高压直流输电系统电磁暂态简化模型的解析算法
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摘要
提出一种基于状态空间法的高压直流(HVDC)输电简化模型的解析算法,用于模拟逆变侧交流故障下直流系统的暂态响应。首先利用准稳态模型对HVDC系统的整流侧做简化;然后把不同工况下的换流器写成统一的形式,并把简化后的HVDC系统模型用一个分时段线性的非齐次微分方程组来描述;最后,通过引入辅助变量,将非齐次方程转化为齐次,从而使计算复杂度大大降低,同时简化后的系统可以用解析算法求解。控制系统用微分-代数方程组描述,用变步长数值积分法求解。在Matlab里编写相应程序实现所提简化模型的解析算法,并与PSCAD里搭建的双端电磁暂态模型进行比较,以验证所提算法的准确性。
In this paper, an analytic solution for simplified high voltage direct current(HVDC)system based on state space method is proposed, which is mainly used to simulate the transient response of DC system under AC fault on the inverter side. Firstly, the rectifier side of HVDC system is simplified using quasi-steady model. Secondly, the converter under different conditions is described as a uniformed express, and the simplified HVDC system is described by a piecewise linear inhomogeneous differential equations. Finally, the inhomogeneous differential equations are transformed into homogeneous ones by introducing auxiliary variables, which greatly reduces the computational complexity. Meanwhile, the simplified system can be accurately solved by analytical algorithm. The control system is described with differential-algebraic equations and solved by the variable-step numerical integration method. According to the analytical solution of the simplified model proposed in this paper, the corresponding program is coded in Matlab and compared with the double-terminal HVDC model built in PSCAD to verify the accuracy of the proposed solution.
In this paper, an analytic solution for simplified high voltage direct current(HVDC)system based on state space method is proposed, which is mainly used to simulate the transient response of DC system under AC fault on the inverter side. Firstly, the rectifier side of HVDC system is simplified using quasi-steady model. Secondly, the converter under different conditions is described as a uniformed express, and the simplified HVDC system is described by a piecewise linear inhomogeneous differential equations. Finally, the inhomogeneous differential equations are transformed into homogeneous ones by introducing auxiliary variables, which greatly reduces the computational complexity. Meanwhile, the simplified system can be accurately solved by analytical algorithm. The control system is described with differential-algebraic equations and solved by the variable-step numerical integration method. According to the analytical solution of the simplified model proposed in this paper, the corresponding program is coded in Matlab and compared with the double-terminal HVDC model built in PSCAD to verify the accuracy of the proposed solution.
引文
[1]周浩.特高压交直流输电技术[M].杭州:浙江大学出版社,2014.
[2]Lopez B L,Davis-Moon L,Sterious W,et al Quasi-static stability of HVDC systems considering dynamic effects of synchronous machines and excitation voltage control[J].IEEE Transactions on Power Delivery,2006,21(3):1501-1514.
[3]周长春,徐政.直流输电准稳态模型有效性的仿真验证[J].中国电机工程学报,2003,23(12):33-36.Zhou Changchun,Xu Zheng.Simulation validity test of the HVDC quasi-steady-state model[J].Proceedings of the CSEE,2003,23(12):33-36.
[4]Hammad A E,Kuhn W.A computation algorithm for assessing voltage stability at AC/DC interconnections[J].IEEE Transactions on Power Systems,1986,1(1):209-215.
[5]毕如玉,林涛,陈汝斯,等.交直流混合电力系统的安全校正策略[J].电工技术学报,2016,31(9):50-57.Bi Ruyu,Lin Tao,Chen Rusi,et al.The security correction strategy in AC and DC hybrid power system[J].Transactions of China Electrotechnical Society,2016,31(9):50-57.
[6]李崇涛,林啸,赵勇,等.高压直流输电系统暂态过程的解析解法(一):数学模型[J].电网技术,2017,41(1):1-7.Li Chongtao,Lin Xiao,Zhao Yong,et al.An analytical solution for transient process of HVDCtransmission system(Part 1)-mathematical model[J].Power System Technology,2017,41(1):1-7.
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[8]申洪明,黄少锋,费彬,等.基于数学形态学的换相失败检测新方法[J].电工技术学报,2016,31(4):170-177.Shen Hongmin,Huang Shaofeng,Fei Bin,et al.Anew method to detect commutation failure based on mathematical morphology[J].Transactions of China Electrotechnical Society,2016,31(4):170-177.
[9]赵畹君.高压直流输电工程技术[M].北京:中国电力工业出版社,2004.
[10]王增平,刘席洋,李林泽,等.多馈入直流输电系统换相失败边界条件[J].电工技术学报,2017,32(10):12-19.Wang Zengping,Liu Xiyang,Li Linze,et al.Boundary conditions of commutation failure in multiinfeed HVDC systems[J].Transactions of China Electrotechnical Society,2017,32(10):12-19.
[11]Prabha Kundur,电力系统稳定与控制[M].北京:中国电力出版社,2001.
[12]王玲,文俊,李亚男,等.谐波对多馈入直流输电系统换相失败的影响[J].电工技术学报,2017,32(3):27-34.Wang Ling,Wen Jun,Li Yanan,et al.The harmonic effects on commutation faliure of multi-infeed direct current transmission systems[J].Transactions of China Electrotechnical Society,2017,32(3):27-34.
[13]唐庚,徐政,薛英林.LCC-MMC混合高压直流输电系统[J].电工技术学报,2013,28(10):301-310.Tang Gen,Xu Zheng,Xue Yinlin,et al.ALCC-MMC hybrid HVDC transmission system[J].Transactions of China Electrotechnical Society,2013,28(10):301-310.
[14]王少辉,唐飞,向农.华东电网多直流同时换相失败仿真分析[J].电力系统保护与控制,2017,45(12):16-21.Wang Shaohui,Tang Fei,Xiang Nong.Commutation failure simulation analysis of East China power grid multiple HVDC lines[J].Power System Protection&Control,2017,45(12):16-21.
[15]王锡凡,现代电力系统分析[M].北京:科学出版社,2003.
[16]Hairer E,Wanner G.Solving ordinary differential equations II:stiff and differential-algebraic problems[M].2nd ed.Berlin,Heidelberg:Springer,1996.
[17]Atighechi H,Chiniforoosh S,Jatskevich J,et al.Dynamic average-value modeling of CIGRE HVDCbenchmark system[J].IEEE Transactions on Power Delivery,2014,29(5):2046-2054.
[18]Faruque M O,Zhang Yuyan,Dinavahi V.Detailed modeling of CIGRE HVDC benchmark system using PSCAD/EMTDC and PSB/Simulink[J].IEEE Transactions on Power Delivery,2006,21(1):378-387.
[19]董曼玲,谢施君,何俊佳,等.采用ATP/EMTP的CIGRE HVDC建模与仿真[J].高电压技术,201036(3):796-804.Dong Manling,Xie Shijun,He Junjia,et al.Modeling and simulation of CIGRE HVDC system using ATP/EMTP[J].High Voltage Engineering,2010,36(3):796-804.
[2]Lopez B L,Davis-Moon L,Sterious W,et al Quasi-static stability of HVDC systems considering dynamic effects of synchronous machines and excitation voltage control[J].IEEE Transactions on Power Delivery,2006,21(3):1501-1514.
[3]周长春,徐政.直流输电准稳态模型有效性的仿真验证[J].中国电机工程学报,2003,23(12):33-36.Zhou Changchun,Xu Zheng.Simulation validity test of the HVDC quasi-steady-state model[J].Proceedings of the CSEE,2003,23(12):33-36.
[4]Hammad A E,Kuhn W.A computation algorithm for assessing voltage stability at AC/DC interconnections[J].IEEE Transactions on Power Systems,1986,1(1):209-215.
[5]毕如玉,林涛,陈汝斯,等.交直流混合电力系统的安全校正策略[J].电工技术学报,2016,31(9):50-57.Bi Ruyu,Lin Tao,Chen Rusi,et al.The security correction strategy in AC and DC hybrid power system[J].Transactions of China Electrotechnical Society,2016,31(9):50-57.
[6]李崇涛,林啸,赵勇,等.高压直流输电系统暂态过程的解析解法(一):数学模型[J].电网技术,2017,41(1):1-7.Li Chongtao,Lin Xiao,Zhao Yong,et al.An analytical solution for transient process of HVDCtransmission system(Part 1)-mathematical model[J].Power System Technology,2017,41(1):1-7.
[7]李崇涛,林啸,赵勇,等.高压直流输电系统暂态过程的解析解法(二):算法与算例[J].电网技术,2017,41(1):8-13.Li Chongtao,Lin Xiao,Zhao Yong,et al.An analytical solution for transient process of HVDCtransmission system(Part 2),algorithm and example[J].Power System Technology,2017,41(1):8-13.
[8]申洪明,黄少锋,费彬,等.基于数学形态学的换相失败检测新方法[J].电工技术学报,2016,31(4):170-177.Shen Hongmin,Huang Shaofeng,Fei Bin,et al.Anew method to detect commutation failure based on mathematical morphology[J].Transactions of China Electrotechnical Society,2016,31(4):170-177.
[9]赵畹君.高压直流输电工程技术[M].北京:中国电力工业出版社,2004.
[10]王增平,刘席洋,李林泽,等.多馈入直流输电系统换相失败边界条件[J].电工技术学报,2017,32(10):12-19.Wang Zengping,Liu Xiyang,Li Linze,et al.Boundary conditions of commutation failure in multiinfeed HVDC systems[J].Transactions of China Electrotechnical Society,2017,32(10):12-19.
[11]Prabha Kundur,电力系统稳定与控制[M].北京:中国电力出版社,2001.
[12]王玲,文俊,李亚男,等.谐波对多馈入直流输电系统换相失败的影响[J].电工技术学报,2017,32(3):27-34.Wang Ling,Wen Jun,Li Yanan,et al.The harmonic effects on commutation faliure of multi-infeed direct current transmission systems[J].Transactions of China Electrotechnical Society,2017,32(3):27-34.
[13]唐庚,徐政,薛英林.LCC-MMC混合高压直流输电系统[J].电工技术学报,2013,28(10):301-310.Tang Gen,Xu Zheng,Xue Yinlin,et al.ALCC-MMC hybrid HVDC transmission system[J].Transactions of China Electrotechnical Society,2013,28(10):301-310.
[14]王少辉,唐飞,向农.华东电网多直流同时换相失败仿真分析[J].电力系统保护与控制,2017,45(12):16-21.Wang Shaohui,Tang Fei,Xiang Nong.Commutation failure simulation analysis of East China power grid multiple HVDC lines[J].Power System Protection&Control,2017,45(12):16-21.
[15]王锡凡,现代电力系统分析[M].北京:科学出版社,2003.
[16]Hairer E,Wanner G.Solving ordinary differential equations II:stiff and differential-algebraic problems[M].2nd ed.Berlin,Heidelberg:Springer,1996.
[17]Atighechi H,Chiniforoosh S,Jatskevich J,et al.Dynamic average-value modeling of CIGRE HVDCbenchmark system[J].IEEE Transactions on Power Delivery,2014,29(5):2046-2054.
[18]Faruque M O,Zhang Yuyan,Dinavahi V.Detailed modeling of CIGRE HVDC benchmark system using PSCAD/EMTDC and PSB/Simulink[J].IEEE Transactions on Power Delivery,2006,21(1):378-387.
[19]董曼玲,谢施君,何俊佳,等.采用ATP/EMTP的CIGRE HVDC建模与仿真[J].高电压技术,201036(3):796-804.Dong Manling,Xie Shijun,He Junjia,et al.Modeling and simulation of CIGRE HVDC system using ATP/EMTP[J].High Voltage Engineering,2010,36(3):796-804.