基于多频率相量模型的动态同步相量测量算法
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摘要
电力系统中由于发电出力与负载不平衡导致基波频率偏移,进而造成同步相量测量精度迅速下降。基于此,该文提出基于多频率相量模型的动态同步相量测量算法。首先,算法利用多个不同旋转频率的子相量来描述真实频率附近的有效信息,并以此对动态相量进行建模;其次,通过计算粗估频率、调用离线矩阵、修正离散傅里叶变换结果及相移运算等步骤来获得精确的相量测量值。最后,仿真结果表明,算法虽然增加了有限的运算量,但在频率斜坡变化、功率振荡等动态工况中,能够减小频率偏移带来的不利影响,提供准确的测量结果。
When the power system was suffered from unbalance and fault, the fundamental frequency would deviate from the nominal frequency, and the measurement accuracy of synchrophasor estimator also would rapidly reduce. Therefore, a dynamic synchrophasor estimator was proposed based on multi-frequency phasor model. The multi-frequency phasor model was employed to reflect the effective information around real frequency, and to establish a phasor model including multi-frequency phasor. The accuracy phasor value could be obtained by estimating rough frequency, looking the matrix table calculated offline, revising the discrete Fourier transform(DFT) value and shifting phasor. Test results of both simulated signals and PSCAD/EMTDC generated signal show that the proposed estimator can provide accurate phasor estimations under dynamic conditions of frequency ramping and power oscillation at the cost of limited increase of computational burden.
When the power system was suffered from unbalance and fault, the fundamental frequency would deviate from the nominal frequency, and the measurement accuracy of synchrophasor estimator also would rapidly reduce. Therefore, a dynamic synchrophasor estimator was proposed based on multi-frequency phasor model. The multi-frequency phasor model was employed to reflect the effective information around real frequency, and to establish a phasor model including multi-frequency phasor. The accuracy phasor value could be obtained by estimating rough frequency, looking the matrix table calculated offline, revising the discrete Fourier transform(DFT) value and shifting phasor. Test results of both simulated signals and PSCAD/EMTDC generated signal show that the proposed estimator can provide accurate phasor estimations under dynamic conditions of frequency ramping and power oscillation at the cost of limited increase of computational burden.
引文
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[15]徐全,陆超,刘映尚,等.基于泰勒级数和离散傅里叶变换的综合自适应相量算法[J].电力系统自动化,2016,40(19):37-43.Xu Quan,Lu Chao,Liu Yingshang,et al.Comprehensive adaptive phasor algorithm based on Taylor series and discrete Fourier transform[J].Automation of Electric Power Systems 2016,40(19):37-43(in Chinese).
[16]Agrez D.Weighted multipoint interpolated DFT to improve amplitude estimation of multifrequency signal[J].IEEE Transactions on Instrumentation and Measurement,2002,51(2):287-292.
[17]Belega D,Petri D.Accuracy analysis of the multicycle synchrophasor estimator provided by the interpolated DFT algorithm[J].IEEE Transactions on Instrumentation and Measurement,2013,62(5):942-953.
[18]Belega D,Fontanelli D,Petri D.Dynamic phasor and frequency measurements by an improved Taylor weighted least squares algorithm[J].IEEE Transactions on Instrumentation and Measurement,2015,64(8):2165-2178.
[19]汪芙平,靳夏宁,王赞基.实现动态相量测量的FIR数字滤波器最优设计[J].中国电机工程学报,2014,34(15):2388-2395.Wang Fuping,Jin Xianing,Wang Zanji.Optimal design of FIR digital filters for dynamic phasor measurement[J].Proceedings of the CSEE,2014,34(15):2388-2395(in Chinese).
[20]IEEE Std.C37.118.2011-IEEE standard for Synchrophasor measurements for power systems[Z].2011.
[21]Zhan L W,Liu Y,Liu Y L.A Clarke transformation-based DFT phasor and frequency algorithm for wide frequency range[J].IEEE Transactions on Smart Grid,2017,DOI:10.1109/TSG.2016.2544947.
[22]汤涌.电力系统强迫功率振荡分析[J].电网技术,1995,19(12):6-10.Tang Yong.The analysis of forced power oscillation in power system[J].Power System Technology,1995,19(12):6-10(in Chinese).
[2]Xie Xiaorong,Xin Yaozhong,Xiao Jinyu,et al.WAMS applications in Chinese power systems[J].IEEE Power and Energy Magazine,2006,4(1):54-63.
[3]何江,周京阳,王明俊.广域相量测量技术在智能电网中的应用[J].电网技术,2009,33(15):16-19.He Jiang,Zhou Jingyang,Wang Mingjun.Application of wide area phasor measurement technology in smart grid[J].Power System Technology,2009,33(15):16-19(in Chinese).
[4]王宾,孙华东,张道农.配电网信息共享与同步相量测量应用技术评述[J].中国电机工程学报,2015,35(S1):1-7.Wang Bin,Sun Huadong,Zhang Daonong.Review on data sharing and synchronized phasor measurement technique with application in distribution systems[J].Proceedings of the CSEE,2015,35(S1):1-7(in Chinese).
[5]Mai R K,He Z Y,Fu L,et al.A dynamic synchrophasor estimation algorithm for online application[J].IEEE Transactions on Power Delivery,2010,25(2):570-578.
[6]Liu H,Bi T S,Yang Q X.The evaluation of phasor measurement units and their dynamic behavior analysis[J].IEEE Transactions on Instrumentation and Measurement,2013,62(6):1479-1485.
[7]毕天姝,刘灏,杨奇逊.PMU算法动态性能及其测试系统[J].电力系统自动化,2014,38(1):62-67.Bi Tianshu,Liu Hao,Yang Qixun.Dynamic performance of PMU algorithm and its testing system[J].Automation of Electric Power Systems,2014,38(1):62-67(in Chinese).
[8]Mai R K,He Z Y,Fu L,et al.Dynamic phasor and frequency estimator for phasor measurement units[J].IET Generation,Transmission&Distribution,2010,4(1):73-83.
[9]耿池勇,高厚磊,刘炳旭,等.适用于同步相量测量的DFT算法研究[J].电力自动化设备,2004,24(1):84-87.Geng Chiyong,Gao Houlei,Liu Bingxu,et al.study of DFT algorithm in synchronized phasor measurement[J].Electric Power Automation Equipment,2004,24(1):84-87(in Chinese).
[10]Macii D,Petri D,Zorat A.Accuracy analysis and enhancement of DFT-based synchrophasor estimators in off-nominal conditions[J].IEEE Transactions on Instrumentation and Measurement,2012,61(10):2653-2664.
[11]刘世明,郭韬,吴聚昆,等.适用于频率偏移情况下同步相量测量的DFT算法研究[J].电网技术,2016,40(5):1522-1528.Liu Shiming,Guo Tao,Wu Jukun,et al.Study of DFT algorithm for synchrophasor measurement under frequency offset[J].Power System Technology,2016,40(5):1522-1528(in Chinese).
[12]de la O Serna J A.Dynamic phasor estimates for power system oscillations[J].IEEE Transactions on Instrumentation and Measurement,2007,56(5):1648-1657.
[13]麦瑞坤,何正友,薄志谦,等.动态条件下的同步相量测量算法的研究[J].中国电机工程学报,2009,29(10):52-58.Mai Ruikun,He Zhengyou,Bo Zhiqian,et al.Research on synchronized phasor measurement algorithm under dynamic conditions[J].Proceedings of the CSEE,2009,29(10):52-58(in Chinese).
[14]符玲,韩文朕,麦瑞坤,等.基于时频信息的动态同步相量测量算法[J].中国电机工程学报,2015,35(23):6075-6082.Fu Ling,Han Wenzhen,Mai Ruikun,et al.Time-frequency information-based dynamic phasor estimator[J].Proceedings of the CSEE,2015,35(23):6075-6082(in Chinese).
[15]徐全,陆超,刘映尚,等.基于泰勒级数和离散傅里叶变换的综合自适应相量算法[J].电力系统自动化,2016,40(19):37-43.Xu Quan,Lu Chao,Liu Yingshang,et al.Comprehensive adaptive phasor algorithm based on Taylor series and discrete Fourier transform[J].Automation of Electric Power Systems 2016,40(19):37-43(in Chinese).
[16]Agrez D.Weighted multipoint interpolated DFT to improve amplitude estimation of multifrequency signal[J].IEEE Transactions on Instrumentation and Measurement,2002,51(2):287-292.
[17]Belega D,Petri D.Accuracy analysis of the multicycle synchrophasor estimator provided by the interpolated DFT algorithm[J].IEEE Transactions on Instrumentation and Measurement,2013,62(5):942-953.
[18]Belega D,Fontanelli D,Petri D.Dynamic phasor and frequency measurements by an improved Taylor weighted least squares algorithm[J].IEEE Transactions on Instrumentation and Measurement,2015,64(8):2165-2178.
[19]汪芙平,靳夏宁,王赞基.实现动态相量测量的FIR数字滤波器最优设计[J].中国电机工程学报,2014,34(15):2388-2395.Wang Fuping,Jin Xianing,Wang Zanji.Optimal design of FIR digital filters for dynamic phasor measurement[J].Proceedings of the CSEE,2014,34(15):2388-2395(in Chinese).
[20]IEEE Std.C37.118.2011-IEEE standard for Synchrophasor measurements for power systems[Z].2011.
[21]Zhan L W,Liu Y,Liu Y L.A Clarke transformation-based DFT phasor and frequency algorithm for wide frequency range[J].IEEE Transactions on Smart Grid,2017,DOI:10.1109/TSG.2016.2544947.
[22]汤涌.电力系统强迫功率振荡分析[J].电网技术,1995,19(12):6-10.Tang Yong.The analysis of forced power oscillation in power system[J].Power System Technology,1995,19(12):6-10(in Chinese).