1.Wuhan University Wuhan 430072 China; 2. Central South University Changsha 410083 China; 3. Hunan University of Science and Technology Xiangtan 411201 China
Abstract:The random perturbation of power load can influence the accuracy of load model. By considering the measurement error and random perturbation of power load as an unknown-but-bounded (UBB) error, a load modeling method was proposed based on the Hardy space theory and Carathéodory-Fejér interpolation (CFI). The load model was mapped into linear load model set with prior information in Hardy space. Consistency problem between measured data and model set was formulated to a linear matrix inequality. The feasible solution here was used to construct a high-order transfer function. Simulation results show that when the random perturbation error range from 1%~10%, the output root mean square error(RMSE)is below 0.03, and the model can still match the output well under inaccurate UBB error boundary. The variations of load composition in a certain scale have little effect on model parameters. Simulations using measured data from the phase measurement unit in a power station demonstrate the practicality and validation of the proposed method when exiting UBB error.
[1] Kosterev D N, Taylor C W, Mittelstadt W A. Model validation for the August 10, 1996 WSCC system outage[J]. IEEE Transactions on Power Systems, 1999, 14(3): 967-979. [2] Maitra A, Gaikwad A, Zhang P, et al. Using system disturbance measurement data to develop improved load models[C]//Power Systems Conference and Exposition, PSCE'06, 2006: 1978-1985. [3] Kim B H, Kim H. Measurement-based estimation of the composite load model parameters[J]. Journal of Electrical Engineering & Technology, 2012, 7(6): 845-851. [4] 李欣然, 钱军, 王立德, 等. 配电网集结等效的异步电动机综合负荷模型及其总体测辨建模[J]. 电工技术学报, 2009, 24(4): 175-185. Li Xinran, Qian Jun, Wang Lide, et al. Synthesis induction motor model of power composite load considering distribution network structure[J]. Transactions of China Electrotechnical Society, 2009, 24(4): 175-185. [5] 韩冬, 马进, 贺仁睦. 基于Bootstrap的实测负荷模型参数优选[J]. 电工技术学报, 2012, 27(8): 141-146. Han Dong, Ma Jin, He Rengmu. Parameter optimization of measurement-based load model based on Bootstrap[J]. Transactions of China Electrotechnical Society, 2012, 27(8): 141-146. [6] 宋人杰, 李文明. 一种提高静态负荷模型参数辨识精度方法的研究[J]. 电力系统保护与控制, 2013, 41(6): 89-92. Song Renjie, Li Wenming. Research on improving the precision of static load model parameter identification[J]. Power System Protection and Control, 2013, 41(6): 89-92. [7] 黄玉龙, 陈迅, 刘明波, 等. 动态负荷模型参数辨识的微分进化算法[J]. 电工技术学报, 2013, 28(11): 270-277. Huang Yulong, Chen Xun, Liu Mingbo, et al. Differential evolution algorithm for dynamic load model parameter identification[J]. Transactions of China Electrotechnical Society, 2013, 28(11): 270-277. [8] Visconti I F, Lima D A, Costa J, et al. Measurement-based load modeling using transfer functions for dynamic simulations[J]. IEEE Transactions on Power Systems, 2014, 29(1): 111-120. [9] 张红斌, 汤涌, 李柏青. 差分方程负荷模型参数分散性的研究[J]. 中国电机工程学报, 2006, 26(18): 1-5. Zhang Hongbing, Tang Yong, Li Boqing. Study on dispersing of difference equation load model parameters[J]. Proceedings of the CSEE, 2006, 26(18): 1-5. [10] 肖锋, 李欣然, 王立德, 等. 基于神经网络的并行差分方程综合负荷模型[J]. 电力系统及其自动化学报, 2009, 21(1): 41-47. Xiao Feng, Li Xinran, Wang Lide, et al. Parallel difference equations load model based on neural network[J]. Proceedings of the CSU-EPSA, 2009, 21(1): 41-47. [11] Yang J, Wu M, He Y, et al. Identification and application of nonlinear dynamic load models[J]. Journal of Control Theory and Applications, 2013, 11(2): 173-179. [12] Kim Y G, Song H, Kim H R, et al. Particle swarm optimization based load model parameter identifi- cation[C]. IEEE Power and Energy Society General Meeting, 2010: 1-6. [13] Hain Y, Kulessky R, Nudelman G. Identification-based power unit model for load-frequency control purposes[J]. IEEE Transactions on Power Systems, 2000, 15(4): 1313-1321. [14] 熊传平, 曹军杰, 陈谦. 基于小波分析的电力负荷模型辨识数据去噪[J]. 河海大学学报(自然科学版), 2011, 39(4): 470-474. Xiong Chuanpin, Cao Junjie, Chen Qian. A wavelet- based method for de-noising data of electric load modeling[J]. Journal of Hohai University (Natural Sciences) 2011, 39(4): 470-474. [15] Milanese M, Belforte G. Estimation theory and uncertainty intervals evaluation in presence of unknown but bounded errors: linear families of models and estimators[J]. IEEE Transactions on Automatic Control, 1982, 27(2): 408-414. [16] Rosenblum M, Rovnyak J. Hardy classes and operator theory[M]. NewYork: Clarendon Press Oxford University Press, 1997. [17] Adamjan V M, Arov D Z, Kreĭn M G. Analytic properties of Schmidt pairs for a Hankel operator and the generalized Schur-Takagi problem[J]. Sbornik: Mathematics, 1971, 15(1): 31-73. [18] 丁思奇, 曼苏乐, 胡志勇, 等. 基于鲁棒 H ∞ 控制的静止同步补偿器研究[J]. 电力系统保护与控制, 2012, 40(13): 98-103. Ding Siqi, Man Sule, Hu Zhiyong, et al. Study of STATCOM based on robust H ∞ controller[J]. Power System Protection and Control, 2012, 40(13): 98-103. [19] Ying S, Ge T, Ai J. H ∞ parameter identification and H 2 feedback control synthesizing for inflight aircraft icing[J]. Journal of Shanghai Jiaotong University (Science), 2013, 18(3): 317-325. [20] 周克敏, 多伊尔, 格洛弗, 等. 鲁棒与最优控制[M]. 北京: 国防工业出版社, 2002. [21] Nikolov N, Pflug P, Thomas P J. Spectral Nevanlinna-Pick and Carathéodory-Fejér problems for n ≤3[J]. Indiana University Mathematics Journal, 2011, 60(3): 883-893. [22] Bolotnikov V. On the Carathéodory-Fejér interpolation problem for generalized Schur functions[J]. Integral Equations and Operator Theory, 2004, 50(1): 9-41. [23] Chen J, Nett C N. The Carathéodory-Fejér problem and H ∞ identification: a time domain approach[C]. Proceedings of the 32nd IEEE Conference on Decision and Control, 1993: 68-73. [24] 俞立. 鲁棒控制: 线性矩阵不等式处理方法[M]. 北京: 清华大学出版社, 2002. [25] 王振树, 李林川, 牛丽. 基于贝叶斯证据框架的支持向量机负荷建模[J]. 电工技术学报, 2009, 24(8): 127-134. Wang Zhenshu, Li Linchuan, Niu Li. Load modeling based on support vector machine based on Bayesian evidence framework[J]. Transactions of China Electro-technical Society, 2009, 24(8): 127-134. [26] 章健. 电力系统负荷模型与辨识[M]. 北京: 中国电力出版社, 2007. [27] 李欣然, 徐振华, 宋军英, 等. 基于功率空间的分时段负荷模型参数在线修正[J]. 电工技术学报, 2012, 27(8): 147-156. Li Xinran, Xu Zhenhua, Song Junying, et al. On-line revising algorithm for load model parameters of substation in different daily periods based on the measured active power[J]. Transactions of China Electrotechnical Society, 2012, 27(8): 147-156. [28] 陈迁, 徐箭, 孙元章, 等. 考虑气温影响的负荷模型参数不确定性建模[J]. 电力自动化设备, 2011, 31(10): 17-22. Chen Qian, Xu Jian, Sun Yuanzhang, et al. Model of liad model parameter uncertainty considering temperature[J]. Electric Power Automation Equipment, 2011, 31(10): 17-22. [29] 王茂海, 鲍捷, 齐霞, 等. 相量测量装置(PMU)动态测量精度在线检验[J]. 电力系统保护与控制, 2009, 37(10): 48-52. Wang Maohai, Bao Jie, Qi Xia, et al. Online assess- ment of phasor measurement unit's performance based on sample data[J]. Power System Protection and Control, 2009, 37(10): 48-52. [30] 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 perfor- mance of PMU algorithm and its testing system[J]. Automation of Electric Power Systems, 2014, 38(1): 62-67.