基于Carathéodory-Fejér插值定理考虑误差界的负荷建模方法  

Load Modeling Considering Error Boundary Based on Carathéodory-Fejér Interpolation Theorem

作　　者：唐秀明[1] 袁荣湘[1] 陈君[2,3] 彭小奇[2] 

机构地区：[1]武汉大学电气工程学院,武汉430072 [2]中南大学信息科学与工程学院,长沙410083 [3]湖南科技大学信息与电气工程学院,湘潭411201

出　　处：《电工技术学报》2015年第20期176-184,共9页Transactions of China Electrotechnical Society

基　　金：国家自然科学创新研究群体科学基金(61321003);国家自然科学基金青年项目(61105080);湖南省教育厅高等学校科研项目(13A016)资助

摘　　要：电力负荷的随机小扰动影响负荷建模的准确性。将负荷的随机小扰动及测量数据误差用未知但有界的非构造性误差描述,基于哈代空间理论和Carathéodory-Fejér插值定理提出了考虑误差界的负荷建模方法。该方法把电力负荷映射为哈代空间的满足先验参数的线性模型集,将实测数据与模型相容的条件转化为线性矩阵不等式约束,根据Nehari定理及Carathéodory-Fejér插值定理,构造出满足线性矩阵不等式的最不利情况下的负荷传递函数模型。仿真结果表明,在幅值为1%-10%的随机扰动下本文的负荷模型输出方均根误差为0.03以下,当误差界信息不准确时该建模输出仍能较好地拟合输出响应;一定范围内的负荷构成比例改变对模型参数的影响不大。采用实测相量测量单元数据建模的模型输出也与实测吻合得较好。该负荷建模方法能解决负荷的随机小扰动及测量噪声对模型准确性的影响。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 Carath6odory-Fej6r 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.

关 键 词：负荷建模 误差界 线性矩阵不等式 Carathéodory-Fejér插值定理 

分 类 号：TM714[电气工程—电力系统及自动化]