基于正交多项式拟合的PMU现场测试参考值计算方法

为给现场运行的同步相量测量装置(phasor measurement unit,?PMU)性能分析提供准确的相量参考值，保证其数据质量，提出了基于正交多项式拟合的高精度相量测量方法。该方法利用Legendre多项式的正交性特点，对信号模型进行Legendre多项式拟合，以此来构建一种基于Legendre多项式的正交拟合相量模型。在此基础上，通过分析对比不同拟合参数求解方法的复杂度，提出了基于Cholesky分解的相量参考值计算方法，为非线性拟合参数求解计算量大的问题提供一种新的解决方法，并通过迭代修正来保证测量精度。进一步地，根据分析揭示的最优窗长和拟合阶数，实现算法的高精度测量和高效率计算。仿真与硬件测试表明，测量精度均满足标准要求10倍及以上，可在硬件中实时稳定运行，并为PMU现场测试校准提供参考值。

Calculation method of a PMU field test reference value based on orthogonal polynomial fitting

To provide an accurate phasor reference value for the performance analysis of a synchronous phasor measurement unit (PMU) running on site and to ensure its data quality, a high-precision phasor measurement method based on orthogonal polynomial fitting is proposed. This method uses the orthogonality of Legendre polynomials to fit the signal model, so as to construct an orthogonal fitting phasor model. By analyzing and comparing the complexity of different fitting parameter solution methods, a phasor reference value calculation method based on Cholesky decomposition is proposed. This provides a new solution for the problem of a large amount of calculation of nonlinear fitting parameters, and ensures the measurement accuracy through iterative correction. Further, according to the optimal window length and fitting order revealed by the analysis, a high-precision measurement and efficient calculation of the algorithm are realized. The simulation and hardware test show that the measurement accuracy meets the standard requirements by a factor of 10 or more. It can run stably in real time on the hardware and provide reference values for PMU field test and calibration. This work is supported by the National Natural Science Foundation of China (No. 51627811 and No. 51725702).