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针对基于有限长单位冲激响应(finite impulse response,FIR)数字滤波器的同步相量测量原理,首先从理论上推导基波、谐波和噪声引起的测量误差与滤波器频响特性的关系,由此定义滤波器多项技术指标,并通过建立总向量误差和频率测量误差与这些技术指标的函数关系,制定实现同步相量和频率测量的FIR数字滤波器组的最优设计准则。其次,针对离散傅里叶变换(discrete Fourier transform,DTF)类动态相量测量原理,推导这类算法的等效数字滤波器组,根据最优设计准则求解优化问题,进行滤波器自由参数最优选取,实现滤波器的最优设计,并给出长度分别为2、3和4周波的相量测量滤波器,以及4和5周波的频率测量滤波器组的设计结果。最后,将同长度最优设计算法与相关性能评估中表现优越的4周波TWLS算法进行性能比较,仿真实验表明,两者在静态和动态各类测试中,总体均表现出非常接近的优越性能,而在抗谐波性能方面,优化算法具有明显优势。
Aiming at the principle of synchronous phasor measurement based on finite impulse response (FIR) digital filter, the relationship between the measurement error caused by fundamental wave, harmonics and noise and the frequency response characteristics of the filter is theoretically derived. Thus a number of technical specifications of the filter are defined and the optimal design criteria of the FIR digital filter bank for realizing the synchronized phasor and frequency measurement are established by setting up the functional relationship between the total vector error and the frequency measurement error and these technical indicators. Secondly, aiming at the principle of discrete Fourier transform (DTF) dynamic phasor measurement, an equivalent digital filter bank of this kind of algorithm is deduced. According to the optimal design criteria, the optimization problem is solved and the optimal parameters of the filter are optimized The optimum design of the filter is achieved, and the design of the phasor measurement filter with length of 2, 3 and 4 cycles and the frequency measurement filter banks of 4 and 5 cycles are given. Finally, the performance comparison of the 4-cycle TWLS algorithm with the best length design algorithm and correlation performance evaluation is performed. The simulation results show that both of them show very close superior performance in all kinds of static and dynamic tests, In the anti-harmonic performance, the optimization algorithm has obvious advantages.