Engineering Error Analysis Of Phasor Measurement Principle Based On Fourier Transform

Phase angle is an important state variable which reflects the actual operation of the power grid. It enables dispatchers to observe the real-time running state of the system and make accurate judgments. Therefore, the research and development of PMU based on GPS has a great practical value in increasing measurement accuracy.As the power grid has been in a state of fluctuation, real-time voltage signal is a signal composed by the non-periodic signal and decaying DC signal, rather than a standard sine signal. And that means the signal frequency is no longer a single fundamental frequency. It will bring errors to the measurement if we still use the phase measurement method of the steady state.Inevitably, there are differences between practical Fourier transform phasor measurement method and theoretical method. As there is no concept of infinite time in the engineering applications, the infinite time integral, the finite time integral of the real-time voltage signal and single-cycle phase angle calculation of the continuous Fourier transform were analyzed separately considering this application condition, and analytical description of dynamic voltage signal phase angle configuration at the specified frequency is presented for the situation of a single real root and a pair of conjugate complex roots. Through the comparison with the theoretical calculation results and numerical verification, we acquire the influences of finite time integration on the accuracy of phase angle measurement.Since the computer can only deal with discrete and finite length signals, continuous and non-periodic signals need to be truncated and dispersed, and then we can obtain the fundamental phase angle by DFT algorithm of engineering available, but the discrete sampling points cause the picket-fence effect, the lost signal information will result in calculation errors. And implicit periodicity of DFT extents the truncated non-periodic signal periodically, changing the characteristics of original signal completely. The conversion of algorithm from the continuous Fourier transform to the discrete Fourier transform also affects the phase angle measurement. This paper deduced the phase measurement equations of the discrete Fourier transform, and the differences were concluded from the aspects of sampling points, conversion algorithm by comparing with the theory of phase angle measurement based on the continuous Fourier transform.Finally, the influence of deviating angle, corresponding to the decaying DC signal, on the system monitoring and power flow were analyzed. The phase angle data acquired from the PMU were alright for the system’s real-time running state monitoring. However, the influence of phase fluctuation on power flow has a lot with the number of characteristic roots. The influence of a single root or a pair of conjugate complex roots on power flow is relatively small, and the combined action of the multiple characteristic roots brings a great deviating angle, which may generate inaccurate power flow results. By the phase angle perturbation method, this paper carried out the simulation analysis and verification calculation on the standard IEEE 3 machines and 9 buses system.