Dynamic Synchrophasor Estimates Under Complex Out-of-band Interference

The application of some nonlinear,switched power electronics and generator stator ground fault protection technologies in power systems may introduce out-of-band interference(OBI)to power signals.Since the OBI frequency is close to the fundamental frequency,the spectral interference between the OBI spectrum tone and the fundamental spectrum tone is serious,resulting in a large decrease in the synchrophasor estimation accuracy.Resultly,it is difficult to meet the high-order application needs of the M-class synchrophasor measurement unit(PMU).Accordingly,this paper analyzes the impact of OBI on fundamental measurements and proposes dynamic phasor measurement algorithms for the case that the power signal contains a single and multiple OBI signals,respectively,which helps to accurately extract the fundamental signal and provides a reliable data basis for the security and stability of the power system under OBI.Considering the influence of OBI on the extraction of the fundamental signal,this paper analyzes the mutual influence between the fundamental signal and the OBI signal based on the Discrete Fourier Transform(DFT),and gives the error expression caused by OBI to the fundamental signal under nominal frequency condition and frequency devation condition,respectively.In addition,this paper pointed out that both the frequency deviation and OBI frequency will affect the measurement error.Aiming at the problem that the signal contains a single OBI signal,the paper first improves the multi-frequency phasor model,and establishes a mixed phasor model composed of the OBI phasor and the dynamic fundamental phasor,in which the OBI phasor and the dynamic fundamental phasor are expressed by Taylor series,respectively.Then,the preestimation of the fundamental frequency and OBI frequency is realized by the rough fundamental phasor and the rough OBI phasor obtained by DFT.In order to reduce the computational burden,the proposed algorithm can invoke the corresponding coefficient matrices according to whether the power signal contains OBI or not.Finally,the performance of the proposed algorithm is evaluated via the field data and computer-generated signals.The simulation results show that the proposed algorithm keeps the maximum TVE within 0.001%in the frequency devation test,and keeps the maximum TVE under 1% in the power modulation test.Overall,the proposed algorithm obtains good phasor estimation performance.Aiming at the problem that the signal contains multiple OBI signals,a dynamic synchrophasor estimation algorithm considering OBI based on Kaiser window is proposed in this paper,with the trade-off among the measurement accuracy,response time and computational burden.Firstly,a dynamic phasor model is proposed based on Taylor series.The model is solved by the least square method with different parameters of Kaiser window.Then,a comprehensive evaluation formula is established to assess the measurements under different parameters of Kaiser window,and the parameters suitable for OBI are selected.Finally,simulation signals are used to investigate the algorithm performance.The results show that the proposed algorithm can alleviate the influence of OBI and holds higher accuracy by keeping TVE below 1% compared to the comparison algorithms,with a reasonable increment in computation.The theoretical research and simulation test of the paper show that the proposed dynamic synchrophasor measurement algorithms can effectively reduce the spectral interference between the OBI signal and the fundamental signal,and improve the measurement accuracy of the fundamental phasor under OBI.The proposed algorithms can meet the M-class PMU measurement requirements under static/dynamic conditions,and provide a reference for the development of a new generation of high-performance PMU.