Research On High-precision Estimation Method Of Power Signal Parameters In Short Time Window

The frequency-domain interpolation correction method based on Discrete Fourier Transform(DFT)has an efficient and fast calculation method FFT(Fast Fourier Transform)and is easy to implement in hardware.It is favored in a large number of power signal parameter estimation applications such as power quality analysis,harmonic power measurement,and real-time synchronization monitoring of power grids.However,in the face of the more widely used single-frequency and multi-frequency real sinusoidal signals in engineering practice,the interpolation method based on the complex analytical signal spectrum model is directly used under the short-term fluctuation period,and there is a serious estimation deviation due to the long spectrum leakage.Undoubtedly,it greatly limits the popularization and application of this method.At the same time,under the interference of background noise,the variance based on the existing DFT interpolation method is difficult to consistently and effectively reach the Cramer-Rao Lower Bound(CRLB)of the unbiased estimation of the relevant signal parameters.This affects the application of interpolation methods in accurate parameter estimation to a certain extent.From the perspective of the uncertainty composition of parameter estimation,the existing DFT interpolation method based on the complex analytical signal spectrum model is systematically analyzed for the estimation performance of noisy single-and multi-tone real sinusoidal signals and the key factors that affect the estimation performance of the interpolation algorithm and the specific influencing mechanism are obtained.On this basis,following the construction of spectrum equations and accurate analysis as the core route of parameters estimation,the corresponding solutions are discussed for the parameter estimation problems of single-and multi-tone real sinusoidal signals under a short-time window.Effective frequency-domain interpolation correction methods are put forward one by one,and the estimation performance of each method is systematically analyzed and strictly mathematically demonstrated.The main research content of this thesis and the corresponding innovative results are as follows:(1)Aiming at the problem of single-tone real sinusoidal signal frequency estimation,a high-precision frequency estimation method using generalized discrete-time Fourier transform(DTFT)spectrum samples at arbitrary intervals for interpolation is proposed,referred to as the IpDTFT algorithm.Under the prerequisite of accurately considering the spectral leakage component from the conjugate negative frequency to ensure that the spectral model is unbiased,the algorithm constructs a DTFT spectral equation suitable for any position based on the idea of spectral transformation.Furthermore,according to different auxiliary spectrum intervals,the analytical formulas of the unbiased frequency estimation based on 3-point and 5-point spectrum interpolation are successively obtained through accurate analytical equations.Finally,to minimize the influence of background noise on the variance of the algorithm's estimation,a simple single-step iteration is used to optimize the performance of the algorithm,thereby ensuring that the Mean Square Error(MSE)of the algorithm's frequency estimation under noise interference can consistently approach the optimal in the entire domain.The proposed IpDTFT algorithm has the following innovations: it breaks the limitation that the previous interpolation algorithm is only applicable to the discrete DFT spectrum at fixed and equal intervals,which confirms that it is feasible to use arbitrary interval samples of the DTFT spectrum for interpolation to achieve unbiased frequency estimation;only a single-step iteration is enough to ensure that the estimation variance can uniformly approach the optimal in the entire domain.(2)To further improve the frequency estimation performance under noise disturbance,an accurate frequency estimation method based on improved IpDTFT is proposed for single-tone real sinusoidal signals,called a IpDTFT.By changing the analysis method of the related spectrum equations,the a IpDTFT algorithm can achieve unbiased frequency estimation with less 3-point spectrum interpolation under any auxiliary spectrum interval condition.At the same time,the frequency estimation variance is almost strictly symmetrical about the frequency offset v under any Cycles in Record(Ci R)of ??1,and its minimum will theoretically be completely close to the unbiased estimated CRLB with the auxiliary spectral line interval approaches 0.Therefore,a single-step iteration can ensure that the algorithm MSE can uniformly approximate the CRLB in the entire domain.Besides,after some simple expansion transformation calculation,the analytical method of a IpDTFT can be further extended to accurate frequency and damping factor estimation of real damped sinusoidal signals with continuous spectrum characteristics.The proposed a IpDTFT algorithm has the following innovations: it solves the problem that the estimated variance distribution of the aforementioned IpDTFT method is asymmetric and its minimum value cannot effectively reach the CRLB;the deduced spectral equation analysis method greatly expands the applicable range of the method.(3)Aiming at the parameter estimation problem of multi-tone real sinusoidal signals under a short-time window,a multi-point DFT interpolation method considering the effects of total leakage is proposed,namely CAL-IpDFT.First,taking advantage of the linear proportional recurrence characteristics of the equally spaced discrete DFT spectral lines of the Maximum Sidelobe Decay Window(MSDW),the spectrum leakage from other disturbance frequency components is equivalently approximated by Taylor series polynomials,combined with the spectrum leakage from the conjugate negative frequency of the measured frequency component,and a spectral parameter model that takes full leakage into account is obtained;Furthermore,a multi-spectral line equation set is established according to the approximate accuracy of spectrum leakage,and the general analytical expression for frequency estimation under any multi-spectral line can be obtained through the accurate solution.Finally,the frequency estimation is used as the known prior information,and the weighted least square method is used to obtain an accurate estimate of the amplitude and phase.The proposed CAL-IpDFT algorithm has the following innovations: based on the sidelobe fast decay characteristics of the MSDW,the spectrum leakage interference from other tones is effectively parameterized,which solves the problem that the spectrum leakage cannot be quantified under the premise that the parameters of other tones are unknown;based on the established spectrum approximate model including all leakage,a clear general analytical expression for frequency estimation can be derived recursively,which breaks the limitation that the interpolation algorithm is only applicable to single-frequency signals.The performance of the three interpolation algorithms proposed in this thesis is verified from three aspects: theoretical analysis,simulation comparison,and experimental testing.The results show the effectiveness and superiority of the proposed algorithms.