Frequency Estimation Research Based On Complex Adaptive Linear Predictor And Application To Unbalanced Three-phase Voltages

System frequency is an important parameter for controlling the load balance in grid systems.The operating status of grid systems can be monitored by tracking the frequency variations.Therefore,the frequency estimation algorithm that can effectively get rid of harmonics and noise interference is particularly important for the stable operation of power grid systems.In this context,the adaptive algorithms based on minimizing mean square errors are widely used in the environment of noise and harmonics because of its simple procedure,high computational efficiency,and robust performance.In this paper,the following work is carried out around the application of this adaptive algorithms in power systems:The theoretical basis of frequency estimation is studied.Firstly,the complex signal model used in the estimation algorithm of this paper is introduced,and the complex Gaussian white noise is introduced.Then according to the probability related knowledge,the lower limit of the mean square error of the parameter estimation,Cramer-Rao lower bound,is studied.The CRLB of the complex signal model is deduced in details,which is regarded as the important reference of the performance of frequency estimation algorithm.Then the concept of unbalanced power system is introduced,including the common faults in power systems.The transformations of the three-phase voltage to complex signal model,the Clarke transform,and the non-circular description of the complex signals in unbalanced power systems are introduced.Two classic adaptive frequency estimation algorithms are studied,including algorithms that based on least squares and least mean squares.For the LS algorithm,the basic RLS algorithm is introduced first.Because the estimation is biased,by subtracting the calculated estimation bias,the BCRLS algorithm,which is an offset-compensation version of RLS,is obtained.The following is an introduction to the RTLS algorithm.Different from BCRLS,it does not require a priori knowledge of noise variances.Then it is followed by the performance simulations including frequency tracking and estimation variances for the above three algorithms;for the LMS's algorithms,we introduce the complexed LMS algorithms,CLMS,and give the expression of frequency estimation.Since the algorithm only uses the information of a single voltage,the frequency tracking characteristics in an unbalanced power system are not good.Then the ACLMS algorithm that based on widely linear models is introduced,it makes full use of the wide linearly model and the second-order augmented statistical information,and can still effectively track the system frequency in unbalanced power systems.The CDFE,a complex-domain direct frequency estimation algorithm that based on LMS is studied.The algorithm can achieve unbiased frequency estimation by minimizing the modified mean square error function.Firstly,the frequency tracking expression of the CDFE algorithm and the theoretical estimation formula and variance in steady-state environment are deduced.Then the algorithm is simulated and validated in the environment of large-scale frequency changes to verify the compatibility between theoretical variances and actual mean squared errors.This algorithm is compared with the ACLMS mentioned above in various simulation environments.The results show that the CDFE algorithm can still accurately estimate non-equilibrium without fully utilizing the second-order statistics of non-circular signals.The frequency value of the system performs better in some respects.The drawback of the ACLMS algorithm lies in the large amount of calculation and complicated calculation formulae,and these aspects are just the advantages of the CDFE algorithm.The variable-step-size version——VSS-CDFE algorithm is studied.Based on the original CDFE,this algorithm improves the step size factor.The algorithm uses the improved scheme of the steepest descent method to obtain the time-varying expression of the step size factor,and calculates the steady-state variance of the VSS-CDFE algorithm on this basis.Since the value of the time-varying step size factor decreases during the iterative process,the convergence speed slightly decreases compared to the original CDFE,but the performance of the steady-state variance improves obviously.Experimental results show that the VSS-CDFE algorithm converges faster with the same estimation variance as CDFE.