The Fast Filter Bank For The Frequency Estimation Technology

System frequency is a key parameter in the control of generation-load imbalance in power grids,and the state of the grid can be monitored by tracking the change of frequency.It is difficult to track the frequency of the system accurately due to the influence of some undesriable situations such as switch operation or in the presence of harmonics and noise caused by some power electronic equipment and arc furnaces,etc.Therefore,to seek and develop a reliable and accurate algorithm of the system frequency estimation is esstenial for the stability and safe operation in power system.In view of the better frequency characteristic,anti noise ability and low complexity of the fast filter(FFB)compared to the Fast Fourier Trasform,this thesis focuses on the application of FFB in the frequency estimation in power system and the main research is as follows:(1)Under the deep investigation of the tree structure of FFB,Frequency-Response Masking principle,node-modulated design mathnologies and the matrix expression theory,this thesis proves the frequency shift characteristics among each FFB channel and presents the derivation formula of the response of each channel in the time-domain and analysises the relationship between FFB and FFT represponse expression.(2)After the study of the classical two-stage frequency estimation algorithms based on the FFT operation,the analysis of advantages of the FFB in the coarse estimation stage is first presented and two kinds of FFB-based fine estimation method(namely FFB1,FFB2)are proposed.The FFB1 algorithm is similar to the algorithms based on the three consecutive FFT ouput in the frequency-domain and uses the output samples of the consecutivne three channel closest to the peak output channels in the FFB.By operation of the Taylor expansion,the fractional part of the estimated frequency bin is obtained.The FFB2 algorithm,based on the characteristics of the FFB equivalent coefficient,exploits the relationship between the output of FFB channel and the sample value at the middle-instant of the input signal.Simulation shows that the mean square error of the two proposed algorithms is lower than that of the FFT-based family algorithms and approximated to the CRB in the case with the low noise.(3)By replacing the FFT operation with FFB in the Smart Discrete Fourier Transform(SDFT)algorithms,the performance of the methods is improved obviously.Simulation shows that the mean square error of the proposed enhanced SDFT method is lower about 3dB than that of the Comnplex Least Squares SDFT(CLS-SDFT)algorithm.(4)To improve the ability to anti-noise of the SDFT algorithms,the the framework of the Total Least Squares(TLS)is first introduced into the SDFT algorithms(TLS-SDFT)and simulation in the case where the power system experiences noisy or moderate harmonic distoraction,modulation in amplitude or phase angle,is demonstrated.The result shows that the mean square error of the TLS-SDFT algorithm in the low-noise case is lower than that of the SDFT algorithm by 20dB,which is about 10dB lower than that of the CLS-SDFT algorithm,and it is approximated to the CLS-SDFT algorithm in the high-noise case.In addition,the frequency tracking performance of the TLS-SDFT algorithm is consistent with the CLS-SDFT algorithm in other cases mentioned above.(5)By replacing the FFT operation with the FFB operation of the SDFT and CLS-SDFT algorithm,the result shows that mean square error performance of the enhanced version is better than that of the original SDFT algorithm and mean square error ratio of CLS-SDFT decreases by about 3dB.In order to the further improvement of the anti-noise ablity and resolution of Prony algorithms,this thesis also studies the method using FFT and FFB to filter the signal,and then uses Prony algorithm to estimate the frequency.The simulation results show that the average error of the Prony algorithm with prefiltered by the FFB algorithm is less about 10dB than that of the FFT version in the case of harmonic interference.