Improved Algorithms Based On Smart DFT For Frequency Estimation In Unbalanced Systems

Noncircular signals are widely used to describe the dynamic characteristics of unbalanced systems,such as the unbalanced three-phase voltages of a power system,I-Q imbalance in communication systems and so on.Based on the proper(second order circular)statistical behavior of the noncircular signals,a series of estimation models can be extended for a more general form.Smart DFT(SDFT)is a simple and precise frequency estimation algorithm based on frequency domain transformation,and this method can avoid estimation deviations caused by the spectrum leakage and the fence effect.Frequency estimation algorithms based on noncircular signals and SDFT are studied in this paper,and the main contents related to this study are organized as follows:Firstly,the basic theory of unbalanced systems is studied,introducing the basic characteristics and researching tools of noncircular signals.In order to make use of all the available second-order information,we introduce the pseudocovariance matrix and a wide linear model.Taking the unbalanced three-phase power system as an example,the general expression of noncircular signal is derived,and it is pointed out that there is a certain transformation relationship between the complex noncircular signals and the real sinusoidal signals.Secondly,the fundamental theory and methods of frequency estimation are studied,including the basic mathematical model of frequency estimation.According to the knowledge of probability theory,the lower bound of the mean square error of parameter estimation(CRB bound)is studied,which is an important reference in frequency estimation.Moreover,two classical and efficient estimation theories in frequency are introduced,consisting of least squares and linear prediction,which are the key reference for the following proposed algorithms.Thidly,a series of the proposed three-point methods based on SDFT are studied,including the zeroSDFT,the window-SDFT,the CLS and the CRPHD.The zero-SDFT method can effectively improve the estimation accuracy without increasing the computational complexity,and the window-SDFT method can effectively restraining the interference of harmonics.The CLS algorithm utilizes the least squares framework to reduce estimation deviation caused by noise.Comparatively,the CRPHD method further deals with the noise item in formula derivation and more accurate estimating effects can be obtained as a result.The benefits of our proposed method are verified by simulations for unbalanced system conditions in the presence of noise,as well as for real-world measurements.Last but not least,the two proposed adaptive algorithms based on SDFT are studied,consisting of the sdft-DFE and sdft-IFE methods.Using the least mean square approach,the sdft-DFE is computationally efficient and it provides unbiased and direct frequency measurements on a sample-by-sample basis.The sdftIFE method is proposed for a second-order adaptive finite impulse response(FIR)notch filter with constrained zeros.Meanwhile,the technique of estimating input noise variance is employed to remove the bias existing in the estimated filter parameter.Computer simulations are included to corroborate the improved estimation performance and to show their comparative performance with original adaptive frequency estimators in unbalanced environments.