Widely Linear Adaptive Frequency Estimation of Unbalanced Three-Phase Power Systems

Abstract

Abstract-A novel technique for online estimation of the fundamental frequency of unbalanced three-phase power systems is proposed. Based on Clarke's transformation and widely linear complex domain modeling, the proposed method makes use of the full second-order information within three-phase signals, thus promising enhanced and robust frequency estimation. The structure, mathematical formulation, and theoretical stability and statistical performance analysis of the proposed technique illustrate that, in contrast to conventional linear adaptive estimators, the proposed method is well matched to unbalanced system conditions and also provides unbiased frequency estimation. The proposed method is also less sensitive to the variations of the three-phase voltage amplitudes over time and in the presence of higher order harmonics. Simulations on both synthetic and real-world unbalanced power systems support the analysis.Index Terms-Augmented complex least mean square (CLMS) (ACLMS), complex noncircularity, frequency estimation, unbalanced three-phase voltage, widely linear modeling.

Maximum Likelihood Parameter Estimation of Unbalanced Three-Phase Power Signals

“…For comparison, statistical performance of the conventional block based least squares (LS) frequency estimation algorithm was also considered [16]. To achieve unbiased frequency estimates for unbalanced power systems, the underlying LS observation model was modified by employing the widely linear (WL) framework to give the WL-LS model; we refer to [42], [43] for more detail. In the implementation of the considered algorithms, the sampling frequency f s of the simulated power systems was fixed at f s = 1000 Hz, K = 100 consecutive voltage samples were used as the available observations for the coarse search of the augmented periodogram peak by the DFT operation.…”

Distributed Widely Linear Kalman Filtering for Frequency Estimation in Power Networks

“…Statistical signal processing in the complex-domain underpins a number of disciplines, including wireless communications [31], [32] and power systems [16]. Although it may be convenient to process complex-valued data by representing the real and imaginary parts as a bivariate signal in the real domain, any intuition and physical meaning inherent in processing in the complex domain would be obscured.…”

“…The widely linear model for the complex-valued αβ voltage at any node i is therefore given by [16]- [18] …”

“…The classical diffusion scheme in (16) obtains the weighted average of the estimated states x a i,n|n in the neighbourhood N i under the assumption that each node is estimating the same optimal state. However, the state estimate of the State Space Model 2, which is given by…”

“…Our earlier work showed that this αβ voltage admits a widely linear autoregressive model under both balanced and unbalanced system conditions [16]. It was also shown that standard, strictly linear, complexvalued estimators applied to the complex αβ voltage introduce biased estimates for unbalanced system conditions, widely linear estimators (also known as "augmented" estimators) are able to provide optimal and consistent estimates of the system frequency over a range of operating conditions [16]- [19].…”