Kalman Filtering with Harmonics Whitening for P Class Phasor Measurement Units

Abstract

The need for increasingly accurate and fast Phasor Measurement Units (PMUs), especially for active distribution systems monitoring, requires to achieve challenging trade-offs between measurement uncertainty and responsiveness. This is particularly important for protection-oriented (i.e., P Class) PMUs. In order to improve estimation accuracy with no need to prolong the data record size and the related delays, this paper presents a Taylor Kalman Filter (TKF) enhanced with a preliminary stage able to whiten possible narrowband disturbances over short observation intervals. The use of dynamic estimators such as the TKF is motivated by the need to track possible sudden amplitude or phase changes of voltage or current AC waveforms, which are likely to occur in smart grids. However, while a basic TKF is very sensitive to disturbances different from white noise, the proposed whitening-technique is able to greatly improve the estimation accuracy of synchrophasor amplitude, phase, frequency and Rate of Change of Frequency (ROCOF) under the influence of harmonics and amplitude or phase step changes even over one-cycle observation intervals, with just a minor performance degradation in the other P Class testing conditions reported in the IEEE/IEC Standard 60255-118-1:2018.

A Tuned Whitening-Based Taylor-Kalman Filter for P Class Phasor Measurement Units

“…2 is confirmed also by the results reported in Tables I and II. Observe that, while the TKF is sensitive to harmonics, particularly the low-order ones (as expected [12]), the W-TKF estimator greatly reduces their impact. Quite importantly, the relative impact of harmonics whitening on TKF decreases and becomes negligible as the harmonic order grows.…”

“…This is mainly due to the tuning of the TKF output matrix consisting of submatrices ( 17)-( 18), since in this case no sinusoidal disturbances affect the acquired signal. The W-TKF results shown in Tables I and II are better than those reported in [12] since in this paper the noise floor is lowered by the whitening transformation, as explained in Section III.B. • The excellent harmonics rejection capability of the whitening-based methods shown in Fig.…”

“…i) by adjusting the observation interval length in order to use only the samples that belong to one or two full power line cycles, regardless of possible off-nominal frequency deviations and ii) by replacing the noise subspace eigenvalues with much lower values to improve signal spectral purity. Both such solutions improve the accuracy of the original W-TKF algorithm [12].…”

“…(most of which are reported in the IEEE/IEC Standard) are reported and compared with those obtained with both the basic TKF and the W-TKF presented in [12]. In Section V some experimental results in different steady-state and transient conditions are shown.…”

“…This paper provides a partial response to the problems above by proposing a multistep estimator, called Tuned Whiteningbased Taylor-Kalman Filter (TW-TKF), that is able to greatly mitigate the uncertainty contributions due to both off-nominal system frequency deviations and large harmonic distortion even over one-cycle-long observation intervals. The TW-TKF results from an extension of the Whitening-based Taylor-Kalman Filter (W-TKF) presented in [12], and it outperforms both the W-TKF and the basic TKF in the most critical testing conditions reported in the IEEE/IEC Standard. Since the whitening technique used to decorrelate possible narrowband interferers tends to desensitize the TKF ability to track dynamic magnitude and/or angle phasor oscillations as the observation intervals length grows, the proposed technique is particularly effective over short intervals and, consequently, for P Class PMUs.…”