Accurate estimation of phase angle for three-phase systems in presence of unbalances and distortions

Md. Zahidul Islam, Md. Shamim Reza*, Md. Maruf Hossain, Mihai Ciobotaru

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


The amplitude and phase imbalances can occur in three-phase voltage systems due to unbalanced loading and/or unsymmetrical grid faults. In this case, the conventional Clarke transform cannot produce accurate orthogonal signals, and hence a phase-locked loop (PLL) relying on the conventional Clarke transform is not able to produce accurate phase angles of three-phase voltage systems. This article proposes a three-phase PLL relying on an adaptive Clarke transform (ACT) algorithm for tracking the accurate phase angles of grid voltages in the presence of distortions and both the amplitude and phase imbalances. The proposed method includes bandpass filter in each phase to reject dc offset and harmonics. An algorithm is reported to track the unbalanced amplitudes and phase angle deviations of filtered voltages. A set of analytical expressions are presented for the coefficients of ACT matrix to make them adaptive under the amplitude and/or phase unbalanced conditions. A PLL is used to track the phase angle from the orthogonal signals generated by the ACT. A phase correction algorithm is also used to reject the phase error caused by the fixed tuned bandpass filter, which makes the method frequency adaptive without using any frequency feedback loop. The ACT is capable of generating orthogonal signals under unbalanced condition, whereas the conventional Clarke transform fails to do so. When compared with delayed signal cancellation (DSC)-based PLLs, the proposed method produces accurate results regardless of voltage unbalances and distortions. The simulation and experimental results are presented to verify the usefulness of the proposed method.

Original languageEnglish
Article number9001712
Number of pages12
JournalIEEE Transactions on Instrumentation and Measurement
Publication statusPublished - 2022


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