Three-Phase PLL Based on Adaptive Clarke Transform Under Unbalanced Condition

This letter proposes a three-phase phase-locked loop (PLL) algorithm relying on an adaptive Clarke transform (CT) under amplitude and/or phase angle unbalanced condition. Analytical expressions for coefficients of matrix associated with the adaptive CT are derived and used to generate orthogonal signals. An auxiliary algorithm is also proposed to track the actual amplitudes and phase angle deviations. Unlike the conventional CT relying on constant coefficients, the adaptive CT can generate accurate orthogonal signals from the three-phase voltages including phase angle and/or amplitude imbalances. As a result, the proposed PLL is not affected by the unbalanced phase angles with/without amplitude imbalances. The advantages of the proposed adaptive CT-based PLL method is illustrated by both simulation and experimental results.