HARMONIC MINIMIZATION FOR THREE-PHASE GRID-TIED INVERTERS UNDER UNBALANCED GRID VOLTAGES

Abstract

 In an unbalanced three-phase system, dq-current control of a grid-tied inverter becomes challenging due to the presence of harmonics. These harmonics originate from fluctuations in the dq-axis signals, which, in turn, result from the unbalance in the corresponding αβ waveforms. This paper introduces a straightforward Clarke transformation featuring minimal adaptive parameters to address this issue. In the proposed method, the amplitude and phase information are extracted using the Fourier transform. Unlike the conventional Clarke transformation, where amplitude and phase disturbances persist due to the use of constant coefficients that apply fixed scaling to the input waveforms—thus failing to restore balanced αβ components—the proposed approach effectively mitigates these disturbances. The amplitude imbalance is minimized through waveform normalization, while phase deviations are corrected by deriving orthogonal waveforms via a trigonometric identity that adaptively manipulates the scaling parameters to maintain balance. The effectiveness of the proposed method was validated and compared with the conventional Clarke transformation through simulations under various unbalanced conditions. Furthermore, both transformation methods were implemented within a dq-current control scheme using a Synchronous Reference Frame Phase-Locked Loop (SRF-PLL). The results demonstrate that the proposed method achieves a Total Harmonic Distortion (THD) of 2.33% in the absence of low-order harmonics, compared to 13.3% when such harmonics, particularly the 3rd and 5th components, are present.