A Clarke Transformation-Based DFT Phasor and Frequency Algorithm for Wide Frequency Range

Despite its wide applications in power grid monitoring, the classic discrete Fourier transform (DFT)-based synchrophasor estimation algorithms suffer from significant errors when the power system operates under off-nominal frequency conditions. This phenomenon is caused by spectral leakage of DFT and becomes even more severe for single-phase synchrophasor estimation. To address this issue, a theory to eliminate the spectral leakage-caused errors is proposed and a Clarke transformation-based DFT synchrophasor estimation algorithm is proposed to implement the theory in this paper. The Clarke transformation constructs a second signal that has exactly 90° phase angle difference from the original single-phase input signal and helps eliminate the estimation errors for a wide frequency range. The proposed algorithm is tested under the conditions required in the phasor measurement unit standard C37.118.1-2011 and C37.118.1a-2014, as well as the harmonic and noise conditions not required in the standard to verify its performance. More importantly, the idea of using Clarke transformation can be used for other DFT-based synchrophasor algorithms in order to achieve higher synchrophasor measurement accuracy under dynamic conditions. An example is presented at last to demonstrate the expandability of the proposed idea.