Real Time Phasor Data Processing using Complex Number Analysis Methods

Event detection and analytic calculations in both Wide Area Measurement Systems (WAMS) and in distribution systems including Phasor Measurement Unit (PMU) based microgrid control systems often use the independent components of the phasors (e.g. frequency or Voltage) rather than the vector representation of a phasor. This paper introduces the use of the discrete time complex Fourier Transform based on complex number phasor data to track the real-time dynamic behaviour of the power grid. The specific property in which real and imaginary valued signals are mapped to complex and complex conjugate parts of the Fourier Transform can be used to compute the Fourier Transform of two signals simultaneously. One signal is placed in the real part of the time domain, while the other is place in the imaginary part. The notion of computing Fourier Transforms of signals that contains both a real part and an imaginary part carry over to PMU data to detect disturbances that may in both the real/imaginary or amplitude/phase part of the phasor.