Frequency Domain Techniques for Modeling Distribution or Transmission Networks Using Capacitor Switching Induced Transients

This paper presents two frequency domain methods to model and identify the equivalent impedance transfer function of a distribution or transmission system using recorded voltage and current transients due to capacitor switching. The first frequency domain method discussed was the fast Fourier transform method of identifying the frequency components of the voltage and current, then using the voltage and current spectra to find the impedance transfer function. The second method first obtains estimates of the sample auto and cross-correlation functions. These functions are then used, via the FFT, to find the respective power spectra of the signals, and finally to find the impedance transfer function. The FFT method was found to produce accurate results when the frequency components signal to noise ratios are large. The power spectral identification method and the coherence function added a measure to reject the frequency components that are contaminated with noise, but this method suffers from spurious cross correlations between the voltage and current. Once the impedance transfer function has been identified, several techniques were investigated that fit a parametric model to the function. Two polynomial transfer functions were fit to the real and imaginary parts of the impedance. These polynomials resulted in accurate representations of the impedance function of the system. The second parametric method discussed used the poles and zeroes identified from the impedance transfer function to develop an equivalent circuit representation of the system. This equivalent circuit did not fit the estimated impedance/frequency characteristics as well as the polynomial transfer function.