A frequency-domain equivalent-based approach to compute periodic steady-state of electrical networks

Abstract

An alternative hybrid time/frequency domain approach to compute the periodic steady-state of an electrical network is presented. The network under analysis can include a variety of linear and nonlinear components, e.g., PV-buses, nonlinear reactors, and electronic devices. In the proposed approach, the linear part of the network is modeled in the frequency-domain (FD) via an equivalent input-admittance and all nonlinear components but PV-buses are resolved in the time-domain (TD). The FD equivalent is interfaced to the nonlinear components via discrete Fourier transform (DFT) operations, accounting for harmonic and interharmonic frequencies. The interfacing voltage/current variables are solved through a global Gauss–Seidel procedure; PV-buses are solved via a local Newton-type iterative procedure. It is shown that the proposed approach achieves faster computations than traditional hybrid methods due to (i) the compact FD equivalent representation of the linear part of the network and (ii) the Gauss–Seidel iterative scheme that avoids calculation and inversions of Jacobians. A sample network is used to compare the proposed method with a Newton-type solution scheme; the resulting waveforms are also compared with those given by the PSCAD™/EMTDC™simulation software.