Computation of the periodic steady state in systems with nonlinear components using a hybrid time and frequency domain methodology

The basic principles of an efficient new methodology for the calculation of the nonsinusoidal periodic steady state in power systems with nonlinear and time-varying components are described. All linear parts, including the network and part of the loads, are represented in the frequency domain, while nonlinear and time-varying components, mainly loads, are represented in the time domain. This hybrid process is iterative, with periodic, nonsinusoidal, bus voltages as inputs for both frequency domain solutions and time domain simulations: a current mismatch is calculated at each bus and used to update the voltages until convergence is reached. Thus the process, but not the solution, is decoupled for the individual harmonics. Its efficiency is enhanced by the use of Newton type algorithms for fast convergence to the periodic steady state in the time domain simulations. Potential applications of this methodology are in the computation of harmonic power flow and in the steady state initialization needed in the calculation of electromagnetic transients