Periodic Steady-State Solution of Electric Systems Including UPFCs by Extrapolation to the Limit Cycle

This paper details a technique in the time domain for the fast periodic steady-state solution of systems with unified power-flow controllers (UPFCs) incorporating three strategies for the practical representation of the UPFC commutation process. The computation of the periodic steady-state solution of power systems with UPFCs including the proposed UPFC control strategies is efficiently obtained by extrapolation to the limit cycle using a Newton method based on a numerical-differentiation procedure. The periodic steady-state solution is validated against the solution obtained with the electromagnetic transient program PSCAD/EMTDC and against an implementation with the power system blockset of SIMULINK.