Simultaneous solution of control system equations in EMTP

The existing approach for solving control systems in the Electromagnetics Transients Program is to insert one-time-step delays for breaking feedback loops when one or more nonlinear functions is encountered. Although this approach may remain acceptable for several well-behaved cases, it provides a nonsimultaneous solution for a nonlinear system. Fast varying components may create instabilities in such a solution and/or simply end up in a wrong operating region. In some cases, it imposes severe limitations on the integration time step for minimizing delays. This paper presents a new Jacobian matrix-based formulation for eliminating numerical delays in the solution of control system equations.