Calculation of transients in a system of algebraically connected dynamic components using a new numerical algorithm

An efficient numerical algorithm is presented for the solution of transients in systems consisting of dynamic components with both slow and fast eigenvalues, interconnected at their terminals by an algebraic network. The approach consists of producing algebraic input-output equivalents for the individual components by implicit integration of their differential equations. The adopted implicit integration is by parts leaving the impulse response intact and unaffected by the numerical discretization. The effect of this procedure is excellent convergence with large step sizes, resulting in significant savings in computation. The method has been tested on a conveniently chosen large circuit and compared to alternative algorithms. It is successfully applied to the solution of power system transients problems (dynamic stability, switching transients). Although described for linear systems, the method can be applied for nonlinear systems, linearized after each step around the new operating point.