An improved algorithm for fast discrete time domain modelling of power electronic circuits

Abstract

An exact solution of the state differential quations for a power electronic circuit, incorporating a time discretization and a Basis Transformation, is presented. An eigen value -eigen vector expansion of the system matrix allows for the efficient evaluation of the State Transition matrix and Particular Integral. A binary search algorithm, without requiring the recalculation of the exponential matrix, can be used to obtain the state switching times. The Basis Transformation results in an exact solution when the input forcing function has an arbitrary time variation. Examples that illustrate the features of the method are presented.to the conventional Discrete Time Domain modelling method. The result can be termed the Modified Discrete Time Domain method. As a result of these modifications, the discrete time approach becomes very general as well as being computationally efficient. The closed form derivation of the new algorithm is presented and a comparison with the existing analytical models is provided. The efficiency of the improved algorithm is illustrated by several examples. Finally a step by step procedure of the improved discrete algorithm is outlined for transient, direct steady state or small signal analysis of power electronic circuits and systems.

Efficient simulation of switched networks using reduced unification matrix

“…Their solutions are where is the initial time and is the initial state at and the value of the state vector is to be computed. With the assumption of a constant input vector over one switching cycle and by letting (8) For a fair comparison of the state-space approach and the RUM method which uses the "first-order" backward Euler formulas, (8) can now be approximated [32], [34] by (9) where and Because state-space representation does not exist for the two-switch example circuit and "it will be extremely difficult to define all possible combinations of thyristor conduction " [4, p. 1292] for the third ac regulator example circuit, the comparison between the RUM method and the state-space approach will be centered on the second and typical example boost converter circuit. Accordingly, when (9) is used for the boost converter circuit in Fig.…”

“…The simulation time of these approaches has been improved through the truncated Taylor series [6], Chebyshev series [7], and trigonometric expansion [8]. Nevertheless, they have several drawbacks [4], such as lengthy state equation formulations and a limited number of switches.…”