TABLE OF CONTENTS State variables are the parameters of a system that completely define its energy storage state. State variable analysis was the dominant technique in transient simulation prior to the appearance of the numerical integration substitution method.
Early state variable programs used the 'central process' method [1] that breaks the switching operation down into similar consecutive topologies. This method requires many subroutines, each solving the set of differential equations arising from a particular network topology. It has very little versatility, as only coded topologies can be simulated, thus requiring a priori knowledge of all possible circuit configurations.
The application of Kron's tensor techniques [2] led to an elegant and efficient method for the solution of systems with periodically varying topology, such as an a.c.-d.c. converter. Its main advantages are more general applicability and a logical procedure for the automatic assembly and solution of the network equations. Thus the programmer no longer needs to be aware of all the sets of equations describing each particular topology.
The use of diakoptics, as proposed by Kron, considerably reduces the computational burden but is subject to some restrictions on the types of circuit topology that can be analysed. Those restrictions, the techniques used to overcome them and the computer implementation of the state variable method are considered in this chapter.
State variable (or state space) analysis represents the power system by a set of first order differential equations, which are then solved by numerical integration. Although the inductor current...
