Time-domain steady-state analysis of nonlinear electrical systems

Time-domain steady-state analysis is based on an algebraic objective function obtained by numerical integration of a system of ordinary differential equations and a method for computing the zero or the fixed point of the objective function. This paper reviews the most important aspects of time-domain steady-state analysis. First, the formulation of network equations is discussed and properties of importance for steady-state analysis-smoothness and stability of the solution of the differential equations-are reviewed. A selection of objective functions is presented, and the properties of these functions are derived from the results on network equations. The objective functions are computed chiefly by numerical integration of the network equations, and since this is the computationally most expensive part of a steady-state analysis, the next section is devoted to the discussion of efficient integration methods specially suited for steady-state problems. The section concentrates on both classical backward-differentiation formulas and variants with improved stability and accuracy properties. The methods for solving the algebraic objective equations are traditionally termed quick steady-state methods. This paper considers Newton iteration, quasi-Newton optimization, and extrapolation. Because of the framework established in the previous sections, these methods can be dealt with in a fairly uniform manner, thus emphasizing the methods as algorithms for computing zeros or fixed points of algebraic objective functions. Finally, the methods are compared for rate of convergence, computational efficiency, and storage requirements.