Implementation of sensitivity calculations in a general-purpose simulation program Original Research Article

This paper describes the implementation of sensitivity calculations in a general-purpose simulation program ESACAP. It is well known that exact derivatives of a steady state or time domain solution with respect to any parameter in a nonlinear dynamic system can be obtained at very little additional computational effort. The algorithm using already available Jacobians in a numerical integration scheme is applied to backward-differentiation formulas (BDFs) of variable step and order. Sensitivity calculation in the ESACAP version of the BDFs based on scaled differences is described. The main purpose of this paper is to identify the additional pieces of code required for sensitivity calculations in connection with a general problem-description language. The paper also describes the computation of exact derivatives in small-signal frequency-domain analyses including poles and zeros of transfer functions. Results from typical ESACAP simulations with sensitivities are presented.