Nonlinear power system component modeling using symbolically assisted computations

A new technique has been developed that uses symbolically assisted computations to automatically construct time domain power system component models. The generated models are in the algebraic companion form (ACF). The ACF is a generalization of the resistive companion form that is widely used in time-domain simulators. It is based on a quadratic representation of the across/through variable relationship, which results in improved robustness and computational efficiency especially for large scale nonlinear system applications. Manual construction of ACF models is time consuming since it requires computation of both first and second partial derivatives of all through variables with respect to all across variables. This task is simplified using the automatic differentiation technique (ADT). This modeling tool has been implemented within the virtual test bed (VTB) simulation environment. The VTB is an interactive simulation environment which allows analysis of mixed discipline systems and provides advanced visualization capabilities. The ADT models allows users to easily generate their own efficient VTB models by just typing in the continuous domain differential equations expressing the through variables with respect to the across variables. In order to demonstrate the presented methodology, several examples of ADT generated ACF models are presented.