Acausal Modeling and Simulation of the Standalone Solar Power Systems as Hybrid DAEs

Abstract

Due to the presence of algebraic constraints as well as existing of different modes of operation, a standalone solar power system consisting of photovoltaic arrays, battery bank, electrical load, and a converter is becoming a complex system that can no longer be modeled using the conventional block diagram approach. While the block diagram approach is based on causal interactions between a chain of the ordinary differential equations (ODE), a more appropriate acausal approach solves a flat model of the system consisting of hybrid differential algebraic equations (HDAE). In effect, this paper proposes a nonlinear HDAE-based model of a standalone solar power system. The proposed model is presented using the Modelica language that allows object-oriented and acausal modeling of the multi-mode systems. Next, a general purpose solver is employed to simulate the system. The results of the simulation shows proper match with the information available in the components datasheet. It is shown that the simulation provides a sufficiently accurate prediction of all the system behaviors, which is vital for any model-based controller, including mode transitions.