A new approach for solving DAE systems applied to distribution networks

A practical electric distribution system is a nonlinear network, which is generally governed by a large number of differential and algebraic equations (DAE). For instance, the ordinary differential equations are defined by the dynamics of the generators (e.g., small-scale hydro generation units) and the loads, as well as distributed generation (DG) units and their controllers. Algebraic equalities are described by the distribution network current balance equations and internal static behaviors of passive devices. In this paper, a rigorous approach is used to convert a semi-explicit DAE system into an explicit ordinary differential equations (ODE) system. In this way, it is possible to apply the robust and well consolidated implicit integration methods to solve the semi-explicit DAE systems as for implicit ODE system. Two applications of the methods are presented. In the first example, the procedure solves the classical Robertson´s problem, while in the second case study the dynamic behavior of a simple distribution system with a generator, an induction motor and an admittance load is reported. The results indicate that the proposed procedure is able to reach exactly the same results obtained by applying the classical solution procedure, without any further assumption about the nature of the results obtained.