Solving Power System Differential Algebraic Equations Using Differential Transformation

This paper proposes a novel non-iterative method to solve power system differential algebraic equations (DAEs) using the differential transformation, which is a mathematical tool able to obtain power series coefficients by transformation rules instead of calculating high order derivatives and has proved to be effective in solving state variables of nonlinear differential equations in our previous study. This paper further solves non-state variables, e.g., current injections and bus voltages, directly with a realistic DAE model of power grids. These non-state variables, nonlinearly coupled in network equations, are conventionally solved by numerical methods with time-consuming iterations, but their differential transformations are proved to satisfy formally linear equations in this paper. Thus, a non-iterative algorithm is designed to analytically solve all variables of a power system DAE model with ZIP loads. From test results on a Polish 2383-bus system, the proposed method demonstrates fast and reliable time performance compared to traditional numerical approaches including the implicit trapezoidal rule method and a partitioned scheme using the explicit modified Euler method and Newton Raphson method.