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Discrete solutions of electric power systems based on a differentiation matrix and a newton method

A time-domain approach based on a discrete representation of the differentiation operation is presented in this paper to compute periodic steady-state solutions of electric power systems. The finite-dimensional representation of the derivative operator reproduces the exact derivative of a trigonometric polynomial. The time-domain representation of the electric network in terms of ordinary differential equations is transformed into a nonlinear algebraic formulation and solved using a Newton algorithm, where the unknowns of the algebraic equations are the samples of the state variables. Besides, the incorporation of sparse techniques improves the efficiency of the discrette-time solution in terms of storage and computational effort. Test cases incorporating nonlinear devices such as transformers, electric arc furnaces and STATCOMs are presented to illustrate the effectiveness of this method. Comparative results are reported using the well-known finite-difference method.