Steady-State Solution of a Wind Park Using the Finite Differences and the Newton Methods

An efficient discrete-time approach for the computation of the steady-state operating point of a wind park is presented in this paper. The Finite Differences method and a Newton approach are applied to determine the steady-state solution of the wind park. Besides, the incorporation of sparse techniques improves the efficiency of the discrete-time solution in terms of storage and computational effort. The wind park is modeled using a time domain frame of reference, suitable for stability studies. While the wind generators are described with a reduced order model for the asynchronous machine, the wind turbine model takes into account the dimension of the turbine and incorporates a pitch angle controller. Each wind generator incorporates a capacitor bank at its terminals for reactive compensation of the induction generator. The dynamic response of a 100 MW wind park is reported using measured wind speed sequence as input to each wind generator. Furthermore, comparisons in terms of convergence and computational effort required to determine the steady-state solution are reported with the Finite Differences method and a Brute Force method. Speed up factors up to 42 are obtained for a 100 MW wind park described with 300 ordinary differential equations.