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.Index Terms-Wind parks, finite differences method, dynamic response, steady-state, sparse techniques, Newton method.
I. NOMENCLATUREd, q subscript for direct-and quadrature-axis quantities, respectively δ angle of the rotor flux E induced rotor voltage H constant of inertia i subscript designating wind turbine number n number of wind turbines in the wind farm p c point of connection R a rotor radius r, s subscript for rotor and stator variables, respectively R con resistance between the point of connection and the infinite bus R resistance of the couple circuit ρ air air density P number of pair of poles P wt wind turbine power r s, X s stator resistance and reactance, respectively r r, X r rotor resistance and reactance, respectively T m ,T wt mechanical torque and wind turbine torque V dpc ,V qpc d and q axis voltages at the point of common coupling. V dsi ,V qsi d and q axis stator phase voltages V s infinite bus voltage V wind wind speed X reactance of the couple circuit X con reactance between the point of connection and the infinite bus x m magnetizing reactance x r rotor leakage reactance The authors are with the II. INTRODUCTION IND power has been used for centuries to develop different kind of human activities. The first wind turbine installation for power supply was developed at the beginning of the 20 th century, while the operation of large wind farms as sustainable energy resources became a reality during the last quarter of the 20 th century [1]. As a consequence, new projects are currently being proposed around the world in order to provide a source of power free of CO 2 emissions and green house gases [2].A review of the literature reveals that the analysis of wind parks has been favored with the application of different methods to calculate the steady-stat...