Model Order Reduction of DFWTs Based Wind Power System With Inhomogeneous Initial Condition

Although model order reduction based on balanced truncation (BT) has excellent performance in preserving accurate output of doubly-fed wind turbine based wind power system (DFWT-WPS), these applications are usually based on zero-initial condition. However, due to the inhomogeneous initial condition caused by soft-starting operation, the direct application of BT will lead to large response deviation. Therefore, this paper presents a method to construct the reduced order model of DFWT-WPS considering inhomogeneous initial condition, while reserving advantages of BT. Firstly, the system output is decomposed into two independent system outputs according to Duhamel principle. The first system contains zero-initial condition with input (standard BT model, SBTM) and the second system contains inhomogeneous initial condition without input. Secondly, the second system is converted into an equivalent one with dirac delta function as the input and zeroinitial condition (SBTM). Then, the two SBTMs are applied BT and the outputs are superimposed to get the reduced order response of the DFWT-WPS. One step further, the accurate upper bound of the error between the reduced order system and the original one is derived. Finally, the paper takes 20 /60 /120 DFWTs in parallel under different wind speed conditions as examples to verify the effectiveness of the proposed method with inhomogeneous initial condition.