*Article* **Short-Circuit Current Calculation and Harmonic Characteristic Analysis for a Doubly-Fed Induction Generator Wind Turbine under Converter Control**

#### **Jing Li \*, Tao Zheng and Zengping Wang**

State Key Laboratory for Alternate Electrical Power System with Renewable Energy Source, North China Electric Power University, Beijing 102206, China; zhengtao\_sf@126.com (T.Z.); wangzp1103@sina.com (Z.W.) **\*** Correspondence: lijing\_ncepu@ncepu.edu.cn; Tel.: +86-158-1146-2585

Received: 30 August 2018; Accepted: 14 September 2018; Published: 17 September 2018

**Abstract:** An accurate calculation of short-circuit current (SCC) is very important for relay protection setting and optimization design of electrical equipment. The short-circuit current for a doubly-fed induction generator wind turbine (DFIG-WT) under excitation regulation of a converter contains the stator current and grid-side converter (GSC) current. The transient characteristics of GSC current are controlled by double closed-loops of the converter and influenced by fluctuations of direct current (DC) bus voltage, which is characterized as high order, multiple variables, and strong coupling, resulting in grea<sup>t</sup> difficulty with analysis. Existing studies are mainly focused on the stator current, neglecting or only considering the steady-state short-circuit current of GSC, resulting in errors in the short-circuit calculation of DFIG-WT. This paper constructs a DFIG-WT total current analytical model involving GSC current. Based on Fourier decomposition of switch functions and the frequency domain analytical method, the fluctuation of DC bus voltage is considered and described in detail. With the proposed DFIG-WT short-circuit current analytical model, the generation mechanism and evolution law of harmonic components are revealed quantitatively, especially the second harmonic component, which has a grea<sup>t</sup> influence on transformer protection. The accuracies of the theoretical analysis and mathematical model are verified by comparing calculation results with simulation results and low-voltage ride-through (LVRT) field test data of a real DFIG.

**Keywords:** doubly-fed generator; converter control; short-circuit current; second harmonic component; low-voltage ride-through (LVRT) field test data
