Wind Energy Conversion System (WECS) using a Doubly Fed Induction Generator (DFIG) is popular due to its control flexibility and higher conversion efficiency, but maintaining the operational stability and optimal efficiency under dynamic wind conditions is still a control challenge. In this paper, a nonlinear mathematical model for a DFIG based WECS was developed from fundamentals and its characteristics near the operating point were studied. A Proportional Integral (PI) controller and a Linear Quadratic Regulator (LQR) controller were designed to control the system and the behavior of the closed-loop system with these controllers was studied. While the designed PI controller failed to ensure stability, the LQR controller was giving stability but an LQR controller is vulnerable to loss of stability under uncertainties due to parameter variations or changes in operating points. A suboptimal \(H_{\infty }\) controller was then synthesized to obtain robust control. The closed-loop system performance of the DFIG system with the proposed controller was found to be stable and superior to PI and LQR controllers in terms of performance.

使用双馈感应发电机（DFIG）的风能转换系统（WECS）由于其控制灵活性和更高的转换效率而广受欢迎，但是在动态风况下保持运行稳定性和最佳效率仍然是控制挑战。本文从基本原理出发，建立了基于DFIG的WECS的非线性数学模型，并研究了其在工作点附近的特性。设计了比例积分（PI）控制器和线性二次调节器（LQR）控制器来控制系统，并研究了具有这些控制器的闭环系统的行为。尽管设计的PI控制器无法确保稳定性，LQR控制器具有稳定性，但由于参数变化或工作点变化，在不确定性下，LQR控制器很容易失去稳定性。次优然后合成\（H _ {\ infty} \）控制器以获得鲁棒控制。发现具有所提出的控制器的DFIG系统的闭环系统性能稳定并且在性能方面优于PI和LQR控制器。