# Nonlinear Model Predictive Control for Doubly Fed Induction Generator with Uncertainties
## 1 Introduction  
Given the increasing demand for electrical energy and the environmental challenges associated with fossil fuels, there is a significant emphasis on utilizing clean and renewable energy sources [1; 2; 3]. Among various renewable energy sources, wind energy is one of the most convenient and cost-effective options, and in several countries, a significant portion of the electricity demand is met through the operation of wind power plants. Integrating these power plants into the electricity transmission and distribution network can introduce dynamic and static effects on the overall network performance. The variable speed of the wind, resulting in fluctuations in the input power of the wind turbine, can lead to variations in the frequency and voltage of the power grid [4]. Hence, it is crucial to comprehensively examine and evaluate the conditions and consequences of utilizing wind power plant capacities on the power grid. This includes investigating key aspects such as active power-frequency requirements, reactive power-voltage requirements, fault protection, power quality, and controller performance [5]. In recent years, the DFIG has emerged as a prominent component in the global wind turbine market, serving as an alternative to traditional variable speed generators [6]. A mechanical shaft system connects the wind turbine to the DFIG. This setup involves a low-speed turbine shaft connected to a high-speed generator shaft through a gearbox. The DFIGcomprises a wound rotor induction generator. Its stator windings are directly connected to the grid, while the rotor windings are connected to the grid through two back-to-back AC/DC converters. [7; 8; 9]. The rotor side converter (RSC) and grid side converter (GSC) are voltage source converters employing pulse width modulation (PWM). This topology enables independent control of active and reactive power, and the power rating of the converters is only one-third of the turbine's rated power, making it a cost-effective solution. So far, many studies have been presented regarding the issue investigated in this paper, some of them are mentioned here. In ref. [10], an evaluation is conducted to compare the performance of the transfer function-based model and the state space-based model in the context of MPC design for DFIG. In ref. [11], a novel variable-step model predictive control strategy is presented with the aim of enhancing the capability of wind turbines to continue operating without disconnecting from the grid in the event of a fault. The methodology involves two key steps. Firstly, a predictive-control state-space model of a doubly fed wind farm is formulated based on its operational principles. Subsequently, model predictive control is implemented on the rotor side of the DFIG to achieve rapid tracking of the rotor current to the prescribed reference value during the low-voltage ride-through of the DFIG. In ref. [12], an updated model predictive control technique is suggested. This research aims to regulate the generator in two aspects; firstly, to closely track the reference wind speed with high precision utilizing both the rotor side and grid side converters; secondly, to mitigate system errors. The suggested approach involves the optimization of a function, incorporating current magnitude errors derived from the discrete mathematical model to predict the switching state of the converter. In ref. [13], an innovative Lyapunov-based model predictive control strategy is introduced for a multi-drive system based on a nine-switch inverter. This drive system comprises two AC motors and a singular nine-switch inverter designed to supply power to multiple induction motors. MPC is chosen as the preferred feedback strategy in AC-drive applications, owing to its rapid dynamic characteristics and its ability to effectively address multiple control objectives. In ref.