**1. Introduction**

Energy plays a vital role in the day-to-day existence of human life. A major part of energy generation comes from burning fossil fuels, such as coal and natural gas. With increasing concern over the emission of greenhouse gases and the reducing capacities of non-renewable resources, increased attention is being paid to the consumption of renewable energy sources. Renewable energy sources have a positive impact on the improvement in the economy of a country. Amid the different types of renewable energies, wind power has been extensively used for its low impact on the environment, reduced cost, and other benefits [1–3]. In general, the wind system tends to have fixed speed or variable speed wind turbine (WT) generators. The variable speed WT is the most popular among them for extracting the maximum energy from the wind [4]. Customary variable speed WT generators do not allow frequency regulation resulting in changes in grid frequency, and this highlights the necessity for frequency regulation technologies in WTs [4–6].

The doubly fed induction generator (DFIG) stands out to be one of the most soughtafter systems as WT generators. In DFIG, the stator windings are directly coupled to the grid, while the rotor windings are connected through slip-rings and back-to-back

**Citation:** Aljafari, B.; Pamela Stephenraj, J.; Vairavasundaram, I.; Singh Rassiah, R. Steady State Modeling and Performance Analysis of a Wind Turbine-Based Doubly Fed Induction Generator System with Rotor Control. *Energies* **2022**, *15*, 3327. https://doi.org/10.3390/en15093327

Academic Editor: Davide Astolfi

Received: 31 March 2022 Accepted: 30 April 2022 Published: 3 May 2022

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voltage source converters [7]. The converter at the grid side is termed grid side converter (GSC) and at the rotor side as rotor side converter (RSC). These are coupled by DC-link, which assists to retain the voltage deviations within an acceptable range. Such a structure offers several advantages such as fixed frequency power generation under variable wind speeds, decoupled control of active and reactive power, and different operating modes. In addition, the DFIG has the choice of small converter ratings, and consequently fewer losses with better efficiency and reduced cost. At present, the DFIG structure contributes to approximately 50% of the wind power market [8]. The RSC control embraced robust stator flux-oriented vector control (FoC) as it is the most comprehensive and proven one. The purpose of the vector control is to make the AC machine behave like a DC machine, which includes carrying out a decoupling between the flux and torque components. In DFIG, the FoC allows to decouple the active and reactive powers effectively, and hence it is employed for analyzing the DFIG under a steady state (SS). Similarly, the main function of GSC control is to keep the DC-link voltage almost constant and to provide reactive power when required as per the grid codes. The control technique adopted for it is the grid voltage-oriented vector control. It also maintains the output frequency fixed on the other hand the output voltage will be adjusted in order to facilitate the active and reactive power exchange.

#### *1.1. Literature on DFIG Steady-State Analysis (SSA)*

Many attempts have been made to carry out the SSA of DFIG due to its ever-increasing popularity. However, a comprehensive SSA along with a computer simulation model and performance analysis would provide a detailed understanding of the DFIG wind turbine's operational characteristics. With this viewpoint, the present work was carried out and the relevant literature is presented. In 2018, a SS mathematical model of DFIG was derived using the spatial vector technique under different operation zones of the wind turbine [9]. This method allows determining the operating points of any wind turbine by knowing the data and parameters of the wind turbine. In the same year, the stator flux-oriented vector control of DFIG-based wind turbines using space vector pulse width modulation was carried out and their performances were studied in [10] and found to be more effective. Later, in 2019, a computer simulation of DFIG and a vector control implementation for GSC and RSC were carried out to provide active power to the grid [11]. Subsequently, the stator field-oriented control (SFOC) of DFIM was discussed in [12], which is based on the sliding mode flux observer algorithm and the strategy is found to be effective under parameter variations. In 2020, the SSA of DFIG is presented with different magnetizing strategies for specific operating wind turbine modes [13]. This work discusses the mathematical modelling of DFIG in SS using stator flux-oriented vector control which is found too effective. In 2021, simplified SS modelling of DFIG with its operational features in a standalone wind energy conversion system with rotor control is discussed in [14]. Later, an SS solution to synchronous DFIG (sDFIG) orientated by references of the rotor flux for RSC and stator voltage for GSC is suggested. The analysis is summarized, and it is concluded that the sDFIG performs well when wind speed is lower than its critical value [15]. Another recent article on DFIM rotor flux orientation vector control with machine modelling for a wide speed range application is discussed in [16]. In 2022, the computation of SS values of DFIG using an accurate method for calculation is proposed in [17]. The simulation time domain results summarize that the SS values are matching with initialization values. As stated above, a comprehensive work of SS performance analysis with a working computer simulation model could be a promising work.

#### *1.2. Significance of the Paper*

The SSA of DFIG can be implemented in a global optimization environment to design the DFIG converters associated with the wind turbine. The analytical technique is a useful tool for minimizing the non-linear optimization process, which may be time-consuming and inefficient for handling digital issues. A single solution for the rotor control variables V<sup>r</sup> and ψ exists for each SS operating point. This helps to derive the SS characteristics from a given torque-speed array emulating a three-blade wind turbine. Proper SS conditions prevent the system from numerical instability. A computer simulation study of the DFIG generation system makes it possible to create an adequate model description. The design purpose is an interpretation of the physical nature of work processes as well as the developer systems' competency needs. The developed computer simulation shall be used to investigate the DFIG in a wide speed range of 900 to 1800 rpm. The SSA under certain operating modes provides information about the syst-em's behavior including stator and rotor active power, power losses, current variations, and voltage variations. The overall paper structure is as follows: initially, a literature review on the present work is briefly presented with the paper's significance in Section 1. Section 2 describes the SS mathematical modelling, MATLAB simulation and the control of a doubly fed induction generator is presented. In Section 3, the steps for implementing and analyzing the DFIG's SS performance are presented along with the results. In Section 4, the validation of the system design with SS plots is carried out with relevant results and a comparative analysis is presented. Finally, the findings are concluded in Section 5.
