Model Reference Control for Wind Turbine Systems in Full Load Region based on Takagi-Sugeno Fuzzy Systems

TL;DR

This work tackles the challenge of controlling a wind turbine in the full-load region by mapping its nonlinear dynamics to a Takagi-Sugeno (TS) fuzzy descriptor model and synthesizing a Model Reference Control (MRC) with a Parallel Distributed Compensation Controller (PDC-C). The TS-based model is augmented with tracking error to align the nonlinear WT with a linear reference model, and the controller gains are obtained by constrained LMI optimization, enforcing drive-train damping via a $\,\mathcal{D}$-region. The methodology is demonstrated on the NREL 5-MW wind turbine, extending from a 1-DOF rotor-dynamics representation to an elastic drive train and including actuator dynamics for generator torque, enabling simultaneous reference tracking of rotor speed and torque. Simulation results under turbulent wind, gusts, and an emulated Fault Ride Through (FRT) scenario show robust tracking and stability provided by the LMI-based TS-MRC synthesis, indicating potential for DVPP applications and applicability to other RES with near-linear closed-loop behavior.

Abstract

This paper presents a novel Model Reference Control (MRC) approach for wind turbine (WT) systems in the full load region employing a fuzzy Parallel Distribution Compensation Controller (PDC-C) derived using a Takagi-Sugeno (TS) fuzzy System approach. Through first-order Taylor series expansion, local linear submodels are generated and combined via triangular membership functions to develop a TS descriptor model. From here, the MRC PDC-C is synthesized by a constrained LMI optimization procedure, including damping characteristics of the elastic drive train, to track the desired rotor speed and generator torque based on the reference model dynamics. The controller is tested on the nonlinear WT model in simulation studies under various wind conditions, such as turbulent wind, wind gusts, and a Fault Ride Through (FRT) scenario where the generator torque is set to 0 p.u. for 150 ms.

Figures (9)

• Figure 1: Basic PDC control structure of the MRC approach. $\boldsymbol{x}$ and $\boldsymbol{x}^\text{r}$ denote the plant and reference model states respectively whereas $\boldsymbol{y}$ and $\boldsymbol{y}^\text{r}$ describe the output. $\boldsymbol{\varepsilon}=\boldsymbol{y}^\text{r}-\boldsymbol{y}$ denotes the tracking error incorporated in the MRC state vector through integration then denoted as $\boldsymbol{x}_\text{I}$. $\boldsymbol{u}$ is the plant input and $\boldsymbol{z}$ the premise variables. $\boldsymbol{w}$ is the reference signal to the reference model. $\Bar{\boldsymbol{\mathrm{K}}}_i$ is the MRC PDC-C.
• Figure 2: Linearisation points for controller synthesis on WT power curve (left) and torque coefficient surface (right).
• Figure 3: Linearisation points for controller synthesis on WT $\beta_\text{r}-v$ curve.
• Figure 4: $\mathcal{D}$-Region representation in the complex plane for a minimum and maximum decay constraint $\alpha_\text{min}$ and $\alpha_\text{max}$ and a desired damping through a cone with angle $\theta$.
• Figure 5: WT behavior under MRC PDC-C in different turbulent wind conditions with change in reference torque under constant rotational speed reference. The colors of the plot lines relate to the turbulent wind speed.