Subspace Predictive Control for Vertical Axis Wind Turbines

Abstract

To extract energy from wind, both Horizontal Axis Wind Turbine (HAWT)s and Vertical Axis Wind Turbine (VAWT)s are used. Different from the HAWT, the axis of rotation of the VAWT is perpendicular to the ground. This vertical design offers some unique advantages for the VAWT. For example, the generator of the VAWT is located on the ground, hence the maintenance costs are lower compared to the HAWT. Furthermore, the VAWT can be upscaled easier than the HAWT to harvest more energy from a single turbine. These benefits demonstrate the potential of VAWTs for offshore applications. However, the VAWT’s blade suffers from periodic aerodynamic loads from the periodically varying Angle of Attack (AOA), and unsteady aerodynamic phenomena, which harm the durability and hence the economic feasibility of the VAWT.

This thesis aims at resolving the blade loads mitigation problem of the VAWT. For wind turbines, pitching the blade is a common way to reduce the loads on the blade. There have been studies done that focus on the power maximization for the VAWT. However, research on the pitch control system for load reduction is lacking. To tackle the blade loads mitigation problem, a data-driven approach called Subspace Predictive Control (SPC) is used to control the individual pitch actuation of a two-bladed 1.5 m H-Darrieus VAWT.

This closed-loop control strategy consists of two parts, an online identification block and an optimal control law based on the identified system. The online identification method applied is called Recursive Predictor-Based Subspace Identification (RPBSID). It can estimate the system parameters online by using the input and output data collected from the VAWT system. Then, two different types of controllers are designed to reduce the blade loads. In the first approach, the constrained Model Predictive Control (MPC) is used. The optimal control input is calculated by solving a finite horizon constrained optimization problem. The individual pitch control action can be automatically adapted based on the online identified model. In the second approach, a Linear-Quadratic Regulator (LQR) is used as a comparison to the first approach. The LQR solves an infinite horizon unconstrained optimization problem to obtain the optimal state-feedback law. The control gain can be calculated analytically.

Both approaches are first tested on a Simulink model, which is based on the interpolation of lookup tables computed by the Actuator Cylinder (AC) model and blade element theory. Under a stepwise wind condition, the SPC approach shows the potential to reduce the normal load on each blade. It is also found that the MPC is more robust and easier to implement, compared to the LQR. Then, the MPC based SPC is applied to a mid-fidelity simulation tool called Qblade to acquire more realistic results. The controlled pitch trajectory shows good load reduction results under both uniform and turbulent wind conditions. The work presented in this thesis provides a control strategy to reduce the blade loads on VAWTs following a data-driven manner and demonstrates the capability of MPC based SPC in VAWTs’ application.