مدل قدرتمند کنترل پیشگویانه برای زوایای مشترک پره ها در سیستم های مبدل انرژی باد Robust Model Predictive Control for Collective Pitch in Wind Energy Conversion Systems

1.INTRODUCTION Wind energy is one of the fastest growing energy sources worldwide. The installed wind power reached 456 GW in Oct. 2016 (WWEA 2016). The yearly growth rate in 2015 was 16.8%. It was 16.5% in 2014. The environmental and economic merits of utilizing wind energy contributed to this steady growth of the installed wind power. Control systems are utilized to increase extracted power, enhance power quality, and mitigate mechanical stresses to improve the economics of wind energy systems performance. The wind turbine operation modes rely on the value of the wind speed. Typically, there are three regions of operations. Region 1 is defined by the wind speed below the cut-in value. During the operation in region 1, the wind turbine is utilized to accelerate the rotor for startup. Region 2 is defined by the wind speed below the rated value and above the cut-in value. The control system target during the operation in region 2 is to extract maximum power (Jonkman et al. 2007). Region 3 is defined by the wind speed above the rated value and below the cut-out value. The control system target during the operation in region 3 is to regulate the generator power to its rated value, regulate the generator speed to its rated value and reduce the flapwise moment on the turbine blades. Pitch control is used to achieve the controller objectives in region 3. Pitch control consists of individual pitch control (IPC) and collective pitch control (CPC). Reducing the moment on the blades is the main target of the IPC (Jonkman et al. 2007). Regulating the generator power and speed are the main targets of the CPC. Several approaches to designing a controller for CPC are addressed in the literature. A robust controller is proposed for the CPC based on H2/H∞ based techniques by (Hassan et al. 2012). A fuzzy-logic-based CPC is designed by (Van, Nguyen & Lee 2015). The generator’s power and speed are used as control inputs for the fuzzy-logic-based controller. A common drawback to controllers suggested by (Hassan et al. 2012) and (Van, Nguyen & Lee 2015) is that constraints on pitch angle are not considered. Model predictive control is proposed in the literature for CPC to take care of the pitch constraints. Model predictive control (MPC) is a model based optimizer which uses the system model to predict its future behavior and select the optimal control actions that satisfy constraints. A fuzzy based model predictive controller is proposed to control the collective pitch angle by (Lasheen & Elshafei 2016). A multiple model predictive control is used to maximize energy captured from a wind turbine and to control the collective pitch angle so as to maintain rated output power by (Soliman, Malik & Westwick 2011). However, the work in (Soliman, Malik & Westwick 2011) does not discuss the stability of the nonlinear model. A common drawback to controllers suggested by (Lasheen & Elshafei 2016) and (Soliman, Malik & Westwick 2011) is the use of state observers without considering stability analysis. Uncertainties have important consequences in the theory of MPC since they affect both the issues of stability and constraints satisfaction. Hence, research efforts on MPC have focused on the robustness issue. One of the promising approaches to handle system uncertainty is to employ the tube –based MPC approach as in (Rawlings & Mayne 2012) and (Goodwin et al. 2014). The tube –based MPC approach can be summarized in four steps. First, an upper bound of the uncertainty and its effect on the system constraints are calculated. Second, based on the effect of the uncertainty on the system constraints, modified system constraints are obtained. Third, MPC is designed to control the system without uncertainty to satisfy the modified constraints (nominal trajectory). Fourth, all possible trajectories of the uncertain system are bounded inside a tube. The center of this tube is the nominal trajectory