A Comparative Study of MPC and Economic MPC of Wind Energy Conversion Systems

Abstract

In this work, we perform a comprehensive comparative study of two advanced control algorithms-the classical tracking model predictive control (MPC) and economic MPC (EMPC)-in the optimal operation of wind energy conversion systems (WECSs). A typical 5 MW wind turbine is considered in this work. The tracking MPC is designed to track steady-state optimal operating reference trajectories determined using a maximum power point tracking (MPPT) algorithm. In the design of the tracking MPC, the entire operating region of the wind turbine is divided into four subregions depending on the wind speed. The tracking MPC tracks different optimal reference trajectories determined by the MPPT algorithm in these subregions. In the designed EMPC, a uniform economic cost function is used for the entire operating region and the division of the operating region into subregions is not needed. Two common economic performance indices of WECSs are considered in the design of the economic cost function for EMPC. The relation between the two economic performance indices and the implications of the relation on EMPC performance are also investigated. Extensive simulations are performed to show the advantages and disadvantages of the two control algorithms under different conditions. It is found that when the near future wind speed can be predicted and used in control, EMPC can improve the energy utilization by about 2% and reduce the operating cost by about 30% compared to classical tracking MPC, especially when the wind speed varies such that the tracking MPC switches between operating subregions. It is also found that uncertainty in information (e.g., future wind speed, measurement noise in wind speed) may deteriorate the performance of EMPC.Energies 2018, 11, 3127 2 of 23 capture as much energy as possible from the wind; when the WECS is operated in the full load mode, the typical control objective is to regulate the blade pitch angle to maintain both the output power and the generator speed at their rated values to ensure the safety of the equipment [2]. The operation of a WECS may switch between these two operating modes frequently due to the variation of wind speed. This poses great challenges in the controller design for WECSs.In the literature, many control strategies have been proposed for the control of WECSs with the purpose of either maximizing wind energy capture or maintaining the system at rated power. When a WECS operates in partial load mode, the maximum power point tracking (MPPT) is one of the most effective approaches for extracting energy from wind. Existing research studies primarily focus on three MPPT algorithms, namely, tip speed ratio (TSR) control, hill-climb search (HCS) control, and power signal feedback control [3,4]. In these algorithms, the optimal steady-state reference trajectories are calculated. These reference trajectories are then sent to the feedback control layer. The main objective of the feedback control layer is to drive a WECS to track the optimal reference trajectories. In the feedback control lay...

Wind Turbine Control Using Nonlinear Economic Model Predictive Control over All Operating Regions

“…where θ is the shaft torsional angle, w g is the generator angular speed, and N g is the gearbox ratio. Assuming that the low-speed shaft is one spring and one damper, the two-mass model is used to describe the drive train from a low-to a high-speed shaft through a gearbox as follows [17,26]:…”

“…Secondly, the shaft torsional angle and tower displacement must be considered in the economic index l e2 to reduce the fatigue of the tower structure caused by the tower deflection [19] and the gearbox load caused by the drive-shaft torsion [26]:…”

“…The proposed NEMPC in this paper has a unique weight in the objective function, while the weights must be chosen carefully for every input and state in the classical NMPC strategy [19]. In addition, in [25,26], an EMPC strategy has been designed for wind turbine control systems for all regions. In [26], the wind speed is produced based on the Van der Hoven spectrum [27], in which the wind speed is considered as a slowly-changing average wind speed superposed by a rapidly-changing turbulence wind speed.…”

“…In addition, in [25,26], an EMPC strategy has been designed for wind turbine control systems for all regions. In [26], the wind speed is produced based on the Van der Hoven spectrum [27], in which the wind speed is considered as a slowly-changing average wind speed superposed by a rapidly-changing turbulence wind speed. However, these EMPC approaches pay no special attention to the mitigation of mechanical loads on the tower in the economic objective function.…”

Sensitivity-based dynamic performance assessment for model predictive control with Gaussian noise

“…In [21], an economic model predictive controller with extended horizon was proposed and it was shown that in the nominal condition the transient or asymptotic average performance of EMPC is no worse than the traditional tracking MPC if the prediction horizon is sufficiently large. However, in the presence of model-plant mismatch (e.g., measurement and process noise, process disturbance, parameter uncertainty), whether EMPC can achieve better economic performance than the traditional tracking MPC is uncertain as demonstrated in the applications of EMPC to a post-combustion carbon capture plant [8], a wind energy conversion system [7], and a coal-fired boiler-turbine system [30]. There is a need of control performance assessment methods for EMPC in the presence of model-plant mismatch.…”