Model predictive control of wakes for wind farm power tracking

TL;DR

The paper addresses wind-farm power tracking under time-varying winds where wake interactions limit performance. It introduces a receding-horizon MPC that couples wake transport dynamics, a Gaussian wake model, and a wind-turbine model to optimize yaw and axial induction over a finite horizon. By reformulating the nonlinear optimization as a MIQCQP through polynomial approximations of wake quantities and a piecewise-affine erf, the approach enables real-time operation and robust power tracking with even turbine loading. A three-turbine case demonstrates effective power tracking, wake steering capability, and real-time solver performance, signaling applicability to larger farms and future work on higher-fidelity wind conditions.

Abstract

In this paper, a model predictive control scheme for wind farms is presented. Our approach considers wake dynamics including their influence on local wind conditions and allows to track a given power reference. In detail, a Gaussian wake model is used in combination with observation points that carry wind condition information. This allows to estimate the rotor effective wind speeds at downstream turbines based on which we deduce their power output. Through different approximation methods, the associated finite horizon nonlinear optimization problem is reformulated in a mixed-integer quadratically-constrained quadratic program fashion. By solving the reformulated problem online, optimal yaw angles and axial induction factors are found. Closed-loop simulations indicate good power tracking capabilities over a wide range of power setpoints while distributing wind turbine infeed evenly among all units. Additionally, the simulation results underline real time capabilities of our approach.

Figures (4)

• Figure 1: Simple example of a wind farm with three turbines and local coordinate systems. The solid circles represent op and the empty circles represent wt.
• Figure 2: Three dimensional wake forms and their defining parameters. From the turbine on the left, the wake form starts with smaller wake widths, $\sigma_y$ and $\sigma_z$, and higher wind speed deficit at the centre. With increasing distance in $x$-direction, the wake widths become larger, which leads to a flatter wind speed deficit distribution. Additionally, the centre wind speed deficit decreases. Due to the nonzero yaw misalignment, $u_\gamma$, of the wt the wake centre is deflected by $\delta_y$.
• Figure 3: Point on downstream wt rotor disc and rectangular approximation.
• Figure 4: Simulation results for three turbine farm. The results for combined farm power, turbine power, yaw misalignment, axial induction factor and solver times are depicted. The controller's sampling time is indicated by a dashed black line in (e).