Optimisation of the Absolute Sine for Dynamic Induction Control

Abstract

The clustering of wind turbines in a wind farm results in overall efficiency losses as downstream wind turbines operate in the wake of their upstream neighbours. Wind farm flow control (WFFC) strategies have emerged to reduce these wake effects with the goal of maximising overall performance. Dynamic induction control (DIC) aims to enhance the wake breakdown and restore the wake's energy content through dynamic thrust variations. The control signals are often found through the economic model predictive control (EMPC) method, which relies on an internal model to incorporate future system behaviour in the determination of the next optimal control input. These models are designed to capture the most dominant wake characteristics while remaining computationally efficient. We employ the two-dimensional free-vortex wake (FVW) model presented from [1], which models the wake through vortex element pairs released from the edges of the actuator disc. The power of the two-turbine wind farm is maximised through EMPC, improving performance by 9.64\% over greedy control simulations. However, the EMPC method inherits finite horizon effects, resulting in large control horizons to optimise. In this study, we address these limitations by employing an absolute sine parameterisation in the FVW model to limit the finite horizon effects and reduce the dimension of the optimisation problem. The significant dimension reduction allows for a grid search to find the optimal infinite horizon steady-state solution, improving the mean steady-state performance by 2.43\% over the baseline results from [1]. Additionally, we focus on converging towards this optimum through finite horizon EMPC optimising over the amplitude and offset. Grid search analyses reveal sensitivity towards initialisation due to the appearance of local minima around the infinite horizon optimum. A maximum success rate is realised for very large control horizons, maximising the probability of converging towards the infinite horizon optimum. Accounting for the inherited system delay in the objective function also realises a maximum success rate but for shorter control horizons, which significantly decreases the simulation time. The final controller design terminates simulations ten times faster through the absolute sine parameterisation compared to the baseline simulation from [1] while maximising the probability of convergence towards the infinite horizon optimum.