A Novel Wake Interaction Model for Wind Farm Layout Optimization

Abstract

Optimizing the turbine layout in a wind farm is crucial to minimize wake interactions between turbines, which can lead to a significant reduction in power generation. This work is motivated by the need to develop wake interaction models that can accurately capture the wake losses in an array of wind turbines, while remaining computationally tractable for layout optimization studies. Among existing wake interaction models, the sum of squares (SS) model has been reported to be the most accurate. However, the SS model is unsuitable for wind farm layout optimization using mathematical programming methods, as it leads to non-linear objective functions. Hence, previous work has relied on approximated power calculations for optimization studies. In this work, we propose a mechanistic linear model for wake interactions based on energy balance, with coefficients determined based on publicly available data from the Horns Rev wind farm. A series of numerical tests was conducted using test cases from the wind farm layout optimization literature. Results show that the proposed model is solvable using standard mathematical programming methods, and resulted in turbine layouts with higher efficiency than those found by previous work.

Wind farm layout optimization on complex terrains – Integrating a CFD wake model with mixed-integer programming

“…To describe the WFLO problem, the wind farm is discretized into possible turbine locations with corresponding binary decision variables denote if a turbine is located at each location or not. The formulation used in this work, identical to that of the work of Kuo et al [21,22], has an objective function of maximizing the sum of the kinetic energy experienced by each turbine, as follows. Let the wind farm domain be divided into a total of N cells, let K be the number of turbines to be placed (considered a constant in the formulation), and let x i be a binary variable denoting whether a turbine is placed in the i-th cell.…”

“…A number of mixed-integer programming formulations have been developed to tackle the WFLO problem [3,[20][21][22]. A MIP model consists of an objective function, a set of constraints, and a mix of integer and continuous variables.…”

“…Deterministic optimization approaches such as mixed-integer programming (MIP) [2,3,[20][21][22] have been shown to be promising in solving WFLO problems. These models can provide global solutions and optimality bounds for relatively small problems.…”

Study of cooperative wake control for multiple wind turbines under variable wind speeds/directions

“…32 In this paper, the three most commonly used wake superposition models that are linear superposition model (LS), sum of energy deficit model (SED) and sum of square model (SS), are selected to be combined with the ANN wake model to predict the total power of multiple wind turbines, and their expressions are shown in Table 1. 33,34 In the table, n is the number of upstream wind turbines; U 0 is the inflow speed of the first wind turbine; u j is the inflow speed at the position of the j th upstream wind turbine; u ij is the wind speed deficit of i th downstream wind turbine caused by the j th upstream wind turbine. Subsequently, to evaluate the performance of different combined models, we select the results of CFD simulation as the reference to calculate the cumulative prediction errors under different incoming wind speeds, while the wind direction angle is set to 0°.…”

Offshore wind farm wake modelling using deep feed forward neural networks for active yaw control and layout optimisation

“…Most analytical wake models include an independent approach for the superposition of wakes in order to form an array of multiple wind turbines, as well as the interactions between them [32], [33].…”