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Offshore wind farm layout optimization using mathematical programming techniques

Beatriz Perez, Roberto Minguez, Raul Guanche

TL;DR

This paper tackles offshore wind farm layout optimization to maximize expected annual energy production (AEP) by minimizing wake losses. It introduces a sequential global optimization approach that starts with a stochastic heuristic initial layout and then applies nonlinear programming with restarts to identify high-quality local optima, enabling parallel computation and adherence to KKT optimality. The method uses the Jensen wake model and an AEP evaluation that integrates over Weibull wind-direction sectors, yielding a notable improvement for Alpha Ventus (approximately 304.8 GWh vs 293.3 GWh in the baseline). The results demonstrate wake-reduction gains, improved efficiency per area, and discuss practical considerations and limitations for scaling to larger offshore farms.

Abstract

Offshore wind power is a renewable energy of growing relevance in current electric energy systems, presenting favorable wind conditions in comparison with the sites on land. However, the higher energy yield has to compensate the increment in installation and maintenance costs, thus the importance of optimizing resources. One relevant aspect to increase profitability is the wind farm layout. The aim of this paper is to propose a new method to maximize the expected power production of offshore wind farms by setting the appropriate layout, i.e. minimizing the wake effects. The method uses a sequential procedure for global optimization consisting of two steps: i) an heuristic method to set an initial random layout configuration, and ii) the use of nonlinear mathematical programming techniques for local optimization, which use the random layout as an initial solution. The method takes full advantage of the most up-to-date mathematical programming techniques while performing a global optimization approach, which can be easily parallelized. The performance of the proposed procedure is tested using the German offshore wind farm Alpha Ventus, located in the North Sea, yielding an increment of expected annual power production of 3.52% with respect to the actual configuration. According to current electricity prices in Germany, this constitutes an expected profit increment of almost 1 M per year.

Offshore wind farm layout optimization using mathematical programming techniques

TL;DR

This paper tackles offshore wind farm layout optimization to maximize expected annual energy production (AEP) by minimizing wake losses. It introduces a sequential global optimization approach that starts with a stochastic heuristic initial layout and then applies nonlinear programming with restarts to identify high-quality local optima, enabling parallel computation and adherence to KKT optimality. The method uses the Jensen wake model and an AEP evaluation that integrates over Weibull wind-direction sectors, yielding a notable improvement for Alpha Ventus (approximately 304.8 GWh vs 293.3 GWh in the baseline). The results demonstrate wake-reduction gains, improved efficiency per area, and discuss practical considerations and limitations for scaling to larger offshore farms.

Abstract

Offshore wind power is a renewable energy of growing relevance in current electric energy systems, presenting favorable wind conditions in comparison with the sites on land. However, the higher energy yield has to compensate the increment in installation and maintenance costs, thus the importance of optimizing resources. One relevant aspect to increase profitability is the wind farm layout. The aim of this paper is to propose a new method to maximize the expected power production of offshore wind farms by setting the appropriate layout, i.e. minimizing the wake effects. The method uses a sequential procedure for global optimization consisting of two steps: i) an heuristic method to set an initial random layout configuration, and ii) the use of nonlinear mathematical programming techniques for local optimization, which use the random layout as an initial solution. The method takes full advantage of the most up-to-date mathematical programming techniques while performing a global optimization approach, which can be easily parallelized. The performance of the proposed procedure is tested using the German offshore wind farm Alpha Ventus, located in the North Sea, yielding an increment of expected annual power production of 3.52% with respect to the actual configuration. According to current electricity prices in Germany, this constitutes an expected profit increment of almost 1 M per year.

Paper Structure

This paper contains 24 sections, 10 equations, 10 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Wake models
  3. Layout problem definition
  4. Data
  5. Wind data
  6. Turbine data
  7. Wake effect data
  8. Wind farm data
  9. Problem variables
  10. Constraints
  11. Minimum distance
  12. Wind farm area limits
  13. Objective function: Annual Energy Production (AEP)
  14. Wind farm reorientation and renumbering
  15. Velocity evaluation due to the wake effect
  16. ...and 9 more sections

Figures (10)

  • Figure 1: Flow diagram: calculating the Annual Energy Production (AEP).
  • Figure 2: Renumbering of the turbines after the base change.
  • Figure 5: Graphical interpretation of the combined heuristic-gradient base layout optimization strategy.
  • Figure 6: Characteristic curves of 5MW NREL Turbine: a) Power output, and b) Trust coefficient.
  • Figure 7: Wind rose for the Alpha Ventus location.
  • ...and 5 more figures