Optimal Layout of Offshore Wind Farm Cluster: A Three-stage Game Model With Priori Coalition

Game theory is widely used in the field of decision-making and control engineering. In order to adapt to the trend of constructing and managing multiple adjacent offshore wind farms (OWFs) in the form of clusters, a novel three-stage game model with priori coalition (PC) based on the classic game theory is introduced in this article to simulate the realistic process of layout planning in an OWF cluster. The first stage constructs the framework of the game strategy and introduces the concept of coalition game, including the coalition structure (CS), the PC, the strategy and the objective function of the PC. The second stage is a profit distribution strategy based on an extended Shapely value which is called Owen value. This stage is the core of the game, because the unfair distribution of profit will lead to the break of the PC. In the third stage, core theory is used to judge whether the CS is stable. In addition, the Gaussian model is used to simulate the wake losses and when solving the optimal layout under the CS, the pure Nash equilibrium (PNE) is used as the equilibrium strategy. Finally, a multiple population genetic algorithm is proposed for solving the PNE under different CSs. The simulation results validate the proposed model and also reflects that the largest PC is preferred by the players.