The coalitional aggregation of wind energy: A stochastic duality approach

Abstract

The inherent uncertainty of wind power poses a major challenge to modern electricity grid. This paper mainly investigates a scenario where a crowd of wind power producers form a coalition by cooperatively offering their aggregated power output, aiming to mitigate these risks created by the inherent uncertainty of wind power. The main results are as follows. Firstly, a stochastic two-stage programming problem is proposed to formulate the capacity management with respect to a wind power producers’ coalitional game. Secondly, we give a constructive proof to illustrate that a wind power producers’ coalitional game has a nonempty core using the theory of cooperative game. Meanwhile, we also show that the form of a coalition always reduces their expected costs. Thirdly, we propose a stochastic duality approach to design a fair cost allocation scheme for players of a wind power producers’ coalition. Finally, we consider a concave function structure, indicating that there exists economies of scale, and extend this proposed duality theory to the wind power producers’ coalitional game under a concave capacity investment cost structure. Furthermore, we find that a wind power producers’ coalition is balanced under the concave capacity investment cost function. Our results provide an incentive for collaboration strategies in wind power setting, and promote sustainable development of wind power.