A cooperative game for the realized profit of an aggregation of renewable energy producers

The aggregation of renewable energy has significant potential to mitigate undesirable characteristics such as intermittency and variability and thereby facilitate grid integration. Using cooperative game theory, it has been shown that aggregation is also beneficial for renewable energy producers because they can increase their expected profit by making a coalition, bidding a joint contract that maximizes the expected profit and sharing the profit in a way that keeps the game stable. However, we show that the realized (as opposed to expected) profit of the coalition, using the contract that maximizes the expected profit, cannot be suitably distributed among its members. We propose an alternative coalition contract and prove that it allows for a satisfactory distribution of the realized profit among the coalition members keeping the game stable. We design a new payoff allocation that lies in the core of the game of the realized profit. Finally, we analyze the cost of stabilizing the game by evaluating the loss of expected profit that a coalition incurs by bidding the stabilizing contract.