A cooperative game-theoretic approach for the payment method of virtual power plant units with heterogeneous reliability

In this work we consider a virtual power plant composed of several unit types, which are characterized by different reliability values. In addition, we assume a simple model of market participation of the virtual power plant, where its income is proportional to the quantity, which can be generated with sufficient reliability by its component units and analyze the question, how a fair distribution of the resulting income among the component units may be determined. We study the problem in the framework of game theory using the concept of transferable utility cooperative games. By analyzing the characteristic function of the resulting game in the case of various examples we conclude that the most common solution concept of cooperative game theory, the Shapley value, does not necessarily results in a core-stable (i.e. fair) allocation in the case of the problem, furthermore we show that the core is not necessarily non-empty.