Abstract
This paper presents a coalitional game for value sharing in energy communities (ECs). It is proved that the game is super-additive, and the grand coalition effectively increases the global payoff. It is also proved that the model is balanced and thus, it has a nonempty core. This means there always exists at least one value sharing mechanism that makes the grand coalition stable. Therefore, prosumers will always achieve lower bills if they join to form larger ECs. A counterexample is presented to demonstrate that the game is not convex and value sharing based on Shapley values does not necessarily ensure the stability of the coalition. To find a stabilizing value sharing mechanism that belongs to the core of the game, the worst-case excess minimization concept is applied. In this concept, however, size of the optimization problem increases exponentially with respect to the number of members in EC. To make the problem computationally tractable, the idea of clustering members based on their generation/load profiles and considering the same profile and share for members in the same cluster is proposed here. K-means algorithm is used for clustering prosumers’ profiles. This way, the problem would have several redundant constraints that can be removed. The redundant constraints are identified and removed via the generalized Llewellyn’s rules. Finally, value sharing in an apartment building in the southern part of Finland in the metropolitan area is studied to demonstrate effectiveness of the method.
Highlights
With the desire to achieve sustainable development, the Paris Agreement recommended all parties to put forward their best efforts to alleviate urgent threat of climate change [1]
Optimization problems are solved via GNU linear programming kit (GLPK) solver in Pyomo Python module using an Intel Core i5 CPU 1.9 GHz, with 16.0 GB of RAM
The results demonstrate great performance of prosumer clustering and redundant constraint removal in reducing problem size and runtime, it is likely that clustering prosumers in a small number of clusters leads to inaccurate shares for the prosumers
Summary
With the desire to achieve sustainable development, the Paris Agreement recommended all parties to put forward their best efforts to alleviate urgent threat of climate change [1]. To tackle the issue, [16] has applied the nucleolus concept to allocate the extra benefit to the coalition members It has compared the results with those achieved by the Shapley values and demonstrated that value sharing based on the nucleolus concept is stabilizing. Reference [10] has used optimization-based value sharing mechanisms to stabilize ECs. That study has compared nucleolus concept and the worst-case excess minimization problem. Value sharing mechanism based on the analytical formula allocates the whole cooperation benefit to consumers if the community net consumption is negative This may result in dissatisfaction of producers who have invested on local generation facilities. A computationally efficient procedure is developed to solve the worst-case excess minimization problem This provides the opportunity to find a fairer and still stabilizing value sharing mechanism for ECs.
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