Assessing modeling choices for distributed energy resources in demand side management based on the Shapley value

Distributed Energy Resources (DERs), i.e., small-scale electricity systems composed of local generators, storage systems and flexible demand, play a crucial role in Demand Side Management (DSM). In order for DSM measures to control a huge number of DERs in an optimal way, a balance between their model complexity and level of detail needs to be found. To deal with this challenge, we propose the evaluation of different white-box model variants, consisting of a different set of submodels, based on the Shapley value and the maximal power of the DER. The resulting Shapley value is used to assess which submodels contribute most to the model’s utility, which we measure by its accuracy. The approach is applied to a heat pump case study using a white-box modeling framework. In the modeling framework, four submodels are defined and assessed by utilizing the proposed approach. Their contributions are quantified based on the corresponding Shapley values, which are 10.58, 0.68, 0.25 and 0.52 kW respectively. Specifically, the contribution of the larger hot water storage (HWS), i.e. 0.52, is quantified as 2.08 times than that of the smaller HWS, i.e. ... mehr0.25, despite the larger HWS having only 1.39 times the storage capacity of the smaller HWS. It indicates that the contribution of the storage submodel is not linearly proportional to its physical capacity. The results demonstrate the feasibility of the proposed approach for white-box DER models and extend its applicability beyond black-box models in which it has primarily been studied. Therefore, this work provides a new perspective on utilizing the properties of the Shapley value to assess DER modeling choices.