Stochastic Optimal Control Problem and Sensitivity Analysis for a Residential Heating System

We consider a network of a residential heating system (RHS) composed of two types of agents: a prosumer and a consumer. Both are connected to a community heating system (CHS), which supplies non-intermittent thermal energy for space heating and domestic hot water. The prosumer utilizes a combination of solar thermal collectors and CHS heat, whereas the consumer depends entirely on the CHS. Any excess heat generated by the prosumer can either be stored on-site or fed back into the CHS. Weather conditions, modeled as a common noise term, affect both agents simultaneously. The prosumer’s objective is to minimize the expected discounted total cost, taking into account storage charging and discharging losses as well as uncertainties in future heat production and demand. This leads to a stochastic optimal control problem addressed through dynamic programming techniques. Scenario-based analyses are then performed to examine how different parameters influence both the value function and the resulting optimal control strategies. For a common noise coefficient σ0=0.4, the prosumer incurs an approximate 16.08% increase in the aggregated discounted cost from the case of no common noise. For a discharging efficiency ηE=10.9, the maximum aggregated discounted cost increases by approximately 1.85% as compared to the perfect discharging efficiency. Similarly, for a charging efficiency ηE=0.9, we observe an approximate 1.94% increase in the aggregated discounted cost as compared to a perfect charging efficiency. Furthermore, we derive insights into the maximum expected discounted investment that a consumer would need to make in renewable technologies in order to transition into a prosumer.