Stochastic Optimal Control of Prosumers in a District Heating System

TL;DR

The paper tackles cost-optimal management of residential prosumers in a district heating network under uncertainty by formulating a stochastic optimal control problem with state variables for deseasonalized residual demand $Z$ and external storage temperature $Q$. A dynamic programming approach yields a Hamilton–Jacobi–Bellman framework, which is discretized into a stable, backward-in-time finite-difference scheme that respects state- and control-constraints and uses a terminal liquidation cost. Numerical results reveal the optimal storage strategies and value functions under basic, strongly seasonal, and weak insulation scenarios, illustrating how insulation and seasonality affect when to discharge, store, or sell energy to CHS. The methodology provides actionable insights for proactive, storage-enabled prosumer operation and demonstrates a scalable way to compute the optimal policy in realistic DH networks.

Abstract

We consider a network of residential heating systems in which several prosumers satisfy their heating and hot water demand using solar thermal collectors and services of a central producer. Overproduction of heat can either be stored in a local thermal storage or sold to the network. Our focus is the minimization of the prosumers expected discounted total cost from purchasing and selling thermal energy and running the system. This decision making problem under uncertainty about the future production and consumption of thermal energy is formulated as a stochastic optimal control problem and solved with dynamic programming techniques. We present numerical results for the value function and the optimal control.

Figures (15)

• Figure 1: Model of the prosumer's residential heating system.
• Figure 2: Residual demand.
• Figure 3: Temperature in external storage with residual demand and a given control .
• Figure 4: Set of feasible controls $\pazocal{K}_a$ with unsatisfied demand (Left) and overproduction (Right) for an imperfect insulation and non-constant seasonality.
• Figure 5: Set of feasible controls $\pazocal{K}^n_d$ with unsatisfied demand $z=z_1,z_{max},\frac{z_{max}}{2}$ (Left) for and overproduction $z=z_2,z_{min},\frac{z_{min}}{2}$ (Right) for a weak ES insultation at a time $t_n$.

Theorems & Definitions (18)

• lemma thmcounterlemma
• proof
• remark thmcounterremark
• remark thmcounterremark
• remark thmcounterremark
• remark thmcounterremark
• remark thmcounterremark
• remark thmcounterremark
• lemma thmcounterlemma
• proof