Optimal Control of Dynamic District Heating Networks

TL;DR

This paper formulates and analyzes an optimal control problem for dynamic district heating networks modeled by differential-algebraic equations, proving existence of solutions and demonstrating practical applicability through numerical experiments.

Contribution

It establishes the existence of unique solutions and optimal controls for DAE-based district heating network models, with validation on real network data.

Findings

Existence and uniqueness of solutions proved

Optimal controls exist for the system

Numerical experiments confirm practical relevance

Abstract

In the present paper an optimal control problem for a system of differential-algebraic equations (DAEs) is considered. This problem arises in the dynamic optimization of unsteady district heating networks. Based on the Carath\'eodory theory existence of a unique solution to the DAE system is proved using specific properties of the district heating network model. Moreover, it is shown that the optimal control problem possesses optimal solutions. For the numerical experiments different networks are considered including also data from a real district heating network.