A Two-Stage Polynomial Approach to Stochastic Optimization of District Heating Networks

TL;DR

This paper introduces a two-stage stochastic polynomial optimization method to determine high-performance operating strategies for district heating networks under demand uncertainty, optimizing supply temperature and flow rates.

Contribution

It develops a generalized moment problem framework and a hierarchy of relaxations to approximate optimal strategies for heating networks with uncertain demand.

Findings

Optimal strategies can approach the performance of fully variable control.

The method effectively computes near-optimal set-points under various network parameters.

Fixed-temperature variable-mass-flow strategies perform close to fully variable strategies.

Abstract

In this paper, we use stochastic polynomial optimization to derive high-performance operating strategies for heating networks with uncertain or variable demand. The heat flow in district heating networks can be regulated by varying the supply temperature, the mass flow rate, or both simultaneously, leading to different operating strategies. The task of choosing the set-points within each strategy that minimize the network losses for a range of demand conditions can be cast as a two-stage stochastic optimization problem with polynomial objective and polynomial constraints. We derive a generalized moment problem (GMP) equivalent to such a two-stage stochastic optimization problem, and describe a hierarchy of moment relaxations approximating the optimal solution of the GMP. Under various network design parameters, we use the method to compute (approximately) optimal strategies when one or both of the mass flow rate and supply temperature for a benchmark heat network. We report that the performance of an optimally-parameterized fixed-temperature variable-mass-flow strategy can approach that of a fully variable strategy.