  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.
