Centralized control of district heating networks during failure events using discrete adjoint sensitivities

Real-time control of district heating networks in the case of failures requires for accurate and fast strategies able to guarantee thermal comfort to all connected users. In this paper, we demonstrate a control framework that responds to these essential requirements. We minimize a global measure of discomfort based on a smooth maximum approximation. The optimization problem is solved through a gradient-based algorithm that can be naturally integrated with distributed meter readings leading to high accuracy of both forward and sensitivity analysis. Objective function gradients are computed by a discrete adjoint method, which is fast and nearly insensitive to the dimensionality of the optimization problem. The proposed framework is tested with numerical experiments on a reference medium-size distribution network in Turin. Results show that the thermal comfort of most critical users increases quickly, yielding to a nearly homogeneous discomfort distribution at the end of the optimization process. Studying the effect of the inlet pressure head on the optimized system performance reveals that a centralized operation results in increased robustness of the network and allows reducing backup pumping equipment. Furthermore, applying the proposed framework at the distribution network level yields remarkable benefits also in case of failures in the main transportation network.