Gradient-based identification of hydraulic resistance for optimal pump control in meshed district heating network

Accurate hydraulic resistance is essential for optimal pump control in meshed district heating networks (DHNs). However, actual resistances often deviate from design values due to pipeline aging, corrosion, or topology changes, which can reduce control effectiveness. Identifying hydraulic resistance is further complicated by the underdetermined nature of the network, as measurements are typically available only at heating substations, while the number of pipelines far exceeds the number of observable nodes in the absence of additional sensors. To address this issue, a physics-constrained gradient descent-based identification framework is proposed. Hydraulic resistance is iteratively updated using gradient descent with analytically derived gradients, relying only on pressure data under multiple operating conditions. A loss function is first defined to quantify discrepancies between observed and simulated pressures, and its analytical gradient with respect to normalized resistance is derived. The estimated resistance converges to consistent and stable equivalent values across a wide range of perturbation levels. These identified resistances effectively capture the hydraulic behavior of the network and form the basis for the optimal pump control (OPC) strategy proposed in this study. Compared to the constant pressure difference control (CPDC) strategy, the OPC strategy can save approximately 10.4% of pumping energy during the heating period.