Stability Analysis and Mitigation of Thermo-Hydraulic Oscillations in Multi-Supplier District Heating Systems

In fourth-generation district heating systems (DHSs), the supply temperature of modern heat sources such as heat pumps and waste heat can potentially be reduced by mixing in hot water from combustion-based producers, thereby increasing efficiency and facilitating integration into networks with unrenovated buildings. However, this approach introduces the risk of thermo-hydraulic oscillations driven by mixing dynamics, transport delays, and mass flow adjustments by consumers. These oscillations can increase wear and cost and may potentially lead to system failure. This study addresses the asymptotic stability of multi-supplier DHSs by combining theoretical analysis and practical validation. Through linearization and Laplace transformation, we derive the transfer function of a system with two suppliers. Using pole-zero analysis, we show that transport delay can cause instability. We identify a new control law, demonstrating that persisting oscillations depend on network temperatures and low thermal inertia and enabling stabilization through careful temperature selection, thorough choice of the slack supplier, or installation of buffer tanks. We validate our findings using dynamic simulations of a nonlinear delayed system in Modelica, highlighting the applicability of such systems to real-world DHSs. These results provide actionable insights for designing robust DHSs and mitigating challenges in multi-supplier configurations by relying on thoughtful system design rather than complex control strategies.