A Flow Balance Index-Based Method for Evaluating the Balance Degree of Flow Allocation in Heating Networks

To address the critical issue of uneven flow allocation in district heating systems, this paper proposes a novel, systematic evaluation framework centered on the Flow Balance Index. The basic approach transforms discrete actual flow rates of users across the entire network into a continuous, normalized flow allocation curve. By analytically examining the geometric concavity of this curve, the overall imbalance level of the system is intuitively captured, which is further quantitatively represented by calculating the Flow Balance Index. The primary innovation of this method lies in shifting from local, point-based deviation metrics to a global, mathematical quantification of flow distribution balance by calculating the area of allocation deviation. To verify the effectiveness of this method, a parameterized branched heating network was constructed, simulating ideal balance, mild imbalance, and severe imbalance conditions. Within these simulated scenarios, the calculated Flow Balance Index successfully differentiated the varying degrees of global imbalance, yielding specific values of 0.16, 0.46, and 0.91, respectively. The results demonstrate that this method provides both an intuitive identification tool and an objective, scale-independent quantitative target for refined flow regulation strategies.