Ensuring limited-supply compliance through a standby hydraulic design Method for looped district heating networks

District heating networks (DHNs) provide low-carbon, large-scale heat for cold-climate cities, yet their growing scale, aging infrastructure, and rising demand make hydraulic reliability increasingly critical. In this study, we developed a quantitative standby hydraulic design framework for single-source single-loop DHNs that integrates both normal and major failure scenarios. A pair of redundancy indicators, the pipe-diameter adjust coefficient and the system-power adjust coefficient, is introduced to coordinate hydraulic redundancy in pipe diameter and pump head. Then, we established a typical single-source single-looped DHNs model and used the standby hydraulic design framework. We varied the load density, load patterns, and reliability parameters, to study their influence on hydraulic bottlenecks and standby requirements. Results show that hydraulic standby performance improves when user heat loads gradually decrease from the heat source toward the flow-convergence point and when the distance between adjacent users increases in the same direction. Quantitative relationships between the adjustment coefficients and the limited-supply coefficient are derived (e.g., for n > 5 with uniform pipe-length distribution, [x] = 0.305ah0.5ad2.625), enabling the creation of practical design charts for engineering use. A real DHN case study involving thirteen idealized and actual configurations validates the method and the practical design charts, with the relative deviation between the recommended and calculated ah values ranging from 2.84 % to 35.94 % and remaining within 20 % for most scenarios. The proposed framework provides a scalable and practical foundation for reliability-oriented DHN planning and offers guidance for enhancing the resilience of future urban heating systems.