Objective　Under the framework of China’s dual-carbon targets， district heating systems are shifting from coal-fired sources to multi-sources together with multi-sink modes dominated by waste heat. A unified network should integrate heat sources and heat sinks whose temperature grades vary over an extremely wide range. However， existing serie

s

-cascade approaches require heat exchange units to be arranged strictly in the order of grades， limiting their applicability in complex networks. This study proposes a genera

lized framework， with termed temperature grade sharing， which redistributes the temperature grade among adjacent heat exchange processes through additional bypass pipes， thereby decoupling grade matching from the physical arrangement.

Methods

2

The average temperature difference of source–sink is defined to quantify the grade mismatch， which classifies the system into four scenarios： heating-supply deficiency or surplus， and heat-recovery deficiency or surplus. Four configurations were constructed correspondingly： heating-supply upper--three-pipe and lower-three-pipe systems and heat-recovery upper--three-pipe and lower-three-pipe systems. Entransy dissipation analysis was adopted to demonstrate that grade sharing converted single large-temperature-difference mixing into small-temperature-difference mixing across both interfaces， ensuring a strict reduction in mixing losses. An analytical relationship was then developed to correlate the achievable reduction in the network return temperature with the original return-side mixing temperature difference and relative heat load of the grade-deficient process.Results and Discussions　Based on the analytical relationship between the reduction in the mixing-entransy dissipation and heat load of total branch， an analytical design map was established for the impact of temperature grade sharing on the overall network return temperature （Fig. 11）. Operating under a large-temperature difference， a low-return temperature route with the fixed supply temperature and heat load， allows a substantial reduction in the return temperature. The low return temperature enhances the transport temperature difference and reduces the required flow rate of circulation， thereby establishing the conditions for expanding network transport capacity and multi-source waste-heat integration without enlarging pipe diameters or equipment scales. For a representative boundary， i.e.， a relative heat load of 20% and an original mixing temperature difference at return-side of 20 K， the network return temperature can be lowered by 1.57 K， which aligns with the analytical map. The four configurations collectively cover all four typical mismatch scenarios； their design parameters are identical， and within a branch， the borrowed and returned grades offset one another， leaving the total driving force unchanged. At equipment level， an absorption heat exchanger requires only an additional bypass pipe and a circulating pump； while no extra heat-exchange components are required.

Conclusion

2

The proposed temperature-grade sharing framework decouples the cascade utilization from the physical arrangement. It provides a methodological foundation and a viable engineering pathway for the system-wide allocation of temperature grades in waste-heat-driven district heating systems， supporting the flexible integration and dynamic operation of multi-source together with multi-sink networks during dual-carbon transition.