**7. Conclusions**

An improved superstructure for HENs synthesis which contains the utilization of multiple utilities within inner- and inter-stages has been presented to integrate with the utility system. The coupling relationship between HENs and Rankine cycle-based utility systems is investigated and extended by considering various locations of steam heaters. The HEN structure has an impact on steam distribution and accordingly determines the operation of the utility system, thus in the study, the stream matches and heat transfer area of HEN, as well as the multi-level steam distribution, fuel consumption and power generation in utility system are all optimized to minimize the TAC of the whole system. Results are discussed and analyzed with case studies. The obtained economic benefits, 20.4% and 3.7% cost cuts for the cases separately, have demonstrated the method very well. It is concluded that the thermal property and quantity of steam have great effect on fuel consumption, power generation and heat transfer area, leading to an economic trade-off; relieving the location limit on steam heaters could create better solution, in terms of using more lower pressure steam not only at stream ends. Future research will be launched to develop this method to deal with the simultaneous synthesis problem of industrial park HEN and utility system with considering the selection of primary energy sources, e.g., fuel, solar, nuclear, wind, etc.

**Author Contributions:** Methodology, Y.S. and L.L.; validation, Y.S., L.L., Y.Z., L.Z. and J.D.; writing—original draft preparation, Y.S.; writing—review and editing, L.L., Y.Z., L.Z. and J.D.; visualization, Y.S.; supervision, L.L.; project administration, L.L.; funding acquisition, L.L. All authors have read and agree to the published version of the manuscript.

**Funding:** This research was funded by Natural Science Foundation of China (No.21878034 and 21776035) and the Fundamental Research Fund for Central Universities of China (DUT18LAB11).

**Conflicts of Interest:** The authors declare no conflict of interest.
