*2.1. The Framework for Energy Allocation Analysis Based on Sankey Diagrams*

This study divided the energy flow process into five sub-sections: energy sources, intermediate conversion, end-use conversion devices, passive system and final services. In order to keep in line with previous work for later comparison, the concept and scope of each section refer to Ma et al. [6], which is detailed described in Appendix C, Table A2.

We used the Sankey diagram tool to present the energy flow process. The diagrams were plotted on the software called "e!Sankey" [20]. The framework of the energy flow Sankey diagram is shown as Figure 1. In the diagram, the energy flows from left to right with the allocation in different departments. The vertical lines show different stages of energy flow. In the specific Sankey diagrams, the width of the arrow shows the values of energy and the colors show different energy types or uses.

**Figure 1.** The framework of the energy flow Sankey diagram.

The core of energy allocation analysis is to allocate the energy loss in intermediate conversion stage into the energy consumption responsibility of the end-use stages. Therefore, the energy loss is not shown in energy flow process, and there are only energy allocation among different uses in the whole process from supply to service. How should we look at the energy allocation diagram? Except the clear demonstration of the energy flow process distinguished in different categories, different departments and different links, one of the advantages of the map is an effective combination of three levels of supply-conversion-demand: looking from the left side, it's the distribution of supplies (such as energy sources), from the right side, it's the allocation of demands (such as final services), while in the middle is the condition of specific technical departments (such as end-use conversion devices and passive systems). These will also be the key links to be discussed in the following text.
