**1. Introduction**

Controlling energy-related carbon emissions and realizing a low-carbon transition in the energy system are important ways to globally address climate change and achieve sustainable development [1]. Considering that energy-related carbon emissions are closely related to complex energy flows in the energy system, it is necessary for policymakers to understand carbon emissions from the perspective of overall energy systems so as to formulate more targeted emission reduction policies [2]. As climate change becomes more severe, recent researches are stimulated to analyze energy-related carbon emissions and emission responsibility underlying the entire process of energy flow, and to discern the changing trend.

In the area of energy system analysis, Sankey diagrams are popular and useful tools for visualizing processes [3], which use arrows to show the flow of a certain object (e.g., energy, exergy, resources, etc.) with width representing the quantity and the colors indicating the types. Some recent examples of Sankey diagrams applied to energy system analysis are shown in Table 1. The literature shows

that the Sankey diagrams have been widely used to analyze energy flow or greenhouse gas (CO2) flow processes.


**Table 1.** Studies applying Sankey diagrams to energy system analysis.

*Abbreviations*: GHG: Greenhouse gas; Mtoe: Million tons of oil equivalent; EJ: 1018 Joules; PJ: 10<sup>15</sup> Joules; CHP: Combined heat and power; Mtce: Million tons of coal equivalent; Mt: Million tons.

In this field, Cullen and Allwood [4] were early scholars who proposed a systematic energy allocation analysis method based on Sankey diagrams. The method suggested that energy losses in energy conversion sectors should be calculated into and compensated for in the end-use energy consumption but not be presented separately, so as to evaluate the primary energy consumption responsibility of end use sectors and final energy services. This method was then followed by many other scholars, for example, Ma et al. [6] applied the method to national level mapping China's energy flow diagram, Chong et al. [7] introduced it to Malaysia showing the allocation of primary energy consumption responsibility in the energy system. Furthermore, the method was applied to regional energy flow such as China's provinces [8] and Canada's territories [9]. Recent researches also used the method to map CO2 flow diagrams [12], however, through our literature review, we found some limitations in three main aspects:


apply the idea of energy allocation analysis to carbon allocation analysis to show the emission responsibility comprehensively.

• Most of existing work using Sankey diagrams focused on the situation of a certain year. Although some research presented carbon flow diagrams in different years [12], it still lacked systematical comparison of diagrams in different years. While comparing these diagrams might reveal in-depth structural changes and trends of energy transition. Considering this, a new method for comparing Sankey diagrams and evaluating structural changes is needed.

Recognizing the above limitations, this paper aims to develop a method for analyzing energy-related carbon flow from the perspective of comprehensive energy flow, quantitatively comparing different Sankey diagrams and evaluating the structural changes and trends with energy transition. Firstly, we introduced energy allocation analysis to carbon flow analysis, fully considering the carbon emission responsibility allocation in the whole energy flow process from energy sources, intermediate conversion, end-use conversion devices, passive systems to final services. Secondly, we mapped the energy flow and the energy-related carbon flow Sankey diagrams. Thirdly, we defined the structural changes of Sankey diagrams from three dimensions, proposed index including total amount change (T), relative growth rate (R) and occupation ratio change (O), i.e., TRO index, compared different Sankey diagrams and discussed the political and practical reasons behind these changes.

To apply the method to actual objects, we chose China as a case for its tremendous and dynamic energy consumption and energy-related carbon emissions (see Appendix A, Figure A1). China accounted for 23.6% of global energy consumption and 27.8% of global energy-related CO2 emissions as the largest energy consumer and CO2 emission source in 2018 [13]. We chose the decade of 2005–2015 as the research period, because in this decade China's energy development experienced a tough transition. In this period, to achieve energy transition, China issued a package of energy plans ([14–19] as listed in Appendix B, Table A1). These policies resulted in great influences on the energy system and energy-related carbon emissions. Choosing this period can help us understand the notable changes of carbon emissions brought by the transition of the energy system and compare the results with relevant policies to verify this method.

The contribution of this work is to provide a method for analyzing national energy-related carbon emissions and evaluating structural changes based on Sankey diagrams and apply this method to China's case study from 2005 to 2015. Although some parts of methodology referred closely to previous work of energy allocation analysis of China [6], we further introduced the method to carbon allocation analysis of China, mapped its energy-related carbon flow Sankey diagrams in 2005 and 2015 (as well as a newly updated energy flow Sankey diagram in 2015). Additionally, the TRO index was proposed to compare the Sankey diagrams. This method can help us comprehensively understand national energy-related carbon emissions and the structural changes behind energy transition.

The rest of this paper is organized as follows: Section 2 introduces the method for depicting carbon flow process, evaluating structural changes, and data input; Section 3 discusses the carbon flow Sankey diagram results, TRO index decomposition, and the uncertainty; finally, Section 4 presents the conclusions.
