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This paper is the second in a two-part series on the concavity-convexity of the distribution system security region (DSSR). In Part I, the concave-convex characteristics and mechanism of DSSR are revealed by observing many case grids. In Part II (this paper), the concave-convex principle of DSSR is revealed through mathematical deduction. Firstly, the relevant concepts of sub-regions are proposed, and a DSSR model based on the union of sub-regions is developed. Secondly, the concave-convex principle of DSSR is proposed. The proposed criteria show that the security region of a distribution system with a single load transfer path for each feeder is convex, while that with multiple load transfer paths for some feeders can be concave or convex. Thirdly, the proposed criteria are deduced mathematically. Fourthly, based on the criteria, a method is proposed to judge whether a DSSR is concave or convex. Fifthly, the proposed criteria and method are verified through several cases, and the DSSR concavity-convexity of real distribution systems in China is also analyzed. Finally, the applications of DSSR concavity-convexity are illustrated. This work lays a mathematical foundation for the research of the topological properties of DSSR and is also useful for the application of DSSR. • The DSSR mathematical model based on the union of sub-regions is developed. • Three criteria are proposed and proved, revealing the concave-convex principle of DSSR. • A judgment method for DSSR concavity-convexity is proposed based on these criteria. • The DSSR concavity-convexity of real distribution systems in China is analyzed. • The application values of DSSR concavity-convexity are demonstrated. [ABSTRACT FROM AUTHOR]

Over the recent decades, China’s building energy consumption has been growing rapidly. Also the fuel mix has been changing quickly with more natural gas & electricity and less coal being used. Meanwhile, the technologies used in building sector are improving in efficiency. In this paper, the impact of technical progress and the use of renewable energy in building sector are analyzed. The energy saving and emission reduction potential of building sector are also measured. China TIMES model is used to model the future energy consumption and carbon emissions in building sector. The modelling results indicate that building energy consumption is expected to grow to around 41.6EJ in the reference scenario in 2050. The energy saving potential in 2050 can be up to 4EJ due to the improvement of both building insulation (envelop) and energy use technologies. Renewable energy used in buildings can be a great contributor to the carbon mitigation in buildings. China’s building sector can reach a relatively low-carbon future with more low- and non-carbon fuels consumed. [ABSTRACT FROM AUTHOR]