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There are two types of renewable energy widely used in China: air-source heat pump and compact all glass solar vacuum pipe water heating systems. To compare the performance of these supply systems, test systems were installed on two adjacent apartment buildings with the same structure, shape, and material. Both sets of equipment were placed in the same environment for the same 31-day period. The performances and performance parameters of the systems were systematically analyzed. The system energy consumption ratio of the compact all glass solar vacuum pipe water heating system was greater than that of the air-source system on 81% of the days in the study period. However, extension theory analysis showed that the weight coefficients for the performance parameters of the two systems were equivalent over the study period. The grey relational degree between the system performance and the parameters were also calculated. The grey correlation degrees of the compact all glass solar vacuum pipe water heating system's properties with outlet temperature, inlet temperature, environment temperature, solar radiation, and sunshine time were 0.69, 0.71, 0.68, 0.70, and 0.68; and the grey correlation degrees of the air source heat pump water heating system's properties with outlet temperature, inlet temperature, environment temperature, solar radiation, and hours of sunshine were 0.71, 0.73, 0.71, 0.65, and 0.72. Furthermore, multivariate regression equations were used to study the changes of other parameters when one of the single variables changes.

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The air source heat pump water system test bench and the compact all-glass vacuum tube solar water heating system test bench are (were) built on the roof of two adjacent teacher’s apartment buildings with the same structure, shape and material were constructed to study the performance of energy supply systems for different types of renewable energy buildings. The energy supply system performance and the performance parameters are comprehensively and systematically analyzed in the same environment conditions of the same period. The results show that the weight coefficients of the performance parameters of the two energy supply systems are equal by means of extension theory analysis. At the last, the comprehensive correlation degree Kj(1) of water outlet temperature on the performance of renewable energy power supply system is 2.07, the comprehensive correlation degree Kj(2) of water inlet temperature is 2.04, the comprehensive correlation degree Kj(3) of air temperature is 2.14, the comprehensive correlation degree Kj(4) of solar radiation is 4.97, and the comprehensive correlation degree Kj(5) of sunshine hours is 3.78.