A matrix modelling method based on the production structure is proposed and a general exergy matrix model for the multi-energy integrated system is established, which provides a simple and effective tool for the contribution rate calculation of the external fuel exergy to the multi-energy integrated system. The proposed method is verified by a case study of a solar-aided 600 MW coal-fired power generation system. The influence of two fuel product definitions and different simplified systems on the calculation results is analyzed. The results show that the contribution rate of solar exergy is 4.24 % when the product is defined as the output exergy. But the solar exergy contribution rate is only 1.77 % when the product is defined as the exergy increment and output power. Inappropriate system simplification can also cause the contribution rate of external fuel to deviate from the original value.