To accommodate surplus electricity and decarbonize, power-to-gas (PtG) is being widely considered in the integrated energy system with high proportion of renewable energy. However, the reaction model of PtG should be refined for the sake of making a precise operation strategy and economic evaluation. Compared with the ordinary model of power-to-gas process, this article makes two main improvements. First, an explicit expression of electrolytic process is given according to the usage of electricity. In the refined electrolytic model, the recovery of the extra heat in the electrolytic process and the compression of feed-in gas is explored. Second, the response model of the methanation process to the intermittency of the renewable energy is established. Considering the increasing coupling of power system and water network, we formulate a day-ahead scheduling program for an integrated power and water system (IPWS). Thus, the role of double regulation of power-to-gas is more noticeable. Finally, the accuracy and economical performance of the refined model of power-to-gas is demonstrated through case studies. The results show a significant body of recoverable extra heat reaching 26.6% of the total power consumption. Also, it shows a dramatic growth in PtG's consumption by 61.9% considering compression consumption. Moreover, the information gap decision theory (IGDT) is applied in the unit commitment scheme. Based on IGDT, the impact of the renewable energy uncertainty on the decision-making of IPWS operator is discussed.