With the rapid increase in the proportion of natural gas for power generation, the operations of the power system are increasingly relevant to the supply of natural gas. To improve the reliability of power generation, some additional gas storage equipment should be set up in gas power plants. This paper considered different constraints, objective functions and gas flow/power flow equations at different time scales and built multi-time period optimized configuration and scheduling of gas storage models for gas power plants. Case studies demonstrated the following: (1) The most economical gas storage capacity could be obtained by the first optimal configuration model considering the long-term seasonal fluctuations of gas loads and gas prices. (2) The second model can not only obtain the minimum gas storage configuration capacity to meet the short-term peak load demand but also obtain the day-ahead gas storage schedule. That is, the remaining gas storage capacity at the initial and final points of each day. Moreover, the results can provide some suggestions on the reconstruction of natural gas pipelines. (3) The charge scheme of the gas storage obtained from the third scheduling model considering the uncertainty of the power load forecast can adapt to a certain fluctuating load interval.