Recently, interests on microgrids have been growing as clean power systems. Microgrids include small scaled distributed generation such as wind and solar power as well as diesel generators as main power sources. To operate a microgrid effectively, optimal scheduling for the microgrid is important. Especially, in the grid-connected mode, power trades between the microgrid and the power grid should be considered in optimal scheduling. In this paper, mathematic models for optimal operation of a microgrid were established based on the linear programming. In particular, the shiftable load was considered in the models to optimize it in microgrid operation. To show feasibility of the proposed models, they were applied to optimal microgrid operation and the results were discussed.