Power grids connected to renewable energy sources must cope with fluctuating output by those sources. One method to do so is for the power grid company to accept bids to increase grid stability. These bids are accepted via capacity market auction of increasing grid stability. These offers are to increase the maximum power capacity by using power stations (both utility and non-utility stations) and by reducing electricity consumption via demand response. One candidate for achieving this is a district heating and cooling (DHC) system installed with combined heat and power. However, the electricity adjustment (EA) operation needed by the DHC for the auction is complicated because the system consists of boilers, water heaters, chillers, generators, and other items. To investigate the possibility of using DHC systems for capacity market auctions, this paper proposes two models for operating a DHC system: electricity-adjustment capacity (EAC) provision and EA operation. In addition, to develop methods for evaluating the cost of the proposed operational methods, a model DHC system is formulated with an actual DHC system as a basis. Using the models, numerical simulations are conducted by particle swarm optimization. Then, the running costs of EAC, EA, and normal operation are calculated. The results:show that the running costs of the proposed operations are relatively stable by day and season, not varying beyond the range of +/- 10%. Nevertheless, the running costs in spring and fall are be lower than those in summer and winter. The cost of providing EAC is no more than 1% the cost of normal operation, and the cost of EA itself is no more than 2% that of normal operation.