To enhance energy efficiency, promote the utilization of renewable energy sources, and enhance microgrid reliability, we present a capacity optimization approach for grid-connected microgrid systems that accounts for thermal power unit climbing constraints. Specifically, we investigate the capacity allocation problem of a grid-connected microgrid that comprises a wind turbine, photovoltaic cells, biomass generators, and battery energy storage devices. Our proposed approach considers the basic constraints of the microgrid system, as well as the thermal power unit ramping rate constraints, with the probability of power supply loss serving as the reliability indicator for system operation. To optimize the capacity allocation of each power generation unit, we establish a multi-objective optimization model that incorporates both the operating and environmental protection costs of the microgrid system. We leverage a multi-objective particle swarm optimization algorithm to solve the model and obtain the optimal capacity allocation. Our findings demonstrate that the addition of thermal power unit ramping rate constraints in grid-connected microgrid operations leads to a reduction in environmental protection costs, an increase in energy storage device capacity, and an improvement in system reliability.