This paper presents an optimization strategy for the economic dispatch of an AC microgrid integrating heterogeneous generators, a battery energy storage system (BESS), and a solid-state transformer (SST). The proposed approach is implemented in Python, combining Pandapower for AC power flow validation with a Genetic Algorithm (GA) implemented through PyGAD. The optimization problem is formulated with mixed-integer decision variables: binary variables to represent generator status and continuous variables for generator and BESS power setpoints. The model accounts for nonlinear effects introduced by SST and BESS efficiencies, enabling accurate estimation of operating costs. Case studies are carried out for multiple load scenarios, considering both grid-connected and islanded operation. Results demonstrate that the proposed method ensures technically feasible operation while minimizing total operating cost. The approach is suitable for microgrids of tens to hundreds of kVA and provides a foundation for future integration into Energy Management Systems (EMS) for community microgrids.