In this paper, the optimal operation of Battery Energy Storage Systems (BESS) in AC microgrids is addressed through coordinated active and reactive power management under both grid-connected and standalone modes, aiming to minimize energy losses and \({CO}_2\) emissions. The proposed framework integrates a parallel Crow Search Algorithm (PCSA) with the Successive Approximation power flow method, providing a robust and computationally efficient solution. Its performance is evaluated on a 33-bus AC microgrid representative of Medellín City, using real demand and generation profiles. A parallel JAYA algorithm is also implemented for benchmarking, with 100 independent runs in both operating modes. The main contributions include: (i) a unified optimization framework for simultaneous active and reactive power control of BESS; (ii) validation of PCSA as a fast and reliable alternative to conventional convex optimizers; and (iii) evidence of BESS benefits in reducing losses, mitigating emissions, and enhancing voltage stability. Results confirm that the proposed methodology consistently outperforms the benchmark with superior accuracy and significantly lower processing times across all scenarios.