Mathematical-Programming Modeling of Power-Electronics-Based Microgrid Systems

The emergence of power-electronics-based microgrid systems is driven by the shift to cleaner energy, transportation electrification, renewable integration, grid modernization through smart grid advancements, and growing demand for energy-efficient solutions. For utilities, these systems present unique opportunities for enhancing grid resilience, improving load management, and enabling distributed energy resource integration. This work presents a modeling and simulation approach for microgrid systems that uses mathematical programming to represent power flow and capture the system dynamics. By solving an optimization problem at each time step, the method enables evaluation of power distribution and system performance under a range of operating conditions, without requiring detailed component-level specifications. This work introduces a baseline Mathematical Programming Approach (MPA), which assumes an idealized omniscient controller, and an extended Controller-Augmented MPA (CMPA), which explicitly incorporates the behavior of practical controllers. While MPA is valuable for early-stage design studies by offering insight into optimal operation and system limitation, it overlooks the influence of suboptimal control logic and uncertainty. CMPA addresses this by decoupling controller behavior from physical system dynamics, enabling more realistic modeling of power-electronics-based systems. Together, these approaches provide a versatile framework for researchers and utilities to evaluate microgrid architectures, explore control strategies, and assess system resilience.