Microgrid sizing with EV flexibility: Cascaded MILP and embedded APSO-MILP approaches

The optimization of microgrid sizing and energy management (EM) presents a significant challenge due to the complexity of decision variables and constraints. This study addresses these challenges by proposing two distinct optimization algorithms aimed at enhancing microgrid component sizing and EM efficiency. The first approach, a cascaded Mixed-Integer Linear Programming (MILP) methodology, operates in two distinct stages. In the first stage, an annual optimization over 8760 h determines the optimal sizes of microgrid components and their energy management strategies, excluding electric vehicle (EV) flexibility to reduce computational complexity. This stage employs a single MILP formulation where both investment and operational decisions are jointly optimized. The second stage conducts a series of 24-h MILP optimizations for each day of the year, incorporating EV flexibility as a decision variable. This structure allows for refined energy management that adapts to daily variations in renewable generation, EV availability, and demand, while preserving the long-term sizing decisions established in the first stage. The second approach, an embedded Accelerated Particle Swarm Optimization-MILP (APSO-MILP) algorithm, performs an iterative 24-h optimization across the entire year, inherently integrating EV flexibility into both sizing and operational decisions. In this hybrid framework, APSO is responsible for exploring optimal capacity configurations for the microgrid components, while MILP handles detailed daily energy management for each capacity set. By coupling the global search capability of APSO with the precision of MILP under linear constraints, this approach ensures more adaptive and accurate system sizing. The embedded structure enables the algorithm to continuously update and refine component sizes and operational strategies based on performance feedback, thereby achieving improved cost and emission outcomes over the full operational timeline. Both algorithms seek to minimize the Levelized Cost of Energy (LCOE) and Life Cycle Emissions (LCE) over the microgrid’s operational lifespan. The microgrid under study consists of photovoltaic panels, wind turbines, a battery energy storage system (BESS), power converters, and an electric grid connection serving both EV charging stations and university building loads. Additionally, both optimization strategies account for battery degradation and load shedding, incorporating the Value of Lost Load (VoLL) as a constraint. Results indicate that the embedded APSO-MILP algorithm outperforms the cascaded MILP approach, significantly reducing LCOE and LCE–by approximately 194 % and 520 %, respectively—when considering load shedding and EV flexibility. Moreover, the APSO-MILP approach effectively prevents load shedding across all scenarios, whereas the cascaded MILP method experiences occasional shedding under constrained conditions. Both algorithms highlight the seasonal dependency of energy sources, with increased reliance on energy injections from the grid during autumn and winter, underscoring the importance of BESS in maintaining energy balance. This study provides a comparative evaluation of two advanced optimization techniques for microgrid planning, demonstrating the critical role of EV flexibility and integrated optimization in reducing both economic and environmental costs. The findings offer valuable insights for decision-makers seeking to optimize microgrid configurations while ensuring cost-effectiveness, sustainability, and energy reliability.