Multi objective moth swarm algorithm for optimizing electric vehicle integration in distribution grids

The rapid integration of electric vehicles (EVs) into distribution grids introduces significant challenges, including heightened energy losses, voltage instability, and increased operational costs. Traditional optimization methods often address these issues in isolation, failing to balance the complex, multi-objective nature of modern grids with high EV penetration and renewable variability. This paper proposes a mixed-integer multi-objective optimization framework to simultaneously minimize operational costs, energy losses, load shedding, and voltage deviations over a 24-hour horizon. The model integrates EV charging/discharging dynamics, renewable energy management, demand-side flexibility, and coordinated control of grid devices such as On-Load Tap Changers (OLTC) and Static Voltage Regulators (SVR). A novel Multi-Objective Moth Swarm Algorithm (MOMSA) is introduced to efficiently navigate the non-convex solution space, leveraging moth-inspired exploration-exploitation mechanisms. Simulations on a 33-bus distribution network demonstrate MOMSA's superiority over conventional algorithms (e.g., HOA, PSO, GA), achieving a 19.2% cost reduction compared to non-EV-integrated scenarios and outperforming peers by 7.4-15.7% in total cost, energy loss reduction, and voltage stability. Sensitivity analyses under varying electricity prices, renewable intermittency, and uncoordinated EV charging validate the model's robustness, highlighting its adaptability to real-world uncertainties. The results underscore MOMSA's capability to enhance grid reliability, economic efficiency, and sustainability in EV-rich environments, addressing critical gaps in existing literature through comprehensive multi-objective coordination and scalable optimization.