## 1 Introduction
MPC is an advanced control strategy that uses a dynamic model of the system to predict future states and optimize control actions over a receding horizon. By continuously updating its predictions based on real-time data, MPC can effectively manage the charging and discharging of EVs, taking into account constraints such as electricity prices, grid conditions, and user preferences [4]. This capability makes MPC particularly well-suited for DSM in environments with high penetration of renewable energy sources, where variability in generation can pose significant challenges to grid stability [5]. The integration of renewable energy sources, such as solar and wind power, adds another layer of complexity to grid management. Renewable energy is inherently variable and uncertain, making it difficult to predict supply and match it with demand. The use of EVs as mobile energy storage units offers a potential solution to this problem. By optimizing the charging schedules of EVs, it is possible to store excess renewable energy during periods of low demand and release it during peak periods, thereby smoothing out fluctuations in the grid [6]. This not only helps to stabilize the grid but also maximizes the utilization of renewable energy, reducing reliance on fossil fuels and lowering carbon emissions [7]. As modern charging infrastructures evolve within smart cities, the integration of renewable energy sources into electric vehicle charging systems becomes increasingly important. The use of renewable energy not only aligns with global sustainability goals but also presents a viable solution to stabilize the grid by reducing dependence on traditional energy sources during peak demand periods. By incorporating renewable energy into charging infrastructures, fluctuations in supply can be mitigated through intelligent demand-side management and model predictive control. This approach allows EVs to act as mobile storage units, optimizing energy consumption while simultaneously minimizing costs and environmental impact. Consequently, the adoption of green energy in EV charging infrastructures is a critical step towards achieving long-term sustainability in urban environments. The effectiveness of MPC in managing DSM and integrating renewable energy has been demonstrated in numerous studies. For instance, [PERSON] et al. [8] proposed an intelligent DSM framework that integrates renewable energy sources and uses real-time price-based demand response to optimize energy consumption. Their simulations showed that the proposed system significantly reduced electricity costs, peak loads, and carbon emissions compared to traditional methods [8]. Similarly, [PERSON] et al. [9] developed a predictive control framework for building-to-grid systems that integrates renewable energy and energy-storage systems. Their results demonstrated the potential of MPC to reduce electricity costs and load ramp rates without compromising indoor climate comfort [9]. Despite these advancements, several challenges remain in the widespread adoption of MPC for DSM in the context of EV integration. One of the primary challenges is the computational complexity of MPC algorithms, particularly in large-scale systems with thousands of EVs. The need for real-time optimization over a receding horizon requires significant computational resources, which can limit the scalability of MPC in practical applications. Additionally, the variability and uncertainty associated with renewable energy generation can complicate the optimization process, requiring robust algorithms that can adapt to changing conditions [10]. Another challenge is the integration of user preferences into the DSM framework. While MPC can optimize charging schedules to minimize costs and stabilize the grid, it must also consider the preferences and constraints of EV users, such as the desired state of charge and departure times. Balancing these competing objectives requires sophisticated algorithms that can dynamically adjust to user inputs while maintaining overall system efficiency [11; 12].