mixed integer linear programming (milp)

One of the most pressing challenges in power systems is the environmental impact, which is so critical that the Smart Grid (SG) includes it as one of the three key pillars in its framework. Renewable energy sources offer a potential solution by reducing reliance on fossil fuels and lowering carbon dioxide emissions, which are detrimental to the environment and contribute to global warming. However, certain renewable sources, such as photovoltaic (PV) cells, have uncontrollable power generation, posing a new challenge for grid stability. A viable solution to this issue is the implementation of Energy Storage Systems (ESS). These systems can store excess energy produced by renewables during periods of overproduction and release it when needed to enhance economic operation. In this paper, a Unit Commitment (UC) problem is performed in the presence of PV cells, ESS (in the form of batteries), and imported power from neighboring grids. The problem is modeled and simulated in MATLAB, where the inherent nonlinearity is managed by applying a Mixed-Integer Linear Programming (MILP) approach. Also, the simulation framework is designed with flexibility, enabling it to accommodate various piecewise linearization and different configurations of thermal units in the grid. The simulation results demonstrate an optimal economic operation with a total cost of approximately 124.57 $/MWh achieved through effective integration of solar energy and energy storage systems.

The growing demand for sustainable development and the integration of renewable energy sources emphasize the critical role of energy hubs (EHs) in modern power systems. EHs synergize electrical, cooling, and heating equipment with demand response (DR) programs and renewable energy resources (RERs) to optimize energy management. This study proposes a combined energy system (CES) framework to manage uncertainties in energy sources and demands, including cooling, heating, wind speed, solar irradiation, and energy prices. The objective is to maximize EH profits by integrating DR programs and RERs across various scenarios. The study utilizes the Slime Mould Algorithm (SMA), the Genetic Algorithm (GA), and the Mixed-Integer Linear Programming (MILP) method to compare performance. The optimization focuses on minimizing operational costs while maximizing renewable energy utilization. Without DR integration, SMA generates 1500 kW from photovoltaic (PV) systems and 2000 kW from wind turbines at a cost of $500,000. Conversely, GA generates 1400 kW from PV and 1800 kW from wind turbines, costing $550,000, while MILP results in 1550 kW from PV and 1950 kW from wind turbines at $510,000. With DR integration, SMA reduces costs to $450,000, GA incurs $500,000, and MILP achieves $460,000. DR programs enhance load management, peak shaving, and load shifting, contributing to cost reduction and efficiency. Simulation results confirm SMA's effectiveness in managing energy resources within a microgrid, optimizing renewables, and significantly reducing costs. SMA consistently outperforms GA and MILP, demonstrating superior cost-effectiveness and resource optimization. This study underscores the importance of advanced optimization algorithms like SMA in modern energy systems, offering a reliable and cost-efficient solution for EHs and supporting sustainable energy management and environmental sustainability.