# Optimizing Battery Energy Storage with Mixed Integer Linear Programming (MILP)

Published 22/05/2024 By NAG

#### Introduction to Battery Energy Storage Systems (BESS)

Battery Energy Storage Systems (BESS) play a crucial role in managing power supply, enhancing the reliability of renewable energy sources, and stabilizing the electrical grid. As the demand for efficient energy storage solutions grows, so does the importance of sophisticated optimization techniques. One such technique is Mixed Integer Linear Programming (MILP), a powerful mathematical approach used to optimize decision-making processes.

#### What is Mixed Integer Linear Programming?

Mixed Integer Linear Programming (MILP) is a mathematical method used to solve optimization problems where some of the variables are required to be integer values. It is particularly useful in scenarios where decisions are discrete, such as scheduling, resource allocation, and, as in our case, managing operations of BESS. NAG introduced a new high-performance MILP solver at Mark 29.3 of the NAG Library, and we’ve used this in our latest optimization example.

#### Mathematical Modelling of BESS

The mathematical model for optimizing a BESS involves several components:

• Objective Function: The goal is to minimize the total operation cost of the utility including generators and batteries.
• Variables: These include battery and generator schedules, battery specification and imported power.
• Constraints: The model includes load balance, power limit, up and down time limit and power rating limit.

#### Example Scenario

Consider a simple scenario where a BESS is used to store electricity generated or imported at a lower cost, and supply to the utilities when cost is high. The optimization model needs to decide the best times to charge or discharge the battery to maximize profits over a given time horizon.

#### Implementing the Model in Python

Using Python, with the new MILP solver in the NAG Library, you can implement and solve the BESS optimization model. The process involves:

1. Defining the problem parameters (e.g., time intervals, electricity prices, battery specifications).
2. Setting up the objective function and constraints in a form that the MILP solver can understand.
3. Using the solver to find the optimal charging and discharging schedule.

#### Benefits and Challenges

Implementing BESS with MILP offers several benefits, including improved efficiency and profitability in energy storage and the ability to integrate seamlessly with renewable energy sources. However, challenges such as modelling accuracy, computational complexity, and the dynamic nature of energy markets also need to be addressed. Using Mixed Integer Linear Programming provides a clear pathway to enhance energy storage management, making it more cost-effective and aligned with energy demands. As technology advances, the integration of such models will become increasingly important in our shift towards sustainable energy solutions.

#### View the Modelling Process. Try the Solver

At Mark 29.3 the NAG Library features a new Mixed Integer Linear Programming (MILP) solver. Try the solver with a no-obligation 30-day trial or arrange a call with our Optimization team to discuss your challenge. Follow the links to learn more.

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