MATLAB Implementation of Economic Load Dispatch Using Sparrow Search Optimization

Introduction

Economic Load Dispatch (ELD) plays a crucial role in power system operations by determining the optimal power output of multiple generating units, ensuring that demand is met at the lowest possible cost. In this blog post, we explore how the Sparrow Search Algorithm (SSA)—a relatively new nature-inspired optimization technique—can be implemented in MATLAB to efficiently solve the ELD problem.

About the Sparrow Search Algorithm

The Sparrow Search Algorithm (SSA) is an advanced metaheuristic algorithm inspired by the foraging and anti-predation behavior of sparrows. It is gaining popularity due to its strong global search capability and simple implementation. The version of SSA used here is based on a paper published in System Science and Control Engineering, under the Taylor and Francis group.

Problem Setup: Economic Load Dispatch

The objective is to optimize the power generation of three generators over a 24-hour period. Each hour has a different load demand, and the goal is to supply this demand while minimizing the total fuel cost. The generators have associated fuel cost coefficients and operational constraints, such as minimum and maximum generation limits.

Input Data and Configuration

Before running the SSA, the following data must be provided:

• 24-hour load demand profile

• Fuel cost coefficients for each of the three generators

• Lower and upper bounds for generator output

• Number of search agents and maximum number of iterations

This data is passed into the optimization routine to start the search for the optimal generation values.

Objective Function

The core of the optimization problem is the objective function, which calculates the fuel cost for a given power generation scenario. This function is defined using a custom script (get_function_details) and is essential for guiding the algorithm toward cost-effective solutions.

Implementation in MATLAB

Once the SSA is configured with the problem data and objective function, the MATLAB script is executed. SSA iteratively updates the power generation values of the three generators, aiming to minimize the fuel cost while satisfying the power demand at each hour.

The output during execution includes:

• Objective function value per iteration

• Power generation for each generator

• Sum of total generation and power losses

• Final minimized fuel cost for each time step

Results and Output

The results are compiled in a tabular format where each row corresponds to an hour in the 24-hour schedule. The columns include:

• Hour (1 to 24)

• Load demand

• Power generation from each of the three generators

• Total power generation

• Power loss

• Total fuel cost (including power loss)

This data clearly shows how the SSA dynamically adjusts the generator outputs to meet demand while minimizing cost and losses.

Performance and Visualization

The final output includes a graph plotting the objective function value versus iterations, which helps visualize the convergence behavior of SSA. This confirms that the algorithm efficiently reaches a near-optimal or optimal solution over time.

Conclusion

The Sparrow Search Algorithm proves to be a powerful tool for solving the Economic Load Dispatch problem in power systems. Its ability to minimize fuel cost while handling constraints and varying demand makes it highly suitable for real-world applications. Implementing SSA in MATLAB provides a hands-on way to understand and apply modern optimization techniques in the energy domain.