Energy Systems Optimization: A Linear Programming Approach to Power Grid Management

Abstract

This study presents a Linear Programming (LP) model for optimizing
power generation in energy systems with the objective of minimizing
total generation costs while meeting demand and operational
constraints. The model was formulated to allocate generation across
multiple units and demand nodes and implemented using Python’s
PuLP library. A case study involving three generators and three
demand centers was analyzed. The LP solution achieved a minimum
total generation cost of $7,200, compared to the baseline cost of
$9,000, representing a 20% cost reduction. Furthermore, the model
ensured all demand was satisfied without violating generator or
transmission capacity limits. Dual variable analysis revealed the
marginal cost of demand increments and confirmed economic dispatch
principles. These results validate the effectiveness of LP as a
computationally efficient and reliable approach for optimal power
flow and cost minimization in modern grid operations, with potential
extensions to renewable integration and smart grid applications.