A Novel Enhancement of the Classical Lambda Iteration Method for Solving Economic Load Dispatch Problem of Cost Function With Integrated Renewables

Abstract

This paper presents a novel enhancement to the classical lambda iteration method for solving the economic load dispatch problem under modern power system conditions. The traditional LI method works well for simple cost functions, but it struggles with the complexities caused by valve-point effects and the growing use of renewable energy sources. Unlike metaheuristic methods that can be flexible but usually require a lot of computing power and are sensitive to how their settings are adjusted, the new λ-algorithm keeps the straightforward and predictable features of the original method while making it suitable for complicated situations involving non-convex costs and renewable energy sources. The algorithm incorporates mechanisms to handle non-smooth cost functions and account for variability from wind and solar generation. Its effectiveness is tested using simulations on four standard systems: an IEEE 57-bus system without renewable energy that cost $288,576; a modified IEEE 57-bus system with renewable energy that cost $283,774; a 38-generator system with a smooth cost function that cost $9,417,174.09 and CPU time of 1.3708 seconds; and a 40-generator system with valve-point effects that cost $121,714.07 and CPU time of 235.05 seconds. In all situations, the developed λ-algorithm provides affordable solutions while greatly cutting down on computing time, showing that it could be a useful, easy-to-use, and adaptable option for today's ELD problems.