Lagrangian Method Based on Population Applied to Optimal Power Flow Problems

This paper approaches the issue of finding multiple optima in Optimal Power Flow (OPF) problems using a modified Artificial Immune System (AIS) algorithm. The original AIS algorithm is a methodology based on natural immune systems and intends to capture three major immunological principles: hypermutation, receptor edition and cellular memory. These characteristics enable the assessment of multiple optima using local and global search. The proposed algorithm improves the original AIS methodology by enhancing the hypermutation process (HP) and applying another immunological principle: the maturation control. The new HP uses numerical information gathered during the convergence process to reduce the number of clones, while the maturation control is responsible for eliminating redundant antibodies, reducing the initial population. Finally, to ensure optimality, the algorithm uses an approach based on the augmented Lagrangian function to find the Karush-Kuhn-Tucker (KKT) conditions. Several case results obtained with different systems illustrate the proposed AlS-based approach.