Comparative Analysis of the Julia and AMPL Computational Tools Used in the Radial Distribution Network Optimization Problem - Hoyos Vallejo, Juan Camilo; Quintero Restrepo, Jaime (Ingeniería, 2024)
Context: Research on the development of mathematical models to optimize electric power distribution systems has become increasingly important in recent years. Choosing the right optimization tools and solvers to address optimization problems in these systems has therefore become fundamental. Method: Nonlinear and mixed-integer nonlinear mathematical models addressing optimal capacitor placement and the allocation of distributed generation were implemented in the AMPL and Julia platforms. These models together with the Ipopt, Knitro, and Bonmin solvers, were tested and compared using 33-, 69-, and 83-bus test systems. Results: The comparative analysis shows that AMPL allows for a more direct and adequate implementation of this type of optimization problem, while Julia requires more elaborate constructions. The experimental results show significant reductions in system losses through optimal capacitor and distributed generation placement. Conclusions: AMPL offers a faster learning curve and a syntax that is more suitable for mathematical modeling. On the other hand, Julia provides superior versatility and access to a wider diversity of solvers. Although the evaluated nonlinear solvers proved to be suitable for the non-convex models and reached equivalent solutions, Knitro, a commercial solver, exhibited shorter processing times. In this sense, choosing between free or commercial alternatives involves a compromise between processing times and the available budget. Furthermore, solving the aforementioned optimization problems effectively minimized losses in the test systems. These models are basic versions that can be extended to more complex optimization problems.