Modeling and Optimization of Power Transmission Capacity of Transmission Lines Using an Enhanced Evolutionary Algorithm

Resumo

The power transmission system in Brazil faces challenges due to aging infrastructure, as it has not been updated over the decades. With over 170,000 km of transmission lines, many operate with outdated configurations, limiting their capacity. In this context, a new methodology based on Differential Evolution (DE) algorithms is proposed to optimize the geometry of conductor bundles, aiming to increase the natural power of the line (SIL), while complying with safety limits and technical regulations. This study is based on the need to modernize transmission lines and make them more efficient. The adopted methodology is based on two main steps: electromagnetic modeling of the transmission line, along with the formulation of the optimization problem, and the application of three variants of the Differential Evolution algorithm. For modeling the transmission line problem, the calculation of electric charges is based on the voltage phasors applied to the conductors using Maxwell's potential coefficient matrix. The ground-level electric field is determined using Gauss's Law and the principle of superposition. The surface electric field is calculated using successive images. The SIL is calculated from the voltage and the ratio between the positive-sequence inductance and capacitance of the transmission line. In the optimization process, three variants of the Differential Evolution algorithm are applied: the Conventional DE, which uses random combinations of individuals; the DE with Per-vector dither, which applies a perturbation to each individual; and the Per-generation dither, which applies a perturbation to the entire generation of individuals.The methodology is applied to a 345 kV transmission line with two conductors per phase. There is a significant increase in the ground-level electric field values, although they remain within regulatory limits. The optimized geometries increase the bundle radius and reduce the phase spacing, resulting in an approximate 20% increase in SIL for all strategies. All surface electric field values remain below the calculated critical value.In summary, the proposed methodology is effective in optimizing the transmission capacity of transmission lines. The optimized geometries provided significant gains in SIL while complying with all considered constraints. The methodology can be expanded to include more realistic constraints and the use of hybrid optimization methods.