Densidade de corrente de Maxwell no modelo do circuito elétrico global: nova modelagem da origem e da trajetória das descargas atmosféricas - Rodrigues, Ednardo Moreira (2019)
Lightning present risks to human and animal life and to power grids. This natural phenomenon stems, mostly, from Cumulonimbus storm clouds, which function as generators in the global electric circuit model (GECM). The GECM is described by means of Maxwell’s current density. In the atmosphere, Maxwell’s current density has four terms, two of which are still subject of discussion in academia: the convection current density and the lightning current density. The convection current density model is proposed in three stages: (i) auto-ionization, (ii) diffusion and (iii) precipitation. At auto-ionization, the availability of charges is estimated through the water auto-ionization. At step ii, the rate of charging of a cloud particle is established as a function of its growing rate related to its size and physical state. At stage iii, a separation of charges occur due to different precipitation rates of the cloud particles responsible for the typical three or four-pole structure in storm clouds. Analytically, convection current densities of 53 nA.m ́2 can be reached in a storm, while the value accepted by the global electric circuit model is 56 nA.m ́2 . A simulation was carried out in three dimensions of a simplified storm cloud. The variation of the electric conductivity of air in function of the altitude was taken into account. This time-domain simulation was carried out through a Finite Element Method modeling using COMSOL Multiphysics R software. The air current density inside of the cylinder makes the potential and electric field increase with time. The air’s dielectric strength of 111 kV.m ́1 at a 5 km height was overcome in 1 min and 15 s, and the difference of potential stabilized at 230 MV, exceeding the GECM’s value of 200 MV in 15 %. These results indicate that the cloud’s electrification model proposed provides an adequate description of the storm cloud’s charging process. In this work it is also proposed a model for the lightning trajectory, which is important for the elaboration of lightning incidence models for . The proposed incidence model is based on the deflection of the electric field due to the ionization of the medium, and is therefore named EFD. This deflection can be found through a numerical solution to Poisson’s equation using Finite Element Method. The results obtained through EFD simulations are similar to MEG for structures with symmetric distribution of electric potential, such as a high- voltage three-phase transmission line. However, for a HVDC line, the electrogeometric model does not take into account the different potentials at each pole of this line. That explains the importance of a physical model, like EFD, and not simply geometrical. Four lightning current levels (3 kA, 5 kA, 10 kA e 16 kA) are used according to Associação Brasileira de Normas Técnicas (2015) NBR 5419. The EFD analysis showed that the classic positioning of the arrestor cables on a HVDC line present considerable shielding failure, especially on the positive pole, as 90 % of cloud-ground lightning are of negative polarity. Thus, a horizontal shifting of the arrestor cables was proposed, reducing SFW in 50 % for lightning with current peak of 3 kA. For the other current levels, SFW was under 1 m, which can be negligible in comparison to the altitude between 2 to 5 km at which lightning originate. The simple EFD proved itself efficient in comparison to classical incidence models. In order to make the trajectories generated by the model closer to the real phenomenon, however, distributions (textures) of electric permittivity of air were created by means of the fBm technique. Many textures were created to represent different storms and, at each one, 73 lightning were simulated for the four current levels previously presented. The air-termination system for a three-phase transmission line was assessed in two transverse planes: (i) the tower plane and (ii) in the middle of the span region. The analysis for the tower plane indicate that the air-termination system intercepted 96.94 % of lightning with current peak of 2.9 kA. In the span region the efficiency of the air-termination dropped to 84.46 % for this same current level.