# Impact of Grounding Modeling on Lightning-Induced Voltages Evaluation in Distribution Lines
## 5 Test Cases  
This section presents the test cases related to the comparison between two different grounding modeling, i.e., the low-frequency grounding resistance (\(R_{LF}\)) and the harmonic grounding impedance (\(Z(\omega)\)). Let us consider a 1.2 km matched three-phase DS (Figure 1). The three-phase conductors' heights are 10, 11 and 12 m, respectively, while the shield wire height is 14 m. The horizontal distance between each conductor and the shield wire is 2.4 m. The conductors' diameter is 1.83 cm, while the shield wire diameter is 0.72 cm. The span between each tower is 50 m. To consider the influence of the adjacent towers, a total of five towers are modeled in detail, because the towers in longer distance have little impact on the overvoltage. According to [52], for lightning-related phenomena adjacent towers place a moderate influence. Each tower is 14 m high and with a base diameter of 0.5 m. According to Equation (3), a value of \(Z_{c}=244.17\)\(\Omega\) is considered. The propagation velocity along the tower is considered to be 0.8c [53; 54]. Moreover, the insulators are modeled taking into account their parasitic capacitance. The value of parasitic capacitance of each insulator is 7.68 nF, and they were calculated considering the information in [55; 56; 57]. Each tower is grounded with a grounding system as shown in Figure 2. This is a typical configuration for grounding distribution networks in the State of Minas Gerais, Brazil. It consists of three vertical rods 2.5 m long interconnected by a horizontal galvanized steel cable 6 m long. The vertical rods are copper-plated steel, with a diameter of 15 mm. The equivalent circuit of the system composed of a three-phase distribution line, tower and grounding system is shown in Figure 3.  
Two cases for the soil parameters will be considered. The soil conductivity and permittivity will be frequency-dependent according to [31], where \(\sigma_{0}=10\) mS/m and 1 mS/m, respectively. These cases correspond to two different grounding harmonic responses according to the grounding modeling proposed in Section 4. Figures 4 and 5 show \(Z(\omega)\) and \(R_{LF}\) of the two considered cases. Based on the behaviors described in these figures, it is possible to verify that: (i) grounding can only be represented by \(R_{LF}\) in the low-frequency range, where \(Z(\omega)\) tends to \(R_{LF}\); (ii) the limit frequency of the low-frequency range increases with a reduction in conductivity; (iii) in the intermediate-frequency range there is a predominance of capacitive behavior of the grounding, verified by the decrease of \(Z(\omega)\) in relation to the \(R_{LF}\); (iv) the limit frequency of the intermediate-frequency range also increases with the reduction in conductivity and (v) only in the high-frequency range inductive effect is predominant, mainly for higher conductivity values. Thus, the response of the system under study (DS and grounding) will be a direct function of the frequency spectrum of the electromagnetic signal that requests it. As a consequence, it is expected that the overvoltages in the insulator string are sensitive to grounding modeling. Figure 1: Line configuration. Figure 2: Grounding grid of the distribution tower. When we consider a grounding model described by \(R_{LF}\), the implementation in the EMT-type software is trivial, while when we consider the harmonic grounding impedance, it is possible to obtain the synthesis of the electric circuit to be implemented in the EMT-type software by using the approach presented in Section 4. The general layout of the circuit obtained from the Vector fitting approach is described in Figure 6, while the values of the passive circuit are proposed in Tables 1 and 2 for \(\sigma=10\) mS/m and in Tables 3 and 4 for \(\sigma=1\) mS/m.