#
A New Approach to Include Complex Grounding System in Lightning Transient Studies and EMI Evaluations^{ †}

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^{†}

## Abstract

**:**

## 1. Introduction

## 2. Parameters of the Grounding System

## 3. Modeling the Grounding System

## 4. Grounding Model Verification

#### 4.1. Grounding Rod of 15 m Length

#### 4.2. Grounding Grid of 10 m Meshes with Total Size 3600 m${}^{2}$

## 5. Integration of Grounding and Transmission System

## 6. An Example of Results: Case Study

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Glossaries

Symbol | Unit | Description | Page(s) |

a | m | Grounding conductor radius...................................... | 2, 4, 5, 7 |

$\alpha $ | - | Decay constant of double exponential source...................... | 4–6 |

$\beta $ | - | Crest constant of double exponential source....................... | 4–6 |

C | F | General term describing capacitance............................. | 2 |

d | m | Grounding conductor burial depth................................ | 2, 4–7 |

${E}_{c}$ | V/m | Critical electric field for soil ionization............................ | 2, 8 |

${E}_{soil}$ | V/m | Electric field strenght exerted on the soil.......................... | 2 |

G | S | General term describing conductance............................. | 2 |

I | A | General term describing current................................... | 6 |

${I}_{soil}$ | A | Current leaked from the ground per-unit lenght conductor to the soil................................................................ | 2 |

$\widehat{I}$ | A | Current magnitude of double exponential source.................. | 4–6 |

${J}_{soil}$ | A/m${}^{2}$ | Current density leaked to the soil................................. | 2 |

L | H | General term describing inductance............................... | 2 |

s | m | Grounding conductor spacing. | |

l | m | General term describing length................................... | 2, 5, 8 |

${\alpha}_{arr}$ | - | MOA Exponential factor to form the V-I characteristic............. | 12, 13 |

${k}_{seg}$ | - | MOA Voltage segment factor to form the V-I characteristic........ | 12, 13 |

${U}_{arr}$ | V | MOA Reference voltage for operation............................. | 12, 13 |

${\mu}_{0}$ | H/m | Permeability of vacuum: 4π × 10^{−7}. | 2 |

$\u03f5{r}_{soil}$ | - | Relative permittivity of the soil.................................... | 2, 4–7 |

${\u03f5}_{0}$ | F/m | Permittivity of vacuum: $\approx 8.8542\times {10}^{-12}$......................... | 2 |

${\rho}_{soil}$ | $\mathsf{\Omega}$m | Resistivity of soil.................................................. | 2, 4–7 |

U | V | General term describing voltage.................................. | 6 |

Y | S | General term describing admittance............................... | 2, 4 |

Z | $\mathsf{\Omega}$ | General term describing impedance............................... | 2, 4 |

$Z{c}_{c}$ | - | Cable surge impedance based on the lossless transmission line model ............................................................ | 7 |

$Z{c}_{l}$ | - | Transmission line surge impedance based on the lossless transmission line model........................................... | 7 |

## Abbreviations

Symbol | Description | Page(s) |

AWG | American Wire Gauge ............................................ | 5, 6 |

CIGRE | Conseil International des Grands Réseaux Électriques............. | 1 |

EMF | ElectroMagnetic Field. | 4, 5 |

EMI | ElectroMagnetic Interference ...................................... | 1, 2, 8 |

ICHVE | International Conference on High Voltage Engineering and Application ....................................................... | 10 |

IEEE | Institute of Electrical and Electronics Engineers ................... | 8 |

MTL | Multi-conductor Transmission Line ............................... | 4, 5 |

## Appendix A. Software and Integration

#### Appendix A.1. Software Versions

- MathWorks Matlab version 9.3, R2017b, 64-bit (14 September 2017)
- MathWorks Simulink version 9.0, R2017b, 64-bit (24 July 2017)
- MathWorks Simscape version 4.3 (18 November 2017)

- Powersys EMTP-RV 3.5 32-bit (17 January 2017)
- Powersys FMI Add-On for Matlab/Simulink (15 March 2018)

#### Appendix A.2. Matlab/Simulink and EMTP-RV FMI Interface

**Figure A1.**The Matlab/Simulink FMI interface to EMTP-RV with the signals transferred between the softwares and block representation of the integration.

## Appendix B. Matlab/Simulink Simulation Log Definition

Node (Figure 1) | Log-File Name | Grid Segment (Figure 2) | Element | Series Selection |
---|---|---|---|---|

${V}_{l1}$ | simlog_scc_grounding_system. | X/Y’y-dir’_’x-dir’. | l1.v. | series.values/time |

${A}_{l1}$ | simlog_scc_grounding_system. | X/Y’y-dir’_’x-dir’. | l1.i. | series.values/time |

${V}_{l2}$ | simlog_scc_grounding_system. | X/Y’y-dir’_’x-dir’. | l2.v. | series.values/time |

${A}_{l2}$ | simlog_scc_grounding_system. | X/Y’y-dir’_’x-dir’. | l2.i. | series.values/time |

${V}_{1n}$ | simlog_scc_grounding_system. | X/Y’y-dir’_’x-dir’. | p1.v. | series.values/time |

${V}_{2n}$ | simlog_scc_grounding_system. | X/Y’y-dir’_’x-dir’. | p2.v. | series.values/time |

${A}_{g}$ | simlog_scc_grounding_system. | X/Y’y-dir’_’x-dir’. | g.i. | series.values/time |

${V}_{gc}$ | simlog_scc_grounding_system. | X/Y’y-dir’_’x-dir’. | p.v. | series.values/time |

${A}_{c}$ | simlog_scc_grounding_system. | X/Y’y-dir’_’x-dir’. | c.i. | series.values/time |

## Appendix C. EMTP-RV Surge Arrester Parameterization V-I characteristics

Segment | ${\mathit{k}}_{\mathbf{seg}}$ | ${\mathit{\alpha}}_{\mathbf{arr}}$ | ${\mathit{U}}_{\mathbf{arr}}$ (pu) |
---|---|---|---|

1 | 4.23208099271728 × 10${}^{9}$ | 2.40279296219991 × 10${}^{1}$ | 2.98198270953446 × 10${}^{-1}$ |

2 | 2.81773645053899 × 10${}^{10}$ | 2.66219333383972 × 10${}^{1}$ | 4.81500000000002 × 10${}^{-1}$ |

3 | 4.15144087019289 × 10${}^{8}$ | 2.00870413085783 × 10${}^{1}$ | 5.24450368910346 × 10${}^{-1}$ |

4 | 2.63271405014350 × 10${}^{12}$ | 3.52906710089596 × 10${}^{1}$ | 5.62230840318764 × 10${}^{-1}$ |

5 | 3.21774149817822 × 10${}^{6}$ | 1.11310570543270 × 10${}^{1}$ | 5.69192036592734 × 10${}^{-1}$ |

6 | 1.93774621300766 × 10${}^{5}$ | 5.36270125014300 | 6.14408449804349 × 10${}^{-1}$ |

## References

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**Figure 3.**Voltage distribution along an horizontal copper wire in ground (length l = 15 m, conductor radius a = 0.012 m, at soil depth d = 0.6 m) in soil of ${\rho}_{soil}$ = 70 $\mathsf{\Omega}$m and $\u03f5{r}_{soil}$ = 15: (

**a**) the reproduced results for comparison from the research given in [11] (p. 818); and (

**b**) results from implemented model with excitation current $\widehat{I}$ = 36 A of double exponential waveform ($\alpha $ = 32 × 10${}^{3}$, $\beta $ = 7.6 × 10${}^{6}$).

**Figure 4.**Voltage distribution in a grounding grid consisting of 6 × 6 meshes of 10 m size. The grounding grid consist of copper conductors of AWG 2/0, buried at d = 0.6 m in soil of ${\rho}_{soil}$ = 100 $\mathsf{\Omega}$m and $\u03f5{r}_{soil}$ = 36: (

**a**) the reproduced results for comparison from research given in [7] (p. 31); and (

**b**) results from implemented model with excitation current $\widehat{I}$ = 1 kA of double exponential waveform ($\alpha $ = 38 × 10${}^{3}$, $\beta $ = 2.54 × 10${}^{6}$).

**Figure 7.**Ignoring grounding system: transmission system nodal voltages and CIGRE 1.2/50 $\mathsf{\mu}$s injected current stroke in far-end (l${}_{l}$ = 10 km).

**Figure 8.**Application case when the grounding system is added: (

**a**) the effect in the transmission system; and (

**b**) the results at the surge arrester injection point.

**Figure 9.**Application case when the grounding system is added: (

**a**) nodal voltage measurement values for selected points in the grounding grid; (

**b**) the overall voltage distribution in the grounding grid at peak; and (

**c**) the overall voltage distribution in the grounding grid at corner peak.

**Table 1.**Required number of logged variables for grounding grid of two different square mesh sizes and total area values.

Grounding Grid | Area | Variables |
---|---|---|

5 × 5 m mesh | 1600 m${}^{2}$ | 6480 |

3600 m${}^{2}$ | 14040 | |

10 × 10 m mesh | 1600 m${}^{2}$ | 3600 |

3600 m${}^{2}$ | 7560 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Steinsland, V.; Sivertsen, L.H.; Cimpan, E.; Zhang, S. A New Approach to Include Complex Grounding System in Lightning Transient Studies and EMI Evaluations. *Energies* **2019**, *12*, 3142.
https://doi.org/10.3390/en12163142

**AMA Style**

Steinsland V, Sivertsen LH, Cimpan E, Zhang S. A New Approach to Include Complex Grounding System in Lightning Transient Studies and EMI Evaluations. *Energies*. 2019; 12(16):3142.
https://doi.org/10.3390/en12163142

**Chicago/Turabian Style**

Steinsland, Vegard, Lasse Hugo Sivertsen, Emil Cimpan, and Shujun Zhang. 2019. "A New Approach to Include Complex Grounding System in Lightning Transient Studies and EMI Evaluations" *Energies* 12, no. 16: 3142.
https://doi.org/10.3390/en12163142