# Evaluation of Filtered Spark Gap on the Lightning Protection of Distribution Transformers: Experimental and Simulation Study

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## Abstract

**:**

## 1. Introduction

## 2. Filtered Spark Gap-Based Model

#### 2.1. High Voltage Laboratory Experimental Setup

^{2}wire, resistance 571.8 $m\mathsf{\Omega}$, inductance 119 μH and (2) dimension 110 mm × 400 mm, 33 turns approximately, 0.33 mm

^{2}HV cable, resistance 450.8 $m\mathsf{\Omega}$, inductance 35 μH.

#### 2.2. Software Simulation Setup

#### 2.2.1. Applied Impulse

#### 2.2.2. Transformer Model

#### 2.2.3. Spark Gap

_{0}that the gap voltage becomes greater than v

_{0}, to time t in which the integral becomes greater than or equal to D.

_{0}are determined via the volt–time curve of the system and observing the withstand voltage of the dielectric under standard lightning overvoltages. Analytical and statistical methods are used to predict the behavior of the spark gap and calculate the best values for the aforementioned parameters [31]. However, more often than not, for the sake of simplicity and under the standard overvoltage impulses, k is set to 1.00 and the other two parameters are adjusted accordingly [30,32] as described in Section 3.

#### 2.2.4. Placement of the Inductor-Based Filter

## 3. Model Validation

#### 3.1. Test 1) Applying 110 kV and 125 kV Impulses in the Presence of the Spark Gap

#### 3.2. Test 2) Applying 110 kV and 125 kV Impulses in the Presence of the Proposed Filtered Spark Gap

## 4. Case Studies

#### 4.1. Case 1) Applying 110 kV and 125 kV Impulses in the Presence of the Filtered Spark Gap with Large and Small Inductors

#### 4.2. Case 2) Sensitivity Analysis over the Inductor Size Under 110 kV and 125 kV Impulses in the Presence of the Filtered Spark Gap

## 5. Comparisons and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Laboratory setup: (

**a**) complete laboratory setup and (

**b**) close-up for connecting the inductor and spark gap to the transformer terminal.

**Figure 2.**(

**a**) Adjustable spark gap with a brass electrode and (

**b**) connection of the spark gap to the middle terminal.

**Figure 4.**Connecting two voltage surges in series in Electromagnetic Transients Program-Restructured Version (EMTP-RV).

**Figure 6.**Generated lightning impulse voltage by connecting two surges in series, 125 kV, Laboratory Test and EMTP-RV model.

**Figure 10.**Comparison of the 110 kV laboratory impulse voltage with the impulses simulated in EMTP-RV by using the coefficients of double exponential functions adjusted for the 110 kV and 125 kV impulses.

**Figure 11.**Applied impulse 110 kV in the presence of the spark gap, laboratory test and EMTP-RV model.

**Figure 12.**Applied impulse 125 kV in the presence of the spark gap, laboratory test and EMTP-RV model.

**Figure 13.**Applied impulse 110 kV in the presence of 35$\mathsf{\mu}\mathrm{H}$ filtered spark gap, laboratory test and EMTP-RV model.

**Figure 14.**Applied impulse 110 kV in the presence of 119$\mathsf{\mu}\mathrm{H}$ filtered spark gap, laboratory test and EMTP-RV model.

**Figure 15.**Applied impulse 125 kV in the presence of the 35$\mathsf{\mu}\mathrm{H}$ filtered spark gap, laboratory test and EMTP-RV model.

**Figure 16.**Applied impulse 125 kV in the presence of 119$\mathsf{\mu}\mathrm{H}$ filtered spark gap, laboratory test and EMTP-RV model.

**Figure 17.**Applied impulse 110 kV in the presence of 500$\text{}\mathsf{\mu}\mathrm{H}$ filtered spark gap, EMTP-RV model.

**Figure 18.**Applied impulse 125 kV in the presence of 500$\mathsf{\mu}\mathrm{H}$ filtered spark gap, EMTP-RV model.

**Figure 19.**Applied impulse 110 kV in the presence of the 5$\text{}\mathsf{\mu}\mathrm{H}$ filtered spark gap, EMTP-RV model.

**Figure 20.**Applied impulse 125 kV in the presence of the 5$\mathsf{\mu}\mathrm{H}$ filtered spark gap, EMTP-RV model.

**Figure 22.**Applied impulse 125 kV in the presence of the (

**a**) spark gap, (

**b**) surge arrester, and (

**c**) filtered spark gap.

**Figure 23.**Applied impulse 110 kV in the presence of the (

**a**) spark gap, (

**b**) surge arrester, and (

**c**) filtered spark gap.

**Figure 24.**Comparison of the current flows after the connection points of the spark gap (SG) and surge arrester (SA).

**Figure 25.**Comparison of the current flows before the connection points of the spark gap (SG) and surge arrester (SA).

Inductor Size | $30\text{}\mathsf{\mu}H$ | $25\text{}\mathsf{\mu}H$ | $20\text{}\mathsf{\mu}H$ | $15\text{}\mathsf{\mu}H$ | $10\text{}\mathsf{\mu}H$ | $5\text{}\mathsf{\mu}H$ |
---|---|---|---|---|---|---|

Peak value (kV) | −110.222 | −109.417 | −108.659 | −107.977 | −107.483 | −107.973 |

Front time ($\mathsf{\mu}\mathrm{s}$) | 2.51 | 2.47 | 2.40 | 2.29 | 2.00 | 1.24 |

Inductor Size | $30\text{}\mathsf{\mu}H$ | $25\text{}\mathsf{\mu}H$ | $20\text{}\mathsf{\mu}H$ | $15\text{}\mathsf{\mu}H$ | $10\text{}\mathsf{\mu}H$ | $5\text{}\mathsf{\mu}H$ |
---|---|---|---|---|---|---|

Peak value (kV) | −124.361 | −124.202 | −124.018 | −123.799 | −123.600 | −123.798 |

Front time ($\mathsf{\mu}\mathrm{s}$) | 2.05 | 2.01 | 2.00 | 1.98 | 1.96 | 1.49 |

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**MDPI and ACS Style**

Pourakbari-Kasmaei, M.; Mahmood, F.; Krbal, M.; Pelikan, L.; Orságová, J.; Toman, P.; Lehtonen, M.
Evaluation of Filtered Spark Gap on the Lightning Protection of Distribution Transformers: Experimental and Simulation Study. *Energies* **2020**, *13*, 3799.
https://doi.org/10.3390/en13153799

**AMA Style**

Pourakbari-Kasmaei M, Mahmood F, Krbal M, Pelikan L, Orságová J, Toman P, Lehtonen M.
Evaluation of Filtered Spark Gap on the Lightning Protection of Distribution Transformers: Experimental and Simulation Study. *Energies*. 2020; 13(15):3799.
https://doi.org/10.3390/en13153799

**Chicago/Turabian Style**

Pourakbari-Kasmaei, Mahdi, Farhan Mahmood, Michal Krbal, Ludek Pelikan, Jaroslava Orságová, Petr Toman, and Matti Lehtonen.
2020. "Evaluation of Filtered Spark Gap on the Lightning Protection of Distribution Transformers: Experimental and Simulation Study" *Energies* 13, no. 15: 3799.
https://doi.org/10.3390/en13153799