# An Approach to Diagnostics of Geomagnetically Induced Currents Based on Ground Magnetometers Data

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

^{2}). However, ANN-based methods are less interpretable and require more computer resources.

## 1. Introduction

^{2}, which is not sufficient to provide effective diagnostics of GIC for objective reasons.

## 2. Initial Data, Their Preliminary Analysis and Preprocessing

_{F}is total downtime of the data source, T is an operating time, T

_{W}is number of informative values (total operating time) for the time period T. In this example T = 525,600 min (365 days).

_{i}and T2F

_{i}are the time until the i-th system recovery after a failure and the time before the i-th system failure, respectively; N

_{F}and N

_{W}are the number of system failures and the number of failover recoveries, respectively; k = 1 or k = 0, if at the time of the start of observation the system was in a working or inoperative state, respectively.

_{i}= |B

_{i}

_{+1}−B

_{i}

_{−1}|/2Δt. At the final stage, to minimize the stochastic component, the time series are averaged over 15-min ranges. Thus, the size of the final sample includes ~35,040 values (including gaps) for each data source, which is enough to identify statistical relationships. In magnetometer data analysis, the main attention has been paid to the east–west component Y, because this component corresponds to the north–south (X) telluric electric field Ex, driving GIC along the latitudinally extended power line [16].

## 3. Statistical and Correlation Analysis

## 4. Synthesis and Validation of ML Models for the GIC Diagnostics

^{2}showed that, for the diagnostics of the GIC values |J

_{VKH}|, the use of the geomagnetic field variability from nearby magnetic stations is reasonable. Here, we apply the methods based on multiple linear regression and an artificial neural network (ANN). The regression relationship is as follows:

^{T}= (x

_{1,}x

_{2, …,}x

_{k}) is a vector of regressors; β

^{T}= (β

_{1,}β

_{2, …,}β

_{k}) is a vector column of coefficients; and k is a number of model input variables.

_{1}= λ, λ

_{2}= 0, where λ is a regularization parameter) and ridge regression (λ

_{2}= λ, λ

_{1}= 0) [21]:

**X**is the n×k predictor matrix of standardized variables;

**y**is the response vector.

_{SOD}/dt| has the least quality at a sufficiently high correlation coefficient with the objective function (Table 3). This may indicate the multicollinearity of the regressors and the necessity to exclude |dY/dt| from SOD analysis.

_{0}= 0.1; β

_{1}= 90.56 × 10

^{−3}; β

_{2}= 32.25 × 10

^{−3}; β

_{3}= 32.36 × 10

^{−3}; β

_{4}= 0.37 × 10

^{−3}.

## 5. Discussion

## 6. Conclusions

^{2}) compared to the regression methods (MSE = 0.122 A

^{2}). However, the ANN methods are less interpretable and require more computational power when implemented. The MSE of the obtained relationship for the GIC diagnostics is ~7.5 times lower than the MSE of similar expressions obtained previously in [12]. This advancement has been achieved thanks to a detailed analysis and careful selection of feature objects, comprising statistical analysis of heavy tails, pairwise correlation analysis, and assessing the quality of the regression model’s feature objects, etc.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Kataoka, R.; Ngwira, C. Extreme geomagnetically induced currents. Prog. Earth Planet. Sci.
**2016**, 3, 23. [Google Scholar] [CrossRef] - Danilov, G.E. Improving the quality of the operation of power lines; Direct-Media: Moscow, Russia; Berlin, Germany, 2015; p. 127. [Google Scholar]
- Schrijver, C.J.; Dobbins, R.; Murtagh, W.; Petrinec, S.M. Assessing the impact of space weather on the electric power grid based on insurance claims for industrial electrical equipment. Space Weather
**2014**, 12, 487–498. [Google Scholar] [CrossRef][Green Version] - Boteler, D.H. Modeling geomagnetic interference on railway signaling track circuits. Space Weather
**2021**, 19, e2020SW002609. [Google Scholar] [CrossRef] - Sakharov, Y.; Kudryashova, N.; Danilin, A.; Kokin, S.; Shabalin, A.; Pirjola, R. Influence of geomagnetic disturbances on the operation of railway automatics. MIIT Bull.
**2009**, 21, 107–111. [Google Scholar] - Pilipenko, V.A. Space weather impact on ground-based technological systems. Solar-Terrestrial Phys.
**2021**, 7, 68–104. [Google Scholar] [CrossRef] - Kozyreva, O.V.; Pilipenko, V.A.; Zakharov, V.I.; Engebretson, M.J. GPS–TEC response to the substorm onset during April 5, 2010, magnetic storm. GPS Solut.
**2017**, 21, 927–936. [Google Scholar] [CrossRef] - Sakharov, Y.A.; Danilin, A.N.; Ostafiychuk, R.M. Registration of GIC in Power Systems of the Kola Peninsula. In Proceedings of the 2007 7th International Symposium on Electromagnetic Compatibility and Electromagnetic Ecology, St. Petersburg, Russia, 26–29 June 2007; pp. 291–292. [Google Scholar]
- Marshall, R.A.; Smith, E.A.; Francis, M.J.; Waters, C.L.; Sciffer, M.D. A preliminary risk assessment of the Australian region power network to space weather. Space Weather
**2021**, 9, S10004. [Google Scholar] [CrossRef][Green Version] - Marshall, R.A.; Waters, C.L.; Sciffer, V.D. Spectral analysis of pipe-to-soil potentials with variations of the Earth’s magnetic field in the Australian region. Space Weather
**2010**, 8, S05002. [Google Scholar] [CrossRef] - Švanda, M.; Smičková, A.; Výbošťoková, T. Modelling of geomagnetically induced currents in the Czech transmission grid. Earth Planets Space
**2021**, 73, 229. [Google Scholar] [CrossRef] - Vorobev, A.; Pilipenko, V.; Sakharov, Y.; Selivanov, V. Statistical relationships of variations in the geomagnetic field, auroral electrojet and geoinduced currents. Solar-Terrestrial Phys.
**2019**, 5, 48–58. [Google Scholar] - Vorobev, A.; Pilipenko, V.; Sakharov, Y.; Selivanov, V. Statistical properties of the geomagnetic field variations and geomagnetically induced currents. In Problems of Geocosmos–2018; Springer Proceedings in Earth and Environmental Sciences; Springer: Cham, Switzerland, 2020. [Google Scholar]
- Vorobev, A.V.; Pilipenko, V.A. Geomagnetic data recovery approach based on the concept of digital twins. Solar-Terrestrial Phys.
**2021**, 2, 48–56. [Google Scholar] [CrossRef] - Gjerloev, J.W. The SuperMAG data processing technique. J. Geophys. Res.
**2012**, 117, A09213. [Google Scholar] [CrossRef] - Yagova, N.V.; Pilipenko, V.A.; Sakharov, Y.A.; Selivanov, V.A. Spatial scale of geomagnetic Pc5/Pi3 pulsations as a factor of their efficiency in generation of geomagnetically induced currents. Earth Planets Space
**2021**, 73, 88. [Google Scholar] [CrossRef] - Vorobev, A.; Vorobeva, G. Properties and type of latitudinal dependence of statistical distribution of geomagnetic field variations. In Trigger Effects in Geosystems; Springer Proceedings in Earth and Environmental Sciences; Springer: Cham, Switzerland, 2019. [Google Scholar]
- Kleimenova, N.G.; Kozyreva, O.V. Spatiotemporal dynamics of geomagnetic pulsations Pi3 and Pc5 during extreme magnetic storms in October 2003. Geomagnet. Aero.
**2005**, 45, 71–79. [Google Scholar] - Freeman, M.P.; Forsyth, C.; Rae, I.J. The influence of substorms on extreme rates of change of the surface horizontal magnetic field in the United Kingdom. Space Weather
**2019**, 17, 827–844. [Google Scholar] [CrossRef][Green Version] - Apatenkov, S.V.; Pilipenko, V.A.; Gordeev, E.I.; Viljanen, A.; Juusola, L.; Belakhovsky, V.B.; Sakharov, Y.A.; Selivanov, V.N. Auroral omega bands are a significant cause of large geomagnetically induced currents. Geophys. Res. Lett.
**2018**, 47, e2019GL086677. [Google Scholar] [CrossRef] - Zou, H.; Hastie, T. Regularization and variable selection via the elastic net. J. R. Stat. Soc. Ser. B
**2005**, 67, 301–320. [Google Scholar] [CrossRef][Green Version] - Kononenko, I.; Šimec, E.; Robnik-Šikonja, M. Overcoming the Myopia of Inductive Learning Algorithms with RELIEFF. Appl. Intell.
**1997**, 7, 39–55. [Google Scholar] [CrossRef] - Heyns, M.; Gaunt, C.T.; Lotz, S.; Cilliers, P. Data Driven Transfer Functions and Transmission Network Parameters for GIC Modelling. Electr. Power Syst. Res.
**2020**, 188, 106546. [Google Scholar] [CrossRef] - Pulkkinen, A.; Hesse, M.; Habib, S.; Van der Zel, L.; Damsky, B.; Policelli, F.; Fugate, D.; Jacobs, W. Solar Shield: Forecasting and mitigating space weather effects on high-voltage power transmission systems. Nat. Hazard.
**2009**, 53, 333–345. [Google Scholar] [CrossRef] - Ingham, M.; Rodger, C.J. Telluric field variations as drivers of variations in cathodic protection potential on a natural gas pipeline in New Zealand. Space Weather
**2018**, 16, 1396–1409. [Google Scholar] [CrossRef]

**Figure 1.**Geography of data sources: magnetometers (green circles) and GIC recording station (red circle). Black solid lines denote the 330/440 kV power lines.

**Figure 2.**A fragment of the time series (averaged over 15-min intervals) of the initial data, comprising the magnetic storm on 17 March 2015. In the time series of the Y component of the geomagnetic variations, the baseline has been excluded.

**Figure 3.**Statistics of the distribution of the GIC magnitudes |J| at VKH station (

**a**) and the rate of the change of the Y-component of geomagnetic variations recorded at IVA station (

**b**) for 2015 (Δt = 1 min). Red solid and dashed lines correspond to PDF and SF of the log-normal distribution, green solid and dashed lines describe the tail of the distribution and the PDF and SF of the generalized Pareto distribution; the black solid line corresponds to ESF.

**Figure 4.**Estimation of the GIC level |J

_{VKH}| using the regression and ANN models for the magnetic storm of 24 February 2015 (Kp = 5) (

**a**) and 17 March 2015 (Kp = 8) (

**b**).

**Figure 5.**Estimation of the GIC level |J

_{VKH}| for 27–28 September 2017 (Kp = 7) event based on expression (6) with regression coefficients for 2015 (green line) and with coefficients recalculated for the period under consideration (red line). The values of the time series are averaged over 15 min intervals.

No. | Data Source | Coordinates | ||||
---|---|---|---|---|---|---|

Geographic | Geomagnetic | |||||

Station | Code | Latitude, [N] | Longitude, [E] | Latitude, [N] | Longitude, [E] | |

1 | Vykhodnoy | VKH | 68.83 | 33.08 | 64.41 | 125.95 |

2 | Ivalo | IVA | 68.56 | 27.29 | 64.97 | 121.14 |

3 | Kevo | KEV | 69.76 | 27.01 | 66.25 | 121.60 |

4 | Sodankylä | SOD | 67.37 | 26.63 | 63.96 | 119.54 |

5 | Lovozero | LOZ | 67.97 | 35.02 | 64.77 | 114.60 |

No. | Data Source | T_{W} | T_{F} | N_{F} = N_{W} | <T2R> | <T2F> | ||
---|---|---|---|---|---|---|---|---|

[min] | [%] | [min] | [%] | [min] | [min] | |||

1 | VKH | 511,200 | 97.26 | 14,400 | 2.74 | 7 | 2057.1 | 73,028.6 |

2 | IVA | 478,290 | 91.00 | 47,310 | 9.00 | 13 | 3639.2 | 36,791.5 |

3 | KEV | 525,521 | 99.98 | 79 | 0.02 | 8 | 9.9 | 65,690.1 |

4 | SOD | 521,160 | 99.16 | 4440 | 0.84 | 5 | 888.0 | 104,232.0 |

5 | LOZ | 501,623 | 95.44 | 23,977 | 4.56 | 21 | 1141.8 | 23,886.8 |

**Table 3.**Correlation of the values |J

_{VKH}| with values of geomagnetic variations (data averaged over 15 min intervals).

|dY_{LOZ}/dt| | |dY_{IVA}/dt| | |dY_{SOD}/dt| | |dY_{KEV}/dt| | IE-Index | |
---|---|---|---|---|---|

r | 0.882 | 0.878 | 0.847 | 0.841 | 0.772 |

Approach | Metric | |||
---|---|---|---|---|

R^{2} | MSE | RMSE | MAE | |

Regression | 0.807 | 0.122 | 0.349 | 0.168 |

ANN | 0.812 | 0.119 | 0.345 | 0.156 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Vorobev, A.; Soloviev, A.; Pilipenko, V.; Vorobeva, G.; Sakharov, Y.
An Approach to Diagnostics of Geomagnetically Induced Currents Based on Ground Magnetometers Data. *Appl. Sci.* **2022**, *12*, 1522.
https://doi.org/10.3390/app12031522

**AMA Style**

Vorobev A, Soloviev A, Pilipenko V, Vorobeva G, Sakharov Y.
An Approach to Diagnostics of Geomagnetically Induced Currents Based on Ground Magnetometers Data. *Applied Sciences*. 2022; 12(3):1522.
https://doi.org/10.3390/app12031522

**Chicago/Turabian Style**

Vorobev, Andrei, Anatoly Soloviev, Vyacheslav Pilipenko, Gulnara Vorobeva, and Yaroslav Sakharov.
2022. "An Approach to Diagnostics of Geomagnetically Induced Currents Based on Ground Magnetometers Data" *Applied Sciences* 12, no. 3: 1522.
https://doi.org/10.3390/app12031522