# Estimation of geomagnetically induced currents based on the measurement data of a transformer in a Japanese power network and geoelectric field observations

- Shinichi Watari
^{1}Email author

**Received: **26 October 2014

**Accepted: **19 May 2015

**Published: **27 May 2015

## Abstract

Geomagnetically induced currents (GICs) have the potential to cause electric power blackouts. Hence, it is important to study the effects of GICs produced by intense geomagnetic storms. The measurements of GICs were conducted at the Memanbetsu substation, Hokkaido, between December 2005 and March 2008. We obtain the complementary cumulative distribution function (CCDF) of the measured GICs and the empirical equation to estimate GICs using the GIC data and geoelectric field observation data. GICs associated with the past intense geomagnetic storms, e.g., the March 13–15 storm and the October 29–30, 2003 storm, are estimated.

## Keywords

## Background

The effects of geomagnetically induced currents (GICs) on electric power grids have been observed since the 1940s (Boteler 2001). An electric power blackout occurred in Quebec, Canada, during the March 13–15, 1989 storm (Boteler et al. 1989; Kappenman 1989; Boteler 2001). In southern Sweden, the GIC caused an electric power blackout on October 30, 2003 (Kappenman 2005).

The occurrence of strong GICs is often associated with strong auroral electrojet currents at geomagnetically high latitudes (Thomson et al. 2011; Pulkkinen et al. 2012). Japan is located at a geomagnetically lower latitude compared to its geographical latitude. It is believed that the possibility of power grid problems caused by GICs is lower because of the country’s location at geomagnetically low latitude. However, it was reported that long distance telegraph lines between Tokyo and the regions outside Tokyo (the Tokyo-Yokkaichi line, the Tokyo-Matsumoto line, the Tokyo-Ogasawara line, the Tokyo-Guam line, and so on) were affected by GICs caused by a geomagnetic storm on September 25, 1909 in Japan (Uchida 1909). Kappenman (2004) noted that large GICs are produced by geomagnetic disturbances driven by the intensification of the ring and magnetopause currents at low latitudes. Gaunt and Coetzee (2007) reported damage to transformers caused by GICs in South Africa as a result of series of intense geomagnetic storms between the end of October and the beginning of November in 2003. The geomagnetic latitude of South Africa is similar to that of Japan. This suggests a possibility of GIC effects in countries with lower geomagnetic latitudes such as Japan if an extremely large geomagnetic storm, such as the Carrington storm on September 1–2, 1859, occurs (Watari et al. 2001; Tsurutani et al. 2003; Committee on the Societal and Economic Impacts of Severe Space Weather Events 2008; The working group on extreme solar weather of the Royal Academy of Engineering 2013). Pulkkinen et al. (2012) and Bernabeu (2013) made studies on extreme 100-year geoelectric field scenarios. In Spain located in low geomagnetic latitude, Torta et al. (2014) studied the effect of GICs on the Spanish high-voltage power network.

In a Japanese power network, GIC measurements were conducted between December 2005 and March 2008 as part of the close collaboration among National Institute of Information and Communications Technology (NICT), Hokkaido Electric Power Co., and Solar-Terrestrial Environment Laboratory (STEL) at Nagoya University (Watari et al. 2009). We obtained the empirical equations of GICs using the GIC measurement data and geoelectric field data and estimated GICs associated with the past intense geomagnetic storms.

## Methods

### Data

## Results and discussion

### Observed GICs in Hokkaido

Large GIC events measured between December 2005 and March 2008

Number | Date and time (UT) | Max. GIC of 1-s data (A) | Geomagnetic disturbances at Memanbetsu |
---|---|---|---|

1 | 14 December 2006 at 23:55 | 3.85 | SC storm (max. ∆ |

2 | 10 November 2006 around 10:04 | 2.23 | Gradual storm (max. ∆ |

3 | 23 May 2007 at 10:40 | 1.81 | Positive bay |

4 | 30 November 2006 around 09:09 | 1.75 | Gradual storm (max. ∆ |

5 | 9 July 2006 at 21:39 | 1.59 | Sudden impulse |

6 | 14 April 2006 around 10:15 | 1.58 | Gradual storm (max. ∆ |

7 | 19 August 2006 around 14:22 | 1.52 | Gradual storm (max. ∆ |

### Probability occurrence of GICs and electric field observation

*x*

_{crit}is expressed below.

*p*(

*x*) follows a power law distribution:

*α*and

*C*are some fixed values.

*x*

_{crit}during some time Δ

*t*assuming the events occur independently of one another. The probability of in Δ

*t*is given by the equation below.

*N*is the number of events in the data set and

*τ*is the total time span of the data set.

*N*becomes the number of events equal to or greater than 0.5 A. The exponent value of

*α*of 5.11 and the value of

*C*of 0.0030 are obtained by using the data in Fig. 4. We can calculate the probability using Eq. 3. For example, the probability with 95 % confidence interval of GIC value equal to or greater than 10 A is 5.8 × 10

^{−8}[3.5 × 10

^{−10}, 9.5 × 10

^{−6}]. The probability of GIC ≥ 100 A is 4.5 × 10

^{−12}[2.6 × 10

^{−14}, 7.8 × 10

^{−10}]. According to Eq. 4, the probabilities with 95 % confidence interval of GIC ≥ 10 A in 50 and 100 years are 0.67 [0.0067, 1.0] and 0.89 [0.013, 1.0], respectively. And the probabilities of GIC ≥ 100 A in 50 and 100 years are 8.7 × 10

^{−5}[5.0 × 10

^{−7}, 1.4 × 10

^{−2}] and 1.7 × 10

^{−4}[1.0 × 10

^{−6}, 2.9 × 10

^{−2}], respectively.

*N*is the number of data equal to or greater than 0.003 V/km. The exponent value of

*α*of 4.98 and the value of C of 2.11 × 10

^{−9}are obtained by using the data in Fig. 5. The probability with 95 % confidence interval of geoelectric fields |E| equal to or greater than 1.0 V/km is 5.3 × 10

^{−10}[4.9 × 10

^{−12}, 5.7 × 10

^{−8}] and that of |E| ≥ 5.0 V/km is 8.7 × 10

^{−13}[8.1 × 10

^{−15}, 9.3 × 10

^{−11}]. Using Eq. 4, the probabilities of |E| ≥ 1.0 V/km in 50 and 100 years are 1.2 × 10

^{−2}[1.1 × 10

^{−4}, 7.3 × 10

^{−1}] and 2.4 × 10

^{−2}[2.3 × 10

^{−4}, 9.3 × 10

^{−1}], respectively. The probabilities of |E| ≥ 5.0 V/km in 50 and 100 years are 2.0 × 10

^{−5}[1.9 × 10

^{−7}, 2.2 × 10

^{−3}] and 4.0 × 10

^{−5}[3.7 × 10

^{−7}, 4.3 × 10

^{−3}], respectively.

Largest geoelectric fields observed between 1958 and 2014 at the Memanbetsu Observatory

Number | Date and time (UT) | Max. |E| of 1-min data (V/km) | Geomagnetic disturbances at Memanbetsu |
---|---|---|---|

1 | 13 March 1989 at 21:58 | 0.184 | SC storm (max. ∆ |

2 | 8 November 1991 at 22:17 | 0.137 | SC storm (max. ∆ |

3 | 29 October 2003 at 19:54 | 0.123 | SC storm (max. ∆ |

4 | 30 October 2003 at 19:54 | 0.120 | SC storm (max. ∆ |

5 | 14 March 1989 at 00:03 | 0.115 | SC storm (max. ∆ |

6 | 15 July 2000 at 21:36 | 0.115 | SC storm (max. ∆ |

7 | 24 March 1991 at 04:02 | 0.115 | SC storm (max. ∆ > 467 nT) |

8 | 6 November 2001 at 02:02 | 0.104 | SC storm (max. ∆ |

*ΔH*| of difference of 1 hour values of horizontal component of Memanbetsu geomagnetic field greater than values of horizontal axes. There is a power law relation for the value equal to or greater than 20 nT/hour (see the vertical dotted line in Fig. 6).

*N*is the number of data equal to or greater than 20 nT/hour. The exponent value of α of 4.45 and the value of

*C*of 3.90 × 10

^{3}are obtained by using the data in Fig. 6. The probability with 95 % confidence interval of |Δ

*H*| equal to or greater than 500 nT/hour is 5.41 × 10

^{−7}[5.4 × 10

^{−9}, 5.5 × 10

^{−4}]. Using Eq. 4, the probabilities of |Δ

*H*| ≥ 500 nT/hour in 50 and 100 years are 1.9 × 10

^{−2}[2.1 × 10

^{−3}, 1.0] and 3.5 × 10

^{−1}[4.3 × 10

^{−3}, 1.0], respectively.

### Estimation of GIC and discussion

*E*

_{ x }and

*E*

_{ y }are the horizontal components of the local geoelectric field and

*a*and

*b*are the site-dependent system parameters.

*ε*(

*t*) is the noise term.

*a*and

*b*are given by the equations

*a*and

*b*are obtained as 38.1 and −7.4 A km/V, respectively. The blue line of Fig. 7 shows the estimated GIC using Eq. 5. The estimated value of GIC is approximately half of the observed value around the maximum of GIC in Fig. 7. Ogawa (2002) noted that it is necessary to consider a gain factor between the electric field at a site and the regional electric field. The gain factor is assumed to be 1 in the analysis of this paper. Figure 8 shows the 1-s geoelectric field values associated with the GIC values shown in Table 1. According to this figure, the GIC of the December 14–15, 2006 event, 3.85 A, is larger comparing with other events.

*Re*(

*α*), −

*Re*(

*β*)) obtained by Eq. 8 is used for analysis of an underground conductivity anomaly. The arrow points direction of conductive layer. Figure 9 shows the values of Parkinson arrow for several frequencies calculated by using geomagnetic field data of Memanbetsu shown in Fig. 2. According to this figure, Parkinson arrow points eastward. This suggests existence of conductive layer in east of Memanbetsu. Uyeshima et al. (2001) suggested a significant coast effect in eastern Hokkaido based on the observation by the network-magnetotelluric (network-MT) method. Consideration of underground conductivity is necessary to understand the measured GIC data as a future work.

*a*and

*b*obtained from the December 14–15, 2006 event. According to our result, the expected maximum absolute values of GICs are approximately 6.2 and 4.2 A, respectively.

*R*

_{ s }(Ω) and the winding resistance of the transformers

*R*

_{ w }(Ω) are assumed for both ends.

*E*

_{∥}(V/km) is the uniform electric field parallel to a power line,

*r*(Ω/km) is the power line resistance per unit length, and

*L*(km) is length of the power line. GIC is proportional to electric fields as shown Eq. 9. For the sufficiently long power line, Eq. 9 becomes

*E*

_{∥}. If we assume that

*r*is 0.05 Ω /km for 187-kV power lines,

*R*

_{S}is 0.1 Ω,

*R*

_{w}is 0.1 Ω, and

*L*is 100 km, Eq. 9 becomes

*E*

_{∥}as shown in the Eq. 11. According to the result from Eqs. 5, 6, and 7, GIC is also calculated using Eq. 12.

Using a DC power source as a proxy of GICs, Takasu et al. (1994) performed experiments on DC excitation for scale models with linear dimensions that were one third to one half of those of actual power transformers. Distortion of wave forms of AC currents was observed by the applied DC currents of several tens ampere to the scale models. A maximum temperature rise of approximately 110 °C was measured in the case of the core plate and the core support made by magnetic steel for a GIC level of approximately 200 A for three phases. From Eq. 12, the geoelectric field parallel to the power line, *E*
_{∥} of 5.2 V/km, is necessary for the GIC level of 200 A. We need further studies on GIC levels affecting the power grids to know an effective level of geoelectric fields.

## Conclusions

We studied the GIC data measured at the Memanbetsu substation, Hokkaido, using the geoelectric and geomagnetic field data observed at the Memanbetsu Observatory, JMA, and obtained the empirical equation to estimate GICs associated with the past intense geomagnetic storms. GICs associated with the March 13–15, 1989 storm and the October 29–30, 2003 storm were estimated by using the Eq. 8. Estimated maximum absolute values of the GICs are approximately 6.4 and 4.2 A, respectively. Our estimation seems to be approximately half of the observed values according to the December 14–15, 2006 event shown in Fig. 7. It is necessary to consider the effect of regional underground conductivity for the estimation as a future work. The CCDF of the GIC data is calculated. According to it, the probabilities of extremely large values of the GIC seem to be low. However, it is based on the measurement of approximately 2 years and there is a large uncertainty. We need more long-term data as noted by Hapgood (2011).

## Declarations

### Acknowledgements

The GIC measurements in Hokkaido, Japan, were conducted as part of the close collaboration among NICT, Hokkaido Electric Power Co., and STEL at Nagoya University. We would like to thank the Hokkaido Electric Power Co. for the GIC measurements at the Memanbetsu substation. We thank the Kakiok3a Magnetic Observatory, JMA, for providing us with geomagnetic and geoelectric field data and the lists of magnetic storms at the Memanbetsu Observatory. Finally, we wish to acknowledge the anonymous reviewers and the editor, Dr. Ikuko Fujii, for their valuable comments and suggestions.

## Authors’ Affiliations

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