the impact of geomagnetic disturbances on power system...

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The impact of geomagnetic disturbances on power system voltage and

reactive power reserves: a comparative study considering uniform and non-

uniform E-fields

Bruno Leonardi1, Bruce English

1, Devin Van Zandt

1, Jennifer Gannon

2

1GE Energy Consulting

2United States Geological Survey (USGS)

SUMMARY

Under periods of intense solar activity, the electric power grid can be subjected to geomagnetically induced

currents (GICs). In this study, it will be shown how GICs can be calculated for a utility scale system and how

different geomagnetic disturbances (GMDs) can affect GICs. Both uniform and non-uniform E-fields are used

and all simulations were performed using the GE PSLF1

GMD package.

Results on a high load case of the Eastern Interconnect (EI) of the United States indicate that significant

differences can exist in GIC magnitude and direction depending on the GMD storm type. These differences

will vary significantly depending on whether a uniform or non-uniform E-field is used as a disturbance. A

summary of system wide voltage profiles, reactive power reserves and voltage stability margin (VSM) are

calculated for different GMD scenarios. Depending on the intensity of the GMD storm, steady state voltage

stability can be compromised.

KEYWORDS

Geomagnetic disturbances, GMD, geomagnetically induced currents, GIC, power system analysis, non-

uniform electric fields.

1. INTRODUCTION

For over a century, geomagnetic disturbances (GMDs) caused by solar storms have received increased

attention from the science community due to the potential disruptions that they cause in modern man-made

infrastructure such as the telegraph system, railroads and the electric power grid, among others.

One of the strongest and perhaps most well-known GMD storms ever recorded took place in 1859. The event

was recorded by a few astronomers, one of them being the British astronomer R. C. Carrington. The storm was

later named after him and is today known as the Carrington event [1]. Although the modern electric power grid

as we know it had not been developed at the time, service disruptions in the telegraph system in Europe and

North America were reported.

Solar storms are more frequent during periods of intense solar activity. Figure 1 shows how solar activity has

varied for nearly three decades. Solar activity shows periods of peaked activity which occur every 11 years, on

average [2], and is gauged by the number of sunspots observed.

1 PSLF is a trademark of General Electric International, Inc.

[email protected]

21, rue d’Artois, F-75008 PARIS CIGRE US National Committee

http : //www.cigre.org 2013 Grid of the Future Symposium


During these periods of intense activity, events such as coronal mass ejections (CME) and solar coronal holes

create energized particles that travel across space and reach Earth. Once in contact with the outer layers of

Earth’s magnetosphere and ionosphere, these charged particles generate ionospheric currents called electrojets.

These electrojets then induce a perturbation on Earth’s magnetic field (B-field), thus creating an electric field

(E-field) near the Earth’s surface, which then induces a voltage potential difference that drives the GICs [3].

0

20

40

60

80

100

120

140

160

180

200

Sun

spo

t n

um

ber

Year

Solar activity cycle

Measured

Smoothered

Predicted

Figure 1: Solar cycle showing peaks of increase solar activity

Previous reports have correlated GMDs with periods of peaked solar activity [3]. Perhaps the most widely

known GMD incident that caused an impact on the power grid is the March 13, 1989 North American solar

storm.

On that day, a storm of magnitude K-9 was identified as the cause of a major blackout in the Hydro-Quebec

system [4]. On that occasion, power system transformers entered half-cycle saturation cycles due to the DC

GICs flow and became harmonic current injection sources. The increased level of harmonic current caused

protective equipment to trip multiple SVCs in the system. Other cascading outages followed causing roughly

83% of the total generation in the Hydro-Quebec system to trip. System restoration took approximately 9

hours.

Given the potential threat that GMDs may pose to bulk power system reliability, the Federal Energy

Regulatory Commission (FERC) has directed the North American Reliability Corporation (NERC) to create

reliability standards to address the potential impact of GMDs.

Among many objectives, tools that can enable the industry to simulate the effect of GMDs on the power grid

were deemed necessary. With that need in mind, a GMD package for GE PSLF has been developed. This

package enables the simulation of a GMD event and converts its effects into the AC power system analysis. In

this paper, the package will be used to demonstrate how a GMD event can be simulated and followed by a

steady state analysis. The package can easily handle large networks and enables the user to simulate the effect

of uniform and non-uniform E-field profiles.

The GMD package enables a high fidelity E-field map to be represented, creating the possibility of simulating

an actual recorded GMD event. In other words, as long as E-field measurements are available in space and

time, any type of non-uniform E-field map can be simulated.

In order to cover the aforementioned topics, this manuscript is structured as follows: in section 2, a

mathematical formulation of the problem is presented. Section 3 summarizes the results for an undisclosed area

in the EI of the United States and section 4 has the conclusions.

2. MATHEMATICAL FORMULATION


Given the low frequency of the varying magnetic and electric fields, the GIC calculations are herein considered

and refereed as a DC phenomenon. Therefore, all inductances and capacitances in the network will be

considered a short circuit or open circuit for GICs, respectively.

In order to calculate the GICs flowing in the transmission network, a network solution needs to be found. All

the formulations described in this paper come from basic circuit algebra and modelling guidelines described in

[3], where the basis for GIC calculation in the bulk power system is laid down. Reference [4] indicates that

GICs flowing into transformers will create an additional MVAr demand with characteristics of a constant

current load. Large-scale simulations have been performed using the methodology and results for a large case

are presented in [5].

Although this paper discusses some aspects of the scientific phenomena, most of its focus will be directed at

the impact of GMDs on the power system as described in Figure 2 below. However, other electrical aspects

such as equipment performance and electromagnetic/harmonic analysis [4], although important, are not in the

scope of this study. In short, this study will analyze the impact of GMDs on bulk power systems from a

planning standpoint.

Science component Power systems engineering component

Solar flare

Earth magnetic

field variation

Soil conductivity

model

Induced E-field and voltage near earth’s surface

DC voltage and GIC

calculation

Additional VAR demand due to

transformer saturation

Power systems steady state

and dynamic analysis

Figure 2: GMD components

Assuming that an E-field map created by a GMD is available, the amount of induced current along a

transmission line can be calculated as follows:

L

DC dlEV

(1)

The integral of the electric field E

along a transmission line path L will create an induced DC voltage that will

drive GICs across the network. The GIC magnitude can depend on the line path, DC line resistance and E-field

direction and magnitude. If a uniform E-field is considered, the line path will not influence the induced DC

voltage along the line. An E-field map contains several E-field magnitude and direction values associated to a

certain latitude and longitude information as shown in (2).

tlonglatfE ,, (2)

ρ t

B

ρ

),( stE

ρ

IVY bus

ρ

)(GICfQ

ρ


In this study, both uniform and non-uniform E-fields are considered. A representation of a non-uniform E-field

in PSLF is given in Figure 3, where an E-field map is laid over Google Earth2.

Figure 3: Example of non-uniform E-field created in GE PSLF and overlaid on Google Earth

After the E-field scenario has been defined, a network representation needs to be created. Since only the

resistive portion of the network is considered to calculate GICs, only transmission lines and transformers are

used to form the Ybus. Loads are usually isolated from GICs by a step down transformer with delta connection

on the low voltage side.

The E-field induced voltage (Vdc) and transmission line DC resistance (Rdc), which can be estimated from the

AC resistance available in a power flow database, are used to calculate the nodal current injections to the

network as shown in Figure 4. Similarly, DC resistances of transformers, their ground mat resistance and

winding connections are also used to form the Ybus.

Figure 4: Transmission line equivalent for GMD analysis showing induced voltage and nodal current

injection

Once the Ybus matrix is created, the DC bus voltage and substation voltages in the entire network can be

calculated as follows:

2 © 2012 Google Inc. All rights reserved. Google and the Google Logo are registered trademarks of Google Inc. Google,

Google Earth and the Google logo are registered trademarks of Google Inc., used with permission.

Rdc/3

Idc = 3 Vdc/Rdc


IVYbus (3)

GICs can be computed throughout the network once DC voltages at all buses are available. The GIC flow

though transformer neutrals will cause half-cycle saturation and additional reactive power consumption which

can be calculated as:

iDCii IkQ 0 (4)

In (3), Q0i represents the additional transformer reactive consumption due to saturation, ki is a factor that

depends on transformer construction type (single/three phase, core, shell, auto-transformer, etc) and IDCi is the

DC GIC current flowing through transformer neutral to ground connection [4], [9].

The additional reactive power load has characteristics of a constant current power, thus being dependent on its

terminal voltage [4]. Its representation in a power flow case is governed by the following equation:

iii VQQ 0 (5)

In PSLF, the value of ki does not automatically depend on transformer rated kV, although the user can set a

flag if he wants this dependence to occur. The user can also set this parameter to any desired value. If no value

is provided, a default value depending on each transformer type will be assigned. This default value for ki will

directly impact the amount of reactive load added to the system due to transformer saturation as indicated in

(4). As more research is done in the area, it is expected that more representative values will be made available.

Once this additional reactive loading for all saturated transformers are added to the power flow case, power

system analysis follows. In this study, it will be shown how different types of E-field scenarios can affect

system voltage stability in a steady state context. Results demonstrate that system voltage profile can be

significantly affected by GMD storms that extend over a large area, even for uniform E-field scenarios of

moderate intensity.

3. CASE STUDY

In this paper, GMD storms that create both uniform and non-uniform E-field are considered for comparative

purposes. The main objective is to show how the assumption of a uniform E-field may not be adequate to

represent the impact of GMD storms on bulk power systems. The studied system represents an area in the EI

case. The total number of buses in the case is 71874, but close to 1000 have their lat/long info available.

3.1. Uniform E-field

Initially, a constant E-field of magnitude 2V/km is applied in various directions from 0 to 315 degrees at 45

degree intervals, thus creating a total of 8 scenarios to be studied. The naming convention used to specify the

field intensity throughout the paper is the following: U_EF_XX, meaning: uniform E-field at XX degrees. In

section 3.1.2, the suffix XX is used to represent the field intensity.

Once the E-field scenario that depletes system voltages the most is found, its direction will be fixed and the E-

field magnitude will be increased until power flow convergence cannot be achieved. Additional MVAr due to

transformer saturation, here designated as additional GMD load, will then be calculated and added to the power

flow case in 10% increments of the total GMD load. This procedure facilitates power flow convergence and


also allows the user to know how much of the GMD load can be tolerated in a hypothetical strong storm, in

case convergence with full GMD loads does not happen.

3.1.1. Uniform E-field: constant magnitude and varying direction

3.1.1.1. Voltage impact

A direct consequence of additional VAr consumption at saturated transformers system wide is voltage sag

caused by increased power flows. This voltage sag will depend on how large the additional GIC induced VAr

load is at transformers terminal. Figure 5 shows the voltage magnitudes at selected buses for multiple GMD

scenarios. This is the base case scenario and only buses that have at least 0.03pu change in magnitude for at

least one GMD scenario are selected.

As can be seen from Figure 5, the additional VAr loading from transformer half cycle saturation will cause

voltage magnitudes to sag. However, in some buses, voltage magnitudes will rise even with additional VAr in

the system. This localized voltage rise is due to additional SVD switching and generator VAr production when

operating at remote regulation mode.

As voltages begin to drop, SVDs will switch in more capacitive elements in order to control the voltage

magnitude at their controlled buses within the specified dead band. Moreover, generating units that are

remotely regulating bus voltages will see their terminal voltages raise due to increased VArs injection at its

terminals. If no SVD switching, transformer tap switching and remote voltage regulation occur, voltage sags

will be predominant across the entire network.

It is also interesting to notice the correlation of bus voltage magnitudes for E-fields that are 180 degrees apart

from each other. Since the amount of VArs consumed by saturated transformers does not depend on the

direction of the GIC currents, the transformer VAr load should be the same when the E-field are 180 degrees

apart. This is due to the fact the induced DC line voltage will be of the same order of magnitude but with

opposed polarity, thus generating the same GIC with opposed directions in both cases.

0.85

0.9

0.95

1

1.05

1.1

1.15

0 10 20 30 40 50 60

Bu

s vo

ltag

e m

agn

itu

de

(p

u)

Bus number

Uniform E-field: 2 V/Km

Base case

U_EF_0

U_EF_45

U_EF_90

U_EF_135

U_EF_180

U_EF_225

U_EF_270

U_EF_315

Figure 5: Voltage magnitudes at selected buses for different uniform E-field scenarios

3.1.1.2. Reactive power reserves


Although bus voltage magnitudes can be an indicator of system loading due to GIC, a more complete system

picture can be obtained if reactive power reserves across the system are monitored as well. In Figure 6, the

reactive power reserves of selected generators are plotted for each GMD storm scenario. Only units that had a

reduction of 30MVAr or more for at least one GMD scenario are included in the chart.

As expected, reactive power resources are depleted across the entire network. Similarly to bus voltages, the

same reduction pattern is observed at each 180 degrees. Although the reduction in reactive reserves is not very

significant in the studied case, reactive reserve depletion can become a major problem in heavily loaded

conditions. Extinguishment of critical reactive power reserves will cause further voltage sag and control

actions might be needed in order increase voltage profile and the amount of voltage stability margin [7].

Figure 6: Generator reactive power reserve at selected units

3.1.2. Uniform E-field: varying magnitude and constant direction

In this section, the E-field magnitude is varied from 0 to 8V/km in 2 V/km increments. At 10V/km, only 70%

of the total additional MVAr load could be added to the case before the system diverged. The two main

contributing factors to this observation are: the power flow case used already represents a stressed high load

condition of the EI; the values used for ki will directly affect the amount of VAr due to GICs – the tool uses

default values for ki depending on transformer type, although users can set these values to any value they want.

Both assumptions will lead to a large demand of VArs, thus pushing the system close to voltage instability.

3.1.2.1. Voltage impact

Voltage sags in the system are widespread and increase with the magnitude of the E-field. Figure 7 below

shows how voltage magnitude drops in the studied area at buses rated 230kV and above. Only buses that have

a base case variation of 0.03pu for at least one scenario are reported.

Similarly to what we have observed in the previous section, there is a significant voltage drop at relatively low

E-field storms when a uniform E-field is considered. For the buses shown in Figure 7, there is a drop of almost

0.05pu at high voltage buses when the E-field is only 8V/km. This is an indication that not even a necessarily

strong uniform E-field can create a large additional demand of VARs. In practice, GMD storms will create

non-uniform E-field maps and system response will not be so drastic.


Figure 7: System wide voltages sags at buses rated above 230kV

3.1.2.2. Reactive Reserve impact

Reactive power reserves will deplete proportionally to the amount of additional MVAr from saturated

transformers. Since this additional load varies linearly with GICs and GICs vary linearly with the magnitude of

the electric field, the reactive power reserve depletion should decay at an approximately linear rate with the E-

field magnitude. Figure 8 show how the sum of all generator reactive reserves drop inside the studied area. The

rate of decay is almost linear, as expected. It is also not necessary that all reactive reserves are exhausted

before the system goes under a voltage collapse. In this case, there is approximately 6GVAr of reserves still

available before power flow convergence cannot be reached. This is a well know phenomenon and the

exhausted reactive reserves are also known as basin reactive reserves for the area [8].

Figure 8: Sum of generator reactive power reserves in the area of interest

3.1.2.3. Voltage Stability Margin (VSM) impact

Since voltage instability is one possible outcome of GMD storms, the amount of voltage stability margin was

calculated for multiple E-field scenarios and presented in Figure 8. The PV curves are calculated at a bus


located in the area of interest. Both active and reactive loads are increased in the area as well as active power

generation. The calculated amount of voltage stability margin is reported in Table 1.

The amount of stability margin decays as the E-field strength increases. Also, the initial voltage magnitude

drops as the additional VAr loads due to GICs are added to the system. It is interesting to observe that in this

case, even a uniform E-field of magnitude 10V/km will create a total amount of additional VAR demand that

will bring the system to collapse.

Figure 9: PV curves for various E-field scenarios

Table 1: Voltage stability margin in studied area

Scenario Voltage Stability Margin (in MW)

Base case 4953.2

U_EF_2 4623.0

U_EF_4 4623.0

U_EF_6 3962.6

U_EF_8 1320.9

3.2. Non-uniform E-field

A total of 5 non-uniform E-field scenarios (NU_EF_1 to NU_EF_5) were created in order to investigate how

changes in the E-field uniformity and intensity affect bulk power system performance. The scenarios created

have the E-field varying in both direction and magnitude from north to south and east to west, west to east and

vice versa. An example of a non-uniform E-field (EF_5) pointing northwest is shown in Figure 10. Other E-

field maps will not be shown here for the sake of space.

These scenarios do not represent any historical GMD storm and their usage is limited to the objective of

showing how a generic event would affect the power grid. In case historical GMD storm data is available, it

can be easily entered into the tool for analysis.

In order to be able to simulate non-uniform E-fields, an interpolation algorithm is used in locations where no

measured E-field is available. Interpolation is extremely fast and most of the time spent in the simulation is


consumed by power flow calculations. Network solution to calculate the bus and substation DC voltages is

extremely fast. For instance, the factorization of the Ybus and forward/backward substitutions take an average

of 0.058s for the continental EI case.

50 60 70 80 90 100 110 120 13020

25

30

35

40

45

50

55

60

65

Longitude(degrees)

Lati

tude

(deg

ree

s)

E-Field (NU EF 5)

Figure 10: Scenario E - non-uniform E-field map for pointing northeast

In reality, the induced E-field is a complicated response of the Earth’s conductivity, magnetic field

perturbations driven by geomagnetic fluctuations, and transverse effects due to geological and coastal

boundaries. Figure 11 shows an example of estimated electric field intensity at a snapshot in time during the

October 2003 Halloween event. In this example, the E-field is calculated from historical magnetic field

measurements taken at US Geological Survey observatories, combined with 1D conductivity profiles for 23

approximate physiographic regions across the continental US [10]. As improvements continue to be made to

conductivity models, magnetic field interpolation routines, and incorporation of coastal boundary effects,

storm scenarios such as this can be used to assess the impact of realistic non-uniform E-field fluctuations

across an entire bulk power system. Initial assessments suggest that, during the largest observed storms from

1985 - 2010, E-field values near 1.8V/km can be observed regionally.

_E)


Figure 11: October 2003 E-field intensity scenario (orange > 0.5V/km, yellow >0.25 V/km, green 0-0.25

V/km)

3.2.1. Voltage impact

Similarly to uniform E-fields, non-uniform E-fields will also cause a similar voltage sag in most buses across

the network. In this study, the magnitude of the E-field was allowed to vary form 0 V/km to a max of 2V/km in

both the x and y axis. Although the magnitude of the non-uniform E-field can reach a value as larger as the

uniform E-fields used in the previous section, the impact on system wide voltages seems a little less intense.

Figure 12 shows system voltage magnitude at buses that have a change of at least 0.01pu between the base case

and the at least one of the GMD scenarios. Only four bus voltages had a magnitude change greater than 0.03pu,

compared to almost 60 buses for the uniform E-field scenarios. This indicates that even with higher peak value,

non-uniform E-fields tend to cause a less significant system wide voltage sag compared to uniform E-fields.

Figure 12: Voltage magnitudes at selected buses for different non-uniform E-field scenarios

3.2.1. Reactive Reserve Impact


Figure 13 shows the generators whose reactive reserves had a reduction of 30MVAr or more for at least one

non-uniform scenario. Differently from uniform E-fields, where 21 generators had a reduction of 30MVAr or

more for at least one scenario, only 8 units had their reserves depleted more than 30 MVAr. These results are

in line with the voltage sags observed above and indicate a less severe impact on the system from a voltage

stability point of view compare to the uniform E-field scenarios.

Figure 13: Generator reactive power reserve at selected units

Moreover, these results indicate that using uniform E-fields to study the impact of GMDs on power systems

might be a conservative approach. As indicated by the results obtained in this study, when a uniform E-field is

considered over a large geographical area, it tends to create more VAr losses due to transformer saturation than

a non-uniform E-field with similar magnitude.

For NU_EF_E, only 5552 lines have GICs greater than 0.0001A/phase and are listed in Figure 14 below. More

than 95% of the GICs flowing on transmission lines are smaller than 10A in this case, and the highest line GIC

is 210.81 A/phase.

Figure 14: GIC current on transmission lines for NU_EF_E


4. CONCLUSIONS

The study presents the simulation of GMD on a highly stressed EI case. Independently of the nature and

intensity of the GMD storm, power system voltage stability and system wide voltage profile will be affected.

Various uniform E-field scenarios were studied and storm magnitude had its direction varied in order to find

the worst condition.

The final conclusion pertaining the voltage stability limits is that the amount of reactive power reserves

available, as well as transformer factor ki will directly affect the amount of voltage stability margin. High

values of ki will cause increased VAr load due to GICs, even at moderate E-field scenarios. Highly loaded

cases, such as summer base cases, have a reduced amount of reactive power reserves, which will contribute to

reduced stability margins even at moderate E-field scenarios.

Results also indicate that using a uniform E-field to represent a GMD storm over a large area may be a

conservative approach as it will create a significant voltage sags and high reactive power consumption. Non-

uniform E-field scenarios created a less significant system impact while not consuming excessive amounts of

generator reactive power reserves. In reality, E-field profiles are non-uniform and the ability to simulate actual

GMD events is important in order to fine tune tools for GIC calculation in large power systems. As future

work, we plan to investigate the correspondence between past GMD events and measured GIC data to further

improve computational models.

5. ACKNOWLEDGMENT

The authors would like to thank Mr. Mark Walling and Mr. James Cronen for their insightful discussions about

non-uniform E-field representation.

6. BIBLIOGRAPHY

[1] R. C. Carrington, “Description of a singular appearance seen in the sun on September 1st, 1859”.

Monthly notices of the royal astronomical Society, Vol. 20, p.13-15, 1859.

[2] Usoskin, Ilya G.; Mursula, Kalevi; Arlt, Rainer; Kovaltsov, Gennady A., “A Solar Cycle Lost in 1793-

1800: Early Sunspot Observations Resolve the Old Mystery”. The Astrophysical Journal Letters,

Volume 700, Issue 2, pp. L154-L157, 2009.

[3] NERC, “Effects of Geomagnetic Disturbances on Bulk Power Systems”. Interim report, February 2012.

[4] R. Walling, A. Khan, “Characteristics of transformer exciting current during geomagnetic

disturbances”, IEEE Transactions on power delivery, vol. 6, no. 4, October 1991.

[5] T. Overbye, T. Hutchins, K. Shetye, J. Weber, “Integration of Geomagnetic Disturbance Modeling into

the Poewr Flow: A Methodology for Large Scale system Studies”. NAPS 2012.

[6] P. R. Barnes, D. T. Rizy, B. W. McConnell, F. M. Tesche, E. R. Taylor Jr., “Electric Utility Experience

Industry with Geomagnetic Disturbances”. Oak Ridge Report: ORNL 6665, 1991.

[7] B. Leonardi, V. Ajjarapu, “An Approach for Real Time Voltage Stability Margin Control via Reactive

Power Reserve Sensitivities”, IEEE Transactions on Power Systems Vol. 28, No. 2, May 2013.

[8] R. A. Schlueter, S. Z. Liu, K. Ben-Kilani, “Justification of the voltage stability security assessment and

diagnostic procedure using a bifurcation subsystem method”, IEEE Transactions on Power Systems,

vol. 15, no. 3, August 2000.

[9] X. Dong, Y. Liu, Kappenman, J., “Comparative analysis of exciting current harmonics and reactive

power consumption from GIC saturated transformers”, IEEE Power Engineering Society Winter

Meeting, 2001.

[10] Fernberg, P., “One-Dimensional Earth Resistivity Models for Selected Areas of Continental United

States and Alaska”, EPRI Technical Update, 1026430, 2012.

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