ECE 530 – Analysis Techniques for
Large-Scale Electrical Systems
Lecture 26: Geomagnetic Disturbance
(GMD) Modeling
Prof. Hao Zhu
Dept. of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign
haozhu@illinois.edu
12/9/2014
1
Announcements
•
•
Homework 8 due on Thursday Dec 11
Final exam on Monday Dec 15 from 1:30 to 4:00pm in
this room (ECEB-4026)
– Closed book, closed notes; you can bring in two note sheets
(one new note sheet and exam 1 note sheet), along with
simple calculators
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In the News: Ice and Power Lines
Quebec Ice Storm,
January 1998;
Some places got
more than three
inches of ice!
Image source: http://i.imwx.com/web/spia-index-web.jpg
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High Impact, Low Frequency Events
•
•
•
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Over the last several years NERC has been considering
high-impact, low frequency events (HILFs)
These are events that can cause wide-scale, catastrophic
damage, beyond that caused the more frequent events
like ice storms and hurricanes
Several types of HILFs identified by NERC in June
2010 report: 1) Coordinated Attack, 2) Pandemic, 3)
Geomagnetic Disturbances (GMDs), 4)
Electromagnetic Pulse (EMP)
Here at UIUC we have been focused on GMDs, with
some work planned on EMPs
4
GMD References
•
•
•
•
NERC Interim GMD Report issued in late Feb 2012
–
available at http://www.nerc.com/files/2012GMD.pdf
IEEE Spectrum, Feb. 2012
GMDs have the potential to severely
disrupt operations of the electric
grid, yet power engineers have had
few tools to help them assess the
impact of GMDs on their systems
Recent research and development
is helping to move GMD assessment
into the realm of power system
planning and operations engineers
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Geomagnetic Disturbances
(GMDs)
•
Solar events can cause changes in the earth’s magnetic
field (i.e., dB/dt). These changes in turn produces an
electric field at the surface
– Changes in the magnetic flux are usually expressed in
nT/minute; from a 60 Hz perspective an almost dc electric field
– 1989 North America storm produced a
change of 500 nT/minute, while a
stronger storm (e.g., 1921) could
produce more than 5000 nT/minute variation
– Storm “footprint” can be continental in scale
– For reference, Earth’s magnetic field is normally between
25,000 and 65,000 nT, with higher values near the poles
Image source: J. Kappenman, “A Perfect Storm of Planetary Proportions,” IEEE Spectrum, Feb 2012, page 29
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March 8-9, 2012 “Event”
•
Below example shows results for a relatively small
storm that occurred in March 2012 (Ottawa at 45.4N)
Less than
100 dB/dt,
compared
to 500 for
the 1989
event and
5000 in
1921
Image source: www.intermagnet.org/apps/plt/plot_result_int_e.php
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March 1989 Storm that
Caused Quebec Blackout
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GMD Impact Overview
•
•
Change of geomagnetic field induces electric field
Geomagnetically induced currents (GICs) flow across
the transmission grid
Changes of
geomagnetic
field (dB/dt)
Electric field on
Earth’s surface
(E-field)
DC currents flow
on HV lines
(GICs)
Transformer
damage and
voltage collapse
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Electric Fields and
Geomagnetically Induced Currents
•
As described by Faraday’s law, changes in the magnetic
flux intensity produce a (non-uniform) electric field on
the surface; values are impacted by ground conductivity
– Electric fields are vectors with a magnitude and direction;
•
•
values are in units of volts/mile (or volts/km);
– A 2400 nT/minute storm could produce 5 to 10 volts/mile.
The electric fields cause geomagnetically induced
currents (GICs) to flow in electrical conductors such as
the high voltage transmission grid
Currents are quasi-DC (frequencies much below 1 Hz)
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Electric Fields and
Geomagnetically Induced Currents
•
•
•
•
Three phases appear to be in parallel to GIC
The induced voltages that drive the GICs can be
modeled as dc voltages in the transmission lines.
The magnitude of the dc voltage is determined by
integrating the electric field variation along the line
As long as the electric field is uniform, the integration
is path independent
V  E  dl
k
•

R
So the electric field tangential to the line is
Ek ,T  Ek cos( k , E   k , L )
With the voltage then Vk  Ek ,T Lk
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Geomagnetically Induced Currents
(GICs)
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Uniform vs. Nonuniform
Electric Fields
•
•
For some situations uniform electric field models can
be used (i.e., constant magnitude and direction)
The actual electric fields produced by a GMD will be
nonuniform, and depend, in part, upon the ground
resistivity
E ( )  B( ) * Z ( )
– Because of the low frequency, currents can penetrate 100's of
kms into the ground
– One dimensional models are commonly used, but there is
actually quite a bit of uncertainty in the underlying ground
resistivity
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1D Conductivity Example
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Maximum Electric Field and
Latitude
Note:
magnetic
latitude is
not the
same as
geographic
latitude
Image Source: http://www.nerc.com/comm/PC/Geomagnetic%20Disturbance%20Task%20Force%20GMDTF%202013/Day2_all_final.pdf
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Magnetic Latitude
Note that
almost
all of the
US and
Europe
are
above
40 degrees
magnetic
latitude
Image Source: http://hfradio.org/swp_proplab/maglat00.gif
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An Example Nonuniform Field
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Power System Impacts of GICs
•
The dc GICs are superimposed upon the ac currents.
In transformers this can push the flux into saturation
for part of the ac cycle
• This can cause large
harmonics; in the positive
sequence (e.g., power flow
and transient stability)
these harmonics can be
represented by increased
reactive power losses on the transformer.
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Mapping Transformer GICs to
Transformer Reactive Power Losses
•
•
Transformer specific, and can vary widely depending
upon the core type
– Single phase, shell, 3-legged, 5-legged
Ideally this information would need to be supplied by
the transformer owner
– Currently support default values or a user specified linear
•
•
mapping
For large system studies default data is used when
nothing else is available. Values change with core type
Still debate in the industry with respect to the
magnitude of damage GICs would cause in transformers
(from slightly age to permanently destroy)
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Four Bus Example
IGIC ,3Phase
150 volts

 93.75 amps or 31.25 amps/phase
1  0.1  0.1  0.2  0.2 
Substation A with R=0.2 ohm
Neutral = -18.7 Volts
Neutral = 18.7 Volts
Bus 3
DC = 18.7 Volts
1.001 pu
Bus 1
DC = 28.1 Volts
0.999 pu
Substation B with R=0.2 ohm
Bus 2
765 kV Line
DC =-28.1 Volts
0.997 pu
Bus 4
DC =-18.7 Volts
1.000 pu
3 ohms Per Phase
slack
GIC/Phase =
31.2 Amps
High Side = 0.3 ohms/ Phase GIC Input = -150.0 Volts High Side of 0.3 ohms/ Phase
GIC Losses = 15.6 Mvar
GIC Losses = 15.6 Mvar
The line and transformer resistance and current values are
per phase so the total. Substation grounding values are total
resistance. Brown arrows show GIC flow.
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The Impact of a Large GMD
From an Operations Perspective
•
•
•
•
•
•
There would be a day or so warning but without
specifics on the actual magnitude
It could strike quickly (they move at millions of miles
per hour) with rises times of less than a minute, rapidly
covering a good chunk of the continent
Reactive power loadings on hundreds of transformers
could sky rocket, causing heating issues and potential
large-scale voltage collapses
Power system software like state estimation could fail
Control room personnel would be overwhelmed
The storm could last for days with varying intensity
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GMD Enhanced Power Analysis
Software
•
•
By integrating GIC calculations directly within power
analysis software (like power flow) power engineers can
readily see the impact of GICs on their systems, and
consider mitigation options
GIC calculations use many of the existing model
parameters such as line resistance. But some nonstandard values are also needed; power engineers would
be in the best position to provide these values, but all
can be estimated when actual values are not available
– Substation grounding resistance, transformer grounding
configuration, transformer coil resistance, whether autotransformer, whether three-winding transformer, generator
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step-up transformer parameters
GIC G-Matrix
•
With knowledge of the pertinent transmission system
parameters and the GMD-induced line voltages, the dc
bus voltages and GIC flows can be calculated by
solving a linear equation I = G V
– The G matrix is similar to the Ybus except 1) it is augmented
•
to include substation neutrals, and 2) it is just conductances
– The current vector contains the Norton injections associated
with the GMD-induced line voltages
Factoring the sparse G matrix and doing the
forward/backward substitution takes about 1 second for
the 62,600 bus Eastern Interconnect Model
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Four Bus Case G Matrix
•
Below image shows the G matrix for the four bus case
Substation A with R=0.2 ohm
Neutral = -18.7 Volts
Neutral = 18.7 Volts
Bus 3
DC = 18.7 Volts
1.001 pu
Bus 1
DC = 28.1 Volts
0.999 pu
Substation B with R=0.2 ohm
Bus 2
765 kV Line
DC =-28.1 Volts
0.997 pu
Bus 4
DC =-18.7 Volts
1.000 pu
3 ohms Per Phase
slack
GIC/Phase =
31.2 Amps
High Side = 0.3 ohms/ Phase GIC Input = -150.0 Volts High Side of 0.3 ohms/ Phase
GIC Losses = 15.6 Mvar
GIC Losses = 15.6 Mvar
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GIC Transformer Modeling
•
•
•
•
How the transformers are grounded is quite important
for GIC studies
– No flow through the delta windings, or ungrounded wyes
Common for generator step-up transformers (GSUs) is
grounded-wye high side, delta low side
At the transmission to distribution common
configuration is delta high, grounded-wye low
Transmission autotransformers are usually groundedwye with a delta tertiary
I Effective ,r  I GICH ,r
I GICL , r

at , r
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Autotransformer Example
•
The below figure is a one-line for a four bus system
with an autotransformer between buses 2 and 3
G Matrix
SubA
SubB
SubC
1
2
3
4
SubA
25
0
0
-20
0
0
0
SubB
0
80
0
0
-75
0
0
SubC
0
0
30
0
0
0
-25
1
-20
0
0
21
-1
0
0
2
0
-75
0
-1
126
-50
0
3
0
0
0
0
-50
51.25
-1.25
4
0
0
-25
0
0
-1.25
26.25
T.J. Overbye, K.S. Shetye, T.R. Hutchins, Q. Qiu, J.D. Weber, "Power Grid Sensitivity Analysis of Geomagnetically Induced
Currents," IEEE Transactions on Power Systems, vol. 28, pp. 4821-4828, November 2013
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Determining GMD Storm Scenarios
•
•
The starting point for the GIC analysis in the power
flow is an assumed storm scenario; this is used to
determine the transmission line dc voltages
Feb 2012 NERC report recommended for planning
purposes a similar approach could be used
– Uniform electric field: All locations experience the same
•
electric field; induced voltages depend on assumed direction
– Maximum value in 1989 was 1.7 V/km (2.7 V/mile)
We also consider a more detailed non-uniform model
– Non-uniform electric field: Magnitude of electric field varies
according a some function; induced voltages in lines depend
on magnitude and assumed direction
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GIC Flows in Eastern Interconnect for
a Uniform 2.5 V/Mile, N-S Field
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GIC Visualization for EPRI Test
System – East Field
Case is described in: R. Horton, D. Boteler, T.J. Overbye, R. Pirjola, R.C. Dugan, "A
Test Case for the Calculation of Geomagnetically Induced Currents," IEEE
Transactions on Power Delivery, vol. 27, pp. 2368-2373, October 2012.
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GIC Visualization for EPRI Test
System – North Field
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Integrated Geographic Information
•
The potentially time-varying GMD induced dc voltages
are determined by knowing the latitude and longitude of
the transmission lines
– Just knowing the geo-coordinates of the terminal buses should
•
be sufficient
– Actual transmission path isn't usually needed
Hence buses need to be mapped to substations, and
substations to their geo-coordinates
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Power Flow Convergence Issues
•
•
Integrated GIC modeling can certainly impact power
flow convergence since the GIC induced reactive power
losses simultaneously add lots of reactive power.
Several techniques can help prevent divergence
– Just calculating the GICs without solving the power flow
– Not calculating GMD induced voltages for equivalent lines
– Gradually increasing the assumed electric fields to avoid
–
–
–
simultaneously adding too much reactive power at one time
Only calculating the GIC transformer reactive power losses for
specified areas; reactive power doesn’t tend to travel far
Limiting the size of the GMD
Freezing the transformer taps and switched shunts in certain
problematic areas
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Integrating GIC Calculations into
Power System Planning
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•
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A large GMD could cause substantially different
power system flows and voltages
Studies allow for testing various mitigation strategies
– Operational (short-term) changes include redispatching
generation to avoid long distance power transfers and
reducing transformer loading values, and strategically
opening devices to limit GIC flows
– Longer-term mitigation actions include the installation of
GIC blocking devices on the transformer neutrals (such as
capacitors) and/or increased series capacitor compensation
on long transmission lines
There are many potential research directions to pursue
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Research Example: Determining
Mitigation Strategies
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•
•
GIC flows can be reduced both through operational
strategies such as strategically opening lines, and
through longer term approaches such as installing
blocking devices
Algorithms are needed to provide power engineers
with techniques that go beyond trial-and-error
Such approaches require a coupling between the GIC
calculations and the power flow solutions
– For example, determining lines that would 1) substantially
reduce the GIC flows and 2) are not crucial from an
operational perspective
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Small System Operational
Mitigation Example
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•
The system on the
right shows how the
GIC impacts can be
reduced by doing
generation dispatch
to allow opening a
345 kV line
Research is going
on to determine
optimal solutions
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Large System Planning Example
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•
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A power system in northern Midwest region
Equivalencing: 865 subs, 751 transformers in study area
Local blocking effects: substation selection
Reactive power loss based criteria: max and sum QLoss
H. Zhu and T.J. Overbye,"Blocking Device Placement for Mitigating the Effects of Geomagnetically Induced Currents,"
IEEE Transactions on Power Systems, 2015 (IEEE early access)
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