# IEEE Electrification Magazine - December 2015 - 14

```Figure 1. A solar flare interacting with Earth's magnetic field, causing
a GMD. [Image courtesy of NASA (http://sec.gsfc.nasa.gov/sec_
resources_imagegallery.htm).]

solution of the system as constant current loads to assess
their effect on system voltages.
the system data needed for them. This is shown with the
help of tutorial-type examples using the GIC Analysis
module of PowerWorld Simulator, starting from a simple
four-bus case, followed by a 20-bus test system and an
powerworld.com/gloversarmaoverbye), and the GIC fourbus and 20-bus cases (http://www.powerworld.com/products/simulator/add-ons-2/simulator-gic) to follow along
with the examples.

modeling electric Fields
The first step in modeling GMD effects on the power
grid is to calculate the GIC flow in a power system. Being
quasi-dc, GICs can be determined by solving the following
dc equation:
VGIC = G -1 I,

(1)

where G is a "conductance matrix," similar in form to the
power system admittance matrix Ybus, but consisting of
only conductance values determined by the parallel combination of three phases of elements such as transmission
lines, transformer windings, and substation grounding. I is a vector of the Norton equivalents of the dc voltages induced as a result of the electric field. VGIC consists
of the calculated nodal dc voltages, which are then used
for determining GIC flows through the system.
The coupling between the GICs and the power flow is
the GIC-induced reactive power loss for each transformer.
These losses have been found to vary linearly with the
transformer terminal voltage and the transformer GICs.
These losses are then included in the ac power flow

Bus 1

Bus 2

→

E

G

G

Ra
Rb
Rw 1

Vdc
+
+

Rgnd1

Rw 1

Rc

→

-
dc

-

dc

Rw 1

→

E . dl

Rw 2
Rw 2
Rw 2

+

-

Rgnd2

dc

Figure 2. The power system model used in GIC analysis. R a, R b, and
R c are the resistances of each phase of the transmission line, R w
are the transformer winding resistances, and R gnd represent substation grounding resistances.

14

I E E E E l e c t r i f i cati o n M agaz ine / december 2015

As mentioned previously, GICs are driven by GMD-induced
geoelectric fields at the Earth's surface. The geoelectric
field calculations can be quite involved, potentially requiring detailed models of the Earth's crust conductivity, and
can be significantly influenced by the presence of nearby
bodies of salt water.
The impact of the GMD-induced electric fields can be
modeled as dc voltage sources in series with the transmission line resistances. To calculate the GMD-induced voltage Vdc, generally the electric fields are integrated over the
length of each transmission line, as shown in Figure 2.
This results in a path dependent integral. However, in the
common situation in which the electric field is assumed
to be uniform over the length of the line, Vdc can be calculated using
Vdc = E N L N + E E L E,

(2)

where E N is the northward electric field (V/km), E E is the
eastward electric field (V/km), L N is the line's northward
distance (km), and L E is the eastward distance (km).
Readers are encouraged to open the "GIC_FourBus"
case in PowerWorld Simulator and follow the steps to
input an electric field. This case consists of two generators
with generator step-up transformers (GSUs) and a 765-kV
transmission line. Buses 1 and 3 belong to Substation A,
whereas Buses 2 and 4 are in Substation B.
To perform GIC analysis in PowerWorld Simulator, click
GIC Analysis Form. To model a uniform electric field, the
two inputs required are the electric field magnitude and
direction, as shown in Figure 3. The direction is specified
in degrees, where 0° means north, 90° is east, and so on.
For an example study, specify the maximum field as
1 V/km and the storm direction as 90°. Then, click "Calculate GIC Values."
For this eastward, 1 V/km electric field, E E = 1 V/km. The
transmission line is 170.8 km long and is oriented west-
east (Bus 1 is the "from" bus, and Bus 2 is the "to" bus),
which implies that the eastward length L E = 170.8 km.
Hence, using (2), Vdc = 1 ) 170.8 = 170.8 V. This is depicted

```
http://www http://www.powerworld.com/gloversarmaoverbye http://www.powerworld.com/prod http://sec.gsfc.nasa.gov/sec_

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