# IEEE Electrification Magazine - December 2015 - 15

```in the blue box in Figure 4, which shows the one-line diagram for this case. Note that the dc representation of this
test system is similar to the circuit shown in Figure 2.
To study another GMD scenario,
change the input to 1 V/km, 0° (i.e.,
northward), and click "Calculate GIC
values." In this case, no dc voltage is
induced in the transmission line
because the electric field is exactly
perpendicular to the transmission
line (i.e., Vdc = 1 ) 0 + 0 ) 1 = 0 V) .
Figure 5 shows the system one-line
diagram with these results.
So far, this four-bus example has
introduced some of the model inputs
needed for GIC studies that are not
usually present in a standard power
flow case; for instance, the mapping of
buses into substations. Also required
are the substation or bus latitude and longitude coordinates
from where the line lengths and orientations are calculated.
This data can be accessed and modified by going to "Tables
and Results" and then "Substations" in the GIC Analysis Form.
The line lengths calculated using this method do not account
for the actual geographic route of a line, but they are a reasonable engineering approximation.
In addition to the single-snapshot, uniform electric
field analysis described in this section, spatiotemporal
variations in electric fields (i.e., nonuniform) can also be
applied for GIC studies. However, the basic induced electric field principle remains the same as in Figure 2. An
example of a spatially varying, nonuniform electric field is
shown later in the article.

1-V/km eastward electric field, which induced 170.8 V in
the transmission line. The dc resistance values of the line,
transformer windings, and substation grounding are
shown in the one-line diagram in
Figure 4. The three phases for the
transmission line and transformers
are in parallel, so the total threephase resistance of the line is
(3/3) Ω = 1 Ω, and (0.3/3) Ω = 0.1 Ω for
each of the transformers. Only the
high-side winding resistance is
considered here, since the low side
is delta connected and does not
have a path to ground for the GICs.
These resistances are connected in
series with the Substation A and B
grounding resistances, which are
0.2 Ω each, resulting in

GIC studies can
in determining
appropriate
strategies to
mitigate the system
impacts of GICs.

GIc calculations and dc model data
Continuing from the four-bus example shown in Figure 4,
the actual GICs in the system are easy to calculate for a

I GIC,

per phase

=

170.8

^1 + 0.1 + 0.1 + 0.2 + 0.2 h

1
* 3 = 35.58 A,

with the GIC flow direction being from the from bus
(Bus 1), to the to bus (Bus 2). An important point in
interpreting the results is to differentiate between the
per-phase GICs in transmission lines and transformers
and the total three-phase GICs in these devices. Since
the three phases are in parallel, the conversion between
them is straightforward, with the total current just
three times the per-phase current. The convention commonly used for GIC analysis is to use the per-phase current for transformers and transmission lines and the
total three-phase current for the substation neutral.
The GIC calculations for this simple four-bus example
could be shown manually. In general, the matrix form
in (1), i.e., VGIC = G -1 I, is used for calculating GICs, especially for large systems. As mentioned earlier, GICs are
assumed to be quasi-dc from a 60-Hz grid perspective.

Figure 3. The GIC Analysis Form, with the electric field input dialog.

IEEE Elec trific ation Magazine / d ec em be r 2 0 1 5

15

```

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