# IEEE Electrification Magazine - December 2015 - 17

```Figure 6 shows that the transformer winding resistances have been manually set to 0.3 Ω for the HV winding and
0.1 Ω for the LV winding in the four-bus case. As an example of winding resistance estimation, toggle the Bus  2-
Bus  4 transformer resistance field to "No, Auto Default"
and click "Calculate GIC values." The software estimates
the HV winding's dc resistance to be 0.29261 Ω. The LV
winding resistance field is blank since it is not grounded
and hence does not affect GIC calculations. Here, the software assumed both transformers to
be GSUs, and since most GSUs are
usually grounded-wye-delta, this
winding configuration is assumed for
them.
Similar input data are also needed
for the configurations of the windings
(wye, grounded-wye, delta, etc.). It is
also important to identify autotransformers, since they affect the path of
GIC flows and the effective resistance
seen by them. Again, if the data are
not available, defaults and estimates
can be used. The default settings for
determining whether a transformer is
an autotransformer are based on 1) a
maximum turns ratio and 2) a minimum HV winding voltage level in kilovolts, both of which can be modified
in the "Options" menu under the step
"DC Current Calculation."

per-unit value of I Effective is the rated peak per-phase current in the HV winding. In the simplest case of a grounded
wye-delta transformer, such as is common for GSUs,
I Effective is just the current in the grounded winding. For
transformers with multiple grounded windings and autotransformers, the value of I Effective depends upon the current in both coils
I GIC^Lh
I Effective = I GIC^Hh + a t ,

(4)

where I GIC(H) is the per phase GIC
going into the HV winding (or the
series winding of an autotransformer), and I GIC(L) is the per-phase GIC
going into the LV of the transformer.
For an autotransformer, the current
going into the common winding is
the sum of currents in the HV and LV
winding.
Going back to the four-bus case from
Figure 4, the I Effective in both transformers
equals the per-phase current in their HV
windings, which is the same as the perphase in the transmission line = 35.56 A.
In Figure 4, the transformer losses
were calculated using (3) as follows.
The data for K can be seen under
"Tables and Results > Transformers >
GIC Model First Segment Slope." (The
meaning of "First Segment Slope" is explained in the next
paragraph.) For the transformer at Substation A, K = 1.067,
whereas the one in Substation B has K = 0.534. The bus ac
voltages can be seen under "Tables and Results > Buses >
PU Volt," where the values are 0.9987 pu for Bus 1 and
0.99687 for Bus 2. Given the system base is 100 MVA, and
the I Effective,pu in both transformers equals 0.333, this yields
Q GIC = 0.99687 ) 1.067 ) 0.333 ) 100 = 35.5 M v a r a n d
Q GIC = 0.99687 ) 0.534 ) 0.333 ) 100 = 17.7 Mvar, as shown
in the yellow boxes in Figure 4.
Transformer studies have shown that, for threephase, three-limb transformers, the relationship
between the GICs and the GIC-induced reactive power
losses might be better approximated by using a piecewise linear model as opposed to the linear model used
for other types of transformers. These piecewise linear
relationships and their associated K values for different

GIC calculation
requires the dc
resistances of the
various elements
of a power system,
including lines,
transformer
windings, and
substation
grounding.

Transformer Impacts and Voltage effects
Once the GIC flow in the system has been determined,
the effective GICs in the transformers are used to calculate the GIC-induced reactive power losses Q GIC (in
Mvar) in them using

1-3

2-4

Q GIC = Vpu KI Effective,pu S Base,

(3)

where Vpu is the per unit ac terminal voltage at the HV
side for the transformer, S Base is the system three-phase
base, and K is a unitless, transformer-specific scalar that
depends on the core-type and number of phases. I Effective is
an "effective" per-phase current that depends on the type
of transformer. The base current used for calculating the

Figure 6. Transformer data and results for the four-bus test system.

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

17

```

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