An Accurate Method of Determining Conductor Short
Circuit Withstand Capability
Lucas Cook, P.E.
2021 IEEE Power & Energy Society General Meeting (PESGM) | 978-1-6654-0507-2/21/$31.00 ©2021 IEEE | DOI: 10.1109/PESGM46819.2021.9638243
NEI Electric Power Engineering Inc.
Lakewood, CO USA
lcook@neieng.com
When designing a wind or solar plant collection system, it is
important to verify that the cable conductors and concentric
neutrals can withstand the worst-case short circuit event during
the life of the project. Existing standards provide equations for
calculating the withstand capabilities of these conductors.
However, these standards provide no guidance on what current
value should be used in these equations. It will be shown that
two commonly used methods are inaccurate, with one being
overly conservative, and one being insufficient. An accurate
method of determining the correct current value will be
presented. The impacts to the cable sizing of two representative
projects will be explored for all three methods. It will be shown
that the accurate method prevents unnecessary cable up-sizing
compared to the overly conservative method but causes
additional cable up-sizing compared to the insufficient method.
To conclude this paper, it is suggested that the new method be
incorporated into the relevant standards to provide clarity to
practicing engineers and to ensure that cables are properly sized
in any underground cable installation.
experience temperatures higher than their rating. In the United
States, there are a few standards which the industry relies upon
to perform these calculations. However, these standards make
no mention of which current value needs to be considered. An
engineer may run a short circuit analysis using a power system
modelling software, but have a difficult time determining
which current to use in the calculation (e.g. symmetrical,
asymmetrical ½-cycle, etc.)
Index Terms—Asymmetrical current, Cable, Collection System,
Concentric Neutral, DC Offset, Distribution, Renewable, Short
Circuit, Solar, Underground, Wind, Withstand, X/R
In addition, the three different calculation methods and
their impacts to final cable sizes will be compared so that any
renewable energy project stakeholder may understand the
impacts of the computational methods being used by their
engineer.
I.
INTRODUCTION
When designing an underground medium voltage (MV)
collection system for a wind or solar project, the engineer
must consider the ability of the underground cables to
withstand the worst-case short circuit event. Underground
cable installations are relatively expensive compared to
overhead installations. A renewable energy project owner will
expect to reliably operate the project for 20+ years. Reducing
the possibility of cable failures and the associated capital
expense during the life of a project is the main benefit to
proper cable sizing. The possibility of re-using existing
underground collection systems for future repower efforts
makes it even more important to size cables properly from the
start.
During a short circuit event, it is possible that the MV
cable conductor and concentric neutrals, as well as any trench
grounding conductors will be subjected to high amounts of
short circuit current. The goal of a short circuit withstand
analysis is to verify that the cable and its components will not
This paper will contemplate two simple methods that
engineers are currently using (one overly conservative, and
one overly aggressive). A new, accurate method will be
presented to calculate an equivalent current for use in the short
circuit withstand calculation. The key feature of this
equivalent current is that it accurately accounts for the DC
offset (X/R ratio) of a fault current without being overly
conservative. The equation to calculate this equivalent current
has been derived and can be easily implemented by anyone
performing these calculations.
II.
EXISTING CALCULATION METHODS
A.
Conductor Withstand
In a typical short circuit study, the withstand capability of
the main conductor of the cable is verified using the following
equation from page 9 of ICEA P-32-382. The variable “I” is
labeled simply as the “Short Circuit Current – Amperes” [1].
(1)
B. Concentric Neutral Withstand
The concentric neutral short circuit withstand is
determined using an equation from ICEA P-45-482, shown
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below. The variable for current is labeled as “short-circuit
current, ampere” [2].
(2)
C. Application of Existing Equations
Selecting the fault currents to use in the above equations
seems to be left to the discretion of the engineer. Leaving the
selection of fault current open to interpretation may lead to
confusion, since there are several fault current choices such as
symmetrical, ½-cycle asymmetrical, peak asymmetrical, etc.
If an engineer chooses the symmetrical fault current, he will
not properly account for the system’s X/R ratio. Large X/R
ratios may be present on wind and solar projects due to the
often-large main power transformers (MPT’s) used at the
project substations. The remainder of this paper will propose a
correct method to perform this short circuit analysis and
compare the impacts of the various approaches.
III.
DERIVATION OF AN EQUIVALENT CURRENT
To properly account for the DC offset of a fault current, it
must first be recognized how the fault current mathematically
adds heat to the cable. The key quantity in an energy
absorption problem is the square of the current multiplied by
time (I2t). Examining the power equation clarifies this (P =
I2R). Multiplying this expression by time will provide energy.
Hence, energy absorption is proportional to I2t.
This derivation also requires an equation of the total
(asymmetrical) fault current (from basic circuits theory). That
equation is shown below.
(3)
The approach for deriving an equivalent current will be to
integrate the square of equation (3) from a time of 0 seconds
(start of the fault) to an arbitrary clearing time (t), set that
expression equal to an equivalent current squared multiplied
by time (Ieq2t), and solving for the equivalent current.
Squaring equation (3) and rewriting as a function of time (t)
yields the following expression.
(4)
The following equations show the result of the integration
and solving for the equivalent current.
(5)
(6)
(7)
Equation (7) is the final expression for an equivalent
current. This equation may be used to determine the current
values to use in the ICEA equations. This equation will allow
an engineer to accurately determine the impacts of DC offset
with the greatest amount of accuracy.
For avoidance of doubt, the proposed methodology is to
use RMS current values in these equations. RMS values are
representative of the actual energy absorbed in any situation.
IV.
IMPACT TO A PROJECT’S CAPITAL EXPENSE
Two sample wind projects (A and B) of approximately 300
MW consisting of 12 (twelve) underground 34.5 kV feeders
were considered. The final cable short-circuit sizing was
completed using three different fault currents:
•
Symmetrical
•
½-Cycle Asymmetrical
•
Equivalent (see section III)
The impacts to cable sizes and quantities is the focus of
this analysis. A base cable bill of materials (BOM) is
established based on ampacity only and shall serve as the
starting point for each case. The short circuit withstand of all
cables is iteratively verified, upsized, re-verified, and upsized
again until there are no short circuit withstand violations. The
key design parameters of the system are listed below:
•
•
Two (2) MPT’s per Project:
o
Project A: 105/140/175
Impedance, X/R = 52
MVA,
10%
o
Project B: 105/140/175
Impedance, X/R = 49
MVA,
9.5%
The following possible cable sizes:
o
1/0 AWG, 2/3 Neutral
o
4/0 AWG, 1/2 Neutral
o
500 kcmil, 1/3 Neutral
o
1000 kcmil, 1/8 Neutral
o
1250 kcmil, 1/8 Neutral
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o
1500 kcmil, 1/8 Neutral
•
Clearing time for ground and phase faults: 10 cycles
•
Concentric Neutral Split Factor: 70%
•
Utility Fault Current (at 345 kV):
o
Project A: 7 kA
o
Project B: 11.5 kA
B. Project B Results
Tables 3 and 4 below display the same data for Project B.
A. Project A Results
As shown in Table 1 below, considering short circuit
withstand beyond the base case results in a substantial
difference in cable quantities. This should reinforce the fact
that short circuit withstand needs to be considered as part of a
prudent collection system design.
Table 1 – Project A Cable Quantities in Feet
Cable
Size
1500
kcmil
1250
kcmil
1000
kcmil
500
kcmil
4/0
AWG
1/0
AWG
method results in approximately 20,000 feet of additional
cable upsizing compared to the symmetrical current method.
This confirms that using the symmetrical current without
regards to DC offset can lead to undersized cables.
Table 3 – Project B Cable Quantities in Feet
Cable
Size
1500
kcmil
1250
kcmil
1000
kcmil
500
kcmil
4/0
AWG
1/0
AWG
Base
Asym.
Sym.
Eq.
219,381
219,381
219,381
219,381
281,550
303,582
281,550
281,550
474,204
452,172
474,204
474,204
278,889
281,778
278,889
278,889
124,353
336,510
224,331
243,378
Cable Size
510,915
295,869
410,937
391,890
1500 kcmil
1250 kcmil
Table 2 – Project A Cable Quantity Differences in Feet
500 kcmil
1500 kcmil
1250 kcmil
1000 kcmil
500 kcmil
4/0 AWG
1/0 AWG
1000 kcmil
Eq. – Sym.
Eq. – Asym.
Eq. – Base
4/0 AWG
-
-
-
1/0 AWG
-
(22,032)
-
-
22,032
-
-
(2,889)
-
19,047
(93,132)
119,025
(19,047)
96,021
(119,025)
As shown in Table 2, the asymmetrical current method
results in substantially more cable upsizing than the
equivalent method, confirming that using the asymmetrical
current is overly conservative. In addition, the equivalent
Asym.
Sym.
Eq.
230,451
230,451
230,451
230,451
225,258
267,699
225,258
225,258
368,565
326,124
368,565
368,565
200,913
264,918
200,913
220,035
89,457
255,618
233,613
243,096
358,755
128,589
214,599
185,994
Table 4 – Project B Cable Quantity Differences in Feet
Conclusions are best drawn by comparing the
difference in cable quantities between the equivalent current
method and the other methods. See Table 2 below.
Cable Size
Base
Eq. – Sym.
Eq. – Asym.
Eq. – Base
-
-
-
-
(42,441)
-
-
42,441
-
19,122
(44,883)
19,122
9,483
(12,522)
153,639
(28,605)
57,405
(172,761)
As shown in Table 4, the asymmetrical method once
again results in more cable upsizing compared to the
equivalent current method. The equivalent current method
results in approximately 29,000 feet of additional cable
upsizing compared to the symmetrical current method, further
reinforcing the point that DC offset must be considered.
Only two projects have been considered in this
analysis. The key result is that 20,000-30,000 feet of larger
cable was required when using the equivalent current method
as opposed to the symmetrical current method. The typical
cable sizes that require upsizing are 1/0 and 4/0. If another
project has a particularly large amount of 1/0 and 4/0 cable
runs, the impact of the DC offset on cable quantities may be
even greater. Conversely, projects that have very few 1/0
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and 4/0 cable runs may not be as impacted by adopting the
equivalent current method.
Due to the mathematical impact that X/R has on the
equivalent current method, it is expected that larger system
X/R ratios will result in the need for additional cable upsizing
when using the equivalent current method.
V.
CONCLUSION
It should be emphasized that only two possible
collection system topologies and one design basis have
been considered in this paper. Although this set of
assumptions is considered by the author to be typical and
representative of most wind projects, the impacts of the
different calculation methods on a project may vary.
Regardless of the actual system under consideration,
it is proposed that equation (7) always be used for these
calculations to provide an accurate assessment of the fault
current that a conductor may experience. Engineers often
use overly conservative calculation methods to account for
unknown variables that they may have not accounted for.
Continuing to use the asymmetrical fault current method,
while technically overly conservative, may be a valid way
of account for some uncertainty in the calculation (e.g. fault
current duration). However, if an engineer wishes to
perform the short circuit withstand as accurately as
possible, equation (7) offers him this ability. Finally, using
the symmetrical fault current no longer appears to be a
valid approach, as the X/R of the system will impact the
cable’s ability to withstand a short circuit event.
REFERENCES
[1]
[2]
ICEA Short Circuit Characteristics of Insulated Cables, ICEA Std. P32-382, February 2013
ICEA Short Circuit Performance of Metallic Shields and Sheaths on
Insulated Cable, ICEA Std. P-45-482, February 2013
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