Estimating Cable Lengths can Produce Errors in Arc Flash Hazard Calculations and Underestimate PPE.

1. 1
Arc Flash Hazard,
When Over-Estimating Under-Estimates a Problem
Del John Ventruella, PE
Abstract: When one undertakes an arc flash
study, one must develop a model based on the
power system of interest. The model requires
estimates of conductor lengths. To insure that
the arc flash study that one is performing does
not underestimate the magnitudes of the short
circuit currents present within the power
system, and to allow for limitations in the
procedure by which one develops the model,
typically visual inspection, one must carefully
estimate the lengths of conductors.
This requires that one avoid over-estimates of
conductor lengths or risk computing short circuit
currents that are below the magnitudes of short
circuit and arc flash currents that are actually
present at the ends of conductors, where circuit
breaker panels or substations are located. If
one over-estimates the short circuit current, the
time delay of the circuit breakers affected will
tend to be reduced based on the typical time
current curve characteristic of circuit breakers.
If the response time of a circuit breaker is
reduced in terms of the time current curve plots
due to higher short circuit current level
estimates being produced, and if these short
circuit current level estimates are in error, the
actual energy released could be much greater
because the circuit breaker will trip in response
to the actual short circuit current magnitude,
which will be lower than that which is calculated
using shorter conductor lengths, and will
typically involve a trip characteristic that
involves a longer time delay (perhaps a long
time trip rather than a short time trip, or a short
time trip rather than an instantaneous trip).
This could dramatically increase the Personnel
Protective Equipment level that is required
compared to the level predicted in a study.
Introduction
The selection of Personnel Protective
Equipment is based on the magnitude of the
energy released.
Power is energy per unit time, so energy is:
E = R(I2
)t.
This is computed as:
(Rlower) Isc-lower
2
tsc-lower > (Rhigher) Isc-higher
2
tsc-higher,
If the variation between Isc-higher and Isc-lower is
small enough while the magnitude of tsc-lower is
sufficiently greater than tsc-higher due to a much
greater circuit breaker response time associated
with the lower fault current, the energy
released for the lower short circuit current
could be much greater if the circuit breaker
requires considerably more time to respond to
the lower arc flash current level (perhaps a long
time trip response rather than an instantaneous
or short time trip response). This assumes that
Rlower and Rhigher are roughly equal for
approximately the same short circuit or arc
flash level.
Arc Flash current levels at low Voltage tend to
be proportional to the fault current level.
Experience demonstrates that arc flash currents
are diminished by some twenty percent1
relative to the three-phase fault level.
If the time required for a trip response
associated with the lower arc flash current
affects a greater time delay, perhaps several
seconds due to a long time trip unit reacting for
a lower level current, which is much longer than
the short time or instantaneous delay of the
higher short circuit current estimate, the total

2. 2
energy released for the lower level arc flash
current will actually be substantially greater
than that computed for the higher current.
If the short circuit current estimated due to
shorter than actual conductor length places the
trip response time to the right of a trip device
characteristic segment that is vertical, and if the
short circuit current (arc flash current) is
actually to the left of the trip device
characteristic, the time difference in the
response of the trip device could be so great as
to dramatically increase the Personnel
Protective Equipment (PPE) level that is
required. Note that PPE levels are based on the
computed short circuit current and time delay
and the minimum arc flash current level
calculated to be present.
If the arc flash current level computed based on
the conductor length is too great, based on too
short an estimate of conductor length, the time
required for the circuit breaker response could
be much less than that which occurs in reality,
and the PPE required to provide adequate
protection to personnel in reality could similarly
increase dramatically in comparison. In effect,
personnel could be left inadequately protected
from arc flash hazard due to estimates of
conductor length that are too short. Even with
a suitable engineering study, this fact could
never be described within its pages if the
engineer is not aware of this danger, or if the
engineer’s work environment does not grant
the time to consider this possibility while
performing the study.
Analysis
The concept being presented is illustrated in
Figure 1.0.
Figure 1.0 – Time Current Curve Illustration of
Circuit Breaker with Long Time and
Instantaneous Trip Devices and Two Arc Flash
Currents with Response Times, Each Separated
by a Few Hundred Amperes (Roughly the
Thickness of the Circuit Breaker’s Time Current
Curve).
If the length of a cable is underestimated, the
calculated arc flash may appear to force a
response to the fault level on the right (see
Figure 1.0). In reality, a more realistic estimate
of the cable length may make it respond to the
arc flash current level on the left (also Figure
1.0), involving a much longer response time
(perhaps several seconds instead of roughly one
tenth second).
In Figure 1.0, the energy released for the 15 kA
current is:
I2
tR = 15 kA 2
(0.10 sec.)R = 22,500,000 A2
R sec.
The energy released for the 14.7 kA current is:
I2
tR = 14.6 kA 2
(7.0 sec.)R = 1,512,630,000 A2
R
sec.
If the arc flash current in reality is only (roughly)
300 Amperes (the thickness of the circuit
breaker trip characteristic) lower than the
computed value, the energy released will
actually be greater for 14.7 kA of arc flash
current than for 15 kA of arc flash current. It is
thus clear that if the arc flash current is

3. 3
estimated to be over-valued, in a manner
consistent with the estimation of short circuit
current and too short conductor length
estimates, the actual energy released and the
arc flash personnel protective equipment (PPE)
level could be considerably greater than that
predicted by the arc flash study, based on a
higher short circuit estimate (and a lower circuit
breaker response time), would predict.
The single-line diagram for the power system to
be examined to prove this concept follows in
Figure 2.0.
Figure 2.0 – Sample Single-line Drawing with
Buses One, Two, and Three Shown
The system consists of a utility source, a
transformer that steps the Voltage down from
12.47 kV to 480 V. and a single cable extending
the system. This model, as realized in Table 1.0,
with an approximate 500 foot long conductor,
might represent an older system in which two
or three conductors have been “daisy chained”
to produce the single, 500 foot long conductor
that is modeled. An available short circuit MVA
(SCMVA) of 100 is used in this model, and may
represent utility loads in urban areas where the
magnitude of the three-phase short circuit
current is intentionally reduced by controls
imposed by the utility.
Short Circuit Calculations for Model of Figure 1.0
Utility PU Impedance
100000000 12470 1.555009 Ohms
VA VOLTS 1 pu Z
Transformer PU
Impedance
2500000 5.75% 2.3 pu Z
0.0052992 2.3
Ohms pu

4. 4
Cable PU Impedance
Cable Ohms
0.118 Per 1000 ft
Cable Imp. % of 500 Ft.
pu Cable
Imp. Cable Length
0.0590 100.0% 25.61 100% (500 Ft.))
0.0575 97.5% 24.97 97.5% (475 Ft.)
0.0561 95.0% 24.33 95% (450 Ft.)
0.0546 92.5% 23.69 92.5% (425 Ft.)
0.0531 90.0% 23.05 90% (400 Ft.)
Short Circuit Currents
Total Pu
Impedance Current (A) Bus
Currents at Buses In
System
Utility 1.00 4630 1
Trans. Sec. 3.30 36450 2
Cable End 28.91 4161 3 100% of 500 Ft. Cable
(Based on 28.27 4255 3 97.5% of 500 Ft. Cable
500 Ft. 27.63 4354 3 95% of 500 Ft. Cable
Total Cable 26.99 4457 3 92.5% of 500 Ft. Cable
Length) 26.35 4565 3 90% of 500 Ft. Cable
Table 1.0 – Short Circuit Calculations (Includes Multiple Calculations of Current Based on Various Cable
Lengths at Bus Three)
The short circuit currents at each bus are clearly
marked in Table 1.0 (relative to Figure 2.0). The
values for Bus Three are shown for various
estimated lengths of the conductor, from 100%
of the conductor length to 90% of its length.
With circuit breaker characteristics typically a
few hundred Amperes in horizontal thickness, it
is clear that errors in estimating cable lengths,
and particularly so-called “conservative”
estimates of length (producing higher short
circuit current magnitudes) can produce results
that leave the arc flash current estimate to the
right of the time current curve short time or
instantaneous response characteristic, while
the actual fault level may exist to the left of the
time current curve, in the long time range
(given some 400 Amperes of variation between
100% accuracy at 500 feet and 90% accuracy at
450 feet). If the true, lower arc flash current
level were computed it could add seconds to
the response time, while leaving the arc flash
current essentially in the same range as it was,
producing a need for much more elaborate PPE
(or eliminating the possibility of PPE) than
would exist if the short time or instantaneous
trip were to respond to an arc flash.

5. 5
Short Circuit Currents for Various Sources, Transformers, and Cables
(480 V) (480 V)
Current at Bus Current at Bus Difference in
12470
V Transformer Cable Length 480 V at End of Cable (A) at End of Cable (A) Current
SCMVA kVA (Feet) Cable Size (100% of Length) (90% of Length) (Amperes)
100 2500 500 #8 822 911 89
2.3 0.3295 143
pu value Ohms pu Z
100 500 500 500 MCM 5299 5548 249
11.5 0.0235 10
pu value Ohms pu Z
500 2500 500 #8 827 917 90
11.5 0.3295 715
pu value Ohms pu Z
500 500 500 500 MCM 5493 5761 268
57.5 0.0235 51
pu value Ohms pu Z
Note: Cable is #8, or 0.659 Ohms per 1000 Ft. OR
Cable is 500 MCM, or 0.047 Ohms per 1000 Ft.
Transformer is 5.75% impedance.
Table 2.0 – Variations in Current due to Estimation Based on Cable Size and Available SCMVA at Source
Causes
What might cause circuit breakers to be set in a
manner that would produce results that would
push the time current curve characteristic so far
to the right in the time current curve plot? One
might imagine a few easily, the most obvious of
which would be conditions under which many
circuit breakers exist in series in older buildings,
so that there is a need to make the most of the
area of the time current curve when
coordinating circuit breakers. From the
perspective of the person developing the
settings, the results of the arc flash study and
coordination study may appear to produce a
perfectly legitimate result in terms of circuit
breaker settings, if the possibility of failure to
properly estimate cable lengths and
overestimates of short circuit current are not
considered.
Table 2.0 illustrates the variation in short circuit
current that would result due to variations in
conductor length and available SCMVA (short
circuit MVA). The short circuit current variation
could be as great as approximately 250
Amperes for a ten percent error in judgement
of cable length for a 500 MCM cable. Based on
this, for transformers that are rated at 480 Volt
and no larger than 2500 kVA, and with an
available SCMVA of 500 MVA or less, and a
single cable or string of daisy chained cables of
500 feet in length with 500 MCM rating, the
maximum error would be roughly 250 Amperes.

6. 6
Given the results of Table 2.0, one could, by
making certain that the highest valued vertical
transition to the next slowest trip element of
the circuit breaker’s protective device is at least
200% of 250 Amperes to the left of the
computed minimum arc flash current level, or
500 Amperes to the left of the protective trip
device element’s intended trip for arc flash, to
insure that one need not concern oneself with
the risk of error due to estimation of cable
lengths. (See Figure 3.0.) Of course, to be
precise the specific system configuration must
be considered in each instance (as in Table 2.0)
and compared to the circuit breaker’s time
current curve plot, which is a rather time
consuming task.
Figure 3.0 – Illustration of Application of Results
of Table 2.0
The horizontal “gap” that must be maintained
and is illustrated in Figure 3.0 becomes even
worse as “estimates” of cumulative or daisy-
chained cable lengths become worse, as shown
in Table 3.0 for a 20% error.

7. 7
Short Circuit Currents for Various Sources, Transformers, and Cables
(480 V) (480 V)
Current at Bus Current at Bus
Difference
in
12470
V Transformer Cable Length 480 V at End of Cable (A)
at End of Cable
(A) Current
SCMVA kVA (Feet)
Cable
Size (100% of Length) (80% of Length) (Amperes)
500 500 500 500 MCM 5493 6057 564
57.5 0.0235 51
pu value Ohms pu Z
Note: Cable is #8, or 0.659 Ohms per 1000 Ft. OR
Cable is 500 MCM, or 0.047 Ohms per 1000 Ft.
Transformer is 5.75% impedance.
400 Feet of length estimated
Table 3.0 – Illustration of Growth of Magnitude of Error in Arc Flash Current Due to Error in Estimate of
Length of Cable (20%) (If a margin of 200% were deemed reasonable, this would require an 1100 A
“gap” between the minimum arc flash current and the rightmost portion of the vertical characteristic
transitioning to the next slowest trip response by the circuit breaker providing protection on the source
side.)
The Cure
There is a simple cure for this problem of under-
estimating cable lengths (save for computations
of the sort performed in Table 2.0 under an
assumed “certainty” in the maximum error
inherent in the estimation of the cable/wire
length). There exist today circuit breakers with
“maintenance” switch3
settings that are
designed to respond very quickly in a very
sensitive manner to arc flash current once the
“maintenance” switch on the circuit breaker has
been activated. (This is a solution
recommended in the National Electrical Code,
Article 240.87, Arc Energy Reduction.4
) These
devices typically respond in an instantaneous
manner to very low level faults in the event that
the maintenance switch is triggered. The
maintenance switch thus is placed in the “on”
position whenever work is being performed on
the load side of the circuit breaker.
There may be other solutions, such as turning
the instantaneous trip to a very low setting
whenever work is being performed on the load
side of circuit breakers, but this must be
considered in the course of an arc flash study to
allow for the starting of motors or other inrush
loads that may normally occur while energized
work is being performed.
Conclusion
Errors in the measurement of cable lengths can
produce inaccurate Arc Flash Studies and circuit
breaker settings that can appear to conform to
lower level PPE requirements (due to very
short, circuit breaker response times) while in
fact producing unrealistically high short circuit
trip intervals. As a result of much longer
response times to lower short circuit currents
by circuit breakers in reality, much greater PPE
requirements can result in general.

8. 8
If studies are performed by third parties, it may
be impossible, given the “assembly line”
mentality of many service providers, for such
errors to be caught, and where not identified,
they can produce grave dangers to personnel
and passers-by (particularly if PPE may not, in
reality, be possible to specify for a given
location and circuit breaker setting). It is, after
all, clear that long table allowing for estimates
in cable lengths are absent from most arc flash
studies. The only other potential solution,
substantially improving the estimate of
conductor lengths during data collection, is
probably unrealistic, although it might be
conceivable if estimation within 10% of the
cable length is perceived as possible, and
computing the potential error in short circuit
current as a result is undertaken (as in Table
2.0) in the course of the study.
It is virtually inevitable that slight errors in
estimates of conductor lengths will be made.
Such approaches to estimating cable lengths
actually assure adequately rated circuit
breakers in short circuit studies. Such errors
can have the opposite effect in arc flash studies.
Arc flash studies can be useful, but only if errors
in conductor length do not produce PPE levels
that underestimate arc flash durations. The use
of circuit breakers equipped with
“maintenance” switches (or potentially by
having an alternate, much lower setting for
each circuit breaker where work is to be
performed on the load side) are possible
solutions to this serious and potentially
unrecognized problem in Arc Flash studies.
Time consuming calculations (of the type
undertaken in Table 2.0 and Figure 3.0) are less
likely to occur to estimate the extent of the
offset from vertical transitions (between trip
types) in circuit breaker time current curves
based on short circuit current levels, and would
only be of value if the error in the length of the
cable estimates could be assured.
Bibliography
1. Fault Arc Resistance (magnitude), 3-Phase
Short-Circuit Current (Isc) at any Point Within a
LV Installation, http://www.electrical-
installation.org/enwiki/3-phase_short-
circuit_current_(Isc)_at_any_point_within_a_LV
_installation .
2. Energy Expressed In Terms of Current,
https://en.wikipedia.org/wiki/Joule_heating .
3. Arc Flash Reduction Maintenance System,
http://www.eaton.com/Eaton/ProductsServices
/Electrical/ProductsandServices/CircuitProtectio
n/ArcflashReductionMaintenanceSystem/index.
htm .
4. Electrical Maintenance Switch, NEC, Article
240.87, Arc Energy Reduction.
5. Anixter Technical Handbook (English Edition),
Page 92, Cable Impedance, 1/0 cable.
Biography
Del John Ventruella is licensed as a Professional
Engineer in the District of Columbia. He
completed the Bachelors of Science degree in
Electrical Engineering from The Rose-Hulman
Institute of Technology in Terre, Haute, Indiana
and immediately went to work for a multi-
national firm offering power systems
engineering studies to heavy industry, hospitals,
and airports. In time he came to assume
responsibility for his own territory, and began
completion of the Masters of Science degree in
electrical engineering at The University of
Alabama at Birmingham. He specialized in
power systems, but also completed coursework
in robotics and control systems. He has
authored papers for the IEEE, and presented
them at local meetings and international
conferences.