Making Sense of the Numbers

By Jim Phillips | Nov 15, 2012
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One of the first steps in performing an arc flash hazard calculation study is to request the short-circuit data from the electric utility company. This information is critical because it defines the magnitude of current that could flow from the utility and is used as a starting point for arc flash calculations.

In addition to requesting this data for normal operating conditions, it should also be requested based on minimum short-circuit current conditions, if available. The minimum condition could be for a utility transformer or transmission line out of service or similar scenario. The minimum value can then be used to determine if the lower current could result in a protective device operating more slowly, which may increase the total incident energy during an arc flash.

Too many numbers—now what?
Unfortunately, a single standardized format for short-circuit data does not exist. Instead, depending on the individual utility, data may be provided in one of several different formats such as the following:

• Short-circuit amperes (A)
• Short-circuit megavolt-amperes (MVA)
• Per-unit and symmetrical components

Of course, with multiple formats, confusion could (and often does) result. I will compare the different formats using a three-phase short-circuit current of 6,000A at the 23-kilovolt (kV) level. Since arc flash calculations are based on a three-phase model, only the three-phase short-circuit calculations are used. Some of the values are slightly rounded.

Short-circuit ampere format
This is the simplest format because it defines the short-circuit current in terms of amperes at a specified location. As an example, the utility has provided the following information:

Short-circuit amperes three-phase = 6,000A
Voltage = 23 kV line-to-line

Since the data is already in terms of amperes, no additional calculations are necessary.

Short-circuit MVA format
Utility companies often provide short- circuit data in terms of short-circuit MVA. This format combines the short-circuit current with the voltage and the square root of 3 (for a three-phase representation) to provide the data in terms of short-circuit power. Below is an example of the MVA format.

Three-phase short-circuit
MVA = 240 MVA
Voltage = 23 kV line-to-line

To convert three-phase short-circuit MVA to short-circuit current in amperes, use the following equations:

Short-circuit amperes = [MVA x 1,000] / [kV line-to-line x the square root of 3]
where 1,000 is the conversion from MVA to kVA
Short-circuit amperes = [240 MVA x 1,000] / [23 kV line-to-line x 1.732]
Short-circuit amperes = 6,000A

Per-unit and symmetrical components format
The per-unit and symmetrical component format can appear to be the most complex of all. The term “per-unit” is simply the decimal equivalent of percent, i.e., 50 percent is equal to 0.5 per unit. In general, the per-unit method takes every electrical quantity and scales it by a reference value known as a base quantity. The utility derives the base values from two numbers: the MVA base and kV base.

Symmetrical components is a method used for solving complex unbalanced power system problems. Such terms as positive, zero and negative sequence are part of the vocabulary of this method, and although the actual theory can be quite complex, calculating the short-circuit current using this approach is not that difficult.

The example below illustrates short-circuit data using the per-unit system and symmetrical components:

MVA base = 100 MVA
kV base = 23 kV line-to-line
Z1 = 0.418 p.u.

Z1 is referred to as the positive sequence impedance and represents the equivalent impedance of the utility in this case. One hundred MVA and 23 kV are the base power and voltage used to determine the “base values” necessary for the calculations.

For the three-phase short-circuit current, only three steps are needed to convert the per-unit and symmetrical component values to short-circuit current in amperes:

Step 1: Calculate the base current (I base) using the following equation:

I base= [MVA base 1,000] / [kV base x the square root of 3]
= [100 MVA x 1,000] / [ 23kV x the square root of 3]
= 2,510A

Step 2: Calculate the per-unit three-phase short-circuit current (I p.u.) with the following equation:

I p.u. = V p.u. / Z1

V p.u. in the equation above is the per-unit voltage. In the absence of being provided the per-unit voltage, which is usually the case, it is common to assume it is 1.0 p.u. This means the actual voltage is 100 percent of the base voltage, so for this example:

V p.u. = 1.0
I p.u. = 1.0 / 0.418 = 2.39 p.u.

Step 3: Convert per-unit short-circuit current to amperes with the following equation:
I amperes= I p.u. I base
= 2.39 p.u. 2,510A
= 6,000A

Different methods = same results
Although the three methods seem quite different from each other and some are more complicated, they all produce the same result, which can be used as the starting point for arc flash calculations.

PHILLIPS, founder of and, is an internationally known educator on electrical power systems and author of “Complete Guide to Arc Flash Hazard Calculation Studies.” His experience includes industrial, commercial and utility systems, and he is a member of the IEEE 1584 Arc Flash Working Group. Reach him at [email protected].

About The Author

PHILLIPS, P.E., is founder of and provides training globally.  He is Vice-Chair of IEEE 1584 Arc Flash Working Group, International Chair of IEC TC78 Live Working Standards and Technical Committee Member of NFPA 70E.  He can be reached at [email protected].






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