Three Phase Amps

Three Phase Amps

Purpose

Electrical services are usually sized by amperage, kilovolt-amps (kVA), or by horsepower (HP) requirements. In order to size metering equipment properly, it is often necessary to calculate amps when the transformer size (kVA) is known. Never get in a habit of adding amps! However, when calculating amps based upon installed kVA capacity, you do need to add up the total kVA. The correct formula is given below for calculating three phase amps. This formula works for transformer banks with closed Wye or Delta secondary (3 transformers) configurations. The key to using this formula is to use the line to line voltage provided by the transformer bank, not the line to neutral voltage!

The following formula may be used for calculating three-phase amps:

kVA X 1,000

Three-phase amps = -----------------------------------------

1.732 X Line to Line voltage

Example 1:
Assume you are using 3 – 100 kVA 120/240 volt transformers. The line to line voltage of the transformer bank is 240 volts. Therefore, use 240 volts in the formula. Since you are using 3 – 100 kVA transformers, the total capacity will be 300 kVA.

300 kVA X 1,000 300,000 VA

Three-phase amps = ------------------------- = --------------------- = 721.71 amps

1.732 X 240 V 415.68V

Rule of Thumb

To avoid using the above formula, use the following chart for an Amps per kVA constant:

Line to Line                  Amps
          Voltage                      per kVA
            208 volts        =            2.8
            240 volts        =            2.4
              480 volts        =            1.2

Example 2:
Assume you are using 3 – 100 kVA 120/240 volt transformers. The line to line voltage of the transformer bank is 240 volts. Therefore, use 2.4 for the Amps per kVA constant in the formula. Since you are using
3 – 100 kVA transformers the total capacity will be 300 kVA.

Amps per
Three-phase amps = kVA Constant X Total kVA = 2.4 X 300 kVA = 720 amps

Notice the answer is extremely close to the answer given by the exact formula used in example 1. Sizing equipment is made very easy by remembering these three little Amps per kVA constants. Simply choose the correct line to line voltage, multiply the corresponding Amps per kVA constant times the total installed transformer capacity and you are done. No long formula, no division, no square root of 3, etc…

Example 3:
Assume you are using 3 – 25 kVA 120/240 volt transformers with paralleled windings for a 120/208 volt Wye secondary. The line to line voltage of the transformer bank is 208 volts. Therefore, use 2.8 for the Amps per kVA constant in the formula. Since you are using 3 – 25 kVA transformers the total capacity will be 75 kVA.

Amps per
Three-phase amps = kVA Constant X Total kVA = 2.8 X 75 kVA = 210 amps

Once again, sizing equipment is made very easy by using the appropriate Amps per kVA constant.

Example 4:
Assume you are using 3 – 37.5 kVA 240/480 volt transformers with a 480 volt secondary. The line to line voltage of the transformer bank is 480 volts. Therefore, use 1.2 for the Amps per kVA constant in the formula. Since you are using 3 – 37.5 kVA transformers the total capacity will be 112.5 kVA.

Amps per
Three-phase amps = kVA Constant X Total kVA = 1.2 X 112.5 kVA = 135 amps

Open Delta Transformer Secondary

An open Delta transformer secondary only requires two transformers. However, the total transformer capacity is reduced to 86% of the total kVA. Therefore, the previously used rule of thumb may be applied along with 86% to calculate three phase amps for open Delta transformer banks.

Example 5:
Assume you are using 2 – 50 kVA 120/240 volt transformers with a 240 volt open Delta secondary. The line to line voltage of the transformer bank is 240 volts. Therefore, use 2.4 for the Amps per kVA constant in the formula. Since you are using 2 – 50 kVA transformers the total capacity will be 100 kVA X 86% = 86 kVA.

Amps per
Three-phase amps = kVA Constant X Total kVA = 2.4 X 86 kVA = 206.4 amps

Never Add Amps!

Adding amps may be done under certain circumstances, however, it is also responsible for many incorrectly sized electrical installations. Therefore, unless you are certain you thoroughly understand how circuits work, it is best not to get in the habit of adding amps.

Example 6:
In the following diagram, amperage has been measured on all three phases. Each phase has been measured at 100 amps. This is a balanced 100 amp three phase load. Not a 300 amp load! The conductors connecting the transformers and the rest of the main secondary service must be capable of carrying 100 amps not 300 amps. Once again, do not get in the habit of adding amps!

Metering Equipment & Transformer Sizing

Example 7:
An electrician says a new three-phase 120/240 volt Delta service will require up to 600 amps. Use the previously stated rule of thumb in reverse. Divide 600 amps by the Amps per kVA constant for a line to line voltage of 240 volts. 600 divided by 2.4 is 250. 250 is the total kVA required. Each transformer will need to be a minimum of 83 kVA to carry a balanced 600 amp load. Many electrical utilities would install 3 – 75 kVA transformers even though they are only capable of delivering 540 amps on a continuous basis. If 600 amps are only required for short periods of time, and the transformers are fused properly, the transformers will not be harmed. If in doubt, install 3 – 100 kVA transformers, which can provide 720 amps. Current transformers with a 200/5 ratio with a RF of 3.0 would be appropriate. Be sure to use a class 20 meter since the 200/5 CT’s can deliver up to 15 amps under these load conditions.

Example 8:
An electrician says a new three-phase 120/208 volt Wye service will require up to 400 amps. Use the previously stated rule of thumb in reverse. Divide 400 amps by the Amps per kVA constant for a line to line voltage of 208 volts. 400 divided by 2.8 is approximately 143. 143 is the total kVA required. Each transformer will need to be a minimum of 48 kVA to carry a balanced 400 amp load. Install 3 – 50 kVA transformers which can provide up to 420 amps. Current transformers with a 200/5 ratio with a RF of 2.0 would be appropriate. A class 10 or 20 meter may be used.

Example 9:
An electrician says he needs to hook up a three-phase 40 HP 480 volt water well. Most books list 1 HP = 746 watts, but when sizing equipment always assume 1 HP = 1 kVA. Therefore, 40 HP = 40 kVA. Three 15 kVA transformers are required to provide a total of 45 kVA. Since the line to line voltage will be 480 volts, 40 kVA multiplied by 1.2 (480 volt Amps per kVA constant) = 48 amps. Obviously a class 100 or 200 self-contained meter can be used for this load. However, if you do not wish to use a 480 volt rated meter due to safety and reliability concerns, use 480:120 volt voltage transformers with 50/5 ratio CT’s. 200/5 CT’s with 1 turn may also be used if the water well has no auxiliary light loads to worry about. If the water well is either on (full load) or off (no load), then light load conditions which could cause accuracy errors if CT’s are too large do not exist. (Always strive provide an instrument rated meter with a minimum of .25 amps to improve light load accuracy).