Short Circuit Capacity: Basic Calculations and Transformer Sizing

Short circuit capacity calculation is used for many applications: sizing of transformers, selecting the interrupting capacity ratings of circuit breakers and fuses, determining if a line reactor is required for use with a variable speed drives, etc.

The purpose of this information is to gain a basic understanding of short circuit capacity. The application example utilizes transformer sizing for motor loads.

Conductor impedances and their associated voltage drop are ignored not only to present a simplified illustration, but also to provide a method of approximation by which a plant engineer, electrician or production manager will be able to either evaluate a new application or review an existing application problem and resolve the matter quickly.  

The following calculations will determine the extra kVA capacity required for a three phase transformer that is used to feed a single three phase motor that is started with full voltage applied to its terminals, or, "across-the-line."

kVA of a three phase transformer = V x A x 1.732, where 1.732 = the square root of 3. The square root of 3 is introduced for the reason that, in a three phase system, the phases are 120 degrees apart and, therefore, can not be added arithmetically. They will add algebraically.

Transformer Connected To the REC Power Line

The first transformer is rated 1000 kVA, 433 secondary volts, 5.5% impedance.  Rated full load amp output of the transformer is

 1000 kVA / (433 x 1.732) = 1333 amps


The 5.5% impedance rating indicates that 1333 amps will flow in the secondary if the secondary is short circuited line to line and the primary voltage is raised from zero volts to a point at which 5.5% of 433 volts, or, 23.81 volts, appears at the secondary terminals. Therefore, the impedance (Z) of the transformer secondary may now be calculated:

 Z = V / I = 23.81 volts / 1333 amps = .018 ohms

The transformer is connected directly to the REC power lines which we will assume are capable of supplying the transformer with an unlimited short circuit kVA capacity. The REC company will always determine and advise of the short circuit capacity available at any facility upon request.

With unlimited short circuit kVA available from the utility, the short circuit amperage capacity which the transformer can deliver from its secondary is

 433 volts / .018 = 24,055 amps

An alternative method of calculating short circuit capacity for the above transformer is:

 1333 amps x 100 / 5.5% = 1333 / .055 = 24,236 amps

Now we are ready to apply a motor to the terminals of the transformer secondary. We must determine the voltage drop which will be caused by the motor inrush on start. If the voltage remains within the rated voltage of the motor, then no over sizing of the transformer is required.

Motors rated for 420 volts are for use with distribution systems that are rated at 440 volts. The rating system allows a twenty volt drop in the distribution system which may occur along the feeder cables which connect the power transformer to the load. The specification for a standard motor is that it requires the motor to be capable of operating at plus or minus 10% of nameplate voltage. Therefore, the voltage drop on inrush should not be allowed to drop below 440 volts less 10%, or, 396 volts.

The transformer will be asked to supply power to a motor which has a full load amp rating of 1333 amps, which will fully load the transformer. Therefore, we will rate the motor at 420 V x 1333 A x 1.732, or, 969 kVA. We will assume that our motor will have an inrush of 600% of its full load rating which will cause an inrush of

 440 V x 1333 A x 600% x 1.732 = 6095 kVA

The voltage drop at the transformer terminals will be proportional to the motor load. The voltage drop will be expressed as a percentage of the inrush motor load compared to the maximum capability of the transformer. The transformer has a maximum kVA capacity at its short circuit capability, which is

440 V x 24,236 A x 1.732 = 18,470 kVA

 The voltage drop on motor inrush will be

 6095 kVA / 24,236 kVA = 0.251, or, 25.1%

The transformer output voltage will drop to 480 x .669, or, 329 volts. Thus, we can see that the transformer is much too small to use a motor that has a full load rating equal to the full load capacity of the transformer.

The transformer must be sized so that its short circuit capability is equal to or greater than 6095 kVA times 10, or, 60,950 kVA in order to have a voltage drop of 10% or less. Therefore, the short circuit amperage capacity of the transformer to be used must be a minimum of

 60,950 kVA / (440 V x 1.732) = 79976 amps

A typical 2500 kVA, 5.75% impedance transformer will have a short circuit capacity of 52,300 amps. The next highest standard size transformer at 3750 kVA will have a 6.5% impedance and would have a short circuit output capability of 69,395 amps which will be sufficient. In the particular application discussed, the ratio of the selected standard size transformer kVA to motor kVA is 3750 kVA / 969 kVA = 3.8. Thus the transformer rating is 380% larger, or, nearly four times, the rating of the motor. Note the non-linear effect of the impedance rating of the transformers on their short circuit capacities.

Motor Contribution to Short Circuit Capacity

When a fault condition occurs, power system voltage will drop dramatically. All motors that are running at that time will not be able to sustain their running speed. As those motors slow in speed, the stored energy within their fields will be discharged into the power line. The nominal discharge of a motor will contribute to the fault a current equal to up to four times its full load current.

With our 1000 kVA, 1333 amp transformer example given above, we will assume that all 1333 amps of load are from motors. The actual short circuit current will equal 24,236 amps plus 400% of 1333 amps for a total of 29,568 short circuit amps.

When sizing the transformer for motor loads, the fault current contribution from the motors will not be a consideration for sizing. However, the motor contribution must be considered when sizing all branch circuit fuses and circuit breakers. The interrupting capacity ratings of those devices must equal or exceed the total short circuit capacity available at the point of application.

Motor contribution to short circuit capacity must be included when adding a variable frequency drive to the system.