Calculation of transformer power for supplying of three-phase motors

A transformer supplying a motor should be selected in such a way so that it will not change the motor parameters. During start-up the motor absorbs a high current which causing a big voltage drop at the secondary of the transformer and a significant voltage drop supply network. This has an adverse influence on the operation of other loads and can result in the stalling and contactor drop leading to blackout of loads. Reduction of voltage during start-up can be limited to an admissible range (usually Uallowed ≥ 0.85xUn), by application of a bigger transformer and larger cabling, but it increases the cost of installation. It is therefore better to reduce motor starting current to avoid an unnecessary oversizing of network elements, including transformer.

A simplified selection of transformer power rating to suit a 3-phase motor is presented below. The power specified on the rating plate of the motor is the rated mechanical power (Pn) delivered to the shaft. This is real power expressed in kilowatts (kW). The real electrical power (P) absorbed the the motor at rated load depends on the motor efficiency and can be expressed by the following formula:

where: Pn – mechanical power returned on motor shaft, ηn – motor rated efficiency

The current absorbed by motor during normal operation and rated mechanical load depends on power factor of motor and it is expressed by the following formula:

where: Un – motor rated voltage, cos φn – power factor at rated load

The total power (Sc) absorbed by motor during rated operation is the apparent power expressed in kVA, which is expressed by the following formula.

The transformer supplying a 3-phase motor should be selected with a higher apparent power (ST) than the power (Sc) absorbed by the motor. St is expressed in kVA accordance to the following simplified formula:

where k is a coefficient ( k > 1)

The k coefficient may be omitted when selecting transformers for low-power motors.
For higher power motors, the coefficient k should be taken into consideration.
The value of k coefficient depends on torque, starting current, start-up duration and power factor at motor start-up.
Note: Power factor at start-up it is considerably lower than at rated load.  

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