Worked problem

Size a Three-Phase Transformer for a Mixed Load

Total the connected kVA of lighting, receptacle, HVAC and miscellaneous loads, add growth, choose a standard kVA rating, and find the primary and secondary full-load currents.

Electrical & Power · Last reviewed

Given

A small commercial building on a 480 V primary, 208Y/120 V secondary, 3-phase dry-type transformer. Calculated loads: lighting 18 kVA, receptacles 24 kVA, HVAC 45 kVA, miscellaneous 12 kVA. The owner wants 20% spare capacity for future load.

Find

The standard transformer size and the full-load current on each side.

Solution

  1. Connected load = 18 + 24 + 45 + 12 = 99 kVA.
  2. With 20% growth: 99 × 1.20 = 118.8 kVA.
  3. Standard three-phase kVA ratings run 75, 112.5, 150, 225 and 300. 112.5 kVA is below 118.8, so choose 150 kVA.
  4. Secondary full-load current = kVA × 1000 ÷ (√3 × V) = 150,000 ÷ (1.732 × 208) = 416 A.
  5. Primary full-load current = 150,000 ÷ (1.732 × 480) = 180 A.

Answer

150 kVA | 416 A secondary at 208 V | 180 A primary at 480 V

Common mistakes

  • Adding kW instead of kVA when the loads have different power factors.
  • Using single-phase kVA = V × I ÷ 1000 on a three-phase transformer. The √3 is missing.
  • Sizing to exactly the connected load and leaving no capacity for growth or the inrush of motor starting.
  • Treating the transformer rating as the demand load. Real demand is often below the connected total, and the code has its own demand-factor rules for specific load types.

Try a variation: a larger building

  1. Connected load is 140 kVA. With 25% growth: 140 × 1.25 = 175 kVA.
  2. The next standard size above 175 kVA is 225 kVA.
  3. Secondary full-load current at 208 V = 225,000 ÷ (1.732 × 208) = 625 A.
  4. Primary full-load current at 480 V = 225,000 ÷ (1.732 × 480) = 271 A.
  5. The expected loading on day one is 140 ÷ 225 = 62%.

Rules of thumb

Three-phase full-load current is about 2.78 A per kVA at 208 V and 1.20 A per kVA at 480 V. They let you check a transformer current quickly. A 150 kVA unit at 208 V is about 417 A, which matches the 416 A calculated.

Related tools and labs

Calculators, labs and simulators are part of the All-Access Pass.

More worked problems

Questions

Why 150 kVA and not 118.8 kVA?

Transformers are made in standard sizes. You pick the first standard size at or above the calculated load.

Does this size the primary and secondary protection?

No. The overcurrent protection and conductors follow the code rules for transformers, which use these currents as the starting point.

What about the transformer impedance and short-circuit current?

That is a separate calculation. See the short-circuit problem in this section.

Does transformer impedance matter for sizing?

It does not set the kVA size, but it affects the voltage regulation under load and the available fault current. Check both after you choose the size.

What about transformer efficiency rules?

Many jurisdictions regulate the minimum efficiency of distribution transformers. Check the rules that apply to the project when you specify the unit.

Educational material. Examples use simplified, hypothetical inputs and are not a design, a construction document or professional engineering advice. Confirm requirements with the codes and standards adopted where the work is built and with a licensed engineer.

← All worked problems