Introduction #

This guide is for electrical engineers, facility managers, and designers who need to size three-phase transformers for industrial and commercial distribution. It solves the problem of calculating transformer kVA from load (kW and power factor) or from line voltage and current, and of handling unbalanced loads. Use this knowledge when specifying three-phase transformers, verifying nameplate kVA, or converting between line and phase quantities.

For the overall sizing process, see the Transformer Sizing Guide.

Single-Phase vs Three-Phase Transformer Sizing #

Single-phase transformers serve single-phase loads (lighting, small motors, outlets). Three-phase transformers serve three-phase loads (motors, chillers, industrial machinery, distribution boards). Industrial and commercial facilities typically use three-phase transformers for main distribution because most loads are three-phase and three-phase delivery is more efficient. Sizing principles are the same: determine load kVA, apply diversity and power factor, add safety margin, and select standard size. The difference is the formula used to get kVA from voltage and current: single-phase uses V × I; three-phase uses √3 × V_L × I_L (line voltage and line current). For the overall process, see the Transformer Sizing Guide. To convert kW to kVA when you have power factor, use the PF–kW–kVA tool; for full sizing use the Transformer Size Calculator.

Three-Phase Transformer kVA Formula #

For balanced three-phase load, apparent power (kVA) is:

Formula:

S (kVA) = (√3 × V_L × I_L) ÷ 1000

Where:

  • V_L = line-to-line voltage (V)
  • I_L = line current (A), same for each phase in a balanced load
  • √3 ≈ 1.732

Why √3: In three-phase, phase voltage V_ph = V_L ÷ √3 (wye) and line current I_L equals phase current I_ph in wye. Power per phase = V_ph × I_ph; total power = 3 × V_ph × I_ph = 3 × (V_L ÷ √3) × I_L = √3 × V_L × I_L. So the √3 relates line quantities to total three-phase apparent power. For delta connection, the same expression holds for total power in terms of line voltage and line current.

When load is given in kW and power factor, kVA = kW ÷ PF; the formula above is used when you have voltage and current (e.g. from measurement or equipment nameplate).

Line Voltage vs Phase Voltage Explained #

  • Line voltage (V_L): Voltage between two line conductors (e.g. L1–L2). This is the voltage normally specified (e.g. 400 V, 415 V, 480 V).
  • Phase voltage (V_ph): In wye, voltage between one line and neutral: V_ph = V_L ÷ √3. In delta there is no neutral; phase voltage equals line voltage (V_ph = V_L).

For transformer sizing, use line voltage and line current in the kVA formula. Equipment nameplates and distribution voltages are usually given as line-to-line. Ensure the transformer’s primary and secondary voltage ratings match the system line voltages.

Example: Three-Phase Transformer Sizing Calculation #

Given: Balanced three-phase load 200 kW at 0.88 PF. Voltage 480 V line-to-line. Safety margin 25%.

Step 1 – Required kVA:
kVA = 200 ÷ 0.88 ≈ 227.3 kVA.

Step 2 – With margin:
227.3 × 1.25 ≈ 284.1 kVA.

Step 3 – Standard size: Select 300 kVA transformer.

Check with current (optional):
I_L = (227.3 × 1000) ÷ (√3 × 480) ≈ 273.4 A. The transformer must be capable of 273 A per phase on the secondary at 480 V (and corresponding primary current at primary voltage).

Common line voltages and same load (200 kW, 0.88 PF, 25% margin → ~284 kVA):

Line voltage (V) Required kVA (with margin) Typical selection
400 V ~284 kVA 315 kVA
415 V ~284 kVA 315 kVA
480 V ~284 kVA 300 kVA

The kVA is set by load and margin; the line voltage sets the current (I_L = kVA × 1000 ÷ (√3 × V_L)). Lower voltage means higher current for the same kVA, so cable and protection must be sized for that current.

Load Balance and Its Impact on Sizing #

Balanced load means equal current (and power) on all three phases. The kVA formula and sizing above assume balance. Unbalanced load means one or two phases carry more current than the third. The transformer must be sized for the worst phase: the phase with the highest current (or highest phase kVA) determines the required capacity. If phase A is 100 kVA and phases B and C are 60 kVA each, total is 220 kVA but the transformer is effectively limited by the 100 kVA phase; severe unbalance can force a larger transformer than the simple sum of phase kVA would suggest. In practice: calculate per-phase kVA where imbalance is known, take the maximum phase demand, apply safety margin, and round up to standard size. Unbalance also increases losses and can cause neutral current in four-wire systems; consider load balancing to reduce transformer and cable loading.

Common Three-Phase Sizing Mistakes #

Mistake 1: Using Phase Voltage Instead of Line Voltage in the Formula #

Error: Using phase voltage (e.g. 277 V on a 480 V wye system) in the kVA formula instead of line-to-line voltage.

Correct approach: The standard three-phase formula uses line voltage V_L: S (kVA) = (sqrt(3) x V_L x I_L) / 1000. Using V_ph understates kVA by a factor of sqrt(3) and leads to undersizing. Always use line-to-line voltage and line current.

Mistake 2: Ignoring Power Factor #

Error: Sizing from kW only (e.g. 200 kW to 200 kVA) when power factor is less than 1.

Correct approach: Always use kVA = kW / PF. A 200 kW load at 0.88 PF requires 227 kVA, not 200 kVA. Use the PF-KW-kVA tool to convert; then apply safety margin and round up to standard transformer size.

Engineering recommendation: For three-phase sizing, start from load kVA (kW / PF) or from measured/nameplate line voltage and line current. Apply diversity and safety margin per the Transformer Sizing Guide, then round up to the next standard size. For unbalanced installations, size on the maximum phase demand and document the assumption.

Frequently Asked Questions #

Q1: What is the three-phase transformer kVA formula? #

A: For balanced three-phase load, S (kVA) = (sqrt(3) x V_L x I_L) / 1000, where V_L is line-to-line voltage (V) and I_L is line current (A). When load is given in kW and power factor, use kVA = kW / PF first, then apply safety margin and select standard size.

Q2: How does unbalanced load affect three-phase transformer sizing? #

A: Size for the phase carrying the highest current (or highest phase kVA). Do not use the average or the sum of phase kVA without checking the worst phase. Severe unbalance can require a larger transformer than the simple total would suggest; document the assumption.

Conclusion #

Three-phase transformer sizing uses the formula S = sqrt(3) x V_L x I_L with line voltage and line current. Always use kVA from kW and power factor; apply safety margin and round up to standard size. For unbalanced loads, size on the maximum phase demand. Verify with the calculator and match transformer connection (delta/wye) to the system.

About the Author: David Kim, P.E. is a senior power systems engineer with 14+ years of experience in transformer design, substation engineering, and industrial power systems. Former ABB application engineer specializing in transformer selection and 3-phase distribution. Has designed distribution systems for manufacturing facilities, data centers, and commercial buildings. All content in this guide has been reviewed and validated by licensed engineers.