# Transformer Sizing with Mixed Loads (Three-Phase & Single-Phase)

I am trying to size/validate the rating on the medium voltage main transformer for an industrial plant. For some reason I can't find many resources that indicate how to properly do this when you have mixed loads. Mixed loads meaning three-phase three pole, single-phase two pole, and single-phase one pole loads.

Suppose, for example, the transformer feeds a 3$$\\phi\$$, 4W panelboard with the following loads:

• (2) -- 100 A, 600 VAC, 3$$\\phi\$$, 3P
• (2) -- 50 A, 600 VAC, 1$$\\phi\$$, 2P
• (2) -- 15 A, 347 VAC, 1$$\\phi\$$, 1P

What is the proper way of determining the supply transformer rating?

My thoughts/work:

1. I could simply calculate the apparent power using both the three-phase and single-phase formulas and add them together. Resulting in:

$$S_{TOTAL} = \sqrt3 * 600 V_{LL} * 200 A + 600 V_{LL} * 100 A + 347 V_{LN} * 30 A = 278 kVA$$

1. I could also recognize that the legs need to be distributed in the panelboard -- the three-phase load will be added to all phases, but single-phase loads can't be split up evenly. Resulting in:

$$S_{TOT} =99.3 kVA * 3 = 297.9 kVA$$

1. Neither of these items take into account standard transformer sizing, derating, power factor, demand factor, or allowable loading.