Technical Article

# Sizing Transformers for Single- and Three-Phase Loads

December 03, 2023 by Ahmed Sheikh

## This article spotlights the principles of sizing wye and delta-connected transformers to efficiently handle single- and three-phase loads.

Sizing a transformer involves meticulously considering single- and three-phase loads to ensure optimal performance and efficiency.

##### Image used courtesy of Adobe Stock

For accurate sizing, the total KVA of the transformer must be calculated, factoring in the power demand from both three-phase and single-phase components. Single-phase loads add load to only one phase at a time, emphasizing the importance of sizing based on the largest individual phase load. This principle becomes particularly significant when dealing with wye-connected transformers, where each phase must have sufficient capacity to handle its share of the load. In the case of delta-connected transformers, which lack neutral, single-phase loads can only be connected between two of the three secondary line voltages. The calculation for transformer size in a delta-connected system involves determining the KVA of the individual phase with the largest total load and multiplying that number by three. This ensures each phase can handle its specific load, preventing under-sizing issues from a simplistic total load calculation.

Typically, the load won't consist solely of three-phase equipment; there will always be a mix of lighting, receptacles, and other single-phase loads requiring supply alongside the three-phase load. Three-phase, wye-connected transformer secondary windings supply four-wire systems, including a neutral wire; the single-phase loads for lighting and receptacles can be connected between one of the line conductors and the neutral. In the 480 Y 277-V system shown in Figure 1, 277-V single-phase lights can be connected between the line conductors and the neutral.

##### Figure 1. A 480 Y 277-V transformer secondary supplying three-phase loads and single-phase 277-V lighting. Image used courtesy of Ahmed Sheikh

In a 208 Y 120-V system like that shown in Figure 2, 120-V lights and receptacles can be connected between the line conductors and the neutral.

##### Figure 2. A 208 Y 120-V transformer secondary supplying three-phase loads and single-phase 120-V lighting and receptacles. Image used courtesy of Ahmed Sheikh

Single-phase loads operating at line voltage can be connected between two of the three-line conductors in either a wye or delta system, as shown in Figure 3.

##### Figure 3. Single-phase line voltage loads connected to the secondary of wye or delta transformers. Image used courtesy of Ahmed Sheikh

In situations with single-phase and three-phase loads, it is essential to determine the transformer KVA based on the largest KVA load on any of the transformer phase windings. Remember, the total power of a three-phase system is equal to the sum of the power in the individual phases. A balanced three-phase load like a motor will have one-third of its power supplied by each of the three phases in a three-phase transformer, but single-phase loads will add load to only one phase at a time.

Tech Tip

With three-phase and single-phase loads, the largest phase load determines the transformer size.

Because three-phase transformers often comprise three equally sized single-phase transformers, each transformer phase windings must have enough capacity to supply the load connected to it. If the phase windings must supply their share of the three-phase load plus a single-phase load, then the size of the individual phase with the largest load will determine the size of the three-phase transformer. The KVA rating of the largest phase winding will be multiplied by three to give the total KVA of the transformer.

Example: A 480 Y 277-V three-phase transformer must supply three-phase motors that draw a total of 235 amps. In addition, 10—20-amp lighting circuits supply 277-V lighting fixtures. The total KVA of the three-phase motor load is:

$\frac{1.73\times235\,amps\times480\,volts}{1000}=195.05\,KVA$

The total KVA of the lighting loads is:

$\frac{10\times20\,amps\times277\,volts}{1000}=55.4\,KVA$

The total load is 195.05 KVA + 55.4 KVA = 250.45 KVA. If we balance the lighting circuits as evenly as possible, as shown in Figure 4, two of the phase windings of the transformer will have to supply 295 amps: 235 amps for their share of the motor load, plus 60 amps for 3 – 20-amp lighting circuits. The third-phase winding must supply 315 amps: 235 amps for its share of the motor loads, plus 80 amps for 4 – 20-amp lighting circuits. It should be clear that the one phase with the extra lighting circuit would have to supply more power than the other two phases, and because all the phase windings of a three-phase transformer will generally be made the same size, we should use this largest phase to determine the size of the transformer.

### Sizing a Wye-Connected Transformer

If the transformer is connected in a wye, we can determine the transformer size in one of two ways:

1. Choose the largest of the three-line amperages and then calculate the minimum KVA of the transformer with the three-phase power formula. In our example, the calculation is:

$\frac{315\,amps\times480\,volts\times1.73}{1000}=261.5\,KVA$

2. Use the largest line amperage to calculate the single-phase power of that one phase and then multiply that phase power by three. For our example, the calculation is:

$\frac{315\,amps\times277\,volts}{1000}=87.25\,KVA\,for\,ONE\,phase.$

This single-phase power multiplied by three gives the transformer size:

87.25 KVA×3 = 261.8 KVA

which is essentially the same value as the 261.5 KVA we calculated using the first method. In this calculation, we must use the single-phase voltage multiplied by the line amperage of the three-phase system because we are calculating the single-phase power of only one winding. In the Wye system, the line amperage and the phase amperage are the same, but the phase voltage = line voltage ÷ 1.73.

### Sizing a Delta-Connected Transformer

If the transformer was delta-connected and there were single-phase loads connected to it, they could only be connected between two of the three secondary line voltages because there is no neutral in the delta system. The phase voltage is the same as the line voltage for these single-phase loads.

When there are single-phase and three-phase loads connected to a delta transformer, there is only one way to calculate the size of the transformer: We must determine the KVA of the individual phase with the largest total load and then multiply that number by three.

Example: A 480-V three-phase transformer must supply three-phase motors with a total amperage of 135 amps and four single-phase heaters that each draw 12 amps. The loads are shown in Figure 5.

##### Figure 5. Single-phase and three-phase loads are connected to a three-phase 480-V transformer. Image used courtesy of Ahmed Sheikh

As you can see, one of the phase windings must supply two single-phase heaters, while the other two phases will have to supply only one heater. The total KVA the transformer must supply for three-phase motors is:

$\frac{135\,amps\times480\,volts\times1.73}{1000}=112\,KVA$

The total KVA the transformer must supply for four single-phase heaters is:

$\frac{12\,amps\times480\,volts\times4}{1000}=23\,KVA$

The total KVA is: 112 KVA + 23 KVA = 135 KVA

A three-phase transformer of this size, however, would be able to supply 135 KVA ÷ 3 = 45 KVA per phase. If each phase of the transformer must supply one-third of the motor loads, it must have 112 KVA ÷ 3 = 37.3 KVA capacity for the motor loads. One phase must also have the capacity to supply two 12-amp single-phase heaters or 24 amps x 480 V = 11.5 KVA. This one phase must have a total capacity of 37.3 KVA + 11.5 KVA = 48.8 KVA. As you can see, this is 3.8 KVA, more than the 45 KVA that would be available if we simply sized the transformer based on the total KVA of the load.

Tech Tip

With a delta-connected transformer, the size must be based on three times the largest phase power.

When a transformer is sized based only on the total load supplied, the assumption is that each of the three phases will supply one-third of the total load. Adding single-phase loads can result in one phase supplying more than one-third of the total load. We must calculate transformer size based on the actual load supplied by each phase. In the previous example, the correct transformer size is 48.8 KVA x 3 = 146.4 KVA. This size transformer will have the capacity to supply the largest phase load of 48.8 KVA.

Tech Tip

Sizing a delta transformer based only on total load can lead to one undersized phase.

Both the wye and delta examples show the importance of balancing the single-phase load as evenly as possible on each of the three phases of the transformer. If the load is not balanced properly, the size of the transformer may have to be increased beyond what is needed just to supply the extra load on the unbalanced phase.

### Transformer Sizing Takeaways

Learning to size transformers for both wye and delta-connected configurations is crucial in ensuring the seamless integration of single and three-phase loads. This knowledge plays a vital role in accurately determining the transformer's size based on the largest phase load, preventing potential issues of under-sizing. The ability to balance single-phase loads across transformer phases optimizes performance and facilitates the selection of appropriately sized transformers, ultimately contributing to the reliability and efficiency of electrical systems. Understanding the intricacies of transformer sizing is essential for those involved in electrical design and maintenance, serving as a cornerstone for robust and well-functioning power distribution networks.