How Do We Size Transformers?

Written By Mark Delle Bovi

Transformers come in various shapes and sizes, as well as wiring configurations and ratings. In this article we will discuss the different types of transformers and how to properly size them for standard applications using both single phase and three phase systems.

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Transformer Basics

Transformers are used to convert energy within a building or facility. A typical application would be converting a higher distribution voltage down to a utilization voltage so it can be used by equipment. A transformer will usually contain two or more windings, called the primary and secondary, which transform the power from the input to the output terminals. This is done through the process of electromagnetic induction, often called “magnetic coupling”. It is important to remember that the primary and secondary coils of a transformer are electrically isolated meaning they are not physically connected inside the transformer. For this reason, transformers may also be used for isolation purposes for sensitive equipment. Transformers are considered separately derived systems in the National Electrical Code, since they are stand-alone isolated systems. Transformers are rated by VA or Volt-Amps. 

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1 Phase vs 3 Phase

Most applications an electrician will find in the field will be a single-phase or three phase system. Single-phase systems are relegated to residential homes and very small buildings. This would commonly be 120/240V 3-wire or 120/208V 4-wire systems in the US. Three phase systems are common in large commercial buildings such as office buildings, industrial buildings, schools, restaurants etc. Essentially, Three-phase power systems offer a more efficient way to transmit and utilize large amounts of power in large scale buildings. Common 3 phase systems seen in the US would be 120/208V 4-wire, 240V 3-wire, and 277/480V 3- and 4-wire systems.

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Step-up and Step-Down Transformers

Transformers can be used in either a step-up or step-down configuration. A step-up transformer would take a voltage at the primary (incoming winding of transformer) and “step it up” to a higher voltage in the secondary (outgoing winding of transformer). Conversely, a step-down transformer would take a voltage on the primary and drop it down to a lower voltage on the secondary. This same concept is also applied to the Current on the primary and secondary but inversely. For example, in a Step up transformer, where the voltage is being raised on the secondary, the current would be lowered on the secondary. A transformer is always trying to maintain the same VA or Volt-Amp rating on the primary as it has on the secondary.  So by changing the applied voltage, a transformer’s current will change proportionally to output the same amount of VA.

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The amount a transformer steps up or steps down voltage is determined by the internal turns ratio of the primary and secondary coils. This means the number of times the conductor is wrapped around the iron core, actually effects the voltage change. The turns ratio is found by taking the number of turns in the primary winding and dividing it by the Number of turns in the secondary winding. Below is an example of a transformer with a 1:2 turns ratio. 

Np = Number of turns in the primary winding

NS = Number of turns in the Secondary winding

NpNs= 5001000=1:2 Ratio

Something to consider when working with step-up transformers is inrush current. Inrush current is the amount of current the transformer will draw for a few seconds upon initial energization. Transformers have a very large in rush current upon energization which can be anywhere from 6 to 8 times the full-load-current. This is an important consideration when choosing an overcurrent protection device for the primary side of the transformer. Due to the larger primary currents, this is more of a design consideration on setup-ups rather than step-downs. This is especially dangerous when using a fused disconnect switch on the primary of a setup-up transformer. It is common that the large in rush currents will actually fuse or weld the copper fingers in the switch together since it is not designed to handle the large amount of in rush. To avoid this particular situation, always consider either a fused high pressure contact switch or a molded-case circuit breaker with an electronic trip module. 

Transformer Sizing and Calculations

The NEC does not dictate the sizing of the transformer itself, it is up to the designer or installer to determine the proper size. Below is a list of standard transformer sizes offered on the market. We will look at a few examples of sizing transformers in this article. For 3 phase transformers we always multiply the Voltage by 1.732 due to the relationship of the phase angles of the incoming power. With single-phase applications we don’t do this. Also, as a side note, it’s considered “good practice” to provide up to 15% of spare capacity on the transformer to prevent overheating.   

  • 3 kVA
  • 6 kVA
  • 9 kVA
  • 15 kVA
  • 30 kVA
  • 37.5 kVA
  • 45 kVA
  • 75 kVA
  • 112.5 kVA
  • 150 kVA
  • 225 kVA
  • 300 kVA
  • 500 kVA
  • 750 kVA
  • 1,000 kVA

Single phase transformer formula:               Three phase transformer formula:

Volts x Amps1000=kVA                                 Volts x Amps x 1.7321000=kVA

Using the above equations, we can always solve for Voltage, Amps or Volt Amps if any two values are given to us.

Example 1: Size a transformer for 100A 240V 1 phase load connected to a 480V 1 phase system.

Volts x Amps1000=kVA = 240 x 1001000=25kVA

Since the load is 25kVA, it’s higher than a standard sized 15VA transformer, but smaller than a 30kVA transformer so we would choose the 30kVA – the next higher size. We also notice this provides a minimum spare capacity of 15% (25kVA X 1.15 = 29kVA).  Our transformer would be a step-down 30kvA 480V 1 phase primary, 240V 1 phase secondary. 

Example 2: Size a transformer for 50A 208V 3 phase load connected to a 480V 3 phase system.

Volts x Amps x 1.7321000=kVA = 208 x 50 x 1.7321000=18kVA

Since the load is 18kVA it is higher than a 15kVA transformer, but smaller than a 30kVA transformer so we would choose the 30kVA option. We also notice it is over the spare capacity recommendation of 15% (18kVA X 1.15 = 21kVA).  Our transformer would be a step-down 30kvA 480V 3 phase primary, 120/208V 3 phase secondary. 

Example 3: Size a transformer for 17A 277/480V 3 phase load connected to a 208V 3 phase system.

Volts x Amps x 1.7321000=kVA = 480 x 17 x 1.7321000=14kVA

14kVA is slightly lower than a 15kVA transformer however it is below the 15% recommended spare capacity (14kVA x 1.15 = 16kVA). In this scenario we would want to choose a 30 kVA transformer. This is indeed, a recommendation, not a requirement.  We could choose the 15kVA transformer for this application, however it does not give any spare capacity.  In this case we are choosing a step-up 30kvA 208V 3 phase primary, with a 277/480V 3 phase secondary. 

Example 4: find inrush current for example 2 and example 3. 

Example 2 inrush current (Step-Down):

Volts x Amps1000x Volts x 1.732 x 6=Amps = 301000 x 480 x 1.732 x 6=216 Amps

Example 3 inrush current (Step-Up):

Volts x Amps1000x Volts x 1.732 x 6=Amps = 301000 x 208 x 1.732 x 6=650 Amps

If comparing the step-up to the step-down, the step-up has over 300% higher in rush current compared to that of the step-down. This is an important consideration when choosing overcurrent protection for the primary.  

Conclusion

In closing to summarize what we learned about transformers:

  1. Consider 15% spare capacity when sizing transformers.
  2. Understand the difference between sizing 3 phase and 1 phase transformers. 
  3. Must Choose standard size transformer available.
  4. Understand the differences between step up and step-down transformers
  5. Carefully select primary over current protection devices based on in rush current for larger step-up transformers. 

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