3 Simple Steps to Size a Distribution Power Transformer

How to size the protection and cabling for a distribution power transformer?

Let's narrow the scope of this article to oil-type transformers, three-phase, delta-wye configuration, less than 5 MVA, and medium-voltage primary and low-voltage secondary.

Applicable codes include CSA C22.2 Part 1 (CEC), NEC Article 450, IEEE C37.91, and IEEE 141.

Step 1 - Calculate the transformer kVA based on downstream loading

We want to size the transformer so that it is 125% larger than the expected largest continuous loading. In other words, we want the transformer to run at a maximum of 80% loaded (the inverse of 125%).

To calculate the transformer size (kVA), we require the downstream loading. A load flow study is outside the scope of this article. Let's consider that this value is provided to us.

Using the three-phase power equation:

$S = \sqrt{3} * V_{line-to-line} * I$

We can calculate the required power for a given secondary current and voltage:

$S = \sqrt{3} * 0.48\: kV * 800\:A$

$S = 665\: kV\!A$

Now, we want the transformer oversized by 125% (to run at 80% loaded), therefore:

$S' = 665 kVA * 1.25 = 831 kVA$

We want to round to a standard, common size. In this example, transformer manufacturers will most likely recommend 1000 kVA.

$S_{transformer} = 1000 kVA$

Notice that we didn't use any transformer upstream information to determine the transformer size.

Step 2 - Calculate the protection size from the transformer size

Before we calculate the cable sizing, we first calculate the protection elements.

For this oil-filled transformer, we are following 26-250 and Table 50 of the Canadian Electrical Code (CEC) or NEC Article 450.3.

CEC stipulates that when there is no secondary protection, the primary of the transformer shall be protected by a fuse rated no more than 150% of the transformer's primary full load current or by a breaker rated no more than 300% of the transformer's primary full load current.

When there is secondary or thermal overload protection, Table 50 provides the maximum protection for the primary and secondary devices. The idea here is when there is additional protection for overload, the requirements loosen for maximum protection.

• For a transformer impedance of 7.5% or less and secondary voltage greater than 750V, the primary maximum protection of 150% (fuse) and 300% (breaker) ratings increase to 300% (fuse) and 600% (breaker) with secondary protection of 150% (fuse) or 300% (breaker).
• If the secondary voltage is less than 750V, the secondary protection is maximum 250% for a fuse or breaker.

NEC advises that for transformers over 1000V (our distribution transformer), we follow Table 450.3(A).

However, we want to size the protection tighter (closer to the transformer's full load rating) than 150% (fuse) or 300% (breaker) to avoid unnecessary large cables. The larger the protection size, the larger the cables needed.

If we use 125% of the primary full load current, we typically have enough margin to avoid nuisance tripping due to transformer inrush current, but tight enough to save on cable costs.

Let's use a fuse for our example.

$I_{primary} = \frac{S_{transformer}}{\sqrt{3} * V} = \frac{1000\:kV\!A}{\sqrt{3} * 4.16\:kV} = 138\:A$

$I_{maximum\_primaryfuse} = I_{primary} * 1.50 = 207\:A$

$I_{primaryfuse} = I_{primary} * 1.25 = 172.5\:A$

For a 1000 kVA transformer, the 4160V primary fuse protection calculates to 172.5A. As such, we will select a standard rating of 175A primary fuse for the 138A rated transformer primary.

Step 3 - Calculate cable size

As per Canadian Electrical Code 26-256, the transformer primary and secondary conductors shall be sized as not less than 125% of the transformer respective full load current. This is the minimum cable size without derating (choking) the transformer size.

However, CEC 26-256 4) indicates that when the transformer overcurrent protection is more than 125% of the rated primary or secondary current, the cables shall be protected as per CEC 14-100 and 14-104.

To put it simply, the cables should be sized for at least 125% of the rated ampacity of the transformer, unless the protection is more than this 125% value, in which case the cables shall be sized for the protection size.

Let's continue our example.

The primary protection is a 175A fuse. Because we rounded up from 172.5A to 175A, our primary protection is ~127% of the primary rated current. Therefore, we need to size the cables to the 175A (size the cables to the protection size). If we selected a fuse at 200A, our cable shall be sized for 200A ampacity rating.

However, if we had rounded down our primary fuse selection, from 172.5A to 150A, the fuse would be ~108% of the primary rated current. This means that 26-256 1) would apply — the cable shall be sized for 125% of the transformer primary and secondary rating. This would be minimum 172.5A cable ampacity on the primary. Side note — 108% for fuse protection on the primary is a little too tight for transformer nuisance tripping, so we will keep with the 175A fuse.

Interesting note — cable designs end up being ~156% of the expected maximum continuous current. The transformer is sized for 125% of the continuous load and then the cables are sized 125% of the transformer. 1.25 x 1.25 = 1.56

Other commentary

Keep in mind with primary fuse protection, it can take minutes or longer for a slow overload to trip. Fuses aren't reliable for overload protection as they are designed for protecting against short-circuits. Even fuse current double the transformer rated current can take tens of seconds to blow. Fuses are an economical protection method for a disposable asset. Transformers that are more critical should be considered for more purpose-built protection schemes, such as differential relaying.

If the transformer is installed in a location where only qualified workers can access ("supervised location"), secondary protection is not required (NEC 450.3(A)). However, I would still highly recommend it.

NEC 450.3(A) also allows increased maximum overcurrent ratings on secondary protection (250% instead of 125%) when less than 1000V, when installed in a supervised location.

It helps to understand the reasoning behind why Table 50 depends on the secondary voltage and the transformer impedance. It comes down to available fault current downstream of the transformer. As the transformer impedance decreases, the available fault current downstream increases. A higher fault current requires a higher rating of protection. The same principle applies for transformer secondary voltage. A lower secondary voltage means a higher secondary current and higher secondary fault current.

This article is not engineering advice but rather for educational and information purposes only. Please consult an engineer for your application.