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Wye Transformer Calculations 10/3/2003
Extracted from Mike Holt's Illustrated Guide to Electrical Calculations:

To correctly specify a transformer with wye winding connections, you need to know wye calculations. In our previous Calculations article, we looked at transformer calculation definitions and some specifics of delta transformer calculations. Now we turn our attention to the differences between delta and wye transformers and to wye transformer calculations. We'll close by looking at why the ability to do these calculations is so important-but you will likely see the reasons as we go.

Wye-connected transformer secondaries have one lead from each of three 1 transformers connected to a common point (neutral). The other lead from each of the 1 transformers is connected to the line conductors (Figure 12-8). This configuration is a "wye," because in an electrical drawing it looks like the letter Y. Unlike the delta transformer, it does not have a high leg.

The ratio is the relationship between the number of primary winding turns to the number of secondary winding turns-and thus a comparison between the primary phase voltage and the secondary phase voltage.

For typical delta/delta systems, the ratio is 2:1-but for typical delta/wye systems, the ratio is 4:1 (Figure 12-7).
In a typical delta/delta, the ratio is 2:1.
If the primary phase voltage = 480V, the secondary phase voltage = 240V.
In a typical delta/wye, the ratio is 4:1. If the primary phase voltage = 480V, the secondary phase voltage = 120V.
Delta and wye also differ in regard to their phase voltage vs. line voltage and phase current vs. line current

Delta: EPhase = ELine; ILine = IPhase x square root of 3.
Wye: IPhase = ILine;
ELine = EPhase x square root of 3.
These differences affect more than just which formulas you use for transformer calculations. By combining delta-delta and delta-wye transformers, you can abate harmonic distortion in an electrical system. We'll look at that strategy in more detail, after addressing wye calculations.

Wye voltage calculations

You can use the wye voltage triangle (Figure 12-21) to calculate wye 3 line and phase voltages. Place your finger over the desired item, and the remaining items show the formula to use.

In a wye transformer, the 3 and 1 120V line current equals the phase current (IPhase = ILine). See Figure 12-22.

Let's apply this to an actual problem. What is the secondary phase current for a 150 kVA, 480 to 208Y/120V, 3 transformer (Figure 12-24)?

Answer: (a) 416A

ILine = 150.000 VA/(208V x 1.732) = 416A, or IPhase = 50,000 VA/120 = 416A.

Remember, in a wye system, ILine = IPhase.

Line Current vs. Phase Current

Since each line conductor from a wye transformer is connected to a different transformer winding (phase), the effects of 3 loading on the line are the same as on the phase (Figure 12-25). A 36 kVA, 208V, 3 load has the following effect:

LINE: Line power = 36 kVA
ILine = VA Line/(ELine x square root of 3)
ILine = 36,000 VA/(208V x square root of 3) = 100A
PHASE: Phase power = 12 kVA (any winding)
IPhase = VA Phase/EPhase
IPhase = 12,000 VA/120V = 100A
Wye Transformer Balancing and Sizing

Before you can properly size a delta-wye transformer, you must ensure the secondary transformer phases (windings) or the line conductors are balanced. Note that balancing the panel (line conductors) is identical to balancing the transformer for wye transformers. Once you balance the wye transformer, you can size it according to the load on each phase. The following steps will help you balance the transformer:

Step 1: Determine the VA rating of all loads.

Step 2: Split 3 loads: one-third on Phase A, one-third on Phase B and one-third on Phase C.

Step 3: Split 1, 208V loads (largest to smallest): one-half on each phase (A to B, B to C, and A to C).

Step 4: Place 120V loads (largest to smallest): 100% on any phase.

Wye transformer sizing example: What size transformer (480 to 208Y/120V, 3 phase) would you need for the following loads?

208V, 36 kVA, 3 heat strip
two 208V, 10 kVA, 1 loads
three 120V, 3 kVA loads
three 1, 25 kVA transformers
one 3, 75 kVA transformer
a or b
none of these
Answer: (c) a or b

Phase A = 23 kVA
Phase B = 22 kVA
Phase C = 20 kVA

Phase A (L1)
Phase B (L2)
Phase C (L3)
Line Total

36 kVA, 120V, 3
12 kVA
12 kVA
12 kVA
36 kVA

10 kVA, 208V, 1
5 kVA
5 kVA
10 kVA

10 kVA, 208V, 1
5 kVA
5 kVA
10 kVA

3 kVA, 120V
3 kVA*
3 kVA

3 kVA, 120V
3 kVA*
3 kVA

3 kVA, 120V
3 kVA*
3 kVA

23 kVA
22 kVA
20 kVA
65 kVA

* Indicates neutral (120V) loads.

The table sums up the kVA for each phase of each load. Note that the phase totals (23 kVA, 22 kVA and 20 kVA) should add up to the line total (65 kVA). Always use a "checksum" like this to ensure you have accounted for all items and the math is right.

If you're dealing with high-harmonic loads, the maximum unbalanced load can be higher than the nameplate kVA would indicate. Matching the transformer to the anticipated load then requires a high degree of accuracy for if you are going to get a reasonable level of either efficiency or power quality.

One approach to such a situation is to supply high-harmonic loads from their own delta-delta transformer. Another is to supply them from their own delta-wye and double the neutral. Which of these-or the several other approaches-you should choose depends on the characteristics of your loads and how well you lay out your power distribution system.

For example, you might put your computer loads (which have switching power supplies) on a delta-delta transformer, which you would feed from a delta-wye transformer. This would greatly reduce the presence of harmonics in the primary system, partly due to the absence of a neutral connection. But, the behavior of the delta-delta transformer itself, combined with the interaction of delta-delta and delta-wye, will also cause a reduction in harmonics. Notice the word "might" in the question of whether to implement this kind of design. Grounding considerations can make it an undesirable approach, depending on the various loads and the design of the overall electrical system. There are many ways to mix and match transformers to solve power quality problems-this is only one example.

Due to uptime or power quality concerns with complex loads, you may need to mix and match transformer configurations as in the example above. And that is something you can't do that unless you understand both delta and wye calculations.

Another issue is proper transformer loading. As a rule of thumb, 80% loading is a good target. If you overload the transformer, though, it goes into core saturation and output consists of distorted waveforms. The clipped peaks typical of saturated transformers cause excess heating in the loads. This issue of transformer loading means just to get basic power quality and reasonable efficiency, you are going to have to do the transformer calculations.

So, it's important not to oversimplify your approach to transformer selection. It's usually best to do all the calculations using the nameplate kVA. Then, design the distribution system as though all loads are linear. When that's done, identify which loads are high-harmonic (e.g., electronic ballasts, computer power supplies, motors with varying loads). At this point, you can efficiently work with a transformer supplier to develop a good solution.

Now that you understand delta and wye transformer calculations, you can see how important they are to being able to do a quality installation any time you are specifying transformers or considering adding loads to existing transformers. This ability is also important if you are trying to solve a power quality problem or a problem with "unexplained" system trips. You may wish to sharpen this ability by purchasing an electrical calculations workbook or taking on this kind of work in your electrical projects.

Mike Holt's Comment: This is a very technical article and I know the graphics would make it easier to understand, but it's a business decision I'm made not to give "everything away". If you have any questions with this newsletter or if you feel I have made an error, please let me know.

Copyright 2003 Mike Holt Enterprises,Inc.