|Wye Transformer Calculations
|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
Wye-connected transformer secondaries have one lead from each of
three 1Ø transformers connected to a common point (neutral). The other lead from
each of the 1Ø 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
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.
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
Delta: EPhase = ELine; ILine = IPhase x square root of 3.
Wye: IPhase = ILine;
ELine = EPhase x square root of 3.
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 3Ø
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 3Ø and
1Ø 120V line current equals the phase current (IPhase = ILine). See Figure
Let's apply this to an actual problem. What is the secondary phase
current for a 150 kVA, 480 to 208Y/120V, 3Ø transformer (Figure
ILine = 150.000 VA/(208V x 1.732) = 416A, or IPhase = 50,000 VA/120
Remember, in a wye system, ILine = IPhase.
vs. Phase Current
Since each line conductor from a wye transformer is
connected to a different transformer winding (phase), the effects of 3Ø loading
on the line are the same as on the phase (Figure 12-25). A 36 kVA, 208V, 3Ø 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)
PHASE: Phase power = 12 kVA (any winding)
IPhase = VA
IPhase = 12,000 VA/120V = 100A
Wye Transformer Balancing
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 3Ø loads: one-third on Phase A,
one-third on Phase B and one-third on Phase C.
Step 3: Split 1Ø, 208V
loads (largest to smallest): one-half on each phase (A to B, B to C, and A to
Step 4: Place 120V loads (largest to smallest): 100% on any
Wye transformer sizing example: What size transformer (480 to
208Y/120V, 3Ø phase) would you need for the following loads?
kVA, 3Ø heat strip
two 208V, 10 kVA, 1Ø loads
three 120V, 3 kVA loads
three 1Ø, 25 kVA transformers
one 3Ø, 75 kVA transformer
a or b
none of these
Answer: (c) a or b
Phase A = 23 kVA
Phase B = 22
Phase C = 20 kVA
Phase A (L1)
Phase B (L2)
36 kVA, 120V, 3Ø
10 kVA, 208V, 1Ø
10 kVA, 208V, 1Ø
3 kVA, 120V
3 kVA, 120V
* Indicates neutral (120V)
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
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.
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
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
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
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
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.
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