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 importantbut you will likely see the reasons as
we go.
Wyeconnected 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 128).
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 turnsand thus a comparison between the
primary phase voltage and the secondary phase voltage.
For typical
delta/delta systems, the ratio is 2:1but for typical delta/wye systems, the
ratio is 4:1 (Figure 127). 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 deltadelta and deltawye 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 1221) 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
1222.
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
1224)?
416A 360A 180A 104A 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 3Ø loading
on the line are the same as on the phase (Figure 1225). 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)
= 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 deltawye 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: onethird on Phase A,
onethird on Phase B and onethird on Phase C.
Step 3: Split 1Ø, 208V
loads (largest to smallest): onehalf 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, 3Ø phase) would you need for the following loads?
208V, 36
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
kVA Phase C = 20 kVA
Phase A (L1) Phase B (L2) Phase C
(L3) Line Total 36 kVA, 120V, 3Ø 12 kVA 12 kVA 12
kVA 36 kVA 10 kVA, 208V, 1Ø 5 kVA 5 kVA 10
kVA 10 kVA, 208V, 1Ø 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 highharmonic 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
highharmonic loads from their own deltadelta transformer. Another is to supply
them from their own deltawye and double the neutral. Which of theseor the
several other approachesyou 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 deltadelta transformer, which you would feed from a deltawye 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
deltadelta transformer itself, combined with the interaction of deltadelta and
deltawye, 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 problemsthis 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 highharmonic (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.

