Delta Transformer Calculations 
9/17/2003 
Extracted from Mike Holt's Illustrated Guide to Electrical Calculations
To correctly specify a transformer with delta winding
connections, you need to know how to do the related calculations.
The
names for transformers configurations such as delta and wye derive from the way
the windings are connected inside the transformer. These connections determine
the way the transformer will behave, and so they also determine the methods of
calculation required for properly applying a given
transformer.
Deltaconnected transformers have the windings of three 1Ø
transformers connected in series with each other to form a closed circuit. The
line conductors connected where two 1Ø transformers meet. This configuration is
a "delta system," because in an electrical drawing it looks like a triangle
(Greek symbol Dfor the letter "delta"). Many call it a highleg system because
the voltage from Line 2 to ground is higher than that of the other legs. For
example, a 120V delta transformer will have a 208V leg (Figure
121).
Graphics are not included in this
newsletter.
Definitions
To avoid confusion, we need to clarify
some key terms:
Line: The ungrounded (hot) conductor(s). See Figure 122
and Figure 123.
Line Current: The current on the ungrounded conductors
(Figure 123, B1 and B2). In a delta system, the line current is greater than
the phase current by the Square Root of 3 (which is approximately 1.732). In a
wye system, the line current equals the phase current.
Line Voltage: The
voltage between any two line (ungrounded) conductors (Figure 123, A1 and A2).
In a delta system, the line voltage equals the phase voltage (Figure 1211).
But, the delta transformer also has a highleg.
Phase Current: The
current flowing through the transformer winding (Figure 123, D1 and D2). In a
delta system, the phase current is less than the line current by the Square Root
of 3. In a wye system, the phase current equals the line current.
Phase
Load: The load on the transformer winding.
Phase Voltage: The internal
transformer voltage generated across any one winding of a transformer. For a
delta secondary, the phase voltage equals the line voltage. In a wye system, the
phase voltage is less than the line voltage by the Square Root of 3 (Figure
123, A2 and C2).
Ratio: The number of primary winding turns divided by
the number of secondary winding turns.
Unbalanced Load: (Neutral
Current). The load on the secondary grounded (neutral) conductors.
With
these terms defined, we are ready to tackle transformer calculations. We will
look specifically at delta transformers.
Delta transformer
current.
In a delta transformer, the line current does not equal the
phase current (as it does in a wye transformer). Because each line from a delta
configured transformer is connected to two transformer phases, the line current
from a 3Ø load will be greater than the phase current by the Square Root of 3.
Note these formulas:
ILine = IPhase x square Root of 3 ILine =
VALine/(ELine x Square Root of 3) IPhase = ILine/Square Root of 3 IPhase
= VAPhase/EPhase You can use the delta triangle (Figure 1218) to calculate
delta 3Ø line and phase currents. Place your finger over the desired item, and
the remaining items show the formula to use.
If you plug some numbers in,
you can more clearly see the effects of the delta configuration on currents.
Let's try this with a 240V, 36 kVA, 3Ø load (Figure 1215).
Line: Total
line power = 36 kVA
ILine = VALine/(ELine x Square Root of 3) ILine =
36,000 VA/(240V x Square Root of 3) ILine = 87A, or ILine = IPhase x 3 x
Square Root of 3 ILine = 50A x 1.732 = 87A Phase: Phase power = 12 kVA
(per winding)
IPhase = VAPhase/EPhase IPhase = 12,000 VA/240V = 50A,
or IPhase = ILine/Square Root of 3 IPhase= 87A/1.732 = 50A We can
also use the formula: ILine = VALine / (ELine x Square Root 3). What is the
secondary line current for a 480 to 240/120V, 150 kVA, 3Ø delta transformer
(Figure 1213)?
416A 360A 180A 144A Answer: (b)
360A
ILine = VALine/(ELine x Square Root of 3) ILine = 150,000
VA/(240V x 1.732) = 360A You can calculate the phase current of a delta
transformer winding by dividing the phase VA by the phase volts:
IPhase =
VAPhase/EPhase
The phase load in VA of a 3Ø, 240V load = line load/3 (1/3
of load on each winding The phase load in VA of a 1Ø, 240V load = line load
(all on one winding) The phase load in VA of a 1Ø, 120V load = line load
(all on one winding) Now, let's work an example problem. What is the
secondary phase current for a 480 to 240/120V, 150 kVA, 3Ø delta transformer
(Figure 1214)?
416A 360A 208A 104A Answer: (c) 208A
Phase power = 150,000 VA/3 per phase = 50,000 VA per phase IPhase =
50,000 VA/240V IPhase = 208A Try running these numbers with a 10A load
and then with a 75A load. You'll gain a greater appreciation for what happens in
a delta system.
Delta transformer balancing
To properly size a
delta/delta transformer, the transformer phases (windings) must be balanced. You
can do that with a twostep process:
Step 1. Determine the VA rating of
all loads.
Step 2: Balance the loads on the transformer windings as
follows
3Ø Loads: onethird of the load on each of the phases. 240V,
1Ø Loads: 100% of the load on Phase A or B. You can place some 240V, 1Ø load on
Phase C when necessary for balance. 120V loads: 100% of the load on C1 or
C2. To size the panelboard and its conductors, you must balance the loads in
amperes. Why balance the panel in amperes? Why not take the VA per phase and
divide by phase voltage? Answer: Line current of a 3Ø load is calculated by the
formula:
IL = VA/(ELine x Square Root of 3) IL = 150,000 VA/(240V x
1.732) = 208A per line. If you took the perline power of 50,000 VA and
divided by one line voltage of 120V, you would come up with an incorrect line
current of 50,000 VA/120V = 417A.
Delta transformer sizing
Once
you balance the transformer, size it to the load of each phase. Size the "C"
transformer using two times the highest of "C1" or "C2." The "C" transformer is
actually a single unit. If one side has a larger load, that side determines the
transformer size.
Let's try a practice problem. What size 480 to 240/120V
transformer is required for the following loads: one 240V, 36 kVA, 3Ø heat
strip; two 240V, 10 kVA, 3Ø loads; three 120V, 3 kVA loads (Figure
1219)?
three 1Ø, 25 kVA transformers one 3Ø, 75 kVA transformer
a or b none of these Answer: (c) a or b
Phase A (L1 and
L2) Phase B (L2 and L3) C1 (L1) C2 (L3) Line
Total One 240V, 36 kVA, 3Ø 12 kVA 12 kVA 6 kVA 6
kVA 36 kVA Two 240V, 10 kVA, 1Ø 10 kVA 10 kVA 20
kVA Three 120V, 3 kVA, 1Ø 6 kVA* 3 kVA* 9
kVA 22 kVA 22 kVA 12 kVA 9 kVA 65 kVA
*
Indicates neutral (120V) loads
Phase winding A = 22 kVA Phase winding
B = 22 kVA Phase winding C = (12 kVA of C1 x 2) = 24 kVA Now that you
understand some transformer calculation basics and specifics on delta
transformer calculations, you will be able to size delta transformers correctly.
You find deltadelta transformers most often in special applications. The most
common configuration is the deltawye. In the case of a deltawye transformer,
you now know how to size the primary side. In our next Calculations article,
we'll address the wye transformer calculations and you will then be able to size
any combination of delta and wye.
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.

