When more power is needed - three transformers can be tied together. We call this three-phase. Here’s a simple way of comparing single-phase to three-phase power.

*Single-Phase*

*Three-Phase*

Think of single-phase as one guy driving a stake into the ground; Three-phase as three guys, working together, driving the same stake into the ground.

Generating Three-Phase

Three-phase power is delivered from a generator with three separate windings. These windings are equally spaced around a rotating cylinder (rotor) with each winding occupying one-third of the rotor circumference. Three-phase generator windings are spaced 120˚ apart for a total of 360.˚

Because the three source voltages timed at three different intervals, they can be transmitted over just three conductors (rather than the six conductors needed to transmit three separate single-phase loads).

A three-phase system can produce 173% higher effective voltage than a single-phase system. This is very useful for higher power loads such as large motors. We calculate the total voltage (of all three lines of a three-phase transformer) by multiplying the voltage of each single winding (phase) by the square root of 3 (√3). The reason for this is the angles of each phase are always 120° apart.

By using this trigonomic formula (don’t get scared) we can see where we derive the square root of three.

Wye Connection

One way of tying three transformers together is in parallel (+ to +) and (- to -). This is called a Wye connection. Here’s how a Wye connection is wired...

We call each of the single-phase transformer windings Phases. By combining three single-phase transformers (L1-L2-L3) we designate this our Line connection. We really only draw three-phase from the Line side. Also, Line Amps on a Wye connected transformer always equals the Phase Amps. It would seem that current would not remain the same in a parallel circuit. But, three transformers wired in parallel are not like three resistors in parallel. Transformers produce, instead of consume voltages, so the opposite rules would would apply in this case.

A more simplified representation of a Wye looks like this...

A more simplified representation of a Wye looks like this...

If we tie together three single-phase, 120 volt, transformers in a Wye configuration our output voltage would look like this...

Why do we get 208 volts, three-phase on the Line side (L1-L2-L3) ? Just multiply 120 volts times the square root of 3 (√3). Remember phase angles of three 120 volt sources.

120 volts x 1.732 (33) = 208 volts

We can also get 208 volts, single-phase on the Line side of this transformer by connecting (L1-L2)...

As you see, we are connecting only two of the three single-phase transformers available. We still only get 208 volts (120 x 33) from this connection, and it is just single-phase. But, we have the capability of using two transformers (“A” & “B”) to help share the load. Also, we can use two other possible connections (L2-L3) and (L1-L3) to feed other 208 volt, single-phase loads.

Guess what ! Yes, it’s even possible to get 120 volts, single-phase out of the same transformer.

Guess what ! Yes, it’s even possible to get 120 volts, single-phase out of the same transformer.

Remember, we have the benefit of a neutral conductor and, by connecting(L2-N) we can feed 120 volt, single-phase loads. And, seeing that we are only using one single-phase transformer (“B”), that leaves two other possibilities (L1N) and (L3-N) for serving other 120 volt circuits. What’s also very useful is that we can balance three 120 volt circuits on just one neutral. In other words, A 208/120 volt (Wye configured) transformer could supply120 volt, single-phase equipment (like fluorescent lights), 208 volt, single-phase equipment (like range or oven), and 208 volt, three-phase equipment (like heavy machinery). This is what makes three-phase so great!

Delta Connection

Another way of tying three transformers together is in series (+ to -). This is called a Delta connection. Here’s how a Delta connection is wired...

A more simplified representation of a Delta configuration looks like this...

By connecting three (240 volt) single-phase transformers (Delta) we get 240volts, three-phase. We don’t multiply by 33 because Line volts equals Phase volts on Delta transformers. It would seem that voltage, would not remain the same in a series type circuit. But, three transformers wired in series are not like three resistors in series. Transformers produce, (instead of consume) voltages,so the opposite rules would would apply in this case.

Connect (L1-L2) and you’ll get 240 volts, single-phase. Connecting (L2-L3)or (L1-L3) will also give us 240 volts, single-phase. Notice how three different240 volt (1Ø) loads utilize three different transformers.

We can still get 120 volts, (single-phase) out of a 240 volt Delta system, but it’s going to take some additional work. We are going to have to center-tap oneof the 240 volt, single-phase transformers. It’s customary to center-tap transformer “C.”

As you can see, we can get 120 volts, (single-phase) from a Delta configuration (L2-N) (L3-N). Unfortunately, all 120 volt loads must be carried on poor transformer “C.”

Types Of Three-Phase Transformers

With the possibility of wiring both the primary and secondary of three-phase transformers, there are four possible configurations...

(1)

(2)

(3)

(4)

The most commonly used three-phase transformer is a Delta/Wye configuration. It’s used primarily for power distribution from utilities to residential and commercial services.

(1)

__Wye/Wye__is commonly used for interior wiring systems.(2)

__Wye/Delta__is used to step-down utilities high line voltages.(3)

__Delta/Delta__is often used for industrial applications.(4)

__Delta/Wye__is popular for stepping down transmission lines to four-wire services when neutrals are needed.The most commonly used three-phase transformer is a Delta/Wye configuration. It’s used primarily for power distribution from utilities to residential and commercial services.

The given voltage designations for a Delta/Wye three-phase transformer is: Primary-Line/Secondary-Line/Secondary-Phase

Or in this case:

Delta/Wye (480/208/120)

Delta - Wye (Phase-To-Phase)

Or in this case:

Delta/Wye (480/208/120)

Delta - Wye (Phase-To-Phase)

Let’s not forget that three-phase is a product of three individual single-phase transformers. When calculating the Phase-To-Phase relationship the same rules apply as any single-phase transformer. In other words, Our Phase-To-Phase voltage below is 480 to 120 which is a ratio of 4:1.

We can also use the the same ladder chart we used for a typical single-phase transformer.

Don’t forget that this is just one of three single-phase transformers. There may be efficiency or power factor losses between the primary and secondary phases. But, we’ll assume that this transformer is 100% efficient with no power factor loss so the Primary vA will equal the Secondary Watts. Calculate the Primary vA, Primary Amps and Secondary Watts assuming that our Secondary Amps

= 100.

= 100.

Did you get 12,000 Primary vA ? Multiplying 12,000 by 3 (three transformers) will give us 36 kVa (36,000 vA). We’ll call this our Line kVa, which is the sum total of all three-phases. In other words, our transformer rating is 36kVa.

It’s important to understand the difference between Phase and Line. Phase is the single-phase transformer relationship. Line is the result of the combination of all three transformers hooked together.

It’s important to understand the difference between Phase and Line. Phase is the single-phase transformer relationship. Line is the result of the combination of all three transformers hooked together.

A Delta - Wye (Line-To-Line)

There are a few of rules we must remember...

Yes, we can use the ladder Line-To-Line on three-phase transformers Check this out...

Knowing the values of Secondary Line Amps (100) and Secondary Line Volts (208) we would multiply going up the ladder to find Secondary Line Watts. In this case, because we are dealing with three-phase we’ll multiply our answer by /3 (1.732). Here’s what it looks like...

Line Amps (100) x Line Volts (208) x √3 (1.732) = Line Watts (36,000)

I know! You get 36,0256.6 watts. The problem is that 208 volts (3Ø) is not exactly 208 volts. 120 volts x 1.732 = 207.84. So we round up! Remember whenever we see 3Ø, the square root of three 1.732 must be involved.

On the Primary side. stepping down the ladder...

On the Primary side. stepping down the ladder...

Primary vA (36,000) / Primary Volts (480) ÷ (√3) (1.732) =

Primary Amps (43.3)

Primary Amps (43.3)

**Yes, we can use the ladder Line-To-Line on three-phase transformers Check this out !**

Just cover the value you need to know.The key to using the ladder in three-phase is multiplying the answer by √3 going up the ladder, and divide the answer by (√3) going down the ladder...

Just cover the value you need to know.

Line Amps (43.3) = Line Watts (36,000) / Line Volts (480) x √3 (1.732)

*Don't forget to divide the answer (33 line amps) by the square root of three*(1.732)

*to get the final answer 43.3 line amps.*

A Delta - Delta Transformer

A Delta/Delta connected transformer looks like this...

There are the rules we must remember...

(1) Primary v/A = Secondary Watts (at 100% Efficiency)

(2) Delta Line Watts = Phase Watts x 3 (or) Phase Watts = Line Watts ÷ 3

(3) Delta Phase Volts = Delta Line Volts

(1) Primary v/A = Secondary Watts (at 100% Efficiency)

(2) Delta Line Watts = Phase Watts x 3 (or) Phase Watts = Line Watts ÷ 3

(3) Delta Phase Volts = Delta Line Volts

Delta - Delta (Phase-To-Phase)

Although our transformer is connected Delta/Delta the Phase-To-Phase situation has not changed. We still have three single-phase transformers. Let’s do some calculations for a Delta/Delta 480/240/120 transformer. First we must find the Secondary Watts, then the Primary vA and Primary Amps...

We know that the secondary phase watts (240 x 10 = 2400 watts). Now we can calculate secondary line watts. Remember secondary line watts equals secondary phase watts times three. Why ? Because there are three single phase transformers. So, it's 2400 watts times 3 or

__7,200 watts__.Seeing that our transformer is 100% efficient. The secondary line wattage (volt amps) and the primary line wattage are the same. Remember transformers don't transform wattage. Only the ratio of volts and amps. Now we can work our way down the ladder for amps and resistance.

Three-Phase Transformer Chart