Click play to watch the video for this worked out problem:
What’s in this Article? Click below to jump to any section:
- Introduction
- Solving for phase voltages
- Solving for center tapped voltage magnitudes
- Solving for center tapped voltage angles
- Solving for the high leg voltage method 1
- Solving for the high leg voltage method 2
- Completed high leg delta circuit diagram
- Completed high leg delta phasor diagram
- Conclusion
1. Introduction
The most common mistake made when calculating the voltage magnitude across the high leg of a 4 wire delta transformer secondary with a center tapped winding is not including the phase angles when you sum the voltages.
Remember, these are complex numbers, so to calculate the high leg voltage you’ll need to add up the complex value of each voltage.
Let’s start with a 240 volt rated three-phase delta secondary transformer with a center tapped B phase winding:
2. Solving for Phase Voltages:
Since the three-phase delta transformer is rated for 240V, each of the phase winding voltages (also equal to the line voltages of the connected system) will have a magnitude of 240V:
Let’s assign a voltage reference of zero degrees for the A phase winding (VAB), and then calculate the voltage angles for the B and C phase windings (VBC, VCA), assuming a balanced and positive ABC sequence system:
3. Solving for The Center Tapped Voltage Magnitude:
Next, let’s calculate the center tapped voltage magnitudes from B to neutral, and neutral to C. When a winding is center-tapped, it divides the turns ratio of that winding by half when connecting to the neutral connection:
Notice the subscripts for these voltages. The first subscript always notes the positive (+) voltage reference, and the second subscript notes the negative (-) voltage reference.
4. Solving for The Center Tapped Voltage Angle:
The phase angle and voltage polarity for both of the center tapped winding voltages from B to neutral, and neutral to C will match that of the B phase winding voltage (VBC) that it is tapped from.
The B phase winding has a positive voltage reference measured from B, and a negative voltage reference measured from C, which means the voltage polarity reference will be from B (+) to neutral (-) and neutral (+) to C (-):
It helps to look at the circuit diagram while completing this step.
5. Solving for The High Leg Voltage Method 1:
We are now ready to calculate the voltage across the high leg of the 4 wire delta transformer secondary with one center-tapped winding.
The high leg occurs across the A to neutral phase (VAN). We can calculate it starting at A, going in a clockwise direction to N:
The high leg voltage magnitude is approximately 208 volts with an angle of negative 30 degrees when a reference of zero degrees for the A Phase voltage (VAB) is used.
Changing the reference angle of the A phase voltage (VAB) would only result in a different angle for the high leg voltage. The magnitude of the high leg voltage would remain the same.
6. Solving for The High Leg Voltage Method 2:
We can also calculate the high leg voltage starting at A and going in a counterclockwise direction to N:
Again we find that the high leg voltage magnitude is approximately 208 volts with an angle of negative 30 degrees when a reference of zero degrees for the A Phase voltage (VAB) is used.
Changing the reference angle of the phase voltage (VAB) would only result in a different angle for the high leg voltage. The magnitude of the high leg voltage would remain the same.
7. Completed High Leg Delta Circuit Diagram:
Below is the completed high leg delta circuit diagram with a B phase center-tapped winding with all voltages filled in for the above example.
The phase winding voltages of the transformer (VAB, VBC, VCA) appear in red.
The center tapped winding voltages (VBN, VNC) and the high leg voltage (VAN) appear in orange.
8. Completed High Leg Delta Phasor Diagram:
Below is the completed voltage phasor diagram for the above example.
The phase winding voltages of the transformer (VAB, VBC, VCA) appear in red.
The center tapped winding voltages (VBN, VNC) and the high leg voltage (VAN) appear in orange.
9. Conclusion:
The benefits of a high leg delta is the ability to deliver power at additional voltage magnitudes compared to a standard three-phase delta connection.
For example, a 240V three-phase standard delta connection is only able to provide power to:
- Three-phase 240V loads connected across all three terminals
- Single-phase 240V loads connected across any of the phase windings
However, a 240V three-phase delta connection with a center tapped winding is able to provide power to the same loads as the three-phase standard delta connection in addition to:
- Single-phase 120V loads across the center tapped winding and neutral (VBN, VNC)
- Single-phase 208V loads across the high leg connection (VAN).
Greater care must be taken not to overload or unbalance a high leg delta connection.
Per NEC 408.3(E)(1), the B phase shall have the higher voltage to ground for 3-phase 4-wire, delta-connected systems, so the standard convention is for the neutral to be connected in between the A and C phase.
Thanks for the contribution Andrew
This guy is wrong in so many ways. The tap is supposed to be between A and C phases. The B phase is only used for phase to phase loads. There is no breaker that is rated for single pole 208. This is only 120/240 three-phase Delta.
In section 5 of this article, should it say VAN = VAB + VBN?
Instead of VAN = VAB + VAN?
Thanks!
Hello Zach,
Thank you for your contribution.
Do you know if we have can use this High Leg Delta with the Neutral Isolated ? Or shall it be connected to the ground ?
This is by far the best explained tutorial of a high leg 4 wire delta transformer I’ve ever come across. Thanks for spelling it out for us and walking us through how to obtain the three voltages. Thanks Zach – your PE Review course is by far the best I’ve come across. Video was a huge help!
great article!! I will absolutely be printing this article and bringing it with me.
hello Zach,
thank you for your artical.
I feel very confused before about the 4 wire leg delta tranformer.
right now I can understand.
I’ve used these before in my work or they have at least come up before but now I feel like I truly understand the uses or ways these units work.
Another great article that goes much farther in depth than other resources I have came across! Thank you!
Very well explained. Thanks for the article.
This is seriously the best video and article that Zach has available. Any questions you may have about high leg deltas are immediately cleared up once you watch this video.
Thanks Zach. Your breakdown helps me understand the basics behind very complicated subject.
Very helpful article. I never knew anything about a center tapped or high leg delta circuit/phasor diagrams.
Hi Zach,
This article helps me to understand more about high leg delta transformer and the phasor/circuit diagram.
Amazing article!! I will printed it out and have it with me during Oct. 2019 PE Exam.
Great information Zach! It’s good to know another way to get 120V & 208V other than delta-wye transformer. Thank you.
This is a must-read article for the PE exam. Really easy to understand once you have gone through your phasor basics.
First of all, I did not like Delta’s connection at all until I start preparing the PE exam. Zach has done a great job in demystifying the 4-wire-high-leg delta transformer connection for us by focusing on the essential aspect of the concept. In colleges, professors tend to provide so much info that it can be confusing if you rely on college lectures to prepare for PE exam. Zach, on the other hand, provided what you need to understand the concept. Basically, he gives you what you need to pass the PE exam and that why we are here at this time. Thanks Zach
All other references I have seen have not explained it quite like this. Now it makes sense! Thanks!
OMG. I work in the electrical utility industry and not until after reading this article did it really make sense. I mean I knew the basics of high leg delta transformers, but this article really breaks down the HOWs and WHYs behind it.
When I first saw this, I had no clue how to go about it but once I write out the KVL equations and phasor diagrams it all makes sense. Thanks for providing this well-explained article.
Voltage from N to A (hi-leg) = SQRT(240^2 – 120^2)= 207.8
Why not use a formula multiplying the phase to phase voltage by the square root of three divided by 2. 240v x (3^2)/2= 207.8v
I get the same answer with a simpler formula.
PROBLEM WITH DELTA POWER. IT IS 2024 AND I INSTALL CNC MACHINES. BECAUSE OF THE HIGH LEG IN DELTA POWER YOU CAN BE PUTTING 185 TO ONE OF THE LEGS. IF THE MACHINE PULLS FROM THESE LEGS 110 VOLTS TO RUN A DEVICE. THE 185 CAN RUIN THIS DEVICE. ALSO Y IS USUALLY 208 VOLTS WHERE ALL 3 LEGS TO GROUND MEASURE THE SAME. ALSO IN DELTA I HAVE FOUND SOME SHOPS TRY TO PULL 110 FEOM THE BREAKER BOX. IF THEY ARE NOT CAREFULL AND THEY PULL FROM THE WRONG LEG THEY MAY BE PUTTING 185 TO A 110 OUTLET. I CAN NOT SEE THE ADVANTAGE OF DELTA IN THE MODERN CNC MACHINE TOOL WORLD. MAY BE ITS TIME TO GET RID OF DELTA POWER. THIS HAS CAUSED ELECTRICAL PROBLEMS IN MODERN MACHINERY. THE ONLY WAY TO GET RID OF THE HIGH LED IS TO BUY AN INSULATION TRANSFORMER. PLEASE RESPOND. ALSO ON A SIMPLE AIR COMPRESSOR IF THE MOTOR STARTER COIL IS 110 VOLTS AND THE ELECTRICIAN IS NOT CAREFUL AND THEY PUT THE HIGH LEG TO THIS 110 VOLT CIRCUIT THEY CAN BURN UP THE COIL IN THE STARTER. IN MY 55 YEARS OF DOING THIS MOST ELECTRICIANS DO NOT UNDERSTAND 3 PHASE POWER. ALSO MOST DO NOT UNDERSTAND GROUND RODS AND DO NOT OWN A PHASE CHECKER. WRONG PHASE GOING INTO A 3 PHASE CHILLER WILL RUIN THE UNIT IN 5 SECONDS. THESE CHILLERS COST $18,000. A PHASE CHECKER COST ONDER $30.00. HOW DO ELECTRICIANS GET THERE LICENSE WITHOUT OWNING A 3 PHASE CHECKER.