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Transformer configuration names like and derive from the way the windings are connected inside the transformer. These connections determine the way the transformer will behave, and they also determine the methods of calculation required for properly applying a given transformer.
To fix that, we made a complete step by step break down analysis on the open delta transformer connection starting with a standard three phase delta connection and finishing with a two-winding open delta connection. This is by far the most complete and in-depth information you will find on the internet or elsewhere on the subject of open delta transformer connections.
Below is a diagram of three single phase transformers connected in delta to form a three phase delta transformer. With the chosen reference angle and a balanced, positive sequence system we can determine the delta phase voltages:.
When this is true, the delta phase current will be exactly in phase with the delta phase voltage, and the active power output in watts P will be equal to the apparent power volt-amp rating S of the transformer:. Since we know that each delta phase current is now in phase with each delta phase voltage, the phase currents will have the same angle as their respective phase voltage. This lets us determine the complex value of each delta phase Delta transformer hook up.
Notice each phase current has the same angle as the ly determined delta phase voltage since power factor is equal to unity.
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If we graph the delta phase current and delta phase voltage on the same phasor diagram we can verify that power factor is unity since the angles are equal for each pair of phase current and phase voltage. Recall that this is the correct relationship that will result in maximum power output for the delta transformer:.
Theta is equal to the difference between the phase voltage angle and the phase current angle. Since these angles are equal, theta is equal to zero for each pair:.
The maximum power delivered by a three phase delta transformer is equal to three times the delta phase voltage magnitude times the delta phase current magnitude. Note that we can use either the secondary phase voltage with the secondary phase current, or the primary phase voltage with the primary phase current and still get the same answer.
Since the active power output in watts is equals the apparent power rating of a transformer in volt-amps during maximum power conditions, we can check our work by adding up the power ratings of each individual single-phase transformer used to make the three phase transformer:. So far, nothing has changed for the delta A-phase and C-phase voltage, but we are not so sure about the delta B phase voltage just yet:.
We will use a positive polarity reference at B Delta transformer hook up a negative polarity reference at C, just like what the line would see prior to the winding failure. Looking at Delta transformer hook up as a KVL loop, we can see that we have two voltages in series which we can add by summing the values.
Starting from the B to C connection we have negative A-phase delta voltage followed by the negative C-phase delta voltage from the A to C connection. The magnitude of the voltage across the missing winding has neither increased or decreased in value, it is equal to the magnitude of the same balanced phase voltage.
The angle of the voltage across the missing winding has also neither increased or decreased in value. It is still equal to the angle of the voltage that was there prior to the winding failure.
The surprising finding is that the connected three phase system sees no difference in the supply voltage with the missing winding! The open delta phase voltages are identical to the three phase delta voltages prior to the winding being removed:. The resulting open delta phase voltage phasor diagram Delta transformer hook up identical to the delta phase voltage phasor diagram with all three windings in service:.
This is where it gets a little bit more difficult. First, recognize that there is no change in the system line voltage since the open delta phase voltage is identical to the three phase delta phase voltages.
The result of this is that the angles of each system line current will be the same as before. The magnitudes of the system line currents will still be balanced and equal, but will be different in value since the KCL formulas for a three phase delta no longer apply with the missing winding:.
Recognize that when we look at each of the single-phase transformers individually, even though the B phase transformer is no longer connected, it does not affect the full load amps of each of the two remaining single phase transformers that make up the two remaining windings of the open delta transformer. The result is that each phase current in the two remaining open delta windings will have the same magnitude as before.
However, since the KCL relationship has been changed by removing a connection between the B an C phase, the angles will be different than before:. Looking at the open delta digram, the C line current is now equal to the C phase current for the open delta connection since the B winding is missing. Since we Delta transformer hook up the magnitude of the C line current, and the angle of the C phase current, we can determine the complex value for Delta transformer hook up.
The C-line current and the C-phase current both have a magnitude equal to the phase current magnitude with an angle of degrees. Looking at the open delta diagram, the B-phase current is equal to the negative B-line current since they are flowing in opposite directions. This is the same as multiplying the complex value by negative one to change the direction. Multiplying a vector by negative one does not change the magnitude, it only rotates the vector by positive or negative degrees. Since the B-phase current equals the negative B-line current, we know that their magnitudes are equal.
Three phase transformer connections
We already know the B-phase current magnitude and the B-line current angle. We can find the Delta transformer hook up B-phase angle by rotating it degrees and solving for the complex values for both:. The B phase and line current are equal in magnitude, and degrees apart.
Looking at the open delta diagram and using KCL node equations, the A-line current is now equal to B-phase current minus the C-phase current. We will use a phase current magnitude of 1 so that we can plug these values into our calculator and solve to see if the magnitude or angle increases or decreases with this new KCL relationship:.
Even though the open delta can still serve a three phase load provided it has enough capacity, to find the maximum power we will only be looking at the two windings that remain. Note that we are not using line values because we want to find the complex sum of both remaining individual single phase transformers that each make up the two remaining phase windings of the open delta transformer:.
Even though the open delta configured transformer Delta transformer hook up operating at maximum power conditions the phase currents and phase voltages are no longer perfectly in phase and have a displacement between them that is no longer equal to zero degrees. Intuitively we know that an open delta transformer cannot supply as much power as a standard three phase delta since one of the windings is missing.
This only works we are comparing an open delta three phase transformer with the same single phase transformer ratings. For example, if a three phase delta transformer loses one of its windings, or, if the same rated single phase transformers are used to make both a three phase delta transformer and an open delta transformer. In both Delta transformer hook up, the magnitudes of the phase voltage and phase current will be equal between the two types of delta transfomers:.
Three phase transformer connections
An open delta transformer can only supply This is quite a large decrease in power when only losing a third of the overall three phase transformer windings. Three single phase transformers rated for 10MVA Determine the maximum power that this three phase transformer can deliver. Note that both methods yield the same maximum value of 30MW of power delivery by the three phase delta transformer. The first method we used the secondary voltage and the secondary FLA for the phase voltage and phase current magnitudes. Delta transformer hook up could have just as easily used the primary voltage and the primary FLA instead try it and verify the.
Two single-phase transformers rated for 10MVA Notice that the three phase open delta transformer with two windings will only deliver Again we used the secondary voltage and the secondary FLA for the phase voltage and phase current magnitudes but we could have just as easily used the primary voltage and primary FLA values instead to get the same try it and verify. While in operation, one winding fails without damaging the other two.
Open delta transformer connection
The transformer continues to provide power in an open delta configuration. Determine the percentage of power that the open delta configuration is able to supply compared to when all three windings were in service. We can do this by dividing the max power we determined for the open delta transformer by the max power we determined for the delta transformer.
The The second way to calculate this is to compare the formulas for open delta maximum power to standard delta maximum power. Since the phase voltage magnitudes and phase current magnitudes are equal, they will cancel. Notice that we still get the same answer without having to know the actual values of the phase voltage or phase current magnitudes! Great article. You are right on. There are hardly any articles online that cover this topic. I appreciate your efforts and will share this information with my coworkers.
Can you create an example like that, but for an open delta with different size Transformers. What would be the maximum 3 phase power output for that configuration? I really enjoyed the explanation Delta transformer hook up open delta transformers that you present in this article using circuit analysis. My other references only provide a brief description and equation.
Understanding the basics of delta transformer calculations
This really helped me visualize and understand the concept of Open delta systems. It was really frustrating to find any easy simple explanations on this topic! Great explanation of a difficult topic. I will definitely be bringing a printout of this article into the exam. This is a great article. Seeing each step and explanation why you are doing something is beyond what you can find in any resource! Zach, thank you very muchsuch an amazing article, i never found such explanation anywhere else, you made it very easy to derive.
This was a very helpful article, as there are not many reference materials that deal with open-delta transformer configuration. This was another one of those topics that I was completely unfamiliar with before I began studying for the PE Exam. Zach did a really nice job explaining the topic in this article, and he also did a great job covering in the live class.
Great article with detailed overview. I could never find a good article on open delta connections, and even less remember the ificance of them. This cleared it up immediately. Thanks Zach!! To all aspiring PE takers…this course beats all others!!! I was always afraid of the open transformer type question.
Thanks for breaking it down and making it understandable. I must say when it come to understanding the Open Delta Transformer it was difficult, but after going this article I feel a lot better regarding this topic. This article was very helpful. I love this article.