but in the delta configuration, line to neutral and line to line voltages are the sameUpon further reflection this morning, the solution given in the book is just working the problem on a per-phase basis. Don't worry about the open delta, it supplies a 3 phase balanced load. If you then divide that total load by 3 and use the line to neutral voltage which is 254, you get the current.
Flyer brings up an excellent point! So, in general mathematical terms, how does the load connected to this delta configured transformer differ from the 500kVA load placed between phases B and C on the 3-phase, 4-wire system given in NCEES #110?^In delta configuration, there is no line-neutral voltage. The reduction by the sqrt(3) actually applies to the current rather than the voltage. Mathematically, however, there is no real difference between a delta and a wye connected transformer so long as you are dealing with voltages and currents external to the transformer. That enables you to treat either as if it is wye-connected for the purposes of determining line currents and how they affect voltage drops etc.
I don't have NCEES # 110 but the first difference is the load is balanced in this problem which enables you to handle it per-phase if you want. I would guess the best way to solve #110 is careful use of phasors but since I don't have problem just guessing a bit.Flyer brings up an excellent point! So, in general mathematical terms, how does the load connected to this delta configured transformer differ from the 500kVA load placed between phases B and C on the 3-phase, 4-wire system given in NCEES #110?
DK_PE's approach is very elegant, however isn't the resultant impedance (i.e., Z=V^2/S@arccos(0.8)[email protected]) the impedance of the load, not the delta phase impedance? The equivalent wye impedance would be Zy=Zd/3.
I apologize if I'm confusing the issue.
I agree and the answer is different when you make or don't make the conversion and so it's hard to tell on the exam whether you should or should not make the conversion.I don't see any advantage in this case to perform a delta - wye conversion
But we are looking for the kVA rating of the two individual single phase transformers and so S = IV with no sqrt(3) factor. Therefore, it does matter whether we use line or phase value correctly.The math to derive the formula |S|=SQRT(3)xVLLxIL works out the same way for a Wye or Delta system. I only showed it once. The difference is where the SQRT(3) comes from. In a Wye system it works out from the relationship between phase-phase and phase-neutral voltages, in a Delta the SQRT(3) comes from the relationship between phase current and line currents.
It's the same answer I got above.I was just showing you a quick way to find your line current external to the transformer. I come up with 65.6 A when using |S|=SQRT(3)xVLLxIL, which is exactly what the NCEES came up with for a line current... Then the transformer voltage being 440V, 65.6 A x 440V = =28.9 kVA rating per transformer. Is that the correct answer for the problem?
The short answer is that they could do either. I've seen both in sample questions. You have to read the questions carefully. They could ask for the minimum acceptable size and have an answer just below what is required. If you go with your first instinct and pick the closest answer (giving you a slightly under-sized transformer) rather than the next available size up...........One question for all: Would the NCEES ask for 28.9 kVA, 29 kVA, whatever or would they ask for the actual transformer rating? I don't think I've ever seen a transformer rated 29 kVA. It would be 30 kVA probably.
Just curious if give you mathematical answer choices or if they give you real-world answer choices.
So in response to that, do they want you to think like a student or any engineer? I could as an engineer choose to use a 25 kVA knowing that it will be slightly overloaded, but that it could be well within what I find acceptable for use and it is a very common size. As a student I would say "Definitely it has to be a minimum of 28.9 kVA because the math says so" I suppose it goes back to "Read the question carefully!"It's the same answer I got above.I was just showing you a quick way to find your line current external to the transformer. I come up with 65.6 A when using |S|=SQRT(3)xVLLxIL, which is exactly what the NCEES came up with for a line current... Then the transformer voltage being 440V, 65.6 A x 440V = =28.9 kVA rating per transformer. Is that the correct answer for the problem?
The short answer is that they could do either. I've seen both in sample questions. You have to read the questions carefully. They could ask for the minimum acceptable size and have an answer just below what is required. If you go with your first instinct and pick the closest answer (giving you a slightly under-sized transformer) rather than the next available size up...........One question for all: Would the NCEES ask for 28.9 kVA, 29 kVA, whatever or would they ask for the actual transformer rating? I don't think I've ever seen a transformer rated 29 kVA. It would be 30 kVA probably.
Just curious if give you mathematical answer choices or if they give you real-world answer choices.
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