Suppose you have a 3-Phase AC transmission line circuit with a phase to phase RMS voltage of 100 kV @120 degrees (100/root3 kV, phase to ground). Now alongside this line is another 100 kV RMS phase to phase 3-phase line. What is the highest RMS voltage that can exist between the near phase conductors of each circuit, assuming they are not in phase? Is it 200 kV? (I assume it is 0 if they are in phase). How is this calculated using voltage vectors? Thanks.
What do you mean by "near phase conductors of each circuit"? The conductors in the two transmission line that are physically the closest to each other. or The phase voltage in each transmission line that are the closest to each other. Assuming that the neutrals are grounded, the maximum possible line to line voltage is 2*100/root3 kV.
I meant the max posible line to line voltage between the conductor of one circuit and the physically closest conductor of the other circuit, assuming that the physically closest conductor of the other circuit was not in phase with the near conductor of the 1st circuit. I was assuming that if the conductor of one circuit was 100/root3 phase to ground at 120 degrees, and the nearest (physically) conductor of the other circuit was 100/root3 phase to ground at 300 degrees (voltage directed 180 degrees opposite the first circuit conductor), then the voltage between the 2 would be 200/root3 phase to ground, or 200 kV phase to phase. Is this incorrect? (I am looking at air breakdown flashover between the 2 bare conductors in question in close proximity to each other). And yes, assume both circuits are effectively grounded. Thanks.
Wouldn't the difference between the two lines just look be a sine wave of amplitude (the max value at 180° phase difference) 200kV? Phase to ground voltages are the same for all 3 phases on both circuits.
The maximum line to line voltage is 115.4 kV. 200 kV line to line voltage is not possible. See attached sketch.
But it seems that your calc gives the max phase to ground voltage, which is strange, because I'm looking for phase to phase voltage. If you multiply 115.4 by sq rt 3, you get digoff's answer. Can you explain why you would use the line-to-ground voltage difference to get the line - to- line voltage difference. Thanks.
The neutrals of these two systems are joined together, so the phase to phase voltage dosn't matter. The phase to phase voltages can't add unless they are joined together. The RMS phase to neutral voltage of each system is 100 / 1.732 or 57.73 KV. The peak value of this is 57.73 * 1.414 or 81.64 KV If the two systems happen to be exactly out of phase, then one line would be at plus 81.64 KV and the other would be at minus 81.64 KV. So the total voltage would be 163.28 KV. This is the peak voltage where flashover would be most likely to occur. Divide by 1.414 to get RMS if you want it.
Well, that agrees with Carl Pugh's response. But I don't understand why if I placed a voltmeter in between the 2 conductors of the different circuits in question, why would i read a line to ground voltage and not a line to line voltage? Surely the voltage beteen 2 conductors of the same circuit is line to line (100 kV), so why do I get line to ground voltage when i measure between different circuits?
Don't forget that these two systems are not in a fixed phase relationship, unlike the phases of a single system. So, although the normal 3 phases can only have a voltage between phases of 1.732 times the phase to neutral voltage, if they are not in phase, the voltage can be 2 times the phase to neutral voltage. This happens when the voltages are at their maximums but of opposite polarity. Also, of course, the voltage could be anything from 2 times the phase to neutral voltage to zero, depending on how the phases occur. This can't happen either with a single 3 phase system.
The fact that you are dealing with three-phase systems is irrelevant in the discussion here. The principle would be the same if the question was about two monophase systems. What's important is that the two systems have a common point between them. Just consider two AC sources that have their negative terminal hooked up together. If the phase angle between them is 180 degrees, the highest voltage you can measure between their positive terminals is the sum of the amplitudes of their voltage oscillation. Here you got two 57.73 kV RMS AC sources which have their negative terminals connected to the same point. The fact that two other AC source pairs are also connected doesn't change anything. However if the discussion was about two systems that have no common node, their would be no answer. As if you were asking what you would get by measuring the voltage between the positive terminals of two batteries lying on your table.
Thank you both for your answers, which surprised me. If the earth serves as the ground rather than a continous neutral wire, I assume the answer remains the same? That is, the voltage between any 2 wires of different 3-phase AC circuits can not be higher than twice the line to ground voltage of each circuit?
If the "ground" was an efficient connection, then, sure. It would be as good as a piece of wire joining the neutrals together. However efficient connections to physical ground (ie dirt) are very difficult and expensive to achieve. It is the very peak voltage of the sinewave that is the important part if you are worried about wire spacing. If you are still surprised by this result, maybe you could try drawing up a diagram of it or even substituting batteries to represent the maximum voltage condition. There is no hurry, so just post again if you like. Maybe you can identify what you are having a problem with. You probably know that the arc-over voltage of a pair of conductors in air is about 30 KV / CM but this depends on the diameter of the conductors. The diameter may be more than the diameter of the wires if there is a corona discharge as there may be in this case with these very high voltages. Coronal discharge makes a discharge less likely
Thanks, I've got it now, my thanks to you, Carl, and Lotus for your clear explanations. My problem is that I'm a Civil Engineer with only a basic understanding of electricity.