For a 3 wire motor, if we connect with a 4 core cable and one core is earthed and both ends, whether it will make any voltage or current flow in the redundant (bare) core?
Again, if a 4 core cable is connected to a 3 wire system, whether any voltage will be generated in the fourth core even though the fourth core is not connected at both ends. If yes why?
Simple explanation is when one wire is ran along side of a current
carrying wire, the none current wire behaves like the secondary of a
transformer. You will see voltage but the current potential is almost non existent. Grounding that wire should cancel and harmful potential voltage. Maybe someone else can explain better.
I may be wrong but here is my opinion.
The spare core would be similar to the ground wire.
Yes there will be some current induced by the magnetic field and some by the capacitive coupling. The magnetic coupling would be greatest at start.
Some might say that the field is balanced being 3 phase, but in a typical cable the 4th wire is not equidistant from each phase.
The two basic ways to couple voltage or current on to another conductor are electrostatic (capacitive coupling, voltage based) and magnetic (inductive coupling, current based). Radiated noise is not relevant to this discussion. In the following cases:
Case #1: "For a 3 wire motor, if we connect with a 4 core cable and one core is earthed and both ends, whether it will make any voltage or current flow in the redundant (bare) core?"
If we consider inductive coupling and the fourth wire is grounded at both end, you will induce current on the fourth wire because you have a complete loop (grounded at both ends, e.g. connected via the ground). Think about inductive coupling as being like a transformer, which needs loop(s) to work. The induced current will flow in the opposite direction to the current flows in the power cables (this is interesting as we have three different currents flowing in different directions in the power cables, which tend to cancel each other out in a balance load situation). You will also have ground current in the fourth wire due to the difference between the ground potential at the points where you grounded your cable (e.g. not all grounds are equal). Since most of the motor cables are long, there can be substantial difference in ground potential at the two grounds (particularly during lightning events). This is generally not an issue for electrical safety or equipment grounding if you have a good equipotential plant ground grid. This is also why it is generally a bad idea to connect shield grounds at both ends. In regard to voltage in this case, since the fourth conductor is connected to ground, the cable should be essentially at ground potential and only small voltage drops due to the coupled ground current should exist in a properly designed grounding system. The amount of inductive coupling will be the greatest when the motor starts. There will also be a larger coupling when the motor stops and the motor magnetic field collapses.
There will be a capacitive coupling (visualize distributed capacitors between the power cables and the grounded conductor) from the power cables to the fourth cable, which is essentially at ground potential (there will be a small capacitive currents returned to ground on the fourth conductor and back to its source potential). This may be balanced out somewhat with a balanced load and twisted cables.
Case #2: "Again, if a 4 core cable is connected to a 3 wire system, whether any voltage will be generated in the fourth core even though the fourth core is not connected at both ends. If yes why?"
Here there are two cases here: Case #2a: First there the cable is grounded at one end and in Case #2b where the fourth wire is not physically grounded at all.
There is no magnetically coupled current or voltage on the fourth conductor in either of these cases because there is not a complete current path to induce any current (again think about inductive coupling being like a transformer, which needs loop(s) to work).
Case #2a: For capacitive coupling, visualize a set of distributed capacitors from the power cables to the fourth conductor, which is at ground potential. There will be a small capacitive currents returned to ground and back to its source potential. The fourth cable should be at essentially ground potential. This may be balanced out somewhat with a balanced load and proper grounding.
Case #2B: For capacitive coupling, visualize a set of distributed capacitors from the power cables to the fourth conductor, which is floating (at an unknown voltage) and a second set of distributed capacitors from the fourth wire to ground potential. Since we do not know what the potential of the fourth wire is, the best practice is to effectively ground the cable (particularly if it is bare).
This discussion does not cover coupling of EMI to wires other than the fourth wire.
That being said and realizing that I don't know what electrical code you are under. The US National Electrical Code (NEC), would require that an equipment ground for the motor and that bare fourth wire is probably suppose to be used as an equipment ground conductor. In my experience, the motor frame is connected to the plant earth grid at the motor and an equipment ground cable is connected between the motor control MCC ground and the motor field (at the peckerhead). Follow your electrical code.
William (Bill) L. Mostia, Jr. PE
ISA Fellow, FS Eng. (TUV Rheinland)
WLM Engineering Co.