Residual CT and unbalanced current

[mull982]

I am confused about how a residual CT arrangement on a 3wire system with 3CT's works. If the secondary of these 3 CT's are connected in a wye arrangement will there be neutal current flowing in the CT secondary neutral for unbalanced current flowing in the primary circuit due to unbalanced L-L loads causing unbalanced current in the primary?

I know that this arrangement is used for detecting ground faults because phase current will not be balanced as ground fault current will not be returning through any of the phase CT's. I would expect the same for unbalanced currents on the primary?

If there is no neutral element on the CT secondary circuit and a relay calculates this value is this done simply by vectorally adding the 3 primary phase currents. For example if the 3 phase currents are balanced in magnitude and angles then they will sum to zero when added vectorally. If these primary currents are unbalanced and have different magnitudes or angles then when adding them vectorally they will result in some magnitude representing a neutral current which would be seen by a relay. Is this correct?

How does the above now compare to a core CT or zero sequence CT around all three phases? Will this core CT see unbalanced current similar to a residual arrangement or will this CT only see ground fault current?

 

[rcwilson]

On a 3-wire system any current going out one phase has to return on one of the other phases. If it doesn't, there is a fault and the fault current is returning to the source through some other path that is not appropriate.

Since any current in one wire returns on another wire, there is no combination of unbalanced currents in the wires that could result in the three currents not vectorially adding to zero, unless there is a fault.

The zero sequence or ground fault CT adds the currents by surrounding all three conductors. With no fault, all current going out the black wire is coming back on the red or blue wire so the net magnetic field seen by the CT is zero.

Put three identical CT's in place on the wires and they will faithfully reproduce the currents. Add the currents together by connecting all the CT secondary wires together
in the residual connection. As long as there is no fault there will be no current flowing in that CT secondary neutral wire, (neglect difference in CT ratios, CT errors and CT saturation).

Bottom line, 3-wire currents always add to zero. If they don't, you have a faulted system.

Look at it another way. Put an unbalanced load of 10 amps on A and 0 on B & C. Is that possible? Where does the 10 amps go without a neutral? Obviously, that scenario is not possible on a 3-wire system. Put a 10 amp load A-B. No current is in C. Add them together and you will get 0 amps because the current in A & B are 180 degrees opposite from each other. Now add a 5 amp load B-C and a 20 A load C-A. All currents going out one wire come back on the other. The net result (I don't have time tonight to do the math and apply superposition theory) is the currents in the three phases will all add to zero.

 

[mull982]

On a 3-wire system any current going out one phase has to return on one of the other phases. If it doesn't, there is a fault and the fault current is returning to the source through some other path that is not appropriate.

Since any current in one wire returns on another wire, there is no combination of unbalanced currents in the wires that could result in the three currents not vectorially adding to zero, unless there is a fault.

The zero sequence or ground fault CT adds the currents by surrounding all three conductors. With no fault, all current going out the black wire is coming back on the red or blue wire so the net magnetic field seen by the CT is zero.

Put three identical CT's in place on the wires and they will faithfully reproduce the currents. Add the currents together by connecting all the CT secondary wires together
in the residual connection. As long as there is no fault there will be no current flowing in that CT secondary neutral wire, (neglect difference in CT ratios, CT errors and CT saturation).

Bottom line, 3-wire currents always add to zero. If they don't, you have a faulted system.

Look at it another way. Put an unbalanced load of 10 amps on A and 0 on B & C. Is that possible? Where does the 10 amps go without a neutral? Obviously, that scenario is not possible on a 3-wire system. Put a 10 amp load A-B. No current is in C. Add them together and you will get 0 amps because the current in A & B are 180 degrees opposite from each other. Now add a 5 amp load B-C and a 20 A load C-A. All currents going out one wire come back on the other. The net result (I don't have time tonight to do the math and apply superposition theory) is the currents in the three phases will all add to zero.

So you are saying that no matter how severe the imbalance on a 3 wire system the resulting residual current will always be 0? Same goes for a core CT?

But when looking at the secondary CT connection the currents on the secondary of the CT's will be unbalanced but will now have a neutral connection on the secondary connection. Why wont the unbalanced current want to take this neutral path?

What if there is a neutral in the primary circuit? Will current then flow in the neutral of the secondary CT connection?

 

[jghrist]

Assuming perfect CTs, the current in each phase of the secondary will equal the primary current divided by the CT ratio. If IA + IB + IC = 0, then IA/n + IB/n + IC/n = (IA + IB + IC)/n = 0/n = 0.

If the primary is 4-wire, then the residual current will equal IN/n where IN is the primary neutral current.

 

[rcwilson]

If it is an un-faulted, three-wire circuit on the primary, the CT neutral/residual connection will not carry any current, neglecting CT errors. The phase currents will add vectorially to zero at the junction point of the three CT secondaries. The effective impedance of the neutral return path is higher than the impedance of the other two phases. The primary currents have to add to zero, because there is no other return path, so the secondary currents have to add to zero also.

Using the example of single phase A-B load with no current in C (maximum unbalance), A phase is 100 Amps at 30 degrees, B phase is 100A at 30+180= 210 degrees, A + B = 0. C= 0 so A+B+C =0. Assume 100:5 CT's with all polarities away from the neutral.

Phase A CT generates a voltage to force a 5A current 30 degrees and the B phase generates a voltage for a current of 5A at 210 degrees. Since these two currents are 180 degrees apart, one CT's voltage can be considered as pushing the current, the other is pulling it. The 5A circulates in the two CT's and no current flows in the neutral, just like the primary. The effective impedance of the neutral wire is higher than the other return path due to this push-pull.

Any unbalanced load on the three-phase, three-wire system can be broken down into a combination of phase-phase loads like the aobve example. Each of them will add to zero at the junction. Add them all together and you still get zero at the junction and no neutral current. (Ignore CT errors).

Add a neutral in the primary for a 3-phase, 4-wire system and the neutral wire in the CT secondary circuit will mimic the primary neutral current + CT errors. A 51N relay in the CT neutral circuit will pick up on ground faults and for unbalanced loads.

 

[mull982]

A 51N relay in the CT neutral circuit will pick up on ground faults and for unbalanced loads.

What about a 51N relay being used on a 3 CT residual configuration on a relay. Will this 51N element only pickup for ground faults?

 

[rcwilson]

What about a 51N relay being used on a 3 CT residual configuration on a relay. Will this 51N element only pickup for ground faults?

Correct, provided the primary system is 3-phase, 3-wire.

Unbalanced load currents only affect residual ground fault 51N relays in a 3-phase, 4-wire system.