Unbalanced Three Phase Load 6

[gcaudill]

I have an electrical system which consists of a delta-wye connected transformer supplying a delta connected load. One corner of the delta is grounded. I have the following load current measurements:
I leg1 = 1115A
I leg2 = 1000A
I leg3 = 1092A

Can someone tell me where the unbalanced current will go? Circulate in the load or exit to ground at the grounded corner? The ground is well connected, low impedance, and terminated to the main grounding bar at the switchgear.

 

[jghrist]

jbartos,

If the path for Ig is not created, all of the Leg 3 current would return to X2 through the cables and none throught the ground. Current from X2 to ground would be zero.

 

[jbartos]

Suggestion to jghrist (Electrical) Apr 18, 2003 marked ///\\jbartos,
If the path for Ig is not created, all of the Leg 3 current would return to X2 through the cables and none throught the ground.
///Please, would you clarify this in view of your posting:
"The ground current is a portion of the Leg 3 load current; part flows to X2 through the cable and part through the ground. "
and in view of the posting by "gcaudill (Electrical) Apr 17, 2003" indicating:

"I hope I made it clear before, the 78A in the ground was measured between X2 and the ground bus at the switchgear, not between X2 and the #1 and #4 annealer sheaves."\\\

Current from X2 to ground would be zero.
///This appears to contradict the test results stated in the "gcaudill (Electrical) Apr 17, 2003" posting, indicating 78A being measured between X2 and the ground bus in the switchgear.\\
///Else, the calculation is impressive.\\\

 

[Shortstub]

gcauddill,
A clearer picture of the process would help!

1) Are the multi-cable feeders, the ones you call leg 1, leg 2, and leg 3, fixed?

Does the wire or cable being annealed go from some reel or spool thru sheave 1 to sheave 2?

Does another wire or cable being annealed from a second reel or spool go thru sheave 3 to sheave 2?

Then do the two annealed wires continue to the quench bath, thru sheaves 3 and 4, respectively?

Finally do they end up on a takeup reel or spool?

 

[jghrist]

jbartos,

Here's how I picture the situation:

The wire being annealed is fed into sheave 1 which is connected to X2. The wire then stretches from sheave 1 to sheave 2 (Leg 1). Sheave 2 is connected to X1. The wire then stretches from sheave 2 to sheave 3 (Leg 2). Sheave 3 is connected to X3. The wire then stretches from sheave 3 to sheave 4 (Leg 3). Sheave 4 is connected to X2 (with a separate cable than the X2-sheave 1 connection). The wire then goes from sheave 4 to a quencher.

Leg 1 is connected ø-ø from X2 to X1. Leg 2 is also connected ø-ø from X1 to X3. Leg 3 is connected ø-ø from X3 to X2. Sheaves 1 and 4 are meant to be at ground potential, but because of voltage drop in the two cables from X2, a voltage to ground exists.

Current through Leg 3 comes from X3 (through 10-250 MCM cables) and from Leg 2. In my example calculations, the current from X3 into Leg 3 is 2100A <80.3°. It adds to the load current in Leg 2, 1201A <-70.9°, resulting in a load current in Leg 3 of 1197A <51.4°.

The current in Leg 3 is supposed to all go back to X2 through the 10-250 MCM cables, but some (78A) goes through the wire to the quencher and then through some ground path back to the transformer ground and then to X2.

If the quencher (and the wire after it leaves the quencher) were isolated from ground, all of the current would be forced to get from Sheave 4 to X2 through the 10-250 MCM cables and there would be no current measured from X2 to the transformer ground.

 

[jbartos]

Suggestion to the previous posting marked ///\\The current in Leg 3 is supposed to all go back to X2 through the 10-250 MCM cables, but some (78A) goes through the wire to the quencher and then through some ground path back to the transformer ground and then to X2.
///This sounds somewhat mysterious how that &quot;some ground path” is in existence. Apparently, there must be some connection in the transformer from X2 to ground bus. This connection would lend itself for ground current measurements, yielding 78A. Then, everything is o.k. and the unbalanced currents path is established.
Then, contrary to the extensive calculations above, which is using zero sequence current equal to zero, there will actually be the zero sequence current flowing through the ground and it will be equal to 78A/3=26A.\\

 

[jghrist]

The &quot;some ground path&quot; is probably through building steel.

There can be unbalanced phase current without zero-sequence current. If the three phase currents are unequal but add to zero, then there is no zero-sequence current. There can be no zero-sequence current if the transformer neutral is isolated. For instance, Ia = 1940.9 <-41.5°, Ib = 1970.3 <-156.6°, Ic = 2100 <80.3°. The currents are not equal (unbalanced), but Ia+Ib+Ic = 0.

There can be no zero-sequence current if the transformer neutral is isolated. It doesn't matter if there is or is not any ground current. If a delta transformer secondary has one corner grounded, a fault to an ungrounded phase would result in ground fault current, but no zero-sequence current.

 

[jbartos]

Suggestion to jghrist (Electrical) Apr 20, 2003 marked ///\\\
The &quot;some ground path&quot; is probably through building steel.
///This may be true, however, the 78A were measured between the transformer X2 terminal and switchgear ground bus as posted above. I was interested in this since this connection establishes path for the ground currents to flow. These are also referred to as common mode currents. They should be accounted for in the model by symmetrical components to have proper electrical energy balance and the model accurate. Else, the mathematical model is inaccurate, i.e. somewhat off.\\There can be unbalanced phase current without zero-sequence current.
///Certainly, if modeled so. See above comments.\\ If the three phase currents are unequal but add to zero, then there is no zero-sequence current.
///Agreed. But if the &quot;if&quot; represents the reality.\\ There can be no zero-sequence current if the transformer neutral is isolated. For instance, Ia = 1940.9 <-41.5°, Ib = 1970.3 <-156.6°, Ic = 2100 <80.3°. The currents are not equal (unbalanced), but Ia+Ib+Ic = 0.
///True, based on the &quot;if&quot;.\\
There can be no zero-sequence current if the transformer neutral is isolated.
///True, but what remains to be added, there is no any other ground connection, e.g. corner ground from transformer terminal X2 to ground as posted above.\\ It doesn't matter if there is or is not any ground current.
///It just depends on the accuracy of modeling. How to account for the electrical energy balance accurately?\\ If a delta transformer secondary has one corner grounded, a fault to an ungrounded phase would result in ground fault current, but no zero-sequence current.
///True, however, the load is also corner grounded as posted above, creating a ground path with 78A flowing through it. The transformer actually has an open wye connection since the transformer neutral is not grounded and the actual neutral is the ground path carrying three zero sequence currents 3xIo=78A. The symmetrical component modeling needs to be adjusted accordingly.\\

 

[jghrist]

jbartos writes (marked with >):
>This may be true, however, the 78A were measured between
>the transformer X2 terminal and switchgear ground bus as
>posted above. I was interested in this since this
>connection establishes path for the ground currents to
>flow.

The connection from X2 to the switchgear ground bus establishes only one end of the path for ground currents. There has to be another connection to ground or ground current will not flow. I surmise that Shortstub is correct that the other connection is at the quencher.

>They should be accounted for in the model by symmetrical
>components to have proper electrical energy balance and
>the model accurate. Else, the mathematical model is
>inaccurate, i.e. somewhat off.

Actually, I modelled the circuit using Kirchoff's voltage law and mesh equations, not using symmetrical components. I calculated the sequence currents from the phase currents after determining the phase currents by mesh equations.

>...the load is also corner grounded as posted above,
>creating a ground path with 78A flowing through it.

The load is corner grounded through the cable connecting it to X2. The only intentional connection to ground is at X2.

>The transformer actually has an open wye connection since
>the transformer neutral is not grounded and the actual
>neutral is the ground path carrying three zero sequence
>currents 3xIo=78A. The symmetrical component modeling
>needs to be adjusted accordingly.

If the transformer has an open wye connection, then there is no neutral path. If there is a ground path, it does not carry any zero-sequence current. Zero-sequence current is not equivalent to ground current. What I mean by ground current is any current that flows through the earth or things like pipes and building steel that are part of the grounding system.

 

[gcaudill]

jghrist's April 19 &quot;picture&quot; of the situation is correct regarding the arrangement of the wire, sheaves, and X1, X2, X3 connections.

I think what I need to do is to take current and phase angle measurements on the conductor gangs that feed sheaves 1-4. This is easier said than done due to the number of conductors and their proximity to danger areas on the machine. I'm not sure if I can get phase angle measurements on the load legs (legs 1-3) as this is even more difficult.

I'm still not sure about the idea of current leakage to ground, via the quench process, causing the 78A measured in the grounding conductor connected to X2. The wire is in contact with the quench water for a very short length prior to contacting sheave #4. But the wire makes no contact with piping, metal, etc, prior to contacting sheave #4.

One last note on my theory of an unbalanced load causing the 78A measured in the grounding counductor connected to X2. If a different number of commutating brushes are used on sheaves #2 and #3, or in other combinations of different sheaves, the ground current more than doubles. For example, last week someone mistakenly installed twice the number of brushes on sheaves #1 and #3 as sheaves #2 and #4. This caused the current in the ground conductor to increase from 78A to 183A. This still leaves me to believe that an unbalanced load is causing the current in the ground conductor.

Questions:
Would a circulating current (due to load unbalance) in the load have to be a zero sequence current, or would it be a sum of the three currents at their respective phase angles?

Unbalanced currents would have one of three options?
- Find its way to the ground conductor at X2?
- Circulate in the load?
- Circulate in the transformer?

 

[jghrist]

There have to be two points of connection to ground for current to flow in the ground. The 78A has to go somewhere. It can't just be absorbed by the earth.

Unbalance load currents can occur without zero-sequence currents or ground currents. Take this simplified example:

Zero impedance in connecting cables.

ø-ø secondary voltages: Vba (X2 to X1) = 50 V <0°, Vcb (X3 to X2) = 50 V <-120°, Vac (X1 to X3) = 50 V <120°

Leg resistances: Leg 1 (X2 to X1) = R1 = 50 milliohm, Leg 2 (X1 to X3) = R2 = 50 milliohm, Leg 3 (X3 to X2) = R3 = 100 milliohm

Current in Leg 1 = I1 = Vba/R1 = 1000A <0°
Current in Leg 2 = I2 = Vac/R2 = 1000A <120°
Current in Leg 3 = I3 = Vcb/R3 = 500A <-120°

Phase a (X1 to Sheave 2) current = Ia = I2-I1 = 1732A <150°
Phase b (sum of X2 to Sheave 1 and X2 to Sheave 4) current = Ib = I1-I3 = 1323A <19.1°
Phase c (X3 to Sheave 3) current = Ic = I3-I2 = 1323A <-79.1°

Zero-seq current = (Ia + Ib + Ic)/3 = 0A

Positive-seq current = (Ia + Ib*1<120° + Ic*1<240°)/3 = 1443A <150°

Negative-seq current = (Ia + Ib*1<240° + Ic*1<120°)/3 = 288.7A<150°

Current from X2 to ground = 0

 

[jbartos]

Suggestion to the original posting gcaudill (Electrical) Apr 1, 2003 marked ///\\I have an electrical system which consists of a delta-wye connected transformer supplying a delta connected load. One corner of the delta is grounded.
///In view of your last posting, where it is indicated that the X2 at the transformer wye is grounded, would you clarify the above &quot;one corner of the delta is grounded.&quot; It can easily be understood that one corner of the load delta is grounded at the load, not at the transformer wye connection X2 to switchgear bus. This would then somewhat correct the situation and interpretation of the problem. However, the ground currents in form of the common-mode current, perhaps leakages would still exists, as generally admitted in above postings, and form the 3xIo current. The symmetrical component calculation should be adjusted accordingly.\\ I have the following load current measurements:
I leg1 = 1115A
I leg2 = 1000A
I leg3 = 1092A

 

[Shortstub]

gcaudill,
The fact that the 78A current changes (although corresponding changes in legs 1,2,3 were not noted) indicates that brush contact is an influence. Is there a way you can measure the current in the cable routed to the quench tank, by means of a large &quot;window&quot; clamp-on ammeter?

 

[Shortstub]

It's time to recap. While I agree with Jghrist's loop around the sheave presentation, thus providing a &quot;closed-delta&quot; load for electrical purposes, I disagree with the sequence.

I believe, that for safety reasons, the &quot;wire&quot; being annealed moves as follows:

1) From wire moves from the source reel to sheave 2.
2) From sheave 2, it moves to sheave 1.
3) From sheave 1, it moves to sheave 3.
4) From sheave 3, it moves to sheave 4 (conductively connected to sheave 2).
5) From sheave 4, it moves to the quench tank.
6) from the quench tank it moves to a takeup reel.

The path described insures that the beginning and end of annealed &quot;wire&quot; loop occurs at sheaves, 2 and 4, respectively. And, because they have the lowest exposure volts to ground, 4.8 Volts, personnel risk is minimized.

Now, then, there are two possible &quot;sneak&quot; paths to ground... one being the quench tank, the other the supply reel. If the feeding reel is well insulated from &quot;ground&quot;, then there will be only one sneak path. The test I suggested earlier should confirm it!

 

[gcaudill]

Shortstub,

Close in your routing, but not exact.
1.) Wire moves from source to sheave 1.
2.) From sheave 1 to sheave 2 (x-former X1).
3.) From sheave 2 to sheave 3 (x-former X3).
4.) From sheave 3 to sheave 4.
5.) Quench process after sheave 4.

Sheaves 1 and 4 are electrically connnedted to x-former secondary X2. Tap X2 is connected to ground.

 

[jghrist]

I think from gcaudil's April 17 comment:

>There are 10 250mcm cables feeding each sheave from the x-
>former secondary. There are 20 cables attached to the x-
>former X2, and 10 cables attached to X1 and X3. The first
>and last sheave are connected to X2.

>Distances:
>x-former X2 to sheave #1 - 10'
>x-former X1 to sheave #2 - 35'
>x-former X3 to sheave #3 - 15'
>x-former X2 to sheave #4 - 35'

that sheaves #1 and #4 are connected to the grounded X2 and that for safety reasons, this is where the wire enters and exits the annealer.

 

[Shortstub]

At last, agreement by... some.

Now then, can we further agree that there is only one intentional ground/earth connection. And, it is at X2, not at the sheave 2/4 corner of the delta formed by the annealed wire path through the four sheaves! If so, then the only path for the mysterious 78A is the quench tank path.

 

[gcaudill]

Shortstub,

Seems like we are on the same page. There is only one intentional ground, at X2 of the transformer. All four sheaves are to be isolated.

Your synopsis is that the only cause for current in the ground is stray current through the quench tank? Not due to any load or current unbalance?

 

[jghrist]

Suggestion:

Measure the current in the wire before sheave 1, between sheave 4 and the quencher, and after the quencher. If there is 78A in the X2-ground connection and 78A in the wire between sheave 4 and the quencher, and nothing in the wire after the quencher, then we have pretty much proven that the quencher is the source of the ground current.

You mentioned that changing the number of commutator brushes changed the amount of ground current. Did it also change the amount of load current?

 

[jbartos]

Suggestion: No matter where the ground current is coming from to the ground connection at transformer X2 terminal, it is the common-mode current or 3xIo, and it is normally taken into calculation consideration, if the calculation is to be accurate. Regular high resistance system grounding at transformer with the neutral may have this current about 5 to 10Amps.

 

[jghrist]

This is not a high resistance grounded system. The transformer has an ungrounded neutral. There will be no zero-sequence current.