# unbalanced 3 phase generator load

#### Smart \$

##### Esteemed Member
Smart \$ ...

Rather than play your "Who's on First" game, I can recommend an excellent text on 3-phase generators!

Regards Phil Corso
What good is that going to do? Does it cover winding current of a line-to-line connected, single phase load on a 3? generator with delta-configured output windings? Even trying to find such a discussion on the internet regarding any delta power source proves difficult. We are typically taught to connect balanced loads. There's some discussion on [relatively minor] unbalanced loads, and unbalanced faults... but none that I could find discussing the apparent extreme single phase load.

Besides, this is basic electrical theory... though not discussed in texts and has nothing to do with generators specifically. When we narrow the discussion to generators, it presents nuances but does not negate the basics.

#### Phil Corso

##### Senior Member
Smart \$

Really,you should read more!

Phil

#### Sahib

##### Senior Member
I thought the SQRT(3) factor appled only to balanced loads? Do you mean to say that Sqrt(3) x 20 = 30?

Phil
I think it applies. In delta connected generator three voltage sources are connected in delta. They should supply the same current through their respective windings to the terminals connected to single phase load respecting the relation ''line current is 1.732 times phase current'' due to delta connection.

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#### GoldDigger

##### Moderator
Staff member
Besides, this is basic electrical theory... though not discussed in texts and has nothing to do with generators specifically. When we narrow the discussion to generators, it presents nuances but does not negate the basics.
So far, every reference that I have found from generator manufacturers states that for pure single phase loads, you need to derate by 1/3 (i.e multiply rated power by .67). But the only thing close to a justification for that is the assertion that "all of the power for a single phase load is coming from only two of the windings."
That is so blatantly lame that I discount it completely.
When I do the math and look only at the heating in the windings as the limiting factor and make the best case assumption that the heat dissipation is limited by the bulk heat removal from the sum of the three windings (and therefore that I could dissipate the heat equivalent of a full rated balanced delta load in only one of the windings) I get two different numbers (if anybody wants to actually see my math, I may consider posting it).
If I assume that the current to the single phase load comes only from the one coil which directly joins the two terminals I connect to, I get a derate factor of .578 (1/sqrt3).
If I assume that Smart Money's analysis of the contribution of the other two windings is correct, I get a derate factor of .707 (1/sqrt2).
Which of those is closer to .67?

#### Sahib

##### Senior Member
Not only in the US, but all three phase generators in other parts of the world can supply single phase loads of various percentages of the rating with negative sequence current limited: 10 % is the maximum negative sequence current. So what is the percentage of negative sequence current in the OP's case?
To calculate the percentage of negative sequence current requires an application of symmetrical components. Assuming the currents in the OP's case have only magnitudes unbalance ( because the phase angle unbalance is not given!), the negative sequence current percentage can be worked out to see it does not exceed the limit (say 10%) given in IEEE std.C37.102-1995-Guide for AC generator protection for continuous negative sequence current capabilities.

#### Smart \$

##### Esteemed Member
Smart \$

Really,you should read more!

Phil
Reading more on this particular issue just clutters my head with things I'll never use in the real world.... confirmed by the Sherlock Holmes role in the current Elementary series on CBS... can't remeber which episode... but I'm not suggesting I consider the show as authoritative.

#### Smart \$

##### Esteemed Member
So far, every reference that I have found from generator manufacturers states that for pure single phase loads, you need to derate by 1/3 (i.e multiply rated power by .67). But the only thing close to a justification for that is the assertion that "all of the power for a single phase load is coming from only two of the windings."
That is so blatantly lame that I discount it completely.
Was that statement regarding delta or wye configured windings. If wye, I think it would be fairly obvious... a single phase line-to-line load (say connected A-B) is handled by two windings (a-n & b-n... c-n is not in the circuit?KCL)

When I do the math and look only at the heating in the windings as the limiting factor and make the best case assumption that the heat dissipation is limited by the bulk heat removal from the sum of the three windings (and therefore that I could dissipate the heat equivalent of a full rated balanced delta load in only one of the windings) I get two different numbers (if anybody wants to actually see my math, I may consider posting it).
If I assume that the current to the single phase load comes only from the one coil which directly joins the two terminals I connect to, I get a derate factor of .578 (1/sqrt3).
If I assume that Smart Money's analysis of the contribution of the other two windings is correct, I get a derate factor of .707 (1/sqrt2).
Which of those is closer to .67?
Well .707 is closer, obviously... but I don't see how you got the numbers to begin with.

Basics say the limit is 50% for single phase loading of a delta-configured output. Say a gennie is rated 120kVA 3? output at whatever the single phase load's power factor is. That's 40kVA per winding. Now let's say the direct-connected winding is conducting to that level for a connected single-phase load. According to my assertion, one-third is half of two-thirds, that means the kVA of the two indirectly-connected windings would be 20kVA each, but the actual load would only be 40kVA + 20kVA = 60kVA. So max single phase load is 60kVA, even though gennie realizes 80kVA. So 60kVA compared to the max 3? load rating of 120kVA is 50%.

#### Smart \$

##### Esteemed Member
I think it applies. In delta connected generator three voltage sources are connected in delta. They should supply the same current through their respective windings to the terminals connected to single phase load respecting the relation ''line current is 1.732 times phase current'' due to delta connection.
The 1.732 phase-to-line relationship only occurs under a balanced load condition. Any unequal magnitude or power factor of phase currents and the 1.732 factor no longer applies.

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#### iceworm

##### Curmudgeon still using printed IEEE Color Books
Yes. No damage to the stator winding of the generator. But damage will be done to the rotor winding due to excessive heat generated by -ve phase sequence current circulating in the rotor winding.
I'll agree to extra heat. How can you establish heat will be excessive if you don't know the design parameters???
Sorry for dragging you guys back. But I'm feeling a bit dumb this morning. Still working on my first cup of coffee

How does a negative sequence alternator stator current put extra heat in to the rotor? The alternator rotor is strictly DC. What circulating currents? This isn't an induction motor rotor cage. Color me confused. :dunce:

ice

#### Sahib

##### Senior Member
The 1.732 phase-to-line relationship only occurs under a balanced load condition. Any unequal magnitude or power factor of phase currents and the 1.732 factor no longer applies.
No. The delta connected voltage source has reaonably matched individual phases and so the 1.732 phase-to-line relationship holds to a high degree of accuracy. Otherwise, the delta connected generator would be damaged by circulating current in its windings, when supplying only one single phase load!

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#### Sahib

##### Senior Member
Good morning ice,
I want to refer you to the web link in post#10 to refresh your memory.

#### iceworm

##### Curmudgeon still using printed IEEE Color Books
Good morning ice,
I want to refer you to the web link in post#10 to refresh your memory.
I had already looked at that. Nothing new there, I am familiar with symetrical components, Stevenson and Grainger, Evans and Wagner, - I've even read a few of Fortescue's papers.

I don't see the connection with negative sequence stator currents inducing circulating currents in an alternator DC rotor.

Do you have a model? If so I'm interested. If not, I can stop wasteing bandwidth

ice

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#### Smart \$

##### Esteemed Member
No. The delta connected voltage source has reaonably matched individual phases and so the 1.732 phase-to-line relationship holds to a high degree of accuracy. Otherwise, the delta connected generator would be damaged by circulating current in its windings, when supplying only one single phase load!
I guess I'll have to put this in steps...

1) In the following depiction of an open delta power source, what is the magnitude and phase angle of the current on each winding?

#### Smart \$

##### Esteemed Member
So far, every reference that I have found from generator manufacturers states that for pure single phase loads, you need to derate by 1/3 (i.e multiply rated power by .67). But the only thing close to a justification for that is the assertion that "all of the power for a single phase load is coming from only two of the windings."
That is so blatantly lame that I discount it completely.
Was that statement regarding delta or wye configured windings. If wye, I think it would be fairly obvious... a single phase line-to-line load (say connected A-B) is handled by two windings (a-n & b-n... c-n is not in the circuit—KCL)
I should note an issue here requiring distinction for a wye configuration and line-to-line connected single phase loads. The max loading reduced by 1/3 is from the perspective of winding kVA... not load kVA. For example, take a 208/120V wye output with rating of 300kVA. Each winding would be 100kVA... at 120V, or 833.3A, which at 208V is 173.2kVA. 173.2kVA compared to 300kVA is 57.8%

#### iceworm

##### Curmudgeon still using printed IEEE Color Books
So far, every reference that I have found from generator manufacturers states that for pure single phase loads, you need to derate by 1/3 (i.e multiply rated power by .67). But the only thing close to a justification for that is the assertion that "all of the power for a single phase load is coming from only two of the windings."
That is so blatantly lame that I discount it completely. ...
GD -
Could be when the generator mfg is saying "pure single phase loads", they are discussing a 12 lead generator wired DD. Those are generally rated at 67% nameplate.

And, I'm thinking you already knew this.

ice

#### Phil Corso

##### Senior Member
Iceworm... Reur post #54:

If you have Stevenson's "Elements of Power Systm Analysis", 2nd edition, the negative-sequence current generates flux that sweeps over the entire rotor, even though the rotor is supplied with DC, at twice line-frequency!

A simlar explanation is given in Wagner & Evans, "Symmetrical Components" 1st edition, in the section titled "Rotating Machines!"

If neither text you possess contain such information let me know!

Regards, Phil Corso

#### Phil Corso

##### Senior Member
Smart \$... Reur post #53:

Referring to your post # 26, the winding which has the Resistor across it is supplying 2/3 or 16A, and the other are each supplying 8A, presumably at +,- 120 degrees. How have you reconciled the angles?

Phil

#### Smart \$

##### Esteemed Member
Smart \$... Reur post #53:

Referring to your post # 26, the winding which has the Resistor across it is supplying 2/3 or 16A, and the other are each supplying 8A, presumably at +,- 120 degrees. How have you reconciled the angles?

Phil
2/3 of 30A is 16A?

...or are you substituting the 24A from post #53?

If the latter, yes 16A is 2/3 of 24A. So 16A @ 0?.

... and 8A @ 0? through the two series-connected windings (+/? 120? relative to each winding's voltage angle).

As to post #53 alone, the answer is 24A @ 0? through both windings.

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#### iceworm

##### Curmudgeon still using printed IEEE Color Books
Iceworm... Reur post #54:

If you have Stevenson's "Elements of Power Systm Analysis", 2nd edition, the negative-sequence current generates flux that sweeps over the entire rotor, even though the rotor is supplied with DC, at twice line-frequency!

A simlar explanation is given in Wagner & Evans, "Symmetrical Components" 1st edition, in the section titled "Rotating Machines!"

If neither text you possess contain such information let me know!

Regards, Phil Corso
Grainger and Stevenson jr, 1994

I'll look at it. but not today. This place is addictive. But I've got to go to work. There are a whole bunch of people that think they should be getting something fortheir money

ice

#### Phil Corso

##### Senior Member
Smart \$...

I strongly contend your assertion that all three windings of the delta-connected generator contribute to the load current is invalid. My simple proof... convert the delta-connected generator into a wye-connected one.

Now if you truly understand Electrical Theory, you must be aware of a very basic tenet, i.e., it is possible to substitute a wye-arrangement for a delta-one, and vice-versa!

Thus, if you substitute a wye-generator for the delta-one, and connect the load to say terminals A and B, terminal C has no connection to the load!

Phil