TWO PM ALTERNATORS IN PARALLEL QUERY

b.shahvir · Jan 11, 2009

Hi Guys,

My query is a bit abstract in nature! But i will be very grateful if someone can provide me with the solution to my query. Here goes;

Consider two Permanent Magnet (PM) Alternators Alt 'A' & Alt 'B' connected in parallel, supplying equal power to a purely 'Resistive' load (unity p.f.). Both the Alternators have equal stator synchronous reactances (stator resistances can be neglected). Please note, they are not connected to the local power grid (infinite bus) i.e. they are connected to a Finite Bus. Now, if i increase the driving torque of say, Alt 'A', then what changes will occur with respect to the following electrical parameters:-

1) Will magnitude of induced emf 'Ea' of Alt 'A' increase/decrease ? Please explain.

2) Will magnitude of induced emf 'Eb' of Alt 'B' increase/decrease ? Please explain

3) Will magnitude of terminal voltage 'Vt' increase/decrease ? If the magnitude of 'Vt' remains constant or decreases (due to armature reaction), then please explain.

4) Can someone please provide me with a practical phasor diagram for the above query. I am asking for one, since the phasor diagrams in textbooks have lot of assumed conditions & hence do not relate to practical conditions!
Any kind of help will be highly appreciated.

Thanks & Regards,
Shahvir

Skeebopstop · Jan 14, 2009

I guess my first question is, how do you increase the torque on one but not the other if they drive the same load?

The output frequency of their generated voltage will be via induced e.m.f and is thus dependant on the speed. Are they driven at the same speed or different speeds? If different speeds you will have them "fighting", as one generated voltage would be out of phase with the other and that would potentially fight and/or add to the torque on the other motor and vice versa.

So the only way I can see it, is if they are driven at the same speed, and therefore the question becomes, how do you increase the torque of a generator without changing the resistive load.

It would be an interesting experiment to perform with the motors connected at slightly different speeds. I envision them both ending up going mental.

Let me know what you think.

Skeebopstop · Jan 14, 2009

"So the only way I can see it, is if they are driven at the same speed, and therefore the question becomes, how do you increase the torque of a generator without changing the resistive load."

What I more meant here, is that if you try to add more torque at the same load, it will initially increase the speed and thus the output voltage. For that torque to be "sustained" at the same speed, the resistive load would have to be decreased to help burn that additionally generated energy to fight the additional torque to keep the speed at a constant.

b.shahvir · Jan 15, 2009

Thanks for your reply Skeebopstop.
If the the alternators go mental due to 'synchronous bond' between the 2 alternators, then how does loading of the 2 PM alternators happen under the conditions; Alt 'A' at 75% loading & Alt 'B' at 25% loading. To increase loading of Alt 'A' to 75%, input torque of Alt 'A' would have to be increased! albiet with a rise in bus frequency.

I basically want to understand the internal happenings in the 2 alternators with respect to the induced EMFs 'Ea', 'Eb' and terminal voltage 'Vt' for the Alt 'A' (75%) - Alt 'B' (25%) loading conditions under steady state conditions.
My query is for academic interest & does not reflect practical requirements.

Thanks & Regards,
Shahvir

KL7AJ · Jan 15, 2009

b.shahvir said:
Hi Guys,

My query is a bit abstract in nature! But i will be very grateful if someone can provide me with the solution to my query. Here goes;

Consider two Permanent Magnet (PM) Alternators Alt 'A' & Alt 'B' connected in parallel, supplying equal power to a purely 'Resistive' load (unity p.f.). Both the Alternators have equal stator synchronous reactances (stator resistances can be neglected). Please note, they are not connected to the local power grid (infinite bus). Now, if i increase the driving torque of say, Alt 'A', then what changes will occur with respect to the following electrial parameters:-

1) Will magnitude of induced emf 'Ea' of Alt 'A' increase/decrease ? Please explain.

2) Will magnitude of induced emf 'Eb' of Alt 'B' increase/decrease ? Please explain

3) Will magnitude of terminal voltage 'Vt' increase/decrease ? If the magnitude of 'Vt' remains constant or decreases (due to armature reaction), then please explain.

4) Can someone please provide me with a practical phasor diagram for the above query. I am asking for one, since the phasor diagrams in textbooks have lot of assumed conditions & hence do not relate to practical conditions!
Any kind of help will be highly appreciated.

For additional information/discussions please email me at b.shahvir@gmail.com

Thanks & Regards,
Shahvir

Hi Shahvir:

This is not an abstract problem at all...it has great practical importance in the real world.

Without even going into the phasor diagrams at all, or without rigorous proof, you can still show some things that will happen.

The two generators will tend to "lock step" with each other....with or without the grid! This is a major factor when connecting two alternators together, whether they're PM machines or not. Whether they will lock or not is not negotiable....they WILL lock. The real issue is the stresses involved when they do so, you can tear generators apart by connecting them if they aren't synchronous beforehand!

Every generator is a motor, and every motor is a generator. When the generators are synchronous, there is the LEAST amount of power transferred between the two devices....whichever is spinning faster will deliver power to the slower device.

So, that's the physics of the system....the math is even more fun!

Hope this helps some,

eric

davebee · Jan 15, 2009

This problem brings a mental picture to my mind - does this make sense?

Imagine two people riding a bicycle built for two. Their pedals are linked together, so they are forced to spin in phase, but at any given time, they will not be pushing with the same force. One could even coast and allow his feet to be pushed by the pedals, but his feet would still spin in phase with his partner.

Now imagine that each pedal has a springy shock absorber between the pedal and the chain ring. Then as one person pedaled harder, his pedals would actually advance very slightly in phase as he pushed harder against the load. So when he made his initial push, his pedals would momentarily increase in speed, but would return to the same speed but slightly advanced in phase as long he continued to push with the additional force.

Does that analogy match the case of two alternators, both pushing against a load, but one pushing harder than another?

Let the speed of the bicycle chain correspond to voltage (or EMF). The speed of the chain at both pedals and the load will be the same, just as for a parallel circuit, all voltages will be the same.

If one guy pushes harder then the overall result will be more speed overall, so analagously, if alternator A pushes harder then all voltages will increase.

I don't know much about phasor diagrams but I'm guessing that the harder working alternator will be more resistive in order to be able to apply greater power under these circumstances, and the slight phase shifting of the spring-mounted pedals would correspond to a shift in phase of the harder-working alternator.

KL7AJ · Jan 15, 2009

davebee said:
This problem brings a mental picture to my mind - does this make sense?

Imagine two people riding a bicycle built for two. Their pedals are linked together, so they are forced to spin in phase, but at any given time, they will not be pushing with the same force. One could even coast and allow his feet to be pushed by the pedals, but his feet would still spin in phase with his partner.

Now imagine that each pedal has a springy shock absorber between the pedal and the chain ring. Then as one person pedaled harder, his pedals would actually advance very slightly in phase as he pushed harder against the load. So when he made his initial push, his pedals would momentarily increase in speed, but would return to the same speed but slightly advanced in phase as long he continued to push with the additional force.

Does that analogy match the case of two alternators, both pushing against a load, but one pushing harder than another?

Let the speed of the bicycle chain correspond to voltage (or EMF). The speed of the chain at both pedals and the load will be the same, just as for a parallel circuit, all voltages will be the same.

If one guy pushes harder then the overall result will be more speed overall, so analagously, if alternator A pushes harder then all voltages will increase.

I don't know much about phasor diagrams but I'm guessing that the harder working alternator will be more resistive in order to be able to apply greater power under these circumstances, and the slight phase shifting of the spring-mounted pedals would correspond to a shift in phase of the harder-working alternator.

Actially, this is a very good analogy.

b.shahvir · Jan 16, 2009

Dear All,

Thanks very much, great help. But i want to understand the steady state conditions during unequal loading e.g. (Alt 'A' 75% - Alt 'B' 25%) between the two alternators and its effect on 'Ea', 'Eb' and 'Vt'.

Also, will both the alternators settle at new values of voltages (Ea, Eb & Vt) and speed (frequency) during post-disturbance conditions or will retain its original values as was during pre-disturbance conditions ?

Kind Regards,
Shahvir

Skeebopstop · Jan 16, 2009

Hey Shahvir,

I don't think you can separate this one from the practical world. In reality this would be something easiest to describe via simulations, but if you wish to simplify into a theoretical realm I would apply the following:

1. Fix the frequencies of each and ignore torque. Just assume that if Alt 'A' has 75% of the overall applied system torque that it operates at 1.5x the frequency of Alt 'B' and then remove torque from the equation. The torque really only becomes applicable if you try to attach this whole system to a control system.

2. The motor would have some given output voltage due to induced e.m.f at some given speed. This you would normally pull out of the characteristic curves. For simplification lets just say it will be 1.5x the voltage of Alt 'B' at 1.5x the frequency of Alt 'B'.

3. So now lets say Alt 'B' has VAC 50V at 50Hz and Alt 'A' VAC 75V at 75Hz, and these conditions are now somehow held stable through some ridiculously complex control system that we will completely ignore.

So now, just plot out the waveforms and look what the load sees. I don't generally work much with phasors but just drawing it out would be easy enough in excel and have a final column with Va - Vb = Vload.

Hope that helps matey,

James

b.shahvir · Jan 17, 2009

Dear James,

Thanks very much for your reply. Theoretical explanation being understood & accepted, the reason for my query are the phasor diagrams. The problem is, if one refers the phasor diagrams pertaining to this particular phenomenon (in textbooks or tech. literatures), one finds that these diagrams do not relate/match with its associated theory.

For e.g., the explanation by Davebee suggests an increase in magnitudes of induced EMFs Ea, Eb and Terminal (Busbar) Voltage Vt at post-disturbance conditions. However, the associated phasor diagrams for this depict magnitudes of Ea, Eb and Vt to be constant even at post-disturbance conditions, with changes in load angle only. Hence, i had requested for practical phasor diagrams which relates with the theoretical explanation it is associated with!

Kind Regards,
Shahvir

b.shahvir · Jan 17, 2009

davebee said:
This problem brings a mental picture to my mind - does this make sense?

Imagine two people riding a bicycle built for two. Their pedals are linked together, so they are forced to spin in phase, but at any given time, they will not be pushing with the same force. One could even coast and allow his feet to be pushed by the pedals, but his feet would still spin in phase with his partner.

Now imagine that each pedal has a springy shock absorber between the pedal and the chain ring. Then as one person pedaled harder, his pedals would actually advance very slightly in phase as he pushed harder against the load. So when he made his initial push, his pedals would momentarily increase in speed, but would return to the same speed but slightly advanced in phase as long he continued to push with the additional force.

Does that analogy match the case of two alternators, both pushing against a load, but one pushing harder than another?

Let the speed of the bicycle chain correspond to voltage (or EMF). The speed of the chain at both pedals and the load will be the same, just as for a parallel circuit, all voltages will be the same.

If one guy pushes harder then the overall result will be more speed overall, so analagously, if alternator A pushes harder then all voltages will increase.

I don't know much about phasor diagrams but I'm guessing that the harder working alternator will be more resistive in order to be able to apply greater power under these circumstances, and the slight phase shifting of the spring-mounted pedals would correspond to a shift in phase of the harder-working alternator.

Thanks Davebee,

I wish you could help me with the phasor diagrams for this particular query.

Kind Regards,
Shahvir

davebee · Jan 19, 2009

Sorry, I can't help with phasors; I've never learned phasor diagrams. But it's an interesting problem to try to understand; hopefully someone else can help.

b.shahvir · Jan 19, 2009

Dear Davebee,

I just want to know whether induced EMFs Ea, Eb and Terminal voltage Vt increases after input torque to Alt 'A' is increased. If there's anyone out there to help me with phasor diagrams, please help!

Thanks & Regards,
Shahvir

b.shahvir · Jan 20, 2009

Skeebopstop said:
Hey Shahvir,

I don't think you can separate this one from the practical world. In reality this would be something easiest to describe via simulations, but if you wish to simplify into a theoretical realm I would apply the following:

1. Fix the frequencies of each and ignore torque. Just assume that if Alt 'A' has 75% of the overall applied system torque that it operates at 1.5x the frequency of Alt 'B' and then remove torque from the equation. The torque really only becomes applicable if you try to attach this whole system to a control system.

2. The motor would have some given output voltage due to induced e.m.f at some given speed. This you would normally pull out of the characteristic curves. For simplification lets just say it will be 1.5x the voltage of Alt 'B' at 1.5x the frequency of Alt 'B'.

3. So now lets say Alt 'B' has VAC 50V at 50Hz and Alt 'A' VAC 75V at 75Hz, and these conditions are now somehow held stable through some ridiculously complex control system that we will completely ignore.

So now, just plot out the waveforms and look what the load sees. I don't generally work much with phasors but just drawing it out would be easy enough in excel and have a final column with Va - Vb = Vload.

Hope that helps matey,

James

Dear James,

How did you arrive at the expression Va - Vb = Vload ? Please elaborate.

Thanks & Regards,
Shahvir

b.shahvir · Jan 23, 2009

davebee said:
This problem brings a mental picture to my mind - does this make sense?

Imagine two people riding a bicycle built for two. Their pedals are linked together, so they are forced to spin in phase, but at any given time, they will not be pushing with the same force. One could even coast and allow his feet to be pushed by the pedals, but his feet would still spin in phase with his partner.

Now imagine that each pedal has a springy shock absorber between the pedal and the chain ring. Then as one person pedaled harder, his pedals would actually advance very slightly in phase as he pushed harder against the load. So when he made his initial push, his pedals would momentarily increase in speed, but would return to the same speed but slightly advanced in phase as long he continued to push with the additional force.

Does that analogy match the case of two alternators, both pushing against a load, but one pushing harder than another?

Let the speed of the bicycle chain correspond to voltage (or EMF). The speed of the chain at both pedals and the load will be the same, just as for a parallel circuit, all voltages will be the same.

If one guy pushes harder then the overall result will be more speed overall, so analagously, if alternator A pushes harder then all voltages will increase.

I don't know much about phasor diagrams but I'm guessing that the harder working alternator will be more resistive in order to be able to apply greater power under these circumstances, and the slight phase shifting of the spring-mounted pedals would correspond to a shift in phase of the harder-working alternator.

Dear Davebee,

Excellent analogy with a 2 pedal bicycle! Thanks.
According to your explanation (analogy), the magnitudes of induced EMFs 'Ea', 'Eb' and terminal voltage 'Vt' would increase. However, according to the E.E. textbooks, they represent the theory for the above case with the magnitudes of 'Ea, 'Eb' and 'Vt' remaining constant (with variation in load angle only). Hence, i request you to elaborate/comment on the same.

Kind Regards,
Shahvir

Skeebopstop · Jan 23, 2009

Would E.E. textbooks referring to load angle and subsequently the phase of your desired phasors, simply be related to frequency and as such fit quite well into the analogies we have placed. So not only does the magnitude change but the load angle, and if load angle is a phasor this is just the frequency.

davebee · Jan 23, 2009

Here's a paper that gives a basic introduction to alternators and phasors in systems connected to a large power grid. It tells about synchronizing, and pole slipping when two alternators get out of phase.

http://canteach.candu.org/library/20030801.pdf

This paper make the point that for alternators connected to a large grid, as defined as the power contribution by individual alternators is less than some small percentage of the overall connected generating power, then each alternator can be considered to not alter either the frequency or the voltage of the grid. Increasing power to one alternator just changes the phase angle between the voltage and current within just that one alternator. That sounds like the result that you're looking at - claiming that a torque increase would not affect the voltage.

But for an isolated system like you first presented, if nothing is changed except that torque is increased to one alternator, I can't see how the voltage would not increase.

I don't know how to prove it, though.

b.shahvir · Jan 24, 2009

Thanks guys, very much grateful.

Let me clarify;
The E.E. textbooks i am referring to depict constancy in the magnitudes of induced EMFs 'Ea', 'Eb' and terminal voltage 'Vt' even in the case of an isolated system (alternators not connected to grid) as i had mentioned earlier. This is moreso prevalent in the presentation of phasor diagrams by these textbooks associated with the said theory.

Hence, this resulted in contradiction with the explanation and the reason for me putting forth this query in the first place, as even i had got confused, since the presented phasor diagrams do not relate to its associated theory (of an isolated system) as is the case.

Also, some experts/textbooks mention that the terminal voltage 'Vt' gets decreased if input torque to any one alternator is increased. This phenomenon is due to 'Armature Reaction'. I request you guys to clarify/comment in this regard.
Sorry for trouble!

Kind Regards,
Shahvir

davebee · Jan 26, 2009

Most references I've found define armature reaction for the specific case of DC generators that have brushes and a commutator. Ideally, as the rotor turns, the brushes change coils at a rotor angle where there is low brush current, but heavy field currents change the magnetic field orientation so cause the brush position to be less than optimal.

Wouldn't this problem not exist for permanant magnet alternators?

I did find one reference that used a different meaning for the term Armature Reaction, so maybe it's a generic term with several meanings.

http://www.seas.gwu.edu/~ecelabs/appnotes/PDF/experiments/power/experiment5.pdf

If nothing else changes, increasing torque to an alternator should result in greater power generated, meaning a higher voltage across a resistive load. If increasing torque results in lower voltage then it seems like something else must change - maybe the alternator speed drops, maybe the other alternator changes its speed. Do your books give any more detail of this case where the voltage either stays the same or drops? What else changes if you increase torque to one alternator?

b.shahvir · Jan 27, 2009

Dear Davebee,

Firstly, let me thank you for your help and all the other people involved in these discussions to solve my doubts.

I have referred several E.E. textbooks, as well as have held discussions on this topic with E.E. experts on other forums. The problem with E.E. textbooks is that they assume several parameters for clarity of explanation. Also, the phasor diagrams presented in these texts mostly consider 'Ea', 'Eb' and 'Vt' to have constant magnitude, the only variable being 'load angle' (σ) which represents variation in phase or loading. This might be to make the explanation simple.

Also, while explaining the concept of 'Armature Reaction' by these texts, the factors responsible for it is shown to be variations in the connected load. The effect of changes in input torque to any one alternator is mostly not considered (the same concept is reflected in the reference link suggested by you). Hence, the doubts.

Coming to forum discussions; several E.E. experts involved in the discussions on this topic explained that increasing the input torque of any one alternator would, in effect, increase the loading on that alternator and hence due to 'Armature Reaction', the terminal voltage tends to decrease (it might be due to inductive loading, but again increase in input torque concept was not considered). Hence, i was unable to grasp this concept and hence it resulted in more confusions! I request you to throw some light on this concept. Also, please comment on whether magnitude of 'Ea' and 'Eb' increases or not, alongwith 'Vt' (in case of isolated system only, as mentioned earlier).
Thanks once again.

Kind Regards,
Shahvir

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TWO PM ALTERNATORS IN PARALLEL QUERY

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