Hi guys,

Suppose I were to increase field excitation (keeping input torque constant) of an isolated synchronous generator feeding a purely resistive load (unity pf). As per alternator theory, increasing excitation will increase terminal voltage of alternator, but the load current will remain constant since input torque is held constant (no VAR output as load is resistive). But how is this possible? Increase in terminal voltage should also cause the load current to increase resulting in increased power output, but the working principle indicates otherwise.

Please guide.

 

With an isolated generator, the terminal conditions are governed by the load. If you increase the terminal voltage with a resistive load, the load current will increase so the load power will increase. The only other variable available is the speed; if the load power increases while the input power remains constant, the speed will fall. Since speed x torque = mechanical power, if the torque is held constant the speed will fall in proportion to the increase in voltage.

 

Thanks for reply

So in case of isolated generator, if terminal voltage 'Vt' increases, the load current increases. This in turn would increase the load angle (delta) between generated EMF 'Eg' and terminal voltage 'Vt'. I hope my understanding of the concept is correct. Is it possible for you to provide a phasor diagram for this phenomenon? I am unable to find one for isolated generator when excitation is increased.

Also, assuming a permanent magnet rotor generator in above case, increasing input torque will increase load angle (delta) resulting in decrease of terminal voltage 'Vt' and increase of load current. But will generated EMF 'Eg' also increase due to increased speed? (since input torque is now increased by admitting more steam, etc.) Kindly clarify.

 

<b>Case 1 - Islanded Synchronous machine</b>

Generally, since the impedance (load and generator synchronous reactance) doesn't change, by increasing the field excitation (and therefore terminal voltage) of the generator, you are proportionally increasing the strength of the emf (E).<pre>
IaXs IaXs
------- ----
E-\ |-Vt E-\ |-Vt
\ | \ |-Ia
\ |-Ia \|
\ |
\ |
\|</pre>
Sorry about the bad phasor diagrams above, however I have tried to illustrate that an increase of Ia by increasing the field excitation will proportionally increase the emf (E). Here you can see that the load angle remains the same.

The only time the load angle will change is if:

- the actual load connected to the generator changes if the generator is the sole source of supply, or

- the excitation changes when the generator is synchronised and connected to a rigid supply network

<b>Case 2 - PMG</b>

I have little experience with PMG machines (other than using them for supplying power for an AVR), however thinking out loud, if you increase the speed (f) by adding more torque to the PMG, then by definition, the emf (E) should also proportionally increase (E = 4.44Nᶲf).

Now, as E increases due to speed, if the load connected to the PMG is resistive, then it would not change. However, since there is inductive reactance in the PMG stator, then that reactance (X = jwL) will change with speed. Therefore, I believe that the load angle should change somewhat. Not sure if I am on the right path here, anyone else?

 

Thanks very much for reply, greatly appreciate your effort with the phasors Actually, I have been dabbling with these phasors for some time now, but the closest I came to was phasors depicting functioning of isolated genset was two gensets connected in parallel to finite busbars. With increase in excitation, Eg increases, Vt increases, but load angle (delta) decreases as magnetic field flux gets strengthened, however active component of current still remains constant, generator now supplies reactive power to the busbars at poor power factor (circulating current).

In 2nd case of isolated PMG, again the closest I came to was phasors depicting two alternators in parallel on finite busbars. Increasing input torque of Gen-1 increases load angle (delta), Eg & Vt remains constant (as field excitation is assumed to be held constant), stator current of Gen-1 increases, power factor changes. Even in this case, I am yet to find a phasor diagram for isolated genset when input torque is increased.

 

There have been plenty of pretty good books and papers showing vector diagrams of synchronous machines, "Performance and design of alternating current machines" by MG Say is one I use as reference.

A few papers on the interweb also go into the detail on generator operation somewhat are:

https://canteach.candu.org/Content Library/20050814.pdf
https://canteach.candu.org/Content Library/20050815.pdf
https://canteach.candu.org/Content Library/20050816.pdf
https://canteach.candu.org/Content Library/20050817.pdf
https://canteach.candu.org/Content Library/20050818.pdf
https://canteach.candu.org/Content Library/20050819.pdf
https://canteach.candu.org/Content Library/20050820.pdf
https://canteach.candu.org/Content Library/20050821.pdf
https://canteach.candu.org/Content Library/20050822.pdf
https://canteach.candu.org/Content Library/20050823.pdf
https://canteach.candu.org/Content Library/20042908.pdf

That entire website has great material if you wish to spend the time to go through them.

 

Thanks very much for your time & effort for presenting these articles. Although I had earlier referred to all of these very resourceful articles, none of them depict the internal changes taking place in an isolated generator due to increase in excitation or load angle such as the one depicted by you in your earlier post.

 

Shahvirb...

does your last post mean that your original query has not been answered to your satisfaction?

Regards,
Phil Corso

 

I agree that they don't. however, if you consider the equivalent circuit these resources provide, then the vector diagrams could be constructed by changing any of the parameters you wish. In this case, the emf and/or frequency.

 

Hi Sir,

Thanks for your kind concern . Although Peter has presented the phasor diagrams for isolated generator in earlier post, I am disappointed I did not find any reference material (on the net or otherwise) that has dealt with the conditions I mentioned w.r.t. isolated generators with unity p.f. load. as I believe the behavior of an isolated generator is different from when operating in parallel with other sync machines on finite/infinite busbars.

Best regards,
Shahvir

 

Dear Peter,

You are absolutely correct. But in case one wants to understand a particular concept accurately, one normally relies on textbooks for help. Unfortunately that is easier said then done. Almost all textbooks assume certain parameters to be constant, eg. terminal voltage, excitation, shaft speed, synchronous reactance, etc. in order to represent phasor diagrams.... but in the real world this is not so.

Although induced emf Eg is a function of rotor speed, terminal voltage Vt decreases with increase in rotor speed due to drop across so called synchronous reactance Xs. But while explaining this concept, the textbooks assume Vt and excitation to be constant. In case one is trying to understand the internal happenings of a permanent magnet (PM) generator, the thought process is defeated due to these theoretical assumptions.

Although earlier I had constructed my own phasor diagrams for 2 PM alternators in parallel on finite busbars, I had no reference material to verify them with.

 

In case of 2 loaded alternators in parallel, what will be the effect of increasing field excitation of Alt-1 if only stator winding resistance is considered neglecting all kinds of winding reactances? Will the system operate stably or become unstable resulting in pole slipping, etc.?

 

Shahvirb...

I suggest you specifically investigate how synchronizing-power, synchronous-reactance, and armature-resistance, all affect performance of paralleled alternators.

Regards,
Phil Corso

 

Shahvirb,

you may be aware that some posters to this forum get upset when formulae are used.

If not, would you mind if I started with a typical generator, i.e., stator, rotor, exciter?

Rehards,
Phil

 

I do not know how & where to investigate them with to my satisfaction.

> I suggest you specifically investigate how synchronizing-power, synchronous-reactance, and
> armature-resistance, all affect performance of paralleled alternators.

 

> If not, would you mind if I started with a typical generator, i.e., stator, rotor, exciter?

OK, will give it a try or maybe offline.

 

I agree that there is not much material out there for PM machines, while what I have read also doesn't show phasor diagrams, they do state that they are very similar to synchronous machines with constant excitation. Based on this, if literature can be found exploring the relationship between speed and terminal voltage of a synchronous machine (either motoring or generating) showing the effect of different speeds on a circuit with phasor diagrams, that should provide some insight. I have not yet found anything showing this in my references, however you could possibly have a chat with some PM machine manufacturing companies. They might be able to help with some explanations. Let me know how you go as I am interested in how they explain this.

 

So if you disregard the inductance of the machine, you can this will be similar as a battery circuit. If emf from one machine (battery 1 voltage) is slightly higher than the emf of the other machine (battery 2 voltage) then machine 1 will supply current to both the load and machine 2.

Note that this is all theoretical, as there is always reactance that needs considering due to the magnetic coupling between the rotor and the stator. Any change in emf will be balanced out between the machines with vars circulating between them.

You are also correct that there are limits to how much the excitation can be changed on a synchronous machine. Each synchronous machine will have a capability diagram which shows how much lagging and leading it can operate.

If it goes too much leading, then the magnetic coupling gets too weak and will "break", this will cause pole slipping in the machine which is extremely damaging.

If it goes too much lagging, then the excitation circuit will overheat and damage will happen to the insulation.

 

> So if you disregard the inductance of the machine, you can
> this will be similar as a battery circuit. If emf from one
> machine (battery 1 voltage) is slightly higher than the emf
> of the other machine (battery 2 voltage) then machine 1 will
> supply current to both the load and machine 2.

This occurs in the final stage of voltage modulation. My topic of interest is limited to the intermediate stage of load sharing. Gradual increase in Vt will result in transfer of load from one machine to another....the 2nd machine being run as a motor in the extreme stage. Actually, seamless load sharing is possible only due to the presence of internal resistances (impedances) of the respective m/cs operating in parallel, in absence of which the operation will be akin to load sharing in isochronous mode.

 

Maybe I misunderstood your question, please correct me if I am wrong, but I thought you were asking about what the behaviour would be if there was theoretically no inductance (j.ohms) whatsoever in the machine windings, i.e. only resistance (ohms)?

If yes, then using ohms law, it is deduced that the current would flow from the highest to the lowest potential. When two of these theoretical generators with no inductance are load sharing (both have a voltage of exactly 240V l-n), the current supplied would be equal between each machine. If one generator voltage was increase to 245V, then this machine would supply current to both the load and the other generator due to the 5V difference between both generators.

If I did misunderstand what you were asking, sorry about that. When considering the machine inductance (and therefore magnetic coupling), if both machines are equally sharing the load, then when you increase the emf on one, what will happen is:

- The magnetic coupling strength for the machine with the higher emf increases, therefore the load angle decreases and as a result the machine increases the power factor towards "lagging"

- The magnetic coupling strength for the machine with the lower emf stays the same as previous, therefore the load angle increases and as a result the machine increases the power factor towards "leading"

- The supply voltage on the common bus would slightly increase

As you can see, the above scenarios, the var load will shift from one machine to the other as the excitation changes on one machine.

None of this considers Hz vs kW relationship which is somewhat independent to Volts vs kvar relationship.