I am working in a power plant as a fresher. I came to know that if steam flow is increased generation output also increases as there is more torque produced. so my question is how does torque effect the load angle???

What is a load angle???

What is grid frequency and how it is calculated???

 

The rotor of the turbine and generator is a device that stores kinetic energy. It is in balance between the power applied from the turbine and the power delivered to the alternator stator.

Power transferred from the rotor to the stator through the magnetic field depends on the sine of the angle between the rotor magnetic field and that developed in the stator. When the two are in alignment, no power is transferred, and when the angle is 90 degrees with the rotor leading, the power transfer is a maximum. When synchronised to an external grid, the stator field is related to the terminal voltage and rotates at a speed set by the entire electrical system.

At any load between the two, the angle will remain constant as long as the power drawn from the alternator matches the power supplied by the turbine. If the turbine power increases slightly, the imbalance increases the energy in the rotor, and this causes it to speed up very slightly. As a result, the rotor moves a little ahead of the stator field, and the angle between the two fields increases. In turn, the electrical power delivered to the alternator increases and the balance is restored. In the new balance condition, the rotor goes back to synchronous speed but at an increased angle. If electrical load increases slightly, the extra power is drawn in the first instance from the rotor which slows it down, decreasing the load angle and restoring the balance.

The change is a dynamic process, and if either the mechanical load increases by a relatively large amount or (more commonly) the electrical load should fall suddenly, the rotor angle will oscillate before stabilizing. Under these conditions it is possible for the rotor angle to exceed 90 degrees, and the electrical power out will then start to fall. The result will be noisy and possibly quite violent as the alternator goes into pole-slipping. On this topic, I recall seeing many years ago a diagram of a mechanical analogue made up of a driven rotor and another rotating part connected to it representing the stator field, with springs connecting the two. Does anyone have more info? This would make a good gadget to build up and get a video of, as this topic is one that causes a LOT of grief.

Cheers,
Bruce.

 

Mohan... in general there are several definitions of "load-angle" in use. The three typically used in Electrical Power Sytem vernacular are:

Load-angle (1): The angle whose cosine is power-factor. Or, the arctan of the X to R ratio of a specific external impedance connected to an AC source of power.

Load-angle (2) per IEEE definition: "The angular displacement, at any specified load (real-power), of the the center line of a field-pole relative to the axis of the armature's magnetomotive force (mmf) wave pattern."

Load-angle (3): The angular displacement between the internally generated voltage, Egp, and the generator's terminal phase-voltage, Vp. If you are interested in vector relationships, let me know!

Regarding your steam flow question resulting in an increase in in the gen's input torque... I suggest you search the Control List Archives! Or, alternately, specify specific operating conditions, e.g., a) isolated gen and load; b) two gen's in parallel supplying a common load; or c) gen connected to an infinite grid!

Regards, Phil Corso (cepsicon [at] aol [dot] com)

 

BRUCE!!!!

the reply posted by you regarding "effect of torque on load angle" is clear. But as a mechanical eng, it was bit difficult for me to understand. so can you explain in brief!!!!!

 

Hi Mohan,

Since you are a mechanical engineer, I will try to explain using a mechanical analogue. (As I said in my previous post, I have seen a photo of something similar to this, used for just this purpose).

Imagine a mechanical coupling between two shafts made by connecting two flanges but with stiff springs replacing the bolts. With no load applied, the alignment of the two parts of the coupling is marked with a reference. Now drive one shaft at a fixed speed and apply a load to the other. To transfer power through the coupling, there must be a torque exerted by the load flange on the drive flange, and to get this torque through the springs, they must deflect. The load flange will take up a position slightly behind the drive flange. We can describe this difference in terms of the angle between radius lines from the centre of rotation to the reference alignment mark on both flanges.

The power transferred between the shafts is proportional to the product of speed and torque. The torque depends on the tangential force produced by the coupling springs, which depends in turn on the tangential displacement of the two reference points. The displacement is approximately proportional to the sine of the angle. The angular displacement can therefore be referred to as the load angle.

In an electrical machine (alternator or motor) the coupling between the mechanical power applied to the rotor and the electrical power in the electrical supply connections is not through springs, but through a magnetic field. The stator field is dependent on the applied voltage. If there is no field excitation and the stator is driven from an external source, a rotating magnetic field will be produced inside the stator. When a magnetic field is developed by the rotor, there is a force between the two magnetic fields that depends on the difference in relative angular positions - if the two fields are aligned, the torque is zero, and as the torque increases the difference in position of the two rotating fields also increases. The tangential component of the torque again depends on the sine of the angular difference.

In a very large electrical system, there is a lot of kinetic energy in all the rotating parts (rotating loads such as induction motors as well as generators). This can be expressed as an "inertia constant" which is the total KE divided by the power. For a hydro turbine, this is typically about 4 seconds while for a steam turbine it may be up to 10 seconds. Because of the coupling effect described above, all the machines on an interconnected system rotate at the same speed (in electrical terms - in mechanical terms, the rotating speed depends on the no of pole pairs). On a continental scale, the total inertia is huge and under most circumstances any realistic change in load will have only a small effect on the total KE. The speed is therefore essentially constant, and is in fact maintained constant by the of selected generators. In a smaller system, where the largest generators or loads are more than 1 or 2 % of total, frequency transients are much more significant and can be observed quite often. But from an overall system point of view, there is a total energy balance between mechanical power in to all the generators and the electrical power out to all the loads (plus losses). Any increase in electrical load is met in the first instance from the rotating kinetic energy of the whole system, causing the speed to reduce slightly. Governors react to this by increasing power to turbines.

To make things a bit more complex, the power transferred between two points over a transmission line also depends on the sine of the phase angle difference in voltage. If too much power is transferred over a line segment, the ends may lose synchronism and in that case you get continental-scale blackouts.

Hope this helps,
Bruce.

 

Bruce,

You've used this description several times before, of a machine increasing speed when it's loaded while being operated in parallel with other machines on a grid. To me, at least, this is somewhat confusing. So, I would like to ask you if my understanding of your interpretation is correct.

Let's start from a zero output condition, where the alternator and it's prime mover are connected to a system with other alternators and their prime movers, but this particular alternator is not producing any excess torque over and above that required to make the alternator frequency (and rotor speed) equal to the grid frequency. In this condition, the relative angle between the magnetic fields of the alternator rotor and the alternator stator is roughly 0 degrees.

Now, let's say that a step change in the amount of energy being admitted to the prime mover is made. The immediate effect of this step change is to increase the speed of the prime mover, but it is mechanically coupled (in this example) to the alternator rotor. The magnetic forces at work in the alternator are trying to keep the rotor magnetic forces directly in line with stator magnetic forces, but the increase in torque actually does cause a "twist" which pulls the two magnetic fields of the alternator very slightly out of alignment with each other. The relationship between the magnetic fields of the rotor and the stator does not return to 0 degrees because the torque is remaining constant, but the actual speed of the alternator rotor (and of the prime mover) does not effectively change <b>except for that brief period of time when the torque was increased</b> and only for an instant because once the change in torque stops the acceleration also stops, though the velocity of the alternator rotor remains virtually constant.

As a result of the increase in torque the alternator output increases, the alternator being a device for converting torque into amps. We say the "load" of the alternator has increased.

You have said that any time the torque being produced by the prime mover driving a generator is increased that the speed of the machine is increasing, and therefore the frequency of the generator is increasing. I might agree with you if the torque increase was the result of a step change in torque, and I would argue that the "increase in speed" is really just a momentary (as in a very small fraction of a second) increase in the acceleration rate.

The acceleration rate would decrease back to, basically, zero when the effects of the magnetic forces in the alternator came to equilibrium. The net effect of the increase in torque would be to change, very slightly, the mechanical orientation of the alternator rotor with respect to the stator which is, effectively, the increase in the load angle. This is the result of the change in the "twist" applied to try to speed up the alternator rotor against the effects of the alternator stator magnetic fields.

I believe the increase in the energy flow-rate into most prime movers is a smooth "ramp" and therefore any change in acceleration rate is very small, though the increase in torque (which is the application of a force over a distance--a "twisting" of sorts) does result in a change in the angle between the magnetic forces of the alternator rotor and the alternator stator. Increasing the torque increases the angle, the "load angle", and decreasing the torque decreases the angle, the "load angle."

While there is likely a change in the acceleration rate for any increase or decrease in torque, be it from a controlled ramp or a step change, I believe the change in speed (rotational velocity; RPM) is so small and for such a short period of time that it is for all intents and purposes negligible. And, it's not the speed of the shaft that is changing, it's just the acceleration rate that's really changing.

The whole concept of a synchronous generator, or alternator, is that the speed of the rotor is fixed because of the magnetic forces in the machine. The frequency of the grid voltage which is flowing through the alternator stator windings is creating magnetic forces that are locking the magnetic forces of the alternator rotor into step (synchronism) and keeping the alternator rotor speed fixed.

An increase in torque from the prime mover tries to increase the speed (rotational velocity) of the alternator rotor, but it can't because of the interaction between the magnetic forces of the alternator rotor and stator. It does result in a "twisting" of the angle between the rotor magnetic forces and the stator magnetic forces, but it doesn't appreciably change the rotational velocity at all. There is a change in the acceleration rate <b>as torque is changing</b>, but the rotational velocity doesn't effectively change because of the magnetic forces at work in the alternator.

Now, that's what I think you're trying to say whey you're talking about a change in speed. I've never really monitored, with a highly accurate device and recorder, the speed of a prime mover or alternator rotor during loading or unloading. I can say, that on a stable grid the speed doesn't appreciably change from no load to full load or from full load to no load.

Now, the angle between the alternator rotor magnetic forces and the alternator stator magnetic fields <b>does</b> change with a change in the torque being produced by the prime mover. As the torque changes, the angle changes, this is the result of the "twisting" at work as the torque changes. And the change in torque is trying to change the speed (rotational velocity), but it effectively can't change the speed.

I hope I'm not splitting hairs here, but I've been trying to comprehend this "speed increase" thing for a long time now, and I've just never seen it. Admittedly, I've never had the instruments to measure and record the effects of changing torque, but in my experience I just don't see any appreciable change in alternator frequency or prime mover speed when changing load, on a stable grid).

I know for a constant load that if the torque of some other prime mover isn't reduced as the torque of some prime mover is increased that the frequency of the grid will increase by 0.000n%, but it is the job of grid regulators to monitor changes in load and generator to keep that frequency as close to nominal as possible by changing loads of other machines as required. But, again, on a large grid with a large load and many, many alternators and prime movers, we're not talking about large changes in speed, only 0.000n%!

So, if you're talking about some other change in speed, or if you would, please quantify the changes in speed (velocity) and with respect to time (acceleration) to clarify my understanding it would be most appreciated.

We all know there is some "springiness" in the relative position of two magnets, and that's effectively what we're talking about with the magnetic forces inside an alternator. A synchronous machine has its magnetic forces applied in such a way that the magnetic forces of the rotor remain "in step" (synchronism) with the magnetic forces of the stator, though they may not always be physically aligned in the same relationship.

 

Hi CSA,

### WARNING ### Mathematics Mode ON ######

The relationship between torque imbalance, speed, acceleration and rotor angle is give by a second-order differential equation.

Torque imbalance = moment of inertia * angular acceleration

Acceleration = rate of change of speed

Speed = rate of change of angle.

Electrical power out is proportional to sine of the relative angle between rotor field induced emf and applied stator voltage.

So we can transpose all that to get the "swing equation" :

Mech power in = MI * double RoC of angle - Damping * angular velocity + K * sin(angle difference)

If you can imagine somehow being able to sit on the rotor of a machine and observe the relative position with respect to the stator rotating field during power changes, you will definitely observe a "velocity" particularly if these are relatively large.

(/Mathematics)

Yes, the speed increase or decrease I am talking about is momentary on a sufficiently large time base. But the time scale is actually of the order of seconds - it is related to the inertia constant of the machine, which may be 1 second for a small GT to 8-10 seconds for a large steam turbine generator.

If you are in North America you have the disadvantage of having a very large grid to work with. In New Zealand we have a relatively small system with some comparatively large machines, and relatively long transmission lines. Dynamic stability of the system was of major concern about 30 years ago and I was involved in developing a simulation of the two systems (one in each island, with a DC link coupling them. Variations in frequency were relatively common (haven't checked recently) and in one generating station, in the far north of the country and connected to the rest of the grid through a 250 km or so long double-circuit 220 kV link, transient power output disturbances were very noticeable when the total system load was changing rapidly (as at around 7 am). I based the model on a total overall power balance accelerating or decelerating the total connected inertia of the system, then looked at the power exported from stations remote from the "centre of gravity" individually as they swung against the average. Results were in close agreement with actual observed system behaviour on a number of incidents.

I have also come across issues caused by insufficient synchronising power capability - in one case, the alternator had to be synchronised at 0 deg and almost dead synchronous speed as the supply system was sized for the very small export load rather than the short-term power flow needed to pull the rotor into synch.

I find the mental picture of a torque balance on the machine shaft, accelerating or decelerating it according to direction of any imbalance and then power angle increasing or decreasing as a result, very helpful. It also saves having to work around the issues of "synchronised" vs "isochronous" using two different approaches. In smaller systems, the infinite bus model may be adequate most of the time but the effect of small transient changes in speed/ angle during power upsets cannot be ignored. Your approach of looking at the relationship between torque and current is also quite useful but I feel is more of a steady-state picture.

Cheers,
Bruce.

 

Mohan... obviously it is harder to describe "load-angle" than it is to "observe" it. Following is a procedure that will produce the "load-angle. All one needs is a piece of chalk, and a stroboscope (even a fluorescent lamp will do.)

1) Use the chalk to mark a fixed-point on the generator where both the fixed-point and rotor are visible. Note, it can also be done at a coupling or other point along the machinery-train axis.

2) Power the stroboscope (or fluorescent lamp) from a source supplied by the generator. The rotor will appear to be standing still because a "burst" of light from the strobe is synchronized to the stator voltage waveform.

3) Pick some identifiable feature on the rotor that is in-line with the stator chalk mark. That "alignment" represents the "load-angle" at no-load.

3) Gradually increase the load on the generator. The point on the rotor will shift relative to the stator reference mark, in the direction of rotation. That displacement is the "load-angle!"

4) Note, if the fluorescent-lamp is used it may "flash" at twice line-frequency.

5) The Caveat:
The stroboscopic effect described above will make trotating elements appear stationary posing a serious danger to those in the area.

Regards, Phli Corso (cepsicon [at] aol [dot] com)

 

Bruce... the Mechanalog Analogy you alluded to in your 27-Nov-09 post was devised by Prof S.B. Griscom in 1926. A description can be found in the Westinghouse Transmission and Distribution Reference Book, ca 1950!

If any one would like a copy of the article, please contact me off-list. But, please recall my admonition regarding anonymity!

Regards, Phil Corso

 

Bruce,

I have no aversion to maths; rather, I just think that in general it doesn't have much of a place in most of the discussions we have here on this forum which are more of a general theoretical nature. Perhaps we need more maths, but that remains to be seen.

When I think of speed in this context I'm not thinking of the rate of change of the angle (as you described speed:

> Speed = rate of change of angle.

Rather, I think of speed as number of revolutions per minute.

Magnetic forces have some "springiness" to them, as we've all noted when playing with magnets. Since the two magnetic fields are not physically locked together in a synchronous machine (motor or generator (alternator)), what's happening is that as more torque is applied to the generator rotor to try to speed it up the "springiness" in the magnetic forces at work in the generator allow the relationship between the two fields to drift further apart from each other. This change in relationship is the load angle.

If too much torque were to be applied for the magnetic forces involved (or, if the magnetic forces involved were not sufficient for the torque being applied) then the magnetic fields can shift by very large amounts, known as "slipping a pole" which can be very dangerous and catastrophic. This is an extreme condition, but does happen.

I'll have to dig out some old reference texts and my HP-41C/V and brush up on my RPN, but I have this feeling that we're not talking about RPM over seconds when we're talking about load changes on the order of 0.0067% speed reference change per second for a machine with a 4% droop characteristic (which, if my maths are correct would be about 0.4% speed reference change per minute). But, experience is what one gets when one was expecting something else, so I may gain some experience here.

And, yes, most of my experience is with much larger grids and smaller machines than the situation you described in NZ.

 

Phil Corso,

i am the person who posted this thread. As you said in your post (DEC 1st). i want a copy of Westinghouse Transmission and Distribution Reference Book and description that is said by Prof S.B. Griscom. I wish you will do the favour.

cheers,
MOHAN

 

Mohan... certainly, just contact me off-list.

Phil Corso (cepsicon [at] aol [dot] com)

 

Bruce / CSA,

what I think (correctly as Mohan explains he is a mechanical engineer) has been left out in the explanation is the role of the AVR / excitation. If the mechanical input torque increases without an increase in excitation the output electrical power won't increase and the load angle will continue to change until you pole slip.

 

If you increase the mechanical input without changing excitation, electrical power out will increase and the power factor will increase (or go more leading). Check the alternator circle diagram.

 

Dear Mr. Phil

Would you please explain why there is a replica / Silhouette of a fan rotating on the fan blades with a slower pace than the fan. It sometimes rotate in the same direction of the fan and sometimes in the opposite direction. Is it something similar to pole slipping of the fan motor or any other disturbance / reaction in the motor itself ? I'm very curious to know this.
I would be very grateful if you kindly explain it briefly.
-Munir

 

Munir... certainly, just contact me off-list. Phil Corso (cepsicon [at] aol [dot] com)