Generator Capability Curve

B

Thread Starter

bulldog1

Looking for some insight on excitation fluxuation and how it affects power, voltage and current with 2 generators running in parallel. Also will turbine output power increase if excitation increases.

Thank You gentlemen.
 
bulldog1,

The basic formula for electrical power is:<pre>P = Vt * Ia</pre>where P = Power (watts; kW; MW)
Vt = Generator Terminal Voltage
Ia = Generator Armature (Stator) Amperes

For three-phase AC (Alternating Current) power, the formula is:<pre>P = Vt * Ia * 3^0.5 * pf</pre>where 3^0.5 = square root of 3
pf = Power Factor (some number less than or equal to 1.0)

AC power generation occurs at a fairly constant voltage; in fact, most generators and their excitation systems are designed with a terminal voltage range of plus-or-minus 5% of rated, which is a pretty small range. Excitation systems are used to control the generator terminal voltage, so changing excitation will have an effect on generator terminal voltage.

So, when one wants to change power one has to increase the generator stator amperes. And the amperes produced by a generator is a direct function to the torque being produced by the generator driving the prime mover, which is a direct function of the energy flow-rate through the prime mover (be it steam, or some kind of fuel (natural gas; distillate; etc.), or water, or air (for wind turbines)).

Generators are devices for converting torque into amperes, in the same way that motors are devices for converting amperes into torque. So, if one wants to increase the electrical power output of the generator, one increases the energy flow-rate into the generator's prime mover and that causes the torque being applied to the generator rotor to increase and the generator then converts that torque to amperes. So, amperes and prime mover energy flow-rate are related to each other.

The square root of three is a constant--it doesn't change. The other variable is power factor, which does change as a function of generator excitation. But, since the excitation system is fairly limited (again, to a typical range of plus-or-minus approximately 5% of rated generator terminal voltage)--<b>AND</b> since the generator is typically operated at a fairly constant generator terminal voltage, these two factors in the three-phase AC power formula can be considered to not have much effect on the power production. (In fact, the square root of three has no effect at all--ever; it's always a constant. The power factor does have an effect, and more so at low loads with respect to the rated generator output.)

To answer your question about whether turbine power will increase with an increase in excitation: No. Turbine power (the turbine is the prime mover driving the generator, supplying torque to the generator which the generator converts to amperes)--and here I'm referring to real power (watts; kW; MW)--will not increase if excitation is increased. And, generally, neither will the generator power output increase if excitation is increased. At very low loads (with respect to generator rating) if the excitation is varied a lot, it will have a small effect on generator power output--but, in general, if one wants to increase the power output of the turbine-generator one has to increase the energy flow-rate into the turbine (the prime mover). Just increasing excitation while holding the energy flow-rate into the prime mover (be it a turbine or a reciprocation engine) will not increase the electrical power output of the generator (the watt; kW; MW).

Two generators connected in parallel with each other--synchronized to each other--will run at the same frequency as the other. On an AC power system, no single generator nor group of generators, can run at speeds faster or slower than the speed which is related to the frequency being produced. (There's another really important formula for AC power generation which is F=(P * N)/120, where F is frequency (in Hertz(, P is the number of poles of the generator field (usually the rotor), and N is the speed of the rotating field (the rotor) in RPM. Very great magnetic forces at work inside every generator keep the rotor locked into the speed which is a direct function of the frequency when synchronized with any other generator(s).)

Back to the first formula, multiplying the generator terminal voltage--which is usually relatively constant during normal generator operation, and which is a function of excitation--times the generator armature (stator) current. Again, since generator terminal voltage remains relatively constant, to increase power one must increase amperes (generator armature amperes), and to increase generator stator amperes one has to increase the energy flow-rate into the prime mover driving the generator.

When the excitation being applied to the generator rotor is exactly equal to that required to make the generator terminal voltage equal to grid/system voltage then the reactive current (VArs) flowing in the generator stator is zero, meaning the power factor is 1.0 (unity). When the excitation is increased such that the generator terminal voltage would tend to try to increase, the VArs flowing in the generator stator will increase in the lagging direction, and the power factor will decrease from 1.0 in the leading direction.

Conversely, if the excitation were decreased from that which was making the generator terminal voltage equal to the grid/system voltage the VArs flowing in the generator stator would increase in the leading direction, and the power factor would decrease from 1.0 in the leading direction.

The reactive capability curve shows the limits of the generator to produce both real power and reactive power. Real power is a function of the torque being applied to the generator rotor, and reactive power is a function of the excitation being applied to the generator rotor. The lines on the reactive capability represent how much real- and reactive power can be produced by the generator while still maintaining the generator cooling so that it doesn't overheat (remember: current flowing in conductors generates heat, and too much heat in a generator will cause the insulation to deteriorate which will result in arcing and sparking and damage).

As for the question about two generators synchronized together, ... Can you provide more detail? Are you referring to two generators supplying a small load (sometimes called an "island load") which is independent of a larger grid/power distribution system? Because this changes things a lot when discussing reactive power (which is a function of the generator excitation).

Two generators supplying a small, independent load, can't change the power factor of the load (the motors, lights, televisions, computers and computer monitors being powered by the generators)--the power factor is whatever the load's aggregate power factor is. The two generators can share in supplying the reactive power required by the load, or only one can produce the reactive power. But, if one tries to change the power factor of a small independent load, the only thing one will succeed in doing is changing the voltage of the load/system.

Similarly, the amount of real power being produced by two generators synchronized together and supplying a load independent of a larger grid must exactly match the requirements of the load--or the system frequency will deviate from rated.

Two or more generators synchronized together are really just one generator, in the same what that all the motors and lights and televisions and computers and computer monitors connected to the group of generators is really just one load. The prime movers and the generators can be used to split the load (real and reactive) between them to power a load that is infinitely larger than any single prime mover and generator could supply. This is quite frequently referred to as "sharing the load," but one has to be very careful when defining what sharing means in this context.

But, if there's an excess of torque being produced by the prime movers driving the generators which are synchronized together then the grid/system frequency will increase. And the speed of <b>ALL</b> of the prime movers and the generators they are driving will ALL increase. Conversely, if there is insufficient torque being produced by the prime movers driving the generators synchronized together then the grid/system frequency will decrease--and so will the speeds of all the prime movers and generators synchronized together.

Hope this helps!

By the way, this has all been covered before--many times--on control.com, along with a wealth of other topics. There is a 'Search' field cleverly hidden at the far right of the Menu bar at the top of every control.com webpage. (Use the Search 'Help' to get the best results!)
 
Thank you CSA,

the generators in parallel are a 250 m.w.unit. One turbine is running at 3600 rpms and the other turbine at 1800 rpms. This is a GE cross compound condensing unit.

My other question was about power factor and generator efficiency and are they directly related?

Thank you again sir.
 
Top