My question is if I have 2 delta connected 11kv syncro-generators supplying a common 3000kw load at 0.8PF. How do I determine the excitation voltage of G1?
The impedances are G1=(0.56+j1.03) and G2=(0.4+j1.5)
The excitation current of G1 is adjusted to deliver 150A lagging and the governors are set so load is shared equally between both machines.
Am I correct (or totally wrong)?
Given G1 delivers 150A.(angle)0 deg
G1 impedance is (0.56+j1.03) OHMS
and V1 is 11000V.(angle)36.87 deg
than E=V+ZI = 11160.14V.(angle)37.25 deg
Are you referring to an isolated system (also called an "islanded" system), where the two prime movers and their generators are supplying a load/loads independent of other prime movers and generators on a grid?
Is either of the generators--or both--connected to a transformer before connecting to a common bus, or are both directly connected to a common bus? And, then, possibly through a single transformer to another bus?
Generator excitation changes affect power factor (VArs). The torque being produced by the prime mover driving the generator affects the Watts being produced by the generator. Excitation is VArs; torque is Watts. (Yes; changing the excitation at very low loads can have an affect on Watts, but it's considered negligible--in my opinion. Every tried to learn about droop speed control from a textbook or reference? I rest my case.)
I'm sorry; I'm not a maths person. And, I've never been able to reliably calculate excitation to control VArs, even on a small, islanded load. There are just too many intangibles--unless you're discussing a theoretical, class-room, ivory-tower situation. And, then, textbooks and references can sometimes be very misleading--because the authors don't really have a lot of real-world experience, and frequently forget to provide specific clarifications about their generalizations.
In my experience, when supplying an isolated, islanded load with one or two prime movers and generators, the prime mover governors are used to control the Watts produced by controlling the energy flow-rate(s) into the prime mover(s). And, prime mover governors can be tuned to "share" load (Watts)--or operated in such a manner as to "share" load (Watts). (Sharing doesn't mean splitting the load equally; it just means to provide the required power smoothly, regardless of how much load (Watts) one generator or the other is supplying. Another important distinction not explained in texts and references.)
And, if one tries to make more load (Watts) than is required by the load (lights and motors and televisions and computers and computer monitors) then what happens is the load doesn't change--but the frequency does, and it increases above desired. Or, if one isn't supplying enough energy flow into the prime movers to produce the Watts required by the load(s) (lights and motors and televisions and computers and computer monitors) then the frequency will be less than desired.
When it comes to reactive "power" (Vars), again--the reactive load is defined by the aggregate reactive power of the load(s) (lights and motors and televisions and computers and computer monitors). And, if one increases the excitation (total) above that required by the load(s) then the system voltage will increase above desired. And, conversely, if one decreases the excitation below that required by the load(s) then the system voltage will decrease below desired. And, the exciter regulators (commonly referred to as "AVRs") are used to control excitation, and can be configured/programmed/operated to control system voltage, VArs, or power factor--or some combination of the two. And to "share" reactive load--in the way the prime mover governors can be configured/programmed/operated to share real load (Watts).
It's different when prime movers and generators are synchronized to a large, or "infinite," grid with many other prime movers and generators, supplying a very large aggregate load (larger than any single prime mover and generator could every supply). In that case, it's possible to control the VArs or power factor of the generator output with the excitation system (AVR), and to control the real power (Watts) produced by the unit with the prime mover governor--without any appreciable affect on grid voltage or -frequency (depending on how large the prime mover and generator is in relation to the other prime movers and generators it is synchronized to).
I wish I could help you with the maths part of your question, but I don't really understand the question and how it was asked (governors are the term used for prime mover control systems--in my experience; and exciter regulators/AVRs are used to control generator excitation). Excitation affects generator VArs, and power factor; energy flow-rate through the prime mover affects generator Watts. And, I have never been able to use formulae to explain how to physically operate a prime mover and generator to anyone. And, the maths wasn't very useful to me when I went to university; it was only after I met a very wise and seasoned power plant operator who was not an engineer and hadn't gone to university and didn't know about vectors and angles and imaginary numbers who was able to make it all finally fit together. And, then I realized a lot of the maths was only for trying to prove why things work the way they do--not how they work the way they do. Unless one is trying to design systems or equipment, and then, well, a transformer designer once said it best; "We calculate the number of turns to achieve the desired ratio--and then we always add two more turns, because of intangibles." I've counted transformer turns (don't ask!), and guess what: The actual number of turns always exceeded the calculated number of turns, many times by two. So, maths only gets one so far--and the rest is experience, and knowledge, and wisdom.
Hope this helps!
I mostly agree with you. However, I noticed that even when a generator is synchronized on large grid, the stator voltage is fluctuating while increasing or decreasing the excitation. The maximum is usually set by the AVR limitation.(+/-10%).
Customers often ask me if we really change the grid voltage while doing +/-Exc. In my opinion we just change the voltage locally but not the "aggregate" voltage of the grid. Am I right?
That's correct. A lot of factors determine how much the generator terminal voltage will change when varying excitation while synchronized to a grid. Some sites will see a bigger change in generator terminal voltage than others.
And, yes, that is trying to change grid voltage--and some sites will have more of an effect on grid voltage than others.
As you say, one generator is trying to "boost" (increase) or"buck" (decrease) the grid voltage, and depending on a lot of variables that one generator may have more or less of an impact than another generator.
The effects of changing excitation is most apparent when when observing the VArs and Power Factor of the generator as they will both change as the excitation is varied. But not the load (Watts) being carried (produced) by the generator. That's a function of varying the energy flow-rate into the generator's prime mover.