Understanding Power Factor 1

[NewGrid]

There is a 3-bus bar system.
On bus1 there is the generator: 30MVA, cosφ=0.8. So active power = 30*0.8=24 MW. And Reactive power=18 MVAr.
On Bus3, there is the load: 15 MVA, cosφ=0.9. So active power = 15*0.9=13.5 MW, Reactive demand=15*sinφ=6.54 MVAr.

The concept of power factor has to do with the phase difference between V and I.
So this means that the generator can produce UP TO 24 MW of active power, and 18 MVAr of reactive power?

 

[waross]

Do you want to talk about power factor or about generator capabilities?
A generator rated at 30MVA/24MW will have a prime mover capable of producing at least 24 MW In practice the prime mover may be over sized 10% or more.
The MVA rating of a generator is the product of the maximum safe current and the rated voltage.
If you exceed the current rating you risk overheating and burn out.
On a prime rated set you often may load up to 110% of the MW rating before the prime mover becomes overloaded and starts to stall, but I have seen a prime power set start to stall the prime mover at just a few percent over the rated MW.
I have seen sets run at a power factor near zero. These were very old sets and the diesel engines were worn out. Also diesel fuel was expensive.
The MVARs were used for voltage adjustment at the end of a long transmission line.
BUT DON'T FORGET THE CAPABILITY CURVE.
At extreme power factors a generator may develop excess heat and the voltage may become unstable. At leading power factors the field may become overheated.
A large generator will have a capability curve supplied by the manufacturer. The generator should not be operated outside the limits of the capability curve.

So this means that the generator can produce UP TO 24 MW of active power, and 18 MVAr of reactive power?

The generator will produce at least 24 MW, probably up to 110% (26.4 MW).
At 100% load the generator may produce 18 MVAR
At less than full load the generator may produce more than 18 MVAR
At zero load the generator may be capable of producing 30 MVAR SUBJECT TO THE CAPABILITY CURVE.

Bill
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"Why not the best?"
Jimmy Carter

 

[electricpete]

As Bill explained well, capability curve describes capability of the generator. It is a curve in the P-Q plane such that the limit on P depends on Q and vice versa.

From the 3-bus problem description, I'm suspecting this is more of a textbook problem (compute bus 2 P and Q). For understanding power factor in general, you should start with the fundamentals, like concepts of beer and suds


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(2B)+(2B)' ?

 

[NewGrid]

When we say that a 100 MVA load has power factor 0.8 , it means that the unit consumes 100*0.8 = 80MW and 100*0.6 = 60MVAr. Correct?

When we say that a 100 MVA generator has power factor 0.8, doesn't it mean that it produces P <= 80MW and Q <= 60MVAr ?

 

[electricpete]

Correct. i.e.

100 MVA at 0.8 power factor corresponds to 80MW and 60MVAR, correct.

Where Q is produced or consumed, probably the way you said although the statement of 0.8pf does not tell us whether load is lagging or leading.

There is a generator rating and a generator operating point, may be different.

You probably knew all that, I was just trying to make sure nothing was glossed over.

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[electricpete]

Let me add a few words to clarify my meaning:

Where Q is produced or consumed, probably the way you said although the statement of 0.8pf does not tell us whether load is lagging or leading.

should have been:

Where Q is produced and where it is consumed (generator or load) is not known since there was no statement about whether the 0.8 pf is lagging or leading. However, most loads are lagging, so it's probably the way you described .

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[waross]

The load determines the power factor.
A generator rated at a power factor of 80% means that the rating of the generator end in KVA is 125% greater than the minimum rating of the prime mover.
That is it is common for a 100 KVA generator end to be mated to a minimum 80 KW prime mover. The ratings are 100 KVA, 80 KW, 0.8 PF.
The actual power factor, as I have said, is determined by the load.
VARs are an imaginary but very useful device to quantify the effect of a phase angle difference between the voltage and the current. Although we talk about VARs as if they were real, they are a description of a phase shift between the Volts and Amps.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[NewGrid]

More data given from simple questions asked in Job interviews: (I rephrase my question about the generator)

1. Generator has POwer Factor = 0.8 lagging. The nominal MVA is 100. ---> We conclude that P=100*0.8=80MW, Q=100*0.6=60MVA .
However, the values 80 and 60 are the maximum values it can produce.
The actual values that the generator will produce are determined by the load!
So if the load is 40MW and 30MVAr, then the generator will produce 40MW and 30MVA.

2. Imagine a 3bus-bar system. At bus1 is the generator (the one described above). At bus 3 there is the load (40MW, 30MVAr).
Bus1 voltage voltage is V1= |V1|<d1 per unit. If |V2|<d2 and |V3|<d3 are the voltages in buses 2 and 3 respectively,
then we can safely say that always |V2|<|V1| , |V3|<|V1|, d2<d1, d3<d1 in other words 'as we move further from the generation
towards the load, the voltages decrease' (as long as no other generators exist in between)

My answers

1. Correct 2. Correct.
What do you think?

 

[electricpete]

2 - not if the load has leading power factor and the lines are (as usual) inductive

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[electricpete]

Typing on phone... Decoupled load flow approximation generally Very useful . Real power flows through induvtive lines according to angle difference. Reactive power flows through lines according to the magnitude difference.

If load has leading power factor, that means vars flow out of it toward generator.

Regarding 1, there may be losses in lines and transformers. ....primarily reactive. Dont know if it's significant.

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[waross]

In the real world things are not that simple. You may have a misconception concerning VARs and you don't understand generators.

1. Generator has POwer Factor = 0.8 lagging. The nominal MVA is 100. ---> We conclude that P=100*0.8=80MW, Q=100*0.6=60MVA .
However, the values 80 and 60 are the maximum values it can produce.

NO
It can probably produce about 88 MW for one hour out of 12.
VARS KVARs MVARs. If the load is less than 80 MW the machine may produce more MVARs.
Some machines produce very little MW but produce MVARs almost up to the MVA limit. (Subject to the capability curve.)
You have mastered the relationships in the basic right angle triangle. But consider this suggestion.
MW = 80
MVA = 100
The root of (MVARs² + MW²) shall not exceed 100 MVA and shall be within the generator capability curve.

Bill
--------------------
"Why not the best?"
Jimmy Carter