Looking for formula for net vars

[c131frdave]

Hello. I make electricity- a lot of it, around 500MW depending on the weather. I have been tasked with an engineering job, however I am no engineer, so I'm hoping someone can help.

I am doing reactive testing for our generators. We generate electricity nominally at 13.8KV, and use a generator step up transformer that brings it to 138KV for the main output bus.

I know the following:

Low side voltage KV = 13.14
Low side MVAR = -42.01
Low side MW = 86.20
GSU transformer impedance (GSU Z) = 13.87%
High side MW = 86.20
High side voltage (using the step up ratio of the GSU) 131.4

My missing value is high side MVARs. I'm told I can use the power transfer formula to calculate the high side MVAR, but I can't seem to figure out how to do that. Any help would be greatly appreciated.

 

[Ingenieur]

S mva = P + j Q = 86.2 mw - j 42.01 mvar = 95.89 / -25.98 deg va
ignoring losses and xfmr Z both sides S should be equal
since P is the same on both sides Q should be equal
are you the EE for a 1/2 Gw generation facility?

with a high xfmr Z I'm surprised P is the same?
is the Z for the 13.8/138 step up power xfmr or the grounding xfmr?
what is xfmr size? 100 mva?

 

[c131frdave]

You know what, you are correct sir. No, I am not an engineer, but the test engineer we hired came up with the data points. And I know from experience that we typically lose 1.4MW approximately on the net side. So my dilemma is worse, I need to know high side MW and MVAR. Thank you for your reply.

 

[Ingenieur]

You know what, you are correct sir. No, I am not an engineer, but the test engineer we hired came up with the data points. And I know from experience that we typically lose 1.4MW approximately on the net side. So my dilemma is worse, I need to know high side MW and MVAR. Thank you for your reply.

is that the 13.8/138 xfmr Z?
what mva is it
what x/r is it
need the xfmr test data for accurate calcs

 

[c131frdave]

is that the 13.8/138 xfmr Z?
what mva is it
what x/r is it
need the xfmr test data for accurate calcs

150MVA
GSU Impedance (150MVA, 138kV Base) 13.87%

Not sure what "x/r" is. Again, I'm not an engineer, I've just been given an engineer's task to complete...

 

[Carultch]

150MVA
GSU Impedance (150MVA, 138kV Base) 13.87%

Not sure what "x/r" is. Again, I'm not an engineer, I've just been given an engineer's task to complete...

X/R is a ratio of reactance (X), to resistance (R). Resistance is a measure of how much a component slows down current from flowing through it, for a given voltage, as it converts electrical energy to another form of energy. Reactance is similar, measured in the same units of Ohms, except instead of energy conversion, it is temporary energy storage that is taking place. Reactance causes a time delay between the voltage and current in the system.

A perfect inductor or perfect capacitor would have an X/R ratio of infinity (+ for inductor, - for capacitor). A perfect resistor would have an X/R of 0.

 

[Ingenieur]

I come up with
basis 150 mva, 138 kv
x/r = 1.74
Z = 8.8 + j 15.3 Ohm
hi side
P 84.8
Q -39.6
ph shift 34 deg

 

[c131frdave]

Thank you. Can you show me through the math? I have three other generators I need to calculate, each with data points at minimum load (approx. 85MW) and max load (approx. 125MW). (Also in layman's terms?) Thanks again!

Edit: Wouldn't the high side VARS be lower? If I'm leading, or absorbing VARs at the generator at -42, and the GSU is using VARs, wouldn't the net be -50 or so? I know if I feed a lagging grid, or export VARS, when I export say 20 MVAR, the grid only gets around 11MVAR according to ComEd. I assume it works the same way for leading.

 

[Ingenieur]

Thank you. Can you show me through the math? I have three other generators I need to calculate, each with data points at minimum load (approx. 85MW) and max load (approx. 125MW). (Also in layman's terms?) Thanks again!

It's a little involved
you know low side current i = S/(sqrt3 x v)
you know real power losses
calc R = P losses / i^2
determine base Z using pu Z, to calc act Z in Ohms
calc xfmr reactance X from Z = R + j X ( R and Z known)
once you have this kvar loss = current^2 x X

 

[Ingenieur]

The gen produces/supplies var
the xfmr consumes/absorbs
-39.6 var is LESS than -42.01
the sign determines lead/lag ~ supply/absorb ~ Cap/Ind
lag is +
lead is -

 

[c131frdave]

The gen produces var
the xfmr consumes
-39.6 var is LESS than -42.01
the sign determines lead/lag
lag is +
lead is -

No, I don't think so. If I have the generator at unity, net side shows around -9MVar. The transformer consumes VARS from the grid when the generator isn't making any. I'm a generator, not a motor. Yes, Lag is feeding the grid with vars, or exporting, and lead is absorbing from the grid, or importing. So if the generator is importing 40MVAR, and the Transformer is pulling in 9 MVAR, the grid, or Net side, would be -49MVAR.

Maybe the terms should be gross and net, rather than high and low. It's just shown high and low on my FERC form...

 

[c131frdave]

Hey, I just got some information from the manufacturer- test results:


144900 to 13110 432252 Watts 0.288%R + j13.825%X = 13.828%Z 150000 KVA @ 85°c X/R Ratio = 47.977
138000 to 13110 429379 Watts 0.286%R + j13.841%X = 13.844%Z 150000 KVA @ 85°c X/R Ratio = 48.354
131100 to 13110 460407 Watts 0.307%R + j14.334%X = 14.337%Z 150000 KVA @ 85°c X/R Ratio = 46.700


There are three taps, so they tested each tap. Does that help? Thanks!!

 

[Ingenieur]

Hey, I just got some information from the manufacturer- test results:


144900 to 13110 432252 Watts 0.288%R + j13.825%X = 13.828%Z 150000 KVA @ 85°c X/R Ratio = 47.977
138000 to 13110 429379 Watts 0.286%R + j13.841%X = 13.844%Z 150000 KVA @ 85°c X/R Ratio = 48.354
131100 to 13110 460407 Watts 0.307%R + j14.334%X = 14.337%Z 150000 KVA @ 85°c X/R Ratio = 46.700


There are three taps, so they tested each tap. Does that help? Thanks!!

that changes everything
the previous was based on 1.4 mw losses
actually only ~0.4 mw
the previous x/r made no sense
new = 17.5725/0.3631 = 48.4

 

[Ingenieur]

Low S = P + jQ = 86.2 mw - j42.01 mvar = 95.9/26 deg mva pf 0.90
High S = 86.03 mw - j39.2 mvar = 94.54/24.5 deg mva pf 0.91

base 150 mva, 138 kv
Z = 0.3631 + j 17.5725 Ohm
x/r = 48.4

somebody check please

 

[Ingenieur]

Xfmr losses at 95.9 mva
P 0.175 mw
Q 2.83 mvar

high side ADDING the Q loss to the low side operating Q
P 86.03 mw
Q -44.84 mvar
S 97/27.5 deg pf 0.887

still not sure why the xfmr Xl Q losses are added to the generated Q

 

[rian0201]

i wonder why is there no power meter at the high side? if its that important to monitor the power...



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[gray.one]

I come up with
basis 150 mva, 138 kv
x/r = 1.74
Z = 8.8 + j 15.3 Ohm
hi side
P 84.8
Q -39.6
ph shift 34 deg

Sorry to be the jerk that only criticizes... but no way the x/r is 1.74. It should be more like 20 for a transformer that size.


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[Ingenieur]

Sorry to be the jerk that only criticizes... but no way the x/r is 1.74. It should be more like 20 for a transformer that size.


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Look at the data, it is correct for the numbers he gave
the power loss he gave was too high giving too high of an r (too low x/r)

he later gave a lower i^2r loss and the revised x/r is 48
confirned by calculation
Please read all the posts

 

[c131frdave]

that changes everything
the previous was based on 1.4 mw losses
actually only ~0.4 mw
the previous x/r made no sense
new = 17.5725/0.3631 = 48.4

Fantastic. Thank you so much.

 

[c131frdave]

i wonder why is there no power meter at the high side? if its that important to monitor the power...



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There is certainly a power meter at the high side- but it is a revenue meter owned by the utility, Commonwealth Edison in our case, which is off limits to us. I am a generator, so all of our metering is on the low side as to look at the gross values at our generator. We don't have access to the high side metering because it is off property at ComEd's switchyard many miles away. There is a caveat to that- we do have metering on the high side for bus voltage and frequency, which is used for synchronization. We also have current signals from ComEd for differential to our protection relays, but unfortunately, our relays are old, and do not have readouts that show values.

These days generators are isolated as much as possible so the evil Russians can't hack our plants...