How to work out real and reactive power losses in transformers & cable

[binnie71]

Hi, I'm trying to work out the real & reactive power losses through transformers and MV cables. However, I'm having trouble finding anything that deals with anything other than (I^2)(R) which only gives real losses and not reactive, nor does it take into account skin effect factor or proximity effect factor. Any help gladly aappreciated.

 

[waross]

Note that reactive power is not a loss but the reactive currents cause losses described by the I²R of the conductors carrying the reactive currents.
That is, a reactive current of 10 Amps and 100 Volts will result in 1000 VA or 1 KVA. This is not a loss. However, the 10 Amps will result in a I²R loss in the conductor supplying the reactive load.
That's great for the classroom but in the real world, given a load that draws a reactive current of 3 Amps and a real current of 4 Amps the total current will be 5 Amps and the I²R losses in the cable will be based this current of 5 Amps.

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

 

[rcw retired EE]

Var "losses" in trasnformers are = I squared X. Use per unit on the transformer KVA base The kVArs in the transformer are = (Xpu x Ipu^2) x kVA rating. Ipu is the per unit load going through the transformer.

Skin effect and resistance of a cable have little effect on the losses.

 

[rbulsara]

rcwilson??? There is no such thing as reactive loss.

Losses are always real and I²R. As Bill said reactive current will cause real losses and so will real load current. If both real and reactive components are present, the resultant current = square root of (square of real current + square of reactive current) will decide the I of the I²R. The cable's R and skin effect has impact on effective R and hence the losses. Similarly R of windings of the transformer affects copper losses.

In transformers there are also no-load or core losses, which again is real. They are caused by the resistance of the core encountered by the eddy currents in the magnetized core plus I²R due to the magnetizing current. These losses are independent of the load and are always present as long as the transformer is energized. This data you need to get from the manufacturer.



Rafiq Bulsara

http://www.srengineersct.com

 

[slavag]

Hello.
I would recommend a grate document from PML ( OK from Schneider Electric )

http://global.powerlogic.com/librar..._notes/Transformer_Line_Loss_Calculations.pdf

Best Regards.
Slava

 

[rcw retired EE]

Rafiq - I agree there is no such thing as reactive power loss, that's why I highlighted it as "losses". The VARS aren't lost they are just used in the transformer.

But many times I have had client's and project managers wonder where all of the MVArs went in their power plant. They can't reconcile the generator output meter with the high voltage utility meter and aux load metering. The generator puts out 0.85 power factor but the utility interconnect is operating at 0.92. Where did the VARS go?

Example:
Generator 400 MW @ 0.85 pf.
Aux load 8 MW at 0.8 pf.
300/400/500 MVA GSU with 10% X at 300 MVA.
Power to GSU is 392 MW, 241 MVAR = 460MVA @ 0.85 pf. The MVAr's used in the GSU will be =300 MVA x 10% x(460/300)^2= 70 MVAr.
Output to utility will be 392 MW and 171 MVAr (neglecting GSU kW loss) = 427 MVA @ 0.92 pf.

Managers treat the VArs like the Watts, comparing how much they produce with how much they deliver and consider the difference to be their auxiliary load + losses.

 

[jghrist]

If you accept the concept of reactive power, I don't see the problem of accepting reactive power losses.

 

[MAGTiger]

Current is reactive only in the context of applied voltage. In the absence of voltage, the current is only current neither active or reactive. If considered in the context of applied voltage, that portion which is not in phase with voltage is producing VARs. However, any current passing through a resistance, causes a voltage drop across the resistance and a I2R loss (watts). The voltage across the resistor is directly in phase with the current. By the way, that voltage dropis likewise out of phase with the applied voltage and so subtracts vectorially.

Neil

 

[dpc]

In the absence of voltage, the current is only current

In the absence of voltage, there won't be much current.



David Castor

http://www.cvoes.com

 

[rbulsara]

Power factor is not the same as efficiency.

Rafiq Bulsara

http://www.srengineersct.com

 

[MAGTiger]

And I thought only the media used quotes out of context to achieve new meaning.

Neil

 

[jghrist]

Reactive power losses are referenced several times in the FERC Principles for Efficient and Reliable Reactive Power Supply and Consumption.

http://www.ferc.gov/eventcalendar/files/20050310144430-02-04-05-reactive-power.pdf

For instance:

Transmission Losses. Although often ignored for computational and presentational simplicity,
losses can be a significant factor in system economics. This is especially true for reactive power
losses.
...For reactive power losses (or consumption) are:
?Qk (?, V, t, ?) = Qijk + Qjik
= -Bk[Vi
2 + (Vj/?k)2 - 2(ViVj/?k)cos(?i - ?j + ?k)] - Vi
2Bcapik - (Vj /?k)2Bcapjk