Solve Transmission Losses: 50kW @ 230V, PF 0.6 Lagging

[SGL18]

I need help with this tutorial question I cannot solve!

a consumer demands 50kW at an effective voltage of 230V. supply system can be represented by a 0.1ohm resistance. Find the transmission losses in the event of the load being supplied with a power factor of 0.6 lagging.

I know the answer works out to be 13.13kW, but can't figure out the solution!

 

[tiny-tim]

Welcome to PF!

Hi SGL18! Welcome to PF!

Show us what you've tried, and where you're stuck, and then we'll know how to help!

 

[SGL18]

i've used the power factor=real power/apparent power (P/S) and from the power triangle i can get the real, reactive and apparent power. Can also get the impedance angle from the power factor using inverse cos function! (cos-1 0.6 = 53.13) and i know other formulas such as real power=p=V.I.cos (angle) but I'm just not sure how to put it together to get transmission loss!?

 

[SGL18]

i Just mananged to solve this using Apparent power instead of real power! P=IV so I=P/V or rather I=S/V then P loss= I (squared)R! Thanks for replying anyway tiny-tim! just started a new power engineering class soe rest assured I'll have plenty more questions! :)

 

[MBgigs]

Hi SGL18 (and/or anyone else who reads this),

I have a similar question but can't seem to work it out from what you've posted.

Question:

A 6.35kV single phase transmission line has a series resistance of 0.01 ohms supplies a 2MW load of 0.9 lagging power factor. Find the power loss in the tansmission line.

Ans: 1.22kW

I know its not particularly difficult but I have tried everything I can and am close to suicide :/

Please help.

 

[tiny-tim]

Welcome to PF!

Hi MBgigs! Welcome to PF!

Show us what you've done so far. ​

 

[MBgigs]

Hi and thanks for replying,

Well I figured find the Power and subtract the given power of 2MW. P = VI* so I need I. Therefore V = IR or IZ.

6350 = (0.01)(I)

I = 635000 (Already I see something is wrong)

I then subbed in for P = VI* and get a ridiculous figure not worth mentioning. I've thrown away (or recycled :) ) my scrap paper working which I won't do from now on but I've tried many other methods using the many available formula's but I am not getting anywhere.

Its been 3 years since I've done anything like this and I've jumped right into the deep end as this is just the basics for 3 phase power.

MBgigs

 

[tiny-tim]

Hi MBgigs!

A 6.35kV single phase transmission line has a series resistance of 0.01 ohms supplies a 2MW load of 0.9 lagging power factor. Find the power loss in the tansmission line.

Ans: 1.22kW

Well I figured find the Power and subtract the given power of 2MW. P = VI* so I need I. Therefore V = IR or IZ.

6350 = (0.01)(I)

Oh I see, you're trying to find I from V and R.

No, you must find I from V and W (and then use power loss = I²R, as SGL18 did) …

what do you get? ​

 

[MBgigs]

I gave that a go but guess I don't know what to do next:

2000000 = (6350)(I)

I = 314.96A

314.96^2 x 0.01 = 992W

 

[tiny-tim]

I gave that a go but guess I don't know what to do next:

2000000 = (6350)(I)

What about the power factor?

 

[MBgigs]

2000000 / 6350 x 0.9 = 349.96I

349.96^2 x 0.01 = 1.224kW (1.2kW) :)

Thanks again for your help. I may be in serious trouble this year :/

All the best.