Maximizing Power Efficiency: Solving an EE Design Problem

[xxcodexx]

Homework Statement

your house is supplied by a voltage from an elcectrical sub station 10km away from your house. the transmition lines have an impedance of 0.2+j1.6 Ohm, if the voltage at your house is 220 ( angle 0 ):
1-calculate Vi and Vs .
2- calculate the power factor at your house.
3- find the value of the reactor that when put in parallel with your house will result in a unit power factor.


Best Wishes

 

[╔(σ_σ)╝]

What have you tried ? Please show us your work.

 

[sanadan]

I don't understand what Vi is that you are supposed to calculate if they have told you that the voltage at your house is Vs?

Without doing any work, you should investigate Thevenin Equivalent Circuits which should produce all of the answers that you seek.

 

[╔(σ_σ)╝]

I don't understand what Vi is that you are supposed to calculate if they have told you that the voltage at your house is Vs?

Without doing any work, you should investigate Thevenin Equivalent Circuits which should produce all of the answers that you seek.

This is a transmission line problem. The regular thevenin doesn't really work since the input impedence depends on your location on the line.

 

[sanadan]

You are likely right, it has been a long time since I looked at transmission line theory. I assumed this was a more elementary power transmission problem.

Although, having said that, I did a work term at a power distribution company and the entire grid is modeled as a thevenin right up to the substation (transmission to distribution step down transformer (144kv to 24.9kv).

 

[╔(σ_σ)╝]

It is true that thevenin can be applied but it is not straightforward in this case. If you removed the source voltage are where just looking into the circuit thevenin works amazingly. However, if you are "in" the circuit thevenin is not so straightfoward since the impedence depends on the line( lossless, lossy etc) and your location. The input impedence equation involves ugly hyperbolic trig functions.

 

[sanadan]

Yah. This is all coming back to me now that I've wiki'd it. But, I haven't seen it since uni 10 years ago so I'm no help to the OP. Hopefully our discussion has at least gave him food for thought.