Maximizing Power Efficiency: Solving an EE Design Problem

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Discussion Overview

The discussion revolves around a homework problem related to electrical engineering, specifically focusing on power transmission and the calculation of voltages and power factors in a transmission line scenario. Participants explore concepts such as Thevenin Equivalent Circuits and transmission line theory.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents a homework problem involving voltage and impedance in a transmission line, asking for calculations of input and source voltages, power factor, and a reactor value for unit power factor.
  • Another participant questions the necessity of calculating Vi, given that Vs is provided, suggesting that Thevenin Equivalent Circuits could be useful for solving the problem.
  • A different participant agrees with the previous point but notes that Thevenin's theorem may not apply straightforwardly in this context due to the nature of transmission lines.
  • One participant reflects on their past experience with power distribution, indicating that Thevenin's theorem can be applied but acknowledges complexities related to the location on the line and the type of transmission line (lossless vs. lossy).
  • Another participant recalls their previous learning about transmission lines and expresses uncertainty about their ability to assist further, while hoping the discussion provides useful insights for the original poster.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of Thevenin's theorem in this scenario, with some suggesting it can be useful while others caution about its limitations in the context of transmission lines. There is no consensus on the best approach to solve the problem.

Contextual Notes

Participants highlight the complexity of the problem due to the dependence on the location along the transmission line and the nature of the line itself, which may affect the input impedance calculations.

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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
 
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What have you tried ? Please show us your work.
 
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.
 
sanadan said:
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.
 
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).
 
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.
 
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.
 

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