Power lost in transmission lines

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SUMMARY

The discussion centers on calculating the resistance of a 500kV transmission line where 7% of the power produced by a typical power station (1000MW) is lost. The initial calculation using the formula P=I²R led to an incorrect resistance of 268 ohms, while the correct answer is 17.5 ohms. Participants emphasized the need to account for the voltage drop along the line and correctly compute the power lost to arrive at the accurate resistance value.

PREREQUISITES
  • Understanding of electrical power formulas, specifically P=I²R and P=VI.
  • Knowledge of power loss calculations in transmission lines.
  • Familiarity with units of measurement in electrical engineering, such as megawatts (MW) and kilovolts (kV).
  • Basic grasp of Ohm's Law and its application in circuit analysis.
NEXT STEPS
  • Study the concept of power loss in transmission lines and its impact on efficiency.
  • Learn about the calculations involved in determining voltage drop in electrical systems.
  • Explore advanced electrical engineering topics, such as transmission line modeling and impedance.
  • Investigate tools for simulating electrical circuits to visualize power loss and resistance.
USEFUL FOR

Electrical engineers, students studying power systems, and professionals involved in energy transmission and distribution will benefit from this discussion.

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Homework Statement



A typical power station produces 1000MW of electrical energy. Seven percent of the power is lost in a 500kV transmission line. Whats the lines resistance?

Homework Equations



P=I2R

The Attempt at a Solution


Thought this problem was simple but I keep getting it wrong.
P=I2R so P=V2/R
7 percent is lost @ 500Kv
so 0.97*1000*106 = (500*10^3)^2/R
R=268ohms but the actual answer is 17.5 ohms?
Thanks
 
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The V in V^2/R is the voltage drop along the line - which you don't know
Work out the power lost, then the total current, then try
 
So P=VI
total I: 1000*10^6/500*10^3=2000A (that can't be right can it, its huge)
0.7*1000*10^6-1000*10^6=9.3*10^9W (power lost)
9.3*10^9=2000^2/R
R=4.3*10^-3ohms- that's too small now?
btw thanks for replying
 

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