Power Systems — Distribution

Why transmission is high-voltage

continues from lesson 2 — values defined earlier in the course stay live here

Line loss is I²R — current squared. Move the same power at 20× the voltage and current drops 20×, so losses drop 400×. That arithmetic, not convenience, is why the grid steps up to hundreds of kV:

P_{send} := 10e6 W

= 10000000 W 10 MW to deliver

R_{line} := 2 ohm

= 2 ohm the long line's resistance

I_{at_24kV} := P_{send} / 24000 V

= 416.67 A current at 24 kV

P_{loss_24} = I_{at_24kV}^{2} \cdot R_{line}

= 347220 W ~347 kW lost — 3.5%!

I_{at_240kV} := P_{send} / 240000 V

= 41.667 A same power at 240 kV

P_{loss_240} = I_{at_240kV}^{2} \cdot R_{line}

= 3472.2 W ~3.5 kW — a hundredth of the loss

✓ pass

P_{loss_240} < \frac{P_{loss_24}}{99}

10× the voltage, ≤1/100 the loss