NapkinCalc

Power Systems — Distribution

Why transmission is high-voltage

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

ELI5: line loss is I²R — it scales with the square of current. Push the same power at 20× the voltage and the current drops 20×, so the loss drops 400×. That brutal arithmetic — not convenience — is why the grid steps up to hundreds of kilovolts for the long haul.

Psend:=10e6WP_{send} := 10e6 W = 10000000 W 10 MW to deliver
Rline:=2ohmR_{line} := 2 ohm = 2 ohm the long line's resistance
Iat24kV:=Psend/24000VI_{at_24kV} := P_{send} / 24000 V = 416.67 A current at 24 kV
Ploss24=Iat24kV2⋅RlineP_{loss_24} = I_{at_24kV}^{2} \cdot R_{line} = 347220 W ~347 kW lost — 3.5%!
Iat240kV:=Psend/240000VI_{at_240kV} := P_{send} / 240000 V = 41.667 A same power at 240 kV
Ploss240=Iat240kV2⋅RlineP_{loss_240} = I_{at_240kV}^{2} \cdot R_{line} = 3472.2 W ~3.5 kW — a hundredth of the loss
✓ pass Ploss240<Ploss2499P_{loss_240} < \frac{P_{loss_24}}{99} 10× the voltage, ≤1/100 the loss

Real-world hook: this is why transmission towers carry such lethal voltages, and why the grid is a constant dance of step-up and step-down transformers between the power plant and your wall.