Power transmission – transformers and losses ΔP = P²R/U²
Design & TechnologyElectrical Engineering & SafetyAges 17–18
Use it with your class: students open it from a link or a QR code, with no account needed.
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Electricity travels from the power plant through a step-up transformer, a high-voltage line and a step-down transformer to reach consumers. Choose a transmission voltage of 22 kV, 110 kV, 220 kV or 500 kV, and drag the line length and wire cross-section to see the line resistance R = ρL/S, the power loss ΔP = P²R/U² and the transmission efficiency change; the wire glows red when the loss is large. A bar chart comparing the loss at all four voltage levels shows why power must be transmitted at high voltage.
Lesson: Structure of the national power system: power plants, substations, the transmission and distribution grid, and line losses
What it shows
Electrical energy travels from power stations to consumers over long lines whose resistance R = ρL/S turns part of the power into heat. For a fixed transmitted power P the line current is I = P/U, so the heat loss ΔP = I²R = P²R/U² falls with the square of the voltage. That is why transformers step the voltage up to hundreds of kilovolts for long-distance transmission and back down near consumers. The model compares four voltage levels from 22 kV to 500 kV, aluminum or copper conductors, and also reports the voltage drop ΔU = I·R and the efficiency H = (P − ΔP)/P.
How to use
Begin at 220 kV with the default 100 MW over 200 km and read the loss and efficiency. Click 22 kV, 110 kV and 500 kV in turn and compare the bars on the chart. Keeping one voltage, double the Wire cross-section or switch Wire material to copper, and compare the saving with that from raising the voltage. Finally increase the power P and Line length L to find when the wire glows red and the loss becomes unacceptable.
Parameters you can change
- Power sent from the plant 10–600 MW
- Transmission voltage 22 kV (distribution grid), 110 kV, 220 kV, 500 kV (long inter-regional line)
- Line length 10–600 km
- Wire cross-section 100–800 mm²
- Wire material ACSR steel-cored aluminum (ρ = 2.8·10⁻⁸ Ω·m), Copper (ρ = 1.7·10⁻⁸ Ω·m)
Questions to explore
- At 100 MW over 200 km, how many times smaller is the loss at 220 kV than at 110 kV, and why?
- Why can a 22 kV line not carry 100 MW over 200 km?
- Which reduces the loss more, doubling the wire cross-section or doubling the transmission voltage, and by what factor?
