Physics · Electricity and magnetism · Grade 11

Power transmission line

Why is electricity transmitted at hundreds of kilovolts?

The situation

The electricity that lights the lamp in your home is generated at a thermal power station hundreds of kilometres away. The station's generator gives about 20 kV, the wires on the huge pylons stretching across the fields carry 220–500 kV, and the socket in your wall gives only 220–230 V. Why don't we transmit the energy at the generator voltage, and what raises and lowers the voltage?

Topic

Alternating current, transformer. Power transmission line: why high voltage

Key ideas

Transformer
I²R loss
Three-phase current

Formulas

\frac{U_{2}}{U_{1}} = \frac{N_{2}}{N_{1}} = k

Ideal transformer: the voltage is proportional to the number of turns. $k > 1$ — step-up, $k < 1$ — step-down.

\frac{I_{2}}{I_{1}} \approx \frac{N_{1}}{N_{2}}, η = \frac{P_{2}}{P_{1}}

Power is almost conserved ( $U_{1} I_{1} \approx U_{2} I_{2}$ ): however many times the voltage rises, the current falls by the same factor. The efficiency $η$ is the ratio of the secondary power to the primary power.

R = ρ \frac{L}{S}

Resistance of one phase wire; for aluminium $ρ \approx 2.8 \cdot 10^{- 8}$ Ω·m, $S$ is the wire's cross-section.

I = \frac{P}{\sqrt{3} U}, Δ P = 3 I^{2} R = \frac{P^{2} R}{U^{2}}

Current in a three-phase line and the heat loss in all three wires.

u (t) = U_{m} \sin ω t, U = \frac{U_{m}}{\sqrt{2}}

Alternating voltage: the effective (r.m.s.) value is $\sqrt{2}$ times smaller than the amplitude, $ω = 2 π \cdot 50$ Hz.

Theory

Why high voltage?

Let the line carry the same power $P$ . The higher the voltage $U$ , the smaller the current $I = P / (\sqrt{3} U)$ . And it is the current that heats the wires: $Δ P = 3 I^{2} R$ . As a result, the loss is inversely proportional to the square of the voltage: $Δ P / P = P R / U^{2}$ . If we raise the voltage 10 times, the loss falls 100 times. The curve on the “Loss against voltage” graph has exactly the $1 / U^{2}$ shape.

How does a transformer work?

A transformer is two windings wound on a common steel core. The alternating current in the primary winding creates an alternating magnetic flux in the core, and this induces the same emf in every turn of the secondary winding (Faraday's law). This is mutual induction: a change of current in one coil produces an emf in the other, $ℰ_{2} = - M d I_{1} / d t$ , where $M$ is the mutual inductance (in henries). That is why the voltage is proportional to the number of turns: $U_{2} / U_{1} = N_{2} / N_{1}$ . With direct current the flux does not change and the transformer does not work — this is the main advantage of alternating current.

Three-phase current

The station supplies three sinusoidal voltages shifted by $120 °$ from one another — three rotating vectors on the phasor diagram. Their sum is zero at every instant, so three wires are enough instead of six. The line wires are marked yellow, green and red (A, B, C). The power of a three-phase line is $P = \sqrt{3} U I$ , where $U$ is the voltage between phases. Some consumers (a phone charger, an electrolysis unit) need direct current: a rectifier — a bridge of diodes — makes it from alternating current; and at the two ends of very long HVDC lines there are controlled converter stations (a rectifier and an inverter) (more in the “Alternating current and RLC” experiment).

Transformer efficiency (lab)

In a real transformer a small part of the energy turns into heat. The core loss in the steel core (hysteresis and eddy currents; to reduce them the core is built from thin steel sheets insulated from one another) does not depend on the load, while the winding loss $I^{2} R$ is proportional to the square of the load. To find the efficiency $η = P_{2} / P_{1}$ , the voltage and current are measured on both sides. At a small load the core loss is relatively large and the efficiency drops; the efficiency is greatest at the load where the two losses are equal. In large transformers the efficiency is above 99 %; in small transformers the share of losses is larger.

Electricity and alternative sources in Uzbekistan

Most of Uzbekistan's electricity (about 87 % in 2021) is produced at thermal power plants burning natural gas; one of the largest is the Syr Darya TPP (≈ 3 GW). Hydroelectric stations, for example the Charvak HPP on the Chirchik River (≈ 0.67 GW), provide about 7 %. The stations' generators give 50 Hz three-phase current; step-up transformers send it into 220 and 500 kV lines, and city substations step it down to 10 kV and 0.4 kV. Alternative energy is growing fast: the 100 MW “Nur Navoi” solar power plant in the Navoi region (2021) and the 500 MW Zarafshan wind power plant, commissioned in 2024. Solar panels give direct current — an inverter converts it to 50 Hz alternating current, and then a transformer raises it to the grid voltage. Solar and wind power depend on the weather, so the grid also needs reserve capacity and energy storage.

Model and simplifications

In the line calculation the transformers are ideal (real ones have an efficiency above 99 %); in the efficiency lab the step-up transformer group is taken to have a rated power of 1000 MV·A, a core loss of 0.6 MW and a winding loss of 2.4 MW at rated load. The load is purely active ( $\cos φ = 1$ ) and only the heating of the wires is taken into account — there is no inductive reactance, corona discharge or loss in the insulators. The wire is at 20 °C, $ρ = 2.8 \cdot 10^{- 8}$ Ω·m. The step-down transformers in the houses are assumed to be chosen for the rated $U$ . In the scene the distance is compressed (11 pylons stand for $L$ km), the wires are drawn thicker, time is slowed down 50 times, and the yellow particles are a symbolic picture of the energy flow.

Did you know?

In the late 1880s the “war of the currents” took place in the USA: Thomas Edison's company promoted direct current, while George Westinghouse and Nikola Tesla promoted alternating current. Alternating current won — its voltage can easily be raised and lowered with a transformer.
Today, power over the longest distances is often transmitted by high-voltage direct current (HVDC). For example, the ±1 100 kV Changji–Guquan line in China is about 3 300 km long.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

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