Describe the use of transformers in high-voltage transmission of electricity

4.5.6 The Transformer

Objective

Describe the use of transformers in high‑voltage transmission of electricity.

1. Why Transmit at High Voltage?

• Power loss in a line is \(P_{\text{loss}} = I^{2}R\) (I = current, R = resistance).
• For a required transmitted power \(P\), the current is \(I = \dfrac{P}{V}\).
• Increasing the transmission voltage V therefore reduces the current and the I²R losses.
• Lower current also means thinner, cheaper conductors can be used for the same power rating.

2. Construction of a Transformer

• Primary winding – coil connected to the source of alternating current.
• Secondary winding – coil that delivers the transformed voltage to the load.
• Core – closed magnetic circuit, normally laminated iron sheets to minimise eddy‑current loss.

3. Principle of Operation

When an alternating current flows in the primary winding it creates a time‑varying magnetic flux \(\Phi\) in the core. This changing flux links the secondary winding and induces an emf according to Faraday’s law. The induced emf is proportional to the rate of change of flux and to the number of turns in the winding.

4. Key Terminology

• Step‑up transformer – secondary has more turns than the primary (\(N{s}>N{p}\)); secondary voltage is higher.
• Step‑down transformer – secondary has fewer turns than the primary (\(N{s}{p}\)); secondary voltage is lower.
• Turns ratio – \(\dfrac{N{p}}{N{s}}\) where \(N{p}\) and \(N{s}\) are the numbers of turns in the primary and secondary.

5. Ideal Transformer Equations

Voltage–turns ratio

\[

\frac{V{p}}{V{s}} = \frac{N{p}}{N{s}}

\]

Power (ignoring losses)

\[

V{p} I{p} = V{s} I{s}

\]

Efficiency of a real transformer

\[

\eta = \frac{P{\text{out}}}{P{\text{in}}}\times100\%

\qquad\text{where }P{\text{out}} = V{s}I{s},\; P{\text{in}} = V{p}I{p}

\]

6. Transformers Used in Transmission

7. Example Calculation

Given: Power‑station output = 500 MW at 20 kV. A step‑up transformer raises the voltage to 400 kV for transmission. Line resistance = 0.05 Ω.

1. Current at generating voltage

   \[

   I{\text{low}} = \frac{P}{V{\text{low}}}

   = \frac{500\times10^{6}\,\text{W}}{20\times10^{3}\,\text{V}}

   = 25\,000\ \text{A}

   \]

2. Current after stepping up

   \[

   I{\text{high}} = \frac{P}{V{\text{high}}}

   = \frac{500\times10^{6}}{400\times10^{3}}

   = 1\,250\ \text{A}

   \]

3. Power loss in the line

   • Low‑voltage loss:

     \[

     P{\text{loss,low}} = I{\text{low}}^{2}R

     = (25\,000)^{2}\times0.05 = 31.25\ \text{MW}

     \]

   • High‑voltage loss:

     \[

     P_{\text{loss,high}} = (1\,250)^{2}\times0.05 = 0.078\ \text{MW}

     \]

   The loss is reduced by a factor of \(\dfrac{31.25}{0.078}\approx 400\), illustrating the economic advantage of high‑voltage transmission.

8. Real‑World Efficiency and Design Considerations

• Losses

  • Copper loss – I²R heating in the windings.
  • Core loss – hysteresis and eddy‑current losses in the laminated iron.

• Large power‑transmission transformers typically achieve 98–99 % efficiency.
• Cooling – oil‑filled or forced‑air systems remove heat from windings and core.
• Voltage regulation – on‑load tap changers adjust the turns ratio to keep the secondary voltage constant despite load variations.

9. Safety and Environmental Aspects

• All high‑voltage equipment is insulated, earthed and clearly sign‑posted to protect personnel.
• Transformers are housed in secure substations with barriers and warning signs.
• Oil‑filled units require spill containment and fire‑suppression measures.
• Acoustic enclosures or silencers reduce noise from cooling fans and magnetostriction humming.

10. Summary

Transformers make long‑distance electricity transmission economical. By stepping up the voltage, they reduce the current and the associated I²R losses, allowing thinner conductors and lower operating costs. After transmission, step‑down transformers bring the voltage to safe levels for distribution to homes and industry. Understanding the construction, terminology, ideal equations, efficiency factors and safety measures enables students to answer IGCSE questions on high‑voltage power transmission confidently.