State the advantages of high-voltage transmission

4.5.6 The Transformer

Learning Objectives

• Describe the construction of a simple iron‑core transformer (primary winding, secondary winding, soft‑iron laminated core).
• State and use the turn‑ratio relationship \(\displaystyle \frac{V_p}{V_s}= \frac{N_p}{N_s}\) and explain its effect on voltage, current and power.
• Explain the principle of operation (mutual induction, Faraday’s law) and the role of the changing magnetic flux.
• State the advantages of high‑voltage transmission and relate them to the transformer’s function in the grid.
• Identify the main loss mechanisms in a real transformer, calculate a simple efficiency, and recall the typical efficiency range (≈ 95 %–98 %).

1. Construction of a Simple Transformer

A basic single‑phase transformer consists of three essential parts:

• Soft‑iron laminated core – provides a low‑reluctance magnetic path. The core is made of thin insulated steel sheets (laminations) to break up circulating eddy currents, thereby reducing eddy‑current loss.
• Primary winding – insulated copper wire wrapped around one limb of the core; connected to the supply.
• Secondary winding – insulated copper wire wrapped on the same core; delivers the transformed voltage.

Both windings are electrically isolated from each other but are magnetically coupled through the core.

2. Principle of Operation

1. Alternating current in the primary creates a time‑varying magnetic flux \(\Phi(t)\) in the core.
2. The same changing flux links the secondary winding (mutual induction).
3. According to Faraday’s law, an emf is induced in each winding: \[ \mathcal{E}_p = -N_p\frac{d\Phi}{dt},\qquad \mathcal{E}_s = -N_s\frac{d\Phi}{dt} \]
4. Dividing the two expressions gives the turn‑ratio equation: \[ \frac{V_p}{V_s}= \frac{N_p}{N_s} \] where \(V_p\) and \(V_s\) are the rms voltages of the primary and secondary respectively.
5. Neglecting losses, power is conserved: \[ V_p I_p \approx V_s I_s \] Hence the current ratio is the inverse of the turn ratio: \[ I_s = I_p\frac{N_p}{N_s} \] A step‑up transformer (more turns on the secondary) raises the voltage and reduces the current proportionally.

3. Loss Mechanisms & Typical Efficiency

• Core (iron) losses
  • Hysteresis loss – energy dissipated each cycle as the magnetic domains reverse.
  • Eddy‑current loss – circulating currents induced in the solid core; greatly reduced by using laminated steel.
• Copper (I²R) losses – heating of the windings due to the current flowing through their resistance.

Typical overall efficiency of a well‑designed power‑frequency transformer is 95 %–98 %.

Worked Efficiency Example

Assume a 100 kVA transformer with the following losses:

• Core loss = 0.8 kW
• Copper loss (at full load) = 1.2 kW

Output power = 100 kW (ignoring the small difference between kVA and kW at unity power factor).
Efficiency \(\eta = \dfrac{\text{Output}}{\text{Output}+\text{Losses}} = \dfrac{100}{100+0.8+1.2}= \dfrac{100}{102}=0.980\;(\text{or }98\%).\)

4. Why Transmit Electricity at High Voltage?

For a required power \(P\), the current in a transmission line is

\[ I = \frac{P}{V} \]

Resistive (I²R) loss in the conductors is

\[ \text{Loss}= I^{2}R = \left(\frac{P}{V}\right)^{2}R \]

Thus, raising the transmission voltage dramatically reduces the current and the associated I²R loss.

5. Advantages of High‑Voltage Transmission

• Reduced I²R losses – lower current means far less heating of the conductors.
• Smaller, cheaper conductors – a given power can be carried by thinner cables, reducing material cost.
• Higher transmission capacity – more power can be sent on a single line without exceeding thermal limits.
• Longer feasible distances – acceptable losses are maintained over hundreds of kilometres.
• Improved voltage regulation – voltage drop \(\Delta V = IR\) is small, so the delivered voltage stays close to the intended value.

6. Comparison: Low‑Voltage vs. High‑Voltage Transmission

Parameter	Low‑Voltage Transmission	High‑Voltage Transmission
Current for a given power	High (large I)	Low (small I)
Resistive losses (I²R)	Very high	Much lower
Conductor size required	Thick, expensive	Thinner, cheaper
Maximum feasible distance	Short (tens of km)	Long (hundreds of km)
Voltage drop along line	Significant	Minimal

7. Role of the Transformer in the Power Grid

1. Generation: Power is produced at a relatively low voltage (e.g., 400 V).
2. Step‑up transformer raises the voltage to several hundred kilovolts (commonly 110 kV, 220 kV or 400 kV) while reducing the current.
3. The high‑voltage, low‑current electricity travels through long‑distance transmission lines.
4. Near the consumer, a step‑down transformer reduces the voltage to safe, usable levels (e.g., 230 V for domestic supply).
5. Because high voltage is hazardous, the distribution network incorporates insulation, earthing and protective devices before the final step‑down.

8. Worked Example – Using the Turn‑Ratio (Realistic Grid Values)

A power station generates 400 V, 500 A (200 kW). A step‑up transformer with a primary of 100 turns and a secondary of 1000 turns is used to transmit the power at 400 kV.

1. Turn‑ratio: \(\displaystyle \frac{N_s}{N_p}= \frac{1000}{100}=10\).
2. Secondary voltage (ideal): \[ V_s = V_p \times \frac{N_s}{N_p}= 400\;\text{V}\times10 = 4\,000\;\text{V} \] In practice the transformer is designed for a 400 kV output; the same ratio simply scales the voltage up by a factor of 1 000.
3. Secondary current (ideal): \[ I_s = \frac{P}{V_s}= \frac{200\,000\;\text{W}}{400\,000\;\text{V}} = 0.5\;\text{A} \] The current is reduced by the same factor (10) as the voltage is increased.
4. Resistive‑loss comparison (line resistance \(R = 0.05\;\Omega\)):
   • Low‑voltage line: \(I = 500\;\text{A}\) → loss \(= (500)^2 \times 0.05 = 12\,500\;\text{W}\).
   • High‑voltage line: \(I = 0.5\;\text{A}\) → loss \(= (0.5)^2 \times 0.05 = 0.0125\;\text{W}\).
   The high‑voltage system reduces line loss by a factor of about \(10^6\), illustrating why transmission voltages are kept very high.

9. Summary

High‑voltage transmission, made possible by step‑up transformers, is essential for an efficient, economical and reliable power grid. By raising the voltage, the current is reduced, which:

• Minimises I²R losses and heating,
• Allows the use of lighter, cheaper conductors,
• Increases the amount of power that can be carried on a single line,
• Enables electricity to be delivered over hundreds of kilometres with acceptable voltage drop,
• Improves voltage regulation at the consumer end.

Understanding transformer construction, the turn‑ratio, power‑conservation, and loss mechanisms equips students to answer IGCSE‑level questions and to appreciate the real‑world engineering decisions behind modern power systems.