Transformers: Construction and Operation

Why it matters

Transformers are crucial in electrical power systems for stepping up or stepping down voltage levels, enabling efficient power transmission over long distances. They are widely used in various applications, from power generation to distribution and utilization in industries and households.

Key ideas

• Basic Structure: A transformer consists of two or more windings (primary and secondary) wound on a magnetic core. The core is typically made of laminated silicon steel to minimize eddy current losses.
• Working Principle: Transformers operate on the principle of electromagnetic induction. When an alternating current flows through the primary winding, it creates a magnetic field that induces a voltage in the secondary winding.
• Types of Transformers: Based on construction, transformers can be classified into core-type and shell-type. Core-type transformers have windings surrounding the core, while shell-type transformers have the core surrounding the windings.
• Cooling Methods: Transformers can be air-cooled, oil-cooled, or use other cooling methods to dissipate heat generated during operation.
• Efficiency and Losses: Efficiency depends on rating, loading, power factor and design; do not assume a universal range. Losses occur due to winding resistance (copper losses) and core losses (hysteresis and eddy current losses).

Formulas

• V_p / V_s = N_p / N_s
  • V_p: Primary voltage (Volts)
  • V_s: Secondary voltage (Volts)
  • N_p: Number of turns in the primary winding
  • N_s: Number of turns in the secondary winding
• P_in = P_out + Losses
  • P_in: Input power (Watts)
  • P_out: Output power (Watts)
  • Losses: Total losses (Watts)

The voltage/turns ratio is ideal (or an induced-emf ratio); loaded terminal voltages include winding and leakage drops. Transformers require time-varying flux; a steady DC source does not sustain normal transformer action.

Worked example

Given:

• Primary voltage, V_p = 230 V
• Secondary voltage, V_s = 115 V
• Primary turns, N_p = 1000

Find: Number of turns in the secondary winding, N_s.

1. Use the formula for the turns ratio: V_p / V_s = N_p / N_s
2. Substitute the given values: 230 / 115 = 1000 / N_s
3. Solve for N_s: N_s = 1000 * (115 / 230)
4. Calculate: N_s = 500

Answer: The number of turns in the secondary winding is 500.

Common mistakes

• Confusing the primary and secondary windings, leading to incorrect calculations of voltage or turns ratio.
• Ignoring core losses and only considering copper losses when calculating efficiency.
• Forgetting to convert units, especially when dealing with power and voltage levels.

For GATE EE

Questions on this topic often involve calculating the turns ratio, efficiency, and losses in transformers. Practicing problems on different transformer types and cooling methods can be beneficial.

Quick check

1. What is the primary function of a transformer?
2. Name two types of transformer constructions.
3. What factors affect transformer efficiency?

Answers: 1. To step up or step down voltage levels. 2. Core-type and shell-type. 3. Loading, power factor, core loss, winding loss and design.