Synchronous Machines: Performance and Applications

Why it matters

Synchronous machines are crucial in power systems as they are primarily used for power generation and as motors in industrial applications. Understanding their performance and applications helps in optimizing energy efficiency and ensuring stable power supply.

Key ideas

• Synchronous Speed: The speed at which the magnetic field rotates, determined by the supply frequency and the number of poles.
• Power Factor: Synchronous machines can operate at leading, lagging, or unity power factor, making them versatile for power factor correction.
• Excitation Control: On a fixed-voltage, fixed-frequency bus, field current mainly adjusts reactive power within machine capability limits; mechanical input or load determines active power.
• Applications: Used in power plants as generators (alternators) and in industries as motors for constant speed applications.

Formulas

• Synchronous Speed: N_s = 120·f / P
  • N_s: Synchronous speed (RPM)
  • f: Frequency (Hz)
  • P: Number of poles
• Power Factor for sinusoidal voltage and current: PF = cos(φ)
  • PF: Power factor (dimensionless)
  • φ: Phase angle (radians)

Worked example

Given: A 4-pole synchronous machine connected to a 50 Hz supply.

1. Calculate the synchronous speed

   • Formula: N_s = 120·f / P
   • Calculation: N_s = 120·50 / 4 = 1500 RPM

2. Determine the power factor if the current lags voltage by 30°

   • Convert angle to radians: φ = 30° × π/180 = π/6
   • Formula: PF = cos(φ)
   • Calculation: PF = cos(π/6) = √3/2 ≈ 0.866

Final Answer: Synchronous speed is 1500 RPM; Power factor is 0.866 lagging.

Common mistakes

• Forgetting that rotor speed equals synchronous speed in stable steady operation.
• Mixing degree and radian calculator modes, or assuming cos(φ) alone identifies leading versus lagging current.
• Overlooking the effect of excitation on reactive power.

For GATE EE

Questions often involve calculating synchronous speed, power factor, and analyzing the effects of excitation changes. Practice problems on machine characteristics and their impact on power systems.

Quick check

1. What is the synchronous speed of a 6-pole machine on a 60 Hz supply?
2. How does excitation affect the power factor of a synchronous machine?
3. What is the primary application of synchronous generators?

Answers: 1. 1200 RPM 2. It controls reactive power, affecting power factor. 3. Power generation in power plants.