Short Answer:

The efficiency of a synchronous machine is determined by comparing the output power to the input power. Efficiency is calculated using the formula:
Efficiency (%) = (Output Power / Input Power) × 100

To find this, both electrical input and mechanical output must be measured, along with different losses in the machine. Efficiency testing can be done using methods like direct loading, loss segregation, or retardation test, depending on whether the machine is working as a motor or generator.

Detailed Explanation:

Efficiency of a synchronous machine

The efficiency of a synchronous machine indicates how effectively it converts one form of energy into another—electrical to mechanical (motor) or mechanical to electrical (generator). Not all input energy is converted into useful output; some of it is lost as heat, friction, or magnetic losses. Knowing the efficiency helps improve performance, reduce losses, and ensure economic operation.

The general formula used is:

Efficiency (%) = (Output Power / Input Power) × 100

This means, the higher the useful output compared to the input, the better the efficiency.

1. Measuring Input and Output Power:

Depending on whether the synchronous machine is operating as a motor or generator, the input and output measurements differ:

• Synchronous Generator:
  • Input Power = Mechanical power supplied to the rotor shaft (measured by torque and speed)
  • Output Power = Electrical power delivered at the stator terminals (V × I × √3 × Power Factor)
• Synchronous Motor:
  • Input Power = Electrical power drawn from the supply (V × I × √3 × Power Factor)
  • Output Power = Mechanical power delivered at the shaft (Torque × Speed)

In both cases, additional instruments are needed such as voltmeters, ammeters, wattmeters, torque meters, and tachometers.

2. Accounting for Losses:

To get accurate efficiency, losses must be calculated. Major losses include:

• Stator (Armature) Copper Losses: Due to resistance in stator winding (I²R losses)
• Rotor (Field) Copper Losses: In field winding due to DC excitation
• Core (Iron) Losses: Due to hysteresis and eddy currents in stator core
• Mechanical Losses: Due to friction in bearings and air (windage losses)
• Stray Load Losses: Small additional losses from magnetic leakage and harmonics

Total Loss = Copper Losses + Iron Losses + Mechanical Losses + Stray Load Losses

Then:

Efficiency = [(Input Power – Total Losses) / Input Power] × 100

3. Methods of Determining Efficiency:

• Direct Loading Test:
  The machine is loaded directly, and input-output power is measured. Simple but not suitable for large machines due to energy waste.
• Swinburne’s Test (for motors):
  Losses are calculated during no-load run, and efficiency is predicted under load. Suitable for small DC machines, adapted versions for AC machines.
• Loss Segregation Method:
  Different losses are measured or estimated separately using open-circuit, short-circuit, and no-load tests, and total loss is found.
• Retardation Test:
  Used to calculate mechanical losses by observing the rate at which the motor slows down after power is cut off.
• Back-to-Back Test (Hopkinson’s Test):
  Used for large machines. Two identical machines are tested together, one as a motor and the other as a generator, minimizing energy waste.

4. Importance of Efficiency Measurement:

• Ensures machine is operating within safe and economical limits
• Helps in identifying faults or excessive losses
• Used in performance testing and rating of machines
• Supports decisions for upgrades or replacements
• Improves energy savings in power systems

Conclusion:

Efficiency of a synchronous machine is determined by measuring the input and output power, and calculating the losses. Several methods like direct loading or loss segregation are used depending on the machine size and application. Accurate efficiency evaluation ensures proper operation, better performance, and reduced energy waste in electrical systems.