Short Answer:

The torque-angle characteristic of a synchronous machine shows the relationship between the electromagnetic torque produced and the angle (δ) between the rotor magnetic field and the stator magnetic field. This angle is known as the torque angle or power angle.

As the angle increases, the torque also increases, reaching a maximum when the angle is 90 degrees. Beyond this point, torque starts to decrease, and the machine may lose synchronism. This characteristic helps in understanding the machine’s stability and power handling capability during operation.

Detailed Explanation:

Torque-angle characteristics of a synchronous machine

The torque-angle characteristic is a vital concept in synchronous machines, whether operating as motors or generators. It shows how the electromagnetic torque varies with the angle between the rotor and stator magnetic fields. This angle is known as the torque angle (δ) or power angle.

In synchronous machines, the rotor field is produced by DC excitation, while the stator field is created by the three-phase AC supply. These two magnetic fields must remain synchronized for the machine to operate steadily. The angle between them determines the torque developed by the machine.

1. Definition of Torque Angle (δ):

The torque angle (δ) is the angle by which the rotor magnetic field lags or leads the stator magnetic field. In a synchronous motor, the rotor lags behind the stator field, while in a synchronous generator, the rotor leads the stator field.

This angle is small under light load and increases with load. It reflects the load condition and directly influences the torque developed by the machine.

2. Torque-Angle Relationship:

The electromagnetic torque (Te) developed in a cylindrical rotor synchronous machine is given by:

Te ∝ sin(δ)

This means:

• When δ = 0°, sin(δ) = 0 → No torque
• When δ = 90°, sin(δ) = 1 → Maximum torque
• When δ > 90°, torque begins to decrease, and the machine may become unstable

This curve (a sine wave up to 180°) represents the torque-angle characteristic. In normal operation, the machine is kept well below δ = 90° to maintain stability.

3. Importance of Torque-Angle Characteristic:

• Stability:
  The curve shows that synchronous machines can operate stably only when the torque angle is less than 90°. If the angle increases too much, the machine may fall out of synchronism.
• Load Handling:
  As the load increases, δ increases. This characteristic helps determine how much load the machine can safely carry before reaching the stability limit.
• Power Transfer Capability:
  In generators connected to a power system, the amount of power delivered depends on the torque angle. The torque-angle curve shows the maximum power transfer point.

4. Practical Considerations:

In real machines, especially those with salient poles, the torque expression is more complex and includes both synchronous reactance torque and reluctance torque. But the general shape of the curve remains the same: torque increases with angle up to a peak and then falls.

• For non-salient pole (cylindrical) machines: Te ∝ sin(δ)
• For salient pole machines: Te = A·sin(δ) + B·sin(2δ)

But in both cases, torque is maximum at a specific δ and then reduces, showing the limits of machine stability.

5. Applications of Torque-Angle Curve:

• Used in power system stability studies
• Helps in designing protection systems for generators
• Guides control systems in motor drive applications
• Essential in synchronizing machines with the grid

Conclusion:

The torque-angle characteristic of a synchronous machine describes how the developed torque changes with the angle between the rotor and stator fields. It is crucial for understanding machine performance under different load conditions. The torque increases with the angle, reaches a maximum, and then decreases, highlighting the need to operate within stable limits. This characteristic is important for machine design, control, and system stability.