A. 10 degreeB. 30 degreeC. 70 degreeD. 80 degreeAnswer: B. 30 degreeExplanation: For stable operation, the maximum angle of torque angle is 90° i.e. 0 < δ < 90°. But in practical stable systems, the normal value of ‘δ’ lies between 0 to 30°.- In a synchronous generator, the magnetic field rotates at synchronous speed and the rotating magnetic field is created in the stator. These two fields are not fully aligned. The stator field lags the rotating field. This lagging angle is called a load angle or torque angle or power angle. It is denoted by ‘δ’.
- For stability and economic reasons, we operate the transmission line with a power angle in the range of 30° to 45°
- In an unstable system, δ increases indefinitely with time, and the machine loses synchronism.
Important Points:
Equal Area Criteria:- The equal-area criterion is a simple graphical method for concluding the transient stability.
- This principle does not require the swing equation for the determination of stability conditions.
- The stability conditions are recognized by equating the areas of segments on the power angle diagram.
- Starting with the swing equation:
- Where,
- M is the moment of inertia or angular momentum
- δ is the power angle between rotor rotating field and stator rotating field
- Ps is a mechanical input power
- Pe is the electrical output
- Multiply the above equation with dδ / dt
- we get,
- Rearranging, multiplying by dt, and integrating, we have
- At steady-state condition, the torque angle was not changing i.e. before the disturbance.
- dδ / dt = 0
- Also, if the system has transient stability the machine will again operate at synchronous speed after the disturbances, i.e.,
- dδ /dt = 0
- Hence the condition for stability is dδ / dt =0
A. 10 degree
B. 30 degree
C. 70 degree
D. 80 degree
Answer: B. 30 degree
Explanation:
For stable operation, the maximum angle of torque angle is 90° i.e. 0 < δ < 90°. But in practical stable systems, the normal value of ‘δ’ lies between 0 to 30°.
- In a synchronous generator, the magnetic field rotates at synchronous speed and the rotating magnetic field is created in the stator. These two fields are not fully aligned. The stator field lags the rotating field. This lagging angle is called a load angle or torque angle or power angle. It is denoted by ‘δ’.
- For stability and economic reasons, we operate the transmission line with a power angle in the range of 30° to 45°
- In an unstable system, δ increases indefinitely with time, and the machine loses synchronism.
- The equal-area criterion is a simple graphical method for concluding the transient stability.
- This principle does not require the swing equation for the determination of stability conditions.
- The stability conditions are recognized by equating the areas of segments on the power angle diagram.
- Starting with the swing equation:
- Where,
- M is the moment of inertia or angular momentum
- δ is the power angle between rotor rotating field and stator rotating field
- Ps is a mechanical input power
- Pe is the electrical output
- Multiply the above equation with dδ / dt
- we get,
- Rearranging, multiplying by dt, and integrating, we have
- At steady-state condition, the torque angle was not changing i.e. before the disturbance.
- dδ / dt = 0
- Also, if the system has transient stability the machine will again operate at synchronous speed after the disturbances, i.e.,
- dδ /dt = 0
- Hence the condition for stability is dδ / dt =0