Angular Displacement Of Machine Under Power System Stability Calculator

Formula Used:

\[ \delta_a = \theta_m - \omega_s \times t \]

Angular Displacement of Rotor (θm):

Radian

Synchronous Speed (ωs):

Meter per Second

Time of Angular Displacement (t):

Second

Angular Displacement of Machine (δa):

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1. What is Angular Displacement of Machine?

Angular Displacement of Machine is defined as the change in the angular position of its rotating through a specified axis. It is a crucial parameter in power system stability analysis, particularly for generators and motors.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \delta_a = \theta_m - \omega_s \times t \]

Where:

\( \delta_a \) — Angular Displacement of Machine (Radian)
\( \theta_m \) — Angular Displacement of Rotor (Radian)
\( \omega_s \) — Synchronous Speed (Meter per Second)
\( t \) — Time of Angular Displacement (Second)

Explanation: This formula calculates the angular displacement of a machine by subtracting the product of synchronous speed and time from the angular displacement of the rotor.

3. Importance in Power System Stability

Details: Angular displacement monitoring is essential for maintaining power system stability. It helps in analyzing rotor angle stability and preventing system collapse during disturbances.

4. Using the Calculator

Tips: Enter angular displacement of rotor in radians, synchronous speed in meters per second, and time in seconds. All values must be non-negative.

5. Frequently Asked Questions (FAQ)

Q1: What is synchronous speed in power systems?
A: Synchronous speed is the speed at which the magnetic field rotates in synchronous machines, determined by the system frequency and number of poles.

Q2: Why is angular displacement important for generators?
A: It indicates the relative position of the rotor with respect to the rotating magnetic field, affecting power output and system stability.

Q3: What units should be used for input values?
A: Angular displacement in radians, synchronous speed in meters per second, and time in seconds for consistent results.

Q4: Can this calculator be used for motor applications?
A: Yes, the same principles apply to both generators and motors in power system stability analysis.

Q5: What does a negative angular displacement indicate?
A: A negative value may indicate that the machine is operating below synchronous speed or experiencing deceleration.