Question

The Swing Equation describes the relationship between:

• A. Voltage and Current
• B. Power Angle and Rotor Dynamics
• C. Fault Current and Time
• D. Real Power and Reactive Power

Hint:

The Swing Equation is often written in terms of the inertia constant \(H\):
\[ \frac{H}{\pi f} \frac{d^2\delta}{dt^2} = P_m - P_e \quad \text{(in per-unit)} \]
This equation forms the basis for transient stability calculations, such as the Equal Area Criterion.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the physical variables linked by the Swing Equation in power system stability studies.

Step 2: Key Formula or Approach:
The Swing Equation is a non-linear second-order differential equation that models the rotor dynamics of a synchronous machine during disturbances:
\[ M \frac{d^2\delta}{dt^2} = P_m - P_e \] where:
- \(M\) is the angular momentum of the rotor.
- \(\delta\) is the rotor power angle.
- \(P_m\) is the mechanical power input to the generator shaft.
- \(P_e\) is the electromagnetic active power output delivered to the system.

Step 3: Detailed Explanation:

• Under normal steady-state operation, the mechanical power input \(P_m\) is exactly equal to the electrical power output \(P_e\), resulting in zero rotor acceleration (\(\frac{d^2\delta}{dt^2} = 0\)), and the rotor rotates at synchronous speed.

• When a disturbance occurs (e.g., a short-circuit fault, line tripping, or sudden load change), a power imbalance (\(P_m \neq P_e\)) is created.

• This net unbalanced power causes the rotor to accelerate or decelerate according to Newton's second law of motion for rotating bodies.

• The Swing Equation mathematically describes how this acceleration affects the rotor angle \(\delta\) (power angle) as a function of time \(t\).

• Tracking the swing curve (\(\delta\) vs \(t\)) is essential to determine whether the machine will remain in synchronism (transiently stable) or lose synchronization.

• Thus, the Swing Equation directly relates the power angle (\(\delta\)) to the physical rotor dynamics.

Step 4: Final Answer:
The Swing Equation describes the relationship between power angle and rotor dynamics.