Correct Answer - Option 3 : 120

**Swing Equation:**

A power system consists of a number of synchronous machines operating synchronously under all operating conditions.

The equation describing the relative motion is known as the swing equation, which is a non-linear second-order differential equation that describes the swing of the rotor of a synchronous machine.

The transient stability of the system can be determined with the help of the swing equation.

\(M\frac{{{d^2}\delta }}{{d{t^2}}} = {P_a} = {P_s} - {P_e}\)

Where P_{i} is the mechanical power input

P_{e} is the electrical power output

P_{a} is the accelerating power

δ is the angular acceleration

M is the angular momentum of the rotor

**Application:**

Given,

G = 150 MVA

H = 12 MJ/MVA

f = 60 Hz

P_{i} - P_{e} = P_{a} = 80 - 60 = 20 MW

Store Energy = GH = (150 MVA) × (12 MJ/MVA) = 1800 MJ

Using the above formula,

\(M\frac{d^2\delta}{dt^2}=P_i-P_e=P_a\) ---(1)

As, M = \(\frac{GH}{180f}\) = \(\frac{1800}{180\times 60}=\frac{1}{6}\) MJ.sec/elect.deg

From equation (1),

\(\frac{d^2\delta}{dt^2}=\frac{P_a}{M}=\frac{20\ M}{1/6M}=120\) elect.deg./sec

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