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 Pi is the mechanical power input
Pe is the electrical power output
Pa 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
Pi - Pe = Pa = 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
2