Assuming δ to be in electrical degrees, the swing equation is given by the expression:

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Assuming δ to be in electrical degrees, the swing equation is given by the expression:

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\(\frac{\mathrm{H}}{180 \mathrm{f}_{0}} \frac{\mathrm{~d} \delta}{\mathrm{dt}}=\mathrm{P}_{\mathrm{m}}-\mathrm{P}_{\mathrm{e}} \)
\(\frac{\mathrm{H}}{180 \mathrm{f}_{0}} \frac{\mathrm{~d}^{2} \delta}{\mathrm{dt}^{2}}=\mathrm{P}_{\mathrm{m}}-\mathrm{P}_{\mathrm{e}} \)
\(\frac{\mathrm{H}}{180 \mathrm{f}_{0}} \frac{\mathrm{~d}^{2} \delta}{\mathrm{dt}^{2}}=\mathrm{P}_{\mathrm{e}}-\mathrm{P}_{\mathrm{m}} \)
\(\frac{\mathrm{H}}{180 \mathrm{f}_{0}} \frac{\mathrm{d} \delta}{\mathrm{dt}}=\mathrm{P}_{\mathrm{e}}-\mathrm{P}_{\mathrm{m}} \)

Answer 1

Concept:

The swing equation is a second-order differential equation that describes the rotor angle dynamics of a synchronous machine. It is derived from Newton’s second law applied to rotational motion. The general form of the swing equation is:

\[ \frac{H}{180f} \frac{d^2 \delta}{dt^2} = P_m - P_e \]

Where:

H = Inertia constant (in MJ/MVA)
f = System frequency (Hz)
δ = Rotor angle in electrical degrees
P_m = Mechanical input power
P_e = Electrical output power

The equation reflects the accelerating power acting on the rotor as the difference between mechanical and electrical power.

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Assuming δ to be in electrical degrees, the swing equation is given by the expression:

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