The angle $$\delta $$ in the swing equation of a synchronous generator is the

In the following network, the voltage magnitudes at all buses are equal to $$1$$ p.u., the voltage phase angles are very small, and the line resistance are negligible. All the line reactances are equal to $$j1\Omega .$$

The voltage phase angles in rad at buses $$2$$ and $$3$$ are

For a power system network with $$n$$ nodes, $${Z_{33}}$$ of its bus impedance matrix is $$j0.5$$ per unit. The voltage at mode $$3$$ is $$1.3\angle - {10^0}\,\,$$ per unit. If a capacitor having reactance of $$-j3.5$$ per unit is now added to the network between node $$3$$ and the reference node, the current drawn by the capacitor per unit as

In the following network, the voltage magnitudes at all buses are equal to $$1$$ p.u., the voltage phase angles are very small, and the line resistance are negligible. All the line reactances are equal to $$j1\Omega .$$

If the base impedance and the line-to-line base voltage are $$100\Omega $$ and $$\,100kV,\,\,$$ respectively, then the real power in MW delivered by the generator connected at the slack bus is