A single-phase full bridge inverter fed by a 325 V DC produces a symmetric quasi-square waveform across " $a b$ " as shown. To achieve a modulation index of 0.8 , the angle $\theta$ expressed in degrees should be $\_\_\_\_$ . (Round off to 2 decimal places)

(Modulation index is defined as the ratio of the peak of the fundamental component of $V_{d b}$ to the applied DC value)

Consider the buck-boost converter shown. Switch $Q$ is operating at 25 kHz and 0.75 duty-cycle. Assume diode and switch to be ideal. Under steady-state condition, the average current flowing through the inductor is $\_\_\_\_$ A.

Two generators have cost functions $F_1$ and $F_2$. Their incremental-cost characteristics are

$$ \frac{d F_1}{d P_1}=40+0.2 P_1 \text { and } \frac{d F_2}{d P_2}=32+0.4 P_2 $$

They need to deliver a combined load of 260 MW . Ignoring the network losses, for economic operation, the generations $P_1$ and $P_2$ (in MW) are

A 3-bus network is shown. Consider generators as ideal voltage sources. If rows 1,2 and 3 of the $Y_{h s}$ matrix correspond to bus 1,2 and 3 respectively, then $Y_{h s}$ of the network is