The single line diagram of a lossless system is shown in the figure. The system is operating in steady-state at a stable equilibrium point with the power output of the generator being \( P_{max} \sin \delta \), where \( \delta \) is the load angle and the mechanical power input is \( 0.5 P_{max} \). A fault occurs on line 2 such that the power output of the generator is less than \( 0.5 P_{max} \) during the fault. After the fault is cleared by opening line 2, the power output of the generator is \( \frac{P_{max}}{\sqrt{2}} \sin \delta \). If the critical fault clearing angle is \( \pi/2 \) radians, the accelerating area on the power angle curve is _________________ times \( P_{max} \) (rounded off to 2 decimal places).
Two units, rated at 100 MW and 150 MW, are enabled for economic load dispatch. When the overall incremental cost is 10,000 Rs./MWh, the units are dispatched to 50 MW and 80 MW respectively. At an overall incremental cost of 10,600 Rs./MWh, the power output of the units are 80 MW and 92 MW, respectively. The total plant MW-output (without overloading any unit) at an overall incremental cost of 11,800 Rs./MWh is ______________ (round off to the nearest integer). }
Consider the state-space model
\[ \dot{\mathbf{x}}(t) = A \mathbf{x}(t) + B r(t), \quad y(t) = C \mathbf{x}(t) \]
where \( \mathbf{x}(t) \), \( r(t) \), and \( y(t) \) are the state, input, and output, respectively. The matrices \( A \), \( B \), and \( C \) are given below:
\[ A = \begin{bmatrix} 0 & 1 \\ -2 & -3 \end{bmatrix}, \quad B = \begin{bmatrix} 0 \\ 1 \end{bmatrix}, \quad C = \begin{bmatrix} 1 & 0 \end{bmatrix} \]
The sum of the magnitudes of the poles is ____________ (round off to the nearest integer).
The steady-state capacitor current of a conventional DC–DC buck converter operating in continuous conduction mode (CCM) is shown over one switching cycle. If the input voltage is \(30\,\text{V}\), the value of the inductor used (in mH) is ____________ (rounded off to one decimal place). 
In an experiment to measure the active power drawn by a single-phase RL Load connected to an AC source through a \(2\,\Omega\) resistor, three voltmeters are connected as shown in the figure below. The voltmeter readings are as follows: \( V_{{Source}} = 200\,{V}, \quad V_R = 9\,{V}, \quad V_{{Load}} = 199\,{V}. \) Assuming perfect resistors and ideal voltmeters, the Load-active power measured in this experiment, in W, is ___________ (round off to one decimal place). 