List of top Power Systems Questions on Power

Consider a distribution feeder, with \( R/X \) ratio of 5. At the receiving end, a 350 kVA load is connected. The maximum voltage drop will occur from the sending end to the receiving end, when the power factor of the load is: \[ {(round off to three decimal places).} \]

Let \( C \) be a clockwise oriented closed curve in the complex plane defined by \( |z| = 1 \). Further, let \( f(z) = jz \) be a complex function, where \( j = \sqrt{-1} \). Then, \[ \oint_C f(z)\, dz = \underline{{2cm}} \quad {(round off to the nearest integer)}. \] 

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).  

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).

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). 

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). }

During a power failure, a domestic household uninterruptible power supply (UPS) supplies AC power to a limited number of lights and fans in various rooms. As per a Newton-Raphson load-flow formulation, the UPS would be represented as a:
The input voltage \( v(t) \) and current \( i(t) \) of a converter are given by, \[ v(t) = 300 \sin(\omega t) \, {V} \] \[ i(t) = 10 \sin\left(\omega t - \frac{\pi}{6}\right) + 2 \sin\left(3\omega t + \frac{\pi}{6}\right) + \sin\left(5\omega t + \frac{\pi}{2}\right) \, {A} \] where \( \omega = 2\pi \times 50 \) rad/s. The input power factor of the converter is closest to:

In the following circuit, the average voltage \[ V_o = 400 \left(1 + \frac{\cos \alpha}{3} \right) {V}, \] where \( \alpha \) is the firing angle. If the power dissipated in the resistor is 64 W, then the closest value of \( \alpha \) in degrees is: 

Let \( C \) be a clockwise oriented closed curve in the complex plane defined by \( |z| = 1 \). Further, let \( f(z) = jz \) be a complex function, where \( j = \sqrt{-1} \). Then, \[ \oint_C f(z)\, dz = \underline{2cm} \quad \text{(round off to the nearest integer)}. \]

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). 

The steady state capacitor current of a conventional DC-DC buck converter, working in CCM, is shown in one switching cycle. If the input voltage is \( 30~{V} \), the value of the inductor used, in mH, is __________ (round off to one decimal place)

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).

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).