GATE EE 2016 Question Paper (07-Feb-2016) (Shift 2)

A three-phase Voltage Source Inverter (VSI) as shown in the figure is feeding a delta connected resistive load of $30\Omega /phase$. If it is fed from a $600V$ battery, with $180^o$ conduction of solid-state devices, the power consumed by the load, in $kW$, is __________.

A DC-DC boost converter, as shown in the figure below, is used to boost $360V$ to $400V$, at a power of $4kW$. All devices are ideal. Considering continuous inductor current, the rms current in the solid state switch (S), in ampere, is _________.

A single-phase bi-directional voltage source converter (VSC) is shown in the figure below. All devices are ideal. It is used to charge a battery at $400V$ with power of $5kW$ from a source $V_s=220V$ (rms), $50Hz$ sinusoidal AC mains at unity p.f. If its AC side interfacing inductor is $5mH$ and the switches are operated at 20 kHz, then the phase shift $\left(\delta \right)$ between AC mains voltage $\left(V_s\right)$ and fundamental AC rms VSC voltage $\left(V_{C1}\right)$, in degree, is _________.

Consider a linear time invariant system $\dot{x}=Ax$ with initial condition $x\left(0\right)$ at $t=0$. Suppose $\alpha$ and $\beta$ are eigenvectors of $\left(2\times 2\right)$ matrix A corresponding to distinct eigenvalues ${\lambda }_{1}and{\lambda }_2$ respectively. Then the response $x\left(t\right)$ of the system due to initial condition $x\left(0\right)=\alpha$ is

A second-order real system has the following properties:

The damping ratio $\xi =0.5$ and undamped natural frequency ${\omega }_n=10rad/s$, the steady state value at zero is 1.02.

The transfer function of the system is