The operating characteristic of a reactance relay is given by $X \leq 1 \Omega$, where $X$ is the reactance calculated by the relay. Its operating characteristic in the admittance plane (G-B plane, where G and B denote conductance and sustenance, respectively, expressed in $\mho$ ) is given by:

A $$3$$-phase transformer rated for $$33 kV/11kV$$ is connected in delta/star as shown in figure. The current transformers $$\left( {C{T_s}} \right)$$ on low and high voltage sides have a ratio of $$500/5.$$ Find the currents $${i_1}$$ and $${i_2}$$, if the fault current is $$300$$ $$A$$ as shown in figure.

The over current relays for the line protection and loads connected at the buses are shown in the figure.

The relays are IDMT is natural having the characteristic
$${t_{op}} = {{0.14\, \times \,time\,\,multiplier\,\,setting} \over {{{(plug\,\,setting\,\,multiplier)}^{0.02}} - 1}}$$
The maximum and minimum fault current at bus $$B$$ are $$2000A$$ and $$500$$ $$A$$ respectively. Assuming the time multiplier setting and plug setting for relay $${R_B}$$ to be $$0.1$$ and $$5$$ $$A$$ respectively, the operating time of $${R_B}$$ (in seconds) is __________.

Consider a stator winding of an alternator with an internal high resistance ground fault. The currents under the fault condition are as shown in the figure. The winding is protected using a differential current scheme with current transformers of ratio $$400/5$$ $$A$$ as shown. The current through the operating coil is