Consider the protection system shown in the figure below. The circuit breakers numbered from $$1$$ to $$7$$ are of identical type. A single line to ground fault with zero fault impedance occurs at the midpoint of the line (at point F), but circuit breaker $$4$$ fails to operate (''Stuck breaker''). If the relays are coordinated correctly, a valid sequence of circuit breaker operation is b

Suppose we define a sequence transformation between ''a-b-c'' and ''p-n-0''' variables as follows:
$$\left[ {\matrix{ {{f_a}} \cr {{f_b}} \cr {{f_c}} \cr } } \right] = k\left[ {\matrix{ 1 & 1 & 1 \cr {{\alpha ^2}} & \alpha & 1 \cr \alpha & {{\alpha ^2}} & 1 \cr } } \right]\left[ {\matrix{ {{f_p}} \cr {{f_n}} \cr {{f_o}} \cr } } \right]$$ where $$\,\alpha = {e^{j{{2\pi } \over 3}}}\,\,$$ and $$k$$ is a constant
Now, if it is given that:
$$\left[ {\matrix{ {{V_p}} \cr {{V_n}} \cr {{V_o}} \cr } } \right] = k\left[ {\matrix{ {0.5} & 0 & 0 \cr 0 & {0.5} & 0 \cr 0 & 0 & {2.0} \cr } } \right]\left[ {\matrix{ {{i_p}} \cr {{I_n}} \cr {{i_o}} \cr } } \right]\,\,$$ and $$\left[ {\matrix{ {{V_a}} \cr {{V_b}} \cr {{V_c}} \cr } } \right] = z\left[ {\matrix{ {{i_a}} \cr {{I_b}} \cr {{i_c}} \cr } } \right]\,\,$$ then,

Consider the transformer connections in a part of a power system shown in the figure. The nature of transformer connections and phase shifts are indicated for all but one transformer. Which of the following connections, and the corresponding phase shift $$\theta ,$$ should be used for the transformer between $$A$$ and $$B$$?

$$230$$ $$V$$ (phase) $$50$$ Hz, three-phase, $$4$$-wire, system has a sequence $$ABC$$. A unity power-factor load of $$4$$ kW is connected between phase A and neutral $$N$$. It is desired to achieve zero neutral current through the use of a pure inductor and pure capacitor in the other two phases. The Value of inductor and capacitor is......