A dc distribution system is shown in figure with load currents as marked. The two ends of the feeder are fed by voltage sources such that $${V_P} - {V_Q} = 3V.$$ the value of the voltage $${V_P}$$ for a minimum voltage of $$220$$ $$V$$ at any point along the feeder is

A surge of 20 kV magnitude travels along a lossless cable towards its junction with two identical lossless overhead transmission lines. The inductance and the capacitance of the cable are 0.4 mH and 0.5 $$\mu F$$ per km. The inductance and capacitance of the overhead transmission lines are 1.5 mH and 0.015 $$\mu F$$ per km. The magnitude of the voltage at the junction due to surge is

In a transmission line each conductor is at $$20$$ $$kV$$ and is supported by a string of $$3$$ suspension insulators. The air capacitance between each cap-pin junction and tower is one-fifth of the capacitance $$C$$ of each insulation unit. A guard ring, effective only over the line-end insulator unit is fitted so that the voltages on the two units nearest the line-end are equal.

(a) Calculate the voltage on the line-end unit.
(b) Calculate the value of capacitance $${C_x}$$ required.

Incremental fuel costs (in some appropriate unit) for a power plant consisting of three generating units are
$${\rm I}{C_1} = 20 + 0.3\,\,{P_1},\,{\rm I}{C_2} = 30 + 0.4\,\,{P_2},\,{\rm I}{C_3} = 30$$
Assume that all the three units are operating all the time. Minimum and maximum loads on each unit are $$50$$ $$MW$$ and $$300$$ $$MW$$ respectively. If the plant is operating on economic load dispatch to supply the total power demand of $$700$$ $$MW$$, the power generated by each unit is