1. What should be the kVA rating of a capacitor which would raise the power factor of load of 100 kW from 0-5 lagging to 0-9 lagging? [125 kVA] 2. A 3-phase, 50 Hz, 3300 V star connected induction motor develops 250 H.P. (186-5 kW), the power factor being 0-707 lagging and the efficiency 0-86. Three capacitors in delta are connected across the supply terminals and power factor raised to 0-9 lagging. Calculate: (i) the KVAR rating of the capacitor bank. (ii) the capacitance of each unit. [(t) 111.8 kVAR (ii) 10.9 µF] 3. A 3-phase, 50 Hz, 3000 V motor develops 600 H.P. (447-6 kW), the power factor being 0-75 lagging and the efficiency 0.93. A bank of capacitors is connected in delta across the supply terminals and power factor raised to 0.95 lagging. Each of the capacitance units is built of five similar 600-V capacitors. Determine the capacitance of each capacitor. [156 μF] 4. A factory takes a load of 800 kW at 0-8 p.f. (lagging) for 3000 hours per annum and buys energy on tariff of Rs 100 per kVA plus 10 paise per kWh. If the power factor is improved to 0-9 lagging by means of capacitors costing Rs 60 per kVAR and having a power loss of 100 W per kVA, calculate the annual saving effected by their use. Allow 10% per annum for interest and depreciation on the capacitors. [Rs 3972] 5. A station supplies 250 kVA at a lagging power factor of 0-8. A synchronous motor is connected in parallel with the load. If the combined load is 250 kW with a lagging p.f. of 0.9, determine: (i) the leading kVAR taken by the motor. (ii) kVA rating of the motor. (iii) p.f. at which the motor operates. 6. A generating station supplies power to the following: (i) a lighting load of 100 kW; [(1) 28-9 KVAR (i) 57-75 kVA (m) 0-866 lead] (ii) an induction motor 800 h.p. (596-8 kW) p.f. 0.8 lagging, efficiency 92%; (iii) a rotary converter giving 150 A at 400 V at an efficiency of 0.95. What must be the power factor of the rotary convertor in order that power factor of the supply station may become unity? [0-128 leading] 7. A 3-phase, 400 V synchronous motor having a power consumption of 50 kW is connected in parallel with an induction motor which takes 200 kW at a power factor of 0-8 lagging. (i) Calculate the current drawn from the mains when the power factor of the synchronous motor is unity. Power Factor Improvement 117 (ii) At what power factor should the synchronous motor operate so that the current drawn from the mains is minimum. ? 8. A factory load consists of the following: [(i) 421 A (ii) 0-316 leading] (i) an induction motor of 150 h.p. (111-9 kW) with 0-7 p.f. lagging and 80% efficiency; (ii) a synchronous motor of 100 h.p. (74-6 kW) with 0-85 p.f. leading at 90% efficiency; (iii) a lighting load of 50 kW. Find the annual electric charges if the tariff is Rs 100 per annum per kVA maximum demand plus 7 paise per kWh ; assuming the load to be steady throughout the year. [Rs 1,96,070] 9. A 3-phase synchronous motor having a mechanical load (including losses) of 122 kW is connected in parallel with a load of 510 kW at 0-8 p.f. lagging. The excitation of the motor is adjusted so that the kVA input to the motor becomes 140 kVA. Determine the new power factor of the whole system. [0-8956 lagging] 10. A 3-phase synchronous motor is connected in parallel with a load of 700 kW at 0-7 power factor lagging and its excitation is adjusted till it raises the total p.f. to 0.9 lagging. Mechanical load on the motor including losses is 150 kW. Find the power factor of the synchronous motor. [0-444 leading]