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7. A factory has an average demand of 520 000 units per week.

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7. A factory has an average demand of 520 000 units per week. The maximum demand is 25 MVA at 0.8 power factor and the minimum power factor of 0.6 occurs when the demand is 11 MVA. The factory is charged at 2.5 pence per unit with a surcharge of 0.2 pence per unit for each 500 kW by which the maximum demand exceeds 18 MW and a further surcharge of 3% (of charge, plus surcharge) for every increment of 0.05 by which the minimum power factor falls below 0.8. There is a large drive which operates continuously and is powered by an induction motor with draws 2 MW at a power factor of 0.8 lagging. This motor is replaced by a synchronous motor which draws the same power but runs at a power factor of 0.8 leading. Assuming the maximum demand penalty does not change (i) Show that the maximum demand power is 20 MW. (ii) Show that the total weekly charge for the factory is £19 219.20. (iii) Calculate the new power factor and reactive penalty charge when demand is 11 MVA. (iv) Show that the new total weekly cost is £17 644.50. (v) If the synchronous motor costs £250 000, calculate the time required to recover the cost of the motor.

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