3. (i) A medium-sized clothing factory takes its supply at low voltage and has t
ID: 2080443 • Letter: 3
Question
3.
(i) A medium-sized clothing factory takes its supply at low voltage and has the following meter readings for the month of September.
MD (day) 428 kW
MD (night) 87
kW kWh (day) 72180
kWh (night) 10060
If the average power factor is 0.843,
find the bill for the month, using the supplier's tariff shown below.
(ii) A large continuous process foundry works a night shift and takes its supply at high voltage.
For the month of December the following meter readings are recorded.
MD (day) 1792 kW
(night) 1607kW Units
(day) 224368 kWh
(night) 289560 kWh Reactive
(day)131140 kVArh
(night) 195510 kVarh
Chargeable Capacity 2123 kVA
Find the average power factor for the month and calculate the electricity bill.
The Maximum Authorised Capacity For High For Low under this tariff is 20 kVA Voltage Voltag Supply Availability Charge (Code 54) (Code 55) Per month for each of the first 20 kVA of charge capacity £2.55 £2.55 Per month for each KVA of chargeable capacity in excess of 20 kVA £0.75 £1.04 Demand Charge Per month for each of the first 750 kilowatts of maximum demand made in the month £1.36 £1.43 Per month for each of the next 3250 kilowatts of maximum demand made in the month £0.60 £1.36 Per month for each kilowatt of maximum demand £1.36 in excess of 4000 kilowatts made in the month £0.15 Plus per kilowatt of maximum demand made between 0730 and 2330 hours in each of the months mainly in November and March £3.82 £3.92 £7.33 December, January and February £7.46 The average power factor shall be measured at all Between 2330 and 0730 hours one kilowatt of maximum demand shall be deemed to be half of one kilowatt. Unit Charge For each unit supplied between 0730 and 2330 hours in the months of November to March inclusive 4.77p 5.11p For each unit supplied between 0730 and 2330 4.37p hours in the months of April to October inclusive 4.08p For each unit supplied between 2330 and 0730 2.50p 2.55p Reactive Kilovoltampere Hours Charge For each kVAnh supplied at any time in excess of 0.38p half the number of units supplied 0.59pExplanation / Answer
3)
i)
Maximum Demand Day P = 428 kW , S = P/power factor = 428/0.843 = 507.71 kVA
Maximum Demand Night P = 87 kW , S = P/power factor = 87/0.843 = 103.20 kVA
Total kVA Day+Night = 610.91 kVA
Availability Charge = E(20*2.55 + (610.91-20)*1.04) = E 665.54
Demand Charge = E (428 + (87/2))*1.43 = E 674.245
Unit Charge = E (72180*0.0437+ 10060*0.0255) = E 3410.796
Hours of operation in day time is = kWh/kW = 72180/428 = 168.64 h
Reactive units consumed is Q = P*tan(phi)*h = 428 * tan(32.54)*168.64 = 46056.32 kVarh
Excess Reactive units = 72180/2 - 46056.32
Hours of operation at night = 10060/87 = 115.63
Reactive units consumed at night is Q = 115.63 * 87 *tan(32.54) = 6418.80 kVarh
Excess reactive units = 10060/2 - 6418.80 = 1388.80 kVarh
kVar supplied is not given =E (9966.32*0.0059 + 1388.80*0.0059 ) = 66.99 British Pound
Total tariff to be paid in the month of september is = 665.54 + 674.245 + 3410.796 + 66.99 = 4817.571 British Pound
ii)
Maximum Demand Day = 1792 kW and Night = 1607kW
units Consumed Day = 224368 kWh and Night = 289560 kWh
Reactive units consumed Day = 131140 kVArh and Night = 195510 kVarh
Chargeable Capacity = 2123 kVA
Average Power factor of the month cos(phi) where phi = (tan- (Reactive units Day/Active units Day) + tan-(Reactive units Night/Active units Night))/2 = ( (tan- (131140/224368) + tan- (195510/289560) ) / 2 = (30.300 + 34.020)/2 = 32.160
Average power factor is cos(32.160) = 0.846
Tariff of Electric Energy consumed for the month of september is
= (2123 * 0.75 + 1792*1.36 + 803.5*1.36 + 224368 *0.0408 + 289560*0.025 + (131140 -112184) * 0.0038 + ( 195510 - 144780) * 0.0038)
= 1592.25 +2437.12 + 1092.76 + 9154.2144 + 7239 + 72.0328 + 192.774 = 21,780.1512 British Pound
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