A factory takes a steady load of 200 kW at a lagging power factor of 0...
Capacity of phase advancing plant
=P[tanϕ1-tanϕ2]
= 200[0.75 - 0.5774]
= 34.52 kVAR
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A factory takes a steady load of 200 kW at a lagging power factor of 0...
Given data:
Steady load = 200 kW
Power factor = 0.8 lagging
Tariff = Rs. 100 per kVA of maximum demand per annum + 5 paise per kWh
Cost of phase advancing plant = Rs. 500 per kVAR
Annual interest and depreciation = 10%
To calculate the capacity of the phase advancing plant, we need to follow the below steps:
Step 1: Calculate the apparent power (kVA) of the load
Apparent power (S) = Real power (P) / Power factor (cos Φ)
Here, P = 200 kW and cos Φ = 0.8 lagging
So, S = 200 / 0.8 = 250 kVA
Step 2: Calculate the maximum demand (MD) and energy consumption
MD = Apparent power (S) = 250 kVA
Energy consumption = Real power (P) x Time
Assuming 720 hours per month, energy consumption = 200 x 720 = 144000 kWh
Step 3: Calculate the annual cost of maximum demand
Annual cost of maximum demand = MD x Tariff
= 250 x Rs. 100 = Rs. 25000
Step 4: Calculate the annual cost of energy consumption
Annual cost of energy consumption = Energy consumption x Tariff
= 144000 x 0.05 = Rs. 7200
Step 5: Calculate the total annual cost
Total annual cost = Annual cost of maximum demand + Annual cost of energy consumption
= Rs. 25000 + Rs. 7200 = Rs. 32200
Step 6: Calculate the required kVAR of the phase advancing plant
Let the required kVAR of the phase advancing plant be x
Cost of the phase advancing plant = Rs. 500 per kVAR
Annual interest and depreciation = 10%
So, annual cost of the phase advancing plant = (x x 500) x 1.1
Equating the annual cost of the phase advancing plant to the total annual cost, we get:
(x x 500) x 1.1 = Rs. 32200
x = 34.52 kVAR
Hence, the capacity of the phase advancing plant is 34.52 kVAR (option C).