A factory takes a steady load of 200 kW at a lagging power factor of 0...
Peak load of factory, P = 200 kW
Original power factor, cosϕ1=0.8lagging
Max. demand charges, x = Rs. 100/kVA/annum
Charges on phase advancing plant are
y=Rs.500×0.1=Rs.50/kVAR/annum
Most economical p.f.,
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A factory takes a steady load of 200 kW at a lagging power factor of 0...
Most economical power factor for the factory is 0.866 lag.
Given data:
- Load = 200 kW
- Power factor (lagging) = 0.8
- 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 determine the most economical power factor, we need to compare the costs associated with different power factors. The total cost can be divided into two parts: the cost of maximum demand and the cost of energy consumption.
1. Cost of maximum demand:
The cost of maximum demand is given by the tariff, which is Rs. 100 per kVA of maximum demand per annum. The maximum demand is calculated using the formula:
Maximum demand (kVA) = Load (kW) / Power factor
Let's calculate the cost of maximum demand for the given power factor of 0.8:
Maximum demand (kVA) = 200 kW / 0.8 = 250 kVA
Cost of maximum demand = 250 kVA * Rs. 100/kVA = Rs. 25,000
Now, let's calculate the cost of maximum demand for a power factor of 0.866 lag:
Maximum demand (kVA) = 200 kW / 0.866 = 230.94 kVA
Cost of maximum demand = 230.94 kVA * Rs. 100/kVA = Rs. 23,094
2. Cost of energy consumption:
The cost of energy consumption is given by the tariff, which is 5 paise per kWh. The energy consumption can be calculated using the formula:
Energy consumption (kWh) = Load (kW) * Time
Let's assume the time is 1 year. The cost of energy consumption for the given power factor of 0.8 can be calculated as:
Energy consumption (kWh) = 200 kW * 1 year = 200 kWh
Cost of energy consumption = 200 kWh * 5 paise/kWh = Rs. 10
Now, let's calculate the cost of energy consumption for a power factor of 0.866 lag:
Energy consumption (kWh) = 200 kW * 1 year = 200 kWh
Cost of energy consumption = 200 kWh * 5 paise/kWh = Rs. 10
3. Total cost:
The total cost is the sum of the cost of maximum demand and the cost of energy consumption.
For the power factor of 0.8:
Total cost = Cost of maximum demand + Cost of energy consumption
= Rs. 25,000 + Rs. 10
= Rs. 25,010
For the power factor of 0.866 lag:
Total cost = Cost of maximum demand + Cost of energy consumption
= Rs. 23,094 + Rs. 10
= Rs. 23,104
Comparing the total costs, we can see that the most economical power factor is 0.866 lag (Option D) with a total cost of Rs. 23,104.