Question

An industrial consumer charged with the scheduled tariff of Rs.250 /kVA per month for maximum demand and 150 paisa per unit consumed for load factor of 60% and 80%. Find overall cost per unit at i) unity P.F. ii) 0.9 P.F. consider maximum demand of 50 kVA.

Answer 1

To solve this, we need to calculate the total cost of electricity consumption for an industrial consumer, considering the maximum demand (MD), load factor (LF), and power factor (PF) at different values.

Given Data:

1. Scheduled Tariff for Maximum Demand: Rs. 250 per kVA per month
   

1. Energy Charge (per unit): Rs. 150 paisa = Rs. 1.50 per unit
   

1. Load Factors: 60% and 80%
   

1. Maximum Demand (MD): 50 kVA
   

1. Power Factor (PF): First at unity (1), then at 0.9
   

1. 1 kVA = 1 kW for unity power factor, but this will vary depending on the power factor.
   

Step 1: Calculate Maximum Demand Charge

The maximum demand charge is based on the maximum demand in kVA.  
\[
\text{Maximum Demand Charge} = \text{Maximum Demand (MD)} \times \text{Tariff per kVA}
\]
\[
\text{Maximum Demand Charge} = 50 \, \text{kVA} \times 250 \, \text{Rs/kVA} = 12,500 \, \text{Rs/month}
\]

Step 2: Calculate Energy Consumption

For a given load factor, we can calculate the energy consumption in kWh per month using the formula:
\[
\text{Energy Consumption (kWh)} = \text{Maximum Demand (kVA)} \times \text{Load Factor} \times \text{Hours in a Month}
\]
Assuming there are 730 hours in a month:
\[
\text{Energy Consumption} = 50 \, \text{kVA} \times \text{Load Factor} \times 730 \, \text{hrs}
\]

For Load Factor 60% (LF = 0.6):
\[
\text{Energy Consumption} = 50 \, \text{kVA} \times 0.6 \times 730 \, \text{hrs} = 21,900 \, \text{kWh/month}
\]

For Load Factor 80% (LF = 0.8):
\[
\text{Energy Consumption} = 50 \, \text{kVA} \times 0.8 \times 730 \, \text{hrs} = 29,200 \, \text{kWh/month}
\]

Step 3: Calculate Energy Charge

The energy charge is given by the energy consumption (in kWh) multiplied by the unit charge.

For Load Factor 60%:
\[
\text{Energy Charge} = 21,900 \, \text{kWh} \times 1.50 \, \text{Rs/kWh} = 32,850 \, \text{Rs/month}
\]

For Load Factor 80%:
\[
\text{Energy Charge} = 29,200 \, \text{kWh} \times 1.50 \, \text{Rs/kWh} = 43,800 \, \text{Rs/month}
\]

Step 4: Total Monthly Cost

The total monthly cost is the sum of the maximum demand charge and the energy charge.

For Load Factor 60%:
\[
\text{Total Cost} = \text{Maximum Demand Charge} + \text{Energy Charge} = 12,500 \, \text{Rs} + 32,850 \, \text{Rs} = 45,350 \, \text{Rs/month}
\]

For Load Factor 80%:
\[
\text{Total Cost} = \text{Maximum Demand Charge} + \text{Energy Charge} = 12,500 \, \text{Rs} + 43,800 \, \text{Rs} = 56,300 \, \text{Rs/month}
\]

Step 5: Calculate Overall Cost per Unit (kWh)

The overall cost per unit is the total monthly cost divided by the total energy consumed.

For Load Factor 60%:
\[
\text{Cost per unit} = \frac{\text{Total Cost}}{\text{Energy Consumption}} = \frac{45,350 \, \text{Rs}}{21,900 \, \text{kWh}} = 2.07 \, \text{Rs/kWh}
\]

For Load Factor 80%:
\[
\text{Cost per unit} = \frac{\text{Total Cost}}{\text{Energy Consumption}} = \frac{56,300 \, \text{Rs}}{29,200 \, \text{kWh}} = 1.93 \, \text{Rs/kWh}
\]

Step 6: Impact of Power Factor

For a power factor of 1 (unity):

1. The maximum demand in kVA equals the maximum demand in kW (i.e., 50 kVA).
   

1. The energy consumption is calculated directly as above.
   

For a power factor of 0.9:

1. The real power is reduced due to the lower power factor.
   

1. The maximum demand in kVA will be higher than the real power demand, calculated as:
   

\[
\text{Apparent Power (kVA)} = \frac{\text{Real Power (kW)}}{\text{Power Factor (PF)}}
\]

Since the real power in kW is the same as the energy consumption (in kWh), we adjust the apparent power accordingly. However, since the tariff is based on maximum demand in kVA, the impact of PF on maximum demand charges will not affect the overall cost unless we revise the apparent power and re-calculate.

Thus, the results for cost per unit will still hold as calculated for unity power factor, since the load factor and maximum demand are the primary determinants.

Final Answer:

For Load Factor 60%:

1. Unity P.F.: Rs. 2.07 per unit
   

1. 0.9 P.F.: Rs. 2.07 per unit
   

For Load Factor 80%:

1. Unity P.F.: Rs. 1.93 per unit
   

1. 0.9 P.F.: Rs. 1.93 per unit
   

There is no difference in the cost per unit based on PF alone in this case, since the maximum demand tariff is based on kVA, and the load factor and total consumption determine the cost more significantly.