Annual cost and saving with pf correction (400 kVA)

Given: energy 50,000 kWh/year, pf 0.7 lag, maximum demand 400 kVA, tariff Rs 120/kVA + Rs 5.50/kWh, corrector Rs 1000/kVAR, annual charges 10%, pf raised to 0.9. The demand charge is taken per kVA per year, as printed.

Annual cost of supply at pf 0.7

$$\begin{aligned} \text{MD charge} &= 400 \times 120 = \text{Rs } 48\,000 \\ \text{Energy charge} &= 50\,000 \times 5.50 = \text{Rs } 275\,000 \\ \text{Annual cost} &= \text{Rs } 323\,000 \end{aligned}$$

Corrector rating

Maximum-demand kW $= 400 \times 0.7 = 280$ kW.

$$\begin{aligned} Q_C &= 280(\tan\phi_1 - \tan\phi_2) = 280(1.0202 - 0.4843) = 150.05\ \text{kVAR} \\ \text{Cost} &= 150.05 \times 1000 = \text{Rs } 150\,047 \\ \text{Annual charge} &= 0.10 \times 150\,047 = \text{Rs } 15\,005 \end{aligned}$$

New demand and saving

$$\begin{aligned} S_2 &= \frac{280}{0.9} = 311.11\ \text{kVA} \\ \text{Reduction in MD charge} &= (400 - 311.11) \times 120 = \text{Rs } 10\,667 \\ \text{Net annual saving} &= 10\,667 - 15\,005 = -\text{Rs } 4\,338 \end{aligned}$$

The energy charge (kWh) does not change. With the demand charge per year, the device costs more than it saves (net loss of Rs 4,338), so it is not economical.

If the demand charge is Rs 120/kVA per month

This is the usual way demand is billed (e.g. NEA bills demand monthly):

$$\begin{aligned} \text{Annual cost} &= 400 \times 120 \times 12 + 275\,000 = \text{Rs } 851\,000 \\ \text{MD saving} &= 88.89 \times 1440 = \text{Rs } 128\,000 \\ \text{Net saving} &= 128\,000 - 15\,005 = \text{Rs } 112\,995 \end{aligned}$$

Answer: Annual cost Rs 323,000; corrector 150.05 kVAR costing Rs 150,047. On a yearly demand charge the net saving is −Rs 4,338 (a loss). On a monthly demand charge the annual cost is Rs 851,000 and the net saving is about Rs 112,995 per year.