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Annual saving by capacitors for 200 kW factory

Short answer

With 200 kW load, demand charge saving from improving pf 0.85 to 0.9 is Rs 1,960.80. Capacitors of 27.08 kVAR cost Rs 11,375; their loss costs Rs 338.60 and interest/depreciation Rs 1,137.50. Net annual saving is about Rs 485.

A factory takes a load of 200kW at 0.85 pf lagging for 2500 hrs per annum. The tariff is Rs. 150 per KVA plus 5 paisa per KWH consumed. If the pf is improved to 0.9 lagging by means of capacitors costing Rs 420 per KVAR and having a power loss of 100W per KVA, Calculate the annual saving effected by their use. Allow 10% per annum for interest and depreciation.

Saving comes from the reduced kVA demand charge; against it are the capacitor loss (extra kWh) and the interest and depreciation on capacitors. The capacitor kVAR is found from the 200 kW load, and the loss of 100 W per kVA of capacitor rating is taken as 0.1 kW per kVAR.

kVA demand before and after

S1=2000.85=235.29 kVA,S2=2000.9=222.22 kVAReduction=235.29−222.22=13.07 kVASaving in demand charge=150×13.07=Rs 1960.8\begin{aligned} S_1 &= \frac{200}{0.85} = 235.29\ \text{kVA}, \qquad S_2 = \frac{200}{0.9} = 222.22\ \text{kVA} \\ \text{Reduction} &= 235.29 - 222.22 = 13.07\ \text{kVA} \\ \text{Saving in demand charge} &= 150 \times 13.07 = \text{Rs } 1960.8 \end{aligned}

Capacitor rating and its costs

tan⁡ϕ1=0.6197,tan⁡ϕ2=0.4843QC=200 (0.6197−0.4843)=27.08 kVARLoss=0.1×27.08=2.708 kWCost of loss=2.708×2500×0.05=Rs 338.6Capital cost=420×27.08=Rs 11,375Interest and depreciation=0.10×11,375=Rs 1137.5\begin{aligned} \tan\phi_1 &= 0.6197,\quad \tan\phi_2 = 0.4843 \\ Q_C &= 200\,(0.6197 - 0.4843) = 27.08\ \text{kVAR} \\ \text{Loss} &= 0.1 \times 27.08 = 2.708\ \text{kW} \\ \text{Cost of loss} &= 2.708 \times 2500 \times 0.05 = \text{Rs } 338.6 \\ \text{Capital cost} &= 420 \times 27.08 = \text{Rs } 11{,}375 \\ \text{Interest and depreciation} &= 0.10 \times 11{,}375 = \text{Rs } 1137.5 \end{aligned}

Net annual saving

Saving=1960.8−338.6−1137.5=Rs 484.7\begin{aligned} \text{Saving} &= 1960.8 - 338.6 - 1137.5 \\ &= \text{Rs } 484.7 \end{aligned}

Answer: Annual saving ≈ Rs 485 (with 27.08 kVAR of capacitors).

✓ Answer checked by Claude Opus 5.5 (high effort)

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