What are the components of the annual charge at pf 0.75?

MD charge 1200 x 5000 plus energy 900 kW x 3000 h x Rs 5, total Rs 19,500,000

MD on 900 kW only, total Rs 18,000,000

Only energy charge Rs 13,500,000

Which gives the kVAR required?

Q_C = 900(0.95 - 0.75) = 180 kVAR

Why does the total annual charge fall to Rs 18,635,170?

MD charge drops while energy charge is unchanged, and the extra 10% annual cost of apparatus is less than the MD saving

The energy charge falls because kWh is reduced

The capacitor cost is not counted

Asked 3/16
2082 Baisakh · 8 marks

Annual charge and pf improvement for 1200 kVA load

Short answer

i) P=900 kW, MD charge 1200×5000, energy 900×3000×5, total Rs 19,500,000. ii) Qc=900(0.8819−0.3287)=497.9 kVAR; new MD 947.37 kVA, total annual charge including corrector cost Rs 18,635,170.

The load on a certain installation may be considered constant at 1,200 kVA, 0.75 lagging power factor for 3,000 hours per annum. The tariff is Rs 5,000 per kVA maximum demand plus Rs 5 per kWh. i) Determine the annual charge of energy. ii) Power Factor improving apparatus is installed to improve the pf to 0.95 lagging. Determine the kVAR require and the annual charge of energy if the power factor improving apparatus costs Rs 8,000 per kVAR, annual interest and depreciation charges are 10% of the capital cost.

Given: $S = 1200$ kVA at pf 0.75 lag, 3000 h/year, tariff Rs 5000/kVA of maximum demand per year + Rs 5/kWh; pf corrector cost Rs 8000/kVAR, annual interest and depreciation 10%.

i) Annual charge at pf 0.75

\begin{aligned} P &= 1200 \times 0.75 = 900\ \text{kW} \\ \text{MD charge} &= 1200 \times 5000 = \text{Rs } 6\,000\,000 \\ \text{Energy} &= 900 \times 3000 = 2\,700\,000\ \text{kWh} \\ \text{Energy charge} &= 2\,700\,000 \times 5 = \text{Rs } 13\,500\,000 \\ \text{Annual charge} &= \text{Rs } 19\,500\,000 \end{aligned}

ii) After raising pf to 0.95

kVAR required:

\begin{aligned} Q_C &= P(\tan\phi_1 - \tan\phi_2) = 900(0.8819 - 0.3287) = 497.9\ \text{kVAR} \end{aligned}

New maximum demand:

S_2 = \frac{900}{0.95} = 947.37\ \text{kVA}

Annual charges:

\begin{aligned} \text{MD charge} &= 947.37 \times 5000 = \text{Rs } 4\,736\,842 \\ \text{Energy charge} &= \text{Rs } 13\,500\,000 \ (\text{unchanged}) \\ \text{Capital cost} &= 497.9 \times 8000 = \text{Rs } 3\,983\,278 \\ \text{Interest + depreciation} &= 0.10 \times 3\,983\,278 = \text{Rs } 398\,328 \\ \text{Total} &= 4\,736\,842 + 13\,500\,000 + 398\,328 = \text{Rs } 18\,635\,170 \end{aligned}

Item	pf 0.75 (Rs)	pf 0.95 (Rs)
MD charge	6,000,000	4,736,842
Energy charge	13,500,000	13,500,000
Corrector charges	—	398,328
Total	19,500,000	18,635,170

Answer: (i) Rs 19,500,000 per year; (ii) 497.9 kVAR needed, new annual charge Rs 18,635,170, an annual saving of about Rs 864,830.

✓ Answer checked by Claude Opus 5.5 (high effort)

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Annual charge and pf improvement for 1200 kVA load

i) Annual charge at pf 0.75

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