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Annual charge and pf improvement (Rs 1300/kVA tariff)

Short answer

i) P=1200×0.75=900 kW, MD=1200×1300, energy=900×3000×0.80 gives Rs 3,720,000. ii) Qc=900(0.8819−0.3287)=497.9 kVAR, new MD=900/0.95=947.37 kVA, total annual charge with corrector Rs 3,451,328.

The load on a certain installation may be considered constant at 1200 KVA, 0.75 lagging power factor for 3000 hr per annum. The tariff is 1300 per KVA maximum demand plus 80 paisa per KWh. Determine: 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 required and annual new charge of energy if PF correcting apparatus cost to Rs 1200 per KVAr, annual interest and deprecation charge are 10% of capital cost.

Given: S=1200S = 1200 kVA, pf 0.75 lag, 3000 h/year; tariff Rs 1300/kVA of maximum demand per year + 80 paisa (Rs 0.80)/kWh; corrector Rs 1200/kVAR; interest and depreciation 10%.

i) Annual charge at pf 0.75

P=1200×0.75=900 kWMD charge=1200×1300=Rs 1 560 000Energy charge=900×3000×0.80=Rs 2 160 000Annual charge=Rs 3 720 000\begin{aligned} P &= 1200 \times 0.75 = 900\ \text{kW} \\ \text{MD charge} &= 1200 \times 1300 = \text{Rs } 1\,560\,000 \\ \text{Energy charge} &= 900 \times 3000 \times 0.80 = \text{Rs } 2\,160\,000 \\ \text{Annual charge} &= \text{Rs } 3\,720\,000 \end{aligned}

ii) kVAR required for pf 0.95

tan⁡ϕ1=tan⁡(cos⁡−10.75)=0.8819,tan⁡ϕ2=tan⁡(cos⁡−10.95)=0.3287QC=900(0.8819−0.3287)=497.9 kVAR\begin{aligned} \tan\phi_1 &= \tan(\cos^{-1}0.75) = 0.8819, \quad \tan\phi_2 = \tan(\cos^{-1}0.95) = 0.3287 \\ Q_C &= 900(0.8819 - 0.3287) = 497.9\ \text{kVAR} \end{aligned}

New annual charge

S2=9000.95=947.37 kVAMD charge=947.37×1300=Rs 1 231 579Energy charge=Rs 2 160 000Corrector cost=497.9×1200=Rs 597 492Interest + depreciation=0.10×597 492=Rs 59 749New annual charge=1 231 579+2 160 000+59 749=Rs 3 451 328\begin{aligned} S_2 &= \frac{900}{0.95} = 947.37\ \text{kVA} \\ \text{MD charge} &= 947.37 \times 1300 = \text{Rs } 1\,231\,579 \\ \text{Energy charge} &= \text{Rs } 2\,160\,000 \\ \text{Corrector cost} &= 497.9 \times 1200 = \text{Rs } 597\,492 \\ \text{Interest + depreciation} &= 0.10 \times 597\,492 = \text{Rs } 59\,749 \\ \text{New annual charge} &= 1\,231\,579 + 2\,160\,000 + 59\,749 = \text{Rs } 3\,451\,328 \end{aligned}
Itempf 0.75 (Rs)pf 0.95 (Rs)
MD charge1,560,0001,231,579
Energy charge2,160,0002,160,000
Corrector charges—59,749
Total3,720,0003,451,328

Answer: (i) Rs 3,720,000 per year; (ii) 497.9 kVAR, new annual charge Rs 3,451,328 (saving about Rs 268,672 per year).

✓ Answer checked by Claude Opus 5.5 (high effort)

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