Which motor is more economical (two-part tariff)

Compare the annual cost of each motor: demand charge + energy charge + interest and depreciation on the extra capital. The tariff of Rs 250 per kVA of maximum demand is taken as an annual charge, and "the motor costs Rs 1500 less" is read as motor B costs Rs 1500 less than motor A.

Motor A ($\eta$ = 85%, pf = 0.9)

$$\begin{aligned} P_{in,A} &= \frac{35}{0.85} = 41.18\ \text{kW} \\ S_A &= \frac{41.18}{0.9} = 45.75\ \text{kVA} \\ \text{Demand charge} &= 250 \times 45.75 = \text{Rs } 11{,}438 \\ \text{Energy charge} &= 8 \times 41.18 \times 3000 = \text{Rs } 988{,}235 \\ \text{Extra capital cost charge} &= 0.10 \times 1500 = \text{Rs } 150 \end{aligned}$$

Annual cost of A = 11,438 + 988,235 + 150 = Rs 999,823

Motor B ($\eta$ = 90%, pf raised from 0.8 to 0.85)

$$\begin{aligned} P_{in,B} &= \frac{35}{0.9} = 38.89\ \text{kW} \\ \tan\phi_1 &= \tan(\cos^{-1}0.8) = 0.75,\quad \tan\phi_2 = \tan(\cos^{-1}0.85) = 0.6197 \\ Q_C &= 38.89\,(0.75 - 0.6197) = 5.07\ \text{kVAR} \\ \text{Cost of condenser} &= 400 \times 5.07 = \text{Rs } 2026 \\ \text{Interest and depreciation} &= 0.10 \times 2026 = \text{Rs } 202.6 \\ S_B &= \frac{38.89}{0.85} = 45.75\ \text{kVA} \\ \text{Demand charge} &= 250 \times 45.75 = \text{Rs } 11{,}438 \\ \text{Energy charge} &= 8 \times 38.89 \times 3000 = \text{Rs } 933{,}333 \end{aligned}$$

Annual cost of B = 11,438 + 933,333 + 202.6 = Rs 944,974

Comparison

Both motors draw the same kVA, so the higher efficiency of B decides the result.

Answer: Motor B (with condensers) is more economical, saving about Rs 54,849 per year.