Cost-Benefit of a Pump Variable Speed Drive
A facility operates a 75 kW pump continuously at a fixed speed, throttled to 70% of design flow for most of the year. The annual energy use is 480,000 kWh at an average tariff of AED 0.30/kWh. A variable speed drive (VSD) is proposed at a capital cost of AED 260,000, installed. The vendor claims energy savings of 35% based on affinity laws. Maintenance is expected to fall by AED 8,000/year. The facility uses a 10-year evaluation period and a 9% discount rate. The facility's capital budget is constrained and competing projects return about 12% annually.
1. Test the vendor's 35% savings claim using affinity laws and state whether it is credible.
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Affinity laws for a variable-speed pump: flow ∝ speed, head ∝ speed², power ∝ speed³. If the system were purely friction-dominated and the pump ran at 70% speed, power would fall to 0.70³ = 0.343, i.e. a 66% saving. That is the theoretical maximum and explains why vendors quote large figures.
But the facility currently throttles to 70% flow, which means the system has static head and the pump is not simply following a friction curve. At 70% flow, a VSD pump must still produce the head the system requires, which is higher than 0.70² of the design head if there is static lift. The actual speed will be above 70%, and power will be above 0.343 of design. A 35% saving corresponds to power at 0.65 of design, i.e. a speed of about 0.87 of design - plausible if the system has significant static head, but it must be checked against the actual system curve.
Conclusion: 35% is plausible but cannot be accepted from the affinity law alone. The engineer should obtain the system curve, the pump curve, and the actual flow/head profile, and calculate the annual energy at the VSD operating points. The claim should be treated as a maximum, not a guarantee.
2. Calculate the simple payback and the net present value at 9%, and recommend whether to proceed given the 12% hurdle.
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Savings: Energy saving at 35% = 0.35 × 480,000 = 168,000 kWh/year × AED 0.30 = AED 50,400/year. Plus maintenance AED 8,000 = AED 58,400/year.
Simple payback: 260,000 / 58,400 ≈ 4.45 years.
NPV at 9%, 10 years: annuity factor = (1 − 1.09⁻¹⁰)/0.09 = (1 − 0.4224)/0.09 ≈ 6.418. PV of savings = 58,400 × 6.418 ≈ AED 374,800. NPV = 374,800 − 260,000 ≈ AED +114,800.
At the 12% hurdle: annuity factor = (1 − 1.12⁻¹⁰)/0.12 = (1 − 0.3220)/0.12 ≈ 5.650. PV of savings = 58,400 × 5.650 ≈ AED 330,000. NPV ≈ AED +70,000. IRR is well above 12% (roughly 18–19%).
Recommendation: On the vendor's numbers the project clears the 12% hurdle comfortably and should proceed. But the savings are unverified. A sensitivity check is essential: if actual savings are only 20% instead of 35%, energy savings = 0.20 × 480,000 × 0.30 = AED 28,800, plus 8,000 = AED 36,800/year. NPV at 12% = 36,800 × 5.650 − 260,000 ≈ −AED 52,000 - negative.
So the decision hinges on verifying the savings. Recommend proceeding only after metering the actual flow/head profile and confirming savings of at least about 25%; otherwise the project fails the hurdle.