Energy Efficiency

VFD and Motor Energy Savings: The Affinity Laws in Practice

VFD energy savings come from the cube law: power scales with speed^3. Here is how to calculate savings on fans and pumps and size the payback period for a VFD investment.

Fan and pump power follows the Affinity Laws. Power varies with the cube of speed: P2/P1 = (N2/N1)^3. Flow varies linearly with speed: Q2/Q1 = N2/N1. Pressure varies with the square of speed: H2/H1 = (N2/N1)^2. Running a fan at 80% of full speed: power = (0.8)^3 = 51.2% of full-speed power. Running at 60%: power = (0.6)^3 = 21.6% of full-speed power. A 75kW motor running at 80% speed uses 75 x 0.512 = 38.4 kW instead of 75 kW, saving 36.6 kW per operating hour.

Annual energy savings = (baseline kW - reduced kW) x operating hours x energy rate. For the 75kW fan at 80% average speed running 6,000 hours/year at $0.09/kWh: savings = (75 - 38.4) x 6,000 x $0.09 = 36.6 x 6,000 x $0.09 = $19,764/year. VFD and installation cost: $4,000-$8,000 for a 75kW drive. Simple payback = $6,000 / $19,764 = 3.6 months. VFD installations on fans and pumps consistently rank among the highest-ROI energy investments available in manufacturing.

Load profile analysis improves savings calculation accuracy. A motor that runs at 100% load 30% of the time and 70% load 70% of the time saves more than a motor that runs at 85% load all the time, because the cube law gives disproportionate savings at the lowest load points. For accurate savings: integrate power x time across all load points. Many facilities use power logger data (2-4 weeks of continuous measurement) to establish actual load profiles before sizing VFDs.

VFDs are suitable for variable torque loads (fans, pumps, compressors). For constant torque loads (conveyors, positive displacement pumps, mixers with fixed viscosity loads), the affinity laws do not apply and energy savings from speed reduction are smaller. Do not assume cube-law savings for all motor applications. Verify the load type before calculating VFD energy benefits.

VFD installation also reduces mechanical wear on the driven equipment. Soft starting (controlled ramp-up from zero speed) eliminates the mechanical shock of full-voltage starting. Bearing wear, belt wear, and mechanical coupling fatigue are all reduced. On pumps, VFD control also eliminates the energy waste of throttle valves and bypass systems used in fixed-speed systems to control flow. Removing the throttle and running the pump at variable speed gives energy savings on top of the speed reduction savings.

Published 2026-05-28.