VFD Retrofit Energy and Cost Savings (Affinity Cube Law)

A throttled or dampered constant-speed machine keeps drawing near-full power; slowed by a VFD it draws the cube of the speed ratio (the affinity law), so at 60 percent flow it uses about a fifth of the power. The saving is that gap integrated over a three-bin duty cycle - and the whole case turns on the load profile, not the horsepower: the identical drive on the identical pump saves six times less if the pump mostly runs at full flow. A screening estimate, not a metered M&V.

vfd_kwh = full_load_kw x (frac_a^3 x hours_a + frac_b^3 x hours_b + frac_c^3 x hours_c); full_kwh = full_load_kw x (hours_a + hours_b + hours_c); saved_kwh = full_kwh - vfd_kwh; saved_usd = saved_kwh x rate_kwh.

The centrifugal affinity cube law (P / P_full = (Q / Q_full)^3 for a fixed system curve) and the US DOE motor-systems / pump-system energy method, by name; the relations are public.

The affinity laws and the DOE motor/pump-system energy method are public; the DOE MotorMaster and pump-system tip sheets are free at energy.gov. The arithmetic is public.

Estimate. AHJ and licensed professional govern.

Field names used by the API: full_load_kw, frac_a, hours_a, frac_b, hours_b, frac_c, hours_c, rate_kwh, full_kwh, vfd_kwh, saved_kwh, saved_usd

• Affinity cube law part-flow power scales as the cube of the flow (speed) ratio on a fixed system curveaffinity laws
• Duty cycle annual energy is the flow-cubed power summed over the hours in each of three flow binsUS DOE pump-system energy method
• Baseline savings are versus full-speed operation for the same hours; friction-dominated system assumedUS DOE motor-systems method