VFD Retrofit Energy and Cost Savings (Affinity Cube Law)
The number that sells a variable-frequency drive: the annual kWh and dollars it saves on a centrifugal pump or fan. 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.
Formula and source
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.
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