Estimate the percent of annual operating hours spent at each flow/speed level. Must total 100%.
Power Draw by Speed: VFD vs Throttled (Cube Law)
Detailed Analysis
| Parameter | Throttled (Fixed Speed) | VFD Controlled | Savings |
|---|
Energy by Load Bin
| Speed / Flow | % of Hours | Hours/yr | Throttled kWh | VFD kWh | Saved kWh |
|---|
How to Use the Variable Speed Savings Calculator
Use BAS trend data if available. Without it, estimate from application type: VAV air handling in office buildings often spends 40-60% of hours at 60-80% flow; condenser water pumps track cooling load and outdoor temperature closely. For part-load equipment interactions, see the mechanical efficiency calculator.
The throttled power parameter (default 0.70) is the share of full-load power a throttled pump or fan still draws as flow nears zero. The model rises in a straight line from that value to 100% at full flow, so the default gives 94% of full power at 80% flow, 88% at 60% flow and 76% at 20% flow. Raise it toward 0.85 for pumps with flat curves, or lower it for backward-curved fans with outlet dampers.
Shows power at 100/80/60/40/20% speed for both VFD (cube law) and throttled control. The gap between bars widens quickly as speed drops, which is why equipment that spends many hours at reduced flow benefits most from VFD conversion.
VFD Energy Savings for HVAC Pumps and Fans: The Physics and the Numbers
A variable frequency drive saves energy because of one physical relationship: for centrifugal pumps and fans, power falls with the cube of speed. This page applies that relationship to your own load profile, so the result reflects how many hours the equipment really spends below full flow.
The Affinity Laws: Flow, Pressure, and Power
Centrifugal pumps and fans follow three affinity laws as speed changes. Flow scales linearly with speed (Q2/Q1 = N2/N1), pressure or head scales with the square of speed, and power scales with the cube of speed (kW2/kW1 = (N2/N1)3). A pump at 80% speed delivers 80% of design flow but draws only 0.83 = 51.2% of design power. At 60% speed it draws 21.6%, and at 50% speed just 12.5%. The fan laws calculator lets you check any speed, flow or pressure combination before you enter a load profile here.
Dropping from 100% to 80% speed removes 48.8 points of power, and the next step from 80% to 60% removes another 29.6 points. The savings per step shrink as speed falls, but the total keeps growing, which is why equipment with long part-load hours gains far more than equipment running near full load.
Why Throttling Does Not Capture These Savings
A throttled system holds the motor at full speed and closes a discharge valve or damper to add resistance. The flow drops, but the motor only unloads slightly, so power falls far less than the cube law predicts. This calculator models that with a straight line from the "throttled power at zero flow" input (default 0.70) up to 100% at full flow. At 60% flow the default throttled system still draws 88% of full power while a VFD at 60% speed draws 22.3%, which includes a 3% drive loss.
Real-World Load Profiles and Expected Savings
Savings depend on how many hours the equipment runs below full flow. With the default profile (10% of hours at 100% speed, 25% at 80%, 35% at 60%, 20% at 40% and 10% at 20%), the model shows a 63% reduction against throttled operation. Natural Resources Canada reports that variable frequency inverters on fans and pumps cut power use by 30 to 60 percent, which brackets what most variable-load installations achieve. A profile with 90% of hours at full speed and 10% at 80% saves only about 1%, and a 50/50 split between 100% and 80% saves about 20%. Systems that run flat out gain little from a drive.
In Canadian commercial buildings the best candidates are primary and secondary chilled water pumps, condenser water pumps and large supply or return fans. These combine large motors, which lowers the installed cost per kW, with real load swings across the day and the seasons. If a drive also trims your billed demand, the peak demand calculator shows what that reduction is worth. For wider part-load questions, the mechanical efficiency calculator covers the rest of the equipment chain.
Drive Losses, Cost and Payback
The model divides cube-law power by a single drive efficiency (default 97%). The U.S. Department of Energy's tip sheet on adjustable speed drive part-load efficiency lists typical PWM drives at 95 to 97% at full load, falling to about 88 to 95% at 25% load. Because motor power is already tiny at low speed, the error is small, but it slightly favours the VFD at the lowest bins. Check the drive and motor ratings with the VFD sizing calculator before you price the job.
Worked example: a 15 kW pump running 4,000 hours a year at $0.13/kWh with the default profile uses 52,980 kWh throttled and 19,621 kWh with a VFD. That saves 33,359 kWh, or $4,337 a year. At $220/kW the drive costs $3,300, and with a $500 incentive the net cost is $2,800, a payback of 0.6 years. Real projects usually land between 1 and 5 years once smaller motors, fewer hours and installation extras are included.
Frequently Asked Questions
The cube law says that power is proportional to the cube of speed. At 80% speed a pump or fan uses 0.83 = 51.2% of full-speed power, at 60% speed it uses 21.6%, and at 40% speed just 6.4%. This is why small speed reductions cut power so sharply. It is part of the affinity laws, which also say flow is linear with speed and pressure follows the square of speed.
It depends on the load profile. With the calculator's default profile (10% of hours at 100% speed, 25% at 80%, 35% at 60%, 20% at 40% and 10% at 20%) the model shows a 63% reduction. Natural Resources Canada cites 30 to 60 percent power savings for variable frequency inverters on fans and pumps. Equipment that runs near full flow most of the time saves much less, around 1% for a profile with 90% of hours at full speed.
Throttling closes a valve or damper to add resistance while the motor keeps running at full speed. A VFD slows the motor to match the flow needed. With the default setting, a throttled system at 60% flow still draws about 88% of full power, while a VFD at 60% speed draws about 22%. That gap is the source of the savings.
Paybacks of 1 to 5 years are common for commercial HVAC pumps and fans with real load variation and long operating hours. The calculator's 15 kW example, with $2,800 net cost and $4,337 in yearly savings, pays back in about 0.6 years. Smaller motors, fewer hours or flatter load profiles take longer. The calculator assumes $220 per kW installed, and drive cost varies with enclosure type and installation work. Check your electric utility for current VFD incentive programs.
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