How the calculation works
Electrical input power at full flow is the motor rating multiplied by its load, divided by its efficiency. The calculator then works out the power at each flow in your operating profile, for both control methods, and weights it by the time spent there.
Throttle valve or damper
The machine runs at full speed and the valve or damper adds resistance. Shaft power follows the machine's curve, approximated here as a straight line from the zero-flow power to full-flow power:
where Q is the flow as a fraction of design and s the zero-flow power fraction.
Variable frequency drive
Speed is reduced until the machine meets the system curve at the required flow. The system curve has a fixed static part hs and a friction part that rises with the square of flow, so the power needed is:
With no static head this is the familiar cube law of the affinity laws: half the flow needs one eighth of the power.
Worked example
A 75 kW pump motor loaded to 85% at design flow, 94% efficient, in a closed circulating loop (no static head). Throttled power at zero flow is 50%, the VFD is 97% efficient, and the pump runs 6,000 hours a year at 0.12 per kWh with this profile:
| Flow | Time | Throttled kW | VFD kW |
|---|---|---|---|
| 100% | 10% | 67.8 | 69.9 |
| 90% | 20% | 64.4 | 51.0 |
| 80% | 30% | 61.0 | 35.8 |
| 70% | 20% | 57.6 | 24.0 |
| 60% | 10% | 54.3 | 15.1 |
| 50% | 10% | 50.9 | 8.7 |
- Full-flow input power: 75 × 0.85 ÷ 0.94 = 67.8 kW.
- Throttled energy: 360,100 kWh a year. With a VFD: 210,600 kWh a year.
- Saving: 149,500 kWh, or 42%, worth about 17,940 a year.
- If the drive costs 12,000 installed, it pays back in about 8 months.
- At full flow the VFD uses slightly more power than throttling, because of its own losses.
The same pump lifting against 30% static head would save about 32% instead of 42%.
Assumptions and limits
- Pump or fan efficiency is assumed constant as speed changes. On systems with high static head, the machine moves away from its best efficiency point at low speed, so real savings are lower than calculated.
- Motor efficiency is assumed constant. Below about 40% load, motor efficiency falls, which slightly reduces VFD savings at very low flows.
- The throttled power curve is a straight-line approximation. For an accurate baseline, read power at each flow from the manufacturer's curve, or measure it.
- Positive displacement pumps and compressors follow different rules and should not be calculated with this method.
- On systems with high static head, check that the minimum speed still delivers enough pressure to open check valves and reach the outlet.
Questions
How do I build the operating profile?
Use flow meter trends, valve or damper position records, or a few weeks of logged motor current. Group the readings into the flow bands in the table. If you have no data, a short logging campaign is worth doing before buying a drive.
Why does static head reduce VFD savings?
With static head the pump must still produce that pressure at any flow, so the speed cannot fall as far as the pure cube law suggests, and the power falls less.
Does a VFD save energy at full flow?
No. At design flow it adds its own losses of typically 2 to 4%. All the savings come from the hours spent at reduced flow.
What else should I check before installing a drive?
Harmonics on your network, motor insulation suitability for inverter supply on older motors, cable length between drive and motor, bearing currents on larger motors, and whether the motor needs extra cooling at low speed.