This is an excellent and crucial question. Quantifying savings is the key to obtaining approval. The calculation relies on the Affinity Laws for centrifugal pumps and fans. These laws state that power consumption is proportional to the cube of the speed.

The Fundamental Formula:

Power₂ / Power₁ = (Speed₂ / Speed₁)³

Example Calculation:

Let's assume a 100 kW fan motor that currently runs at full speed 24/7, but you only need 100% flow 50% of the time. For the other 50%, you could reduce the flow by 20% using a VFD (running at 80% speed).

Energy Use Without VFD (Throttled with a Damper):

The motor still draws ~100 kW, regardless of the damper position, because the speed is fixed.

Annual Energy: 100 kW * 8760 hours = 876,000 kWh.

Energy Use With VFD (Speed Controlled):

50% time at 100% speed: Power = 100 kW.

50% time at 80% speed: Power = 100 kW * (0.80)³ = 100 kW * 0.512 = 51.2 kW.

Weighted Average Power: (100kW * 0.5) + (51.2kW * 0.5) = 75.6 kW.

Annual Energy with VFD: 75.6 kW * 8760 hrs = 662,256 kWh.

Annual Energy Savings: 876,000 - 662,256 = 213,744 kWh.

Annual Cost Savings (assuming $0.10/kWh): 213,744 kWh * $0.10 = $21,374.

Estimating ROI:

Cost of a 100 kW VFD + Installation: ~$15,000 (varies by brand and complexity).

Simple Payback Period: $15,000 / $21,374/year ≈ 0.7 years (or 8.5 months).

Additional Benefits (Not Quantified Here): Reduced maintenance from soft starts, extended motor and bearing life, improved process control, and reduced carbon footprint.

This dramatic savings, with a payback of less than a year, is typical for centrifugal applications with variable flow requirements. A detailed audit of your specific systems will provide the most accurate figures, but the cube law relationship guarantees significant potential.