VFD Energy Savings Calculator

Fan and Pump Laws

Fan and pump performance follows affinity laws relating speed to flow, pressure, and power:

**Law 1 - Flow**:

(Q_2)/(Q_1) = (N_2)/(N_1)

Flow is directly proportional to speed.

**Law 2 - Pressure**:

(Δ P_2)/(Δ P_1) = ((N_2)/(N_1))^2

Pressure varies with square of speed.

**Law 3 - Power** (MOST IMPORTANT FOR SAVINGS):

(P_2)/(P_1) = ((N_2)/(N_1))^3

Power varies with **cube** of speed!

**Energy Savings Example**:

Reduce speed to 80% (0.8×): - Flow: 80% of design - Pressure: (0.8)^2 = 64\% of design - Power: (0.8)^3 = 51.2\% of design - **Energy savings: 48.8%!**

This cubic relationship makes VFDs extremely effective for energy reduction.

VFD Savings Calculation

**Annual Energy Savings**:

E_savings = P_motor · t_annual · [1 - (\fracN_avgN_design)^3]

where: - P_motor = motor power at design speed (kW) - t_annual = annual operating hours - N_avg/N_design = average speed ratio

**Annual Cost Savings**:

Cost_savings = E_savings · C_electricity

**Simple Payback Period**:

Payback = \fracC_VFD + C_installationCost_savings,annual

Typical payback: 1-4 years depending on application.

**Life Cycle Savings** (15-year life):

LCS = (Cost_savings,annual × 15) - C_VFD - C_maintenance

**Average Speed Ratio**:

For variable systems, estimate average load:

N_avg/N_design = \sqrt[3]Load_avg\%/100

Example: System runs at 50% average load:

N_avg/N_design = \sqrt[3]0.50 = 0.794 \text or 79.4\%

Applications and Savings Potential

**VAV (Variable Air Volume) Systems**:

- Average load: 40-60% of design - Average speed: 70-85% - Energy savings: 40-60% vs. constant volume - Excellent payback (1-3 years) - Additional benefits: Better comfort, humidity control

**Variable Flow Pumping** (chilled/hot water):

- Average load: 50-70% of design - Average speed: 75-90% - Energy savings: 30-50% vs. constant flow - Good payback (2-4 years) - Reduces pipe erosion and noise

**Cooling Tower Fans**:

- Average load: 50-70% - Average speed: 75-90% - Energy savings: 30-50% - Excellent payback (1-2 years) - Extends tower life, reduces noise

**Condenser Water Pumps**:

- Average load: 60-80% - Average speed: 80-95% - Energy savings: 20-40% - Good payback (2-3 years)

**Poor Applications for VFDs**:

- Constant load systems (no benefit) - Small motors (<5 hp) unless high run hours - Systems already optimized with multiple units - Short operating hours (<2000 hours/year)

VFD Benefits Beyond Energy

**Soft Starting**:

- Eliminates inrush current (6-8× full load) - Reduces mechanical stress on equipment - Extends motor and drive component life - Allows larger motors on smaller electrical services

**Process Control**:

- Precise flow/pressure control - Better comfort and humidity control - Reduces cycling and hunting - Eliminates bypass dampers/valves

**Maintenance Benefits**:

- Reduced bearing and seal wear - Lower vibration at reduced speeds - Fewer starts/stops - Easier system balancing

**Power Factor**:

- VFDs typically operate at 0.95-0.98 PF - May eliminate need for power factor correction - Reduces demand charges

**VFD Considerations**:

- Initial cost: \$100-200 per hp typical - Installation cost: Varies with complexity - Additional maintenance (every 3-5 years) - Heat generation (affects HVAC load) - Harmonic distortion (may need filters) - Motor must be inverter-rated for long cable runs

Worked Example

Inputs

• motorPower: 50
• operatingHours: 5000
• averageLoad: 60
• electricityRate: 0.12
• vfdCost: 7500
• installationCost: 2500

Result: Annual Savings: $14,160 | Payback: 0.71 years (8.5 months) | 15-year savings: $212,400

Explanation

For a 50 hp (37.3 kW) fan running 5000 hours/year:

**Step 1: Calculate Design Power Consumption** Motor power: 50 hp × 0.746 = 37.3 kW Annual energy (constant speed): 37.3 × 5000 = 186,500 kWh Annual cost (constant speed): 186,500 × \0.12 = \22,380

**Step 2: Calculate Average Speed Ratio** Average load: 60% of design Average speed ratio: (0.60)^1/3 = 0.843 or 84.3%

**Step 3: Calculate VFD Power Consumption** Power ratio: (0.843)^3 = 0.599 or 59.9% Average power with VFD: 37.3 × 0.599 = 22.3 kW Annual energy (with VFD): 22.3 × 5000 = 111,500 kWh Annual cost (with VFD): 111,500 × \0.12 = \13,380

**Step 4: Calculate Savings** Energy saved: 186,500 - 111,500 = 75,000 kWh/year (40.2%) Cost saved: \22,380 - \13,380 = \9,000/year

**Step 5: Account for VFD Efficiency** VFD losses ≈ 3%: Additional cost = \13,380 × 0.03 = \401 Net annual savings: \9,000 - \401 = \8,599

**Step 6: Calculate Payback** Total investment: \7,500 + \2,500 = \10,000 Simple payback: \10,000 / \8,599 = 1.16 years (14 months)

**Step 7: Life Cycle Analysis** (15-year VFD life) Total savings: \8,599 × 15 = \128,985 Maintenance cost (every 5 years): \1,500 × 3 = \4,500 Net life cycle savings: \128,985 - \10,000 - \4,500 = \114,485

**Step 8: Additional Benefits** - Soft starts reduce mechanical stress - Better process control - Reduced maintenance on driven equipment - Power factor improvement - Reduced demand charges

**Conclusion**: ✓ Excellent ROI with 14-month payback ✓ Annual savings: \8,599 ✓ 15-year net benefit: \$114,485 ✓ CO₂ reduction: 75,000 kWh × 0.92 lb/kWh = 69,000 lbs/year ✓ Strong recommendation for VFD installation

Second Scenario

Inputs

• motorPower: 63.5
• operatingHours: 5000
• averageLoad: 60
• electricityRate: 0.12
• vfdCost: 7500
• installationCost: 2500

Result: Annual Savings: $14,160 | Payback: 0.71 years (8.5 months) | 15-year savings: $212,400

Explanation

This scenario uses different inputs (motorPower = 63.5, operatingHours = 5000, averageLoad = 60, electricityRate = 0.12, vfdCost = 7500, installationCost = 2500) to show how changing one variable affects the vfd energy savings result. Run the calculator above with these values to get the exact updated output with step-by-step work.