🔋Understanding Reactive Power in Practice
What Reactive Power Actually Does
Energy Storage and Release
Inductive loads (motors): Store energy in magnetic fields
Energy oscillates between load and source
No net energy consumed (ideally)
Creates current flow without doing work
Requires conductor capacity and causes losses
Think of it as "electrical breathing"
System Impact Example
100 kW motor at 0.75 power factor
Real current component: 100 kW ÷ (480V × 1.73) = 120A
Reactive component: 100 × tan(41.4°) ÷ (480V × 1.73) = 106A
Total current: √(120² + 106²) = 160A
Conductor must carry 160A, not 120A
33% more current for same useful work
Common Sources of Reactive Power
Induction Motors
No load: 30-50% of full load VAR
75% load: 0.75-0.85 power factor
Full load: 0.8-0.9 power factor
Larger motors have better power factors
Dominant source in industrial plants
Lighting Systems
Fluorescent (magnetic): 0.5 PF
Fluorescent (electronic): 0.95 PF
HID (magnetic): 0.5 PF
LED: 0.9+ PF
Upgrade ballasts for better PF
Transformers
No load: 2-5% of rating (VAR)
Full load: 0.95-0.98 PF
Magnetizing current creates reactive demand
Larger transformers more efficient
Consider load-dependent losses
🏭Industrial Power Factor Correction
Motor-Driven Systems
Individual Motor Correction
50 HP motor: 37.3 kW at full load
Motor PF: 0.8 at full load
Reactive power: 37.3 × tan(36.87°) = 28 kVAR
Capacitor sizing: 70% of motor kVAR = 20 kVAR
Reason: Prevent over-correction at light loads
Install capacitor at motor starter
Pump Station Example
5 pumps × 25 HP each = 125 HP total
Diversity factor: 0.8 (not all run simultaneously)
Average load: 125 × 0.8 × 0.75 = 75 HP (56 kW)
Reactive demand: 56 × tan(41.4°) = 49 kVAR
Central capacitor bank: 50 kVAR with controller
Better than individual correction
Manufacturing Plant Power Factor
Steel Rolling Mill
Main drive motors: 2,000 kW at 0.75 PF
Auxiliary equipment: 500 kW at 0.85 PF
Total real power: 2,500 kW
Motor VAR: 2,000 × 0.882 + 500 × 0.620 = 2,074 kVAR
Target PF: 0.95, Required caps: 1,439 kVAR
Staged switching: 6 × 240 kVAR
Textile Mill Load Profile
Spinning machines: 800 kW at 0.8 PF
Weaving looms: 600 kW at 0.75 PF
Air compressors: 200 kW at 0.85 PF
Lighting/HVAC: 150 kW at 0.9 PF
Combined PF: 0.78, Improvement to 0.92
Install 950 kVAR with auto control
⚡Utility System Reactive Power Management
Transmission System VAR Control
Substation Shunt Compensation
138 kV substation serving 100 MVA load
Load power factor: 0.85 lagging
Load reactive demand: 100 × 0.527 = 52.7 MVAR
Line charging (100 miles): -30 MVAR
Net VAR requirement: 52.7 - 30 = 22.7 MVAR
Install 25 MVAR capacitor bank
Generator Reactive Capability
500 MW generator, 0.85 PF rating
At full MW output: ±312 MVAR capability
At 80% MW output: ±375 MVAR capability
Excitation limits vary with real power
Over-excitation: lagging VAR (inductive)
Under-excitation: leading VAR (capacitive)
Distribution System VAR Management
Feeder Voltage Regulation
12.47 kV feeder, 10 miles long
Peak load: 8 MVA at 0.85 PF
Voltage drop: 5% without compensation
Install 2 MVAR capacitor at 5 miles
Voltage drop reduced to: 3.2%
Capacitor improves voltage profile
Switched Capacitor Control
Peak load (summer): 15 MVAR needed
Light load (winter): 5 MVAR needed
Fixed capacitor: 5 MVAR
Switched bank: 2 × 5 MVAR steps
Control: Voltage/VAR/time/temperature
Automatic switching prevents overvoltage
🏢Commercial Building Power Factor
HVAC System Reactive Loads
Chiller Plant Power Factor
Centrifugal chiller: 500 tons (1,500 kW)
Compressor motor PF: 0.85
Chilled water pumps: 3 × 15 HP at 0.8 PF
Condenser pumps: 3 × 20 HP at 0.8 PF
Cooling tower fans: 4 × 10 HP at 0.85 PF
Combined plant PF: 0.84
Add 250 kVAR to achieve 0.95 PF
Air Handling Unit Motors
Supply fan: 50 HP VFD (37.3 kW)
Return fan: 25 HP VFD (18.6 kW)
VFD power factor: 0.95-0.98 (input)
Motor load varies 40-100% with building load
At 60% load: PF drops to 0.92
VFDs improve PF compared to DOL motors
Office Building Load Analysis
Typical Office Load Breakdown
HVAC (60%): 480 kW at 0.85 PF
Lighting (25%): 200 kW at 0.92 PF
Receptacles (10%): 80 kW at 0.9 PF
Elevators (5%): 40 kW at 0.8 PF
Total: 800 kW, Combined PF: 0.86
Need 250 kVAR for 0.95 PF target
Data Center Considerations
IT load: 500 kW at 0.95 PF (modern servers)
UPS system: 0.9-0.95 input PF
HVAC (precision cooling): 150 kW at 0.85 PF
Lighting: 25 kW at 0.95 PF
Combined PF: 0.92 (better than typical)
Modern IT equipment has good PF
📊Power Quality and Reactive Power
Harmonic Impact on Reactive Power
True vs Displacement Power Factor
Fundamental PF (DPF): 0.85
Current THD: 30% (non-linear loads)
Distortion factor: 1/√(1 + THD²) = 0.958
True PF = DPF × DF = 0.85 × 0.958 = 0.814
Apparent power increases due to harmonics
Harmonic filters needed, not just capacitors
Capacitor-Harmonic Interaction
System impedance at 5th harmonic reduced
Resonance possible with system inductance
Capacitor overheating and failure
Use detuned reactors: 7% impedance typical
Reactor prevents resonance below 7th harmonic
Filter design required for harmonic loads
Economic Impact and Cost Justification
Utility Billing Impact
1,000 kW load at 0.75 power factor
Demand charge: $15/kW × 1,000 = $15,000/month
Poor PF penalty: $8/kVAR above 0.9 PF
Excess kVAR: (1,000/0.75 - 1,000/0.9) = 222 kVAR
Monthly penalty: 222 × $8 = $1,776
Annual penalty: $21,312
System Loss Reduction
Feeder current at 0.75 PF: 1,604A
Feeder current at 0.95 PF: 1,265A
I²R losses reduced by: (1,604/1,265)² = 1.61×
Loss reduction: 38% of transmission losses
For 2% system losses: 0.76% energy savings
Significant savings on long feeders
💡Reactive Power Conversion Tips
Quick Calculations
Power Factor Formulas
PF = 0.8: kVAR = 0.75 × kW
PF = 0.85: kVAR = 0.62 × kW
PF = 0.9: kVAR = 0.48 × kW
PF = 0.95: kVAR = 0.33 × kW
Capacitor Sizing
Motor kVAR ≈ 0.5 to 0.7 × motor HP
Capacitor kVAR ≈ 0.7 × motor kVAR
Plant correction: Use multiplier tables
Design Guidelines
Best Practices
Target 0.95 PF for optimal economics
Use automatic switching for varying loads
Consider harmonics in modern facilities
Monitor voltage during switching operations
Typical VAR/kW Ratios
Induction motors: 0.3-0.9 kVAR/kW
Fluorescent lighting: 0.2-1.2 kVAR/kW
Welding equipment: 0.5-1.5 kVAR/kW
Mixed industrial: 0.4-0.8 kVAR/kW