Apparent Power Conversion Formulas
Complete formulas for converting between different apparent power units including VA, kVA, MVA, and related AC electrical power calculations.
⚡ Basic Apparent Power Unit Conversions
Standard Unit Conversions
VA ↔ kVA
Example: 15,000 VA
15,000 VA = 15 kVA
kVA ↔ MVA
Example: 2,500 kVA
2,500 kVA = 2.5 MVA
VA ↔ MVA
Example: 5,000,000 VA
5,000,000 VA = 5 MVA
AC Power Relationships
Single-Phase Apparent Power
120V circuit, 25A current
In kVA: 3000 ÷ 1000 = 3 kVA
Apparent power: 3 kVA
Three-Phase Apparent Power
480V line voltage, 50A line current
3-phase apparent power: 41.6 kVA
📐 Power Triangle Relationships
Power Components
Apparent Power from Real & Reactive
P = 8 kW, Q = 6 kVAR
Apparent power: 10 kVA
Power Factor Relationship
P = 8 kW, S = 10 kVA
Phase angle: φ = arccos(0.8) = 36.87°
In percentage: 0.8 = 80% PF
Power factor: 0.8 lagging
Real Power Calculations
Real Power from Apparent Power
25 kVA transformer, 0.85 PF
In watts: 21.25 × 1000 = 21,250 W
In horsepower: 21,250 ÷ 746 = 28.5 hp
Real power delivered: 21.25 kW
Reactive Power Component
25 kVA, φ = arccos(0.85) = 31.79°
Check: √(21.25² + 13.17²) = 25 kVA ✓
Reactive power: 13.17 kVAR
🏭 Common Apparent Power Applications
| Equipment | Apparent Power | Power Factor | Real Power |
|---|---|---|---|
| Household Circuit | 1.8 kVA | 0.95 | 1.7 kW |
| Small Motor (5 hp) | 5.2 kVA | 0.85 | 4.4 kW |
| Office Building | 500 kVA | 0.90 | 450 kW |
| Industrial Plant | 2.5 MVA | 0.80 | 2.0 MW |
| Distribution Transformer | 25 kVA | 1.00 | 25 kW |
| UPS System | 100 kVA | 0.90 | 90 kW |
| Power Substation | 50 MVA | 0.95 | 47.5 MW |
🔧 Transformer & Generator Calculations
Transformer Sizing
Load-Based Sizing
Load: 80 kW at 0.8 PF
Add 25% safety factor: 100 × 1.25 = 125 kVA
Standard size: 150 kVA transformer
Recommended: 150 kVA transformer
Current Calculation
150 kVA, 480V secondary
Primary current (4160V): 20.8 A
Secondary full load: 180.4 A
Generator Sizing
Standby Generator
Critical loads: 200 kW, 0.85 PF
Standard size: 350 kVA generator
Emergency generator: 350 kVA
Starting Surge Capacity
50 hp motor starting (37.3 kW)
Running load: 200 kVA
Motor starting: 37.3 kW ÷ 0.2 = 186.5 kVA
Surge capacity needed: 760 kVA
📊 Power Quality Applications
Harmonic Distortion Effects
Total Harmonic Distortion
100 kVA fundamental, 20% THD
Derating factor: 1.02 (2% increase)
True apparent power: 102 kVA
K-Factor for Transformers
Non-linear loads present
LED/computer loads: K-4 to K-13
Standard transformer: K-1
K-13 derated to 86% of nameplate
100 kVA K-13: 86 kVA usable capacity
Use K-rated transformers
Power Factor Correction
Capacitor Sizing
Improve 100 kW from 0.7 to 0.95 PF
φ₁ = arccos(0.7) = 45.57°, tan(45.57°) = 1.02
φ₂ = arccos(0.95) = 18.19°, tan(18.19°) = 0.33
Capacitor bank: 69 kVAR
Demand Reduction
After PF correction to 0.95
Original: S = 100 ÷ 0.7 = 142.9 kVA
Corrected: S = 100 ÷ 0.95 = 105.3 kVA
Reduction: 142.9 - 105.3 = 37.6 kVA
Savings: 26% demand charge reduction
Monthly savings: $500-1500 typical