Reactive Power Conversion Formulas
Complete formulas for converting between different reactive power units including VAR, kVAR, MVAR, and related AC electrical power calculations.
⚡ Basic Reactive Power Unit Conversions
Standard Unit Conversions
VAR ↔ kVAR
Example: 25,000 VAR
25,000 VAR = 25 kVAR
kVAR ↔ MVAR
Example: 3,500 kVAR
3,500 kVAR = 3.5 MVAR
VAR ↔ MVAR
Example: 8,000,000 VAR
8,000,000 VAR = 8 MVAR
AC Reactive Power Relationships
Single-Phase Reactive Power
240V circuit, 30A, φ = 36.87°
Reactive power: 4.32 kVAR
Three-Phase Reactive Power
480V line voltage, 75A line current, φ = 31.79°
3-phase reactive power: 32.9 kVAR
📐 Power Triangle and Reactive Power
Calculating Reactive Power Components
From Apparent and Real Power
S = 50 kVA, P = 40 kW
Reactive power: 30 kVAR
From Power Factor
P = 40 kW, PF = 0.8
φ = arccos(0.8) = 36.87°
Reactive power: 30 kVAR
Leading vs Lagging Reactive Power
Inductive (Lagging) Load
Current lags voltage by φ degrees
Positive reactive power (+Q)
Examples: Motors, transformers, inductors
Creates magnetic fields
Requires reactive power from source
Most common in industrial loads
Capacitive (Leading) Load
Current leads voltage by φ degrees
Negative reactive power (-Q)
Examples: Capacitors, over-excited generators
Creates electric fields
Supplies reactive power to system
Used for power factor correction
🔌 Common Reactive Power Sources and Loads
| Equipment | Reactive Power | Power Factor | Type |
|---|---|---|---|
| Induction Motor (75% load) | +30 kVAR | 0.75 | Inductive |
| Fluorescent Ballast | +15 VAR | 0.5 | Inductive |
| Arc Furnace | +800 kVAR | 0.85 | Inductive |
| Transmission Line | +50 MVAR | 0.95 | Inductive |
| Power Factor Correction Capacitor | -25 kVAR | 0.0 | Capacitive |
| Underground Cable | -10 MVAR | 0.0 | Capacitive |
| Over-excited Synchronous Motor | -20 kVAR | 0.9 | Capacitive |
🔧 Power Factor Correction Calculations
Capacitor Sizing Formulas
Required Capacitive Reactive Power
Improve 200 kW from 0.75 to 0.90 PF
φ₁ = arccos(0.75) = 41.41°, tan(41.41°) = 0.882
φ₂ = arccos(0.90) = 25.84°, tan(25.84°) = 0.484
Required capacitor: 80 kVAR
Capacitor Bank Configuration
480V, 3-phase, 20µF per phase
X_C = 1/(2πfC) = 1/(2π×60×20×10⁻⁶) = 132.6Ω
For 80 kVAR: Need 80/5.2 = 15.4 → 16 capacitor units
Use 16 × 5 kVAR = 80 kVAR bank
Reactive Power in Transmission
Transmission Line Reactive Power
230kV line, X_L = 40Ω, R = 5Ω
Line reactive power: 1,300 MVAR
Shunt Reactor Compensation
500kV system, 100Ω reactor
Shunt reactor: 2,500 MVAR
⚙️ Reactive Power Control Systems
Automatic Voltage Regulation
Generator Excitation Control
Generator rating: 100 MVA, 0.85 PF
Real power output: 85 MW
At unity PF: Q = 0 MVAR
At 0.85 lagging: Q = 85 × tan(31.79°) = 53.1 MVAR
At 0.85 leading: Q = -53.1 MVAR
Range: ±53.1 MVAR reactive capability
Static VAR Compensator (SVC)
Thyristor-controlled reactor: +50 MVAR
Fixed capacitor bank: -75 MVAR
Control range: -75 to +50 MVAR
Response time: 1-3 cycles
Voltage regulation: ±0.5%
Continuous reactive power control
STATCOM and Advanced Controllers
STATCOM Operation
Rating: ±100 MVAR continuous
Overload: ±150 MVAR for 10 seconds
Response time: < 1 cycle
Voltage range: 0.5-1.1 pu
Independent P and Q control
Superior to SVC in weak systems
Dynamic Reactive Power Balance
System load: 800 MVAR inductive
Generator supply: 600 MVAR
Capacitor banks: 150 MVAR
Required compensation: 800 - 600 - 150 = 50 MVAR
STATCOM provides: 50 MVAR
Maintains voltage within ±5%