Types of Power in Three-Phase Systems

• Active Power (P):
  • Represents the real power consumed.
  • Measured in kilowatts (kW).
  • Formula: P = √3 × VL × IL × cos(φ).
• Reactive Power (Q):
  • Represents power stored and released by inductors or capacitors.
  • Measured in kilovolt-amperes reactive (kVAR).
  • Formula: Q = √3 × VL × IL × sin(φ).
• Apparent Power (S):
  • The total power supplied to the system.
  • Measured in kilovolt-amperes (kVA).
  • Formula: S = √3 × VL × IL.

Balanced vs. Unbalanced Loads

• Balanced Load:
  • All three phases carry equal currents, and the system is symmetrical.
  • Simplifies power calculations using the formulas above.
• Unbalanced Load:
  • Phases carry different currents due to unequal loads.
  • Requires individual phase analysis for accurate calculations.

Energy Measurement in Three-Phase Systems

Energy consumption is calculated as:

Energy (kWh) = P × t

where:

• P = Active power in kW.
• t = Time in hours.

Example Problem

Problem: A three-phase motor operates at:

• Line Voltage (VL) = 400 V
• Line Current (IL) = 10 A
• Power Factor (PF) = 0.85
• Operating Time = 5 hours

Solution:

1. Active Power:

   P = √3 × VL × IL × cos(φ) = √3 × 400 × 10 × 0.85 = 5.88 kW

2. Energy Consumption:

   Energy = P × t = 5.88 × 5 = 29.4 kWh

Applications

• Industrial Use: Powers large machinery and motors efficiently.
• Energy Management: Accurate measurement helps reduce costs.
• Commercial Buildings: Supplies lighting, HVAC, and other systems.

Conclusion

Three-phase systems use active, reactive, and apparent power efficiently. Balanced loads simplify calculations, while unbalanced loads require detailed analysis. Accurate power and energy calculations are essential for industrial and commercial applications.