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Phase order and star load (6+j8)

Short answer

Phase order is the sequence (e.g., RYB) in which voltages reach peak. Significance: determines motor rotation, needed for parallel operation and protection. For star load Z=6+j8 Ω, 400 V: phase and line currents are 23.09 A; total power is 9.6 kW.

Define phase order and explain its significance. A three phase balanced star connected load with (6+j8) ohm per phase is supplied by 400V, 50 HZ three phase source. Find the line and phase currents and the total power dissipated in the load.

Phase order (phase sequence)

Phase order is the order in which the three phase voltages (or currents) reach their positive maximum values, for example R → Y → B (RYB, positive sequence) or R → B → Y (RBY, negative sequence).

Significance:

  • It decides the direction of rotation of three-phase induction and synchronous motors. Interchanging any two supply lines reverses the sequence and the motor rotation.
  • It is essential for connecting generators in parallel and for connecting a new supply to an existing system.
  • It decides the readings of the two wattmeters and the line currents in unbalanced loads.
  • It is needed for correct phasor diagrams and for protection relays and phase-sequence meters.

Numerical

Given Z_ph = 6 + j8 = 10∠53.13° Ω, star connected, V_L = 400 V.

  • Phase voltage V_ph = 400/√3 = 230.9 V
  • Phase current I_ph = V_ph/Z = 230.9/10 = 23.09 A
  • Line current I_L = I_ph = 23.09 A (star connection)
  • Power factor = 6/10 = 0.6 lagging
  • Total power P = 3 I_ph² R = 3 × 23.09² × 6 = 9600 W = 9.6 kW

(Check: √3 V_L I_L cos φ = 1.732 × 400 × 23.09 × 0.6 = 9600 W.)

✓ Answer checked by Claude Opus 5.5 (high effort)

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