Question

The magnitude of the phase voltage of an ideal balanced three-phase Y-connected source is 110 V . The source is connected to a balanced Y-connected load by a distribution line that has an impedance of 0.1+0.8i Ω/ϕ . The load impedance is 20.2+14.8i Ω/ϕ . The phase sequence of the source is acb. Use the a-phase voltage of the source as the reference.

Part A: Specify the magnitude and phase angle of the line current IaA.

Part B: Specify the magnitude and phase angle of the line current IbB.

Part C: Specify the magnitude and phase angle of the line current IcC.

Part D: Specify the magnitude and phase angle of the line voltage Vab at the source.

Part E: Specify the magnitude and phase angle of the line voltage Vbc at the source.

Part F: Specify the magnitude and phase angle of the line voltage Vca at the source.

Part G: Specify the magnitude and phase angle of the phase voltage VAN at the load.

Part H: Specify the magnitude and phase angle of the phase voltage VBN at the load.

Part I: Specify the magnitude and phase angle of the phase voltage VCN at the load.

Part J: Specify the magnitude and phase angle of the line voltage VAB at the load.

Part K: Specify the magnitude and phase angle of the line voltage VBC at the load.

Part L: Specify the magnitude and phase angle of the line voltage VCA at the load.

Answer #1

Source Voltage =110V

Phase Sequence of Source = acb

Wire Impedance Z_{w} = 0.1 + 0.8i ohm/phase =
0.80682.9

Load Impedance Z_{L} = 20.2 + 14.8i ohm/phase =
25.0436.2

Total Impedance Z = 20.3 + 15.6i = 25.637.54

Phase current = 110 / 25.6 = 4.30 amp

V_{a} = 1100 = 110 + 0i
Volts

V_{b} = 110120 = -55 +
95.26i Volts

V_{c} = 110-120 = -55 -
95.26i Volts

Part |
Parameter |
Formula |
Result |

D | V_{ab} |
V_{a}-V_{b} |
190.52-30 Volts |

E | V_{bc} |
V_{b}-V_{c} |
190.5290 Volts |

F | Vca | V_{c}-V_{a} |
190.52-150 Volts |

A | I_{aA} |
V_{a}/Z |
4.30-37.5 |

B | I_{bB} |
V_{b}/Z |
4.3082.5 |

C | I_{cC} |
V_{c}/Z |
4.30-157.5 |

G | V_{AN} |
I_{aA} x Z_{L} |
109.22-1.3 |

H | V_{BN} |
I_{bB} x Z_{L} |
109.22118.7 |

I | V_{CN} |
I_{cC} x Z_{L} |
109.22-121.3 |

J | V_{AB} |
V_{A}-V_{B} |
189.17-31.3 Volts |

K | V_{BC} |
V_{B}-V_{C} |
189.1788.7 Volts |

L | V_{CA} |
V_{C}-V_{A} |
189.17-151.3 Volts |

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