How To Understand The Power Control System

Transcription

1 THREE-PHASE CIRCUITS PART I

2 AC GENERATOR Single-phase AC generatr - designed t generate a single sinusidal vltage fr each rtatin f the shaft (rtr). Plyphase AC generatr - designed t generate multiple utf-phase sinusidal vltages fr each rtatin f the rtr by increasing the number f cils n the statr. The three-phase generatr has three inductin cils placed 120 apart n the statr. The three cils have an equal number f turns. the vltage induced acrss each cil will have the same peak value, shape, and frequency. the three sinusidal vltages are ut f phase by 120 Tw types f cnfiguratin: Wye (Y) r Delta (Δ)

3 SINGLE-PHASE AC GENERATOR

4 THREE-PHASE AC GENERATOR

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6 FARADAY S LAW The physical r experimental law gverning the peratin f and AC generatr. The electrmtive frce (EMF) induced in a circuit is directly prprtinal t the time rate f change f magnetic flux thrugh the circuit. The EMF can either be prduced by changing B (induced EMF) r by changing the area, e.g., by mving the wire (mtinal EMF). It is the relative mvement between the cil and the magnet that matters.

7 THREE-PHASE VOLTAGE SOURCES Y-cnnected Surce Δ-cnnected Surce (uncmmn)

8 BALANCED Y-CONNECTED VOLTAGE SOURCE Balanced phase vltages are equal in magnitude and are ut f phase with ne anther by 120 degrees. V = V p 0 V = V p 120 V cn = V p 120 an bn Phase vltages sum up t zer, i.e., V an + Vbn + Vcn = 0 Tw pssible cmbinatins: V V V an bn cn = V 0 p = V 120 p = V 240 p V V V an bn cn = V 0 p = V p = V p a bc (+) acb ( ) psitive phase sequence negative phase sequence

9 Balanced line vltages are equal in magnitude and are ut f phase with ne anther by 120 degrees. V = 3V 30 V = 3V V 3V 150 ab p bc p 90 ca = p Line vltages sum up t zer, i.e., V V + V = 0 ab + bc ca The magnitude f line vltages is 3 times the magnitude f the phase vltages. Line vltages lead their crrespnding phase vltages by 30

10 Y Δ SOURCE TRANSFORMATION V = an V Y θ Y V bn = V Y θ Y 120 Vcn = V Y θ Y 240 Y Δ V 3 θ + 30 ab = V Y Y V 3 θ 90 bc = V Y Y V 3 θ 210 ca = V Y Y

11 Δ Y SOURCE TRANSFORMATION V ab = V θ Δ Δ V an V Δ 3 θ = Δ 30 V bc V Δ θ 120 = Δ Δ Y V bn V Δ 3 θ = Δ 150 V ca = V Δ θδ 240 V cn V Δ 3 θ = Δ 270

12 BALANCED THREE-PHASE LOAD CONFIGURATIONS A balanced lad is ne in which the phase impedances are equal in magnitude and in phase. Tw pssible cnfiguratins: Wye r Delta Cnversin frm Y t Δ r Δ t Y 1 Z Y = Z1 = Z2 = Z3 = ZΔ 3 ZΔ = Za = Zb = Zc = 3ZY

13 Ex. Practice prblem 12.1 Given that Vbn psitive sequence. = V, find V an and V cn, assuming a

14 THREE-PHASE CONNECTIONS Bth the three phase surce and the three phase lad can be cnnected either Wye r DELTA. We have 4 pssible cnnectin types. 1) Y-Y cnnectin 2) Y-Δ cnnectin 3) Δ-Δ cnnectin 4) Δ-Y cnnectin Balanced Δ cnnected lad is mre cmmn. Y cnnected surces are mre cmmn.

15 BALANCED Y-Y CONNECTION

16 Ex. Calculate line currents in the three-wire Y-Y system shwn.

17 Ex. Practice prblem 12.2 A Y-cnnected balanced three-phase generatr with an impedance f 0.4+j0.3 Ω per phase is cnnected t a Y-cnnected balanced lad with an impedance f 24+j19 Ω per phase. The line jining the generatr and the lad has an impedance f 0.6+j0.7 Ω per phase. Assuming a psitive sequence fr the surce vltages and that V = V, find the line vltages and line currents. an

18 BALANCED Y-Δ CONNECTION

19 Ex. A balanced abc-sequence Y-cnnected surce with phase vltage Van = V is cnnected t a Δ-cnnected balanced lad f 8+j4 Ω per phase. Calculate the phase and the line currents.

20 Ex. Practice prblem 12.3 One line vltage f a balanced Y-cnnected surce is V = V. If the surce is cnnected t a Δ-cnnected AB lad f Ω, find the phase and line currents assuming the abc sequence.

21 BALANCED Δ-Δ CONNECTION

22 Ex. A balanced Δ-cnnected lad having an impedance f 20 j15 Ω is cnnected t a Δ-cnnected, psitive sequence generatr having Vab = V. Calculate the phase currents f the lad and the line currents.

23 Ex. Practice prblem 12.4 A psitive-sequence, balanced Δ-cnnected surce supplies a balanced Δ-cnnected lad. If the impedance per phase f the lad is 18+j12 Ω and I a = A, find I AB and V. AB

24 BALANCED Δ-Y CONNECTION

25 Ex. A balanced Y-cnnected lad with a phase impedance f 40+j 25 Ω is cnnected t a balanced, psitive sequence Δ- cnnected surce with a line vltage f 210 V. Calculate the phase currents. Use V ab as a reference.

26 Ex. Practice prblem 12.5 In a balanced Δ-Y circuit, Vab = V and Z Y = 12 + j15 Ω. Calculate the line currents.