Module B.1 Siusoidl stedy-stte lysis (sigle-phse), review.2 Three-phse lysis Kirtley Chpter 2: AC Voltge, Curret d Power 2.1 Soures d Power 2.2 Resistors, Idutors, d Cpitors Chpter 4: Polyphse systems 4.1 Three-phse systems 4.2 Lie-Lie Voltges 1
Three-phse power All of wht we hve doe i the previous slides is for sigle phse iruits. However, lmost ll trsmissio systems i the US re -phse AC systems (the oly exeptios re few DC trsmissio lies). Three-phse AC is preferred over sigle-phse AC euse the ivestmet d opertig osts per MW of trsmissio pity re more ttrtive, d euse -phse system provides ostt power (ot pulstig s we sw efore) You see this i the ext slide. 2
Three-phse power Three sigle phse systems? Or oe three-phse system? odes 1 ode Three sigle phse systems Oe three-phse system 6 wires 4 wires; pitl svigs! Eh eutrl rries full lod urret Eh eutrl rries full lod urret Eh sigle phse iruit delivers istteous power tht vries t 2ω. Lrge geertors & motor lods virte. Neutrl rries little or o urret d therefore e muh smller; pitl svigs! Neutrl rries little or o urret, therefore hs little losses; opertiol svigs! We will show tht three phse iruits deliver ostt istteous power; lrge geertors d motors ru smoothly.
Three-phse power AC geertors o the grid supply -phse power. A iruit digrm for the sttor of typil -phse geertor is provided i the ext two slides. 4
Lie-to-eutrl (phse) voltges The idetified voltges re referred to s lie-to-eutrl voltges, or phse voltges. 5
Lie-to-lie (lie) voltges The idetified voltges re referred to s lie-to-lie voltges, or just lie voltges. 6
Phsor digrm for lie-eutrl (phse) voltges 120 Rottio 120 120 Wht is rottig? The pek vlue of the siusoid; this pek vlue is projeted oto oe of the xes to oti the istteous vlue of the qutity, oept equivlet to writig v (t)=siωt. 120 120 www.imtios.physis.usw.edu.u/jw/phsor-dditio.html 7
Phsor digrm for lie-lie (lie) voltges Rottio 120 120 120 120 120 8
Lie-to-eutrl (phse) & lie-to-lie (lie) voltges - V ˆ + 0 - V ˆ + 120 0 - V ˆ (1 1 120) 0 V ˆ (1 1 120) 0 9
Reltig phse d lie voltges Rottio 0 0 0 10
Wye-oeted soures d lods Î Z Z Î Î Z 11
Bled oditios Bled -phse oditios hve: Lie d phse voltges relted s i previous slides. Z =Z =Z This results i: Iˆ Iˆ 120, Iˆ Iˆ 120, Iˆ 0 Note: I Wye-oeted lods, the lie urret d the phse urret (urret through Z ) re idetil. Î Î Z Z Î Î Z 12
Per-phse lysis Uder led oditios, we my perform sigle-phse lysis o lifted-out -phse d eutrl iruit, s show elow. Î Î Z Z Î Î Z 1 12
Per-phse lysis Î Z Now it is ler tht: Iˆ Z Also, we still hve: P S ˆ I P jq * 1 1 1 V I os, Q1 V 1 I si 14
Per-phse lysis Î Z After we perform the sigle-phse lysis, we my the ompute the -phse qutities ordig to: S S P P, Q Q 1 1 1 15
Three phse power reltios The previous power reltios utilize lie-to-eutrl voltges d lie urrets. Power my lso e omputed usig lie voltges, s developed i wht follows: P1 V I os ˆ V P V 0 V V V 1 I V os I V os V I os P V P 1 I os V I Likewise, we my develop tht Q V I si os 16
I summry: S Three phse power reltios S P P, Q Q 1 1 1 P V I os 1 Q V I 1 si P V I os Q V I si Note 1: I Wye-oetios, the power ftor gle θ is the gle y whih the lie-to-eutrl voltge leds the phse urret. It is ot the gle y whih the lie-to-lie voltge leds the phse urret. More geerlly, the power ftor gle t two termils is the gle y whih the voltge ross those termils leds the urret ito the positive termil. Î Note 2: The text uses ottio V LL for V. 17