Synchronous machines

Transcription

1 Synchronous gnrator (altrnator): transorms mchanical nrgy into lctric nrgy; dsignd to gnrat sinusoidal oltags and currnts; usd in most powr plants, or car altrnators, tc. Synchronous motor: transorms lctric nrgy into mchanical nrgy; usd or highpowr applications (ships, original TGV ) Turbo-altrnator Saliant pols Rotor (inductor) : 2p pols with xcitation windings carrying DC currnt; nonlaminatd magntic matrial θ! = ω/ p Stator: polyphas (.g. 3-phas) winding in slots; laminatd magntic matrial... 01/03/2018 1

2 No-load charactristic olution o th oltag in a stator phas s. intnsity o th xcitation currnt, or a gin rotation spd and with no gnratd stator currnt Th rotor winding, carrying th DC currnt and rotating at spd ω/p, producs in th airgap a sliding m.m.. F (as sn rom thstator). F gnrats a magntic lux dnsity B r (with th sam phas) in th airgap, which inducs sinusoidal.m..s in th stator windings,with a phas lag o π/2. arag charactristic arag charactristic du du rmannt magntization = ( ) with ac = k θ! Φ ( itss spd θ! = constant = 0 ) Magntic lux producd by th inductor and sn by th stator winding Non linarity with hystrsis 2

3 Vctor diagram with load Diagram o magntomoti orcs and magntic lux dnsitis B r (4a) rsulting m.m.. (3) = (1)+(2) (1) Th rotor winding, carrying th DC currnt and rotating at spd ω/p, producs in th airgap a sliding m.m.. F (as sn rom th stator).. m.m.. rom (1) F m.m.. rom (2) (4b) = γ and = δ F (2) Th polyphas currnt in th stator winding producs a sliding m.m.m. F (in phas with ). (3) Th rsulting m.m.. is F r = F +F. (4) F r gnrats a magntic lux dnsity B r (with th sam phas) in th airgap,, which inducs sinusoidal.m..s in th stator windings, with a phas lag o π/2. 3

4 Vctor diagram with load Stator lakag lux Slot lakag lux Diagrams nd-winding lakag lux U = r j X Rsistanc o stator winding (sn by th stator but not coming rom th rotor) R.m.. inducd by lakag lux λ (t) = λ t i 1 = ( λ λ λ m m ) t i 1 t i 2 λ λ = j X with X = ω ( λ λ ) t = r j X F m t i 3 i + i2 + i3 1 = bcaus m 0 Stator lakag ractanc total.m.. γ and F F = γ + δ = = δ r r d = Fr γ = δ + γ quialnt xcitation currnt r no-load.m.. producd by r 4

5 Potir diagram Which xcitation currnt should on impos in th synchronous machin to rach th unctioning point corrsponding to a gin oltag U and currnt in th stator, with a phas shit o ϕ btwn U and? (4) r no-load.m. producd by th quialnt currnt r (2) r = U + R + j X (5) (3) (2) = r δ γ (0) (1) (3) 5

6 Raction Dmagntizing raction Th m.m.. is smallr than th no-load m.m.. ( r < ) Magntizing raction Th m.m.. is largr than th no-load m.m.. ( r > ) nducti bhaiour o th load ( lagging bhind U) Capaciti bhaiour o th load ( in ront o U) 6

7 Zro powr actor charactristic olution o th stator oltag U as a unction o th xcitation currnt, or a gin rotation spd and stator currnt, with a zro powr actor U = ( ) with ac itss spd θ! = constant = constant cos ϕ = 0 ( ϕ = ±π/ 2) xampl: ϕ = π/2 r δ + γ U r X 7

8 Short-circuit charactristic olution o th stator currnt as a unction o th xcitation currnt, or a gin rotation spd and with th stator windings in short-circuit r = U + R + j X = ( ) with ac itss spd θ! = constant U = 0 with r = R + U = 0 j X r X X β δ + β γ r δ + γ Non saturatd machin = β r r 8

9 Simpliid ctor diagram Bhn-schnburg s mthod Synchronous ractanc X s Whn th magntic matrials ar not saturatd, th combind ct o th raction and o stator lakag luxs can b takn into account thanks to a singl paramtr: th synchronous ractanc = r = r constant qual angls OAB and A OB Similar triangls OAB and OA B A, B and C colinar = U + R + j X s Synchronous ractanc 9

10 xprimntal dtrmination o X s Bhn-schnburg s mthod Synchronous ractanc X s U = 0 = + ( R j X s ) cc + j X s with R << Xs cc R = X s cc ( ( ) ) Approximation whn magntic matrials ar saturatd! 10

11 xtrior charactristic Altrnator xtrior charactristic olution o th oltag U on a gin stator phas as a unction o th currnt in this phas, whn th altrnator dris a load charactrizd by a constant powr actor, at constant spd and xcitation U = () with ac itss spd θ! = constant = constant cosϕ = constant 11

12 Ntwork connction Nd or intrconnction o lctric powr plants Daily pak conomical organization o powr production + Stability o th ntwork dspit local dcts Daily load Synchronization o an altrnaltor on an idal (ininitly powrul) AC ntwork Larg numbr o production units in paralll constant oltag and rquncy Th currnt should b zro whn th connction is mad 4 conditions = U R + j X s 1. sam pulsation ω (corrct rotation spd) 2. sam amplituds or and U (adjusting ) 3. no phas shit btwn and U 4. idntical phas ordring (in a 3-phas systm) 12

13 Bhaiour with load lctromagntic powr P lm Acti lctric powr P = 3 U cosϕ Torqu P 3 p C = = U cosϕ ω/ p ω Static instability Static stability ntrnal angl X s = cosϕ sinδ int C = 3 p ω X s U sinδ int ntrnal angl Atr ntwork synchronization, thr is no xchangd currnt. Thn : mchanical powr is proidd to th altrnator, gts ahad o U δ int incrass (until th quilibrium o th lctromagntic and mchanical torqus) a braking torqu is applid to th altrnator, gts bhind U δ int dcrass (ngati torqu) Th ariations o th rotor mchanical angl Δδ mc ar proportional to th ariations o th intrnal (lctric) angl Δδ int Δδ mc Δδ = p int 13

14 Bhaiour with load Static stability δ int < 0 ntrnal angl δ int > 0 ncrasing th mchanical (braking) torqu lads to an incras o th absolut alu o δ int, and a dcras in th absolut alu o C lm unstabl synchronous motor Unstabl altrnator Unstabl ncrasing th mchanical (braking) torqu lads to an incras o δ int, and a dcras o C lm unstabl static stability ncrasing th mchanical (braking) torqu lads to an incras o th absolut alu o δ int t o C lm stabl. Th quilibrium is rachd whn th two torqus ar qual. ncrasing th mchanical (braking) torqu lads to an incras o δ int and C lm stabl. Th quilibrium is rachd whn th two torqus ar qual. 14

15 Bhaiour with load Powr diagram Xs X MB = X s s cosϕ = 3 U cosϕ = P = 3 U 3 U Xs 3 U P lm Acti powr P Altrnator O'B = X X sinϕ = s 3 U sinϕ 3 U s = Xs 3 U Q Racti powr Q Motor 15

16 V-curs (Mordy curs) olution o th stator currnt as a unction o th xcitation currnt o a synchronous machin connctd to an idal ntwork, at constant acti powr undr-xcitd machin "V" Or-xcitd machin Constant acti powr ϕ > 0... ϕ > 0 Ntwork= inducti load Machin = capaciti systm static stability limit 16