Chapter 7 AC Power and Three-Phase Circuits

Transcription

1 Chaper 7 AC ower and Three-hae Crcu

2 Chaper 7: Oulne eance eacance eal power eacve power

3 ower n AC Crcu

4 ower and Energy Gven nananeou power p, he oal energy w ranferred o a load beween and : w p d The average power he average rae of energy ranfer defned a: w. p d

5 Average ower Le T and for any neger ulple of he perod of p, he average power over T he ae a he long er average by leng. The long er average w T p d T T

6 Average ower of a erodc Funcon Suppoe p con of a conan coponen and a perodc funcon, long er average equal o he conan coponen. ax n

7 Average Dpaed ower The average power dpaed by a reor wh a peak curren and a peak volage : /, co co φ ω φ ω

8 Average Dpaed ower Wh an arbrary load: φ coθ Source Supple θ θ φ coθ Load eurn

9 Average Dpaed ower The average power dpaed by he load :, co / co / θ ω ω ω θ [ ] co co co co co co v v p v φ θ ω θ φ ω φ θ ω φ ω φ θ ω

10 Exaple 7. AC ower Calculaon k j k C , W W W k ω

11 For a conan curren hrough a reance: T p d T T T d

12 oo Mean Square alue An effecve conan curren o wh repec o power dpaon ha he followng for: T d T For a perodc curren, he effecve curren equal o he roo ean quare value. The roo-ean-quare defned a T d T Lkewe, he value of a perodc volage T v d T Snuodal Snuodal

13 oo Mean Square alue ω ω.

14 Exaple 7.: MS alue of a Half- ecfed Wave n ω for 0 T 0 for < < T T T / T 0 /, n π d T 4 / 4

15 Maxu ower Tranfer v. Maxu Effcency Eff jx jx,, S X X X X >, 0 For axu power ranfer and

16 Maxu ower Tranfer When jx he pedance are ached for axu power ranfer. * Maxu avalable power 50% effcency: ax / 4

17 Maxu ower Tranfer f he rao X/ fxed bu can be adjued, he axu value of. coθ, X nθ Le d d coθ coθ 0, we have X nθ

18 Exaple 7.3: ower Tranfer fro an Ocllaor., 6 j8 0kΩ Cae : Mached load pedance ax * 6 j8kω. 60µ W, Eff 50% 4 6 Cae : X 4 5.µ W,, 7 4 j7 c 5c 6.3 0kΩ 6.3 Eff 0 6.% 0

19 ower Sye

20 Load n a AC ower Sye For ac power ye operang a a fxed frequency e.g., p 60Hz, frequency-dependen effec can be gnored. n h cae, any load pedance can be wren a: θ jx coθ j nθ

21 haor n MS φ v For Snuod: φ φ v θ

22 eal ower and eacve ower nananeou power : [ ] p co co θ ω φ θ v p p [ co ω φ v ] Qn ω X eal power average aborbed power n W: co θ φ v eacve power rae of energy exchange n Ar: Q n θ X olage-apere reacve

23 eal ower and eacve ower p p p X [ co ω φ v ] Qn ω φ v

24 nducve v. Capacve For a ngle nducor : For a ngle capacor : Q L Q C ωl L C ωc L ωl ωc C A load wh nducve reacance X>0, Q>0 A load wh capacve reacance X<0, Q<0 eacve power ncreae he curren o acheve he ae average power wang power

25 Exaple 7.4: ower-tranfer Effcency 4-j8 6-j8 kw Eff kar Q kw A L L %, % 0 3.7, no capacor, f kw W A L

26 Coplex ower Apparen power n A: Q Coplex power: S * θ jq Magnude of he coplex power apparen power. S The coplex power obey he conervaon law. n oher word, when everal load are conneced o he ae ource, he oal coplex power fro he ource he ae a he u of he coplex power of he load.

27 ower Facor ower facor : pf / S coθ for a pave load, 0,0 pf X S / pf >.

28 ower Facor A load wh pf draw nu ource curren. f he load nducve, Q>0 and θ>0, a laggng power facor curren phaor lag he volage phaor. f he load capacve, Q<0 and θ<0, a leadng power facor curren phaor lead he volage phaor. Connecng a capacor n parallel wh an nducve load can ake pf power-facor correcon. Q ± S ± S pf

29 Table 7.

30 Table 7.

31 Exaple 7.5: Degnng ower-facor Correcon A S ka Q S Q Q Q A k kar Q ka k S A k kar Q ka k S , 9.8, , 7, , 64,

32 Exaple 7.5: Con. ower facor correcon: c 0, Q c Qc C ω c c 57kAr 605µ F 7kW, Q 7kW 44A 500 0

33 Exaple 7.6: provng ower-tranfer Effcency only correc he load A 4 j55 0 j S 4 j55 L 0 83% k j35kar

34 Exaple 7.6: Con. 96% , afer correcon Add Ω kar j kw j S A j j j C j j C j Y C j L eq eq ω ω ω

35 Waeer v M v M v T v M v d T K φ ω φ ω φ ω φ ω γ >> co, co Le co, co angle Seady ae deflecon

36 Waeer e [ ] * γ KM T K M M M co T co ω φ co ω φ K M φ φ v v M d

37 Chaper 7: roble Se 4, 7,, 6, 9,, 6, 3, 34, 40