CHAE AC OWE CACUAON
Conens nroducon nsananeous and Aerage ower Effece or M alue Apparen ower Coplex ower Conseraon of AC ower ower Facor and ower Facor Correcon Maxu Aerage ower ransfer Applcaons
3 nroducon Eery elecrcal dece has a power rang ha ndcaes how uch power he equpen requres; exceedng he power rang can cause peranen daage. e choce of power delery n 5- or 6-Hz ac for s due o he allowed hgh-olage power ransforaon.
nsananeous ower e ndependen wce angular frequency cos cos cos cos cos cos excaon, Assung snusodal wasw as defned s power e nsananeous p p 4
Aerage ower cos cos cos cos cos cos cos oer one perod. power he nsananeous he aerage of e aerage power s d d d d d p 5
6 Aerage ower Con d cos j e * cos Case: for a purely resse crcu, f. Case : 9 for a purely reace cos 9 crcu A resse load absorbs power a all e, whle a load or C absorbs zero aerage power. reace
7 Exaple Gen ha cos377 45 cos377 fnd he nsananeous power and he aerage ol p : cos377 6 cos 55 cos754 344. 6 cos754 45cos377 35 35 W cos 344. W power.
8 Exaple Fnd he he aerage 3 across.. ol : j7 3 j7 power absorbed by when a olage 76.6 66.8 e.576 cos 66.8 s.57666.8 * e.576 66.8 37.4 W an pedance appled
9 Exaple 3 Fnd he aerage power suppledby hesource and he aerage power absorbed by heressor. ol : 53 4 j 53 4.47 6.57.856.57 5.8 cos3 56.57.5 W.8.5 W 4
Effece or M alue e effece s he dc curren ha delers power oa e power absorbed by heressor n he ac crcu s d d d Whle he power absorbed by heressor n he dc crcu s eff eff ressor as alue of eff d a he perodc curren. perodc curren, he sae eff d ac crcu dc crcu
Effece or M alue Con d For any perodc funcon x For hesnusod cos d larly, for cos, e aerage cos, power can be wren as cos cos x, he d he alue s alus s cos gen by cos d
Coplex ower sn cos where gen as he ac load s absorbed by e coplex power are gen n phasor for as olage Consderng he curren and * * j power eace : power eal : e, nce * * Q jq j j
3 Coplex ower Con d s he aerage or real power. e power delered o he load e acual power dsspaed by he load Q s he reace or quardraure power. Un: ol-apere reace A A easure of he energy exchange beween he source and he reace par of he load Q = for resse loads uny pf Q < for capace loads leadng pf Q > for nduce loads laggng pf
uary pedance sn ower eace cos e ower eal ower Apparen Coplex ower * Q Q jq 4
5 ower rangle ower rangle pedance rangle ower rangle
Apparen ower and ower Facor angle ower facor ower facor Apparen power : : cos pf : A un where pf cos cos cos s power e aerage or cos cos are olage he curren and f 6
and pf Con d load an olage curren lags eans pf load a olage curren leads eans pf nce cos pf he oad pedance of Angle ower Facor Angle nduce aggng capace eadng 7
8 CONEAON OF AC OWE Wheher he loads are conneced n seres or n parallel or n general, he oal power suppled by he source equals he oal power delered o he load. us, n general, for a source conneced o N loads,
9 EANNG EAME Deerne real and reace power losses And real and reace power suppled. j.5 e{} cos pf 4 47. 6kA pf.84 4kW pf.84laggng Q 5,839 A * 6.45 A pf cos 3. 86 6.45 3.86 A * losses lne lne losses. j.56.45 4,685 load 4 j, 73A j5.839ka Balance of power suppled losses load 4.685 j.73 4 j5.839 44.685 j37.55ka
ower Facor Correcon s he process of ncreasng he power facor whou alerng he olage or curren o he orgnal load. pf correcon C j jc Mos loads are nduce. C
pf Correcon Con d zero. s because correcon he pf no affeced by s power Noe ha hereal an an Bu an an conseraon ges Applynghe ac power an sn an sn cos cos power, he real alerng whou cos o fro cos pf o ncrease we desre f * C C C C C Q C C Q Q Q Q Q Q
Exaple When conneced o a -, 6 - Hz power lne, a load absorbs 4 - kw a laggng power facor of.8. Fnd he capacance necessary o rase he pf o.95. ol : 6 rad/s We hae 4W pf. 8 pf cos. 8 36. 87 Q cos sn 5 sn36. 87 3A 5A cos When pf s rased o.95, cos.95 8.9 Q Q C 4.5 A cos sn 4.5sn8.9 34.4 A Q Q C Q 3 34.4 685.6 A C 685.6 3.5 F
Exaple 3
4 Exaple Calculae he source coplex power and power facor, how how he power facor can be proed o.95 =* = 3.37*43<7.89+4.43 A =45 <48.3 =876 + j 979.F = cos 7.89+4.43 =.665 New p.f =.95, s = 8.948 Qc = an s an s =6456 A C Qcapacor 6456 3.37 6 878 F
5 Exaple Deerne he power facor as seen by he source. Calculae he aerage power delered by he source. ol : e oal pedance s 6 4 -j 6. 8 j. 6 7 3. 4 e power facor s pf cos 3. 4. 9734 3 7 3.4 4.863.4 5 W pf 34.86pf
Maxu ower ransfer ax * 8, he condon wh axu power, ofnd j d d d d j j j 6
7 Maxu Aerage ower ransfer H H j H j e axu aerage power can be ransferred o he load f = H and = H ax H 8 H f he load s purely resse, hen H H H
Fnd he alue of n he crcu shown for axu power ransfer. 8
oluon 9