CHAPTER II AC POWER CALCULATIONS
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1 CHAE AC OWE CACUAON
2 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 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.
4 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
5 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 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 7 Exaple Gen ha cos cos377 fnd he nsananeous power and he aerage ol p : cos377 6 cos 55 cos cos754 45cos W cos 344. W power.
8 8 Exaple Fnd he he aerage 3 across.. ol : j7 3 j7 power absorbed by when a olage e.576 cos 66.8 s * e W an pedance appled
9 9 Exaple 3 Fnd he aerage power suppledby hesource and he aerage power absorbed by heressor. ol : 53 4 j cos W.8.5 W 4
10 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
11 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
12 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
13 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
14 uary pedance sn ower eace cos e ower eal ower Apparen Coplex ower * Q Q jq 4
15 5 ower rangle ower rangle pedance rangle ower rangle
16 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
17 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
18 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,
19 9 EANNG EAME Deerne real and reace power losses And real and reace power suppled. j.5 e{} cos pf kA pf.84 4kW pf.84laggng Q 5,839 A * 6.45 A pf cos A * losses lne lne losses. j ,685 load 4 j, 73A j5.839ka Balance of power suppled losses load j.73 4 j j37.55ka
20 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
21 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
22 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 Q cos sn 5 sn A 5A cos When pf s rased o.95, cos Q Q C 4.5 A cos sn 4.5sn A Q Q C Q A C F
23 Exaple 3
24 4 Exaple Calculae he source coplex power and power facor, how how he power facor can be proed o.95 =* = 3.37*43< A =45 <48.3 =876 + j 979.F = cos =.665 New p.f =.95, s = Qc = an s an s =6456 A C Qcapacor F
25 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 e power facor s pf cos W pf 34.86pf
26 Maxu ower ransfer ax * 8, he condon wh axu power, ofnd j d d d d j j j 6
27 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
28 Fnd he alue of n he crcu shown for axu power ransfer. 8
29 oluon 9
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