ECE 2100 Circuit Analysis
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1 ECE 00 Crcut Analyss Lesson 3 Chapter : AC Power Analyss (nstant & Ae Power; Max Ae Power Transfer; Effecte or RMS alue, Power Factor, Coplex Power, Power Trangle, Power Factor Correcton Danel M. Ltynsk, Ph.D.
2 ECE 00 Crcut Analyss Chapter AC Power Analyss Copyrght The McGraw-Hll Copanes, nc. Persson requred for reproducton or dsplay.
3 AC Power Analyss Chapter. nstantaneous and Aerage Power. Maxu Aerage Power Transfer.3 Effecte or RMS alue.4 Apparent Power and Power Factor.5 Coplex Power.6 Conseraton of AC Power.7 Power Factor Correcton.8 Power Measureent 3
4 4 Snusodal power at wt Constant power cos ( cos ( cos ( cos ( ( ( ( t t t t t t p w w w. nstantaneous and Aerage Power ( The nstantaneous power, p(t p(t > 0: power s absorbed by the crcut; p(t < 0: power s absorbed by the source.
5 . nstantaneous and Aerage Power ( The aerage power, P, s the aerage of the nstantaneous power oer one perod. P T T 0 p( t dt cos (. P s not te dependent.. When θ = θ, t s a purely resste load case. 3. When θ θ = ±90 o, t s a purely reacte load case. 4. P = 0 eans that the crcut absorbs no aerage power. 5
6 . nstantaneous and Aerage Power (3 Exaple Calculate the nstantaneous power and aerage power absorbed by a passe lnear network f: ( t ( t 65cos (0 t 0 0 sn (0 t 60 Answer: cos(0t 0kW,.0606W 6
7 . nstantaneous and Aerage Power (4 Exaple A current 0 30 flows through an pedance Z 40 Ω. Fnd the aerage power delered to the pedance. Answer: kw 7
8 . Maxu Aerage Power Transfer ( Z TH R TH j X TH Z L R L j X L The axu aerage power can be transferred to the load f X L = X TH and R L = R TH P ax TH 8 R TH f the load s purely real, then R L R TH X TH Z TH 8
9 . Maxu Aerage Power Transfer ( Exaple 3 For the crcut shown below, fnd the load pedance Z L that absorbs the axu aerage power. Calculate that axu aerage power. (Change current source to 6A Answer: 3.45 j0.737w,.49w 9
10 .3 Effecte or RMS alue ( The total power dsspated by R s gen by: P T R Rdt T T 0 0 T dt R Hence, eff s equal to: eff T 0 T dt The alue s a constant tself whch depends on the shape of the functon (t. The effect of a perodc current s the dc current that delers the sae aerage power to a resstor as the perodc current. 0
11 .3 Effecte or RMS alue ( The alue of a snusod (t = cos(wt s gen by: The aerage power can be wrtten n te of the alues: eff cos (θ θ cos (θ θ Note: f you express apltude of a phasor source(s n, then all the answers as a result of ths phasor source(s ust also be n alue.
12 .4 Apparent Power and Power Factor ( Apparent Power, S, s the product of the r..s. alues of oltage and current. t s easured n olt-aperes or A to dstngush t fro the aerage or real power whch s easured n watts. P cos (θ θ S cos (θ θ Apparent Power, S Power Factor, pf Power factor s the cosne of the phase dfference between the oltage and current. t s also the cosne of the angle of the load pedance.
13 .4 Apparent Power and Power Factor ( Purely resste load (R Purely reacte load (L or C Resste and reacte load (R and L/C θ θ = 0, Pf = θ θ = 90 o, pf = 0 θ θ > 0 θ θ < 0 P/S =, all power are consued P = 0, no real power consupton Laggng - nducte load Leadng - capacte load 3
14 .5 Coplex Power ( Coplex power S s the product of the oltage and the coplex conjugate of the current: θ θ θ θ 4
15 .5 Coplex Power ( S θ θ S cos (θ θ j sn (θ θ S = P + j Q P: s the aerage power n watts delered to a load and t s the only useful power. Q: s the reacte power exchange between the source and the reacte part of the load. t s easured n AR. Q = 0 for resste loads (unty pf. Q < 0 for capacte loads (leadng pf. Q > 0 for nducte loads (laggng pf. 5
16 .5 Coplex Power (3 S cos (θ θ j sn (θ θ S = P + j Q Apparent Power, S = S = * = Real power, P = Re(S = S cos(θ θ Reacte Power, Q = (S = S sn(θ θ Power factor, pf = P/S = cos(θ θ P Q 6
17 .5 Coplex Power (4 S cos (θ θ j sn (θ θ S = P + j Q Power Trangle pedance Trangle Power 7
18 .6 Conseraton of AC Power ( The coplex real, and reacte powers of the sources equal the respecte sus of the coplex, real, and reacte powers of the nddual loads. For parallel connecton: S * ( * * The sae results can be obtaned for a seres connecton. * * S S 8
19 .7 Power Factor Correcton ( Power factor correcton s the process of ncreasng the power factor wthout alterng the oltage or current to the orgnal load. Power factor correcton s necessary for econoc reason. 9
20 .7 Power Factor Correcton ( Q c = Q Q = P (tan θ - tan θ = ωc Q = S sn θ = P tan θ C Q ω c P (tan θ tan θ ω P = S cos θ Q = P tan θ 0
21 .8 Power Measureent ( The watteter s the nstruent for easurng the aerage power. The basc structure Equalent Crcut wth load f ( t cos( wt and ( t cos( wt P cos (θ θ cos (θ θ
ECE 2100 Circuit Analysis
ECE 00 Crcut Analyss Lesson 3 Chapter : AC Power Analyss (nstant & Ae Power; Max Ae Power Transfer; Effecte or RMS alue, Power Factor, Coplex Power, Power Trangle, Power Factor Correcton Danel M. Ltynsk,
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