Chap 10 - Summary
trfVItpfVIpfVIp
2sin..2cos...
pfVIP .rfVIQ .
)cos( pfapf
iv
pfa
)sin( pfarf
z
P
Q
pfa
)(tan 1
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Summary-Advanced Circuit Analysis-Lecture Slides, Summaries of Electrical Circuit Analysis
This lecture is part of lecture series on Electrical Circuit Analysis course. It was delivered by Prof. Mursleen Sayed at Bengal Engineering and Science University. It includes: Alternate, Forms, Complex, Power, Average, Power, Transfer, Apparent, Complex, Thevenin, Impedance
Typology: Summaries
2011/2012
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Chap 10 - Summary
t
rf
VI
t
pf
VI
pf
VI
p
^
sin.
cos.
.^
pf VI P^
. ^
rf VI Q^
. ) cos(
pfa
pf^
i v pfa
^
) sin(
pfa
rf^
z Q P
pfa
^
^
) ( tan
(^1)
Chap 10 - Summary ^ Complex Power P + jQ ^ Apparent Power |S| ^ Power factor correction ^ Alternate forms for Complex power^ ^
P = |
(^2) I |R = I eff
2 R/2m
^ Q = |
(^2) I |X = I eff
2 X/2m
^ P = |
(^2) V | eff /R ^ Q = |
(^2) V | eff /X
^ Maximum Average Power Transfer Z
*^ = ZTH
L
^ Maximum Average Power
L (^2) max L (^2) TH
R (^8) / V R (^4) / |V |^
Example 4 ^ ZL
that results in max. average power transfer? ^ Maximum Power transferred? ^ Load resistance can be varied between 0 & 4000
^ Capacitive Reactance can be varied between 0 & -
^ R
& XL^
that transfers most average power?L^0010
Example 4 ^ Z
= 3000 – j4000L
^ P = 10
= 8.33 mW Z= 3605.55 – j2000L^
^ Ieff
^ P =
(^0010) 2 TH L 2 TH L^
)X X( R R^
(^55). 3605 ) 4000 (^2000) ( 3000 R^
2
2 L^
mA (^85). 16 (^4489). 1 ) (^2000) j (^55). (^6605) /( 0 10
0
0
mW 567
. 7 ) (^55). (^3605) ( (^4489). 1
2
Balanced 3-phase circuits ^ Large Amounts of Electric Power^ ^
Generation Transmission Distribution Use ^ Accomplished through 3-phase circuits ^ Power System Analysis^ ^
Analysis of high power generation, transmission anddistribution systems
Balanced 3-phase circuits ^ 3-phase balanced circuits^ ^
Study of 3-phase balanced systems will beundertaken Practically 3-phase systems are designed tooperate in the balanced state
^ 3-phase unbalanced circuits^ ^
Same analysis techniques apply in the study ofunbalanced circuits
3-phase System
Balanced 3-phase voltages ^ Balanced 3-phase voltages consist of^ ^
3 Sinusoidal Voltages 3 Voltages have identical magnitudes 3 Voltages have same frequencies 3 Voltages are out of phase by 120
0
^ Three voltages referred to as^ ^
a, b and c ‘a' phase is the reference phase
Balanced 3-phase voltages
20.0015.0010.005.00 0.00^0 -5.00-10.00-15.00 -20.
0.81.
2.43.
4 4.
5.66.
(^8) 7. 8.89.
10.411.
time t
a b c
Balanced 3-phase voltages ^ V
= a^ ^ V
= b^ ^ V
= c^ ^ Positive Sequence ^ abc (clock wise)
^ V
= a^ ^ V
= c^ ^ V
= b^ ^ Negative Sequence ^ acb
0 m^
0 V^
0 m^
120 V^
0 (^120) V m
0 m^
0 V^
0 m^
120 V^
0 (^120) V m