1. ELE101/102 Dept of E&E,MIT Manipal 1
Power in AC circuit
Power in AC circuit can be written as
jQPS
VIQVIP
jQPjVI
jIIIZZI
+=
==
+=+=
+=∠=
φφ
φφ
φφφ
sin;cos
)sin(cos
)sincos(2
Ia along V axis is called active current. Ia = I cosφ.
Ir is perpendicular to V axis & is called reactive current. Ir = I sinφ
Active power P = V I cosφ = V Ia.
Reactive power Q = V I sinφ=VIr
Apparent power S = V I
φφ -IIthenloadZZ
0VVreferencethebeVoltageLet
∠=⇒∠=
∠=
;inductiveˆ
2. ELE101/102 Dept of E&E,MIT Manipal 2
Complex Power
I
;Iwhere
;
*
*
φ
φ
φ
∠=
−∠=
=∠=+=
Ithen
I
IVIVjQPS
φ
P
Q
S
XC>XL
P
S
Q
φ
XL>XC
I2
R =
I2
X =
3. ELE101/102 Dept of E&E,MIT Manipal 3
Power Triangle
Find P1, Q1 and P2, Q2
Draw the Individual Power triangle
Now PT = (P1+ P2) and QT = (Q1+ Q2)
Now Draw the over all Power triangle
ST = (PT +j QT)
V
R2
XL2
I
2I
Inductiveload
R1
XL1
1I
I
V R
XL
zI
Inductiveload
QT
PT
Q2
P2
Q1
P1
ST
S1
S2
φ1
φ2
φT
4. ELE101/102 Dept of E&E,MIT Manipal 4
Power Factor Improvement
Need for power factor improvement
Method of Improvement:
A capacitor connected in parallel to an
inductive load improves the power factor.
Determination of Capacitor Value:
φT is the over all power angle
φF is the final power angle after connecting the
capacitor across the load.
ST = PT/CosφT & SF = PT/CosφF
QT = (PT/CosφT) * Sin φT
QF = (PT/CosφF) * Sin φF
QC = (QT - QF) = PT(Tan φT - Tan φF)
QC = V2
/ XC
CI
V R
XL
I
zI
Inductiveload
XC
QT
PT
ST
SF
φF
φT QF
QC