Power Triangle
Learning Objectives

Define apparent power.

Calculate apparent power in AC series parallel
networks.

Define the power triangle.

Using the power triangle determine relationships
between real, reactive and apparent power.

Determine if AC series parallel networks are
inductive, capacitive, or purely resistive.
Review
AC Power to a Resistive Load
P  VRMS I RMS
2
V
2
 I RMS
R  RMS
R
(watts)
AC Power to a Inductive Load
QL  I
2
RMS
2
VRMS
XL 
XL
(VAR)
AC Power to a Capacitive Load
QC  I
2
RMS
2
VRMS
XC 
XC
(VAR CAP )
Review
AC Power Summary
Real Power
P = VI (W)
P = I2R =V2/R
P = 0 (W)
P = 0 (W)
Reactive
Power
Q = 0 (VAR)
Q = VI (VARind)
Q = I2XL =V2/XL
Q = VI (VARcap)
= I2XC =V2/XC
Resistance
Reactance
R
XL = L
XC = 1/C
Apparent Power


For a load with voltage V and current I, the
power that “appears to flow” to the load is VI
where V and I are rms values.
S = VI (VA)
S is called the apparent power and has units of
volt-amperes (VA).
Apparent Power


In terms of load impedance Z, apparent power
can be expressed
S = I2Z = V2/Z
(VA)
It is common to see apparent power give in kVA.
Example Problem 1
Determine the real, reactive, and apparent power.
Power Triangle

The power triangle graphically shows the
relationship between real (P), reactive (Q) and
apparent power (S).
P

S
QL

P
QC
S
Power Triangle

From the power triangle we can see that
S  P2  Q2
S  P  jQL or
S  P  jQC
S  S 
P

S
QL

P
QC
S
Power Triangle

We can generalize the equations:
P  P0
Q L  jQL
QC   jQC
I*is complex conjugate of I
S  PQ
S  VI
P

QC

S
Real and Reactive Power

The power triangle also shows that we can find
real (P) and reactive (Q) power.
P  VI cos  S cos
(W)
Q  VI sin   S sin 
(VAR)
P

S
QL

P
QC
S
Example Problem 2
Draw the power triangle for this circuit. Determine
if this is an inductive, capacitive, or resistive
circuit.
Example Problem 3
Determine the value of R and PT & QT. Draw the
power triangle and determine S.