WHITE PAPER:
UNDERSTANDING REAL, REACTIVE, AND APPARENT POWER
Power Calculation–Watts (In-Phase)
Contributed by Cowles Andrus January 2014
This white paper defines the differences between
Real Power, Reactive Power, and Apparent Power in
terms used by the power distribution industry. Here the
relationships between these different types of power
are defined and the basic equations for each are given.
The power discussed in this paper is for alternating
current (AC) not for direct current (DC), however, the
basic definitions are the same. In an AC system, the
units of voltage and current used are in RMS.
Current or Voltage
V
ABSTRACT
+
0
-
I
Time
In physics, power is defined as the amount of energy
consumed or produced per unit of time. The unit of
power in the MKS system is the watt. One watt is equal
to one joule per second. A joule can be defined as the
amount work required to move an electric charge of
one coulomb through an electrical potential difference
of one volt, or one-coulomb volt. Another way of
thinking about a joule is that it is the work required
to pass an electric current of one ampere through a
resistance of one ohm for one second.
positive x positive
negative x negative
= + Watts (Instantaneous)
= + Watts
this is the power delivered into an ideal resistive load Figure 1. Power in-phase
and it is completely absorbed, indicating that the
current and voltage are in phase (refer to Figure 1).
Real power only occurs with a resistive load, and this
power delivery and consumption is what the customer
is paying for. Attention is given to system design to
reduce the reactive component of a power distribution
REAL POWER
system to a minimum, usually by adding capacitors to
offset system inductance, and to keep the voltage and
Real Power (P) is the power that performs work current in phase (Figure 2).
measured in Watts (W). This is the power that is
actually absorbed by a totally resistive load and that If the load is not purely resistive then the Real Power
performs the intended function such as heat, light, or portion will equal the Voltage RMS times Current
mechanical power (e.g. an electric motor or another RMS multiplied by power factor. Power factor is
type of electromagnetic radiation, both of which are cosine Θ equals V1 (the adjacent), divided by V (the Figure 2. Resulting power
absorbed by the surrounding environment). Again, hypotenuse). If the load is purely resistive, V1 and V waveform in-phase
Vector Diagram
Power Waveform
(V and I In-Phase)
I
x
Power
+
Watts
Watts
Watts
V
0
-
y
Time
P = V • I • cosØ where cos Ø = 1
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© 2014 Power Monitors, Inc. • Call Us: 800.296.4120 • www.powermonitors.com
WHITE PAPER:
UNDERSTANDING REAL, REACTIVE, AND APPARENT POWER
will be the same, and the power factor will equal 1. AC Real Power: Voltage and Current can be represented by vectors rotating
Please refer to Figure 3, resolving the voltage vector. counterclockwise; for power, the product of in-phase components is needed. There
is a separate power triangle for each harmonic, not just 60Hz.
REACTIVE POWER
V
Reactive Power (Q) is defined as power flow that
does not perform work (sometimes called “wattless
power”) measured in Volt Ampere Reactive (VAR).
Reactive power is created by a non-resistive load,
either inductive or capacitive. Usually the typical load
in an electrical distribution system is inductive, due
to motor windings and transformers. When reactive
power is created by an inductive load, the current
lags the voltage by 90 degrees. Thus when reactive
power is caused by a capacitive load, the current
leads the voltage by 90 degrees. In an inductive load,
this power transferred down the distribution system to
the inductor, is briefly stored in a magnetic field and
then returned back to the utility a short time later. This
back-and-forth transfer causes more current flow in the
system. In a load that is capacitive, the power is briefly
stored in an electrostatic field before being returned
back into the system. Either way, whether the load is
inductive or capacitive, the current and voltage are
thrown out of phase, making reactive power useless.
Due to either excessive inductance or capacitance,
reactive power is not desired in a distribution system.
the system every 60Hz cycle. Although a considerable Figure 3. AC real power
amount of power can move back and forth, the net real resolving the voltage
power from this is zero – no useful work is done with vector
reactive power. The current flowing to move reactive
power back and forth is real and causes real resistive
losses in the wire, increased transformer heating,
etc. In effect, it causes higher losses in a power
transmission system.
In either case (inductive or capacitive system), reactive
power is sent through the entire distribution system
down to the inductance or capacitance, briefly held in
magnetic or electric fields, and then returned back to
Capacitive and inductive loads can cancel out, leaving
a net resistive load, and reducing reactive power Figure 4. Power
flow. This is the purpose of power factor correction calculation for out of
capacitors. The waveforms in Figures 4 and 5 show phase voltage and current
Resolving Voltage Vector
cos Θ = power factor
cos Θ = V1/V
V1 = V(cos Θ)
sin Θ = reactive factor
sin Θ = V2 /V
V2 = V(sin Θ)
V2
ϴ
x
I
V1
y
P = AC Real (active) Power watts) = Volts x Amps x Power Factor = VRMS x IRMS x cos Θ
Current or Voltage
Power Calculation–Watts (Out-of-Phase)
+
0
Vx I
I
VARS
Vector Diagram
V
VARS
x
0
I
-
V
y
Time
positive x positive
negative x negative
negative x positive
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= + Watts (Instantaneous)
= + Watts
= - VARs
© 2014 Power Monitors, Inc. • Call Us: 800.296.4120 • www.powermonitors.com
WHITE PAPER:
UNDERSTANDING REAL, REACTIVE, AND APPARENT POWER
Resulting Power Waveform
(V and I Out-of-Phase)
Vector Diagram
Watts
Watts
Watts
VARs
VARs
VARs
V• I
+
0
-
VARs
VARs
x
0
I
VARs
V
y
Time
the reason for the losses, a higher current component angle used to describe the phase shift between the
because reactance has caused the voltage and current voltage and current. The larger the phase angle, the
to be out of phase.
greater the reactive power that is generated by the
system.
When a reactive load condition exists, the transmission
system has to not only support the current required for CONCLUSION
the resistive load in watts (Volts x Amperes), but also
the current required for the reactive load in VARs.
Apparent power is a combination of both reactive
power and real power. Real power is a result of the
APPARENT POWER
resistive component, and the reactive power is a
result of capacitive and inductive components. Since
Apparent Power (|S|) is the magnitude of the complex reactive power takes away from a system’s total real
power measured in volt amps (VA). Apparent Power power handling capability, it must be considered in the
is the vector sum of the real power and the reactive design of the power distribution system to ensure that
power combined. In a power distribution system, the apparent power output from a system is sufficient
apparent power is what the system needs to be to supply the load. It is important to understand these
designed to handle. In the real world, loads are usually basic AC power concepts in order for the sources
not purely linear and resistive; most are a combination and distribution system to meet the requirements to
of resistive and reactive and are either inductive or be able to supply the necessary volt-amp power for a
capacitive in nature.
given application. As with any system, understanding
these specifications and being able to make the proper
Volt-Amps = S = Volts x Amps = VRMS x IRMS
measurements validate system requirements will
ensure success.
As new loads are added, it is necessary to have test
equipment available to be able to quantify exactly what Power Monitors Inc. designs and builds different
the apparent power is, so the electrical infrastructure types of test equipment for many power monitoring
can be upgraded to handle the extra load. Sometimes
this may be as simple as adding more capacitance
in places to allow the voltage and current to be more
W (Real Power)
0
in phase, by reducing the reactive power caused by
PF = COS
higher inductance from typical motor loads.
VAR
Figure 6 shows the power triangle, the relationship
between the Apparent Power (S), Real Power (P) and
Reactive Power (Q) and how it relates to the phase
angle. Cos Θ is equal to the power factor. This is the
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VA (
A
ppar
Figure 5. Resulting power
waveform when voltage
and current are out of
phase
Figure 6. The Power
Triangle, the relationship
between Apparent Power
(S), Real Power (P) and
Reactive Power (Q) and
how it relates to the
phase angle
(Reactive Power)
ent P
ower
)
S= √P2 + Q2
P= V x I cos O
Q = V x I sin O
0 = Phase angle between voltage current
© 2014 Power Monitors, Inc. • Call Us: 800.296.4120 • www.powermonitors.com
WHITE PAPER:
UNDERSTANDING REAL, REACTIVE, AND APPARENT POWER
applications, including real power, apparent power,
reactive power and power factor and many others.
With these monitors installed in the proper locations,
a customer can determine exactly what type of power
load the system has. With this information, an operator
can make adjustments as needed to optimize power
factor by reducing the reactive power, thereby reducing
the extra stress and facilitating a longer functional life
of the system.
Cowles Andrus, III
Communications Specialist
candrus@powermonitors.com
http://www.powermonitors.com
800.296.4120
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© 2014 Power Monitors, Inc. • Call Us: 800.296.4120 • www.powermonitors.com