Reactive Power; Apparent Power - Hameg HM8015 Handbuch

B a s i c s o f P o w e r M e a s u r e m e n t
For sine waves the instantaneous power is given
by:
= û sin (ωt + ϕ) · î sin ωt
p
(t)
The active power or true power is equal to the
arithmetic mean of the instantaneous power. The
active power is derived by integrating for a period
T and dividing by the period T as folllows:
T
∫
1
î sin ωt · û sin (ωt + ϕ) dt
P = ––
T
0
î · û · cos ϕ
P = ––––––––––––––
2
P = U · I
eff eff
The power factor will be maximum cos
= 1 at zero phase shift. This is only the case
with a purely resistive circuit.
In an ac circuit which contains only reac-
tances the phase shift will be
the power factor hence cos
active power will be also zero.
HINT
Reactive Power (unit var, designation Q)
Reactive power equals rms voltage times reactive
current.
With the designations:
Q

= reactive Power

V = rms voltage
rms
I = rms current
rms
ϕ
= phase angle between
voltage and current
a vector diagramm
can be drawn as follows:
The reactive power
is derived by:
Q = V · I · sinϕ
rms rms
Reactive currents constitute a load on the
public mains. In order to reduce the
reactive power the phase angle ϕ must be
made smaller. For most of the reactive
power transformers, motors etc. are
responsible, therefore capacitors in par-
allel to these loads must be added to
compensate for their inductive currents.
HINT
26
Subject to change without notice
· cos ϕ
ϕ
= 90° and
ϕ
= 0. The
Example of power including reactive power
With DC the instantanesous values of voltage and
current are constant with respect to time, hence
the power is constant.
In contrast to this the instantaneous value of po-
wer of AC or AC + DC signals will fluctuate, its
amplitude and polarity will periodically change.
If the phase angle is zero this is the special case
of pure active power which remains positive
(exclusively directed from source to load) at all
times.
If there is a reactive component in the circuit
there will be a phase difference between voltage
ϕ
and current. The inductive or capacitive element
will store and release energy periodically which
creates an additional current component, the
reactive part. The product of voltage and current
will therefore become negative for portions of a
period which means that energy will flow back to
the source.
Apparent power (unit VA)
The apparent power is equal to the product of
voltage and current. The apparent power is furt-
her equal to the geometric sum of active and
reactive power as shown in this diagram:
With the designations:
S

= apparent power

P = active power
Q = reactive power
V = rms voltage
rms
I = rms current
rms
the apparent power is derived:
2
S = P + Q
2
= U x J
eff eff