User manual
5 Power quality - a guide
75
where:
P
h
– active power of the h-th order harmonic,
U
h
– RMS voltage of the h-th order harmonic,
I
h
– RMS current of the h-th order harmonic,
h
– phase shift angle between the voltage and current harmonics of the h-th order.
When P
h
power has positive sign (+), then the dominating source of energy of this harmonics is
on the energy supplier’s side. When it is negative, the receiver is the dominating source. It must be
noted that on the basis of harmonics active powers measured in this way one cannot determine that
only one party is the sole source of the harmonics, as the measured value is a resultant of the
supplier and the consumer.
In a situation presented above, we are dealing with two separate sources of energy flow. Un-
fortunately, basing on such measurement, we cannot directly indicate the actual distribution.
In real systems, determination of the dominant source is often sufficient. By grouping the har-
monic components with plus signs, we receive a set of power values which are responsible for the
energy flow from the source to the receiver, which is the useful energy.
On the other hand, the set of harmonics active power values with negative sings makes up this
part of energy which does not play any useful role and is "returned" back to the distribution system.
By adding all active harmonics power values we receive the receiver active power. Hence, we
can notice that there are at least two alternative active power measurement methods.
The first method involves calculation of average active power instantaneous value, which is
calculated on the basis of successive voltage and current:
where U
i
is a successive voltage sample, I
i
is a successive current sample and M is the number of
samples in the measuring window.
The second method involves adding individual harmonics active power values which are ob-
tained by the FFT decomposition:
5.4.2 Harmonics reactive power
The harmonics reactive power values may be calculated in a similar manner as the active power
values:
Knowledge of reactive power harmonics is valuable information used in the development of
reactive parallel compensators of reactive power. Such compensators consist of LC branches tuned
to a specific frequency harmonics.
The sign of the individual power components indicates the character of load for this component.
Example
When the supplier generates active power of harmonic P
hD
= 1 kW, and
the consumer "generates" the power of this harmonics equal to P
hO
=
100 W, then the resultant power measured at the terminals between the
supplier and the consumer is P
h
= P
hD
– P
hO
= 0.9 kW.