User manual
5 Power quality - a guide
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systems with traditional meters is subject to an additional error caused by creation of a virtual zero
inside the meter which has little to do with actual zero of the receiver.
On top of that, the manufacturers usually do not give any information about the applied meas-
uring method.
We may only wait for the next version of the standard, which will define (hopefully) the measur-
ing and testing methods much more precisely, also for non-sinusoidal conditions.
5.3.5 Apparent power
Apparent power S is expressed as the product of RMS voltage and current:
As such, the apparent power does not have a physical interpretation; it is used during designing
of transmission equipment. In terms of value, it is equal to maximum active power which can be
supplied to a load at given RMS voltage and current. Thus, the apparent power defines the maxi-
mum capacity of the source to supply usable energy to the receiver.
The measure of effective use of supplied power by the receiver is the power factor, which is the
ratio of apparent power to active power.
In sinusoidal systems:
In non-sinusoidal systems such simplification is not acceptable and the power factor is calcu-
lated based on the actual ratio of active power and apparent power:
In single-phase systems, the apparent power is calculated as shown in the formula above and
there are no surprises here. However, it turns out that in three-phase systems calculation of this
power is equally difficult as calculation of reactive power. Of course, this is related to actual systems
with non-sinusoidal waveforms which additionally can be unbalanced.
The tests have shown that the formulas used so far can give erroneous results if the system is
unbalanced. Since the apparent power is a conventional parameter and does not have a physical
interpretation, determination which of proposed apparent power definitions is correct could be diffi-
cult. Yet, the attempts have been made, based on the observation that the apparent power is closely
related to the transmission losses and the power factor. Knowing the transmission losses and the
power factor, one can indirectly specify a correct definition of apparent power.
The definitions used so far include arithmetic apparent power and vector apparent power. The
test have shown however that neither the arithmetic definition nor the vector definition give correct
value of the power factor. The only definition which did not fail in such a situation, was the definition
proposed as early as in 1922 by F. Buchholz - a German physicist:
It is based on the effective values of voltage and current, and the power is called the effective
apparent power (for this reason, index "e" is used in marking three-phase systems). Those effective
voltage and current values are such theoretical values which represent voltage and current in an
energetically equivalent three-phase balanced system. Consequently, the key issue is to determine
U
e
and I
e
.
IEEE Standard 1459 specifies the following formula. In three-wire systems: