User manual
PQM-702, PQM-703 Operating Manual
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schools have not been changed for years. This factor is often underestimated, though as a form of
justification it can be said that this theory had not been refuted for 60 years. Secondly, in the 1920s
there were no measuring instruments which could give insight in individual voltage and current har-
monic components and it was difficult to verify new theories. Thirdly, distorted voltage and current
waveforms (i.e. with high harmonics contents) are a result of revolution in electrical power engineer-
ing which did not start before the second part of the last century. Thyristors, controlled rectifiers,
converters, etc. began to be widely used. All these caused very large current distortion in the mains,
and consequently increased harmonic distortion. Only then the deficiencies of Budeanu's theory
became evident. Finally, the scientific circles related to power engineering were aware of the fact
that industrial plants had invested a fortune in the measuring infrastructure (energy meters). Any
change in this regard could have huge financial implications.
However, slow changes in the approach of electrical engineers began to be visible. With time,
as non-linear loads were more and more frequent and the waveforms more and more distorted, the
limitations of used formulas could no longer be tolerated.
A very significant event was publishing by IEEE (in 2000) 1459 standard "Definitions for the
Measurement of Electric Power Quantities Under Sinusoidal, Non-sinusoidal, Balanced, or Unbal-
anced Conditions". For the first time, Budeanu’s definition of reactive power has been listed as not
recommended for new reactive power and energy meters. Many parameters have been also divided
into the part related to the current and voltage fundamental component (first harmonics) and the
part related to remaining higher harmonics. In most cases, it is recognized that the usable part of
energy is transmitted by the 50/60Hz components, with much smaller (and often harmful) participa-
tion of higher harmonics.
The standard also introduced a new parameter – non-active power N which represents all non-
active components of power:
Reactive power is the power of one of the components of the inactive power N. In single-phase
systems with sinusoidal voltage and current waveforms, N equals Q; hence the non-active power
does not have any other components. In three-phase systems, this is true only for symmetrical
sinusoidal systems with a balanced purely resistive load.
Other non-active power components are related to specific physical phenomena. According to
prof. Czarnecki’s theory, which is one of the best in explaining the physical phenomena in three-
phase systems, the power equation in such systems is as follows:
D
s
is the scattered power, which occurs in the system, as a result of changing conductance of
the receiver with frequency. Thus, the presence of reactive elements may result in the scattered
power.
In this equation, reactive power Q appears when there is a phase shift between the voltage and
current harmonics.
D
u
means the unbalanced power which is a measure of unbalance of a three-phase receiver.
This component explains the situation in which an unbalanced three-phase load of a purely resistive
character results in the power factor less than one. Such receiver has no reactive power Q, and
still the results from the power triangle S, P, Q are totally different (the Budeanu’s power theory with
its distortion power could not explain this situation either – in a purely resistive receiver, the distortion
power D
B
equals zero).
An attempt to combine IEEE 1459-2000 standard with the Czarnecki’s power theory leads to
the conclusion that non-active power includes at least three separate physical phenomena, which
influence the reduced effectiveness of energy transmission from the source to the receiver, i.e.
reduction of the power factor: