User manual
5 Power quality - a guide
67
where U
n
and I
n
are voltage and current harmonics of order n, and
n
are angles between these
components.
When this parameter has been introduced, the known power triangle equation was not valid for
circuits with non-sinusoidal waveforms - therefore Budeanu introduced a new parameter called the
distortion power:
Distortion power strain was meant to represent powers occurring in the system due to distorted
voltage and current waveforms.
For years, reactive power was associated with the energy oscillations between its source and
the load. The formula indicates that according to Budeanu’s definition, the reactive power is the sum
of individual harmonics. Due to sin
factor, such components may be positive or negative depend-
ing on the angle between the voltage and current harmonics. Thus, it is possible that the total reac-
tive power Q
B
is zero at non-zero harmonics. Observation that at non-zero components, total reac-
tive power may be zero (according to this definition) is a key to a deeper analysis which finally
allowed proving that in some situations Q
B
may give quite surprising results. The research has
questioned the general belief that there is a relation between energy oscillations and Budeanu re-
active power Q
B
. Examples of circuits may be presented, where despite the oscillating character of
instantaneous power waveform, reactive power according to Budeanu is zero. Over the years, the
scientists have not been able to connect any physical phenomenon to the reactive power according
to this definition.
Such doubts about the correctness of this definition of course also cast shadow on the related
distortion power D
B
. The scientists have started to look for answers to the question whether the
distortion power D
B
really is the measure of distorted waveforms in non-sinusoidal circuits. The
distortion is a situation in which the voltage waveform cannot be “put” on the current waveform with
two operations: change of amplitude and shift in time. In other words, if the following condition is
met:
then, voltage is not distorted in relation to the current. In case of sinusoidal voltage and load which
is any combination of RLC elements, this condition is always met (for sinusoidal waveforms, these
elements maintain linearity). However, when the voltage is distorted, the RLC load does not ensure
absence of current distortion in relation to voltage any more, and the load is no longer linear – it is
necessary to meet some additional conditions (module and phase of load impedance changing with
frequency).
And then, is really D
B
a measure of such distortion? Unfortunately, also in this case the Bude-
anu’s power theory fails. It has been proven that the distortion power may be equal to zero in a
situation when voltage is distorted in relation to current waveform, and vice versa, the distortion
power may be non-zero at total absence of distortion.
Practical aspect of this power theory which relates to improvement of power factor in systems
with reactive power was to be the feature to take the most advantage of correct definitions of reac-
tive power. The compensation attempts based on the Budeanu reactive power and related distortion
power failed. These parameters did not allow even a correct calculation of correction capacitance
which gives the maximum power factor. Sometimes, such attempts resulted even in additional
deterioration of power factor.
How come, then, that the Budeanu’s power theory has become so popular? There may be
several reasons for this. Firstly, engineers got accustomed to old definitions and the curricula in