User manual
PQM-702, PQM-703 Operating Manual
74
Let's try to answer two basic questions:
What is the cause of harmonic components in voltage?
What is the cause of harmonic components in current?
Seemingly, these two questions are almost identical, but separation of current and voltage is
extremely important to understand the essence of this issue.
The answer to the first question is as follows: harmonics in voltage are a result on a non-zero
impedance of the distribution system, between the generator (assuming that it generates a pure
sinusoid) and the receiver.
Harmonics in current, on the other hand, are a result of non-linear impedance of the receiver.
Of course, it must be noted that a linear receiver to which distorted voltage is supplied will also have
identically distorted current waveform.
The literature often uses the statement that "receiver generates harmonics". It should be re-
membered that in such case, the receiver is not a physical source of energy (as suggested by the
word "generates"). The only source of energy is the distribution system. If the receiver is a passive
device, the energy sent from the receiver to the distribution system comes from the same distribution
system. We are dealing here with a disadvantageous and useless bidirectional energy flow. As
mentioned earlier in the section on power factor, such phenomenon leads to unnecessary energy
losses, and the current "generated" in the receiver causes an additional load on the distribution
system.
Consider the following example. A typical non-linear receiver, such as widely used switched-
mode power supplies (i.e. for computers) receives power from a perfect generator of sinusoidal
voltage. For now, let's assume that the impedance of connections between the generator and the
receiver is zero. The voltage measured on the receiver terminals will have sinusoidal waveform
(absence of higher harmonics) – this is imply the generator voltage. The receiver current waveform
will already include harmonic components – a non-linear receiver often takes current only in speci-
fied moments of the total sinusoid period (for example, maximum current can take place at the
voltage sinusoid peaks).
However, the receiver does not generate these current harmonics, it simply takes current in
alternating or discontinuous way. All the energy is supplied solely by the generator.
In the next step, we may modify the circuit by introducing some impedance between the generator
and the receiver. Such impedance represents the resistance of cabling, transformer winding, etc.
Measurements of voltage and current harmonics will give slightly different results. What will
change? Small voltage harmonics will appear, and in addition current frequency spectrum will
slightly change.
When analysing the voltage waveform on the receiver, one could notice that original sinusoidal
waveform was slightly distorted. If the receiver took current mainly at voltage peaks, it would have
visibly flattened tops. Large current taken at such moments results in larger voltage drops on the
system impedance. A part of the ideal sinusoidal voltage is now dropped on this impedance. A
change in the current spectrum is a result of slightly different waveform of voltage supplied to the
receiver.
The example described above and "flat tops" of the sinusoid are very frequent in typical systems
to which switched-mode power supplies are connected.
5.4.1 Harmonics active power
Decomposing receiver voltage and current to harmonic components enables using more de-
tailed analysis of energy flow between the supplier and the consumer.
We assume that the power quality analyzer is connect between the voltage source and the
receiver. Both, supply voltage and current are subjected to FFT, as a result of which we receive the
harmonics amplitudes with phase shifts.
It turns out that the knowledge of voltage and current harmonics and of phase shift between
these harmonics allows calculating the active power of each harmonic individually: