User manual

PQM-702, PQM-703 Operating Manual
78
5.4.5 K-Factor
K-Factor, also called the transformer loss factor is a measure used in determining the require-
ments for power transformers. Higher harmonics in current cause increased heat losses in windings
and metal parts of the transformer. The main reasons is the presence of eddy currents generated
by current components of higher frequencies and by the skin effect.
The transformer temperature increase is directly proportional to current components squared,
the value called K-Factor takes this into account, and the factor is calculated according to the fol-
lowing formula:
 


















where: I
hr
- relative value of the h-th order harmonic component (in relation to the fundamental
component),
I
h
- amplitude of the h-th order of current harmonic component,
I
1
- amplitude of current fundamental component,
h – harmonic order.
In case of this parameter, the higher harmonics are much more important than the lower – each
harmonic component is multiplied by its order squared.
K-Factor is useful when defining the requirements for transformers which must work in condi-
tions of significant current distortion. It t is assumed that the transformer, which works in conditions,
where K =x, will generate x times more heat than at purely sinusoidal current (K=1).
5.5 Interharmonics
Interharmonics are components of the frequency spectrum for voltage or current with a fre-
quency that is not a multiple of the fundamental frequency network (50 or 60 Hz). The cause of
interharmonics may be e.g. asynchronous processes and transient states related to connection
processes, frequency converters that generate the output frequency different from the frequency of
the power supplying mains and introduce into the system spectral interharmonics, arc furnaces,
induction motors and drives with variable load. Ripple control signals, i.e. signals with defined fre-
quencies generated in control systems and introduced into mains should also be considered as
interharmonics components. Interharmonics at frequencies lower than the mains fundamental fre-
quency are called subharmonic components.
The effects of interharmonics may include:
 increased losses in mechanical motors, temperature rise; subharmonics are particularly
harmful elements, as the power loss increases with decreasing frequency,
 flicker; also in this case subharmonics have particularly adverse effects. For example
subharmonic with 8.8Hz frequency causes the modulation of mains voltage within the
range, where human eye is most sensitive to this phenomenon (see also sec. 5.2),
 low-frequency oscillations in mechanical systems,
 interferences in the operation of control and protection systems,
 telecommunications and acoustic interferences,
 saturation of magnetic cores by subharmonic components (e.g. transformers, motors,
etc.).
The interaction of higher harmonics and interharmonics may also lead to unexpected phenom-
ena such as beating-in at low frequencies. For example, ninth harmonic (450 Hz) with interharmonic
of 460 Hz frequency generates the effect of beating-in at the frequency of 10 Hz, despite the fact
that in this frequency spectrum a component of this frequency is not present. Human eye is very
sensitive in this frequency range, and the interaction may lead to a significant flicker effect.
230 V/50 Hz voltage waveform for this case is presented in Fig. 31 (significantly higher level of the
interharmonic was assumed in this case to illustrate the effect better).