The integer multiples of the fundamental frequency
ω
1 are
called harmonics. The RMS value of a non-sinusoidal
waveform (current or voltage) is expressed as:
I
RMS
=
∑
h = 1
h
max
I
(h)
2
The number of harmonics in a waveform gives the
distortion factor, or total harmonic distortion (THD). The
THD is given by the ratio of RMS of the harmonic content
to the RMS value of the fundamental quantity, expressed
as a percentage of the fundamental:
THD =
∑
h = 2
h
max
I
h
I
1
2
× 100 %
Using the THD, the relationship between the RMS current
I
RMS
and the fundamental current I
1
can be expressed as:
I
RMS
= I
1
× 1 + THD
2
The same applies for voltage.
The true power factor PF (
λ
) is:
PF = PS
In a linear system, the true power factor is equal to the
displacement power factor:
PF = DPF = cos ϕ
In non-linear systems, the relationship between power
factor and displacement power factor is:
PF =
DPF
1 + THD
2
Reactive power decreases the power factor and harmonic
loads. A low-power factor results in a high RMS current
that produces higher losses in the supply cables and
transformers.
In the power quality context, the total demand distortion
(TDD) term is often encountered. The TDD does not
characterize the load, but it is a system parameter. TDD
expresses the current harmonic distortion in percentage of
the maximum demand current I
L
.
TDD =
∑
h = 2
h
max
I
h
I
L
2
× 100 %
Another term often encountered is the partial weighted
harmonic distortion (PWHD). PWHD is a weighted
harmonic distortion that contains only the harmonics
between the 14
th
and the 40
th
, as shown in the following
definition.
PWHD =
∑
h = 14
40
I
h
I
1
2
× 100 %
2.1.3 The Effect of Harmonics in a Power
Distribution System
In
, a transformer is connected on the
primary side to a point of common coupling, PCC1, on the
medium voltage supply. The transformer has an impedance
Z
xfr
and feeds several loads. PPC 2 is the point of common
coupling where all loads are connected. Each load is
connected through cables that have an impedance Z
1
, Z
2
,
Z
3
.
Illustration 2.4 Small Distribution System
Harmonic currents drawn by non-linear loads cause
distortion of the voltage because of the voltage drop on
the impedances of the distribution system. Higher
impedances result in higher levels of voltage distortion.
Current distortion relates to apparatus performance, and it
relates to the individual load. Voltage distortion relates to
system performance. It is not possible to determine the
voltage distortion in the PCC knowing only the harmonic
performance of the load. To predict the distortion in the
PCC, the configuration of the distribution system and
relevant impedances must be known.
A commonly used term for describing the impedance of a
grid is the short circuit ratio R
sce
. This ratio is defined as
the ratio between the short circuit apparent power of the
supply at the PCC (S
sc
) and the rated apparent power of
the load (S
equ
).
R
sce
=
S
ce
S
equ
where
S
sc
= U
2
Z
supply
and
S
equ
= U × I
equ
Introduction to Harmonics a...
Design Guide
MG80C602
Danfoss A/S © 05/2019 All rights reserved.
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