The Effect Of Harmonics In A Power Distribution System - Danfoss AHF 010 Design Manual

Introduction to Harmonics a...
The integer multiples of the fundamental frequency ω1 are
called harmonics. The RMS value of a non-sinusoidal
waveform (current or voltage) is expressed as:
h
max
∑
2
I = I
RMS (h)
h = 1
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:
h 2
I
max
∑ h
THD = × 100 %
I
1
h = 2
Using the THD, the relationship between the RMS current
I and the fundamental current I
RMS
2
I = I × 1 + THD
RMS 1
The same applies for voltage.
The true power factor PF (λ) is:
P
PF =
S
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:
DPF
PF =
2
1 + THD
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
h 2
I
max
∑ h
TDD = × 100 %
I
L
h = 2
Another term often encountered is the partial weighted
harmonic distortion (PWHD). PWHD is a weighted
harmonic distortion that contains only the harmonics
th th
between the 14 and the 40
definition.
2
40 I
∑
h
PWHD = × 100 %
I
1
h = 14
MG80C602
Design Guide
can be expressed as:
1
.
L
, as shown in the following
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2.1.3 The Effect of Harmonics in a Power
Distribution System
In Illustration 2.4, 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 and feeds several loads. PPC 2 is the point of common
xfr
coupling where all loads are connected. Each load is
connected through cables that have an impedance Z
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
the ratio between the short circuit apparent power of the
supply at the PCC (S ) and the rated apparent power of
sc
the load (S ).
equ
S
ce
R =
sce S
equ
2
U
where and S = U × I
S =
equ
sc Z
supply
, Z ,
1 2
. This ratio is defined as
sce
equ
11
2 2