2014 International Conference on Power System Technology (POWERCON 2014) Chengdu, 20-22 Oct. 2014
POWERCON 2014 Paper No CP1493 Page 1/8
Abstract— In Voltage Sourced Converter (VSC) based HVDC
systems, the existing harmonics on one side ac system will be
transferred through the dc-link to the other side ac system and
induce a series of harmonics that tend to be more than the origin.
This is also true for the case of one side unsymmetrical ac system;
the fundamental negative-sequence component will be transferred
to the dc-link with the second harmonic is dominant, which in
turn causing a series of harmonics on the other side ac system.
This paper describes the operation of VSC using three switching
functions, which include a fundamental component and carrier
sideband components, using double-edge naturally sampled PWM
to yield their harmonic spectra. The space vector representation
of the VSC’s switching functions is used as a tool for analyzing
and giving the detailed rules of VSC’s harmonic interaction, and
from that, analyzing harmonic propagation through the dc-link.
Based on the methodological analysis, the simulation model of a
suggested project for Northwest power grid - China is built and
implemented using MATLAB/SIMULINK. In the investigation of
harmonic propagation, simulation results show that, the
amplitude of transferred harmonics through the dc-link may be
amplified due to the resonance causing harmonic instability. This
deep understanding of VSC-based HVDC system’s harmonic
propagation characteristic could be beneficial to harmonic
mitigation control.
Index Terms—Voltage sourced converter, VSC-based HVDC,
HVDC harmonic, harmonic propagation, switching function.
I. INTRODUCTION
HE INTRODUCTION of Voltage-Sourced Converter
(VSC)-based HVDC to power system offers the potential
to improve control of power flow and enhance system stability.
However, VSC-based HVDC producing harmonics on both
ac-side and dc-side is inherent by the VSC itself and will
interact with harmonic distortions already existed in the system.
The harmonics of VSC are directly associated with the type of
VSC technologies, modulation techniques and the switching
frequency [1]. A more elaborate understanding of these
harmonics must develop to find adequate approaches to
harmonic elimination, preventing the system from instability
and sizing the components of the system.
Manuscript received July ..., 2014. This work was supported by State Grid
Cooperation of China, Major Projects on Planning and Operation Control of
Large Scale Grid SGCC-MPLG019-2012
Phuchuy Nguyen is with the School of Electrical Engineering, North China
Electric Power University, Beijing 102206, P.R China (e-mail:
[email protected]).
Minxiao Han is with the School of Electrical Engineering, North China
Electric Power University, Beijing 102206, P.R China (e-mail:
[email protected]).
Harmonic interactions between the two sides of the converter
and through the dc-link of HVDC are analyzed in [2] where the
converter is a current-source converter (CSC). In the case of
VSC, a practical case in [3] shows that harmonic instability
may occur if there is an unbalanced second harmonic generated
by a nearby saturated transformer on the ac-side of VSC. Based
on analyzing basic current and voltage equations of CSC and
VSC, the authors in [4] establish simple rules of harmonic
transfer through converters by using switching functions
represented in space vector form. This additional understanding
of harmonic interaction is quite adequate to the analytical and
simulation results in [2] and [3]. The dc equivalent impedance
of VSC is formulated by analyzing the harmonic transfer across
converter in [5]. It is convenient for harmonic resonance
analysis.
This paper presents harmonic transfer rules of VSC. They are
suitable for both two-level and three-level converters, not only
valid for voltage harmonics, but also for current harmonics. The
rules were built after analyzing VSC in both balanced and
unbalanced operating conditions by using switching functions
represented in space vector forms. Unlike previous works just
used the fundamental switching component, this paper also
presents the rules of harmonic transfer under the interaction of
higher order switching components. These rules are adopted
for both positive- and negative-sequence harmonics,
accounting for all harmonics propagated through the dc-link of
VSC-based HVDC. Based on these rules, the dc- and
ac-equivalent impedances of VSC were calculated to give a
clearer view of the harmonic propagation.
The paper has five sections. The first section describes
VSC-based HVDC system suggested for Northwest power grid
– China, used to study harmonic interaction and harmonic
propagation. The second section represents the principle
operation of VSC describing the relationships between both
side quantities under space vector representation. Also, the
switching function of both two-level and three-level converters
are calculated depending on the adopted PWM techniques,
applying double Fourier integral analysis. Thereafter, the rules
of harmonic transfer through VSC are established and applied
to VSC-based HVDC harmonic propagation. The equivalent
impedances are also used to analyze this propagation. Finally, a
Matlab/Simulink model of the VSC-based HVDC system is
built to validate the method.
II. VSC-BASED HVDC SYSTEM
Study on Harmonic Propagation of VSC-based
HVDC Systems
Phuchuy Nguyen, Minxiao Han, North China Electric Power University, Beijing 102206, China
T
2146 Session 4
2014 International Conference on Power System Technology (POWERCON 2014) Chengdu, 20-22 Oct. 2014
POWERCON 2014 Paper No CP1493 Page 2/8
Cable
Cable
AC
system 1
330 kV
AC
system 2
230 kV
Trans. Reactor
AC filter
Reactor
AC filter
Trans.
Cd
Cd
Cd
Cd
Fi
lte
r
Fi
lte
r
Fi
lte
r
Fi
lte
r
Fig. 1. Schematic of study VSC-based HVDC.
tua tub tuc
tka tkb tkc
tia tib tic
pu t
dC2
dC2
1
-1
-1
-1
1
1
nu t
0
0
0
di t
Fig. 2. Three-level voltage sourced converter phase quantities.
apk t
ank t
0
1
1
2
Fig. 3. Step functions of phase a
The VSC-based HVDC system is a point-to-point scheme
which consists of two VSC stations interconnected by 300
kV dc cables and transfers power from 330 kV ac system to 230
kV ac system. Figure 1 represents the system configuration and
its main components. To smooth ac-side output current of the
VSC, a three-phase smoothing converter reactor is placed
between the converter and a converter transformer. The
transformer winding is Yn/Y connection type where the Y
winding is connected to the reactor, resulting in decoupling the
ac system from the triple harmonics produced by the converter.
The ac high-pass filter group is an essential part of the scheme,
located between the converter transformer and the converter
reactor for improving filtering characteristic. On the dc-side of
VSC, the reservoir dc capacitors are used to equalize dc voltage,
enhance the system dynamics, and reduce the dc-side voltage
ripple. The third order tuned filters are connected in parallel
with dc capacitors to suppress the dominant third order voltage
ripple caused by the capacitors. Moreover, dc-smoothing
reactors are also used to smooth dc-side current.
III. VOLTAGE SOURCED CONVERTERS
A. Operation principle
Voltage source converters (VSC) convert a stiff dc voltage
source to ac voltage outputs. For a three-phase VSC connected
to three-phase ac system, communication takes place between
valves connected to the same phase. By switching the correct
IGBTs sequentially at the correct times, the VSC’s three
output-sets can be created at the desired frequency. The various
valve-switching techniques are applied to give different
numbers of harmonic contents and ac voltage magnitude.
In Figure 2, a three-level Neutral Point Clamped (NPC) VSC
forces the ac-side voltage to a certain value determined by the
given switching functions. The switching functions take the
value 1xk , whenever phase ‘x’ is switched to the negative
dc pole, and the value 1xk when it is switched to the positive
dc pole, otherwise, 0xk when it is switched to the
“midpoint.” For the VSC using pulse-width modulation
technique, the 1xk corresponds to the positive half cycle
modulation wave, in contrast, the 1xk corresponds to the
negative half cycle modulation wave.
In general, the relationships between the ac- and dc-side
quantities of VSC can be determined by (1).
a a ad
b b bd
c c cd
u t k t u t
u t k t u t
u t k t u t
)1(
where
xk t : switching function of phase x (x=a, b, c).
xd p xp n xnu t u t k t u t k t (2)
In (2), pu t and nu t are dc-side positive and negative
pole voltages, respectively; xpk t and xnk t are step
functions corresponding to each half cycle of phase x
modulation wave, as shown in Fig.3.
It can be seen that, for phase a, ( ) ( ) 1ap ank t k t and
( ) ( )ap ank t k t is a periodic function, and thus can be expanded
by a Fourier series as [6]
0
1,3,5...
4 1 sin cos
2ap an h
h thtktk
h .
(3)
Adding -2 /3 and 2 /3 to the phase angle of each harmonic
component in (3) will derive the corresponding forms of phase
b and c, respectively.
The dc-side current on the positive dc pole is established in
(4).
/ 2.d a a b b c ci t k t i t k t i t k t i t (4)
If the dc-side voltage / 2p n du t u t u t , the
relationships between the ac- and dc-side quantities of VSC,
without the zero-sequence components, now can be determined
in the form of the space vector [4]:
/ 2dVu t K t u t )5(
*3 Re
4 Vd
i t K t i t (6)
2147 Session 4
2014 International Conference on Power System Technology (POWERCON 2014) Chengdu, 20-22 Oct. 2014
POWERCON 2014 Paper No CP1493 Page 3/8
where
,V Vu t i t : space vector of ac-side voltage and current.
,d du t i t : dc-side voltage and current.
K t : the space vector of three sinusoidal
switching functions.
22
3 a b c
K t k t a k t a k t (7)
2 /3ja e
B. Harmonics in two-level converters
The PWM double-edge natural sampling process involving
the comparison of a modulating sinusoidal wave with a high
frequency triangular carrier, and the single-phase modulation
technique is adopted to minimize harmonic distortion. In
addition, the double Fourier integral analysis can be used as the
most well-known analytical method to determine the harmonic
spectrum of the converter’s output. The analytical expression of
switching function of phase x in the time domain is given by the
following equation [7]:
0
1
0
cos
/ 2
sin / 22
cos
xx
n
m n
xc
k t M t
J mM
m n
m
m t n t
(8)
where
x : a,b, c
M : Modulation index.
0 : Frequency of the modulation wave.
c : Frequency of the carrier wave.
m : Group index (multiple of switching frequency).
n : Sideband harmonic index from each group.
x : Modulation wave phase shift for each phase a, b, or c.
: Carrier wave phase shift.
nJ : First kind Bessel function (see Appendix).
The first term in (8) gives the fundamental component, and
the second term gives the harmonic groups of each multiple of
the carrier frequency and its sidebands. Because
sin / 2 0m n with any m+n are even numbers;
therefore, there are no harmonics at the even multiples of the
carrier frequency. The sideband harmonics are of m c+n 0,
with the limits of m+n are odd numbers.
C. Harmonics in three-level converters
The naturally sampled phase disposition PWM is adopted to
compare modulating sinusoidal waves with two high frequency
triangular carriers. Using the same analytical method as
two-level converter, the analytical expression of switching
function of phase x of a three-level converter in the time domain
is given by the following equation [8]:
0
2 1
2,4,6... 0
2
1,3,5... 0
cos
cos2 1
cos 2 1
cos8 1
cos 2
xx
n
m n xc
k
mn
m n xc
k t M t
J m M n
m m t n t
J n
m m t n t
(9)
where
2 1
1
2 1
2 1
2 2 1 2 2 1
k
mn k
k
k
J J m M
k n k n
(10)
2 1 2 1,n kJ J : First kind Bessel function (see Appendix A).
Similar to two-level converters, the first term in (9) gives the
fundamental component of switching function. Its amplitude
just is dependent on the modulation index but is independent of
the frequency index, mf = c/ 0, and carrier phase shift. The
amplitudes of other harmonics depend on the characteristic of
the Bessel function, which are equal for two sideband
harmonics on opposite sides of the center-placed harmonic in
each group.
It is obvious that, the even- and odd-sideband harmonics
only exist around the odd- and even-carrier multiples
respectively. As a result, the characteristic harmonics on the
ac-side of VSC have odd orders.
IV. VSC’S HARMONIC INTERACTION RULES
A. Space vector representations
As can be seen from (8) and (9), each switching function
includes fundamental switching component and high-order
switching components. The high-order components satisfy
m.mf+n=N(0)=3i, where i is an integer of the fundamental, are
called zero-sequence switching components. It is clear from (4)
that the dc-side current is not affected by the zero-sequence
switching components.
For the high-order switching components satisfy
m.mf+n=N(+)=3i+1 are called positive-sequence switching
components. Also, the other high-order components satisfy
m.mf+n=N(-)=3i-1 are called negative-sequence switching
components. Consequently, the space vector of switching
functions is composed of three components expressed as the
following equation:
1
11
nmnm
m n m n
K t K t K t K t (11)
where
0
0
0
1
3 1
3 1
ˆ
ˆ
j t
j i t
mn mn
j i t
mn mn
K t Me
K t K e
K t K e
)21(
ˆ
mnK and ˆ mnK are different for which either a two-level
converter or a three-level converter is used, but the same
switching component will have the same interaction. It can be
seen from (11), the zero-sequence switching components,
which has triple orders, does not appear.
2148 Session 4
2014 International Conference on Power System Technology (POWERCON 2014) Chengdu, 20-22 Oct. 2014
POWERCON 2014 Paper No CP1493 Page 4/8
B. DC capacitor voltage ripples transfer to AC-side
In the light of dc capacitors working as voltage dividers, the
voltages on dc capacitors are composed of a third harmonic and
higher-order harmonics around switching frequency. The
dominant third harmonic component can be expressed as (13).
Its amplitude decreases with the increase in not only power
factor of the converter, but also the chosen dc capacitors [6].
3 3 0cos 3r ru t U t (13)
The dc-side positive and negative pole voltage now can be
written as the following equation
3 0
3 0
/ 2 cos 3
/ 2 cos 3
p d r
n d r
u t U U t
u t U U t
(14)
As above expression in (3) which includes zero-sequence
harmonics, the space vector representation in (5) is not suitable
for harmonic transfer analyzing in this case. From (1), (2), (3)
and (14), and just considering the fundamental switching
component in (9), the phase a output voltage is:
01
3
0
1,3,5...
3
0
1,3,5...
cos
2
1 sin cos 4
2
1 sin cos 2
2
dc
a
r
h
r
h
MUu t t
MU h h t
h
MU h h t
h
(15)
From (15), the additional harmonics in the ac-side will shift
2 or 4 orders from the switching component, say, the
fundamental in this case. The dominant ac-side voltage
harmonic is the 3rd harmonic followed by the smaller harmonics
such as the 5th, 7th ones, etc. The magnitudes of higher order
voltage harmonics are insignificant. Similarly, under the
interaction of high-order switching components of a carrier
multiple and its sidebands, the new harmonics will have the
same sequences and orders to the characteristic harmonics.
C. Harmonics from DC-side transferred to AC-side
Assuming that the dc-side voltage comprises an rth harmonic
written in the form as:
0 0
0ˆ ˆ 2/soc
jr t jr t
rdrdrdu t u r t u e e (16)
As above state, under the interaction of the zero-sequence
switching components, the dc-side voltage harmonic transfer
through VSC can be explained in (17), the phase a output
voltage for example:
00 0
0.
0
00
ˆ cosˆ cos 3
2
ˆ ˆ
cos 3 cos 3
4
dr
a mnr mn
mn dr
u r t
u t K i t
K u i r t i r t
(17)
These additional harmonics are all zero-sequence harmonics,
therefore, they will not appear in phase-phase voltage.
For the other switching components, substitute (16) to (2)
with the expression of switching function as (12):
1
11
rnmrnmrrV
m n m n
u t u t u t u t (18)
where
00
00
00
1 1
1
3 1 3 1
3 1 3 1
ˆ / 4
ˆ ˆ / 4
ˆ ˆ / 4
j r t j r t
r dr
j i r t j i r t
mnr mn dr
j i r t j i r t
mnr mn dr
u t M u e e
u t K u e e
u t K u e e
(19)
Clearly, the rth harmonic from the dc-side will transfer to the
ac-side and produces two new sideband harmonics with the
same amplitude. Under interaction of the fundamental
switching component, the harmonic with higher order is a
positive-sequence harmonic, and with lower order is a
negative-sequence harmonic. Under interaction of the
high-order switching components, if the order of dc-side
harmonic is smaller than the order of the switching components,
the sequence of the two-sideband harmonics on the ac-side is
the same as the sequence of the switching components.
D. Harmonics from AC-side transferred to DC-side
Assuming ac-side currents superimpose an hth harmonic
component expressed in space vector form as:
00ˆ ˆjh t jh t
Vh h hi t i e i e )02(
The first part in (20) is the positive-sequence harmonic, and
the second one is the negative-sequence harmonic. Substituting
(20) to (6) with the expression of switching function in (12), the
dc-side harmonic current has the form as below:
1
11
dh d h dmnh dmnh
m n m n
i t i t i t i t (21)
where
00
00
00
1 1
1
3 1 3 1
3 1 3 1
ˆ ˆ 4/eR3
ˆ ˆ ˆ 4/eR3
ˆ ˆ ˆ 4/eR3
j h t j h t
hhhd
j i h t j i h t
hhnmhmd
j i h t j i h t
hhnmhmd
i t M i e i e
i t K i e i e
i t K i e i e
(22)
In the case of a balanced harmonic, the ac-side has just only
positive or negative-sequence harmonic. Equation (22) shows
that, under the interaction of the positive-sequence switching
components (including the fundamental component), there is
only one sideband produced on the dc-side. The
positive-sequence harmonic offers the lower order sideband,
while the negative-sequence harmonic offers the higher order
one. In contrast, under the interaction of the negative-sequence
switching components, the positive-sequence harmonic
provides the higher order sideband, but the negative-sequence
harmonic offers the lower order one.
When the ac-side has an unbalanced harmonic, it has both
positive- and negative-sequence components as in (20).
Therefore, there will be two sideband harmonics on the dc-side,
but their amplitudes depend on the amplitude of the origin
components on the ac-side, respectively.
Now, an example of a three-level VSC has frequency index
mf = 27 will be examined for illustrating the above analyses of
harmonic transfer between both sides of the VSC. Assuming
that the dc-side voltage comprises a 6th harmonic, and just
consider the fundamental switching component and the
29th-order (negative-sequence) switching component of the first
group of carrier multiples. As a result, the ac-side will induce
only the positive-sequence 7th harmonic, and
2149 Session 4
2014 International Conference on Power System Technology (POWERCON 2014) Chengdu, 20-22 Oct. 2014
POWERCON 2014 Paper No CP1493 Page 5/8
negative-sequence harmonics with the orders of 5th, 23nd, and
35th. Because of cross-modulation, additional harmonics will be
produced on the dc-side with the 24th order as well as the 36th
order due to the fundamental component. If the 29th-order
switching component is relatively large, under its interaction in
this case, more additional harmonics can be produced on the
dc-side, which also includes the 24th and the 36th harmonics.
However, the phase rotations of these 24th and 36th harmonics
will be opposite to those produced under the interaction of the
fundamental switching component.
V. VSC-BASED HVDC HARMONIC PROPAGATION
A. Harmonic propagation rule
Characteristic harmonics, which are inherent by the VSC,
will be produced on the ac-side, and in-turn, these characteristic
harmonics will be transferred to the dc-side again. Further, the
new harmonics on the dc-link are different from the original dc
component, and they will be transferred to the remote ac system
to produce additional harmonics. Nonetheless, these additional
harmonics will have the same order with the characteristic
harmonics if the two ac systems and the converters on both
terminals are the same.
When the ac system 1 has background harmonics, they will
be conveyed to the ac system 2 with a propagation rule as
shown in Fig. 4.
The rule under Fig. 4 is that, for example, when the ac system
1 has a negative-sequence 5th harmonic, a series of harmonics
will be produced in the ac system 2. Under the interaction of the
fundamental switching component, the positive-sequence 7th
harmonic and the negative-sequence 5th harmonic are
dominant.
B. Harmonics transfer under unsymmetrical condition
When the point of common coupling on one side of the ac
system is subjected to a single phase-to-ground fault, the
HVDC system will operate under unbalanced grid conditions,
and VSC is quite sensitive to the negative-sequence component
in the ac-side voltage [9].
Based on the theory of symmetrical components, an
unbalanced three-phase current comprises three balanced
components of positive-, negative- and zero-sequence
components. The mathematical expression of phase “x” is the
following equation:
0
00
ˆ ˆcos cos sxsxsxsi t I t I t i t (23)
where
ˆ ˆ,s sI I : current amplitude of positive- and negative-sequence
component, respectively.
: phase angle of the negative-sequence component,
relative to the positive-sequence component.
The space vector corresponding to three-phase current
without the zero-sequence component is
00ˆ ˆ j tj t
s s si t i e i e (24)
Equation (24) has a similar form as (20) for unbalanced
harmonics. Therefore, the rule of harmonic transfer in (22)
could be applied to the case of an unsymmetrical ac system. As
a result, a series of non-characteristic harmonics will be
induced on the dc-side of the converter where the 2nd harmonic
is dominant. Again, these harmonics are conveyed to the
remote ac system and produced a series of harmonics where the
positive-sequence 3rd harmonic is dominant. On the other hand,
for the local converter station, the dc-side induced 2nd harmonic
fed back to the ac-side to produce additional positive-sequence
3rd harmonic. Because the local ac system fault is
unsymmetrical, a series of additional low-order
non-characteristic harmonics will be produced on the both sides.
It should be taken into account if resonance occurs in the
system at any frequency.
C. Impedance-Frequency Characteristic of VSC-HVDC
system
Figure 5 illustrates the impedance calculation model of
VSC-HVDC system for studying harmonic propagation. Firstly,
based on the voltage harmonic transfer rule, a voltage harmonic
on the dc-side transfers to the ac system 2 with two sidebands,
the equivalent impedance seen from the dc-side can be
calculated by (25) [10].
2 0 2 0
2 2
2 0 2 0
16
3
ac ac
DC
caca
Z Z
Z
M Z Z
(25)
where 2 0acZ and 2 0acZ are the
positive-sequence (PoS) and negative-sequence (NeS)
equivalent impedance of the ac system 2, respectively.
The equivalent impedance of the dc system takes into
account dc capacitors, cables, dc filters and dc smoothing
reactors. The cables provide shunt capacitance at the
proportional rate to the cable length that exploited to reduce the
size of the dc capacitors [11]. The cables modeled as PI model
and parameters are:
DC
link
1ACZ 2DCZ
2acZ 2acE1acZ1ac
E
1dI
2dI
dcZ
Fig. 5. Principle calculation model of equivalent impedances
h
h
1K t
mnK t
mnK t
1h
1N h
1N h
1K t
mnK t
mnK t
1h
1N h
1N h
r
1K t
mnK t
mnK t
1r
1r
2N r
2N r
2N r
2N r
1AC 1VSC 2VSC-DC link 2AC
Fig. 4. Harmonic propagation in VSC-based HVDC. (+) denote
positive-sequence; (-) denote negative-sequence.
2150 Session 4
2014 International Conference on Power System Technology (POWERCON 2014) Chengdu, 20-22 Oct. 2014
POWERCON 2014 Paper No CP1493 Page 6/8
0 5 10 15 20
0
1
2
3
Harmonic order
(a) Fundamental=0.7598 , THD= 4.41%
M
ag
(%
o
f F
un
da
m
en
ta
l)
0 5 10 15 20
0
2
4
6
Harmonic order
(b) Fundamental=0.7549 , THD= 8.78%
M
ag
(%
o
f F
un
da
m
en
ta
l)
Fig. 8. Spectra of phase current on receiving ac system when sending ac
system has: (a) PoS 2nd background harmonic, and (b) NeS 2nd background
harmonic.
cosh / 2
sinh / 2 /
series c
s ctnuh
Z Z L
Y L Z
(26)
where /c cab cabZ Z Y is characteristic impedance;
cab cabZ Y is the cable propagation constant; L is the length
of the cable; cabZ and cabY are the cable impedance and
admittance per-unit length, respectively.
Based on the rule of the current harmonic transferred through
VSC as analyzed in part IV above, the equivalent impedance
seen from the ac system 1 was calculated by the following
equation [10]:
2
1
2
1
3 '
16
'31
16 "
cdCA
dc
ac
MZ Z
m
Z
m M
Z
(27)
where 'dcZ is the equivalent impedance of the system on
the VSC1’s dc-side; ' and "are defined by the sequence of
the harmonic from the ac-side.
Figure 6 represents the receiving end VSC’s dc equivalent
impedance response under the interaction of the fundamental
switching function. It is obvious that, the equivalent impedance
at the fundamental frequency has a small value, but
dramatically increases at higher frequencies. Consequently, the
higher harmonic orders on the VSC’s dc-side, the lesser effects
on the ac-side will be.
Figure 7 plots negative equivalent impedance using
calculatio
n in (27)
in the case
of
changing
in the
length of
the cable.
As can be
seen, the
system
had no
resonance
at the
backgrou
nd 2nd
harmonic and in a fault condition in the sending end ac system.
Obviously, the equivalent impedances at these orders had quite
small values, meaning that there were insignificant effects on
the receiving end ac system. The lower plot in Fig.7 is the
negative equivalent impedance response, with a reduction in
the dc cable length. A resonance occurred in the case of
unsymmetrical single phase-to-ground fault on the sending ac
system. A practical case is that, the background harmonics in
North-west Power Grid includes second harmonic order.
According to the analysis result in Fig.7, the effect of this 2nd
harmonic’s propagation will not be an issue.
D. Simulation results and analysis
For studying harmonic propagation, a Matlab/Simulink
simulation model was set up for the VSC-HVDC system on
Fig.1. In this model, the sending end VSC was modeled to
operate as power dispatcher while the receiving end VSC was
modeled to operate as dc voltage regulator and reactive power
controller. In each VSC station, the main component, VSC, is a
6-IGBT bridge three-level NPC converter. The VSCs adopt the
SPWM modulation technique, which compares modulation
waves with two triangle carriers. The frequency of the triangle
carrier wave is 1350 Hz.
- Case study 1:
0 1 2 3 4 5 6 7 8 9 10
0
10
20
A
m
pl
itu
de
(O
hm
)
(a) cable length is 1000 km
0 1 2 3 4 5 6 7 8 9 10
0
20
40
A
m
pl
itu
de
(O
hm
)
(b) cable length is 380 km
Harmonic order
-100
0
100
P
ha
se
a
ng
le
(d
eg
)
-100
0
100
P
ha
se
a
ng
le
(d
eg
)
Fig. 7. Negative equivalent impedance response depends on the dc cable
length.
0 1 2 3 4 5 6 7 8 9 10
0
1
2
x 104
Im
pe
da
nc
e
(O
hm
)
DC seen equivalent impedance
Harmonic order
-100
0
100
P
ha
se
a
ng
le
(d
eg
)
0 1 2
0
200
400
600
Fig. 6. DC-side seen equivalent impedance response of the receiving end VSC
0 2 4 6 8 10 12 14 16 18 20
0
1
2
3
(a)PoS background harmonic propagation
Harmonic order
M
ag
(%
o
f f
un
da
m
en
ta
l
0 2 4 6 8 10 12 14 16 18 20
0
2
4
6
8
(b)NeS background harmonic propagation
Harmonic order
M
ag
(%
o
f f
un
da
m
en
ta
l
No harmonic
2nd
5th
7th
Fig. 9. Different background harmonics on the sending ac system causing
spectra of phase current on the receiving ac system.
2151 Session 4
2014 International Conference on Power System Technology (POWERCON 2014) Chengdu, 20-22 Oct. 2014
POWERCON 2014 Paper No CP1493 Page 7/8
0 5 10 15 20
0
2
4
6
Harmonic order
(a) lcab=1000 km , THD= 6.85%
M
ag
(%
o
f F
un
da
m
en
ta
l)
0 5 10 15 20
0
2
4
6
Harmonic order
(b) lcab=380 km , THD= 8.04%
M
ag
(%
o
f F
un
da
m
en
ta
l)
Fig. 10. Spectra of receiving end ac system phase a current when the sending
ac system has un-symmetric single phase-to- ground fault.
0 2 4 6 8 10 12 14 16 18 20
0
2
4
6
8
(a) 100% power transfer capacity
Harmonic order
M
ag
(%
o
f f
un
da
m
en
ta
l
0 2 4 6 8 10 12 14 16 18 20
0
4
8
12
(b) 50% power transfer capacity
Harmonic order
M
ag
(%
o
f f
un
da
m
en
ta
l
Fault
2nd
5th
7th
Fig. 11. Harmonic propagation in different operation conditions of the
VSC-based HVDC system.
The first case was examined with 10% of a 2nd order
background harmonic voltage. As the rules of harmonic
transfer, the receiving end ac system induced the dc component
and the 2nd order harmonic, or the 2nd order and the 4th order
harmonics, which is relative to the sequence of harmonic
source.
The simulation results in this case are presented in Fig.8
which conformed to the analytical rules. For the same
amplitude, the negative-sequence 2nd component (a) gave
stronger effect than the positive-sequence 2nd component (b).
It should also put attention to the appearance of the 5th and the
7th harmonics because of the dc-capacitor voltage ripples. They
could be problematic if the system resonates at these
frequencies.
The rules were the same for the other order of harmonics, but
the effect of different sequence was not so clear as can be seen
in Fig.9.
- Case study 2:
A single phase-to-ground fault at the point of common
coupling at the sending end ac system was considered in this
case. As a result, the voltage was composed of the
negative-sequence fundamental component propagated to the
receiving end ac system and produced an additional 3rd order
harmonic (see Fig. 10).
- Case study 3:
According to the results from the case study 1 and 2, in this
case, the VSC-based HVDC system operates at different power
transfer conditions. The sending end ac system includes the
negative-sequence 2nd and 5th harmonics, the positive-sequence
7th harmonic. The sending end ac system in single
phase-to-ground fault condition was also examined in this case.
Figure 11 plots the simulation results show that decreasing in
power transfer capacity gave a larger effect of harmonic
propagation, especially at the negative-sequence 2nd harmonic.
VI. CONCLUSION
This paper uses the space vector of switching function to
study the harmonic interaction between the two ac-sides of the
VSC. This space vector of switching function comprises of the
fundamental component, higher-order positive- and
negative-sequence switching components. They support a
straightforward tool to understand the origin of
non-characteristic harmonics on both sides of the VSC.
However, in a different way, other non-characteristic
harmonics are produced on the ac-side of the VSC because of
dc-capacitor ripples. Moreover, the impedance-frequency
characteristic of the VSC-based HVDC system was analyzed to
show at which frequencies the system resonates. The
combination of the mathematical analysis of harmonic
interaction and the impedance-frequency characteristic gives a
thorough view of understanding harmonic propagation of
VSC-based HVDC systems. After that, the simulation model of
the system was set up. The simulation results agreed with the
theoretical analysis in all cases.
APPENDIX
A. Bessel function:
dee
j
J jkjkk
cos
.2
1
k
k
k JJ 1
B. Space vector representation of harmonics:
For the three-phase harmonic quantity
ˆ cos
ˆ cos 2 / 3
ˆ cos 2 / 3
na
nb
nc
f t f n t
f t f n t n
f t f n t n
The space vector representation has the form of
2 41 1
3 3
2 41 1
3 3
ˆ
1
3
ˆ
+ 1
3
j n j n jn t
j n j n jn t
ff e e e
f e e e
C. Parameters of studied VSC-based HVDC system
1. Sending end:
Uac1 = 345 kV, f = 50 Hz, Iscmax = 50 kA;
Sb1 = 600 MVA, 345/300 kV
2. DC-link
PDC = 600 MW, UDC = 300 kV, IDC = 1kA
DC capacitor: Cd = 30 F;
Cable: Rc = 13.9 m /km, Lc=0.159 mH/km,
Cc =0.231 F/km, Lcab = 1000 km
2152 Session 4
2014 International Conference on Power System Technology (POWERCON 2014) Chengdu, 20-22 Oct. 2014
POWERCON 2014 Paper No CP1493 Page 8/8
3. Receiving end:
Uac2 = 230 kV, f = 50 Hz, Iscmax = 40 kA;
Sb2 = 600 MVA, 230/300 kV
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2153 Session 4

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