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The Journal of Engineering
The 7th International Conference on Renewable Power Generation
(RPG 2018)
Third-order harmonic currents suppression
method based on selective component
compensation for cascaded H-bridge
STATCOM under asymmetric grid
eISSN 2051-3305
Received on 30th January 2019
Accepted on 30th January 2019
E-First on 28th June 2019
doi: 10.1049/joe.2019.0095
www.ietdl.org
Daorong Lu1 , Haibing Hu1
1Jiangsu Key Lab. of New Energy Generation and Power Conversion College of Automation Engineering, Nanjing University of Aeronautics and
Astronautics Nanjing, Jiangsu, People's Republic of China
E-mail: tcludaorong@nuaa.edu.cn
Abstract: To achieve low cost and compactness, small dc capacitance in dc-link is preferred in the cascaded H-bridge (CHB)
static synchronous compensator (STATCOM). However, small dc capacitance will definitely result in high dc-link ripples among
three clusters, and thus cause severe third-order harmonic currents under the asymmetric grid. In this study, to mitigate the
third-order harmonic currents, a selective component compensation approach for the CHB STATCOM is proposed. To study the
effect of the dc-link ripples on the phase currents, sequence component decomposition is employed to derive the relationship
between the dc-link ripples and the converter voltages. The relationship reveals that the converter voltages contain positive,
negative, and zero sequence components in both fundamental and third-order under the asymmetric grid, while only the positive
and negative sequence components in third-order converter voltages result in third-order harmonic currents due to the three-
wire system. Therefore, the third-order harmonic currents suppression method is proposed by only compensating the positive
and negative components in third-order converter voltages. A 380 V/15 kVA STATCOM prototype is built to verify the proposed
control method.
1Introduction
High penetration of renewable energy sources requires static
synchronous compensator (STATCOM) in power system to
regulate the grid voltage. In medium voltage applications, the
cascaded H-bridge (CHB) converter is often chosen to implement
STATCOM due to the modularity. To achieve low system cost and
small volume for the CHB STATCOM, researchers and engineers
tried to design the dc capacitance as small as possible [1, 2].
However, dc capacitors with small capacitance can generate large
dc-link ripples, which would be modulated to the ac side and result
in third-order harmonic currents when the three-phase grid voltage
is asymmetric [3, 4]. To mitigate the third-order harmonic currents,
a dc-link ripple voltage feedforward control was proposed [5–7]. In
[5], the dc-link ripple voltages were introduced into the modulation
carriers to remove the third-order harmonics in the output voltages,
however, which deteriorates the harmonic performance of the
phase-shift carrier (PSC) sine pulse-width modulation (PWM) [8].
To maintain the harmonic performance of PSC modulation, the dc-
link ripple voltage feedforward was introduced into the three-phase
modulation reference voltages [6, 7]. However, this method affects
the fundamental converter voltages, which is adverse to the
stability of the control system.
To mitigate the third-order harmonic currents under the
asymmetric grid, this study proposes a selective component
compensation approach for the CHB STATCOM with small dc
capacitance. Based on sequence component decomposition, the
sequence components of the converter voltages modulated by the
dc-link ripples are obtained. This approach only compensates the
positive and negative sequence components in third-order
converter voltages, which does not affect other components under
any condition. Therefore, compared to conventional methods, this
approach will introduce fewer harmonics into the modulation
reference voltages and also change the fundamental converter
voltages, which guarantee the stability of the system. The
effectiveness of the proposed control method is verified by the
experiments.
2Circuit configuration of CHB STATCOM
Fig. 1 illustrates the circuit configuration of the star-connected
STATCOM, which consists of N identical H-bridges in each
cluster. PSC PWM is applied to generate the output converter
voltages. usk represents the grid voltages, uk (k = a, b, c, similarly
hereinafter) represents the three-phase output voltages of the
converter and ik represents the output currents. udckj (j = 1,…, N) is
the capacitor voltage of three-phase H-bridge cells, udck is the
cluster voltage which is the sum of the dc capacitor voltages in
phase k, Udck is the dc component of the cluster voltage in phase k.
3Generation mechanism of the third-order
harmonic currents under the asymmetric grid
For the sake of simplification, the switching harmonics of the
converter voltages are neglected in the following derivation. For
each dc capacitor, using Kirchhoff's current law, the current
flowing across each capacitor can be expressed as
C⋅dudckj
dt=dk⋅ik,
(1)
where dk (k = a, b, c) is the modulation reference voltages. The
three-phase modulation reference voltages can be decomposed into
positive, negative, and zero sequence components, which are given
as
da=dap+dan+daz
=Mpcos(ωt) + Mncos(ωt +θn) + Mzcos(ωt +θz),
db=dbp+dbn+dbz
=Mpcos(ωt − 120°) + Mncos(ωt +θn+ 120°) + Mzcos(ωt +θz),
dc=dcp+dcn+dcz
=Mpcos(ωt + 120°) + Mncos(ωt +θn− 120°) + Mzcos(ωt +θz),
(2)
J. Eng., 2019, Vol. 2019 Iss. 18, pp. 5260-5263
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5260
where the subscripts p, n, and z represents the positive, negative,
and zero sequence components, respectively, M is the modulation
index. θn and θz are the initial phases of the negative and zero
sequence modulation reference voltages. ω stands for the
fundamental frequency of the grid voltage.
To derive the dc-link voltages, the output currents are given as
ia=Icos(ωt +φ),
ib=Icos(ωt − 120° + φ),
ic=Icos(ωt − 120° + φ),
(3)
where I and φ represent the magnitude and initial phase of the
currents, respectively. By substituting (2), (3) into (1), three-phase
cluster voltages udck can be derived as (see (4)) . As seen in (4), the
three-phase dc-link ripples with double line frequency consist of
three parts under asymmetric grids: the positive sequence
component udckp, negative sequence component udckn, and zero
sequence component udckz. According to the dc-link ripples in (4),
the converter voltages can be derived as
ur_a=da⋅ur_dca,
ur_b=db⋅ur_dcb,
ur_c=dc⋅ur_dcc,
(5)
where ur-dck represents the dc-link ripples and ur-k is the converter
voltage modulated by the dc-link ripples. According to (5), the
sequence components of the converter voltages are analysed in
Fig. 2.
In Fig. 2, ωx (x = p, n, z, similarly hereinafter) represents the
positive, negative, and zero sequence fundamental components,
respectively. 2ωx and 3ωx have similar representation. According to
the angular speed of the dc-link ripples (2ωx) and the modulation
reference voltages (ωx), the output converter voltages should be
decomposed into third harmonic (3ωx) and fundamental component
(ωx) based on the trigonometric calculation. The detailed sequence
components of the output voltages are analysed in the following.
When the grid voltages are symmetric, the modulation reference
voltages contain only positive sequence component, which leads to
only negative sequence components in the double-line frequency
dc-link ripples according to (4). Therefore, from Fig. 2, only the
zero sequence third-order harmonic and positive sequence
fundamental converter voltages are generated, which will not
induce harmonic currents in the three-phase and three-wire system.
However, when the grid voltage is asymmetric, the converter
voltages contain the positive, negative, and zero sequence third-
order harmonic components as well as fundamental components,
while only the positive and negative sequence third-order harmonic
voltages can generate third-order harmonic currents, which would
degrade the power quality.
4Proposed selective component compensation
method for the third-order harmonic current
suppression
Based on the analysis of Fig. 2, when the grid voltages are
asymmetric, the converter voltages contain the fundamental
components and the third-order harmonics, which can be expressed
as
uk= (Udck+ur_dck) ⋅ dk
=Udck⋅dk+uk_3ωp+uk_3ωn+uk_3ωz+uk_ω,
(6)
where uk_3ωp and uk_3ωn are the positive and negative sequence
third-order harmonics in the converter voltages, which would
generate harmonic currents. To eliminate uk_3ωp and uk_3ωn, a
novel method is proposed by introducing uk_3ωp and uk_3ωn into the
modulation reference voltages, which can be formulated as (7). In
this scenario, the converter output voltages would not contain the
positive and negative sequence third-order harmonics. The control
block diagram of the proposed method is illustrated in Fig. 3.
uk= (Udck+ur_dck) ⋅ dk−uk_3ωp+uk_3ωn
Udck+ur_dck
=Udck⋅dk+uk_3ωz+uk_ω.
(7)
Fig. 1 Circuit configuration of CHB STATCOM
udca=∑
j= 1
N
udcaj =N
4ωC ⋅IMzsin(2ωt +θ1+φ)
udcap
+N
4ωC ⋅IMpsin(2ωt +φ)
udcan
+N
4ωC ⋅IMnsin(2ωt +θ1+φ)
udcaz
+Udca
udcb=∑
j= 1
N
udcbj =N
4ωC ⋅IMzsin(2ωt +θ1+φ− 120∘)
udcbp
+N
4ωC ⋅IMpsin(2ωt +φ+ 120∘)
udcbn
+N
4ωC ⋅IMnsin(2ωt +θ+φ)
udcbz
+Udcb
udcc=∑
j= 1
N
udccj =N
4ωC ⋅IMzsin(2ωt +θ1+φ+ 120∘)
udccp
+N
4ωC ⋅IMpsin(2ωt +φ− 120∘)
udccn
+N
4ωC ⋅IMnsin(2ωt +θ+φ)
udccz
+Udcc
(4)
Fig. 2 Analysis of the sequence components of the output voltages
J. Eng., 2019, Vol. 2019 Iss. 18, pp. 5260-5263
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5261
In Fig. 3, according to (6), the output harmonic voltages are
obtained through multiplying the dc-link ripples (2ωx) by the
modulation reference voltages (ωx).To extract the positive and
negative sequence third-order harmonic components, the
generalised rotating coordinate transform theory is utilised. Finally,
the normalised third-order harmonic components are injected into
the modulation reference voltage to compensate the positive and
negative sequence third-order harmonics of the output voltages.
According to the analysis of Figs. 2 and 3, under the symmetric
grid, this proposed control method will not introduce any harmonic
components to the modulation reference voltages, which is helpful
to the system stability.
5Experimental results
As illustrated in Fig. 4, the 15 kVar CHB STATCOM experimental
platform was constructed by our lab to verify the proposed method.
Table 1 lists the main parameters of the circuit. For the limited
channels of the oscilloscope, a virtual oscilloscope designed by
LabVIEW was used to display the operation waveforms.
5.1 Operation under the symmetric grid
Fig. 5a shows the balanced grid line-voltages. Fig. 5b shows the
three-phase output staircase voltages. Fig. 5c shows the three-phase
currents and Fig. 5d shows the cluster voltages and their ripples
only contain negative sequence component under the symmetric
grid. The three-phase third-order harmonic current contents are
given in Table 2. From Table 2, three-phase currents contain little
amount of third-order harmonics under the symmetric grid, which
meets the requirements of the grid code.
5.2 Operation without the proposed control method under the
asymmetric grid
Fig. 6a shows the three-phase grid line-voltages and the phase A
grid voltage drops 100%. Fig. 6b shows the three-phase staircase
voltages which also became unbalanced to control the phase
currents. Fig. 6c shows the three-phase currents and Fig. 6d shows
the cluster voltages. It is obvious that the dc-link ripples contain
positive, negative and zero sequence components. As a result, the
third-order harmonics in the phase currents are increased, which is
given in Table 3.
5.3 Operation with the proposed control method under the
asymmetric grid
To suppress the third-order harmonic currents, the proposed control
method is adopted. Figs. 7 a and b show the asymmetric grid line-
voltages and the output staircase voltages, respectively. Fig. 7c
shows the three-phase currents and their third-order harmonic
components are given in Table 4. Compared with Table 3, the
Fig. 3 Control block diagram of the proposed control method for the third-
order harmonic current suppression
Fig. 4 Experimental platform
Table 1 Circuit parameters
Variables Symbol Value
rated reactive power Q15 kVar
line to line rms voltage Us400 V
cascaded cell number N5
AC filter inductor L9 mH
nominal dc voltage Udc 75 V
DC capacitor C1 mF
Fig. 5 Waveforms of the system under symmetric grid
Table 2 Third-harmonic components in the currents under
the symmetric grid
Currents Amptitude 3ω currents (%) with the method THD, %
ia0.020 A 0.13 0.94
ib0.024 A 0.16 1.00
ic0.032 A 0.21 1.03
THD, total harmonic distortion.
5262 J. Eng., 2019, Vol. 2019 Iss. 18, pp. 5260-5263
This is an open access article published by the IET under the Creative Commons Attribution-NoDerivs License
(http://creativecommons.org/licenses/by-nd/3.0/)
third-order harmonic currents are greatly reduced by using the
proposed control method.
6Conclusion and future work
This study employs sequence component decomposition to analyse
the sequence components of the converter output voltages. The
analysis reveals that the positive and negative sequence
components in third-order converter voltages would be generated
under the asymmetric grid, which can induce the third-order
harmonic currents. To mitigate the harmonic currents, a selective
component compensation method is proposed by only
compensating the positive and negative components in the third
order. The theoretical analysis is verified on a three-phase 400
V/15 kVar star-connected CHB STATCOM in laboratory prototype.
The experimental results indicate that the proposed control method
can suppress the third-order harmonic currents effectively.
7References
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Fig. 6 Waveforms of the system under asymmetric grid
Table 3 Third-harmonic components in the currents under
the asymmetric grid
Currents Amptitude 3ω currents (%) with the method THD, %
ia0.536 A 3.53 3.64
ib0.331 A 2.17 2.43
ic0.202 A 1.33 1.70
THD, total harmonic distortion.
Fig. 7 Waveforms of the system when the method is activated
Table 4 Third-harmonic components in the currents when
the method is activated
Currents Amptitude 3ω currents (%) with the method THD, %
ia0.064 A 0.42 1.07
ib0.026 A 0.17 1.07
ic0.039 A 0.26 1.12
THD, total harmonic distortion.
J. Eng., 2019, Vol. 2019 Iss. 18, pp. 5260-5263
This is an open access article published by the IET under the Creative Commons Attribution-NoDerivs License
(http://creativecommons.org/licenses/by-nd/3.0/)
5263
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