For a shunt power quality controller (SPQC) the DC side voltage value which is closely related to the compensation performance is a significant parameter. Buy so far, very little discussion has been conducted on this in a quantitative manner by previous publications. In this paper, a method to design the DC side voltage of SPQC is presented according to the compensation performance in the singlephase system and the threephase system respectively. First, for the reactive current and the harmonic current compensation, a required minimal value of the DC side voltage with a zero total harmonic distortion (THD) of the source current and a unit power factor is obtained for a typical load, through the equivalent circuit analysis and the Fourier Transform analytical expressions. Second, when the DC side voltage of SPQC is lower than the aboveobtained minimal value, the quantitative relationship between the DC side voltage and the THD after compensation is also elaborated using the curve diagram. Hardware experimental results verify the design method.
1. Introduction
As advanced equipment for improving the power quality, Shunt Power Quality Controller (SPQC) combines the functions of Shunt Active Power Filter (SAPF)
[1
,
2]
and Static Synchronous Compensator (STATCOM)
[3
,
4]
. The SPQC can be used to compensate both the reactive current and the harmonic current. Threephase voltage source converter is widely employed in SPQC
[5]
. The SPQC has a DC side voltage control loop to keep the DC side voltage as a constant which has a big influence on the compensation performance. When the SPQC is used to compensate the reactive current and the harmonic current, the higher the DC side voltage is, the better the compensation result is. However, with higher DC side voltage, voltage stress of the power device will be larger, and it will increase the cost. In addition, higher DC side voltage will cause bigger converter losses. So, in order to reduce the losses in practical applications, it is desirable to make the constant rated value of the DC side voltage as low as possible. According to the analysis above, the choice of the DC side voltage constant rated value of SPQC is very important, and needs a detailed quantitative analysis and specification.
The researches on the DC side capacitor and DC voltage are very important. In many applications, the DC side voltage is controlled as a constant
[6

8]
. In
[9]
, for a given DC side voltage, the maximum fundamental out voltage was shown in a wind generating system, and, it was very useful that the paper presented the relationship between the DC side voltage and the maximum fundamental output voltage. Furthermore, in
[10]
, the selection of the DC side voltage for the Static Var Generator was presented, and the relationship between the compensation performance and the DC side voltage was also analyzed. These two papers mainly focused on the DC side voltage with the fundamental output voltage. However, the situation that the output voltage and the output current were the harmonic components was not discussed in these two papers. For the PAPF, in
[11]
, an approximate value of the DC side voltage was presented, and the DC side voltage was selected as 1~1.3 p.u.. In
[11]
, the DC side voltage selection methods presented approximate values. However the DC side voltage should be selected more accurately. In
[12]
, the values of the DC side voltage were selected by considering the capability of reactive power compensation and harmonics current reduction. And, the capacitor value was designed to reduce the fluctuations of the DC side voltage caused by load unbalance and load change. The selection method of the DC side voltage was more accurate, but it may be a little complex. Especially, it is difficult to obtain the capability of harmonics current reduction. In
[13]
, the DC side voltage reference was constant and was determined by simulation and experimental studies. Simulation method was valid, but it was inconvenient. In order to design an accurate DC side voltage, in
[14]
, the effect of the DC side voltage on the compensation performance of a PAPF was studied by focusing on 5
^{th}
negative and 7
^{th}
positive harmonic sequences. The minimal required DC side voltage for the linear modulation range was presented. But, only focusing on 5
^{th}
and 7th harmonics was not comprehensive, and the method, which was mentioned in
[14]
to determine a DC side voltage value for all harmonic currents, was too complex. An accurate method to select the DC side voltage was presented in
[15]
for the system load with phase control sixpulse converter. The minimal DC side voltage was obtained by using the voltage instantaneous space vectors in the dq orthogonal coordinates. The optimal instantaneous space vectors voltage was the minimum voltage that always existed inside the hexagon when the SVPWM was used. The selection method of the minimal DC side voltage mentioned in
[15]
was very useful. However, the further study should be presented when the DC side voltage was smaller than the minimal value, because the full compensation for harmonic current was not necessary at most of situations. When the DC side voltage is smaller than the minimal value and the modulation is nonlinear, the influence of the DC side voltage on the compensation performance has not been discussed in published papers. The relationship between the compensation performance and the DC side voltage should be analyzed in a quantitative manner.
This paper focuses on the design method of the DC voltage and the relationship between the compensation performance and the DC voltage. Specifically, the contributions of this paper are:

1) A required minimal value of the DC voltage for full compensation is presented.

2) For the situation where the DC voltage is smaller than the aboveobtained minimal value, the quantitative relationship is detailed between the DC voltage value and the THD after compensation.

3) The DC side voltages of the singlephase system, the threephase system with SPWM control and the threephase system with SVPWM control are analyzed respectively.
2. DC Side Voltage Analysis and Specification
 2.1 System configuration
There are two types of systems which are the singlephase system shown in
Fig. 1
and the threephase system shown in
Fig. 2
, where
u
_{k}
(
k
=
a, b, c
) is the instantaneous value of the source phase voltage,
i
_{Lk}
is the instantaneous value of the load phase current,
i
_{sk}
is the instantaneous value of the source phase current,
i
_{ck}
is the instantaneous value of the output phase current, and
U
_{dc}
is the average value of the DC side voltage. Assume that the system is balanced, the singlephase equivalent circuit is shown in
Fig. 3
, where
u
_{s}
is the instantaneous value of the source voltage,
u
_{L}
is the instantaneous value of the voltage of inductor,
i
_{c}
is the instantaneous value of the output current,
u
_{I}
is the instantaneous value of the output voltage of converter. The losses of the converter are regarded as the active power in the resistor of the inductor
[16]
.
Singlephase main circuit of the SPQC
Threephase main circuit of the SPQC
Circuits of the principle of superposition
 2.2 Design of DC side voltage
The method of analysis adopts the superposition principle of the singlephase equivalent circuit in
Fig. 3
, and the relationship equations are shown in Eqs. (1) and (2).
The maximal value of the output voltage (
u
_{I_max}
) and the DC side voltage are shown in Eqs. (3) and (4), where
k
=1 for the singlephase system,
k
= 1/2 for the Sinusoidal Pulse Width Modulation (SPWM) and
for the Space Vector Pulse Width Modulation (SVPWM) of the threephase system
[17

19]
. The modulation index
m
=1.
There are two basic issues for the PWM control of SPQC: The minimal DC side voltage for full compensation; and the influence on the THD of the source current when the DC side voltage is lower than the minimal value for the part compensation.
The system load is the rectifier with resistive and inductive load. The system load current and the output reference current are shown in
Figs. 4
and
Fig. 5
. In
Fig. 4
, the singlephase load current is the ideal quadrate waveform. In
Fig. 5
, in the threephase system, it is not an ideal waveform and it can be considered as a trapezoidal waveform which the overlap angles are less than 10º (usually occurring in electrical plants)
[20]
.
System load current and reference current (single phase)
System load current and reference current (three phases)
 2.3 Minimal DC side voltage at full compensation (For Singlephase System)
By using the Fourier analysis, the load current can be expressed as Eq. (5), where
ω
is the radian frequency of the fundamental component. The output reference current is shown in Eq. (6).
The inductor voltage can be expressed as Eq. (7).
Assume that
The output current can be shown as Eq. (9).
According Eqs. (7) and (9), the waveform of
f
_{1}
(
ωt
) is shown in the Appendix by using the mathematical software. The peak value of
f
_{1}
(ωt) in Eq. (8) is 25.9 at
ωt
=0. Because the peak value of
ωLI
_{ch}
f
_{1}
(
ωt
) is much larger than the peak value of the source voltage, the peak value of the output voltage can be expressed as Eq. (10), where the source phase voltage is
is the phase between the source phase voltage and the source phase current, and
I
_{cq}
is the RMS value of the output reactive current (assume that
I
_{cq}
is RMS value of the required output reactive current).
When the output harmonic current is zero, the DC side voltage is 1.414(
U
_{s}
+
ωLI
_{cq}
). From Eq. (10), the DC side voltage is related to the phase
φ
and the output harmonic current. Assume that the base of perunit is (
U
_{s}
+
ωLI
_{cq}
) and
k
_{L}
=
ωLI
_{ch}
/(
U
_{s}
+
ωLI
_{cq}
), the DC side voltage in Eq. (10) can be expressed as Eq. (11). The minimal DC side voltage with the typical values of phase
φ
is illustrated in
Fig. 6
. If the peak value of 25.9
ωLI
_{ch}
f
_{1}
(
ωt
) is smaller than the value of (
U
_{s}
+
ωLI
_{cq}
), the DC side voltage is determined by the peak value of (
U
_{s}
+
ωLI
_{cq}
). When the DC side voltage is lower than 1.414(
U
_{s}
+
ωLI
_{cq}
), the DC side voltage is chosen as 1.414(
U
_{s}
+
ωLI
_{cq}
). So, there is an inflection point of the curves. The current of harmonic orders from 5
^{th}
to 25
^{th}
is just considered.
Relationship between the minimal DC side voltage and k_{L} (single phase)
 2.4 Minimal DC side voltage at full compensation (For Threephase system with SPWM control)
When the SPWM is used in threephase system, the load current from 0~π can be considered as Eq. (12) from
Fig. 5
, where
γ
_{1}
is overlap angle.
The Fourier series of load current from 0 to 2π is shown in Eq. (13). And, the output reference current can be obtained as Eq. (14). The RMS value of the output reference current is expressed as Eq. (15), when the current of harmonic orders from 5
^{th}
to 25
^{th}
is just considered.
Assume that the inductor voltage is
u
_{L}
.
I
_{ch}
is the RMS of output current of phase
a
.
u
_{L}
can be expressed as Eq. (16).
Where
The peak value of
f
_{2}
(
ωt
) is
f
(
γ
_{1}
). By using the mathematical software, the values of
f
(
γ
_{1}
) can be obtained according to
γ
_{1}
. The relationship between
f
(
γ
_{1}
) and
γ
_{1}
is illustrated in
Fig. 7
. From
Fig. 7
, the value of
f
(
γ
_{1}
) can be gotten according to the value of
γ
_{1}
.
Relationship between f(γ_{1}) and γ_{1}
Because the peak value of
ωLI
_{ch}
f
(
γ
_{1}
) is much larger than the peak value of the source voltage, the value of the output voltage reaches the peak value at
ωt
=
π
/6. The minimal DC side voltage is shown in Eq. (18). The DC side voltage in Eq. (18) can be expressed as Eq. (19). And, the relationship between the minimal value and
k
_{L}
are carried out in
Fig. 8
with different
γ
_{1}
and
φ
.
Relationship between the minimal DC side voltage and k_{L} (threephase system with SPWM control)
 2.5 Minimal DC side voltage at full compensation (For threephase system with SVPWM control)
When the SVPWM is used in threephase system, the output voltages of inverter are shown in Eq. (20). The output voltages are transformed into
αβ
frame, and the voltage vector are expressed as Eq. (21) and Eq. (22)
[21
,
22]
. The switching vectors are shown in Eq. (23). If the voltage vector exists inside the hexagon in
Fig. 9
, the THD of the source current after compensation is zero
[14]
.
Relationship between space vector and hexagon (for full compensation)
The minimal DC side voltage is shown in
Fig. 10
with different
γ
_{1}
and
φ
by using the mathematical software.
Relationship between the minimal DC side voltage and k_{L} (threephase system with SVPWM control)
3. Analysis of Compensation Characteristics with DC Side Voltage Lower than the Minimal Value
In order to reduce the DC side voltage, the compensation performance can be reduced, as long as the requirement of THD after compensation is satisfied. When the DC side voltage is lower than the minimal value, the modulation control is the nonlinear control. It is very difficult to analyze the relationship between the compensation performance and the DC side voltage. A group of simulation results are present to obtain the relationship between the compensation performance and the DC side voltage in this paper.
 3.1 For singlephase system
In
Fig. 11
, with different
φ
and
k
_{L}
, the THD of the source current is presented. The THD becomes unregulated when the DC side voltage is lower than 1.414 times of the peak value of the source voltage. Because the DC side voltage of inverter is 1.414 p.u. when the output current is zero. If
I
_{cq}
is changed, the base of perunit is also changed to (
U
_{s}
+
ωLI
_{cq}
), and
U
_{dc_pu}
in the figure is based on the perunit value.
Relationship between DC side voltage and compensation performance (single phase)
 3.2 For threephase system with SPWM control
When the DC side voltage is lower than the minimal value, the modulation control is the nonlinear control. A group of simulation results are present to obtain the relationship between the compensation performance and the DC side voltage in this paper. From
Fig. 12
, with different
φ
,
k
_{L}
and
γ
_{1}
, the THD of the source current after compensation is presented. With those curves, the relationship between the compensation performance and the DC side voltage are obtained.
Relationship between DC side voltage and compensation performance for threephase system with SPWM control
 3.3 For Threephase system with SVPWM control
When the DC side voltage is lower than the minimal value, the THD of the source current after compensation is presented in
Fig. 13
with different
φ
,
k
_{L}
and
γ
_{1}
by using the simulation software.
Relationship between DC side voltage and compensation performance for threephase system with SVPWM control
4. Simulation and Experimental Results
The simulation investigation and the experiment were carried out to verify the minimal DC side voltage equations and the output current equations after changing DC side voltages.
For a design example, in threephase system for full compensation, the DC side voltage was related to the phase angle between the source phase voltage and the peak value of inductor voltage. When the system load was diode rectifier with resistive and inductive load, the phase angle was 0º. In
Fig. 14
, the inductor was 0.4mH. The RMS of the source phase voltage was 220V. The output current (RMS) was 93.6A.The modulation index was 1, and the triangular wave modulation SPWM was used.
Compensation result with the minimal DC side voltage (for SPWM)
In
Fig. 14
, the overlap angle was
γ
1=0 and the DC side voltage for full compensation was 1104V according to the theoretical analysis. The compensation result was acceptable with a minimal DC side voltage 1104V and the THD of the source current after compensation was 0.5% (harmonic current from 5
^{th}
to 25
^{th}
order was just considered), which approximately equaled to the theoretical value (0%). The simulation results verified the analysis and the conclusion about the minimal DC side voltage. Because of the current tracking error and the dead time of PWM, in practical applications, the DC side voltage should be higher than the theoretical value, when the SPQC is designed. The theoretical value is the best situation with zero tracking error and one modulation index. The Eq. (11), Eq. (19) and diagrams can be used as a reference of the best situation. However, in the practical applications, the voltage which is lower than 1104V is used, as the compensation result with a THD lower than 5% is satisfied.
In order to verify the analysis results, the hardware experiment has been carried out which is shown in
Fig. 15
. For a design example, the threephase inverter was used. The DSP TMS320F2812 was used to realize the direct current control strategy and the PWM control method. The peak value of the phase source voltage is
U
_{s}
=70.7V, the inductor is 5.5mH, the capacitor of DC side is 3333uF, and
I
_{cq}
is zero.
Experimental hardware view
For the SPWM control, in
Fig. 16
, the overlap angle was 5.9 º and
γ
_{1}
≈17. The output current was 0.086 p.u., and the theoretical DC side voltage was 6.963 p.u.. The dead time of PWM was 4
μ
s and the switching frequency was 15kHz, so the error was approximately 6%, then the minimal DC side voltage was modified as 7.558 p.u.. In
Fig. 17
, the source current after compensation was presented with the minimal DC side voltage. The THD of the source current was very small and it was 3.5%( from 5
^{th}
to 25
^{th}
) after compensation. From the experimental results, the selection method of the minimal DC side voltage was verified. Because of the current tracking error and the dead time of PWM, in practical applications, the DC side voltage should be higher than the theoretical value, when the SPQC was designed. The theoretical value was the best situation with a zero tracking error and one modulation index. The Eq. (19) and diagrams can be used as a reference of the best situation.
Load current
Source current after compensation
The simulation and experimental results verified the design method of the DC side voltage. For a design point of view, the equations and curves of DC side voltage can be used as reference to determine DC side voltage. The dead time of PWM and the current tracking error should be considered, and chooses a suitable DC side voltage according to the desired THD.
5. Conclusion
In this paper, a method to design the DC side voltage of SPQC and the DC side voltage rated value are presented according to the compensation performance. A required minimal value of the DC side voltage for full compensation is obtained for a typical harmonic current. In order to reduce the DC side voltage, the compensation performance can be reduced, as long as the requirement of THD after compensation is satisfied. The quantitative relationship between the DC voltage and the THD after compensation is detailed when the DC voltage is smaller than the aboveobtained minimal value by using the curve diagrams. The curve diagrams can be used as a reference of the best situation, and the DC side voltage should be higher than the best situation with the tracking error and dead time. Hardware experimental results verify the validity of the design method.
Acknowledgements
Project 51307054 supported by National Natural Science Foundation of China.
BIO
Guopeng Zhao He received B. S. degree in Electrical Engineering from Northwestern Polytechnical University, China, in 2003, and M.S. and Ph.D. degrees in Electrical Engineering from Xi’an Jiaotong University, China, in 2006 and 2010, respectively. His research interests are power quality control and applications of power electronics in power systems.
Minxiao Han He received B.S. degree in Electrical Engineering from Xi’an Jiaotong University, China, in 1984, and M.S. and Ph.D. degrees from North China Electric Power University, China, in 1987 and 1995, respectively. He was a visiting research fellow in Queen’s University of Belfast, U.K. and post doctoral research fellow with Kobe University, Japan. He is a Professor in North China Electric Power University, China. His research interests are applications of power electronics in power systems, power quality control and the integration of renewable generation in power network.
Park JiHo
,
Baek YoungSik
2012
“Coordination Control of Voltage Between STATCOM and Reactive Power Compensation Devices in SteadyState,”
J. Electr. Eng. Technol.
7
(5)
689 
697
DOI : 10.5370/JEET.2012.7.5.689
Zhang WenHao
,
Lee SeungJae
,
Choi MyeonSong
2010
“Setting Considerations of Distance Relay for Transmission Line with STATCOM,”
J. Electr. Eng. Technol.
5
(4)
522 
527
DOI : 10.5370/JEET.2010.5.4.522
Pal Yash
,
Swarup A.
,
Singh Bhim
2012
“A Novel Control Strategy of Threephase, Fourwire UPQC for Power Quality Improvement,”
J. Electr. Eng. Technol.
7
(1)
1 
8
DOI : 10.5370/JEET.2012.7.1.1
Sim JunBo
,
Kim KiCheol
,
Son RakWon
,
Oh JoongKi
2012
“Ridethrough of PMSG Wind Power System Under the Distorted and Unbalanced Grid Voltage Dips,”
J. Electr. Eng. Technol.
7
(6)
898 
904
DOI : 10.5370/JEET.2012.7.6.898
Lee SungEun
,
Won DongJun
,
Chung IlYop
2012
“Operation Scheme for a Wind Farm to Mitigate Output Power Variation,”
J. Electr. Eng. Technol
7
(6)
869 
875
DOI : 10.5370/JEET.2012.7.6.869
Reyes M.
,
Rodriguez P.
,
Vazquez S.
,
Luna A.
,
Teodorescu R.
,
Carrasco J. M.
2012
“Enhanced Decoupled Double Synchronous Reference Frame Current Controller for Unbalanced GridVoltage Conditions,”
IEEE Trans. Power Electron.
27
(9)
3934 
3943
DOI : 10.1109/TPEL.2012.2190147
Phan VanTung
,
Lee HongHee
2010
“Enhanced ProportionalResonant Current Controller for Unbalanced Standalone DFIGbased Wind Turbines,”
J. Electr. Eng. Technol.
5
(3)
443 
450
DOI : 10.5370/JEET.2010.5.3.443
Choy YoungDo
,
Han ByungMoon
,
Lee JunYoung
,
Jang Gilsoo
2011
“RealTime Hardware Simulator for GridTied PMSG Wind Power System,”
J. Electr. Eng. Technol.
6
(3)
375 
383
DOI : 10.5370/JEET.2011.6.3.375
Mohod S. W.
,
Aware M.
2008
“Analysis and design of a grid connected wind generating system with VSC,”
in Proceedings of 2008 IEEE Region 10 Conference
Hyderabad, India
Zhao G. P.
,
Han M. X.
2013
“DC voltage design and corresponding compensation performance analysis for static var generator,”
Int. J. Electr. Power & Energy Syst.
43
(1)
501 
513
Wang Y. B.
,
Li J. W.
,
Yu J.
2006
“Comprehensive analysis and design for onecycle controlled DC side APF,”
in Proceedings of IEEE Industrial Technology International Conference
Mumbai, India
Chiang S.J.
,
Chang J. M.
1999
“Design and implementation of the parallelable active power filter,”
in Proceedings of IEEE 30th Annual Power Electron. Specialists Conference
Charleston, SC, USA
Fukuda S.
,
Li D.S.
2004
“A static synchronous compensator using hybrid multiinverters,”
in Proceedings of IEEE 35th Annual Power Electron. Specialists Conference
Aachen, Germany
Tarkiainen A.
,
Pollanen R.
,
Niemela M.
,
Pyrhonen J.
2004
“DClink voltage effects on properties of a shunt active filter,”
in Proceedings of IEEE 35th Annual Power Electron. Specialists Conference
Aachen, Germany
Akagi H.
,
Tsukamoto Y.
,
Nabae A.
1990
“Analysis and design of an active power filter using quadseries voltage source PWM converters,”
IEEE Trans. on Ind. Appl.
26
(1)
93 
98
DOI : 10.1109/28.52679
Zhao G. P.
,
Liu J. J.
2010
“Analysis and specifications of switching frequency in parallel active power filters regarding compensation characteristics,”
J. Power Electron
10
(6)
749 
761
DOI : 10.6113/JPE.2010.10.6.749
Hava A. M.
,
Demirkutlu E.
2007
“Output voltage control of a fourleg inverter based threephase UPS,”
in Proceedings of 2007 European Conference on Power Electronics and Applications
Aalborg, Denmark
Choy YoungDo
,
Han ByungMoon
,
Lee JunYoung
,
Jang Gilsoo
2011
“RealTime Hardware Simulator for GridTied PMSG Wind Power System,”
J. Electr. Eng. Technol.
6
(3)
375 
383
DOI : 10.5370/JEET.2011.6.3.375
Lee SolBin
,
Lee KyoBeum
,
Lee DongChoon
,
Kim JangMok
2010
“An Improved Control Method for a DFIG in a Wind Turbine under an Unbalanced Grid Voltage Condition,”
J. Electr. Eng. Technol.
5
(4)
614 
622
DOI : 10.5370/JEET.2010.5.4.614
Cavallini A.
,
Loggini M.
,
Montanari G.C.
1994
“Comparison of approximate methods for estimate harmonic currents injected by AC/DC converters,”
IEEE Trans. on Ind. Electron.
41
(2)
256 
262
DOI : 10.1109/41.293887
Asiminoaei L.
,
Blaabjerg F.
,
Hansen S.
2005
“Evaluation of harmonic detection methods for active power filter applications,”
in Proceedings of IEEE 2005 Twentieth Annual Applied Power Electronics Conference and Exposition
Austin, Texaa, USA
Lee S.J.
,
Kim H.
,
Sul S.K.
,
Blaabjerg F.
2004
“A novel control algorithm for static series compensators by use of PQR instantaneous power theory,”
IEEE Trans. on Power Electron.
19
(3)
814 
827
DOI : 10.1109/TPEL.2004.826499