- Email: [email protected]
Simulation Research on a SVPWM Control Algorithm for a Four-Leg Active Power Filter
Dec. 2007
Journal of China University of Mining & Technology
J China Univ Mining & Technol
Vol.17
No.4
2007, 17(4): 0590 – 0594
Simulation Research on a SVPWM Control Algorithm for a Four-Leg Active Power Filter ZHOU Juan, WU Xiao-jie, GENG Yi-wen, DAI Peng School of Information and Electrical Engineering, China University of Mining & Technology, Xuzhou, Jiangsu 221008, China Abstract: In this paper the topology of a four-leg shunt active-power filter (APF) is given. The APF compensates harmonic and reactive power in a three-phase four-wire system. The scheme adopted for control of the four-leg active power filter, a 3-Dimensional Pulse Width Modulation (PWM) technique, is presented. The theoretical deduction of a space vector PWM (SVPWM) algorithm is given in this paper. The paper also analyzes the distribution of the voltage-space vector of the four-leg converter in αβγ coordinates and describes methods to determine the location of the voltage-space vector and to calculate duration time. Finally, the algorithm is implemented in simulation; the results show that the total harmonic distortion (THD) of the three phase-current waveforms is reduced. The neutral wire current, after compensation, is about 0 A showing that the topology of the four-leg shunt APF is feasible and the proposed scheme is effective. Key words: three-phase four-wire system; shunt active power filter; 3-Dimensional space vector PWM CLC number: TN 713
1
Introduction
Three-phase three-wire shunt active power filters have been widely studied, with many research results already implemented in practical systems[1]. The three-phase four-wire system is now being widely used in different areas including industry, office and civil buildings and power supplies for cities and factories. This configuration results in problems with harmonics in addition to the potential unbalance of the three phases. Active power filters may be used to effectively compensate the harmonic and reactive power on a three-phase four-wire grid. In the three-phase four-wire system, two devices, namely the four-leg converter and the three-leg converter, have been proposed as active power filters[2–3]. In the former the fourth leg is used to compensate the neutral wire current directly. In the latter, the neutral wire of the three phase power line is connected to the middle point of the DC side, which provides a channel for the neutral wire current. The detection and drive circuits of the switches in the four-leg device are more complicated, whereas an extra capacitor is needed in the three-leg one. Also note that control of the capacitor voltage on the DC side is simpler in the
four-leg configuration. PWM control is the key technology of an active power filter. There are three different schemes of PWM technology, namely triangular wave modulation, hysteresis-band control and space-vector pulse width modulation. SVPWM has the following advantages over other control schemes: 1) The use factor of the DC side voltage is high. 2) Switching losses are low. 3) In applications such as motor drives it can be conveniently used as flux tracking control or current control. 4) It is easy to digitally implement the modulation scheme. Most literature describing SVPWM in active filters has discussed applications in 2-dimensional space. However, when applied to the three phase four wire system, a 2-dimensional SVPWM cannot solve the neutral wire current problem. Thus there is an emergent need to study the 3-dimensional SVPWM using αβγ coordinates[5–6]. This paper presents a scheme to control four-leg active power filters using a 3-dimensional pulse width modulation technique. The distribution of voltage-space vectors in αβγ coordinates, the judg-
Received 10 March 2007; accepted 20 June 2007 Corresponding author. Tel: +86-516-83885667; E-mail address: [email protected]
ZHOU Juan et al
Simulation Research on a SVPWM Control Algorithm for a Four-Leg Active Power Filter
ment of the sectors and the calculation of duration time are analyzed and then tested using simulation results.
2 2.1
where Vg is the DC voltage. This four-leg APF has 16 switch states including 2 zero vectors. They are transformed into αβγ coordinates using (2).
SVPWM Control of a Four-Leg APF
T
T
Topology of three-phase four-wire shunt APF
In this paper, a four-leg converter is used as the APF circuit. The reasons for this are: 1) The use factor on the DC side in the four-leg circuit is higher than for the three-leg converter. 2) The control method for a four-leg converter is simpler and may use existing PWM technology that is based on αβ transformation. The circuit diagram of the three-phase four-wire active power filter with four-leg converter is presented in Fig. 1. The fourth leg is used to compensate the neutral wire current while legs 1, 2 and 3 generate the compensation currents for phases A, B and C, respectively.
591
⎡⎣Vα Vβ Vγ ⎤⎦ = C ⎡⎣Vaf Vbf Vcf ⎤⎦
(2)
where ⎡ 1 2⎢ C= ⎢ 0 3⎢ ⎣1/ 2
−1/ 2
−1/ 2 ⎤ ⎥ 3 / 2 − 3 / 2⎥ . 1/ 2 1/ 2 ⎥⎦
The location of these 16 switch vectors in terms of the αβγ coordinates is shown in Fig. 3. Vγ = V g
Vγ =
2 Vg 3
Vγ =
1 Vg 3
γ
Vγ = 0 Vγ = −
1 Vg 3
Vγ = −
2 Vg 3
V γ = −V g
Fig. 3 Fig. 1
Configuration of three-phase four-wire APF with four-leg converter
2.2 Space vectors of the four-leg APF The equivalent circuit of the four-leg APF, shown in Fig. 2, consists of four legs (a, b, c and f).
Four-leg converter switching vectors in αβγ coordinate space
The diagram of space vectors can be divided into six prisms with every prism further divided into four tetrahedrons. So the 16 switch vectors comprise 24 tetrahedrons. Then the reference voltage vector Vref must be located in the 24 tetrahedrons.
2.3 Determination of location of Vref
Fig. 2
2.3.1 Determination of prism The reference voltage space vector Vref is projected onto the αβ frame, represented in Fig. 4. The projections of Vref in the αβ frame are marked as Vα and Vβ respectively. We can determine which prism the reference voltage vector is located in based on the relationship of Vα to Vβ . The flow chart for doing this is shown in Fig. 5.
Equivalent circuit of four-leg active filter
The switch variable is defined as s. If s jp =1 and s fn =1, s jf =1. If s jn =1 and s fn =1 or s jp =1 and s fp =1, s jf =0. If s jn =1 and s fp =1, s jf =ˉ1, where j = {a, b, c} . Therefore, the AC voltage ( vaf , vbf , vcf ) vector can be obtained by:
⎡⎣ vaf
vbf
T
vcf ⎤⎦ = ⎡⎣ saf
sbf
T
scf ⎤⎦ Vg
(1)
Fig. 4 Projection of Vref on the αβ plane
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Journal of China University of Mining & Technology
Fig. 5
Flowchart used to determine prism information
2.3.2 Determination of tetrahedron Every prism is divided into four tetrahedrons (Fig. 6). Suppose that Vref is located in the tetrahedron named T1, with the neighboring vectors as those corresponding to ppnp, pnnp and pnnn. For the switch state ppnp the polarity of voltages ( Vaf , Vbf and Vcf ) is “0”, “0” and “ˉ”, respectively; for pnnp, it is “0”, “ˉ”and “ˉ”, respectively; whereas for pnnn, it is “+”, “0” and “0”, respectively. Vref is synthesized from the voltage switch vectors corresponding to ppnp, pnnp and pnnn so the polarities of the AC side voltages Vaf , Vbf and Vcf should satisfy the following conditions: Vaf >0, Vbf <0 and Vcf <0. Other situations are summarized in Table 1. Table 1 Prism tetrahedron T1 P1
P2
P3
P4
P5
P6
Vol.17 No.4
Fig. 6
First prism and its 4 tetrahedrons
2.4 Duty cycle calculation of adjacent vectors of Vref Suppose that the reference vector Vref is located in tetrahedron T1 with three adjacent non-zero vectors marked as V1 , V2 and V3 at times t1 , t2 and t3 . The time of the zero vector is t0 , and the DC-side voltage is Vg . The sampling period for SVPWM is Ts . The time of vectors adjacent to Vref are obtained from formula (3), which is shown in Table 1.
Identification of tetrahedrons and duty cycle calculation
V1
V2
V3
AC side voltage
ppnp
pnnp
pnnn
Vaf > 0
Vbf < 0
Vcf < 0
t1
t2
t3
y
w
x
T2
pnnn
ppnn
ppnp
Vaf > 0
Vbf > 0
Vcf < 0
s
ˉw
q
T13
nnnp
pnnp
ppnp
Vaf < 0
Vbf < 0
Vcf < 0
ˉy
s
x
T14
pppn
ppnn
pnnn
Vaf > 0
Vbf > 0
Vcf > 0
s
x
ˉq
T3
npnn
ppnn
ppnp
Vaf > 0
Vbf > 0
Vcf < 0
ˉs
y
q
T4
ppnp
npnp
npnn
Vaf < 0
Vbf > 0
Vcf < 0
ˉw
ˉy
z
T15
nnnp
npnp
ppnp
Vaf < 0
Vbf < 0
Vcf < 0
w
ˉs
z
T16
pppn
ppnn
npnn
Vaf > 0
Vbf > 0
Vcf > 0
ˉs
z
ˉq
T5
nppp
npnp
npnn
Vaf < 0
Vbf > 0
Vcf < 0
ˉw
q
ˉz
T6
npnn
nppn
nppp
Vaf < 0
Vbf > 0
Vcf > 0
x
ˉq
ˉy
T17
nnnp
npnp
nppp
Vaf < 0
Vbf < 0
Vcf < 0
w
x
ˉz
T18
pppn
nppn
npnn
Vaf > 0
Vbf > 0
Vcf > 0
x
ˉz
y
T7
nnpn
nppn
nppp
Vaf < 0
Vbf > 0
Vcf > 0
ˉx
ˉw
ˉy
T8
nppp
nnpp
nnpn
Vaf < 0
Vbf < 0
Vcf > 0
ˉq
w
ˉs
T19
nnnp
nnpp
nppp
Vaf < 0
Vbf < 0
Vcf < 0
q
ˉx
ˉs
T20
pppn
nppn
nnpn
Vaf > 0
Vbf > 0
Vcf > 0
ˉx
ˉs
y
T9
pnpp
nnpp
nnpn
Vaf < 0
Vbf < 0
Vcf > 0
ˉq
ˉy
s
T10
nnpn
pnpn
pnpp
Vaf < 0
Vbf < 0
Vcf > 0
ˉz
y
w
T21
nnnp
nnpp
pnpp
Vaf < 0
Vbf < 0
Vcf < 0
q
ˉz
s
T22
pppn
pnpn
nnpn
Vaf > 0
Vbf > 0
Vcf > 0
ˉz
s
ˉw
T11
pnpp
nnpp
nnpn
Vaf > 0
Vbf < 0
Vcf > 0
z
ˉq
w
T12
nnpn
pnpn
pnpp
Vaf > 0
Vbf < 0
Vcf < 0
y
q
ˉx
T23
nnnp
nnpp
pnpp
Vaf < 0
Vbf < 0
Vcf < 0
ˉy
z
ˉx
T24
pppn
pnpn
nnpn
Vaf > 0
Vbf > 0
Vcf > 0
z
ˉx
ˉw
ZHOU Juan et al
Simulation Research on a SVPWM Control Algorithm for a Four-Leg Active Power Filter
Vref Ts = V1t1 + V2 t2 + V3t3 + V0 t0
(3)
593
Vα , Vβ and Vγ are obtained from (2).
where
3Vβ
x=
y=
z= s=
q= w=
Vg
3 Ts
Vα + Vγ Vg
(4)
Ts
3Vα + 3Vβ 2Vg 3Vα − 3Vβ 2Vg
Simulation Model of a Four-Leg APF
(5)
Ts
(6)
Ts
Vα + 3Vβ − 2Vγ 2Vg Vα − 3Vβ − 2Vγ 2Vg
(7)
Ts
(8)
Ts
(9)
Subsystem1 Subsystem4 Conn1 Conn1 Conn2 Conn2
The simulation model of a four-leg APF was built using MATLAB from the structure shown in Fig. 7. The block surrounded by a dashed line is the simulation model of the APF. The subsystem block is a model for compensatory current detection using a scheme for three-phase four-wire systems based on the dq transformation. Subsystem 2 is the control model for the four-leg APF, which uses close-loop current PI adjustment and voltage feed-forward control strategies. Subsystem 3 is the modulation circuits of the four-leg converter, which is based on the theory introduced above. The main parts of the simulation model for a four-leg converter are described in Figs. 8–10 respectively.
Subsystem5 Conn1 Conn2
Discrete, Ts = 1×10ˉ6 s
+ -i
ia* Out1 ib* ic* ea Out2 eb ec Out3 Subsystem
-1
ia*
-1
ib* va* ic*
-1
ea
+ -i
+ -i + -i
+ -i + -i
+ -i
+ -i
R
eb +v +v +v -
a
b
Fig. 7
Fig. 8
c
vb*
ec ia ib
vc*
ic Subsystem2
0
va* ia vb* vc* va ib vb vc ic v0 Subsystem3
Simulation model of three-phase four-wire active filter
Model of determining of voltage vector space position
Fig. 9
Calculating model of basic voltage vector’s acting time
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Journal of China University of Mining & Technology
Fig. 10 Simulation model of producing trigger pulse
4
Simulation and Analysis of Results
The three phase currents and the neutral wire current waveforms before compensation under an un-
balanced, nonlinear load are shown in Fig. 11. We can see that the three phase currents are seriously unbalanced and the waveforms are distorted. Using spectrum analysis we find a THD of the A phase current of 10.98%; also note that the neutral wire current is very big. The source current and neutral wire current waveforms after compensation by the four-leg APF are shown in Fig. 12. The active power filter uses three dimension SVPWM technology and is controlled by closed-loop PI current adjustment and feed-forward voltage control strategies. The results show that the three phase current waveforms are generally symmetric and the THD is very small. The THD of the phase currents A, B and C are, respectively, 0.13%, 0.27% and 0.24%, which satisfies the requirements of GB/T14549-93, with a neutral wire current after compensation equal to approximately zero.
(a) Three-phase current waveforms
Fig. 11
(b) Neutral wire current waveform
Current waveforms before compensating in unbalanced nonlinear load circuit
(a) Three-phase current waveforms after compensating
Fig. 12
5
Vol.17 No.4
(b) Neutral wire current waveform after compensating
Current waveforms after compensating in unbalanced nonlinear load circuit
Conclusions
This paper has proposed a scheme using three dimensional SVPWM technologies to control a threephase four-wire, four-leg shunt APF. By adopting this scheme the harmonics in a three-phase four-wire sys-
tem can be compensated by closed-loop PI current adjustment and feed-forward voltage control strategies. Moreover, both theoretical analysis and simulation results show that the proposed scheme is effective. The proposed approach can be applied to the control of other types of active power filters.
References [1] [2] [3] [4] [5] [6]
Zhuo F, Yang J, Wang Z A. Active power filter for three-phase four wire system. Journal of Xi'an Jiaotong University, 2000, 34(3): 87–90. (In Chinese) Maur´ıcio A, J¨urgen H¨, Klemens H. Three-phase four-wire shunt active filter control strategies. IEEE Transactions on Power Electronics, 1997, 12(2): 311–318. Zhuo F, Yang J, Hu J F. Main circuit structure and control of the active power filter for three-phase four-wire system. Advanced Technology of Electrical Engineering and Energy, 2000, (2): 1–6. (In Chinese) Li J L, Zhang Z C. Comparison and analysis on control strategy of active power filter. Electric Drive for Locomotives, 2003, (4): 1–4. (In Chinese) Zhang R, Prasad V H, Dushan B. Three-dimensional space vector modulation for four-leg voltage-source converters. IEEE Transactions on Power Electronics, 2002, 17(3): 314–324. MªÁngeles M P, Franquelo L G, Portillo R, et al. A 3-D space vector modulation generalized algorithm for multilevel converters. IEEE Power Electronics Letters, 2003, 4(1): 110–114.
Journal of China University of Mining & Technology
J China Univ Mining & Technol
Vol.17
No.4
2007, 17(4): 0590 – 0594
Simulation Research on a SVPWM Control Algorithm for a Four-Leg Active Power Filter ZHOU Juan, WU Xiao-jie, GENG Yi-wen, DAI Peng School of Information and Electrical Engineering, China University of Mining & Technology, Xuzhou, Jiangsu 221008, China Abstract: In this paper the topology of a four-leg shunt active-power filter (APF) is given. The APF compensates harmonic and reactive power in a three-phase four-wire system. The scheme adopted for control of the four-leg active power filter, a 3-Dimensional Pulse Width Modulation (PWM) technique, is presented. The theoretical deduction of a space vector PWM (SVPWM) algorithm is given in this paper. The paper also analyzes the distribution of the voltage-space vector of the four-leg converter in αβγ coordinates and describes methods to determine the location of the voltage-space vector and to calculate duration time. Finally, the algorithm is implemented in simulation; the results show that the total harmonic distortion (THD) of the three phase-current waveforms is reduced. The neutral wire current, after compensation, is about 0 A showing that the topology of the four-leg shunt APF is feasible and the proposed scheme is effective. Key words: three-phase four-wire system; shunt active power filter; 3-Dimensional space vector PWM CLC number: TN 713
1
Introduction
Three-phase three-wire shunt active power filters have been widely studied, with many research results already implemented in practical systems[1]. The three-phase four-wire system is now being widely used in different areas including industry, office and civil buildings and power supplies for cities and factories. This configuration results in problems with harmonics in addition to the potential unbalance of the three phases. Active power filters may be used to effectively compensate the harmonic and reactive power on a three-phase four-wire grid. In the three-phase four-wire system, two devices, namely the four-leg converter and the three-leg converter, have been proposed as active power filters[2–3]. In the former the fourth leg is used to compensate the neutral wire current directly. In the latter, the neutral wire of the three phase power line is connected to the middle point of the DC side, which provides a channel for the neutral wire current. The detection and drive circuits of the switches in the four-leg device are more complicated, whereas an extra capacitor is needed in the three-leg one. Also note that control of the capacitor voltage on the DC side is simpler in the
four-leg configuration. PWM control is the key technology of an active power filter. There are three different schemes of PWM technology, namely triangular wave modulation, hysteresis-band control and space-vector pulse width modulation. SVPWM has the following advantages over other control schemes: 1) The use factor of the DC side voltage is high. 2) Switching losses are low. 3) In applications such as motor drives it can be conveniently used as flux tracking control or current control. 4) It is easy to digitally implement the modulation scheme. Most literature describing SVPWM in active filters has discussed applications in 2-dimensional space. However, when applied to the three phase four wire system, a 2-dimensional SVPWM cannot solve the neutral wire current problem. Thus there is an emergent need to study the 3-dimensional SVPWM using αβγ coordinates[5–6]. This paper presents a scheme to control four-leg active power filters using a 3-dimensional pulse width modulation technique. The distribution of voltage-space vectors in αβγ coordinates, the judg-
Received 10 March 2007; accepted 20 June 2007 Corresponding author. Tel: +86-516-83885667; E-mail address: [email protected]
ZHOU Juan et al
Simulation Research on a SVPWM Control Algorithm for a Four-Leg Active Power Filter
ment of the sectors and the calculation of duration time are analyzed and then tested using simulation results.
2 2.1
where Vg is the DC voltage. This four-leg APF has 16 switch states including 2 zero vectors. They are transformed into αβγ coordinates using (2).
SVPWM Control of a Four-Leg APF
T
T
Topology of three-phase four-wire shunt APF
In this paper, a four-leg converter is used as the APF circuit. The reasons for this are: 1) The use factor on the DC side in the four-leg circuit is higher than for the three-leg converter. 2) The control method for a four-leg converter is simpler and may use existing PWM technology that is based on αβ transformation. The circuit diagram of the three-phase four-wire active power filter with four-leg converter is presented in Fig. 1. The fourth leg is used to compensate the neutral wire current while legs 1, 2 and 3 generate the compensation currents for phases A, B and C, respectively.
591
⎡⎣Vα Vβ Vγ ⎤⎦ = C ⎡⎣Vaf Vbf Vcf ⎤⎦
(2)
where ⎡ 1 2⎢ C= ⎢ 0 3⎢ ⎣1/ 2
−1/ 2
−1/ 2 ⎤ ⎥ 3 / 2 − 3 / 2⎥ . 1/ 2 1/ 2 ⎥⎦
The location of these 16 switch vectors in terms of the αβγ coordinates is shown in Fig. 3. Vγ = V g
Vγ =
2 Vg 3
Vγ =
1 Vg 3
γ
Vγ = 0 Vγ = −
1 Vg 3
Vγ = −
2 Vg 3
V γ = −V g
Fig. 3 Fig. 1
Configuration of three-phase four-wire APF with four-leg converter
2.2 Space vectors of the four-leg APF The equivalent circuit of the four-leg APF, shown in Fig. 2, consists of four legs (a, b, c and f).
Four-leg converter switching vectors in αβγ coordinate space
The diagram of space vectors can be divided into six prisms with every prism further divided into four tetrahedrons. So the 16 switch vectors comprise 24 tetrahedrons. Then the reference voltage vector Vref must be located in the 24 tetrahedrons.
2.3 Determination of location of Vref
Fig. 2
2.3.1 Determination of prism The reference voltage space vector Vref is projected onto the αβ frame, represented in Fig. 4. The projections of Vref in the αβ frame are marked as Vα and Vβ respectively. We can determine which prism the reference voltage vector is located in based on the relationship of Vα to Vβ . The flow chart for doing this is shown in Fig. 5.
Equivalent circuit of four-leg active filter
The switch variable is defined as s. If s jp =1 and s fn =1, s jf =1. If s jn =1 and s fn =1 or s jp =1 and s fp =1, s jf =0. If s jn =1 and s fp =1, s jf =ˉ1, where j = {a, b, c} . Therefore, the AC voltage ( vaf , vbf , vcf ) vector can be obtained by:
⎡⎣ vaf
vbf
T
vcf ⎤⎦ = ⎡⎣ saf
sbf
T
scf ⎤⎦ Vg
(1)
Fig. 4 Projection of Vref on the αβ plane
592
Journal of China University of Mining & Technology
Fig. 5
Flowchart used to determine prism information
2.3.2 Determination of tetrahedron Every prism is divided into four tetrahedrons (Fig. 6). Suppose that Vref is located in the tetrahedron named T1, with the neighboring vectors as those corresponding to ppnp, pnnp and pnnn. For the switch state ppnp the polarity of voltages ( Vaf , Vbf and Vcf ) is “0”, “0” and “ˉ”, respectively; for pnnp, it is “0”, “ˉ”and “ˉ”, respectively; whereas for pnnn, it is “+”, “0” and “0”, respectively. Vref is synthesized from the voltage switch vectors corresponding to ppnp, pnnp and pnnn so the polarities of the AC side voltages Vaf , Vbf and Vcf should satisfy the following conditions: Vaf >0, Vbf <0 and Vcf <0. Other situations are summarized in Table 1. Table 1 Prism tetrahedron T1 P1
P2
P3
P4
P5
P6
Vol.17 No.4
Fig. 6
First prism and its 4 tetrahedrons
2.4 Duty cycle calculation of adjacent vectors of Vref Suppose that the reference vector Vref is located in tetrahedron T1 with three adjacent non-zero vectors marked as V1 , V2 and V3 at times t1 , t2 and t3 . The time of the zero vector is t0 , and the DC-side voltage is Vg . The sampling period for SVPWM is Ts . The time of vectors adjacent to Vref are obtained from formula (3), which is shown in Table 1.
Identification of tetrahedrons and duty cycle calculation
V1
V2
V3
AC side voltage
ppnp
pnnp
pnnn
Vaf > 0
Vbf < 0
Vcf < 0
t1
t2
t3
y
w
x
T2
pnnn
ppnn
ppnp
Vaf > 0
Vbf > 0
Vcf < 0
s
ˉw
q
T13
nnnp
pnnp
ppnp
Vaf < 0
Vbf < 0
Vcf < 0
ˉy
s
x
T14
pppn
ppnn
pnnn
Vaf > 0
Vbf > 0
Vcf > 0
s
x
ˉq
T3
npnn
ppnn
ppnp
Vaf > 0
Vbf > 0
Vcf < 0
ˉs
y
q
T4
ppnp
npnp
npnn
Vaf < 0
Vbf > 0
Vcf < 0
ˉw
ˉy
z
T15
nnnp
npnp
ppnp
Vaf < 0
Vbf < 0
Vcf < 0
w
ˉs
z
T16
pppn
ppnn
npnn
Vaf > 0
Vbf > 0
Vcf > 0
ˉs
z
ˉq
T5
nppp
npnp
npnn
Vaf < 0
Vbf > 0
Vcf < 0
ˉw
q
ˉz
T6
npnn
nppn
nppp
Vaf < 0
Vbf > 0
Vcf > 0
x
ˉq
ˉy
T17
nnnp
npnp
nppp
Vaf < 0
Vbf < 0
Vcf < 0
w
x
ˉz
T18
pppn
nppn
npnn
Vaf > 0
Vbf > 0
Vcf > 0
x
ˉz
y
T7
nnpn
nppn
nppp
Vaf < 0
Vbf > 0
Vcf > 0
ˉx
ˉw
ˉy
T8
nppp
nnpp
nnpn
Vaf < 0
Vbf < 0
Vcf > 0
ˉq
w
ˉs
T19
nnnp
nnpp
nppp
Vaf < 0
Vbf < 0
Vcf < 0
q
ˉx
ˉs
T20
pppn
nppn
nnpn
Vaf > 0
Vbf > 0
Vcf > 0
ˉx
ˉs
y
T9
pnpp
nnpp
nnpn
Vaf < 0
Vbf < 0
Vcf > 0
ˉq
ˉy
s
T10
nnpn
pnpn
pnpp
Vaf < 0
Vbf < 0
Vcf > 0
ˉz
y
w
T21
nnnp
nnpp
pnpp
Vaf < 0
Vbf < 0
Vcf < 0
q
ˉz
s
T22
pppn
pnpn
nnpn
Vaf > 0
Vbf > 0
Vcf > 0
ˉz
s
ˉw
T11
pnpp
nnpp
nnpn
Vaf > 0
Vbf < 0
Vcf > 0
z
ˉq
w
T12
nnpn
pnpn
pnpp
Vaf > 0
Vbf < 0
Vcf < 0
y
q
ˉx
T23
nnnp
nnpp
pnpp
Vaf < 0
Vbf < 0
Vcf < 0
ˉy
z
ˉx
T24
pppn
pnpn
nnpn
Vaf > 0
Vbf > 0
Vcf > 0
z
ˉx
ˉw
ZHOU Juan et al
Simulation Research on a SVPWM Control Algorithm for a Four-Leg Active Power Filter
Vref Ts = V1t1 + V2 t2 + V3t3 + V0 t0
(3)
593
Vα , Vβ and Vγ are obtained from (2).
where
3Vβ
x=
y=
z= s=
q= w=
Vg
3 Ts
Vα + Vγ Vg
(4)
Ts
3Vα + 3Vβ 2Vg 3Vα − 3Vβ 2Vg
Simulation Model of a Four-Leg APF
(5)
Ts
(6)
Ts
Vα + 3Vβ − 2Vγ 2Vg Vα − 3Vβ − 2Vγ 2Vg
(7)
Ts
(8)
Ts
(9)
Subsystem1 Subsystem4 Conn1 Conn1 Conn2 Conn2
The simulation model of a four-leg APF was built using MATLAB from the structure shown in Fig. 7. The block surrounded by a dashed line is the simulation model of the APF. The subsystem block is a model for compensatory current detection using a scheme for three-phase four-wire systems based on the dq transformation. Subsystem 2 is the control model for the four-leg APF, which uses close-loop current PI adjustment and voltage feed-forward control strategies. Subsystem 3 is the modulation circuits of the four-leg converter, which is based on the theory introduced above. The main parts of the simulation model for a four-leg converter are described in Figs. 8–10 respectively.
Subsystem5 Conn1 Conn2
Discrete, Ts = 1×10ˉ6 s
+ -i
ia* Out1 ib* ic* ea Out2 eb ec Out3 Subsystem
-1
ia*
-1
ib* va* ic*
-1
ea
+ -i
+ -i + -i
+ -i + -i
+ -i
+ -i
R
eb +v +v +v -
a
b
Fig. 7
Fig. 8
c
vb*
ec ia ib
vc*
ic Subsystem2
0
va* ia vb* vc* va ib vb vc ic v0 Subsystem3
Simulation model of three-phase four-wire active filter
Model of determining of voltage vector space position
Fig. 9
Calculating model of basic voltage vector’s acting time
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Journal of China University of Mining & Technology
Fig. 10 Simulation model of producing trigger pulse
4
Simulation and Analysis of Results
The three phase currents and the neutral wire current waveforms before compensation under an un-
balanced, nonlinear load are shown in Fig. 11. We can see that the three phase currents are seriously unbalanced and the waveforms are distorted. Using spectrum analysis we find a THD of the A phase current of 10.98%; also note that the neutral wire current is very big. The source current and neutral wire current waveforms after compensation by the four-leg APF are shown in Fig. 12. The active power filter uses three dimension SVPWM technology and is controlled by closed-loop PI current adjustment and feed-forward voltage control strategies. The results show that the three phase current waveforms are generally symmetric and the THD is very small. The THD of the phase currents A, B and C are, respectively, 0.13%, 0.27% and 0.24%, which satisfies the requirements of GB/T14549-93, with a neutral wire current after compensation equal to approximately zero.
(a) Three-phase current waveforms
Fig. 11
(b) Neutral wire current waveform
Current waveforms before compensating in unbalanced nonlinear load circuit
(a) Three-phase current waveforms after compensating
Fig. 12
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Vol.17 No.4
(b) Neutral wire current waveform after compensating
Current waveforms after compensating in unbalanced nonlinear load circuit
Conclusions
This paper has proposed a scheme using three dimensional SVPWM technologies to control a threephase four-wire, four-leg shunt APF. By adopting this scheme the harmonics in a three-phase four-wire sys-
tem can be compensated by closed-loop PI current adjustment and feed-forward voltage control strategies. Moreover, both theoretical analysis and simulation results show that the proposed scheme is effective. The proposed approach can be applied to the control of other types of active power filters.
References [1] [2] [3] [4] [5] [6]
Zhuo F, Yang J, Wang Z A. Active power filter for three-phase four wire system. Journal of Xi'an Jiaotong University, 2000, 34(3): 87–90. (In Chinese) Maur´ıcio A, J¨urgen H¨, Klemens H. Three-phase four-wire shunt active filter control strategies. IEEE Transactions on Power Electronics, 1997, 12(2): 311–318. Zhuo F, Yang J, Hu J F. Main circuit structure and control of the active power filter for three-phase four-wire system. Advanced Technology of Electrical Engineering and Energy, 2000, (2): 1–6. (In Chinese) Li J L, Zhang Z C. Comparison and analysis on control strategy of active power filter. Electric Drive for Locomotives, 2003, (4): 1–4. (In Chinese) Zhang R, Prasad V H, Dushan B. Three-dimensional space vector modulation for four-leg voltage-source converters. IEEE Transactions on Power Electronics, 2002, 17(3): 314–324. MªÁngeles M P, Franquelo L G, Portillo R, et al. A 3-D space vector modulation generalized algorithm for multilevel converters. IEEE Power Electronics Letters, 2003, 4(1): 110–114.