Research on Restraint Strategy of Narrow Pulses of Three-level Inverter Shuguang Wei,Minyu Li Department of Control Engineering, Academy of Armored Force Engineering Beijing, China
[email protected],
[email protected] proposed algorithm is simple and easy to implement, experimental results verify the feasibility of it.
Abstract—Narrow pulses may appear in specific area of space vector diagram. Because of narrow pulses, switching loss and distortion of output current increase. In this paper, the region of narrow pulses in the space vector diagram is obtained. A restraint algorithm of narrow pulses based on space vector optimization allocation is proposed. In the area of narrow pulses, the sequence and the number of space vector is optimized to avoid narrow pulses according to the basic principle of space vector assignment.The proposed strategy is simple and easy to implement. Experimental results verify the feasibility of the proposed algorithm.
II.
Space vector diagram of three-level inverter is shown in Fig. 1.There are six large sectors(I-VI) in the whole diagram and four small regions(1-4) in each sector.The voltage vector can be divided into one zero vector: U0 (PPP, OOO, NNN) and six positive small vectors: U1P (POO), U2P (PPO), U3P (OPO), U4P (OPP), U5P (OOP), U6P (POP) and six negative small vectors: U1N (ONN) U2N (OON), U3N (NON), U4N (NOO), U5N (NNO), U6N (ONO) and six middle vectors: U8 (PON), U10 (OPN), U12 (NPO), U14 (NOP), U16 (ONP), U18 (PNO) and six large vectors: U7 (PNN), U9 (PPN), U11 (NPN), U13 (NPP), U15 (NNP), U17 (PNP) on the basis of magnitude.
Keywords—T-type inverter; narrow pulses; space vector
I.
INTRODUCTION
There are many inherent advantages such as high efficiency,low output harmonics and low electromagnetic interference in three-level inverter.Therefore, it has been widely used in the field of photovoltaic inverter, motor drive and so on[1-4].There is always time delay in the process of turn-on or turn-off. If the minimum width of pulse is less than the sum of delay time of turn-on and turn-off, switching loss and distortion of output current will increase. Many scholars have made a very fruitful research for reducing narrow pulses. The first way is to eliminate or expand narrow pulses directly, which may lead to loss of normal pulse and increase of harmonic content. The second way is to compensate narrow pulses by injecting zero sequence voltage.The algorithm is simple and easy to implement, but it may produce new narrow pulses in the other phase when dealing with a narrow pulses[58]. The third method is to synthesize the reference vector by the non-nearest vectors. Although narrow pulses can be avoided by this method, it will increase the harmonics of output current[9].
ß U10
C U11
III U12
D U13
U3
IV
U4
U2
H
O
U0
E
I-4
U6
U15
U18
Fig. 1. Three-level space vector diagram.
The reference vector is defined as Ur,and the projection of the reference vector on alpha axis and beta axis is defined as UĮ and Uȕ. The length of line AD is defined as 1. The width of narrow pulses is defined as Tmin. Table I shows the duration of voltage vector in different area of sector I[10]. The sequence diagram of vector assignment is shown in Fig.2. TIME OF VECTOR
T0 =Ts ª¬1 ( 3U D U E ) º¼
978-1-5090-5363-6/17/$31.00 ©2017 IEEE
VI
F
Time of vector
Ts 1 2U E
I
U17 U16 V
c
Area
T1
U8 J
I-2 I-1 Ur I-3 U1 U7 a(¢) UĮ G A
U5
U14
B
U9
Uȕ
TABLE I.
I-2
II
b
In this paper, the region of narrow pulses in space vector diagram is obtained. A restraint algorithm of narrow pulses based on space vector optimization allocation is proposed. In the proposed algorithm, the sequence and the number of space vector is optimized,and then narrow pulses will be avoided.The
I-1
ANALYSIS OF NARROW PULSES DISTRIBUTION
T1 =Ts T2
3U D U E
Ts ª¬1 ( 3U D U E ) º¼
430
T2 =2TsU E
T8 =Ts
3U D U E 1
POO
OOO
OON
0.25T1
0.5T0
0.5T2
POO
PON
OON
I-3
T1
Ts ª¬ 2 ( 3U D U E ) º¼
I-4
T2
Ts ª¬ 2 ( 3U D U E ) º¼
ONN
OOO
OON
T7
Ts
T8
bⳌ
OON
PON
POO
aⳌ
0.5T2
0.5T1
(b) PON
PNN
ONN
0.25T1
0.5T8
0.5T7
0.5T1
PPO
PPN
PON
Ts 2U E 1
T9
0.5T0 Tmin 0.5T1 Tmin 0.5T2 ! Tmin ˄6˅
cⳌ
POO
When the reference vector is located near the point of H, the formula ˄6˅is established.
bⳌ 0.5T8
3U D U E
PNN
PON
POO
There will be narrow pulses in phase a and phase b accoding to Fig. 2(a).
aⳌ bⳌ
As shown in Table II, the region of narrow pulses in other areas could be obtained by the same method.Similiarly we can get the diagram of narrow pulses distribution as shown in Fig. 3.
cⳌ
(c) OON
PON
PPN
PPO
aⳌ
II
b
bⳌ
2TsU E
There will be narrow pulses in phase a and phase b accoding to Fig. 2(a).
(a)
0.25T1
T8
0.5T0 ! Tmin 0.5T1 Tmin 0.5T2 Tmin ˄5˅
0.5T1
ONN
Ts
3U D U E 1
When the reference vector is located near the point of O, the formula ˄5˅is established.
POO
aⳌ
cⳌ
ß B
0.5T9
0.25T2
0.5T8
0.5T2
cⳌ
(d)
4
III
H
J
Fig. 2. The sequence diagram of vector assignment.
UE
0 ;OB: U E
3U D ;HG: U E
3U D 1 ;AB: U E
0.5 ;GJ: U E
IV
1 3U D ;HJ:
The coordinates of every point in sector I are as follows:
V
Fig. 3. The area of narrow pulses distribution.
3 3 ,0 ˅ ˈ A III.
˄ 2 3 3 ,0˅ˈI˄ 3 2 ,0.5˅ˈB˄ 3 3 ,1˅
The line of OH satisfies the following equation: E
3U D 0 d U D d 3 6
A. The reference vector is located in region I-1 When 0.5T7 ! Tmin 0.5T1 Tmin 0.5T8 Tmin is satisfied,there will be narrow pulses in phase a and phase b. To eliminate narrow pulses,the sequence diagram of vector assignment should be adjusted to Fig. 4(a).
˄1˅
Then the formula ˄ 2 ˅ and ˄ 3 ˅ is also established accoding to Table I.
T0
1 2
3U D Ts , T1
0, T2
THE RESTRAINT STRATEGY OF NARROW PULSE
Taking the case of the reference vector located in sector I as an example, the restraint strategy of narrow pulses could be designed as follows:
The case that the reference vector is located near the line of OH is analysed as an example:
U
a(¢) A
VI
2 3U D .
3 6 ,0.5 ˅ ˈ G ˄
3 G
c
O ˄ 0,0 ˅ ˈ H ˄
1
O
In Fig.1 ,the expressions of boundary line between different regions are as follows: OA: U E
I
2
When 0.5T1 Tmin 0.5T2 Tmin 0.5T0 ! Tmin is satisfied,there will be narrow pulses in phase a and phase b. To eliminate narrow pulses,the sequence diagram of vector assignment should be adjusted to Fig. 4(b).
2 3U D Ts ˄2˅
0 T0 Ts 0 T2 Ts T1 0 ˄3˅ When the reference vector is located near the line of OH, the formula ˄4˅is established. 0.5T0 ! Tmin 0.5T1 Tmin 0.5T2 ! Tmin ˄4˅
PPO
POO
OOO
OON
0.25T2
0.5T1
0.5T0
0.5T2
aⳌ bⳌ
There will be narrow pulses in phase a and phase b accoding to Fig. 2(a).
cⳌ
(a)
431
OOO
POO
PPO
TABLE II. Area
Location of the reference vector
Range of vector time
Narrow pules appear or not
Near the line of OG
0.5T0 ! Tmin 0.5T1 ! Tmin 0.5T2 Tmin 0.5T0 ! Tmin 0.5T1 Tmin 0.5T2 Tmin 0.5T0 Tmin 0.5T1 ! Tmin 0.5T2 Tmin 0.5T0 ! Tmin 0.5T1 Tmin 0.5T2 ! Tmin 0.5T0 Tmin 0.5T1 Tmin 0.5T2 ! Tmin 0.5T1 ! Tmin 0.5T2 ! Tmin 0.5T0 Tmin 0.5T2 ! Tmin 0.5T8 ! Tmin 0.5T1 Tmin 0.5T1 Tmin 0.5T2 ! Tmin 0.5T8 Tmin 0.5T1 Tmin T2 Tmin T8 ! Tmin 0.5 T1 ! Tmin 0.5T2 ! Tmin 0.5T8 Tmin 0.5T1 ! Tmin 0.5T2 Tmin 0.5T8 Tmin 0.5T1 ! Tmin 0.5T8 ! Tmin 0.5T2 Tmin 0.5T7 ! Tmin 0.5T8 ! Tmin 0.5T1 Tmin 0.5T7 ! Tmin 0.5T1 Tmin 0.5T8 Tmin 0.5T8 ! Tmin 0.5T1 Tmin 0.5T7 Tmin 0.5T1 ! Tmin 0.5T7 ! Tmin 0.5T8 Tmin 0.5T1 ! Tmin 0.5T7 Tmin 0.5T8 Tmin 0.5T1 ! Tmin 0.5T8 ! Tmin 0.5T7 Tmin 0.5T8 ! Tmin 0.5T9 ! Tmin 0.5T2 Tmin 0.5T8 ! Tmin 0.5T2 Tmin 0.5T9 Tmin 0.5T9 ! Tmin 0.5T2 Tmin 0.5T8 Tmin 0.5T2 ! Tmin 0.5T8 Tmin 0.5T9 Tmin 0.5T2 ! Tmin 0.5T8 Tmin 0.5T9 Tmin 0.5T2 ! Tmin 0.5T8 ! Tmin 0.5T9 Tmin
No
Near the point of O Near the point of G
I-1
Near the line of OH Near the point of H Near the line of HG Near the line of HJ Near the point of H Near the point of J
I-2
Near the line of HG Near the point of G Near the line of GJ Near the line of AJ Near the point of A Near the point of J
I-3
Near the line of GA Near the point of G Near the line of GJ Near the line of BJ Near the point of J Near the point of B
I-4
Near the line of HB Near the point of H Near the line of HJ
PPP
PPO
TABLE OF NARROW PULSES IN SECTOR I
POO
OOO
POO
PPO
PPP
No Yes Yes No Yes Yes Yes No No No Yes Yes Yes No No No Yes Yes Yes No No No
PPO
POO
PON
0.25T2
0.5T1
0.5T8
OON
PON
POO
PPO
aⳌ
aⳌ bⳌ cⳌ
Yes
0.25T0
0.5T2
0.5T1
0.5T0
0.5T1
0.5T2
bⳌ
0.5T2
cⳌ
0.25T0
(b)
(a) PPO
Fig. 4. The restraint strategy of narrow pulses when Ur.is located in I-1
POO
PON
0.5T1
T8
POO
PPO
aⳌ
B. The reference vector is located in region I-2
bⳌ
When 0.5T1 Tmin 0.5T2 ! Tmin is satisfied,there will be narrow pulses in phase b and phase c.To eliminate narrow pulses,the sequence diagram of vector assignment should be adjusted to Fig. 5(a).
0.5T2
0.5T1
0.5T2
cⳌ
(b) Fig. 5. The restraint strategy of narrow pulses when Ur.is located in I-2
When 0.5T1 Tmin T2 Tmin T8 ! Tmin is satisfied, there will be narrow pulses in phase b and phase c.Narrow pulses can not be eliminated completely.The narrow pulses in phase c could be eliminated by the sequence diagram of vector assignment in Fig. 5(b).
C. The reference vector is located in region I-3 When T7 ! Tmin 0.5T1 Tmin is satisfied, there will be narrow pulses in phase a and phase c.Narrow pulses can not be eliminated completely.The narrow pulses in phase a could be eliminated by the sequence diagram of vector assignment in Fig. 6(a).
432
When T8 ! Tmin 0.5T1 Tmin T7 Tmin is satisfied, there will be narrow pulses in phase a and phase c.Narrow pulses can not be eliminated completely.The narrow pulses in phase c could be eliminated by the sequence diagram of vector assignment in Fig. 6(b). POO
PON
PNN
0.5T8
T7
PON
Fig.8 shows the driving pulse of SVPWM algorithm in sector I. As shown in Fig. 8(a), when the reference vector is close to the point of O, there are narrow pulses in the entire sector I.As shown in Fig. 8(b), when the reference vector is close to the line of OH, narrow pulses appear.As shown in Fig. 8(c), when the reference vector is close to the point of H, narrow pulses appear.As shown in Fig. 8(d), when the reference vector is close to the line of HJ, narrow pulses appear.As shown in Fig. 8(e), when the reference vector is close to the point of J, narrow pulses appear.The simulation results verify the theoretical analysis of the narrow pulses distribution.
POO
aⳌ bⳌ 0.5T1
0.5T8
0.5T1
cⳌ
(a) ONN
PNN
PON
PNN
Fig.9 shows the driving pulse of the proposed narrow pulses restraint algorithm in sector I.It is obvious that narrow pulses can be effectively suppressed in every case.
ONN
aⳌ bⳌ 0.5T1
0.5T7
T8
0.5T7
0.5T1
cⳌ
Sa1 (b)
Sb2
Fig. 6. The restraint strategy of narrow pulses when Ur.is located in I-3
Sc2
D. The reference vector is located in region I-4 When T8 ! Tmin 0.5T2 Tmin is satisfied, there will be narrow pulses in phase a and phase c.Narrow pulses can not be eliminated completely.The narrow pulses in phase a could be eliminated by the sequence diagram of vector assignment in Fig. 7(a).
t/s ˄a˅m=0.05 Sa1 Sb2
When T9 ! Tmin 0.5T2 Tmin T8 Tmin is satisfied, there will be narrow pulses in phase a and phase c.Narrow pulses can not be eliminated completely.The narrow pulses in phase c could be eliminated by the sequence diagram of vector assignment in Fig. 7(b). PPO
PPN
PON
PPN
Sc2
t/s ˄b˅m=0.35
PPO
Sa1
aⳌ
Sb2
bⳌ 0.5T2
0.5T9
T8
0.5T9
0.5T2
Sc2
cⳌ
(a) OON
PON
PPN
PON
t/s ˄c˅m=0.577
OON
aⳌ bⳌ
Sa1 0.5T2
0.5T8
T9
0.5T8
0.5T2
cⳌ
Sb2 (b)
Sc2
Fig. 7. The restraint strategy of narrow pulses when Ur.is located in I-4
IV.
t/s ˄d˅m=0.8
EXPERIMENT
In order to verify the correctness of the proposed narrow pulses suppression strategy, a prototype of T-type inverter based on DSP28335 is built. 4MBI300VG-120R-50 of Fuji is used to build the main circuit. The load is three phase symmetrical resistance-inductance load.
433
V.
Sa1
CONCLUSIONS
In this paper, the region of narrow pulses in space vector diagram is obtained. A restraint strategy of narrow pulses based on space vector optimization allocation is proposed.In the area of narrow pulses, the sequence of space vector and the number of segments is optimized for avoiding narrow pulses according to the basic principle of vector distribution.The proposed algorithm is simple and easy to implement,and experimental results verify the feasibility of it.
Sb2 Sc2
t/s ˄e˅m=0.99 Fig. 8. The traditional algorithm
ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China under Grant No. 51507190.
Sa1 Sb2
REFERENCES
Sc2
[1]
Mario Schweizer, Johann W.Kolar, “Design and implementation of a highly efficient three-level t-type converter for low-voltage applications,” IEEE Transactions on Power Electronics, vol. 28, issue 2, pp. 899-900, 2013. [2] Mingchen Gu, Peng Xu,Li Zhang,Kai Sun, “A SiC-based t-type threephase three-level grid tied inverter,” 2015 IEEE 10th Conference on Industrial Electronics and Applications, pp. 1116-1120, 2015. [3] Yang Longfei, “Research of energy converter based on three-level Ttype NPC,” Beijing Jiao Tong University, 2013. [4] Xia Lingfang, “Research on the T-type three-level inverter,” NanjingUniversity of Aeronautics and Astronautics, 2014. [5] Bo Baozhong,Liu Weiguo,Su Yanmin, “Study of compensating technique in PWM control for three-level inverters,” Proceedings of the CSEE, vol. 25, issue 10, pp. 61-63, 2005. [6] Bo Baozhong,Liu Weiguo,Luo bing,Su Yanmin, “Study of narrow pulse width compensation technique for three-level inverter,” Electric power Automation Equipment, vol. 24, issue 8, pp. 27-28, 2004. [7] Li Hao, “Study on key technology of high power three-level converter and drive control system of synchronous motor,” China University of mining&technology, 2010. [8] Wang Chenchen,Guan Bo, “A narrow pulse processing method considering neutral-point potential balance problem of diode-clamped three-level inverters,” Transactions of China Electrotechnical Society, vol. 30, issue 19, pp. 138-141, 2015. [9] Liu H LˈCho G H, “Three-level space vector PWM in low index modulation region avoiding narrow pulse problem,” IEEE transactions on power electronics, vol. 5, issue 5, pp. 482-484, 1994. [10] Du Chao, “Study on key technology of high power three-level converter and drive control system of synchronous motor,” China University of mining&technology, 2009.
t/s ˄a˅m=0.05
Sa1 Sb2 Sc2
t/s ˄b˅m=0.35 Sa1 Sb2 Sc2
t/s ˄c˅m=0.577 Sa1 Sb2 Sc2
t/s ˄d˅m=0.8 Sa1 Sb2 Sc2
t/s ˄e˅m=0.99 Fig. 9. The proposed algorithm
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