 Open Access
 Total Downloads : 83
 Authors : Mr. Kanan Kumar Das
 Paper ID : IJERTV6IS040729
 Volume & Issue : Volume 06, Issue 04 (April 2017)
 DOI : http://dx.doi.org/10.17577/IJERTV6IS040729
 Published (First Online): 01052017
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
SpaceVector based Advanced Pulse Width Modulation Techniques for ZSource Inverter
Mr. Kanan Kumar Das
Lecturer,
Department of Electrical Engineering, Templecity Institute of Technology and Engineering (TITE),
Bhubaneswar, India
Abstract The Performances of an inverter depends on what type of modulation strategies is used to switch. There exists different types of classical and advanced Pulse Width Modulation (PWM) techniques to switch the traditional Voltage Source Inverter (VSI).The advanced PWM techniques are superior to classical PWM techniques in respect of load current ripple, Total Harmonic Distortions, switching losses. The same concept of advanced PWM techniques for VSI is applicable for ZSource Inverter. This paper proposes certain vector sequences based on advanced PWM techniques for ZSI. The proposed vector sequences are analysed in respect of load/line current ripple based on stator flux ripple concept. The superiority of the advanced PWM techniques over classical is verified by simulation study of a ZSI in PowerSim (PSim9.1.1) for RL and different motor load conditions.
Keywords BusClamping, Current Ripple, Pulse Width Modulation, Maximum Boost Control, ZSource Inverter

INTRODUCTION
Zsource Inverter (ZSI) or Impedance Source Inverter (ISI) is extensively used in different field of application like motor drives [1], electric vehicles [2], photovoltaic system [3], uninterruptible power supply [4] etc. The Xshape lattice type impedance network present in between the DC input source and the inverter power circuit, is responsible for the unique buckboost capability of ZSI. The Zsource concept can be applied to all DCtoAC, ACtoDC, ACtoAC and DCto DC power conversion [5]. There exists little interest in the control methodologies improvement for ZSI. Space vector based PWM techniques for ZSI finds little interest among the researchers. This paper presents an extensive study on space vector based PWM techniques for ZSI.
In literature, ZSI has been analyzed for different control strategies like Simple Boost Control (SBC) [5], Maximum Boost Control (MBC) [6] and Constant Boost Control (CBC) [7]. The MBC gives the highest boosting factor and lowest voltage stress across the switching devices. The MBC can be implemented in carrier based PWM approach or space vector based PWM approach [610]. Extensive study has already been done for carrier based PWM approach for ZSI [610]. The space vector based PWM approach with MBC came in picture in the year of 2012 [9]. Further there has a few study of ZSI for BusClamping PWM (BCPWM) technique [10]. BCPWM is one of the advanced PWM techniques introduced for VSI. Further, the advanced Bus clamping PWM (ABCPWM) techniques have been introduced. These ABCPWM techniques are sometimes known as Double Switching PWM techniques as a phase is double switched
over a subcycle. As compared to classical Space vector PWM techniques, the BCPWM and ABCPWM techniques perform better in respect of load current ripple, load current distortions and lesser switching losses. These PWM techniques have been already proved superior performances compare to classical space vector PWM for VSI based motor drive application theoretically as well as experimentally [1114].
In motor drive application, ZSI becomes a popular choice for its unique features. But the lesser harmonic distortion in the line current is desirable features for the drive application. For this reason, this paper introduces certain vector sequences with proper shootthrough period based on advanced PWM techniques. The expressions for line current ripple for different sequences have been derived based on the stator flux ripple concept. For the verification of the superiority of advanced PWM techniques, a model of ZSI has been simulated using standard PowerSim (PSim9.1.1) for RL and different motor load conditions.
The organization of this paper is as follows in sectionII, the discussion regarding conventional ZSI. In sectionIII, the different space vector based advanced PWM techniques for VSI have been presented. In sectionIV, the shootthrough state of ZSI is discussed. The space vector based different PWM techniques for ZSI have been proposed in sectionV. In sectionVI, the Maximum Boost Control for space vector PWM has been presented. In the following sectionVII, the theoretical analysis of line current ripple based on stator flux ripple for different proposed vector sequences have been elaborated. The simulation results for RL load and different motor load conditions for different vector sequences have been presented in sectionVIII.

CONVENTIONAL ZSOURCE INVERTER Conventional ZSource Inverter (ZSI) was introduced in
the year of 2003 by Prof. P.Z. Peng [5]. The boost capability of ZSI is achieved by the application of shootthrough state which is not possible in VSI or CSI (Current Source Inverter). The power circuit for ZSI is shown in Fig1. During the shoot through state, the input diode, Di is in the reverse biased mode and the inductors L1 and L2 get charged by the capacitors C1 and C2. This state is achieved by the application of simultaneously turn on the two switches in a leg or simultaneously turn on the four switches of two legs or simultaneously turn on all the switches of three legs. During the active state, the diode will be in conduction mode and the inductors will discharges to the load side and charge the capacitor. On the zero state, the load side is totally disconnected from the impedance network, the inductors
discharge to the capacitors. By voltsec balance across the inductors the different relationships between different quantities can be found out. The different quantities for ZSI are tabulated in Table1. Where D0 is the shootthrough duty ratio and M is the space vector based modulation index (varies from 0 to 0.866) and Vin is the input DC voltage to the ZSI. The boosting factor, B is defined as the ratio between the Z network output voltages, Vb to the input DC voltage, Vin. The boosting factor depends on D0 which further depends on the shootthrough duration and subcycle period, Ts. Further, D0 depends on the modulation index, M. For different control strategies, the D0 is different. The overall gain of the inverter can be controlled by controlling both modulation index and
boosting factor.
generate the reference vector in continuous fashion, sampling of the reference vector has to be considered inside the hexagon. The reference vector is sampled once in every sub cycle, Ts. As the positions of the space vectors in hexagon are fixed, the reference vector at any position in a sector can be generated by applying nearby active vectors and zero vectors in such way that the voltsec balance over a sample period or subcycle period can be achieved. The time durations for which the active and zero vectors are applied are known as dwell times. The dwell times remain same for all the sectors. The expressions for dwell times corresponding active vector1, active vector 2 and null vector 0/7 in sector1 are as follows
T M Sin(60 – ) T ; T
M Sin T ;T T T T
(1)
1 Sin60 s 2
Sin60 s 0 s 1 2
Fig. 1: Power circuit for conventional ZSI
Table1: Expression for different quantities for Zsource Inverter
Index Symbol Expression
1
where is the angle between the reference vector and the starting vector of the sector (active vector1 in sector1). The range of is 00 to 600. For generating the reference vector, the nearby active vectors and zero vectors need to be applied in a sequence suc that the switching losses in the inverter is minimum and the better quality of output waveforms can be achieved. For that the selection of vector sequence in a sample cycle or subcycle period, Ts should be satisfy the following conditions

At least one zero vector must be present.
Boosting Factor B
Output voltage of Znetwork V b
1 – 2 D 0
Vin
1 – 2 D0
1 – D

Two nearby active vectors must be present.

The maximum no of switching must be less than or equal to three.
Capacitor (C1) Voltage
Capacitor (C2) Voltage Overall Gain
Peak Phase Voltage
VC1
VC2
G
V
0 Vin
1 – 2D0
1 – D 0 V

– 2 D 0 in

M B
3
2 M V


In state transition, only one phase should be switched

The dwell times should be divided among vectors in such way that the VoltSec balanced can be achieved.
The reference vector in any sector can be generated by applying different vector sequences which are obeyed the
ph 3 b


ADVANCED PWM TECHNIQUES FOR VSI PWM techniques can be broadly classified into two
categories namely carrier based PWM techniques and space vector based PWM techniques. Space vector based PWM
above mentioned conditions (1 to 5). The initial vector in the vector sequences can be any vectors among four vectors in sector1 (0,1,2 and 7). Fig3 and Table2 summarises the different valid and notvalid vector sequences possible in sector1.
techniques give better performances compare to carrier based
PWM techniques like better DC bus utilization, lesser Total Harmonic Distortion (THD) and lesser switching losses. Conventional Space Vector PWM (CSVPWM) is one of the most popular and simplest space vector PWM techniques. In
(010) V3 03277230 V2(110)
01277210
03477430
Sector 2
Sector 1
Sector 3
space vector approach, each state of the inverter generates a
V7
(111)
V ref
vector of fixed magnitude and angle with reference in space vector plane. For 2level VSI, there exists eight vectors which can be generated by eight switching state of VSI. Among eight vectors, six are known as active vectors (corresponding switching state is known as active state) and two zero or null vectors (corresponding switching state is known as zero or
(011) V4
V1(100)
Sector 4
Sector 6
(000)
01677610
05477450
V0
Sector 5
null state). Active vectors have fixed magnitude and fixed angle with reference whereas the zero or null vectors have zero magnitude. These eight vectors form a hexagon in space vector plane. The null vectors are located at the origin whereas each corners of the hexagon is occupied by the active vector. The hexagon for 2level VSI is shown in Fig.2(a). The hexagon has six sectors of 600 spatial duration each. Each sector is formed by two active vectors and two zero vectors. The reference vector corresponding desired output voltages revolves inside the hexagon at a continuous fashion. To

V5
05677650
(a)
V6(101)
721127
743347 034430

V3
032230 (B)
723327 (Y+)
(R+)
V2(110)
(01277210) vector sequence is popularly known as conventional space vector PWM. (01211210) and (7212 2127) vector sequence are known as special PWM type1 or

V4
Sector 2
(Y+)
(R)
Sector 3
V7
(111)
Sector 4
(000)
(B+)
V0
054450
(R)
Sector 5
012210
(B)
Sector 1
(Y)
745547
Sector 6
V1(100)
Advanced BusClamping PWM (ABCPWM) type1. Whereas vector sequence (10122101) and (27211272) are named as special PWM type2 or Advanced BusClamping PWM (ABCPWM) type2. In these vector sequences, over a sub cycle period, one phase is switched double and one phase is switched once and another phase remains clamped. Some times these vector sequences are known as Double Switching PWM sequences.
(R+)

V5
016610 761167
056650 (Y)
wt=0
(b)
V6(101)
0 1 2
0 1 0101
1 0121
1 2
7 0127
2 1012
0 1 0 1010
1 0 1210
7 2 1272

V3
Sector 2
V2(110)
(a) (b)
Sector 1
03233230 (B)
72322327 (Y+)
72122127
0 1 2101
0 7210

V4



03433430
74344347
(R)
Sector 3
V7
(Y+)
(111)
2
1
2
74544547
(000)
01211210
01611610
(B)
V1(100)
1
2
7
2
7 2 1
2127
7
2721
(R+)
7212
(Y)
76166167
(B+)
7 2727
(R+)
Sector 4
05655650 (Y)
Sector 6
05455450
(R)
V0
7 2 7272
(011) V4
(001) V5
47433474
(Y+)
30344303
(R)
Sector 3
(010) V3
Sector 4
50544505
(R)
47455474
(B+)
(001) V5
Sector 5 wt=0
(c)
30322303 (B)
Sector 2
V7
(111)
(000)
50566505 (Y)
V0
Sector 5 wt=0
(d)
76566567 (B+)
V6(101)
Sector 1
27233272 (Y+)
27211272
(R+)
10122101
(B)
V2(110)
10166101
(Y)
67611676
(R+)
67655676 (B+)
Sector 6
V6(101)
V1(100)
(c) (d)
Fig.3: Different possible vector sequences starting with (a) vector0, (b) vector1, (c) vector2 and (d) vector7 for 2level VSI in sector1
To reduce the switching loss and current ripple, there exists another two sequences (012210) and (721127). These sequences are known as BusClamping PWM (BCPWM). At high modulation index and same average switching frequency, line current ripple is lesser with BCPWM compare to CSVPWM. On the other hand, at high modulation index and same carrier frequency, the switching loss is lesser in case of BCPWM compare to CSVPWM. At high modulation index, ABCPWM is better than BCPWM like reduction in line current ripple. The hexagon for 300 BCPWM is shown in Fig. 2(b), for each quarter of fundamental cycle, one phase gets clamped either to positive DC link or negative DC link. The swapping of vector sequence in subsectors under a sector (like 721127 is for first subsector in sector1 and 012210 is for second subsector in sector1) gives 600BCPWM. In this PWM, each phase gets clamped middle 600 duration of each fundamental cycle. Fig. 2(c) and 2(d) show the hexagon for 300ABCPWM Type1 and 300 ABCPWM Type2
respectively. The swapping of vector sequence between subsectors in a sector give the 600ABCPWM. From the
Fig.2: Space Vector Hexagon for 2level VSI for (a) CSVPWM (0127 7210), (b)300 BCPWM (012210), (c) Special PWM1 (01211210) and (d)
Special PWM2 (10122101)
sequences it can observe that the number of switching for 012 is 2 where as for the other vector sequences the number of switching is three over a Ts. So for same average switching frequency over the fundamental cycle or line cycle, the sub cycle period for 012 is 2/3 of that for other sequences. On the other hand, for 012, 0121 and 1012, a hase (here BPhase) gets clamped, these vector sequences are also known as Clamping Sequences or Discontinuous PWM sequences. It has been already proven that ABCPWM is better than BCPWM and CSVPWM at high modulation indices at same average switching frequency [1114].
Table2: Different vector sequences for 2level VSI Table4: Different vector sequences for ZSI
Name Vector Sequence
Valid/ notValid
Reason
Name Vector Sequence
CSVPWM
01277210
Valid
conditions (14) are satisfied
Special PWM 1
01211210
Valid
conditions (14) are satisfied
Special PWM 1
72122127
Valid
conditions (14) are satisfied
Special PWM 2
10122101
Valid
conditions (14) are satisfied
Special PWM 2
27211272
Valid
conditions (14) are satisfied
CSVPWM 0
ST1
1 ST2 2
ST3 7
xxxxxxxxx 01011010 notValid
condition 2 is not satisfied
Special PWM 2
Special PWM 2
Special PWM 1
Special PWM 1 BusClamping PWM

ST1

ST3
0 ST1
7 ST3
0
0
7
1
2
ST1
ST1
ST3 ST2 ST2 1
1
2
2
1
ST2
ST2 2
ST2 1
ST2 1
ST2 2
2
xxxxxxxxx
72722727 notValid
condition 2 is not satisfied
BusClamping PWM
7 ST3 2
ST2 1
BusClamping PWM 012210 Valid conditions (14) are satisfied
BusClamping PWM 721127 Valid conditions (14) are satisfied


SHOOT THROUGH STATE FOR ZSI
In ZSI, the shootthrough state is generated in seven possible switching combinations which is listed in Table3. ST1, ST2 and ST3 are generated by simultaneously turning ON both switches of Rphase leg, Yphase leg and Bphase leg of inverter respectively. These shootthrough states give minimum number of switching transition that means minimum switching loss. Each of these type of shootthrough has four kind of switching combination i.e. other two phases can switched in four combination. In the Table3, X denotes either ON (1) or OFF (0).
Table3: Shootthrough states for 2level ZSI
STState
S 1
S4
S3
S6
S5
S2
SubState
Switching
ST1
1
1
X
X
X
X
ST2
X
X
1
1
X
X
4
Minimum
ST3
X
X
X
X
1
1
ST4
1
1
1
1
X
X
ST5
X
X
1
1
1
1
2
Medium
ST6
1
1
X
X
1
1
ST7
1
1
1
1
1
1
0
Maximum
Similarly, ST4, ST5 and ST6 are generated by simultaneously turning ON of RY phases, YB phases and BR phases respectively. These kind of shootthrough states involve more number of switching transitions i.e. switching loss is more as compare to ST1, ST2 and ST3. But the highest switching loss is involved with the shootthrough state ST7 as it is generated by turning ON simultaneously all the switches of
MBC gives maximum boosting factor and less switching stress as the total zero vector state is replaced by shoot through state. The space vector hexagon for ZSI is similar to VSI as shown in Fig.2(a). The difference between vector sequences for VSI and ZSI is only the present of shoot through state in ZSI vector sequence. By inserting proper shootthrough, based on the advanced PWM for VSI, new PWM sequences for ZSI can be produced. Table4 presents the different possible vector sequences for ZSI. It can be observed that for minimize the switching losses, only ST1, ST2 and ST3 shootthrough states have been used in the proposed vector sequences.The division of shootthrough time period should be equal in a Ts. Unlike MBC, in SBC some portion of the traditional zero vector is replaced by shoot through state. The timing diagrams for different PWM techniques for ZSI under SBC are shown in Fig.4. Fig.4.(a) shows the timing diagram corresponding to CSVPWM. In similar fashion, Fig.4.(b) and 4(c) present the timing diagrams corresponding special PWM2 and special PWM1 respectively. The timing diagram corresponding BCPWM is shown in Fig.4 (d). The dark portion in the timing diagrams indicates the shootthrough state duration. As shown from the timing diagrams that the vector sequence is selected in such way that the total number of switching over Ts is less than or equal to 3. The dwell times for different vectors for ZSI are similar to VSI except the zero vector time duration is divided into two equal parts. One part is replaced by total shoot through state period, TST. The shootthrough time duration is equally divided into different shootthrough states for getting symmetric voltage waveform over Ts. The dwell times for ZSI in sector1 are presented in (2). Tm is total zero vector plus shootthrough vector time duration. T0 is the time period corresponding zero vector in SBC.
three phase legs. It involves highest number of switching transitions. So, for minimum switching loss, ST1, ST2 and ST3 are chosen as the desirable shootthrough states.
T M Sin( 60 ) T ; T
1 Sin60 s 2
;
M Sin T
Sin60 s
(2)

SPACE VECTOR PWM FOR ZSI
In section3, the different Space Vector based PWM techniques for 2level VSI have been discussed. All these PWM techniques can be applied to switch ZSI. In [9], the conventional space vector PWM technique for ZSI has been proposed. Few studies have been done for other PWM techniques. A PWM technique for ZSI is implemented considering the following three control strategies Simple Boost Control (SBC), Maximum Boost Control (MBC) and Constant Boost Control (CBC).
Tm Ts T1 T2 ;
T Tm ; T Tm
ST 2 0 2
0 ST1 1
S1 S4 S3
S6 S5
ST2
2 ST3 7
1 ST1 0
S1
S4 S3
S6 S5
T1 T
ST Tm T
ST T1 T
ST T2
ST1
1 ST2 2
comparative study between them can be theoretically analyzed by the measurement of stator flux ripple over the subcarrier cycle. In this section, the theoretical evaluation of RMS stator flux ripple over a subcarrier cycle has been done for different vector sequences. As the number of switching for sequence 0 ST1ST2 (ST stands for ShootThrough) is less compare to
S2 S2
other sequences as shown in the earlier section, the subcarrier
Tm TST
TST
T2 TST Tm
4 3 3 3 4
TS
2 3 2 3 2 3
TS
cycle for this sequence is considered as 0.67Ts but others reains same as Ts. But under maximum boost control

(b)
technique, the zero vectors are replaced by corresponding
shootthrough vectors. Under MBC, the number of switching
0 ST1 1
S1 S4 S3
S6 S5
S2
Tm TST T1
2 3 2
ST2 2
TST T2
3
TS
ST2 1
TST T1
3 2
0 ST1
S1 S4 S3
S6 S5
TST
0.67Tm
S2
2 3
1
0.67 T1
0.67TS
ST2
TST
3
2

T2
(ON to OFF or OFF to ON) for ST1ST2ST and 1ST1
ST2 are same and equal to 4. Whereas under MBC, the number of switching (ON to OFF or OFF to ON) for ST1 ST2ST1 and ST1ST2 are 5 and 3 respectively. For evaluating the theoretical study under same average switching frequency, the subcarrier cycle for ST1ST2ST, 1ST1 ST2, ST1ST2ST1 and ST1ST2 are 0.8Ts, 0.8Ts, Ts and
0.6Ts respectively. For evaluating the time integral of error voltage vector, few quantities have been defined along the q axis and daxis. The quantities are the product of dwell times and the error voltage vector components along the q and d
(c) (d)
Fig.4: Timing diagrams of different PWM techniques for 2level ZSI under SBC: Timing diagram corresponding to (a) CSVPWM (01277210), (b) Special PWM2 (10122101) ,(c) Special PWM1 (01211210) and (d)300 BCPWM (012210)



MAXIMUM BOOST CONTROL
In Maximum Boost Control (MBC), the total traditional zero vector duration is replaced by corresponding shootthrough state duration. As a result, the boosting factor increases and the voltage stress across switching device decreases. As the space vector hexagon is divided into equal six sector and symmetry to each other, the average shootthrough over fundamental cycle is same as that for one sector. The
expression for average shootthrough duration (), average shootthrough duty ratio (0) and boosting factor, B under
axes. The quantities are n1, n2 and nZ corresponding to qaxis component of error voltage vector e1, e2 and e0/7 respectively. e0/7 does not have any component along the d axis. The quantity along the daxis for both e1 and e2 is denoted by A. The quantities are tabulated in the Table6. The
time integral of error voltage vector is drawn in dq reference frame for a particular spatial angle, . The stator flux ripple
vector starts from origin and increasing in a particular direction same as the direction of corresponding error voltage vector. For example, for e1, the stator flux ripple vector will increase in the direction of e1 vector. The tip of stator voltage is forming a geometric shape in the reference frame and comes back to the origin again at the end of the subcycle period
MBC are shown in (3).
V2 Ve2
_ 3 3 2M
2M
q
2 3 M
T ST Ts
Ts Sin 3
Ts Sin d 1
Ts
Vref
0 3
3
V e0/7
Ve1
_ V0/7
_ T ST
2 3M ; B
(3) V 1
D0
Ts
1
4 3M
d

CURRENT RIPPLE ANALYSIS BASED ON STATOR FLUX RIPPLE
The error voltage vector is defined as the difference between the applied voltage vector and desired reference
Fig.5: Error voltage vectors in sector1
Table5:Different error voltage vectors and corresponding q and d
axis components in sector1
vector. The error voltage vector corresponding applied vector
1, 2 and 0/7 are e1, e2 and e0/7 respectively in sector1
Error Vector
Error Vector
qcomponent
Error Vector
dcomponent
as shown in Fig5. Table5 presents the d and q components of
V e1 V 1 V ref
V e1q V 1 CosV ref
V e1d V 1 Sin
error voltage vectors. The load or line current ripple of the inverter can be measured in term of stator flux ripple. The
Ve2 V2 Vref
Ve2q V2 Cos( ) Vref
3
V e2d V 2 Sin ( )
3
stator flux ripple vector is the time integral of error voltage
0
vector. The measurement of stator flux ripple over a sub carrier cycle is an adequate measurement of line/load current ripple over a subcarrier cycle [1215]. As in the previous section, the different vector sequences based on advanced PWM techniques for VSI, have been proposed for ZSI, the
Vez V0/ 7Vref
V ezq V ref
Table6: Different quantities when reference vector in sector1 ST
1 q
(Error VectorSec) q
(Error VectorSec) ST
d ~
n1 ( V1
Cos V
ref
) T1
A V1
2
1
1
Sin T
ST
n (V Sin ( ) V
) T
A V
Sin ( ) Td
2 2
n z
3
V ref
ref 2

T sh
2 3 2
0
~ 0.33 nZ 0.5n1
q
0.67nZ 0.5n1 n3 ~
0.5 A
The shape of the geometry is different for different vector sequences. The stator flux ripple vector can be decomposed into daxis and qaxis components. Further, the components
0.67 nZ 0.5n1
0.33nZ
Tsh T 1 Tsh
3 2 3
d
0.5n1
Tsh T1
T2 3 2
Tsh T1 Tsh
3 2 3
0.5A Tsh T1
T2 3 2
are drawn with respect to time. The variation of components of stator flux ripple vector with respect to time is different for different vector sequences as shown in Fig6. The components consist of linear piece of lines and the slope of the line changes at the switching transition of vector sequence.
TS
ST
(c)
TS
q
ST ST q
~
~
1
2 ST
1 2 d
ST 0.3nZ 0.6n1
q
d ~
0.6n 0.6n ~
0.6A
Z 1
0.264 n 0.8 n d
Z 1
~ 0.264 nZ
0.8A
3Tsh
0.3nZ
3T1
3Tsh
3T2
3Tsh
3T1
3Tsh
3T2
q 0.536 nZ 0.8n1
10 5 10 5
10 5 10 5
~
0.6TS
0.6TS
4Tsh 0.264 nZ
15
0.8T1
4Tsh
15
0.8T2
4Tsh
15
d 4Tsh 15
0.8T1
4Tsh 15
0.8T2
4Tsh 15
0 .8T S
(a)
1
~
0 .8T S
q
(d)
Fig6: The variation of stator flux ripple in dq reference frame over sub cycle and the variation of q and d axis components of stator flux ripple over one subcycle with time for (a) ST1ST2ST, (b) 1ST1 ST2, (c) ST1ST2ST1 and (d) ST1ST2
For evaluating the RMS stator flux ripple over the subcycle, the RMS value of individual d and q axis need to be found.
2 ST
1
The square of linear piece of line becomes parabola. The RMS value of stator flux ripple is summation of individual d and q axis RMS value. RMS stator flux ripple 0127, 1012,
ST
d 0121
and 012
over a subcycle for ST1ST2ST, 1ST1
0.8A
ST2, ST1ST2ST1 and ST1ST2 respectively are expressed in square form in (4a), (4b), (4c) and 4(d) .
0 .4 n1
0.8n 0.4n
2 1 (
)2
1 z 0 .4 A
~ ~
q d
0127 = 3 0.264 1
3 +
4T1
10
4Tsh
10
0.4 n1 0.4nz
4T1 10
4Tsh 10
0.8n2
4T2
5
4T1 10
4Tsh 10
4T1
10
4Tsh 10
4T2
5
3 [(0.264)2 + (0.264)(0.264 + 0.81 )
+ (0.264 + 0.8 )2] 1 +
0.8TS
0.8TS
1 [(0.264 + 0.8 )2
1
(b)
3
1
+ (0.264 + 0.81)(0.536
+ 0.8 ) + (0.536 + 0.8 )2] +
1 1 3
4(a)
1 [(0.536 + 0.8 )2 (0.536 + 0.8 )(0.264 )
3 1
1
+ (0.264 )2] 1 +
1 (0.264 )2 + 1 (
)2 1 + + 2]
6
x 10
3
F1012
2 1
3
2 1
3 0.8 [
12
11
0127
F
RMS Stator flux ripple
1012 = 3 (0.41) 2 + 10
F012
9
1 [(0.4 )2 + (0.4 )(0.4 + 0.4 ) 8
3 1 1 1
7
F0121
2 6
+ (0.41 + 0.4) ] 2 +
5
1 [(0.4 + 0.4 )2 + (0.4 + 0.4 )(0.8 + 0.4 ) 4
3 1
1
1
1
4(b) 3
(degree )
2
+ (0.81 + 0.4)2] 2 +
0 10 20 30 40 50 60
1 [(0.8 + 0.4 )2 (0.8 + 0.4 )(0.4 )
3 1
1
+ (0.4)2]
+ 2
Fig7: Variation of RMS stator flux ripple with over a sector (Vref=0.8 and Ts=1e4 sec)
6
x 10
1 1
1
15
2 9
3 (0.4)2 + 3 (0.8)2 [ +
+ ]
8
8
RMS Stator flux ripple
F1012 F
2 = 1 (0.33 )2 +
7 0127
0121 3
3
6 F012
1 [(0.33 )2 + (0.33 )(0.33 + 0.5 ) 5
3
1
4 F0121
+ (0.33 + 0.51)2]
1 +
2 3
1 [(0.33 + 0.5 )2 + (0.33 + 0.5 )(0.67 + 0.5 ) 2
3 1
1
1
1
+ (0.67 + 0.5 )2] + 0
Vref
1
3
4(c)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1 [(0.67 + 0.5 )2 + (0.67 + 0.5 )(0.67 + 0.5
Fig8: Variation of RMS stator flux ripple with reference vector V
3 1
1
1
0 4
ref
( =30 and Ts=1e sec)
+ ) + (0.67 + 0.5
+ )2] 2 +
It can be observed from 4(a), 4(b), 4(c) and 4(d) that the
2
1
1 2
RMS stator flux ripple depends on the spatial angle ,
3 [(0.67 + 0.51 + 2)2 (0.67 + 0.51 + 2)(0.51 )
+ (0.5 )2] +
1 3
reference voltage magnitude, Vref and subcycle period Ts. Fig 7 shows the variation of RMS stator flux ripple for different vector sequences for a spatial angle variation from 00 to 600 for Vref=0.8 and Ts=1e4 sec. It can be observed that RMS
1 (0.5 )2 1
1 2 1
2
stator flux ripple is lowest for ST1ST2ST1 (F0121) in
3 1 2 + 3 [ + 2 + 4 ]
4
2 = 1 (0.3 )2 +
middle range of . After that vector sequence ST1ST2 gives the lesser RMS stator flux ripple compare to other
012 3
1 2
2
2 1
sequences. Further the Fig8 shows the variation of RMS
stator flux ripple for a range of Vref from 0 to maximum value
3 [(0.3)
+ (0.3)(0.3 + 0.61 ) + (0.3 + 0.61) ]
+
0.866 for spatial angle, = 300 and subcycle period, Ts = 1e 4 sec. It can be observed that at higher value of Vref (at higher modulation index), vector sequence ST1ST2ST1 has
1 [(0.3 + 0.6 )2 + (0.3 + 0.6 )(0.6
+ 0.6 )
lowest ripple compare to other vector sequences.
3 1
1 1
+ (0.6 + 0.6 )2] +
4(d)


SIMULATION RESULTS
1
2
In this section, the simulation study of proposed PWM
1 [(0.8 + 0.4 )2 (0.8 + 0.4 )(0.4 )
techniques have been done and verified with the theoretical
3 1
1
analysis. For the simulation study, standard power electronics
+ (0.4 )2] +
circuit simulator, PowerSim software (PSim9.1.1) have been
1 (0.6
+ 0.6 )2 + 1 (
2
)2 1
1.5
2
selected. All the PWM techniques have been implemented in this software with appropriate logical approach. On the other
3
1
3 0.6
[ + + ]hand, for power circuit, the inductors and capacitors for Z network have been selected according the specified current and voltage ripples. The simulation has been done considering RL load and different motor load conditions.

Simulation study with 3phase RL load
With the following specifications, the simulation study for R L load has been done

Input DC voltage, Vin=162V

Load resistance R=100 .

Load inductance, L=20mH

Switching frequency, fsw=10kHz

Fundamental frequency, f1=50Hz
The simulation study has been done considering variable modulation index and variable boosting factor condition.
8
7.5
1.5
Load Current (A)
1
0.5
0
0.5
1
1.5
1.5
Load Current (A)
1
0.5
0
THD=6.26%
t(sec)
1.1 1.11 1.12 1.13
(c)
7
Line current THD(%)
6.5
6
5.5
5
4.5
1ST1ST2
ST1ST2
ST1ST2ST
0.5
1
1.5
THD=4.18%
t(sec)
1.1 1.11 1.12 1.13
(d)
4
3.5
3
8
ST1ST2ST1
1 1.5 2 2.5 3 3.5 4 4.5
Boosting Factor , B
(a)
Fig.10: Load current and its THD for RL load for (a) ST1ST2ST, (b) ST1ST2ST1, (c) 1ST1ST2 and (d)ST1ST2 (modulation index=0.8)
THD=12.87%
t(sec)
No Load Current (A)
3
2
1
0
1
2
7.5
7
Line current THD(%)
6.5
6
5.5
5
4.5
ST1ST2ST
1ST1ST2
ST1ST2
3 14.04 14.05 14.06 14.07
(a)
THD=4.014%
t(sec)
No Load Current (A)
3
2
1
0
4
3.5
3
ST1ST2ST1 1
2
0.55 0.6 0.65 0.7 0.75 0.8 0.85
Modulation index, M
(b)
3 12.82 12.83 12.84 12.85
(b)
THD=13.65%
t(sec)
3
No Load Current (A)
Fig9: Variation of Simulated line current THD for different (a) boosting 2
factor, (b) modulation index after applying different PWM vector sequence for
RL load (R=100 , L=20mH) 1
0
1.5
Load Current (A)
1
0.5
0
0.5
1
1.5
1.5
Load Current (A)
1
0.5
0
0.5
1
1.5
THD=5.26%
t(sec)
1.1 1.11 1.12 1.13
(a)
THD=3.60%
t(sec)
1
2
3 13.32 13.33 13.34 13.35
(c)
No Load Current (A)
3
2
1
0
1
2
3 13.16 13.17 13.18 13.19
(d)
THD=6.999%
t(sec)
1.1 1.11 1.12 1.13
Fig.11: No Load Motor current and its THD for (a) ST1ST2ST, (b) ST1 ST2ST1, (c) 1ST1ST2 and (d)ST1ST2 (modulation index=0.8)
The selection of the Xnetwork inductors and capacitors by considering the following specifications

Network is symmetric i.e. L1=L2 and C1=C2

Current ripple of the inductors is taken 5% of the input current.

Voltage ripple across the capacitors is 0.1% of capacitor voltage.
The calculated values of inductors and capacitors for Z network are 18.466mH and 429ÂµF.
Fig9 presents the variations of line current THD for different values of modulation index and boosting factor for different PWM techniques with R=100 , L=20mH. It can be observed that ST1ST2ST1 and ST1ST2 vectors give the minimum THD compare to others two vector sequences. Further, at high modulation index, ST1ST2ST1 is better than ST1ST2 as shown in Fig.9(b). Fig.10 shows the line current waveforms for the specified RL load conditions for different vector sequences. It is clearly observed that the quality of waveform is better for ST1ST2ST1 compare to other vetor sequences. Further, the measured THD of line current is lesser compare to that for other PWM techniques. After this, vector sequence ST1ST2 gives lesser THD. Only vector sequence 1ST1ST2 gives higher THD compared to conventional space vector PWM sequence ST1 ST2ST. This simulation study validates the theoretical study which has been presented in the previous section.



Simulation Study With 3Phase Motor Load
A three phase SquirrelCage Induction motor with following specifications has been selected and simulated with ZSI under noload, half full load and full load conditions under different PWM techniques. The specifications are

Rated power=2HP

Rated RMS line to line voltage=208V

Stator resistance=4.2

Rotor resistance=3

Stator inductance=0.001H

Rotor inductance=0.001H

Magnetizing inductance=0.041H

Moment of inertia=0.7kgm2

No of pole=4

Operating frequency=50Hz

The simulation study has been done under modulation index
0.8. The calculated value of input voltage to the ZSI is 243.46V. It can be observed from Fig11 that the vector sequence ST1ST2ST1 gives the better quality of no load current waveform compare to other vector sequences. Under different load conditions, the THD values of load current for different sequences are tabulated in Table7. It can be concluded that for any load conditions vector sequence ST1 ST2ST1 gives the lowest load current THD compare to others. After vector sequence ST1ST2ST1, ST1ST2 give the lowest load current THD. So, the theoretical analysis what has been done in the earlier sections is validated with the simulation study of motor load under different load conditions.
Table7: Load current THD under different load conditions under different PWM techniques
Load 1ST1ST2
Condition
ST1ST2ST
ST1ST2
ST1ST2ST1
No 13.65%
Load
12.87%
6.999%
4.014%
Half 11.8247%
Load
11.484%
7.086%
3.8063%
Full 6.7897%
Load
6.3142%
5.213%
3.9934%


CONCLUSION
This paper proposes certain vector sequences based on advanced Space Vector based PWM techniques. By Psim simulation study of a ZSI, the effectiveness of the proposed techniques have been verified for RL and different motor load conditions. The theoretical analysis and comparison of different sequences have been done by the concept of stator flux ripple which represents the line current ripple. The simulation study is validated with theoretical study. It has been observed that the propose sequences give lesser line current distortions and switching losses (as clamping is present) compare to classical SVPWM except 1ST1ST2 sequence. Further, same PWM techniques can be applied to other type of ZSI topologies like quasiZSI. Experimental validation of the proposed techniques can be future work. Further, hybrid PWM techniques for more reduction of output distortion for ZSI can be implement and verified in future. This study gives a new direction to the researcher in this area for implementing different realtime Space Vector based PWM techniques for different ZSIs.
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