jpe 18-1-1 issn(print): 1598-2092 / issn(online): 2093
TRANSCRIPT
Journal of Power Electronics, Vol. 18, No. 1, pp. 1-10, January 2018 1
https://doi.org/10.6113/JPE.2018.18.1.1
ISSN(Print): 1598-2092 / ISSN(Online): 2093-4718
JPE 18-1-1
© 2018 KIPE
Direct Power Control without Current Sensors for
Nine-Switch Inverters
Lei Pan†, Junru Zhang*, Kai Wang*, Beibei Wang*, Yi Pang*, and Lin Zhu*
†,*School of Control and Mechanical Engineering, Tianjin Chengjian University, Tianjin, China
Abstract
Recently, the nine-switch inverter has been proposed as a dual output inverter. To date, studies on the control strategies for
NSIs have been mostly combined with their application. However, in this paper, a mathematical model and control strategy for
nine-switch inverters has been proposed in view of the topology. A switching function model and equivalent circuit model of a
nine-switch inverter have been built in αβ coordinates. Then, a novel current observer with an improved integrator is proposed
based on the switching function model, and a direct power control strategy is proposed. No current sensors are used in the
proposed strategy, and only two voltage sensors are employed. The performance of the proposed control method is verified by
simulation and experimental results.
Key words: Current observer, Direct power control, Nine-switch converter, Switching function
I. INTRODUCTION
Recently, a novel three-phase three-leg inverter, which is
referred to as a nine-switch inverter (NSI), with nine IGBTs
has been proposed in the literature [1]. This inverter, shown
in Fig. 1, is composed of two three-phase inverter units.
These units are named upper and lower units, and they share
the same dc-link voltage.
In the literature, different modulation methods [2]-[12] and
applications [13]-[25] have been widely reported.
There are two main kinds of modulation methods. These
methods are the carrier-based pulse-width modulation (PWM)
method [2]-[8] and the space-vector modulation (SVM)
method [9]-[12]. PWM can be used for the different frequency
(DF) operation mode and the constant frequency (CF)
operation mode [2], and the research content includes the
carrier-based pulse width modulation mechanism [3], the
constraint relationship between the dc link voltage, phase
difference and voltages of two three-phase ac terminals [4],
the carrier-based pulse width modulation with dead-time
elimination [5], and the switching and conduction losses [7].
SVM can also be used for the DF mode and the CF mode [9],
[10]. In some literatures on SVM, the space vector modulation
mechanism [11] and the spatial distribution of the voltage
vector [12] are developed in-depth.
The applications of NSIs have been proposed in many
fields, such as hybrid electric vehicles [13], power conditioners
[14], [15], torque control [16], wind power systems [17], [18],
uninterruptible power supplies (UPS) [19], photovoltaic
systems [20], [21], and electrical machines [22].
At present, studies on the control strategies for NSIs are
mostly combined with applications [15]-[25]. Considering
that the switches in the NSC are shared by two three-phase
ports, a new adapted control method is proposed to flexibly
control and fully use of the current capacity of the switches
for DFIG wind power systems [17]. In the DVCA strategies
for DFIGs [23], the rotor-side gets more voltage to suppress
overcurrent when the symmetrical grid voltage dips with
dynamic voltage assignment. In addition, the grid-side gets
more current capacity for reactive current compensation with
dynamic current assignment. In the integrated motor drive
and battery charger systems for EVs, grid voltage-oriented
control, which is obtained through a phase-locked loop (PLL)
algorithm with resonance, is adopted to obtain a highly
satisfactory performance [24]. The steady-state control strategy
and transient-management scheme for system dynamics and
grid faults in a NSI are developed to ensure proper perfor-
mance in the steady-state, dynamic operation and enhanced
fault ride-through capability of the FSIG-WT [25].
Manuscript received Sep. 28, 2016; accepted Jul. 29, 2017 Recommended for publication by Associate Editor Sangshin Kwak.
†Corresponding Author: [email protected] Tel: +86-22-2308-5137, Tianjin Chengjian University
*School of Control & Mechanical Eng., Tianjin Chengjian Univ., China
2 Journal of Power Electronics, Vol. 18, No. 1, January 2018
Fig. 1. Nine-switch inverter.
However, in this paper, a mathematical model of a NSI is
established in view of the topology. Then, the direct power
control method for a NSI is proposed based on αβ coordinates.
In this control method, only two voltage sensors are used and
there are no current sensors. In order to improve the control
effect, a new type of current observer, where an improved
integrator with saturated feedback (IISF) is proposed.
Simulation and experimental studies have been carried out to
verify the effectiveness of the proposed scheme.
II. SWITCHING FUNCTION MODEL FOR A NSI
The topology of a NSI is shown in Fig. 1. Considering that
there are three switches in each leg of the NSI, the
semiconductors in each leg can have eight different ON-OFF
positions. However to avoid DC bus short circuit, all three
switches cannot be ON at same time. On other hand to avoid
floating of the loads, at least two switches should be ON.
Therefore, only three ON-OFF positions are possible. The
constraint condition between the three switches in each leg of
a NSI is shown in (1). In (1), A, B or C refers to leg A, B or C,
and U, M or L refers to the upper, mid or lower
semiconductor.
2
2
2
AH AM AL
BH BM BL
CH CM CL
S S S
S S S
S S S
+ + =⎧⎪⎪
+ + =⎨⎪
+ + =⎪⎩
(1)
where SJX=‘1’, when the switch SJX is ON; and SJX=‘0’, when
the switch SJX is OFF (J=A, B, C; X=H, M, L).
From Fig. 1, it is possible to obtain the voltage equation of
a NSI with the switching variable shown in (2).
1 1 2
1 1 2
1 1 2
2 1 2
2 1 2
2 1 2
A c AH c AM AL
B c BH c BM BL
C c CH c CM CL
A c AH AM c AL
B c BH BM c BL
C c CH CM c CL
u u S u S S
u u S u S S
u u S u S S
u u S S u S
u u S S u S
u u S S u S
= −⎧⎪
= −⎪⎪
= −⎪⎨
= −⎪⎪
= −⎪⎪
= −⎩
(2)
where uJY is the voltage between JY( J=A, B,C; Y=1, 2) and
point o.
From Fig. 1, it is also possible to obtain the differential
equation of a NSI, as shown in (3).
1
1 1 1 1 1,0
1
1 1 1 1 1,0
1
1 1 1 1 1,0
2
2 2 2 2 2,0
2
2 2 2 2 2,0
2
2 2 2 2 2,0
A
s s A A n
B
s s B B n
C
s s C C n
A
s s A A n
B
s s B B n
C
s s C C n
diL R i u u
dt
diL R i u u
dt
diL R i u u
dt
diL R i u u
dt
diL R i u u
dt
diL R i u u
dt
⎧= − + −⎪
⎪⎪
= − + −⎪⎪⎪
= − + −⎪⎪⎨⎪ = − + −⎪⎪⎪
= − + −⎪⎪⎪
= − + −⎪⎩
(3)
where unY,0 is the voltage between nY (Y=1, 2) and point o.
In three-phase, three-wire systems, it can be known that:
1 1 1
2 2 2
0
0
A B C
A B C
i i i
i i i
+ + =⎧⎨
+ + =⎩ (4)
From (2), (3) and (4), (5), it can be concluded that:
1,0 1 1 1
1 2
2,0 2 2 2
1 2
( ) / 3
( ) ( )
( ) / 3
( ) ( )
n A B C
c AH BH CH c AM AL BM BL CM CL
n A B C
c AH AM BH BM CH CM c AL BL CL
u u u u
u S S S u S S S S S S
u u u u
u S S S S S S u S S S
= + +⎧⎪= + + − + +⎪
⎨= + +⎪
⎪= + + − + +⎩
(5)
From (2), (3) and (5), it is possible to obtain the switching
function model for a NSI as shown in (6).
1
1 1 1 1
2
1
1 1 1 1
2
1
1 1 1 1
1(2 )
3
1 (2 )
3
1(2 )
3
1 (2 )
3
1(2 )
3
A
s s A c AH BH CH
c AM AL BM BL CM CL
B
s s B c BH AH CH
c BM BL AM AL CM CL
C
s s C c CH AH BH
diL R i u S S S
dt
u S S S S S S
diL R i u S S S
dt
u S S S S S S
diL R i u S S S
dt
= − + − −
− − −
= − + − −
− − −
= − + − −
2
2
2 2 2 1
2
2
2 2 2 1
2
1 (2 )
3
1(2 )
3
1 (2 )
3
1(2 )
3
1 (2 )
3
c CM CL AM AL BM BL
A
s s A c AH AM BH BM CH CM
c AL BL CL
B
s s B c BH BM AH AM CH CM
c BL AL CL
u S S S S S S
diL R i u S S S S S S
dt
u S S S
diL R i u S S S S S S
dt
u S S S
L
− − −
= − + − −
− − −
= − + − −
− − −
2
2 2 2 1
1(2 )
3
C
s s C c CH CM AH AM BH BM
diR i u S S S S S S
dt
⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪ = − + − −⎪⎩
(6)
Direct Power Control without Current Sensors for Nine-Switch Inverters 3
1 2
1( )2
C H C M L M Lu S u S S S Sα α α β β− −
1iα
1 2
1( )
2C H C M L M L
u S u S S S Sβ α β β α+ +
1iβ
1 2
1( )
2C H M H M C Lu S S S S u Sα α β β α− −
2iα
1 2
1( )
2C H M H M C Lu S S S S u Sα β β α β− + −
2iβ
Fig. 2. The equivalent circuit model of NSI in αβ coordinates.
HSα
1cu
2cu
1iα
1sR
1/s
L∫
( ) / 2M L M L
S S S Sα α β β−
HSβ
( ) / 2M L M L
S S S Sα β β α−
1iβ
1sR
1/s
L∫
( ) / 2H M H M
S S S Sα α β β−
LSα
2iα
2sR
1/s
L∫
( ) / 2H M H M
S S S Sα β β α−
LSβ
2iβ
2sR
1/s
L∫
Fig. 3. Current observer for a NSI.
Suppose a balanced three-phase voltage for two AC
terminals, then:
1 1 1
2 2 2
0
0
A B C
A B C
u u u
u u u
+ + =⎧⎨
+ + =⎩ (7)
Substituting (7) into (6) yields:
1
2
[ (1 ) (1 ) (1 )]
[( 1) ( 1) ( 1) ] 0
c AH AM BH BM CH CM
c AM AL BM BL CM CL
u S S S S S S
u S S S S S S
+ + + + + −
+ + + + + =
(8)
(8) describes the constrained relationship between uc1 and
uc2. From (9), it can be seen that the relationship between uc1
and uc2 depends on SXH(X=ABC) and SXL(X=ABC). Namely,
uc1= uc2 when SAH + SBH + SCH = SAL + SBL + SCL.
III. DIRECT POWER CONTROL FOR A NSI
A αβ transformation or Clarke transformation can map the
three-phase instantaneous line current, ia, ib, and ic, into an
instantaneous current on the αβ-axes iα and iβ. Therefore, the
switching function model of a NSI in the A, B, and C
coordinates can be transformed in to the αβ coordinates with
a Clarke transformation, and the transformed switching
function model of the NSI is shown in (9).
1
1
111
1
11
222
2
22
2
2
0 0 0
0 0 0
0 0 0
0 0 0
1( )
2
1( )
2
1( )
2
1(
2
s
s
s
s
s
s
s
s
H M L M L
H M L M L
H M H M L
H M
diL
dt
iRdiL
iRdt
iRdiL
idt R
diL
dt
S S S S S
S S S S S
S S S S S
S S S
α
αβ
β
αα
β
β
α α α β β
β α β β α
α α β β α
α β
⎡ ⎤⎢ ⎥⎢ ⎥
− ⎡ ⎤⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥ − ⎢ ⎥⎢ ⎥= +⎢ ⎥⎢ ⎥⎢ ⎥−⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥ − ⎢ ⎥⎣ ⎦⎣ ⎦⎢ ⎥
⎢ ⎥⎢ ⎥⎣ ⎦
−
−
− −
−
1
2
0
0
0
0
1
1)
c
dc
c
H M L
ui
u
S Sβ α β
⎡ ⎤⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥ ⎡ ⎤
+ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎢ ⎥⎢ ⎥
⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥−⎢ ⎥⎣ ⎦⎢ ⎥−
⎣ ⎦
(9)
According to (9), it is possible to obtain an equivalent
circuit model of a NSI in the αβ coordinates as shown in Fig.
2, when the three-phase voltage is balanced.
Where:
1
1
1
1
3 9 3 3 3
2 8 8 8 8
3 9 3 3 3
2 8 8 8 8
3 9 3 3 3 3
4 8 8 8 4 8
3 9
4 8
H H M L H M L H M L H M L
H H M L H M L H M L H M L
H M H M L H M L H M L H M H M L
H M H
A S S S S S S S S S S S S S
B S S S S S S S S S S S S S
D S S S S S S S S S S S S S S S S
E S S S
α α α α α β β β α β β β α
β β β β β α α α β α α α β
α α α α α α β β β α β β β β β α
β α β
=− + + + +
=− + + + +
=− + + + + +
= +
2
2
2
3 3 3 3
8 8 4 8
3 9 3 3 3 3
4 8 8 8 4 8
3 3 3 3 3 9
8 4 8 4 8 8
3 9
2 8
M L H M L H M L H M H M L
M L H M L M H L H M L M L M L H
M L H M L H M L M L H L M H M L
L
S S S S S S S S S S S S S
A S S S S S S S S S S S S S S S S
B S S S S S S S S S S S S S S S S
D S
β β β α α α β α α β α α β
α α α α α α β β β β α β β β β α
α α β α β α α β β α α α β β β β
α
+ + + +
=− + + + + +
= + + + + +
=− +
2
3 3 3
8 8 8
3 9 3 3 3
2 8 8 8 8
H M L L H M H L M M L M
L H M L H M L H L M H M L
S S S S S S S S S S S S
E S S S S S S S S S S S S S
α α α α β β β β α β β α
β β β β β α α α α β α α β
+ + +
=− + + + +
Therefore, the current observer from Fig. 2 can be obtained
as shown in Fig. 3.
In Fig. 3, there is an integrator in each of the current
observers. This integrator introduces an integral initial value
error and a dc offset error, which eventually leads to
integrator saturation. The current estimation error curves are
provided in Fig. 4, and the simulation condition is described
in section IV.
Therefore, an improved integral method is needed to
overcome this problem.
In Fig. 5, an improved current observer for the upper AC
terminal is adopted. In this observer, an IISF is introduced,
4 Journal of Power Electronics, Vol. 18, No. 1, January 2018
(a) iá1
(b) iâ1.
Fig. 4. Current estimation error curves with an integrator.
HSα
1cu
2cu
1iα
1sR
1/s
L
2
M L M LS S S Sα α β β−
1
cs ω+
c
cs
ω
ω+
C
(a)
HSβ
1iβ
2
M L M LS S S Sα β β α
−
1cu
2cu
1sR
1/s
L1
cs ω+
c
cs
ω
ω+
C
(b)
Fig. 5. Improved current observer for the upper AC terminal of
a NSI.
and the effects of IISF are as follows:
When the system has just started, the current is small or
close to zero, and the IISF is equivalent to a low-pass filter.
When the system is in normal operation, the IISF is
equivalent to an integrator. When the current is beyond the
limiting value, the IISF is also equivalent to a low-pass filter.
The IISF can have the advantages of a pure integrator and
a low-pass filter. It can eliminate the amplitude attenuation of
a low pass filter, and inhibit the current of the dc component.
The threshold value C is determined by the rated current of
the AC terminal, and a certain margin is needed.
After improvement, current estimation error curves are shown
in Fig. 6. With a comparison between Fig. 4 and Fig. 6, it can
be seen that the response speed, overshoot and steady- state
error of Fig. 6 are better than those of Fig. 4. That is to say,
the performance of the current observer with an IISF is
significantly better than the current observer with an
integrator.
In addition, the IISF can be also applied to the lower AC
terminal of a NSI, and the effects are the same as those of the
upper AC terminal of a NSI.
Fig. 6. Current estimation error curves with an IISF: (a) iá1;
(b) iâ1.
1iα
1iβ
2iα
2iβ
1uα
1uβ
2uα
2uβ
1 1 11
1 1 11
=
u u ip
u u iq
α β α
β α β
⎡ ⎤ ⎡ ⎤⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥ −⎣ ⎦ ⎣ ⎦ ⎣ ⎦
2 2 22
2 2 22
=
u u ip
u u iq
α β α
β α β
⎡ ⎤ ⎡ ⎤⎡ ⎤⎢ ⎥ ⎢ ⎥⎢ ⎥ −⎣ ⎦ ⎣ ⎦ ⎣ ⎦
1p
1q
*
1p
*
1q
1pΔ
1qΔ
PI
*
1uα
*
1uβ
AHS
2p
2q
*
2p
*
2q
2pΔ
2qΔ
1iα 1
iβ
1iβ
1iα
PI
PI
*
2uα
*
2uβ
2iα 2
iβ
2iβ
2iα
PI
AMS
ALS
BHS
BMS
BLS
CHS
CMS
CLS
Fig. 7. Proposed direct power control system for a NSI.
In addition, it is possible to conclude the uα1, uβ1, uα2, and
uβ2 from (2).
1 1 2
1 1 2
2 1 2
2 1 2
1( )
2
1( )
2
c H c M L
c H c M L L M
c H M c L
c H M M H c L
u u S u S S
u u S u S S S S
u u S S u S
u u S S S S u S
α α α α
β β α β α β
α α α α
β α β α β β
= −⎧⎪⎪ = + +⎪⎨
= −⎪⎪
= − + −⎪⎩
(10)
Therefore, a direct power control system can be built for a
NSI, and the system diagram is shown in Fig. 7.
IV. SIMULATION AND EXPERIMENTAL RESULTS
Based on Fig. 7, a simulation system is built using Matlab/
Simulink for a NSI, and SVPWM is adopted [11]. The
simulation conditions are the input voltage 500VDC, Rs1=
Rs2=50Ω, and Ls1=Ls2=100mH; and the output line voltages
are 220Vrms with 50HZ for the upper load, and 110Vrms
with 60HZ for the lower load. Fig. 8-13 show simulation
results for the proposed direct power control system of a NSI.
From Fig. 8, it can be seen that the peak values of the
upper and lower line voltages are about 310V and 155V,
respectively. It can also be seen that the frequencies of the
upper and lower line voltages are 50Hz and 60Hz,
respectively. In Fig. 9, the peak values of the line current for
Direct Power Control without Current Sensors for Nine-Switch Inverters 5
(a) Upper load.
(b) Lower load.
Fig. 8. Voltage curves for a NSI.
(a) Upper load.
(b) Lower load.
Fig. 9. Current curves for a NSI.
the upper and lower loads are about 3A and 1.4A, respect-
ively. The frequencies of the upper and lower line current are
50Hz and 60Hz, respectively.
From Fig. 10 and Fig. 11, for the upper load, it can be seen
that the active and reactive powers are about 750W and
435var; the maximum overshoots of the active and reactive
power are about 21W and 20var; and the transition processes
are about 0.01s for the active power and 0.02s for the reactive
power. In addition, the steady-state errors are about 1W for
the active power and 1var for the reactive power.
For the lower load, in Fig. 12 and Fig. 13, it can be seen
that the active and reactive powers are about 155W and
115var; the maximum overshoots of the active and reactive
power are about 8.5W and 7var; the transition processes are
about 0.015s for the active power and 0.02s for the reactive
power. In addition, the steady-state errors are about 0.5W for
the active power and 0.5var for the reactive power.
To confirm the viability of the proposed the direct power
control scheme, as shown in Fig. 7, a laboratory prototype for
a NSI has been developed based on a TMS320F2812 DSP as
shown in Fig. 14. The experimental conditions are the input
voltage 500VDC, Rs1= Rs2=50Ω and Ls1=Ls2=100mH.
Firstly, in the CF mode, the frequencies of the output line
voltages are 50HZ; and the upper and lower load output line
(a) Active power.
(b) Reactive power.
Fig. 10. Power curves of the upper load.
(a) Active power.
(b) Reactive power.
Fig. 11. Power error curves for the upper load.
(a) Active power.
(b) Reactive power.
Fig. 12. Power curves of the lower load.
(a) Active power.
(b) Reactive power.
Fig. 13. Power error curves for the lower load.
6
Fi
Fi
vo
sh
co
Fi
an
va
fr
up
pe
pe
fr
In
3.
ca
fo
ab
re
Fr
ab
st
fo
th
70
th
an
ig. 14. Experime
ig. 15. Line volta
oltages are 110V
how experimen
ontrol system fo
ig. 15 and Fig.
nd lower line v
alues of the pha
equencies of t
pper and lower
eak line curren
eak line curre
equencies of th
n Fig. 18, the T
.69% and 3.32%
an be seen that t
or the upper and
bout 110var an
espectively.
rom Fig. 21, th
bout 5W and 13
ate errors of th
or the upper and
he active power
0ms for the upp
he maximum er
nd 13var for the
ental setup.
(a) Uppe
(b) Lowe
age curves for a
Vrms and 220V
ntal results for
or a NSI.
16 show that
voltage are abo
ase voltage are
the line voltag
load are 50Hz
nt of the upper
ent of the low
he upper and low
THDs of the upp
%, respectively.
the active powe
d lower load, an
nd 435var for
he maximum er
3W for the uppe
e active power
d lower load; a
r are about 30m
per and lower lo
rrors of the rea
e upper and low
Journal of Po
er load.
er load.
NSI.
Vrms, respectiv
r the proposed
the peak value
ut 155V and 3
about 90V and
e and phase v
z, respectively.
load is about
wer load is ab
wer line current
per and lower l
. From Fig. 19
ers are about 17
nd that the react
the upper an
rrors of the act
er and lower lo
are smaller tha
and the transitio
ms for the act
oad, respectively
active power ar
wer load; the stea
ower Electronic
ely. Fig. 15-21
d direct power
es of the upper
310V; the peak
180V; and the
voltage for the
In Fig. 17, the
1.5A, and the
bout 3A. The
are also 50Hz.
line current are
and Fig. 20, it
75W and 700W
tive powers are
nd lower load,
tive power are
oad; the steady-
an 1W and 1W
on processes of
ive power and
y. From Fig. 22
re about 4.5var
ady-state errors
cs, Vol. 18, No
t
W
W
f
,
Fig. 16. Ph
Fig. 17. Cu
Fig. 18. TH
of the rea
upper and
reactive p
lower load
. 1, January 20
(a
hase voltage curv
urrent curves for
(a
HD of the line cu
ctive power are
d lower load;
power are abou
d, respectively.
018
a) Upper load.
(b) Lower load.
ves for a NSI.
(a) Upper load.
(b) Lower load.
r a NSI.
a) Upper load.
(b) Lower load.
urrent.
e smaller than 0
and the transit
ut 20ms and 70
0.5var and 1var
tion processes
0ms for the upp
for the
of the
per and
Direct Power Control without Current Sensors for Nine-Switch Inverters 7
(a) Upper load.
(b) Lower load.
Fig. 19. Active power curves for a NSI.
(a) Upper load.
(b) Lower load.
Fig. 20. Reactive power curves for a NSI.
(a) Upper load.
(b) Lower load.
Fig. 21. Active power error curves for a NSI.
Secondly, in the DF mode, the frequencies of the upper and
lower load output line voltages are 60HZ and 50HZ; and the
upper and lower load output line voltages are 110Vrms and
220Vrms, respectively. Fig. 23-30 show experimental results.
(a) Upper load.
(b) Lower load.
Fig. 22. Reactive power error curves for a NSI.
(a) Upper load.
(b) Lower load.
Fig. 23. Line voltage curves for a NSI.
(a) Upper load.
(b) Lower load.
Fig. 24. Phase voltage curves for a NSI.
Fig. 23 and Fig. 24 show that the peak values of the upper
and lower line voltage are about 155V and 310V; the peak
values of the phase voltage are about 90V and 180V; and the
frequencies of the upper and lower line voltage are 60Hz and
50Hz, respectively.
8
Fi
Fi
ab
ab
cu
TH
4.
po
lo
43
ac
lo
th
tra
60
ig. 25. Line curre
ig. 26. THD of th
Fig. 25 shows
bout 1.4A, and t
bout 2.9A. The
urrent are 60H
HDs of the up
.04%, respectiv
From Fig. 27
owers are abou
oad, and that t
35var for the up
From Fig. 29,
ctive power are
oad; the steady-
han 0.5W and
ansition proces
0ms for upper a
(a) Upp
(b) Low
ent curves for a N
(a) Uppe
(b) Lowe
he line current.
that the peak li
that the peak lin
e frequencies o
Hz and 50Hz, r
pper and lower
ely.
and Fig. 28, i
ut 155W and 70
the reactive po
pper and lower l
it can be seen th
about 5W and
-state errors of
4W for the up
ses of the activ
and lower load,
Journal of Po
per load.
wer load.
NSI.
er load.
er load.
ne current of th
ne current of th
of the upper a
respectively. In
r line current a
it can be seen
00W for the up
owers are abou
load, respective
hat the maximu
20W for the up
the active pow
pper and lower
ve power are ab
respectively.
ower Electronic
he upper load is
he lower load is
and lower line
n Fig. 26, the
are 4.09% and
that the active
pper and lower
ut 115var and
ely.
um errors of the
pper and lower
wer are smaller
load; and the
bout 25ms and
cs, Vol. 18, No
r
Fig. 27. A
Fig. 28. R
Fig. 29. A
From F
reactive p
lower loa
smaller th
and the tr
20ms and
. 1, January 20
(a
(b
Active power cu
(a
(b
Reactive power c
(a
(b
ctive power erro
Fig. 30, it can be
power are about
ad; the steady-s
han 0.5var and
ransition proces
40ms for the u
018
a) Upper load.
b) Lower load.
rves for a NSI.
a) Upper load.
b) Lower load.
curves for a NSI
a) Upper load.
b) Lower load.
or curves for a N
e seen that the m
t 5.75var and 5
state errors of th
3var for the u
sses of the reac
upper and lower
I.
SI.
maximum errors
5var for the upp
he reactive pow
upper and lowe
ctive power are
load, respectiv
s of the
per and
wer are
er load;
e about
ely.
Direct Power Control without Current Sensors for Nine-Switch Inverters 9
(a) Upper load.
(b) Lower load.
Fig. 30. Reactive power error curves for a NSI.
V. CONCLUSION
This paper proposes a novel direct power control method
for a NSI. In the proposed method, a switching function
model and an equivalent circuit model for a NSI have been
built in αβ coordinates. Then, a novel current observer is
proposed, and a novel direct power control method for a NSI
has been proposed with only two voltage sensors. Simulation
and experimental results show the effectiveness of the
proposed method.
In further research, a NSI will be used in a power quality
conditioner, and the proposed equivalent circuit model and
the method will be used in a unified power quality
conditioner to improve the power quality of a power grid.
ACKNOWLEDGMENT
This work was supported by the Universities Science and
Technology Fund Planning Project of Tianjin: [Grant Number
20130419]; Tianjin Research Program of Application
Foundation and Advanced Technology: [Grant Numbers
15JCQNJC04500, 16JCQNJC04200 and 16JCTPJC49600];
Tianjin Science and Technology Support Project: [Grant
Numbers 15zczdsf00080].
REFERENCES
[1] T. Kominami and Y. Fujimoto, “A novel nine-switch
inverter for independent control of two three-phase loads,”
in Proc. IEEE Ind. Appl. Soc. Annu. Conf. (IAS), pp.
2346-2350, 2007.
[2] B. Tabbache, M. A. Allel, M. Abbache, and A. Belila, “A
pulse width modulation strategy for DC-AC nine switches
inverter,” in 15th International Conference on Environment
and Electrical Engineering, pp. 877-882, 2015.
[3] J. S. S. Prasad, R. Ghosh, and G. Narayanan, “Common-
mode injection PWM for parallel converters,” IEEE Trans.
Ind. Electron., Vol. 62, No. 2, pp. 789-794, Feb. 2015.
[4] F. Gao, L. Zhang, D. Li, P. C. Loh, Y. Tang, and H. Gao,
“Optimal pulsewidth modulation of nine-switch converter,”
IEEE Trans. Power Electron., Vol. 25, No. 9, pp. 2331-2343,
Sep. 2010.
[5] F. Gao, L. Zhang, and P. Loh, “Dead-time elimination of
nine-switch converter,” in Applied Power Electronics
Conference and Exposition (APEC), pp. 673-678, 2011.
[6] Y. Chen, G. Wen, and Y. Kang. “Sliding Mode Pulsewidth
Modulation (SMPWM) for Nine-Switch Converter,” IEEE
International Symposium on Industrial Electronics, pp. 1-6,
2013.
[7] Z. Qin, P. C. Loh, and F. Blaabjerg, “Application Criteria
for Nine-Switch Power Conversion Systems with Improved
Thermal Performance,” IEEE Trans. Power Electron., Vol.
30, No. 8, pp. 4608-4620, Aug. 2014.
[8] T. Kominami and Y. Fujimoto, “A novel nine-switch
inverter for independent control of two three-phase loads,”
in IEEE Industry Applications Society Annual Conference
(IAS), pp. 2346-2350, 2007.
[9] N. Jarutus and Y. Kumsuwan, “A comparison between
level- and phase-shift space vector duty-cycle modulations
using a nine-switch inverter for an ASD,” 18th
International Conference on Electrical Machines and
Systems, pp. 1877-1883, 2015.
[10] S. M. Dehghan, A. Yazdian, and F. Ashrafzadeh, “Space
vectors modulation for nine-switch converters,” IEEE
Trans. Power Electron., Vol. 25, No. 6, pp. 1488-1496, Jun.
2010.
[11] S. M. Dehghan, A. Amiri, M. Mohamadian, and M. A. E.
Andersen, “Modular space-vector pulse-width modulation
for nine-switch converters,” IET Power Electron., Vol. 6,
No. 3, pp. 457-467, Mar. 2013.
[12] N. Jarutus and Y. Kumsuwan, “Level-shift space vector
pulse width modulation for a nine-switch inverter,” in 12th
International Conference on ECTI, pp. 1-5, 2015.
[13] S. M. Dehghan, M. Mohamadian, and A. Yazdian, “Hybrid
electric vehicle based on bidirectional Z-source nine-switch
inverter,” IEEE Trans. Veh. Technol., Vol. 59, No. 6, pp.
2641-2653, Jul. 2010.
[14] M. Shahparasti, A. H. Rajaei, A. Yazdian, and M.
Mohamadian, “Interline unified power quality conditioner
based on single stage nine switch inverter,” Power
Electronics and Drive Systems Technology, pp. 319-323,
2012.
[15] L. Zhang, P. C. Loh, and F. Gao, “An integrated nine-
switch power conditioner for power quality enhancement
and voltage sag mitigation,” IEEE Trans. Power Electron.,
Vol. 27, No. 3, pp. 1177-1190, Mar. 2012.
[16] R. Carlos, K. Samir, and C. Roberto, “Dual three-phase
PMSG based wind energy conversion system using
9-switch dual converter,” in Energy Conversion Congress
and Exposition, pp. 1021-1022, 2015.
[17] G. Wen, Y. Chen, P. Zhang, and Y. Kang, “Nine-switch-
converter-based DFIG wind power system and its dynamic
port-current assigned approach for low voltage riding
through (LVRT),” in Applied Power Electronics Confer-
ence and Exposition, pp. 1324-1330, 2015.
[18] M. Heydari, A. Yazdian Varjani, M. Mohamadian, and H.
Zahedi, “A novel variable-speed wind energy system using
permanent-magnet synchronous generator and nine-switch
10
[1
[2
[2
[2
[2
[2
[2
0
AC/AC con
and Technol
19] L. Congwei
nine-switch
phase UPS ap
pp. 1-10, 200
20] P. C. Loh,
energy syste
Ind. Electron
21] N. P. Soe, D
fed inductio
nine-switch
on IEEE In
2011.
22] T. Kominam
inverter for
in Industry A
23] G. Wen, Y
voltage and
converter-ba
ride-through
IEEE Trans.
2016.
24] M. S. Diab,
Massoud, an
integrated m
using symm
Electron., V
25] A. Kirakosy
Khadkikar,
through top
Trans. Powe
2016.
nverter,” in Pow
logies Conferenc
i, W. Bin, N. Z
PWM rectifier
pplications,” Pow
07.
L. Zhang, and
ems for distribu
n., Vol. 60, No. 4
D. M. Vilathgam
on generator for
power converte
ndustrial Electro
mi and Y. Fuj
independent con
Applications Con
. Chen, Z. Zho
current assignm
ased DFIG wind
h (LVRT) under
Ind. Appl., Vol
A. A. Elseroug
nd S. Ahmed, “
motor drive and b
metrical six-phase
ol. 63, No. 9, pp
yan, M. S. E.
“A nine switc
pology for wind
er Del., Vol. 31
Lei Pan recei
Hebei Univer
China, in 2014
Associate Pro
University, T
research inter
and motor driv
Journal of P
wer Electronics,
ce, pp. 5-9, 2011
Zargari, and D.
r-inverter topol
wer Electronics a
F. Gao, “Com
uted generation,
4, pp. 1492-1502
muwa, and K. S.
wind energy g
r,” in 2011 Ann
onics Society, p
jimoto, “A nov
ntrol of two thre
nference, pp. 234
ong, and Y. K
ment strategies
d power system
symmetrical gr
l. 52, No. 4, pp.
gi, A. S. Abdel
“A nine-switch-
battery charger
e machines,” IE
p. 5326-5355, Se
Moursi, P. K
ch converter-ba
d turbine appli
1, No. 4, pp. 17
ived his Ph.D. d
rsity of Techn
4. He is presently
ofessor at Tian
Tianjin, China.
rests include po
ves.
Power Electron
Drive Systems
.
Xu, “A novel
ogy for three-
and Applications,
mpact integrated
,” IEEE Trans.
2, Apr. 2013.
. Low, “Doubly
generation using
nual Conference
pp. 3608- 3613,
vel nine-switch
ee-phase loads,”
46-2350, 2007.
ang, “Dynamic
of nine-switch-
for low-voltage
id voltage dip,”
3422-3434, Jul.
l-Khalik, A. M.
converter-based
system for EVs
EEE Trans. Ind.
ep. 2016.
anjiya, and V.
ased fault ride
ications,” IEEE
757-1766, Aug.
degree from the
ology, Tianjin,
y working as an
njin Chengjian
. His current
ower converters
nics, Vol. 18, No
h
E
n
n
t
electrical m
network-b
circuit des
circuit sim
o. 1, January 2
Junru
Tianjin
in 201
toward
interes
drives.
Kai W
Tianjin
in 201
candid
His re
and mo
Beibei
degree
Electro
Univer
2009,
as a Le
Tianjin
include
motor drives.
Yi P
Nanka
He is
Tianjin
His cu
conver
Lin Z
Tianjin
China,
degree
China,
presen
Chengj
current
based methods
sign, and the de
mulator.
2018
Zhang received
n Chengjian Uni
16, where she
ds her M.S. degre
sts include powe
.
Wang received
n Chengjian Uni
17. He is curre
date of Tianjin
esearch interests
otor drives.
i Wang receive
es in Electrical E
onics from
rsity, Liaoning,
respectively. He
ecturer at Tianjin
n, China. His cu
e power con
Pang received h
i University, Ti
presently work
n Chengjian Uni
urrent research in
rter systems and
hu received her
n University o
, in 2008; and
es from Tianjin
, in 2010 and 20
ntly working as
gjian University
t research inte
for microwave
evelopment of a
d her B.S. degre
iversity, Tianjin,
is presently w
ee. Her current r
er converters and
the B.S. degre
iversity, Tianjin,
ently a master
Chengjian Uni
s are power con
ed his B.S. an
Engineering and
Liaoning Te
China, in 200
e is presently w
n Chengjian Uni
urrent research in
nverter system
his Ph.D. degre
ianjin, China, in
king as a Lect
iversity, Tianjin,
nterests include
electrical motor
r B.S. degree fr
f Commerce, T
her M.S. and
n University, T
15, respectively
a Lecturer at
, Tianjin, Chin
erests include
device modelin
a neural-network
ee from
, China,
working
research
d motor
ee from
China,
degree
iversity.
nverters
d M.S.
d Power
echnical
06 and
working
versity,
nterests
ms and
ee from
n 2015.
turer at
China.
power
r drives.
rom the
Tianjin,
d Ph.D.
Tianjin,
. She is
Tianjin
na. Her
neural-
ng and
k-based