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: panlei4089@163.com 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

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Fig. 16. Ph

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Fig. 18. TH

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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].

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. His current

ower converters

nics, Vol. 18, No

h

E

n

n

t

electrical m

network-b

circuit des

circuit sim

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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

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ntly working as

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t research inte

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d her B.S. degre

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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

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nterests include

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Tianjin,

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