an effective control method for quasi-z-source cascade multilevel inverter-based grid-tie...

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An Effective Control Method for Quasi-Z-Source Cascade Multilevel Inverter based Grid-Tie Single-

Phase Photovoltaic Power System

Yushan Liu, Student Member, IEEE, Baoming Ge, Member, IEEE, Haitham Abu-Rub, Senior Member, IEEE, and Fang Zheng Peng, Fellow, IEEE

Abstract— An effective control method, including system-level control and pulsewidth modulation for quasi-Z-source cascade multilevel inverter (qZS-CMI) based grid-tie photovoltaic (PV) power system is proposed. The system-level control achieves the grid-tie current injection, independent maximum power point tracking (MPPT) for separate PV panel, and dc-link voltage balance for all quasi-Z-source H-bridge inverter (qZS-HBI) modules. The complete design process is disclosed. A multilevel space vector modulation (SVM) for the single-phase qZS-CMI is proposed to fulfill the synthetization of the step-like voltage waveforms. Simulation and experiment based on a 7-level prototype are carried out to validate the proposed methods.

Keywords— Quasi-Z-source inverter; cascade multilevel inverter; photovoltaic power system; space vector modulation.

I. INTRODUCTION A recent upsurge in the study of photovoltaic (PV) power

generation emerges, since they directly convert the solar radiation into electric power without hampering the environment. However, the stochastic fluctuation of solar power is inconsistent with the desired stable power injected to the grid, owing to variations of solar irradiance and temperature. To fully exploit the solar energy, extracting the PV panels’ maximum power and feeding them into grids at unity power factor become the most important. The contributions have been made by the cascade multilevel

inverter (CMI) [1], [2]. Nevertheless, the H-bridge inverter (HBI) module lacks boost function so that the inverter KVA rating requirement has to be increased twice with a PV voltage range of 1:2; and the different PV panel output voltages result in imbalanced dc-link voltages. The extra dc-dc boost converters were coupled to PV panel and HBI of the CMI to implement separate maximum power point tracking (MPPT) and dc-link voltage balance [3], [4]. However, each HBI module is a two-stage inverter, and many extra dc-dc converters not only increase the complexity of the power circuit and control, and the system cost, but also decrease the efficiency.

Recently, the Z-source/quasi-Z-source cascade multilevel inverter (ZS/qZS-CMI) based PV systems were proposed in [5]-[7]. They possess the advantages of both traditional CMI and Z-source topologies. For example, the ZS/qZS-CMI: 1) has high-quality staircase output voltage waveforms with lower harmonic distortions, and reduces / eliminates output filter requirements for the compliance of grid harmonic standards; 2) requires power semiconductors with a lower rating, and greatly saves the costs; 3) shows modular topology that each inverter has the same circuit topology, control structure and modulation [1], [2]; 4) most important of all, has independent dc-link voltage compensation with the special voltage step-up/down function in a single-stage power conversion of Z-source / quasi-Z-source network, which allows an independent control of the power delivery with high reliability [8]-[10]; 5) can fulfill the distributed MPPT [7].

In order to properly operate the ZS/qZS-CMI, the power injection, independent control of dc-link voltages, and the pulsewidth modulation (PWM) are necessary. References [5] and [6] focused on the parameter design of the ZS/qZS networks and the analysis of efficiency. Reference [7] presented the whole control algorithm, i.e., the MPPT control of separate quasi-Z source H-bridge inverter (qZS-HBI) module, and the grid-injected power control. Whereas, the phase-shifted sinewave PWM (PS-SPWM) is the only existing PWM technique for the single-phase ZS/qZS-CMI. The PS-SPWM consumes more resources to achieve the shoot-through states because two more references are compared to the carrier waveform. Additionally, the ZS/qZS-CMI based grid-tie PV system has never been modeled in detail to design the controllers.

Manuscript received October 17, 2012; revised January 31, 2013 and July 16, 2013; accepted for publication August 20, 2013. This work was supported by the National Priorities Research Program under Grant NPRP-EP X-033-2-007 and Grant 09-233-2-096 from the Qatar National ResearchFund (a member of Qatar Foundation).

Copyright © 2009 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to [email protected].

Y. Liu is with the School of Electrical Engineering, Beijing Jiaotong University, Beijing 100044, China, and with the Department of Electricaland Computer Engineering, Texas A&M University at Qatar, Doha 23874, Qatar (e-mail: [email protected]).

B. Ge is with the School of Electrical Engineering, Beijing Jiaotong University, Beijing 100044, China, and with the Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824, USA (e-mail: [email protected]).

H. Abu-Rub is with the Department of Electrical and Computer Engineering, Texas A&M University at Qatar, Doha 23874, Qatar (e-mail: [email protected]).

F. Z. Peng is with the Department of Electrical and ComputerEngineering, Michigan State University, East Lansing, MI 48824, USA (e-mail: [email protected]).



The main contributions of this paper include: i) a novel multilevel space vector modulation (SVM) technique for the single-phase qZS-CMI is proposed, which is implemented without additional resources; ii) a grid-connected control for the qZS-CMI based PV system is proposed, where the all PV panel voltage references from their independent MPPTs are used to control the grid-tie current; the dual-loop dc-link peak voltage control is employed in every qZS-HBI module to balance the dc-link voltages; iii) the design process of regulators is completely presented to achieve fast response and good stability; iv) simulation and experimental results verify the proposed PWM algorithm and control scheme.

The paper is organized as follows: an overview of the whole system with control strategy is presented in Section II; Section III focuses on the system modeling and grid-connected control; Section IV addresses the proposed multilevel SVM technique; Section V designs the regulators; the proposed strategy is verified by simulation and experimental results in Section VI; at last, a conclusion is made in Section VII. Noted that in the derivations of the paper, all the symbols with “^” denote the amplitude, and those with “－” denote the average.

II. DESCRIPTION OF QZS-CMI BASED GRID-TIE PV POWER SYSTEM

Fig. 1 shows the discussed qZS-CMI based grid-tie PV power system. The total output voltage of the inverter is a series summation of n qZS-HBI cell voltages. Each cell is fed by an independent PV panel. The individual PV power source is an array composed of identical PV panels in parallel and series. A typical PV model in [11] is performed considering both the solar radiation and the PV panel temperature.

A. qZS-CMI The qZS-CMI combines the qZS network into each HBI

module. When the kth qZS-HBI is in nonshoot-through states, it will work as a traditional HBI. There are

PVkkPVkk

DCk vBvD

v

211ˆ , DCkkHk vSv ˆ (1)

while in shoot-through states, the qZS-HBI module does not contribute voltage. There are

0ˆ DCkv , 0Hkv (2) For the qZS-CMI, the synthesized voltage is

n

kDCkk

n

kHkH vSvv

11

ˆ (3)

where vPVk is the output voltage of the kth PV array; vDCk is the dc-link voltage of the kth qZS-HBI module; Dk and Bk represent the shoot-through duty ratio and boost factor of the kth qZS-HBI; vHk is the output voltage of the kth module; Sk ∈ {-1, 0, 1} is the switching function of the kth qZS-HBI.

DCnv

1Hv

Hnv

gv

PVnv

1DCv

1PVv

nLi 2

si

Hv

1C

2C2L

1L D

qZS

1PVi*

1PVv1D

11Cv21Li

pCPV Array

1C

2C2L

1L D

qZS

PVniMPPT

AlgorithmnD

nCv 1PV

Array

*PVnv

fr fL

PLL

n

kPVkv

1

**si

n

kPVkv

1

t 0si

n

*si

si

n

k 2

*2PVv

tPI

2PI

PR

Total Voltage Loop

Separate Voltage Loop

Current Loop

2PVv

1D

11S

*ˆDCnv

*1ˆDCv

1nS

2nS

3nS

4nS

11S

12S

13S

14S

MPPT Algorithm

DC-link Voltage Loop

12S 13S 14S

*PVnv

nPISeparate Voltage Loop

PVnv

2D

21S 22S 23S 24S

nD

1nS 2nS 3nS 4nS

1mv

2mv

3mv

)1( nmv

mnv

pC

DC-link Voltage Loop

qZS-CMI SVM

qZS-CMI SVM

qZS-CMI SVM

(a)

*ˆDCkv kLi 2*2kLi

PI P

)1/(1 kkC Dv DCkv

kCv 1

kD

(b)

Fig. 1. (a) qZS-CMI based grid-tie PV power system and (b) dc-link peak voltage control.

B. Control Strategy The control objectives of the qZS-CMI based grid-tie PV

system are: 1) the distributed MPPT to ensure the maximum power extraction from each PV array; 2) the power injection to the grid at unity power factor with low harmonic distortion; 3) the same dc-link peak voltage for all qZS-HBI modules. The overall control scheme of Fig. 1 is proposed to fulfill these purposes.

For achieving the first two goals, the n+1 closed loops are employed, as Fig. 1 (a) shows. They are:

1) Total PV array voltage loop adjusts the sum of n PV array voltages tracking the sum of n PV array voltage references by using a proportional and integral (PI) regulator PIt. Each PV array voltage reference is from its MPPT control independently.



2) Grid-tie current loop ensures a sinusoidal grid-injected current in phase with the grid voltage. The total PV array voltage loop outputs the desired amplitude of grid-injected current. A Proportional + Resonant (PR) regulator enforces the actual grid current to track the desired grid-injected reference. The current loop output’s total modulation signal subtracts the modulation signal sum of the 2nd, 3rd, and nth qZS-HBI modules to get the 1st qZS-HBI module’s modulation signal.

3) The n-1 separate PV array voltage loops regulate the other n-1 PV array voltages to achieve their own MPPTs through the n-1 PI regulators, such as PI2 to PIn, respectively. With the total PV array voltage loop control, the n PV arrays fulfill the distributed MPPT. In addition, the voltage feed forward control is used to generate each qZS-HBI module’s modulation signal, which will reduce the n regulators’ burden, achieve the fast dynamic response, also minimize the grid voltage’s impact on the grid-tie current.

For the 3rd goal, the dc-link peak voltage is adjusted in terms of its shoot-through duty ratio for each qZS-HBI module, as Fig. 1 (b) shows. A proportional (P) regulator is employed in the inductor L2 current loop to improve the dynamic response, and a PI regulator of the dc-link voltage loop ensures the dc-link peak voltage tracks the reference.

Finally, the independent modulation signals vmk and shoot-through duty ratios Dk of the qZS-CMI, k ∈ {1, 2, …, n}, are combined into the proposed multilevel SVM to achieve the desired purposes.

III. SYSTEM MODELING AND CONTROL Fig. 2 shows block diagram of the proposed grid-tie

control with the system model for the qZS-CMI based PV power system. The details will be explained as follows.

A. Grid-Tie Current Loop The kth qZS-HBI module has following dynamic

dtdvCii PVk

pPVkkL 1 (4)

where iL1k is the current of qZS inductor L1; iPVk is the kth PV array’s current; Cp is the capacitance of PV array terminal capacitor.

The qZS-CMI based grid-tie PV system has

sfs

fgH irdtdiLvv (5)

where vg is the grid voltage, is is the grid-injected current; Lf

is the filter inductance, rf is its parasitic resistance. The transfer function of the grid-injected current can be

ffgH

sf rsLsVsV

sIsG

1

)()()()( (6)

A PR regulator [12]

20

20)(

skksG iR

iPPRi (7)

is employed to enforce the actual grid-injected current to track the desired reference.

With a grid voltage feed forward control, the kth qZS-HBI module has the modulation signal

)()(' sGsVvv vfkgmkmk (8) with

)(1)(

snGsG

invkvfk , DCk

mk

Hkinvk v

sVsVsG ˆ)()()( (9)

where v´mk is the regulated modulation signal from the separate voltage control of the kth module, as Fig. 2 shows.

From (8) and (9), there is

n

kinvkvfkginvkmk

n

kinvkmkH

sGsGsVsGv

sGvsV

1

'

1

)]()()()([

)()(

(10)

At the dc-link peak voltage balance control, all dc-link peak voltages are the same. The n qZS-HBI modules have the same transfer function, we assume

)()( sGsG invinvk , nk ,,2,1 (11) Using (6) - (11), the grid-injected current will be

n

kmkinvf vsGsGsI

1

')()()( (12)

Then, the current loop of Fig. 2 is simplified to Fig. 3, and the open-loop transfer function can be obtained as

ff

DCkfinv

m

sio rsL

vsGsGsVsIsG

ˆ)()(

)()()( ' (13)

With the compensation of PR regulator, the transfer function becomes

20

20

230

20

2 )(ˆ)()()(

ffff

iRiPiPDCkioPRiicom rsLsrsL

kkskvsGsGsG

(14)

Consequently, the closed-loop transfer function of grid-tie current control can be obtained by

n

kPVkv

1

**si

n

kPVkv

1

t0sin

*si

si

n

k 2

n

kmkv

1

'

*PVkv

PVkv

)(sGPIt

gv

)(sGPIk

)(sGPRi

mkv

)(1 sGinv1Hv

n

k 1

Hv gv

ff rsL 1 )21(ˆ2

1

11

1

DvD

DC

PVkikD

n

kPVkv

1

)21(ˆ2)1(ˆ

kDCk

ks

DvDi

PVkikD

PVkv)(sGinvkHkv

si

n

k 1

kD1

kD1

n

kvfk sG

1)(

)(sGvfk

1mv

n

kmkv

1

'mkv

…

n

k 1

……

)21(ˆ21

nDCn

n

DvD

……

sC p

1

sC p

1

Fig. 2. Block diagram of the proposed grid-tie control with the model for the qZS-CMI based PV system.



200

20

20

230

20

2

ˆˆ)ˆ()(ˆ

)()()(1)()()(

)()()(

fiRDCkiPDCkfiPDCkff

iRiPiPDCk

invfPRi

invfPRi

s

sic

rkvkvsLskvrsLkkskv

sGsGsGsGsGsG

sIsIsG

(15)

)(* sIs )(sG f)(sGPRi

)(sIs)(' sVm )(sGinv

Fig. 3. Simplified block diagram of the grid current closed loop.

B. PV Voltage Loop From (4), there is

)]()([1

)( 1 sIsIsC

sV kLPVkp

PVk (16)

In addition, the output power of each qZS-HBI module equals to its input power in the nonshoot-through state, the kth qZS-HBI module has the power equation

nshkLPVkDCkDCkHks ivivvi

_1ˆ2ˆˆ

(17)

where nshkLi _1 is the average current of inductor L1 in nonshoot-through state. Using (1), nshkLi _1 can be solved as

)21(ˆ2ˆˆ

_1kDCk

HksnshkL Dv

vii

(18)

In the shoot-through state, the average current of inductor L1 can be expressed as

PVkPVkshkL iii _1 (19) Combining (18) and (19), the average current of inductor

L1 is

)21(ˆ2ˆ)1(ˆ

)1( _1_11

kDCk

HkksPVkk

nshkLkshkLkkL

DvvDiiD

iDiDi

(20)

Then the block diagrams of total and separate PV voltage loops can be obtained in Figs. 4 and 5.

If iPVk is considered as disturbance, with (20) and Fig. 4, the transfer function of the total PV array voltage loop is

shCsLCskGrCsLCkhkhskh

vDD

sCsG

sI

sVsG

pfpiPinvfpfp

iRiPiP

n

k DCkk

k

p

ic

s

n

kPVk

vot

222

034

01201

21

1*

1

22)(22

ˆ)21(1

2)(

)(

)()(

(21) where the coefficients h1 and h2 are

n

k k

kn

k kDCk

invk

DD

DvsGDh

111 21

1)21(ˆ)()1(

,

200

202 ˆˆ fiRDCkiPDCk rkvkvh (22)

The PI regulator s

kksG ItPtPIt )( is applied to track the

total reference voltage coming from MPPT algorithm. Thus,

the open-loop transfer function of total PV voltage loop after compensation can be obtained by

)()()()()(

sDensNumsGsGsG

vcomt

vcomtvotPItvcomt (23)

where

)()

()(

02010

201

21

31

iRiPItiR

iPPtItiPPtiPvcomt

kkkhsk

kkhskkhskkhsNum

,

22

320

45

22

)ˆ(22)(

shCsLC

svkrCsLCsDen

pfp

DCkiPfpfpvcomt

The closed-loop transfer function is

)(1)(

)()()(

sGsG

sVsVsG

vcomt

vcomt

PVt

PVtvct

(24)

here

n

kPVkPVt sVsV

1)()( and

n

kPVkPVt sVsV

1)()( .

Similarly, from Fig. 5, the transfer function of the kth qZS-HBI module’s PV voltage loop, k ∈ {2,…, n}, is

)21(2)1(ˆ

)()21(ˆ2

)1(ˆ

)()()(

kp

ks

invkpkDCk

ks

mk

PVkvok

DsCDi

sGsCDv

DisVsVsG

(25)

which is compensated by PI regulator s

kksG IkPkPIk )( .

Then the resultant open-loop transfer function of the kth qZS-HBI module’s PV voltage loop becomes

)21(2))(1(ˆ

)()()( 2kp

IkPkksPIkvokvcomk DsC

kskDisGsGsG

(26)

Also, the closed-loop transfer function is obtained as

)(1)(

)()()(

sGsG

sVsVsG

vcomk

vcomk

PVk

PVkvck

(27)

)(sGic)(* sIs )(sIs

n

kPVk sV

1

* )()(sGPIt

n

k 1

sC p

1

n

kPVk sV

1)(

kD1PVki

n

k kDCk

k

DvD

1 )21(ˆ1

21

Fig. 4. Block diagram of the total PV voltage loop.

)(* sVPVk )(sGPIk)(sVmk )(sVPVk)(sGinvk

)(sVHk)21(ˆ2

)1(ˆ

kDCk

ks

DvDi

kD1PVki

sC p

1

Fig. 5. Block diagram of the separate PV voltage loop.

C. DC-Link Voltage Control The independent dc-link peak voltage control based on

the inductor-L2 current and the capacitor-C1 voltage is performed for each qZS-HBI module, as Fig. 1 (b) shows. From [13], the kth qZS-HBI module’s transfer functions from the shoot-through duty ratio to the dc-link peak voltage, GVdk (s), and from the shoot-through duty ratio to the inductor-L2 current, GiLdk (s), can be obtained, respectively.



With the employed proportional regulator at the coefficient KdPk for the inductor current loop, as the block diagram of Fig. 6 shows, the closed-loop transfer function of inductor L2 current can be obtained by

)(1)()(

)(2 sGK

KsI

sdsG

iLdkdPk

dPk

kL

kidck

(28)

A PI regulator with the transfer function of

sKKsG VdIk

VdPkviPIk )( is cascaded to the inductor current loop

for controlling the dc-link peak voltage, as shown in Fig. 6. Therefore, the kth qZS-HBI module’s dc-link peak voltage control has the open-loop transfer function

)()()()( sGsGsGsG VdkidckviPIkVdcomk (29) and the closed-loop transfer function

)()()(1)()(

)()()(

sGsGsGsGsG

sVsdsG

VdkidckviPIk

idckviPIk

DCk

kVdck

(30)

)(sGiLdk

)(sGVdk

)(* sVDCk

)(sVDCk

)(sdk

)(2 sI kL

)(2 sI kL

dPkK)(sGviPIk

Fig. 6. Block diagram of the kth module’s dc-link peak voltage control.

IV. PROPOSED MULTILEVEL SVM FOR QZS-CMI As the qZS network is embedded to the HBI module, the

SVM for each qZS-HBI can be achieved by modifying the SVM technique for the traditional single-phase inverter [14]. Using the first qZS-HBI module of Fig. 1 as an example, the voltage vector reference Uref1 is created through the two vectors U1 and U0, by

ssref T

TUTTUU 0

01

11 (31)

where Ts=1/fc and fc is the carrier frequency; the time interval T1 is the duration of active vectors, and the T0 is the duration of traditional zero voltage space vectors. Thus, the switching times for the left and right bridge legs in traditional HBI are {tL, tR} ∈ {T0/4, T0 + T1/2}. However, the shoot-through states are required for the independent qZS-HBI module.

For this purpose, a delay of the switching times for upper switches or a lead of the switching times for lower switches are employed at the transition moments, as Fig. 7 (a) shows. During each control cycle, the total time Tsh of shoot-through zero state is equally divided into four parts. The time intervals of tmin ∈ min {tL, tR} and tmax ∈ max {tL, tR} remain unchanged; tmin- = (tmin - Tsh/4) and tmax+ = (tmax+Tsh/4) are the modified times to generate the shoot-through states; SX1 and SY1 are the switching control signals for the upper switches, SX2 and SY2 are that for the lower switches, {X, Y}∈{L, R}. In this way, the shoot-through states are distributed into the qZS-HBI module without additional switching actions, losses, and resources.

1XSt

maxt

1YS

2/sT

mint

2XS

2YS

4/shT

4/shT

mint

maxt

2/sT 2/sT4/0T 4/0T 4/0T 4/0T2/1T 2/1T

eR

mI

)01(2U

)10(1U

)00(0U)11(3U

nK12

nK22

nn

K22

nn

K12

1refU2refU

3refU

refnU)1( nrefU refU

(a) (b) Fig. 7. The proposed multilevel SVM for the single-phase qZS-CMI. (a) Switching pattern of one qZS-HBI module; (b) synthetization of voltage vectors for the qZS-CMI.

To generate the step-like AC output voltage waveform from the qZS-CMI, a 2π/ (nK) phase difference, in which K is the number of reference voltage vectors in each cycle, is employed between any two adjacent voltage vectors, as Fig. 7 (b) shows. The total voltage vector Uref is composed of n reference vectors Uref1, Uref2, …, Urefn from the n qZS-HBI.

V. CONTROL PARAMETER DESIGN The prototype specifications of qZS-CMI based PV

power system are shown in Table I. For the grid-connected current loop, the PR regulator parameters are designed to get a fast dynamics and zero-steady state error at the grid frequency [12]. The fast dynamic response and stable steady-state performance are taken into account to design the control parameters for total PV voltage control loop, separate PV voltage control loop, and dc-link voltage control loop. The design results are shown in Table II, and the all bode plots are shown in Figs. 8 to 10.

Fig. 8 shows the bode plots of the grid-tie current loop transfer functions Gio(s) and Gicom(s), which are before and after compensation, respectively. The symbol ωn is the corner frequency of Gio(s), which equals rf / Lf from (6); ω0 is the resonant frequency of the PR regulator, i.e., grid frequency of 314 rad/s. After compensation, Gicom(s) provides a large gain inside its band-pass region, making the crossover frequency almost tenfold the corner frequency ωn. Thus, the grid-connected fast response is greatly enhanced without loss of stability, which can be obtained from the bode diagram of closed-loop transfer function Gic(s).

TABLE I. PROTOTYPE SPECIFICATIONS.

Parameters Value

Minimum PV array voltage, VPV,min 60 V Maximum PV array voltage, VPV,max 120 V qZS inductance, L1 and L2 1.8 mH qZS capacitance, C1 and C2 3300 µF PV array parallel capacitance, Cp 1100 µF Filter inductance, Lf 1 mH Carrier frequency, fc 5 kHz



TABLE II. CONTROL PARAMETERS. Parameters Value Parameters Value

kiP 5.15e-3 kiR 0.1592 kPt 1.1464 kIt 10.854 kPk 0.015 kIk 0.05256 kdPk 0.0068 kVdPk 0.0281 kVdIk 2.5254

-400

-300

-200

-100

0

100

200

300

Mag

nitu

de (d

B)

100

101

102

103

104

105

106

-90

-45

0

45

90

135

Phas

e (d

eg)

Bode Diagram

Frequency (rad/s)

Gicom(s)

Gio(s)

ω0 ωn Fig. 8. Bode diagrams of Gio(s) and Gicom(s).

-400

-300

-200

-100

0

100

Mag

nitu

de (d

B)

10-1

100

101

102

103

104

-180

-90

0

90

180

270

Phas

e (d

eg) Gvot (s)

-Gvcomt (s)

-39.1 dB, 146 rad/s

89.5 deg, 0.352 rad/s

189.11 deg, 1.97 rad/s

-50

0

50

100

Mag

nitud

e (d

B)

10-1

100

101

102

103

104

105

-180

-90

0

90

Phas

e (d

eg)

Bode Diagram

Frequency (rad/s)

-Gvcomk (s)

Gvok (s)

-92.5 deg, 79.3 rad/s

(a) (b)

Fig. 9. Bode diagrams of (a) Gvot (s) and -Gvcomt (s); and (b) Gvok (s) and -Gvcomk (s).

-60

-40

-20

0

20

40

60

Mag

nitu

de (d

B)

Frequency (rad/s)10

-210

-110

010

110

210

310

410

5-90

-45

0

45

90

Phas

e (d

eg)

GiLdk(s)

KdPkGiLdk(s)

86 deg, 27 rad/s

-89 deg, 342 rad/s

-89.9 deg, 4.74e4 rad/s

-60

-40

-20

0

20

40

60

Mag

nitu

de (d

B)

Frequency (rad/s)10

010

110

210

310

4-135

-90

-45

0

45

Phas

e (d

eg)

-103.2 deg, 9 rad/s

GVdk(s) GVdcomk(s)

(a) (b)

Fig. 10. Bode diagrams of (a) GiLdk (s) and KdPkGiLdk (s); and (b) GVdk (s) and GVdcomk (s).

Fig. 9 (a) shows the bode plots of total PV voltage control loop transfer functions Gvot (s) and -Gvcomt (s), which correspond to before and after compensation, respectively. The 39.1 dB gain margin and -90.5 deg phase margin show an unstable Gvot (s). By using the zero-pole assignment of GPIt (s), the compensated transfer function -Gvcomt (s) presents stable features, which is also verified from the bode plots of the closed-loop transfer function Gvct (s).

Similarly, the bode plots of separate PV voltage control are shown in Fig. 9 (b). From Fig. 9 (b) and (25), we know that the Gvok (s) is not stable. Compensated by the PI regulator GPIk(s), an 87.5 deg phase margin is shown in -Gvcomk (s). The closed-loop transfer function Gvck (s) also confirms its stable feature.

Fig. 10 shows the bode plots of transfer functions for each module’s dc-link peak voltage control loop. When using a proportional gain KdPk, the inductor L2 current shows a

faster response without loss of the stability, as shown in Fig. 10 (a). From Fig. 10 (b), the dc-link peak voltage closed-loop’s stability is greatly improved by decreasing the crossover frequency. As a result, the closed-loop transfer function GVdck (s) presents a fast and robust characteristic.

VI. SIMULATION AND EXPERIMENTAL VERIFICATIONS A seven-level qZS-CMI for grid-connected PV power

system is prototyped. Two Agilent E4360A Solar Array Simulators (SAS) are used to emulate the electrical behavior of PV arrays. Each SAS has two channel outputs, and each channel is with maximum 120-V maximum power point (MPP) voltage (Vmp) and 5-A MPP current (Imp). Simulation and experimental results are shown in Figs. 11-15.

A. DC-Link Voltage Balance Test

0.1906 0.1908 0.19100

306090

120150

Vpv

1 &

VD

C1 (V

)

T ime (s)

0.1906 0.1908 0.19100

306090

120150

Vpv

2 &

VD

C2 (V

)

T ime (s)

0.15 0.155 0.16 0.165 0.17 0.175 0.18 0.185 0.19 0.195 0.2-500-405

-270

-135

0

135

270

405500

VH

& V

ac (V

)

T ime (s)

vPV1 vDC1

vPV2

vDC2

vac

vH

Fig. 11. Simulation results of qZS-CMI at different PV array voltages.

Shoot-through states

vPV1

vDC1

vDC2

vPV2

(a)

vH vPV2

vPV1 iac, 10 A/div

(b)

Fig. 12. Experimental results of qZS-CMI at different PV array voltages. (a) Two modules’ PV array voltages and dc-link voltages; (b) two PV array voltages, 7-level output voltage, and load current.



The different PV array voltages are performed to the three qZS-HBI modules. The second module’s PV voltage vPV2 is set to 70 V and the others are at 90 V. A 50 Ω resistor is used as ac load in this test. All the voltages in experimental results are 100 V/div.

From (1), the 136-V dc-link voltage of qZS-HBI module is required to support the 230-V grid. Fig. 11 shows the simulation results, where the second module’s dc-link peak voltage is boosted to the same voltage value when compared to other modules, but with a longer shoot-through time interval. And the qZS-CMI outputs the 7-level voltage with equal voltage step from one level to another level.

Fig. 12 shows the experimental results. We can find that the same qZS-CMI output voltages and currents are achieved in Fig. 11 (or Fig. 12), which is derived from the designed dc-link peak voltage control.

B. Grid-Tie Investigation The qZS-CMI is connected to the grid in order to test the

proposed grid-tie control. Fig. 13 shows the PV array’s power-voltage characteristics. The measured PV array voltage and current of each module are used to calculate the actual PV power and the MPPT algorithm searches for the PV voltage reference at the MPP, which is refreshed every 0.05 second. Here, the perturbation & observation (P&O) MPPT strategy is applied in considering the excellent tracking efficiency and easy implementation [15].

0 50 100 1500

100

200

300

400

500

600

700

Pow

er (W

)

Voltage (V)

MPP=(105.2 V, 505.7 W)

MPP=(106.1 V 366.8 W)

38℃, 700 W/m2

25℃, 1000 W/m2

MPP=(120 V, 600 W)

38℃, 900 W/m2

Fig. 13. PV array power-voltage characteristic.

At first, the three modules are all working at 900 W/m2, and the all initial voltage references of MPPT algorithms are given at 105 V from Fig. 13. The second module’s irradiation decreases to 700 W/m2 from 1 s to 2 s in simulation. Fig. 14 shows the simulation results. In the experiments, the same test conditions of irradiation and temperature can be implemented by setting the curves of Agilent SAS. Fig. 15 shows the experimental results.

Fig. 14 (a) shows the total PV voltage (sum of three PV panel voltages) and reference, PV panel voltages and references of modules 2 and 3, respectively.

Fig. 14 (b) is the enlarged detail of Fig. 14 (a). It can be seen that the excellent tracking performance is achieved during 0-1 second; even though the second module’s PV irradiance changes after 1 s, the vPV2 still tracks the reference very well after a very short transient.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

100

200

300

400

Vpv

t & V

pvt*

(V)

Time (s)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

50

100

150

Vpv

2 &

Vpv

2* (V

)

Time (s)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

50

100

150

Vpv

3 &

Vpv

3* (V

)

Time (s)

0.8 1 1.2 1.480

100

120

(a)

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2305

315

325

Vpv

t&V

pvtr

ef (V

)

T ime (s)

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2100

105

110

Vpv

2&V

pv2r

ef (

V)

T ime (s)

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2100

105

110

Vpv

t3&

Vpv

3ref

(V

)

T ime (s) (b)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-400

-200

0

200

400

Vg

(V)

T ime (s)0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-20

0

20

is (A

)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-600

-300

0

300

600

V H (V

)

T ime (s)

(c)

0.95 0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.04 1.05-500

-250

0

250

500

V H (V

)

T ime (s)

0.95 0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.04 1.05-400

-200

0

200

400

Vg

(V)

T ime (s)0.95 0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.04 1.05

-20

0

20

is (A

)

(d)

Fig. 14. Simulation results at the grid-tie case. (a) and (b) for PV voltages at MPPT; (c) and (d) for qZS-CMI output voltage, grid voltage and current.



iPV(1,3), 2 A/div

iPV2, 2 A/div

(a)

Irradiation changes

(b)

Irradiation changes

vPV2, 100 V/div vH, 250 V/div

ig, 20 A/div

vg, 250 V/div

(c)

Fig. 15. Experimental results at the grid-tie case. (a) Three PV panel currents; (b) the second module’s PV panel voltage, qZS-CMI output voltage, grid voltage and the grid-injected current; (c) results zoomed in when the second module’s PV irradiation changes from 900 W/m2 to 700 W/m2.

Figs. 14 (c) and (d) shows that the grid-injected current is exactly in phase with the grid voltage even at the irradiance changing moment. The solar irradiation does not affect the seven-level staircase output voltage of qZS-CMI, but the lower irradiation makes the grid-injected current reduced.

The identical experimental results are shown in Fig. 15. As in Fig. 15 (a), the lower solar irradiation reduces the second module’s PV panel current, the first and third modules’ PV panel currents are not changed due to their constant irradiations. The second module’s low irradiation causes the system power reduced, so the grid-injected current decreases, as Fig. 15 (c) shows. No matter the solar irradiation changes or not, the qZS-CMI always outputs consistent voltage, which verifies the voltage balance ability. In simulation and experiments, the irradiation change may be derived from the shading of cloud or other objects. Figs. 14 and 15 validate the proposed control methods.

VII. CONCLUSION This paper proposed a control method for qZS-CMI

based single-phase grid-tie PV system. The grid-injected power was fulfilled at unity power factor, all qZS-HBI modules separately achieved their own maximum power points tracking even if some modules’ PV panels had different conditions. Moreover, the independent dc-link voltage closed-loop control ensured all qZS-HBI modules have the balanced voltage, which provided the high quality output voltage waveform to the grid. The control parameters were well designed to ensure system stability and fast response. A multilevel SVM integrating with shoot-through states was proposed to synthesize the staircase voltage waveform of the single-phase qZS-CMI.

The simulation and experiment were carried out on the 7-level qZS-CMI prototype. The qZS-CMI based grid-tie PV system was tested. The simulation and experimental results verified the proposed qZS-CMI based grid-tie PV power system and the proposed control method.

In principle, the proposed system can work with the weak grid, even though this paper did not address this topic. In future, we will focus on the application to the weak grid, and the detailed analysis and experimental results will be disclosed in the next paper.

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Balance Control of PV Cascaded Multilevel Grid-Connected Inverters Under Level-Shifted and Phase-Shifted PWMs," IEEE Trans. Ind. Electronics, vol.60, no.1, pp.98-111, Jan. 2013.

[2] F. Filho, H.Z. Maia, T.H.A. Mateus, B. Ozpineci, L.M. Tolbert, J.O.P. Pinto, "Adaptive Selective Harmonic Minimization Based on ANNs for Cascade Multilevel Inverters With Varying DC Sources ,"IEEE Trans. Ind. Electronics, vol.60, no.5, pp.1955-1962, May 2013.

[3] Kouro S., Fuentes C., Perez M., Rodriguez J., "Single DC-link cascaded H-bridge multilevel multistring photovoltaic energy conversion system with inherent balanced operation," in IECON 2012 - 38th Annual Conference on IEEE Industrial Electronics Society, pp.4998-5005, 25-28 Oct. 2012.

[4] Rivera S., Kouro S., Wu B., Leon J. I., Rodriguez J., Franquelo L.G., "Cascaded H-bridge multilevel converter multistring topology for large scale photovoltaic systems," in 2011 IEEE International Symposium on Industrial Electronics (ISIE), pp.1837-1844, 27-30 June 2011.

[5] Liming Liu, Hui Li, Yi Zhao, Xiangning He, Shen Z.J., "1 MHz cascaded Z-source inverters for scalable grid-interactive photovoltaic (PV) applications using GaN device," in 2011 IEEE Energy Conversion Congress and Exposition (ECCE), pp.2738-2745, 17-22 Sept. 2011.

[6] Yan Zhou, Liming Liu, Hui Li, "A High-Performance Photovoltaic Module-Integrated Converter (MIC) Based on Cascaded Quasi-Z-Source Inverters (qZSI) Using eGaN FETs," IEEE Transactions on Power Electronics, vol.28, no.6, pp.2727-2738, June 2013.

[7] D. Sun, B. Ge, F.Z. Peng, A. Haitham, D. Bi, Y. liu, "A new grid-connected PV system based on cascaded H-bridge quasi-Z source inverter," in 2012 IEEE International Symposium on Industrial Electronics (ISIE2012), pp.951-956, 28-31 May 2012.

[8] Li Y., Jiang S., Cintron-Rivera J., Peng F., "Modeling and control of quasi-Z-source inverter for distributed generation applications," IEEE Trans. Ind. Electronics, vol.60, no.4, pp.1532-1541, April 2013.

[9] B. Ge, H. Abu-Rub, F. Peng, Q. Lei, de Almeida A., Ferreira F., D. Sun, Y. Liu, "An energy stored quasi-Z-source inverter for



application to photovoltaic power system," IEEE Trans. Ind. Electronics, vol.60, no.10, pp.4468-4481, Oct. 2013.

[10] H. Abu-Rub, M. Malinowski, K. Al-Haddad, "Power Electronics for Renewable Energy Systems, Transportation and Industrial Applications", John Wiley & Sons, Hoboken, NJ, 2014.

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[12] Zmood D.N., Holmes D.G., "Stationary frame current regulation of PWM inverters with zero steady-state error," IEEE Transactions on Power Electronics, vol.18, no.3, pp. 814-822, May 2003.

[13] Yushan Liu, Baoming Ge, FangZheng Peng, Haitham A.R., Almeida A.T. de, F.J.T.E. Ferreira, "Quasi-Z-Source inverter based PMSG wind power generation system," in 2011 IEEE Energy Conversion Congress and Exposition (ECCE), vol., no., pp.291-297, 17-22 Sept. 2011.

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Yushan Liu (S’12) received the B.Sc. degree in automation from Beijing Institute of Technology, Beijing, China, in 2008. She is currently working toward the Ph.D. degree in electrical engineering, from the School of Electrical Engineering, Beijing Jiaotong University, Beijing.

She is also currently a Research Assistant with the Department of Electrical and Computer

Engineering, Texas A&M University at Qatar, Doha, Qatar. Her research interests include modeling and control of Z-source inverters, cascade multilevel inverters, PV power generation, and battery energy storage.

Baoming Ge (M’11) received the Ph.D. Degree in electrical engineering from Zhejiang University, Hangzhou, China, in 2000.

He was a Postdoctoral Researcher in the Department of Electrical Engineering, Tsinghua University, Beijing, China, from 2000 to 2002, was a Visiting Scholar in the Department of Electrical and Computer Engineering, University of Coimbra, Coimbra, Portugal, from 2004 to 2005, and was a

Visiting Professor in the Department of Electrical and Computer Engineering (ECE), Michigan State University (MSU), East Lansing, Michigan, from 2007 to 2008, and currently he is working with the ECE of MSU; he also is a Professor with the School of Electrical Engineering, Beijing Jiaotong University, Beijing, where he has joined since 2002. His research interests include renewable energy power generation, electrical machines and control, power electronics systems, and control theories and applications.

Haitham Abu-Rub (M’99–SM’07) received the M.Sc. degree in electrical engineering from Gdynia Marine Academy, Gdynia, Poland, in 1990 and the Ph.D. degree from the Gdansk University of Tech nology, Gdansk, Poland, in 1995.

For eight years, he was with Birzeit University, Birzeit, Palestine, where he was first an Assistant Professor and then an Associate Professor and was

the Chairman of the Electrical Engineering Department for four years. He is currently a Full Professor with the Department of Electrical and

Computer Engineering, Texas A&M University at Qatar, Doha, Qatar. His main research interests are the electrical machine drives and power electronics.

Dr. Abu-Rub was a recipient of many international prestigious awards, such as the American Fulbright Scholarship (at Texas A&M University, College Station), the German Alexander von Humboldt Fellowship (at Wuppertal University, Wuppertal, Germany), the German DAAD Scholarship (at Ruhr University Bochum, Bochum, Germany), and the British Royal Society Scholarship (at the University of Southampton, Southampton, U.K.).

Fang Z. Peng (M’92–SM’96–F’05) received the B.S. degree in electrical engineering from Wuhan University, Wuhan, China, in 1983, and the M.S. and Ph.D. degrees in electrical engineering from Nagaoka University of Technology, Nagaoka, Japan, in 1987 and 1990, respectively.

From 1990 to 1992, he was a Research Scientist with Toyo Electric Manufacturing Company, Ltd.,

Toyo, Japan, where he was engaged in the research and development of active power filters, flexible ac transmission system (FACTS) applications, and motor drives. From 1992 to 1994, he was with the Tokyo Institute of Technology, Tokyo, Japan, as a Research Assistant Professor, where he initiated a multilevel inverter program for FACTS applications and a speed-sensorless vector control project. From 1994 to 1997, he was a Research Assistant Professor with the University of Tennessee, Knoxville, where he was also a Staff Member. From 1994 to 2000, he was with the Oak Ridge National Laboratory, where, from 1997 to 2000, he was the Lead (Principal) Scientist with the Power Electronics and Electric Machinery Research Center. Since 2000, he has been with Michigan State University, East Lansing, where he is currently a Professor with the Department of Electrical and Computer Engineering. He is the holder of more than ten patents.

Dr. Peng was the recipient of the 1996 First Prize Paper Award and the 1995 Second Prize Paper Award of the Industrial Power Converter Committee of the IEEE Industry Applications Society Annual Meeting, the 1996 Advanced Technology Award of the Inventors Clubs of America, Inc., the International Hall of Fame, the 1991 First Prize Paper Award of the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, and the 1990 Best Paper Award of the Transactions of the Institute of Electrical Engineers of Japan, and the Promotion Award of the Electrical Academy. He has served the IEEE Power Electronics Society in many capacities, such as the Chair of the Technical Committee for Rectifiers and Inverters, an Associate Editor for the IEEE TRANSACTIONS ON POWER ELECTRONICS, Region 1–6 Liaison, and Member-at-Large.

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