1 mhz cascaded z-source

8/2/2019 1 MHz Cascaded Z-Source

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1 MHz Cascaded Z-Source Inverters for Scalable Grid-Interactive Photovoltaic

(PV) Applications Using GaN Device

Liming Liu, Hui Li

Florida State University

Tallahassee, FL 32310, [email protected],

[email protected]

Yi Zhao, Xiangning He

Zhejiang University

Hangzhou, Zhejiang 310058, [email protected],

[email protected]

Z. John Shen University of Center Florida

Orlando, FL 32826, USA [email protected]

Abstract --This paper presents a scalable cascaded Z-source

inverter for residential PV systems with high efficiency and high

switching frequency. The commercial low voltage Gallium

Nitride (GaN) device with low loss and high frequency is used to

facilitate each Z-source inverter cell modular. The

comprehensive Z-source network is designed based on the

innovative equivalent AC circuit model. A detailed efficiency

analysis is applied to a 3kW single phase grid-connected PV

system with four cascaded Z-source inverter cells and 1MHz

output frequency. The proposed topology also has the advantage

to achieve independent maximum power point tracking (MPPT)

control for each module and therefore improve the PV energyharvesting capability.

Index Terms — Cascaded Z-Source Inverter, Gallium Nitride

(GaN) Device, Photovoltaic (PV) System, Z-Source Network

Design

I. I NTRODUCTION

Current residential photovoltaic (PV) systems are

typically constructed from ten to a few hundred series-

parallel connection PV modules connected to a common DC

bus inverter [1-3]. One main reason that prevents the grid-

connected PV systems from realizing its full market potentialis the power losses due to the module mismatch, orientation

mismatch, partial shading, and MPPT inefficiencies. Theconventional single DC bus inverter and MPPT methods both

can not solve the above issues due to multiple local peak

power points [4-5]. The cascaded dc-dc converter topology,

as shown in Fig.1, can achieve MPPT for each PV module,which reduces the above power loss [6-7]. However, the

configuration has dc-dc and dc-ac conversion stages, which

decreases the overall system efficiency. In addition, the

switching frequency of dc-ac inverter is limited leading to the

big size filter and large electrolyte capacitors. Cascadedmultilevel inverter topology, as shown in Fig.2, can achieve

MPPT for each PV module, single stage energy conversion,

as well support a higher equivalent PWM frequency and a

larger DC bus voltage [8-9]. Nevertheless, the H-bridge

inverter still lacks boost function so that the inverter KVA

requirement has to be increased twice with a PV voltagerange of 1:2. Moreover, the high switching losses at high

switching frequencies still present a daunting challenge.

This paper proposed a scalable cascaded Z-source inverter

configuration for residential PV system as shown in Fig.3.The proposed PV system can achieve single energyconversion and boost function. The commercial low voltage

GaN device can be used to facilitate the each Z-source

inverter cell modular, which reduces losses significantly and

achieves high efficiency [10]. The integrated Z-source

network in each module is immune to shoot-through faults

especially operating at high switching frequency and

enhances the system reliability. Independent MPPT for each

Z-source inverter module can implement an efficient PV

energy conversion.

In this paper, the PV system with equivalent 1MHz output

frequency has been achieved due to advanced GaN devices

and phase-shift PWM technology so the size and weight of line filter can be reduced significantly and good power

quality can be maintained as well. From the capability of

double fundamental frequency (DFF) power oscillation

handling and high frequency ripple attenuation point of view,

the comprehensive Z-source network design has been

developed based on an innovative equivalent AC circuit

model for the single phase PV system. The efficiency of each

Z-source inverter module is analyzed. The effect of

Fig.1 Grid connected PV system with Fig.2 Grid connected PV system with Fig.3 Proposed PV system circuit configuration cascaded DC-DCconverters cascaded H-bridge inverters with cascaded Z-source inverters

978-1-4577-0541-0/11/$26.00 ©2011 IEEE 2738



commercial devices selection for the proposed PV system and

switching pattern on the efficiency has been discussed.

Finally, the detail power loss derivation is provided.

II. SYSTEM DESCRIPTION AND PARAMETERS SELECTION

The 3kW/240V single phase grid-connected PV system

with four cascaded Z-source inverter modules (ZSIM) and1MHz output frequency is developed as shown in Fig.4. The

200V/12A/25mΩ GaN transistors recently introduced to the

market by EPC Corporation are used in each ZSIM. Each

ZSIM is a standardized open-frame power module with

750W. The input voltage of each PV module varies between

60V and 120V under different solar irradiation levels. In

order to generate 1 MHz operation frequency at output

terminals, the switching frequency of each ZSIM is 125 kHz

due to phase-shift PWM modulation method. The dc voltageafter Z-source network is controlled to 135V during non-

shoot-through period. There are two shoot-through states per

switching cycle as shown in Fig.5. T s is the switching cycle

and T st is the shoot-through period. The peak carrier voltage

is V tri. In the most challenge case, PV module is controlled togenerate the full power 750W under lowest PV voltage V pv_low.The peak value of each ZSIM output voltage V peak is equal to

the shoot-through command line Bline. The dc voltage after Z-

source network can be calculated by:

_ 2

dc peak pv lowV V V = − (1)

where V peak is selected to 97.5V considering the possible

maximum output voltage of ZSIM, V pv_low is 60V. The systemcircuit parameters are shown in Table. I. The detailed Z-

source network design is introduced in the following section.

The PV system is able to operate in stand-alone mode andgrid-connected mode through a static transfer switch (STS)

according to the system requirement.

III. Z-SOURCE NETWORK DESIGN

A. Z-source inductor design

The Z-source network design is critical for the system

efficiency evaluation. The Z-source inductors are useful for reducing current ripple, as well Z-source capacitors and input

capacitor can handle voltage ripple. The maximum current

through the inductor occurs during maximum shoot-through

duty cycle, which causes maximum ripple current. In the

design, 40% current ripple through the inductors during

maximum power operation is chosen. Based on Fig.5, the

inductance can be calculated by:

( )1

2

ZC

ZL

sw ZL

V M L

f I

−=

Δ(2)

where V ZC =(V dc+V pv_low)/2 is the Z-source capacitor voltage,

V dc is the dc voltage after Z-source network, M=V peak /V tri is

modulation index, V tri is the carrier peak value, f sw is

switching frequency, Δ I ZL is the allowed maximum Z-source

inductor current ripple.

B. Input capacitor design

For the single phase inverter system, the instantaneousoutput power includes dc component and DFF components.

The peak to peak value of the DFF power is twice dc power,

which is PV power. From the energy conservation point of

view, the DFF power should be absorbed by the input

capacitor and Z-source capacitors, which causes DFF voltageripple. Since the Z-source capacitor voltage V ZC is much

greater than input capacitor voltage V pv, Z-source capacitors

should be used to deal with the DFF power. Otherwise, the

Z-source Module 1

S1 S2

S3 S4

C ZC

L ZL

L ZL

C ZC

200V GaN

60~120V 135V

5.6A

STS

LocalLoad

L f /2 PCC

v1

vs v g

i L1 i g

Z-source Module 2

S5 S6

S7 S8

C ZC

L ZL

L ZL

C ZC

200V GaN

135V

5.6A

Z-source Module 3

S9 S10

S11 S12

C ZC

L ZL

L ZL

C ZC

200V GaN

135V

5.6A

Z-source Module 4

S13 S14

S15 S16

C ZC

L ZL

L ZL

C ZC

200V GaN

135V

5.6A

v2

v3

v4

240V

V pv1

PV

Module C in

V dc1

V dc2

V dc3

V dc4 L f /2

750W

60~120V

V pv2

PV

Module C in

750W

60~120V

V pv3

PV

Module C in

750W

60~120V

V pv4

PV

Module C in

750W

D

D

D

Di pv4

i pv3

i pv2

i pv1

Fig.4 Proposed PV system with four cascaded Z-source inverter modules at3kW

V t r i

V p e a k

Fig.5 Z-source inverter modulation with maximum shoot-through dutyratio

TABLE I: SYSTEM CIRCUIT PARAMETERS

Parameters Symbol Value

Each

Z-sourceinverter module(ZSIM)

DC link voltageV dc1, V dc2

V dc3, V dc4 135V

PV VoltageV PV1, V PV2

V PV3, V PV4 60-120V

Full PV power P in1, P in2

P in3, P in4 750W

Switching frequency f SW 125kHz

Z-source inductor L ZL 18 μH

Z-source capacitor C ZC 2500 μF

Input capacitor C in 25 μF

Cascaded inverter number

n 4

Grid

Filter Inductor L f 100 μH

Rated RMS phasevoltage

V g 240V

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total capacitance will increase which resulting in low power

density. In addition, input capacitor with big capacitance will

cause the phase-shift between V ZC and V pv due to the

equivalent LC filter on DC side, which will increase the

burden of total capacitors to handle the DFF power.

According to the above analysis, the input capacitor is used

for handling most high frequency voltage ripple. The

maximum high frequency voltage ripple occurs during shoot-

through period and PV module only delivers power to input

capacitor. In order to achieve good voltage performance, highfrequency voltage ripple is limited with 1%. The capacitance

can be determined by:

( ) ( )max max

2

_ _ _

1 1

2 2 1%in

sw pv low pv hf sw pv low

P M P M C

f V V f V

− −= =

Δ ×(3)

where ΔV pv_hf is the allowed maximum input capacitor high

frequency voltage ripple, P max is 750W.

C. Z-source capacitor design

The Z-source capacitor is used to handle the DFF voltage

ripple and partly high frequency voltage ripple. In order to

obtain suitable Z-source capacitance, the Z-source inverter

operation mode is firstly analyzed in three different operation

modes as shown in Fig.6. The relationship between voltage,current and operation mode can be expressed by:

( ) ( )

( )

( ) ( )

( )

( )

0 1

0 1

2

0 1

2

2 2

2 sin

sin

ZL ZL ZL st ZC pv ZC pv ZC

nst pv nst st ZC

pv

cin in st pv pv ZL pv ZL Lf

pv nst ZL g

ZC ZC ZC st ZL ZL ZL Lf

nst st ZL g

diV L D V D V V D V V

dt

D V D D V

dV i C D i D i i D i i i

dt

i D i MI t

dV i C D i D i D i i

dt

D D i MI t

ω

ω

⎧= = + − + −⎪

⎪= − −⎪

⎪⎪

= = + − + − +⎪⎨⎪ = − +⎪

= = − + + −

= − −⎩

⎪⎪⎪⎪

(4)

where D st is the shoot-through duty ratio; Dnst = D0+ D1 is the

non-shoot-through duty ratio; D0 is tradition zero duty ratio; D1=Msinωt is active state duty ratio; i Lf = I g sinωt is the AC

filter current; ω=2π ×60 (rad/s); I g is the peak value of the

grid current.

Among AC and DC components included in (4), AC

components are useful for the Z-source capacitors design.They can be extracted from (5) and then converted as (6):

( )

( )

12 cos2

2

1cos2

2

ZL pv ZC ZL nst nst st

pv pv ZLin nst g

ZC ZL ZC nst st g

di L D V D D V

dt

dV C i D i MI t

dt

dV C D D i MI t

dt

ω

ω

⎧= − −⎪

⎪⎪⎪

= − −⎨⎪⎪

= − +⎪⎪⎩

(5)

1

1 12 cos2

2

ZLnst ZL pv ZC

nst st nsht st

pvnst st st in pv ZL

nst nst st nst st nst st

ZL ZL g st

nst

ZC

nst

D L diV V

D D D D dt

D D D C dV i i

D D D D D D D dt

i MI t D i D

C

D

ω

⎛ ⎞ ⎛ ⎞= +⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟− −

⎝ ⎠ ⎝ ⎠⎡ ⎤⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞−

− −⎢ ⎥⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟− − −⎢ ⎥⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎣ ⎦

⎛ ⎞= − − +⎜ ⎟

⎝ ⎠

⎛

1 1cos2

2

ZC ZL ZL g st

nst

dV i MI t D i

dt Dω

⎧⎪

⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪ ⎞ ⎛ ⎞⎛ ⎞⎪ = − − +⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟ ⎜ ⎟⎪ ⎝ ⎠⎝ ⎠ ⎝ ⎠⎩

(6)

wherenst

D M = and 1 st D M = − in the worst case;

1cos2

2 s g

nst

M i I t

Dω = − .

According to (6) and Fig.6, the equivalent AC circuit

model is developed as shown in Fig.7. Due to the DFF

current ripple is absorbed by Z-source network, ACcomponent of PV current can be ignored. Therefore, one can

obtain the relationship of current and voltage as follows:

' ' '

10

10

ZL Cin ZC ZL

ZL ZC s ZL

Cin Cin ZL ZL ZC ZC

M i i i i

M

M i i i i

M

i Z i Z i Z

⎧ −⎛ ⎞+ + + =⎪⎜ ⎟

⎝ ⎠⎪⎪ −⎛ ⎞⎪

− − − =⎨ ⎜ ⎟⎝ ⎠⎪

⎪= +

⎪⎪⎩

(7)

(a) (b) (c)Fig.6 Z-source inverter operation mode: (a) shoot-through state; (b) traditional zero state; (c) active state

+

+

ZL

D st i

Dnst

1

pvi

Dnst

2 in

nst

D Dnst st

DC

−

ZL L

D Dnst st

−

ZC

Dnst

C

ZL

st

nst

i D

D

cini

ZLi

ZC i

si

ZC

V

ZL

V

PV

nst

nst st

V D

D D−

Fig.7 The equivalent AC circuit model of Z-source inverter

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After getting the currentCini ,

ZC i and ZLi , the peak-peak

voltage ripple on input capacitor ΔV pv, Z-source capacitor

ΔV ZC and DC link after Z-source network ΔV dc can be

calculated by (8).

' ' '

' ' '

' ' '

' ' '

' ' ' ' ' '

' ' '

1

2 12

1

2 12

12

2 12

ZL ZC Cin

Cin ZL ZC

pv ZL Cin ZC

ZC

Cin ZL ZC dc

ZL ZC Cin ZC ZL Cin

Cin ZL ZC

Z Z Z M

M Z Z Z

M

V Z Z Z M

V M

Z Z Z V M

Z Z Z Z Z Z M

M Z Z Z

M

⎡ ⎤⎛ ⎞−⎢ ⎜ ⎟⎝ ⎠⎢

−⎢ ⎛ ⎞+ + ⎜ ⎟⎢

⎝ ⎠⎢⎢ ⎛ ⎞

Δ⎡ ⎤ − −⎢ ⎜ ⎟⎢ ⎥ ⎝ ⎠⎢Δ =⎢ ⎥ ⎢ −⎛ ⎞

+ +⎢ ⎥Δ ⎢ ⎜ ⎟⎣ ⎦ ⎝ ⎠⎢⎢

− − −⎢⎢

−⎛ ⎞⎢+ + ⎜ ⎟⎢ ⎝ ⎠⎣

g I

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(8)

where ' '

2

2 11/ ω

⎛ ⎞−⎛ ⎞= ⎜ ⎟

⎜ ⎟⎝ ⎠⎝ ⎠Cin in

M Z C

M ;

' ' 11/ ω

⎛ ⎞=

⎜ ⎟⎝ ⎠ ZC ZC

Z C M ;

' ' 11/

2 1ω

⎛ ⎞⎛ ⎞= ⎜ ⎟⎜ ⎟

−⎝ ⎠⎝ ⎠ ZL ZL Z L

M ; ' 2 120ω π = × .

Based on (2), (3) and (8), the relationship between

voltages ripples ΔV pv, ΔV ZC , ΔV dc and C ZC can be obtained in

the Fig.8. It can be seen from Fig.8 that the ΔV pv is highest.

In order to achieve good voltage performance and power

density, ΔV pv is limited with 5%. Fig.9 shows therelationship among C in, C ZC and ΔV pv. It is obvious that Z-

source capacitors can handle the DFF voltage ripple better

than input capacitor.

IV. EFFICIENCY A NALYSIS

The commercial devices selection and switching patternare both critical for the ZSIM efficiency. The detail Z-source

network parameters and commercial device selection for each

module in Fig.4 are designed in Table II. Considering the

actual operation current, each device includes two 200V GaN

devices in parallel. In order to reduce the size of Z-source

network and effectively handle the DFF and high frequency

ripple, two hybrid capacitors are series and then paralleled

with one ceramic capacitor, which composes one Z-source

capacitor C ZC . The hybrid capacitors are used to handle DFF

power oscillation and the ceramic capacitor deals with high

frequency ripple. By this way, the efficiency of Z-source

network can be improved.

The switching losses and conduction losses of the active

switches are relative to the switching pattern. In this

efficiency analysis, unipolar & frequency multiplication

method is applied. The following power loss analysis focuses

on ‘Module1’ in Fig.4.

A. GaN devices power loss

As mentioned above, each ZSIM includes eight GaN

devices. The power loss of GaN devices includes mainlyswitching loss and conduction loss. The instantaneous

currents on Z-source inductor and AC inductor filter will

C ZC ( μF)

Δ pvV

Δ ZC V

Δdc

V

Fig. 8 The relationship between voltages ripples ΔV pv, ΔV ZC , ΔV dc and C ZC

C in ( μF) C Z C ( μ F

)

Fig.9 Input capacitor voltage ripple with different input capacitance C in

and Z-source capacitor C ZC

TABLE II: Z-SOURCE NETWORK PARAMETERS AND COMMERCIAL DEVICE

Device Parameters

S1~S4Switching Device

CellGaN N/A Vds=200V Ic=12A Rdson=25m

C ZC Hybrid Capacitor EVANS THRQ5 7500μF

Vc=100V@85ºC,Vc=60V@125 ºC

Iripple=6A@tr=30 ºC Resr_hy=35m

Ceramic Capacitor GaN

AMC_201P02W256KJ4C25 μF Vc=200V Iripple=10A Resr_ce=5m

C in Ceramic Capacitor AMC_201P02W256KJ4C 25 μF Vc=200V Iripple=10A Resr_ce=5m

L ZL Ferrite Inductor EI30 18μH N/A Irms=13A Ron=5.2m

D Schottky Diode On Semi MBRF20200CT N/A Vrrm=200V IF=20A VF=0.8V

2741



dominate the power loss, which can be derived as follows.The instantaneous equivalent grid voltage for each ZSIM

in half of fundamental cycle can be expressed as:

( ) _ ( ) sin 1, 2, ,

g peak s

s

nV n V n N

N π

⎛ ⎞= =⎜ ⎟

⎝ ⎠ (9)

where V g_peak is the peak value of the equivalent grid voltage,

that is 60 2 V. N s is the number of switching frequency in

half of fundamental frequency 10402

s s

g

f N

f = .

The instantaneous current through AC filter inductor in

half of fundamental cycle can be given by:

( ) _ ( ) sin 1,2, ,

Lf Lf peak s

s

n I n I n N

N π

⎛ ⎞= =⎜ ⎟

⎝ ⎠ (10)

where I Lf_peak is the peak value of the AC filter inductor

current, that is _

7502

60 Lf peak i = A.

The duty cycle can be determined as:

( )( )

( ) 1,2, , g

s

dc

V n D n n N

V = = (11)

where V dc is the dc link voltage 135V of inverter as shown in

Fig.4.

The shoot-through period can be obtained in (11):

_ 11

2

pv low

st s

dc

V T T

V

⎡ ⎤⎛ ⎞= −⎢ ⎥⎜ ⎟

⎢ ⎥⎝ ⎠⎣ ⎦(12)

where V pv_low is 60V, V dc is 135V and T s is 8 µs.In one switching cycle, the total input charge Qin should be equal to the total output charge Qout . As shown in Fig.6,the total input charge can be expressed as:

in pv sQ I T = (13)

where max _ pv pv low I P V = is 12.5A in the most challenge case.

During shoot-through state and traditional zero state, I Lf (n) is zero. So the total charge on the dc side of inverter can begiven by:

( )( ) ( ) 1, 2, , Lf Lf s sQ I n D n T n N = = (14)

The total charge on the Z-source inductor can be writtenas:

( ) ( )( ) 1,2, ,

ZL ZL s st s

Q I n T T n N = − = (15)

where I ZL (n) is the instantaneous current through Z-sourceinductor.

Based on (12)-(14) and ignoring the charge on inputcapacitor C in, the relationship between Qin and Qout can beexpressed as:

2in ZL Lf Q Q Q= − (16)

Accordingly, I ZL (n) can be calculated by:

( )

( )( )

( )( ) 1,2, ,

2

Lf s pv s

ZL s

s st

I n D n T I T I n n N

T T

+= =

− (17)

In view of Bline and v1 as shown in Fig.5, as well as theunipolar & frequency multiplication method application, theswitching pattern in one switching cycle is addressed in TableIII and Fig.10. The GaN devices S1-S4 turn on and off only

once in one switching cycle, respectively. Due to the free-wheeling diode (D2 and D3), the soft-switching can beachieved at t2 and t3 for S2, and t7 and t8 for S3. In thesetransient processes, the switching loss for S2 and S3 can be

ignored. The switch-on and switch-off instantaneous currentsfor S1-S4 are I Lf (n), 2 I ZL(n), 2 I ZL(n), I Lf (n), respectively. Sothe turn-on energy loss for each ZSIM in half of fundamentalcycle can be calculated as:

_

1

2 ( ) 2 2 ( )2 2

sw on dc Lf dc ZL

n

N s tri tfu tri tfu E V I n V I n

=

+ +⎡ ⎤= +⎢ ⎥

⎣ ⎦∑ i i i i i i i (18)

(a) (b) (c) (d) (e)

Fig.10 Switching patterns under different operation modes in half of switching cycle: (a) active state (t 0-t1); (b) traditional zero state (t1-t2); (c) shoot-through

state (t2-t3); (d) traditional zero state (t3-t4); (e) shoot-through state (t4-t5)

TABLE III: GA N DEVICES SWITCHING PATTERN IN O NE SWITCHING

CYCLE Switch

Period

S1

(D1)

S2

(D2)

S3

(D3)

S4

(D4) State

t0-t1 on off off on Active

t1-t2 onon

(D2)off off

Traditionalzero

t2-t3 on on on off Shoot-through

t3-t4 on on off off Traditional

zero

t4-t5 onoff

(D2)off on Active

t5-t6 on off off on Active

t6-t7 off off on

(D3)on

Traditionalzero

t7-t8 off on on on Shoot-through

t8-t9 off off on onTraditional

zero

t9-t10 on off off

(D3)on Active

Switchingtimes(on/off)

1 1 1 1

Switchingon-off

Transientcurrent

I Lf (n) 2 I ZL(n) 2 I ZL(n) I Lf (n)

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where tri is the current rise time, tfu is the voltage fall time.The calculation of tri and tfu can refer to [11].

The turn-off energy loss for each ZSIM in half of fundamental cycle can be derived by:

_

1

2 ( ) 2 2 ( )2 2

sw off dc Lf dc ZL

n

N s tru tfi tru tfi E V I n V I n

=

+ +⎡ ⎤= +⎢ ⎥

⎣ ⎦∑ i i i i i i i (19)

where tru is the voltage rise time, tfi is the current fall time.The calculation of tru and tfi can also refer to [11].

Consequently, the switching loss for GaN devices can beexpressed as:

( ) _ _ 120 sw sw on sw off P E E = +i (20)

The conduction losses in GaN devices can be calculated

using a GaN –approximation with the drain-source on-state

resistance ( Rdson) and instantaneous current on GaN devices.

Fig.10 shows the instantaneous current on S1-S4 under three

operation modes from t0-t5.In the active state in (a), S1 and S4

turn on simultaneously. The instantaneous current is I Lf (n). In

the traditional zero state in (b), S1 and S2 turn on

simultaneously. The soft turn-on for S2 can be achieved dueto the free-wheeling diode D2. The instantaneous current is I Lf (n). In the shoot-through state shown in (c), the S1 and S3

switch on at the same time, and S2 is still on. In this case, the

current on S1 is I Lf (n)+2I ZL(n). The currents through S3 and

S2 are 2I ZL(n) and I Lf (n), respectively. In the traditional zero

state in (d), S1 and S2 turn on simultaneously. Theinstantaneous current is I Lf (n). In the active state in (e), S1

and S4 turn on simultaneously. The soft turn-off for S2 can

be achieved due to the free-wheeling diode D2. The

instantaneous current is I Lf (n).

Therefore, the equivalent conduction loss for S1 in half of

switching cycle can be given by:

22

1 ( ) ( ) 2 ( )2 2 2

s st st

con Lf dson Lf ZL dson

T T T

E I n R I n I n R

⎛ ⎞

⎡ ⎤= − + +⎜ ⎟ ⎣ ⎦⎝ ⎠i

(21)

The equivalent conduction loss for S2 in half of switching

cycle can be expressed as:

2

2 ( )2

st con Z Lf dson

T E T I n R

⎛ ⎞= +⎜ ⎟

⎝ ⎠(22)

where T z is the traditional zero period in half of switching

cycle.


cycle can be calculated as:

[ ]2

3 2 ( )2

st con ZL dson

T E I n R= i (23)


cycle can be written as:

2

4( )

2 2

s st con Z Lf dson

T T E T I n R

⎛ ⎞= − −⎜ ⎟

⎝ ⎠(24)

Accordingly, the conduction energy loss for each ZSIM in

half of fundamental cycle can be derived by:

[ ]1 2 3 4

1

con con con con con

n

N s

E E E E E =

= + + +∑ (25)

As mentioned above, each device includes two 200V GaN

devices in parallel. So the above conduction energy loss will

be halved. Therefore, the GaN device conduction loss can be

derived by:

1202

concon

E P

⎛ ⎞= ⎜ ⎟

⎝ ⎠i (26)

B. Input diode power loss

The input diode power loss consists of switching loss and

conduction loss. However, the switching loss is very smalland can be ignored. The average current on diode is equal to

I pv. So the conduction loss of input diode can be obtained by:

dcon F pv P V I = (27)

where V F is the forward voltage drop of the diode.

C. Z-source inductor power loss

The Z-source inductor power loss is composed of core

loss and winding loss as follows:2

_ ZL core cop b e on ZL rms P P P k V R I = + = + (28)

where k b is the loss coefficient, V e is the volume of the core

shown in Table II. Ron is the resistance of the winding. I ZL_rms

is the root mean square (RMS) value of the Z-source inductor

current, which can be obtained by (29):

( )2

_

1

120

N s

ZL rms ZL s

n

I I n T =

⎡ ⎤= ⎣ ⎦∑i i (29)

D. Z-source capacitor power loss

Aforementioned, each Z-source capacitor consists of two

series hybrid capacitors and one paralleled ceramic capacitor.

The hybrid capacitors mostly contribute to handle DFF power oscillation and the ceramic capacitor is used to deal with high

frequency ripple. Therefore, the Z-source capacitor power

loss is composed of power loss on hybrid capacitor and

power loss on ceramic capacitor.

As illustrated in Fig.6, the Z-source capacitor instantaneous current in shoot-through state is I ZL(n). In the

traditional zero state, the current is -I ZL(n). In the active state,

the current is I Lf (n)-I ZL(n). In order to investigate the Z-source

capacitor power loss, the average current of Z-source

capacitor in one switching cycle is derived primarily by:

( )

( )( ) ( )

( ) ( )( ) ( ) ( ) _

1 st ZL

s

ZC avg

st Lf ZL ZL

s

T I n D n

T I n

T I n I n D n I nT

⎡ ⎤⎛ ⎞− − −⎢ ⎥⎜ ⎟

⎢ ⎥⎝ ⎠=

⎢ ⎥⎢ ⎥+ − +⎢ ⎥⎣ ⎦

i

i i

(30)

The RMS value of Z-source capacitor current can be

calculated as:

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( ) ( )( )

( )( ) ( )

2

_ 21

1120

N s ZL s

ZC rms

n Lf ZL s

I n D n T I

I I n D n T =

⎡ ⎤− +⎢ ⎥=⎢ ⎥

−⎣ ⎦

∑i i

i

i i

(31)

The above I ZC_rms is separated into two parts: the RMS

values of Z-source capacitor current at 120Hz and other high

frequency.The RMS value of Z-source capacitor current at 120Hz is

given by:

( )2

_ _120 _

1

120

N s

ZC rms ZC avg s

n

I I n T =

= ∑i i (32)

So the RMS value of Z-source capacitor current at other

high frequency is obtained by:

2 2

_ _ _ _ _120 ZC rms hf ZC rms ZC rms I I I = − (33)

As shown in Table II, the equivalent impedance of two

series hybrid capacitors is calculated as:

_

12

2 2 2hy esr hy

sw hy

Z R j f C π

= +ii i i i i

(34)

where Resr_hy is the equivalent series resistor (ESR) of the

hybrid capacitor, f sw is the switching frequency, C hy is the

capacitance of hybrid capacitor.

The equivalent impedance of the ceramic capacitors is

calculated as:

_

1

2 2ce esr ce

sw ce

Z R j f C π

= +i i i i

(35)

where Resr_ce is the ESR of the ceramic capacitor, C ce is thecapacitance of ceramic capacitor.

So the power loss on hybrid capacitors is expressed as;2

2

_ _ _ _ _120

cehy ZC rms hf esr hy ZC rms

hy ce

Z P I I R

Z Z

⎡ ⎤⎛ ⎞⎢ ⎥= +⎜ ⎟⎜ ⎟⎢ ⎥+

⎝ ⎠⎣ ⎦

i i (36)

The power loss on hybrid capacitors is given by;2

_ _ _

hy

ce ZC rms hf esr hy

hy ce

Z P I R

Z Z

⎛ ⎞= ⎜ ⎟⎜ ⎟+⎝ ⎠

i i (37)

The total power loss on Z-source capacitor is presented as:

ZC hy ce P P P = + (38)

E. Input capacitor power loss

The input capacitor power loss is related to the mean

value of input capacitor current and ESR. The input capacitor

is used to handle high frequency ripple, so the ceramic

capacitor is selected as shown in Table II. As described in

Fig.6, the input capacitor instantaneous current in shoot-

through state is I pv. In the traditional zero state, the current is I pv-2I ZL(n). In the active state, the current is I pv+ I Lf (n)-2I ZL(n).

Accordingly, the RMS value of input capacitor current can be

expressed as:

( )

( )( ) ( )( )

( ) ( )( ) ( )( )

2

2

_

12

120 2

2

pv st N

s

cin rms pv ZL s s st

n

pv Lf ZL s

I n T

I I I n T T D n T

I I n I n T D n

=

⎡ ⎤+⎢ ⎥⎢ ⎥

= − − −⎢ ⎥⎢ ⎥

+ + −⎢ ⎥⎣ ⎦

∑

i

i i i i

i i i

(39)

The power loss of input capacitor can be calculated as:

_ _ cin cin rms esr ce P I R= i (40)

where Resr_ce is the ESR of the input capacitor.According to the above analysis, the total power loss

includes the switching and conduction loss of GaN devices,input diode loss, the inductors and capacitors loss on Z-

source network, and the input capacitor loss as shown in

Table IV. The power loss of each 750 W module is calculated

around 33.2 watts so the efficiency is around 95%. Fig.10

TABLE IV: POWER LOSS FOR EACH ZSIM

DeviceNum

berPower Loss Percentage

GaN 8Switching loss 7.649W 23.0%

54.9%Conduction loss 10.589W 31.9%

Diode 1Switching loss 0W 0

30.1%Conduction loss 10W 30.1%

Z-sourceInductor

2Core loss 0.772W 2.3%

7.5%Copper loss 1.704W 5.2%

Z-sourceCapacitor

2 ESR loss 2.25W 6.8% 6.8%

InputCapacitor

1 ESR loss 0.324W 0.7% 0.7%

Total 33.288WEfficiency=(750-33.288)/750=95.

56%

Fig.10 Power loss distribution chart Fig.11 Efficiency curves of ZSIM using diode and SR

2744



shows the power loss distribution. Since the proposed

topology allows each module to switch at only a fraction of

the 1 MHz system frequency, distribution of power losses toa larger number of power devices leading to high efficiency

at 1 MHz and air cooling becomes achievable. This

architecture is particularly suitable for PV system where

distributed PV module can be monitored, controlled,maintained, or replaced if necessary. If synchronous rectifier

(SR) replaces the diode to be in series with PV module, the

efficiency of each z-source inverter module can be increased

from 95% to 96%, shown in Fig.11.

V. CONCLUSION

In this paper, a scalable cascaded Z-source inverter for

residential PV system with 1MHz frequency output has been

presented. The high switching frequency and high efficiency

of modular Z-source inverter cell has been achieved based on

the advanced GaN device, phase-shift PWM technology, and

innovative Z-source network design. In addition, the energy

harvesting capability of the PV system can be improved due

to the independent MPPT control can be realized for eachmodule using the proposed topology. The comprehensive Z-source network design is developed and the detail power loss

derivation is explored to evaluate the system efficiency in this

paper.

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[8] O.Alonso, P.Sanchis, E.Gubis and L.Marroyo, “Cascaded H-BridgeMultilevel Converter for Grid Connected Photovoltaic Generators withIndependent Maximum Power Point Tracking of Each Solar Array,” in

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[9] E. Villanueva, P. Correa, J. Rodriguez, M. Pacas, “Control of a Single-Phase Cascaded H-Bridge Multilevel Inverter for Grid-ConnectedPhotovoltaic Systems,” IEEE Trans. Ind. Electron., vol.56, no.11,

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1 mhz cascaded z-source

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