1 mhz cascaded z-source
TRANSCRIPT
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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],
Yi Zhao, Xiangning He
Zhejiang University
Hangzhou, Zhejiang 310058, [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
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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
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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.
The equivalent conduction loss for S3 in half of switching
cycle can be calculated as:
[ ]2
3 2 ( )2
st con ZL dson
T E I n R= i (23)
The equivalent conduction loss for S4 in half of switching
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
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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.
R EFERENCES
[1] Solar Edge Technologies; “Problems and Disadvantages in CurrentResidential & Commercial On-grid PV Systems” White Paper, 2009,
pp. 1-8[2] National Semiconductor; “Shade Happens,” in the 2nd Annual AEE
Solar Dealers Conference, Mesa, Arizona, February 2009, [Online].Available: http://www.aeesolar.com/trainings/presentations-2009/National_Semi-Q1-2009-AEE-Solar-Conference.pdf
[3] C. Deline, “Partially Shaded Operation of a Grid-tied PV System,” in
Proc. 34th
Photovoltaic Specialists Conference (PVSC), Philadelphia,Pennsylvanian, Jun. 7-12, 2009, pp. 1-6
[4] E. V. Solodovnik, S. Liu, and R. A. Dougal, “Power controller designfor maximum power tracking in solar installations,” IEEE Trans.
Power Electron., vol. 19, no. 5, pp. 1295–1304, Sept. 2004.[5] H. Patel, V. Agarwal, “Maximum Power Point Tracking Scheme for
PV Systems Operating Under Partially Shaded Conditions,” IEEE
Trans. Ind. Electron., vol.55, no.4, pp.1689-1698, Apr. 2008.[6] G.R. Walker, P.C. Sernia, “Cascaded DC-DC converter connection of
photovoltaic modules,” IEEE Trans. Power Electron., vol. 19, no. 4, pp. 1130–1139, Jul. 2004
[7] E. Roman, R. Alonso, P. Ibanez, S. Elorduizapatarietxe, D. Goitia,“Intelligent PV Module for Grid-Connected PV System,” IEEE Trans. Ind. Electron., vol.53, no.4, pp.1066-1073, Aug. 2006.
[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
Proc. 34th
IEEE Power Electronics Specialists Conf. ( PESC’03), Jun.2003, vol. 2, pp. 731-735
[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,
pp.4399-4406, Nov. 2009[10] Efficient Power Conversion Corporation (EPC), “EPC1010-
Enhancement Mode Power Transistor,” [Online]. Available: http://epc-co.com/epc/documents/datasheets/EPC1010_datasheet_final.pdf
[11] Dusan Graovac, Marco Purschel, Andreas Kiep, “MOSFET Power Losses Calculation Using the Data-Sheet Parameters,” Automotive Power , Application Note, vol. 1.1, July 2006
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