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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 21, NO. 6, NOVEMBER 2006
Z -Source
Inverter for Residential
Photovoltaic Systems
Yi Huang, Miaosen Shen, Student Member, IEEE, Fang Z. Peng, Fellow, IEEE, and Jin Wang, Member, IEEE
Abstract—This paper proposes a -source inverter system for
a split-phase grid-connected photovoltaic system. The operation
principle, control method, and characteristics of the system are
presented. A comparison between the new and traditional system
configurations is performed. Simulation and experimental results
are also shown to verify the proposed circuit and analysis.
Index Terms—Photovoltaic (PV), power conditioning, MPPT,
-source inverter.
I. INTRODUCTION
I
T IS believed that the distributed generation market will be
between US $10 and 30 billion by the year 2010. Due to
environmental concerns, more effort is now being put into clean
distributed power like geothermal, wind power, fuel cells, and
photovoltaic (PV) that directly uses the energy from the sun to
generate electricity. The worldwide grid-connected PV system
grows at a rate of 25% every year.
As the energy from the sun is free, the major cost of photovoltaic generation is the installation cost, which is mainly
composed of the costs of solar modules and the interface converter system, also called the power conditioning system (PCS).
With the development of solar cell technology, the price of solar
modules has dropped dramatically. A recent worldwide survey
shows that in the last three years, the retail price of solar modules
has dropped 16.95%. However, at the same time, the prices for
the PCSs almost remain the same. Furthermore, compared with
converters used in drive systems, the prices for the converters
used in PV systems are still up to 50% higher. To lower the cost
of the PCSs has become a very urgent issue of grid connected
PV systems [1].
PCS is required to convert the dc output from PV to grid synchronized 50- or 60-Hz ac. This paper proposes a -source inverter based PCS, which connects the PV arrays for residential systems that are 60-Hz, 120/240-V split phase ac in the
United States. By utilizing the -source inverter, the number of
switching components and the total volume of the system can
be minimized. Thus, the cost of the PCS is minimized.
II. BASICS OF PCS FOR RESIDENTIAL USE
In order to transfer energy from PV arrays into utility grids,
PCS converter systems have to fulfill the following three
Manuscript received March 31, 2005; revised September 8, 2005. This paper
was presented in at IPEC’05, Niigata, Japan, April 4–8, 2005. This work was
supported by the the National Science Foundation under Grant 0424039. Recommended by Associate Editor Z. Chen.
Y. Huang, M. Shen, and F. Z. Peng are with the Department of Electrical
and Computer Engineering, Michigan State University, East Lansing, MI 48824
USA (e-mail: huangyi5@msu.edu).
J. Wang is with the Ford Motor Company, Dearborn, MI 48120 USA.
Digital Object Identifier 10.1109/TPEL.2006.882913
Fig. 1. Traditional PV systems: (a) dc–ac with stepup transformer and (b) dc–ac
with dc–dc boost.
requirements:
1) to convert the dc voltage into ac voltage;
2) to boost the voltage, if the PV array voltage is lower than
the grid voltage;
3) to insure maximum power utilization of the PV modular.
Fig. 1 shows the two most commonly used converter system
configurations in practice. In the system shown in Fig. 1(a), a
transformer at line frequency is utilized to boost the voltage after
the dc–ac inverter. Usually, a line frequency transformer is associated with huge size, loud acoustic noise, and high cost. In
addition, the inverter has to be oversized to cope with the wide
PV array voltage change. The KVA rating of the inverter is doubled if the PV voltage varies at a 1 2 range. So in order to eliminate the transformer and to minimize the required KVA rating of
the inverter, in many applications, a high frequency dc-dc converter is used to boost the voltage to a constant value as shown
in Fig. 1(b). Unfortunately, the switch in the dc–dc converter
becomes the cost and efficiency killer of the system [2], [3].
Another option is to use a single-stage inverter for direct
dc–ac conversion as shown in Fig. 2. For the split-phase system
used in United States’ residential power, two 120-V ac outputs
with same ground and 180 phase difference are required. For
this purpose, there are two circuit choices for the dc–ac inverters
in the PCS: four-switch inverter and six-switch inverter. The
circuit structures of these two choices are shown in Fig. 2.
For the four-switch inverter as shown in Fig. 2(a), the neutral
point is tapped from the center of the two dc capacitors, whereas
in six-switch inverter shown in Fig. 2(b), the neutral point is
connected to the third phase leg.
0885-8993/$20.00 © 2006 IEEE
HUANG et al.:
-SOURCE INVERTER
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Fig. 3. Six-switch inverter control scheme.
6
Fig. 2. Direct PV inverter systems for 120-V split phase residential power.
(a) Four switch inverter. (b) Six switch inverter.
The two phase legs in the four-switch inverter are controlled by
synchronized pulsewidth modulation (SPWM). Two sinusoidal
control references with a 180 phase difference and the
same amplitude are utilized to compare with a triangular
carrier.
The basic control scheme of the six-switch inverter is shown
in Fig. 3. Two of the phase legs, “b” and “c,” have the exact
same SPWM control as in four-switch inverter. The third phase
leg, “a,” is usually controlled to produce a square waveform
with 50% duty ratio at the carrier frequency to serve as the
neutral phase and at the same time achieve the maximum
utilization of the dc bus voltage. The switching frequency of
the third leg can be different from the other two phase legs. By
proper coordinating the control of the neutral phase leg and
the other two phase legs, the equivalent switching frequency
can be doubled, thus the output filter can be optimized. It
is generally believed that the six-switch inverter has better
performance than the four-switch inverter for the split-phase
application [4].
III. PROPOSED
-SOURCE INVERTER SYSTEM
In the proposed PCS, a -source inverter [5] is utilized
to realize inversion and boost function in one single stage.
Fig. 4 shows the proposed system. Unlike the traditional
voltage source or current source inverters, the -source inverter
employs a unique impedance network with split inductor
and capacitor
connected in
shape. With the
impedance network, the -source inverter can advantageously
use the shoot through states to boost voltage. Furthermore,
with the ability to handle the shoot through state, the inverter
Fig. 4. Proposed PCS for PV system.
system becomes more reliable [5], [6]. The inductors and
capacitors in the -source are both energy storage devices,
so their value can be optimally designed to ensure small
size and low cost.
Compared with the systems in Fig. 1, in the proposed system,
there is no bulky transformer nor a dc–dc converter to boost the
voltage in the circuit. The size and cost are minimized. Because
no dead time is needed, the control accuracy and THD value
can also be improved. Furthermore, the split-phase -source
inverter naturally inherits all the advantages of the split-phase
six-switch inverter. Thus, the 120-V ac output filter can be optimized.
Compared with the direct inverter systems in Fig. 2, the
-source inverter has a minimum KVA requirement. For the
inverter system in Fig. 2 with a PV voltage change of 1 2 range,
the PV dc voltage needs to be 340–680 V minimum to produce
a 120 V split-phase power. Therefore, 1200-V IGBTs are
needed in the system. Given a 10-kW PV system, a 20-kW
inverter is needed to cope with the voltage change. Using the
proposed system of Fig. 4, the PV voltage can be designed to be
225–450 V, which can be inverted to 120 V split-phase power
by the -source inverter using 600-V IGBTs. In addition, the
required KVA rating of the -source inverter remains the same
10 kW for a 10-kW PV system.
Therefore, by utilizing the -source inverter, the volume, the
cost as well as the number of active switching devices are minimized. Because of the single stage operation, the efficiency of
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and , which
As described in [5] and [6], the inductors
can be wounded around the same core, have the same inducand
have the same capacitance,
tance, and the capacitors
the relationship between the output ac voltage and input dc
voltage is found as
(1)
where
voltage,
is the output peak voltage,
is the PV output
is the modulation index, which is defined by
(2)
and
is the boost factor, which is determined by
(3)
Fig. 5. Sketch map of the simple boost control.
the system can be greatly improved. In summary, the proposed
system:
1) has only one stage to realize inversion, boost, and maximum power tracking;
2) has the minimized number of switching devices;
3) needs no dead time;
4) can have shoot through state in the inverter;
5) inherits all the advantages of the six switch inverter system.
IV. CONTROL AND OPERATION PRINCIPLE
As shown in Fig. 3, when the triangular waveform is greater
than the maximum value or lower than the minimum value of
the three reference waveforms, all upper three switches or all
bottom three switches are turned on respectively, as indicated
in the shadowed area. During these periods of time, the output
voltage of the inverter is zero, i.e., zero states. For the -source
inverter, the basic idea of control is to turn zero states into shoot
through states and keep the active switching states unchanged,
thus we can maintain the sinusoidal output and at the same time
achieve voltage boost from the shoot through of the dc link [5],
[6].
Fig. 5 shows the boost control method of the split-phase
-source inverter. Phase legs “b” and “c” are controlled by
SPWM to synthesize ac output, and the shoot-through comand
is used to boost voltage as desired. The
mand,
control of these two phase legs is similar to the simple boost
and
control proposed in [5] and [6]. Two straight lines,
are used to control the shoot through duty ratio. When the
carrier is greater than the upper straight line, phase leg “b” goes
to shoot through state, whereas phase leg “c” goes to shoot
through state when the lower straight line is greater than the
carrier. Phase “a” in the inverter is switching at 50% duty cycle
without shoot through. The switching frequency of phase “a” is
the frequency of the carrier. By doing this, each phase leg only
shoots through once during one carrier cycle, the equivalent
switching frequency can be doubled for the output filter.
where is the total shoot-through period per carrier cycle, and
is carrier cycle. In the simple control method [5], [6], the
amplitude of the two straight lines is the peak of modulation
waveform, therefore the relationship between modulation index,
and the shoot through ratio,
can be found as
(4)
Substituting (4) into (3), the boost factor becomes
(5)
From (1) and (5), the peak amplitude of the output can be expressed as
(6)
While the capacitor voltage is
(7)
When the PV output voltage value is high enough to produce the required ac voltage, the shoot through state is no longer
0 and
1. Under this condition, the reneeded, i.e.,
lationship between the inverter peak output voltage and the PV
output voltage can be calculated by
(8)
It also should be noted that the shoot-through states can be
created by shorting both legs “b” and “c,” or all the three legs
simultaneously during any given shoot through state according
to the two straight lines. For all these shoot-through cases, the
resulted boost effect and output voltage waveforms remain the
same.
In the proposed control scheme, only one phase leg is used to
create shoot through at any time, thus minimizing the switching
frequency. However, at the same time, the current stress on each
switch during shoot through is doubled when compared with
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-SOURCE INVERTER
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shooting through two phase legs simultaneously at any time. A
trade off in the control must be made, one can
1) either reduce the switching frequency by shorting one or
two phase legs;
2) or reduce the current stress on each device by shorting all
phase legs during shoot-through periods;
3) to make a decision in real applications, the switching and
conduction losses at different conditions need to be calculated and investigated for different cases.
Fig. 6. Block diagram of the MPPT control.
V. DESIGN GUIDELINE
In the -source based PCS, the maximum voltage over phase
is controlled to maintain the split phase output at diflegs
ferent input voltages. For 120-V split phase output, PV cell with
maximum output voltage of 450 V and can be used. Assume
the minimum output voltage is half of the maximum voltage, to
achieve the same output ac voltage of 120 V, the device voltage
stress can be calculated by manipulating (5) and (6), which results in
(9)
Thus, a 600-V device can be used.
The maximum current stress on the device can be simply calculated based on
(10)
where
is the -source inductor current,
is the maxis the average output
imum transient output power, and
power. The current stress can be reduced by turning on two or
into
all phase legs during shoot through to distribute the 2
different phase legs.
To determine the inductance and capacitance of the -source
network, the input power is assumed to be constant dc. The
ripple power is absorbed by the capacitors of the -source network. The power ripple absorbed by the capacitors is calculated
(11)
where
is the average voltage across the capacitor and is
the total capacitance of two capacitors in the -source. To limit
the voltage ripple to be less than %, the capacitor value can be
calculated.
Based on the voltage ripple across the capacitors, the ripple
voltage across the inductor is the voltage difference between the
capacitor and the voltage across the PN. The capacitor voltage
is already known with % ripple. The PN voltage is zero during
shoot through and 2
for others. Assume the input
,
voltage is a constant dc value, the PN voltage ripple is 2
therefore, the voltage ripple across the inductor is
%
(12)
To limit the ripple to a special percent, the inductance can be
determined.
Fig. 7. Typical V –I and P –V characteristics.
VI. SIMULATION AND EXPERIMENTAL RESULTS
Photovoltaic solar cells have nonlinear – characteristics.
Its output voltage and power change according to temperature
and irradiation. Fig. 7 shows the typical – characteristics for
a PV model. For a specified temperature and irradiation, the intersection of the load line with the photovoltaic voltage-current
characteristic, is the operation point. In real practice, PV models
are first cascaded then paralleled to form PV array, thus to meet
the voltage and power requirement.
Since the proposed -source based PCS is directly connected
to the grid, the PCS will be controlled to transfer maximum
power from the PV array to the grid all the time. Because of
nonlinear characteristic of PV models, the maximum power
can not be achieved by directly connecting the PV models.
Tracking of the MPP must be used to effectively get the maximum output power. Thereby, many researches of the MPPT
have been done [7]–[10]. There have been the perturbation and
observation method, the incremental conductance method, and
the hill climbing method, etc. Here, a simple power feedback
method can be used for the -source based PCS to achieve
MPPT as shown in Fig. 6. The power can be measured and
used as feedback. The PV modules’ voltage can be regulated
to an optimal point, which presents the maximum power. This
special point is tracked to satisfy the relationship of
0. Based on this strategy, the maximum power point can always
be tracked [11].
Fig. 8 shows the – curves of PV array at different temperatures and irradiations. Usually the photovoltaic output voltage
changes mainly with temperature, while the photovoltaic output
current changes mainly with irradiation. With constant irradiation specified, the PV output power decreases when the temperature rises. With constant temperature specified, the PV output
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Fig. 8. V –I characteristics under different conditions.
power increases when the irradiation increases. One of the functions of the PCS is to extract the maximum power out of the photovoltaic at any given temperature and irradiation. Based on the
curves shown in Fig. 8, simulations and experiments are performed to prove the concept proposed in this paper at the following two conditions:
230 V, the maximum PV
1) at 1000 W/m and 60
output power is 7200 W;
450 V, the maximum PV
2) at 250 W/m and 0 C
output power is 3360 W.
For both cases, the simulation and experimental systems are
1 mH at the
setup with the following parameters:
13,300
. The switching freline frequency and
quency is 10 kHz. -source inverter produces PWM voltage
waveforms just like the traditional inverter. Thus, a
filter
is added after the inverter to achieve sinusoidal waveform. The
1 mH and
120
. We assume
filter parameters are
that output voltage range of PV arrays is 1 2. So 600-V IGBTs,
which has maximum dc voltage as 450 V, was used to operate in
225–450 V in experiments. Resistive load is used for the simulations and experiments. For case one, 4 is used for each phase,
whereas 8.57 is used for case 2.
Case 1: 1000 W/m and 60 C
230 V
, is 230 V, to achieve
For the first case, the input voltage,
120-V split phase output, the modulation index can be calculated by the following equation, which is the inverse of (6):
Fig. 9. Simulation results of case 1 under the conditions of 1000 W/m , 60 C,
and V
230 V. (a) Input voltage and Z -source capacitor voltage. (b) Load
voltages and currents. (c) Filter inductor current and Z -source inductor current.
=
(13)
Fig. 10. Experimental results of case 1 under the conditions of 1000 W/m ,
230 V. (a) Z -source capacitor voltage and input voltage. (b)
60 C, and V
Load voltages and currents. (c) Filter inductor current and Z -source inductor
current. (d) Input current and load voltage.
=
The boost factor is
(14)
Thus, the shoot through duty cycle
can be calculated from
(3), which will result in
equal to 0.245. The -source
capacitor voltage would be
(15)
Figs. 9 and 10 show the simulation and experimental results
of case 1. Figs. 9(a) and 10(a) show the simulation and exper-
imental waveform of the input voltage and -source capacitor
voltage waveform, respectively. In both simulation and experimental results, the capacitor voltages are close to 340 V. Meanwhile as shown in Figs. 9(b) and 10(b), the simulation and experimental results of the output voltages are both close to the
desired split phase 120-V rms. The output power can be calculated based on the output voltage and the load current waveforms, which are also shown in Figs. 9(b) and 10(b). As the load
current is 30 A, the total output power of the inverter is around
7200 W. Thus the maximum power output from the PV at this
HUANG et al.:
-SOURCE INVERTER
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Fig. 11. Simulation results of case 2 under the conditions of 250 W/m , 0 C,
450 V. (a) Input voltage and Z -source capacitor voltage. (b) Load
and V
voltages and current. (c) Filter inductor current and Z -source inductor current.
=
condition is realized. Figs. 9(c) and 10(c) show the output filter
inductor and -source inductor current. The -source inductor
average current is around 31 A, which on the other hand, proofs
again that the PV outputs its maximum power. The input current to the inverter is also shown in Fig. 10(d). To get the 170-V
output peak voltage, the input current is around 31 A. The simulation and experimental results are consistent with the theoretical calculations.
Case 2: 250 W/m and 0 C
450 V
For the second case, as the input voltage is much higher,
450 V, the control strategy is different with the first case.
Shoot through is not used for this case.
The modulation index can be calculated as
(16)
As no boost is needed for this case, the boost factor
1.
Thus, the -source capacitor voltage would be the same as the
PV voltage, which is 450 V. At this condition, the theoretical
maximum output power from PV is 3360 W.
Figs. 11 and 12 show the simulation and experimental results
of Case 2. Similar to Case 1, the simulation and experimental
results also verify the analysis as well.
From the above two cases, it can be concluded that the simulation and experimental results show that at different input
voltage, the proposed PV system’s output voltage maintained at
120 V rms, whereas the output power tracked the maximum
PV output power at different temperature and irradiation. The
basic principle of the proposed system was verified.
VII. CONCLUSION
This paper presented a new PV power conditioning system
based on -source inverter. The proposed system realizes the
boost and inversion with maximum power tracking in one
single power stage, thus minimizing the number of switching
devices. All the advantages of the -sources inverter and the
Fig. 12. Experimental results of Case 2 under the conditions of 250 W/m ,
0 C, and V
450 V. (a) Z -source capacitor voltage and input voltage. (b)
Load voltages and currents. (c) Filter inductor current and Z -source inductor
current. (d) Input current and load voltage.
=
six-switch split-phase inverter are inherited and integrated
together to create a highly reliable PCS system with minimized
volume and cost. With the advanced features summarized in
Section III, the proposed system is very promising for PV
power conditioning applications.
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Yi Huang received the B.S. and M.S. degrees in electrical engineering from Wuhan University, Wuhan,
China, in 1998 and 2001, respectively, and is currently pursuing the Ph.D. degree at Michigan State
University, East Lansing.
Her current research interests are dc–ac inverters,
digital control, and photovoltaic inverter systems.
Miaosen Shen (S’04) received the B.S. and M.S. degrees from Zhejiang University, Hangzhou, China, in
2000 and 2003 respectively, and is currently pursuing
the Ph.D. degree at Michigan State University, East
Lansing.
His research interests include motor drives, power
factor correction technique, and electronic ballast.
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 Niigata,
Japan, in 1987 and 1990, respectively.
He was with Toyo Electric Manufacturing Company, Ltd., from 1990 to 1992, as a Research Scientist, was engaged in research and development of
active power filters, flexible ac transmission systems
(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 2000, he worked for Oak Ridge National Laboratory (ORNL), as a Research
Assistant Professor at University of Tennessee, Knoxville, from 1994 to 1997,
and was a Staff Member, Lead (principal) Scientist, Power Electronics and Electric Machinery Research Center, ORNL, from 1997 to 2000. Since 2000, he has
been with Michigan State University, East Lansing, as an Associate Professor
of the Department of Electrical and Computer Engineering. He holds over ten
patents.
Dr. Peng received the 1996 First Prize Paper Award and the 1995 Second
Prize Paper Award of Industrial Power Converter Committee in IEEE/IAS 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
in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS; the 1990 Best Paper
Award in the Transactions of the IEE of Japan (the Promotion Award of the
Electrical Academy). He was Chair of the Technical Committee for Rectifiers
and Inverters, IEEE Power Electronics Society, from 2001 to 2005 and was an
Associate Editor for the IEEE TRANSACTIONS ON POWER ELECTRONICS from
1997 to 2001 and has been an Associate Editor again since 2005.
Jin Wang (S’01–M’05) received the B.S. degree
from Xi’an Jiaotong University, Xi’an, China, in
1998, the M.S. degree from Wuhan University,
Wuhan, China, in 2001, and the Ph.D. degree from
Michigan State University, East Lansing, in 2005,
all in electrical engineering.
He joined the Ford Motor Company, Dearborn, MI,
in 2005. He is currently a Core Engineer for power
electronics systems in Ford’s hybrid vehicles. His research interest includes HEV/FCV, multilevel converters, dc–dc converters, FACTs devices, and DSP
based control systems.