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State space modeling and analysis of buck converter
based PV Inverter
DIVYA TOM
PG Student, SELECT,Chennai,India.
VIT University
[email protected]
Abstract— Traditional buck boost inverter and single phase
inverter has limited voltage range and complex structure .Here
grid connected transformer less photovoltaic inverter, which can
be used for residential applications is presented. Analysis,
derivation of buck converter cascaded with inverter is discussed
in this paper. The output from the circuit is supplied to grid.
Various operating modes of buck depending on input voltage is
analyzed. Here the input voltage source is from photovoltaic cell
(PV).Inverter topology used here has multiple stages and six
switches. The simulation is done using MATLAB software. State
space analysis technique is used to derive transfer function.
Keywords—inverter, photovoltaic, converter
State space analysis is typically used to develop a
small signal model of a converter and then depending on type
of control scheme used, the small signal model of converter is
modified to facilitate the design.
THE PROPOSED BUCK CONVERTER
The topology of buck converter cascaded with inverter [6] is
shown below. S BUCK is the buck switch ON and OFF in
different modes of operation. VIn is the supply voltage from
PV panel. Single phase inverter [4]-[6] is also shown in the
fig2.
INTRODUCTION
Electricity being inevitable part in human’s life .But
it is not readily available. So it should convert from any other
sources like renewable sources. There are many renewable
sources like wind, solar etc. Out of which solar energy is
extensively available. Photovoltaic cells can be used as it
converts sun’s energy to electrical energy [1]. But due to
weather conditions and other parameters the output voltage
from photovoltaic panels may vary (200v to 500 v). So, a dcdc converter with suitable topology is used. That may either
buck or boost depending on input source voltage.
Fig 2. Basic block diagram
III. Proposed dc to ac converter
Fig1. Two stage photovoltaic inverter
This block diagram explains conventional two stage
photovoltaic inverter. Before supplying to the grid [2] it is
passes through two stages of conversion. A dc-dc converter
either buck or boost, depending on input voltage is used and
dc-ac converter for the inversion is used. The middle capacitor
acts as voltage source to inverter [3]. Here, buck cascaded
with inverter circuit is analysed and modelled. Modelling is
done by using state space analysis. Simulation is done using
MATLAB software.
The block diagram of multiple stage buck-boost inverter used
for the proposed system is shown in Fig 3. Dc voltage
obtained from the photo voltaic cells is given as input to dcdc converter. Depending upon the reference value set, dc-dc
converter either boosts or bucks the input voltage to 325Vdc.
Dc voltage is converted to ac voltage by switching the
switches of two arms of H-bridge complementarily. The
obtained 230V, 50Hz, ac voltage is fed to grid.
III.
OPERATION PRINCIPLE
The state variables are i L1 and V C .By applying KVL
and KCL for the loops in the mode of operation in terms of the
state variables
(i) Boost mode
It is based on the voltages of PV panel and
instantaneous grid voltage. If the instantaneous grid voltage is
greater than PV panel’s voltage, then it operate in boost
mode
VIN  VL1  VC  0
Gives,
diL1 VIN  Vc

dt
L1
(ii) Buck mode
ic1  iL1  i0
It is based on the voltages of PV panel and
instantaneous grid voltage. If the instantaneous grid voltage is
lower than PV panel’s voltage, then it operate in buck mode.
This paper deals with buck mode.
Buck switch duty cycle (D BUCK) =
Gives,
dVc1 iL1  i0

dt
C
V0
VIN
i0 
Where VO = Output voltage and VIN = Input dc voltage. If the
range of input voltage is between 200 and 500V and the output
voltage is 340 sin(ɷt). Then,
 diL1   0
 dt  
 dVc  =  1
1

 
 dt   C
340
340 < V IN <500 then 0< D BUCK<
V IN
200 < V IN< 340 then 0<D BUCK< 1
In buck mode, boost switch is always OFF, and buck
switch is ON and OFF. In the circuit BOOST part will act as
input filter.
IV.
Buck mode is operating under two modes. Mode I
and mode II. In mode I, boost switch(S BOOST) is OFF and
buck switch (S BUCK )is ON. In mode II, both buck and boost
switches are OFF.
Mode
S BOOST
S BUCK
Mode I
Mode II
0
0
1
0
1 
L1 

1 
s * L2 

V0  = 0
MODES OF OPERATION
Vc
sL2
1
 iL1   
Vc  +  L1  VIN 
 1 C
 
 iL1 
1   + VIN 
Vc1 
Mode II
Table 1: Different modes of operation
Based on these modes, steady space analysis is conducted and
transfer functions are derived.
V.
SMALL SIGNAL MODELLING
There are two operating modes. Mode I and mode
II.ON and OFF position of switches in each modes are
discussed. Based on position of switches circuit diagram is
drawn.
VIN  VL1  VC  0
Gives,
diL1 VIN  Vc

dt
L1
Mode I
When SBOOST is OFF and S BUCK is ON. The on
position of switch is shown in the figure.
iL1  ic
Gives,
Fig 4: Mode II
Fig 3. Mode I
L2
C
f
dVc1 iL1

dt
C
 diL1   0
 dt  
 dVc  =  1
1

 
 dt   C

1
L1 

0 

1
 iL1   
Vc  +  L1  VIN 
 1 0
 
Table 1.Lists the design parameters
On the basis of the values, input transfer function
obtained,
2.72 *104
V0
=
VIN 1.6 *1013 s 2  5.6 *10 4
 iL1  0 
0   +   VIN 
Vc1  0 
V0  = 0
400µH
2µF
50kHz
a) Design of LC filter
A1

0

1
 C
=
B1
1
L 
 1
C 
0 1
0 
0 
 
=
C1
=
D1 =
A2 =
B2
1 

L1 

1 
s * L2 

0

1
 C
1
 
L1

0 

1
=  L1 
 
0
C2
D2
0
0 
= 
0 
=
0
Thus, using these equations transfer function is
obtained and id given by,
V0
L2 * D
=
VIN CL1L2 s 2  L2  L1D
Component
L1
Specification
200µH
L
V IN
in Henry
8 * i * f
Where, Vin is the supply voltage, f is the switching
frequency. With this design we obtain L =22mH, using below
we have
f 
1
in Hz
2 * pi * LC
Substituting the values of f and L we obtained C= 220µF
VI.
POWER SCHEMATIC DIAGRAM
The schematic diagram of proposed system is shown
in the figure. The buck converter produces a fixed dc voltage
from the PV array whose voltage is varying. Single phase
inverter generates sinusoidal wave.LC filter is used in order
to avoid ripples.
Simulation was done using MATLAB software. The
input voltage varies from 200 V to 400 V. Simulation circuit
for buck cascaded with inverter is shown in fig.LC filter is
also used.
Fig 4.Simulink diagram.
[3]
J. M. Kwon, K. H. Nam, and B. H. Kwon, “Photovoltaic power
conditioning system with line connection,”IEEE Trans. Ind. Electron, vol.
53,no. 4, pp. 1048–1054, Aug. 2006.
[4] Ahmed Mohamed Salamah, Stephen J. Finney “Single-Phase
Voltage Source Inverter with a Bidirectional Buck–Boost Stage for
Harmonic Injection and Distributed Generation” IEEE transactions
on power electronics, vol. 24, no. 2, pp 376- 387, February 2009.
[5] Roman, I.T. “A single-phase current-source inverter with active
power filter for grid-tied PV systems”, 3rd IEEE International
Symposium on Power Electronics for Distributed Generation Systems
(PEDG), Aalborg, pp. 349-356, June 2012.
[6] T. Boutot and L. Chang, “Development of a single-phase inverter
for small wind turbines,” in Proc. IEEE Elect. Comput. Eng. Can.
Conf. (CCECE 1998), Waterloo, ON, Canada, May 24–28, pp. 305–
308.
Fig 5.Output current waveform
Fig.6 Output voltage waveform.
VII.
CONCLUSION
By using MATLAB Simulink tool, buck converter
cascaded with single phase voltage source inverter is
simulated. The simulation results shows that buck converter
with inverter produce sinusoidal wave which can be supplied
to grid. The input voltage varies from 200 V to 400 V. Here,
in simulation input is given as 340 V and the output produces
320V.This type of inverters can be used in harmonic
elimination systems and Distribution systems.
The analysis and state space modeling of buck
converter cascaded with inverter were performed and the
transfer function for the same also derived.
VIII.
REFERENCES
[1]
J. P. Benner and L. Kazmerski, “Photovoltaic gaining greater
visibility,”IEEE Spectrum, vol. 29, no. 9, pp. 34–42, Sep. 1999.
[2] F. Tian, H. Al-Atrash, R. Kersten, C. Scholl, K. Siri, and I. Batarseh
“A single-staged PV array-based high-frequency link inverter
design with grid connection,” in Proc. Appl. Power Electron. Conf. Expo.,
2006, pp. 19–23.