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Acta Polytechnica Vol. 50 No. 4/2010

Single Phase Voltage Source Inverter Photovoltaic Application

J. Bauer

Abstract

Photovoltaic applications have been developing and spreading rapidly in recent times. This paper describes the control
strategy of the Voltage Source Inverter that is the important tail end of many photovoltaic applications.
In order to supply the grid with a sinusoidal line current without harmonic distortion, the inverter is connected to the

supply network via a L-C-L filter. The output current is controlled by the hysteresis controller. To improve the behaviors
of the L-C-L filter, active damping of the filter is being used. This paper discusses controller design and simulation results.

Keywords: voltage source inverter, L-C-L filter, hysteresis controller, pulse width modulation.

1 Introduction
Increasing efforts are being made nowadays to use re-
newable energy sources. Processing the energy ob-
tained from sun, wind or water is coming to the fore.
The energy supplied by these sources does not have
constant values, but fluctuates according to the sur-
rounding conditions (intensity of sun rays, water flow,
etc.). These supplies are therefore supplemented by
additional converters. The most used types are in-
verters orDC/DC converters. The area of high power
converters for solar application is already covered by
industrial manufacturers. However, the area of low
power devices is not fully covered. These converters
are mostly built from commercially produced parts
that can perform demanded functions, but they are
notdeveloped for this typeof applicationandtherefore
the efficiency of the whole system is low. Low power
devices are important in applications where there is
no voltage grid present and electric power is required
(mountains, desert expeditions, etc.)
The simplified block structure of the investigated

system is shown in Fig. 1. A DC/DC converter with
an MPPT (Maximum Power Point Tracker) is con-
nected to the solar array. A second DC/DC con-
verter is connected to the output of this converter.
The second converter raises the voltage acquired from
the solar system to the voltage level demanded by the
VSI.

Fig. 1: Block diagram of the system

2 DC voltage control

The power produced by solar arrays depends on sur-
rounding conditions, e.g. temperature ϑ and intensity

of sunexposure E. The solararrayoutputpower isnot
therefore constant. The output power also depends on
the withdrawn current and voltage. (Fig. 2)

Fig. 2: Output characteristic of the solar cell and themax-
imum power point tracking principle

The MPPT control algorithm ensures that the so-
lar array operates at its optimal point and that it
delivers maximal power. The algorithm periodically
changes the duty cycle of the converter in the de-
fined hysteresis range, it increases the duty cycle, it
decreases the duty cycle, and it compares the pow-
ers delivered by the solar cell. Then it chooses the
duty cycle that corresponds with the maximal deliv-
ered power. If the converter operates on the left side
of the MPP (area 1.), the algorithm will decrease the
duty cycle. When it is operating on the right (area 3.)
of the MPP, the controller will increase the duty cy-
cle. If the converter is operating at MPP (area 2.),
the power obtained on both sides will be lower and
the duty cycle remains the same.
The second DC/DC converter is a boost type full

bridge with galvanic insulation. The converter works
with a fixedduty cycle andboosts the input voltage to
the voltage level required by the inverter. For a single
phase VSI, 400 V should be enough.

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Acta Polytechnica Vol. 50 No. 4/2010

3 Voltage Source Inverter

The VSI is used for converting energy fromDC to AC
voltage. The detailed scheme of the inverter is shown
in the Fig. 3. The power part of the inverter is made
of four MOSFETs and the L-C-L filter is connected
to the output of the inverter. This filter ensures the
sinusoidal shape of the output current.

Fig. 3: Inverter diagram

The inverter in this application can operate in two
differentmodes. Firstly, it can operate in the so-called
“island mode”, which means that the converter acts
as a voltage source and supplies some devices with si-
nusoidal voltage of the common network parameters.
PWM control is used for this purpose. The second
possible operation mode delivers current to the sup-
ply network. PWM control is not suitable for this
operation mode and the current hysteresis control is
therefore used.

3.1 Current control

The simplest hysteresis controller can be realized as
a simple bang-bang regulator. The actual value of
the output current is controlled in order to remain
in a defined area. This method is fast and simple,
and provides good results with an L-C-L filter. The
onlyproblem is the variable switching frequency of the
semiconductor switches that is a direct consequence of
this control strategy. Better results can be obtained
whencontrolof thehysteresiswidth isused. According
to [1], the width depends on the demanded switching
frequency fs of the converter, on the inverter side filter
inductance Li, on the actual value of DC-link voltage
UDC, and on the filter capacitor voltage uCf.

Hy = |uCf |
UDC − |uCf |

LifsUDC
(1)

Implementation of equation (1) causes the switching
frequency to remain approximately constant. The
influence of variable hysteresis width is depicted in
Fig. 4.
A further improvementof the output current shape

involves adapting the hysteresis controller. A simple

Fig. 4: Switching frequency during variable hysteresis con-
trol

hysteresis controller alternates only between two com-
binations (S1, S2) or (S3, S4), whichmeans that either
+UDC or −UDC appears on the output (Fig. 5).

Fig. 5: Bipolar hysteresis controller

With the help of the PWM switching analogy,
bipolar switching can easily be adapted to unipolar
switching. This method generates three output volt-
age levels +UDC, 0 and −UDC. The controller is
shown in Fig. 6. Two hysteresis controllers of differ-
ent hysteresis width are used instead of one. The first
controls switches S2, S3 and the second controls S1,
S4. Outer hysteresis is used in areas where the cur-
rent crosses zero and the drop in the desired current

Fig. 6: Unipolar hysteresis controller

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Acta Polytechnica Vol. 50 No. 4/2010

value is faster than the drop in the output current.
The output current then reaches the outer hysteresis,
and the controller switches from S1 to S4 or vice versa.
This control of the VSI is used when the converter

operates on the supply network and is used for gener-
ation of current. The output voltage is guardedby the
supply network itself. The converter “pushes” current
into the grid.

3.2 PWM control

Hysteresis control cannot operate in “island mode”,
because there is no supply network voltage that can
guard the generated voltage. Then the converter is
supposed to generate output voltagewith a sinusoidal
shape, as in the supply network. The PWM control
algorithm was therefore used for “island mode”. The
controller is shown in Fig. 7. The PI controller is used
in the voltage control loop. The output of the con-
troller is the duty cycle for the modulator.

Fig. 7: Island mode control loop

4 L-C-L filter design

The filter is an important part of every semiconduc-
tor converter. The filter reduces the effects caused
by switching semiconductor devices on other devices.
The generation of the harmonics around switching fre-
quency can be filtered by large inductance connected
to the output of the converter. But the large induc-
tance decreases the dynamics of the system and also
the operation rangeof the converter. Insteadof the in-
ductance the inverter can be equipped with an L-C-L
filter. The L-C-L filter has good current ripple atten-
uation evenwith small inductance values. However, it
can bring also resonances and unstable states into the
system. Thefiltermust thereforebedesignedprecisely
according to the parameters of the specific converter.
In the technical literature we can find many articles
on the design of the L-C-L filters [2, 3].

Table 1: Parameters for calculating the filter components

Grid Voltage (V) 230

Output Power of the Inverter (kVA) 1.5

DC link Voltage (V) 400

Grid Frequency (Hz) 50

Switching Frequency (Hz) 3000

Nowthefilter designwill be described. The system
parameters considered for calculating the components
for a filter with power approx. 1.5 kVA are shown in
Tab. 1.
First, the base values need to be calculated. These

values are later used for calculating the filter compo-
nents.

Zb =
U2n
Sn
=46Ω (2)

Cb =
1

ωnZb
=69.91μF (3)

The first step in calculating the filter components is
the design of the inverter side inductance Li, which
can limit the output current ripple by up to 10% of
the nominal amplitude. It can be calculated according
to the equation derived in [3]:

Li =
UDC

16fsΔIL max
=17.7mH (4)

where ΔIL max is the 10% current ripple specified by
(5)

ΔIL max =0.01
Pn

√
2

Un
=0.234A (5)

The design of the filter capacityproceeds fromthe fact
that themaximal power factor variationacceptable by
the grid is 5%. The filter capacity can therefore be
calculated as a multiplication of system base capaci-
tance Cb

Cf =0.05Cb =3.45μF (6)

The grid side inductance Lg can be calculated as (7)

Lg = rLi =0.32Li =5.7mH (7)

The last step in the design is the control of the reso-
nant frequency of the filter. The resonant frequency
musthaveadistance fromthe grid frequencyandmust
be minimally one half of the switching frequency, be-
cause the filter must have enough attenuation in the
switching frequency of the converter. The resonant
frequency for the L-C-L filter can be calculated as (8)

fres =
1
2π

√
Li + Lg
LiLgCf

=1.30kHz (8)

In order to reduce oscillations and unstable states of
the filter, the capacitor should be added with an in-
series connected resistor. This solution is sometimes
called “passive damping”. It is simple and reliable,
but it increases the heat losses in the system and it
greatly decreases the efficiency of the filter. The value
of the damping resistor can be calculated as (9)

Rsd =
1

3ωresCf
=11.2Ω (9)

So-called “active damping”methodswith a virtual re-
sistor were therefore developed. As mentioned in [4],

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Acta Polytechnica Vol. 50 No. 4/2010

there are four possible ways to place a virtual resistor
for active damping. One of them is shown in Fig. 8.

Fig. 8: A single phase L-C-L filter and an alternative cir-
cuit

Figure 8 shows a model of a single phase L-C-L
filter with resistor damping connected in series with
the filter capacitor. The inverter can be considered
as a current source. The resistor reduces the voltage
across the capacitor by a voltage proportional to the
current that flows through it. In the control loop the
current through Cf is measured and differentiated by
the term sCf Rsd. A real resistor is not used, and the
calculated value is subtracted from the demanded cur-
rent (Fig. 9).

Fig. 9: A single phase L-C-L filter with a virtual resistor

In this way the filter is actively damped with a
virtual resistor without losses. The disadvantage of
this method is that an additional current sensor is re-
quired and thedifferentiatormaybringnoise problems
because it amplifies high frequency signals.

5 Simulation results
A model of the VSI with the control was made with
the help ofMatlab-Simulink SW. All simulations were
made for output current Ig = 3 A, output voltage
Ug = 230 V and output frequency f = 50 Hz. The
switching frequency of the inverter was fs = 3 kHz
a filter with parameters designed in this paper Li =
17.7mH, Cf =3.45μF, Lg =5.7mHanddamping re-
sistor Rsd =11.2Ωwas connected to the output of the
filter. Fig. 10 shows the effects of the virtual damping
resistor from time t =0.1 s when the filter is damped
with a virtual resistor.

Fig. 10: Effect of the virtual resistor on the L-C-L filter

Fig. 11: Simulation results for current hysteresis control

Figure 11 shows the simulation results of the in-
verterwith double hysteresis control. The filtered cur-
rent ig is in the phase with the grid voltage. Except
for small spikes in areas where the current changes
its direction, the shape of the filtered current is sinu-
soidal.
The same simulationswere done for “islandmode”

operation. In this case, the output voltage is regu-
lated to ug =230 V and the current is determined by
the load. The shape of the current is smoother, but
there is a slight phase shift, caused by the output fil-
ter inductance and the load character. The harmonics
content of both currents is good.

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Acta Polytechnica Vol. 50 No. 4/2010

Fig. 12: Simulation results for island mode with PWM
control

6 Conclusion
The control algorithm for a grid connected voltage
source inverter has been presented here. A sinusoidal
line current is produced due to the hysteresis con-
troller. The switching frequency is almost constant
because of the variable hysteresis width control. The
output current filter has been designed and simulated.
The obtained results seem to be promising. However,
wewill not be able to evaluatewhole systemuntil after
it has been realized.

Acknowledgement

This work was supported by the Grant Agency of the
Czech Technical University in Prague, grant No. SGS
10800630. The researchdescribed in thepaperwas su-
pervised by Prof. J. Lettl, CSc., FEE CTU in Prague.

References

[1] Hinz, H., Mutschler, P., Calais, M.: Control of a
single phase three level voltage source inverter for
grid connected photovoltaic systems, PCIM 1997.

[2] Liserre, M., Blaabjerg, F., Hansen, S.: Design
and control of an lcl-filter based three-phase ac-
tive rectifier. In Industry Applications Conference,
2001. Thirty-Sixth IAS Annual Meeting. Confer-
ence Record of the 2001 IEEE, volume 1, 2001.

[3] Araújo, S. V., Engler, A., Sahan, B.: LCL Filter
design for grid-connectedNPC inverters in offshore
windturbines. InThe 7th InternationalConference
on Power Electronics. Daegu (Korea), 2007.

[4] Dahono, P. A.: A method to damp oscillations on
the input lc filter of current-type ac-dc pwm con-
verters by using a virtual resistor. In Telecommu-
nications Energy Conference INTELEC’03, 2003.

About the author

Jan BAUER was born in Prague on January 14,
1983. He studied electrical engineering at CTU in
Prague and was awarded his master’s degree in June
2007. He is currently working on his PhD thesis at
CTU in Prague, FEE at the department of Electric
Drives and Traction. His main fields of interest are
modern control algorithms for inverters and matrix
converters.

Jan Bauer
E-mail: bauerj1@.fel.cvut.cz
Dept. of Electric Drives and Traction
Faculty of Electrical Engineering
Czech Technical University in Prague
Technická 2, 166 27 Praha, Czech Republic

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