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International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 06 Issue: 03 | Mar 2019 www.irjet.net p-ISSN: 2395-0072
© 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 1052
A Systematic Approach to Design Single Phase Transformer less
Inverter for PVG System with Reactive Power Control
Ms. Ruchi Sakhare1, Asst. Prof. Bhushra Khan2
1Student, Dept. of Electrical Engineering, Abha Gaikwad Patil College of Engineering, Maharashtra, India
2Asst. Prof. Bhushra Khan, Dept. of Electrical Engineering, Abha Gaikwad College of Engineering,
Maharashtra, India
----------------------------------------------------------------------***---------------------------------------------------------------------
Abstract - There has been an increasing interest in
transformer less inverter for grid-tied photovoltaic (PV)
system due to low cost, high efficiency, light weight, etc.
Therefore, many transformer less topologies have been
proposed and verified with real power injectiononly. Recently,
almost every international regulation has imposed that a
definite amount of reactive power should be handled by the
grid-tied PV inverter. According to the standard VDEAR-N
4105, grid-tied PV inverter of power rating below 3.68KVA,
should attain power factor (PF) from 0.95 leading to 0.95
lagging. In this paper, a new high efficiency transformerless
topology is proposed for grid-tied PV system with reactive
power control. The new topology structure and detail
operation principle with reactive power flow is described. The
high frequency common mode (CM) model and the control of
the proposed topology are analyzed. The inherent circuit
structure of the proposed topology does not lead itself to the
reverse recovery issues even when inject reactivepowerwhich
allow utilizing MOSFETswitchestoboosttheoverallefficiency.
The CM voltage is kept constant at midpoint of dc input
voltage, results low leakage current. Finally, to validate the
proposed topology, a 1 kW laboratory prototype is built and
tested. The experimental results show that the proposed
topology can inject reactive power into theutility gridwithout
any additional current distortion and leakage current.
Key Words: Common mode, converter, high efficiency,
leakage current, reactive power, transformer less.
1. INTRODUCTION
Due to the increasing the energy demand the new energy
sources requirement is increasing day by day. Now a day’s
fossil fuels are the main energy sources for generating
energy but they cannot sustain for longer change. These
fossil fuels give rise to the emissionofharmful gassessuchas
carbon dioxide and methane gas into the atmosphere and
thus creating environmental pollution. These are the non-
renewable energy sources. Renewablesourcessuchas wind,
hydro-electricity and solar power cooled replacefossil fuels.
Wind power is currently widely used in thehillyareaswhich
can compensate more energy in generation of 2000 MW of
electric power. Similarly PV system had gain more attention
over the years as the best renewable energy sources.
Some of the advantages of PV is that it has long life, low
maintenance charges, ease of installationandnoneedoffuel.
Generally grid connected transformer less inverter are can
be divided into two groups; single stage inverter and two
stage inverter.
In two stage inverter a DC to DC converter connect the PV
panel converts sun light to the DC electricitywithlowoutput
voltage. A DC to DC boost converter is used this DC voltage
can be further converted into the AC voltage with power
electronic system (Inverter).
PV devices:- Several energy sources are therefore energy
conversion including batteriesfuel cellsandwindgeneration
each energy source is connected to inverter through specific
integration technique.
A PV panel creates DC power which is link to a inverter
directly or through a DC to DC converter. This is decreasing
the total cost. Essentially a PV cell has a semiconductor PN
junction diode cell that can converts the lights into
electricity. Differentcell arrangementssuchasseriesparallel
and parallel –series creates a PV model that has a specific
power capacity.
DC-DC power converter:- DC-DC power converter are
basically used in the PV system to change the outputvoltage.
This converter specifically can be used either as the boost
converter or buck converter or a combination of both
converter may be have depending on the desired capacityor
the size of the output voltage to provide appropriate input
voltage for the inverter with the DC voltage stabilizationand
regulation capacity.
2. METHODOLOGY
 A transformer less inverter for grid connected
hybrid system was simulated using
MATLAB/SIMULINK tool.
 This three-phase transformer inverter was capable
of obtain a maximum possiblepowerfromsolarand
wind module. Incremental conductance MPPT
technique was used.
 Therefore, the PV string canbeofdifferentelectrical
parameters and working conditions. Transformer
less condition of the inverter helped the system to
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 06 Issue: 03 | Mar 2019 www.irjet.net p-ISSN: 2395-0072
© 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 1053
convert maximum output power from the hybrid
system to the gird by limiting pulsating power.
 Leakage Current was reduced by placing LC filter
across the output of the inverter. LC filter also
reduced the harmonics produce at inverter output
voltage.
 Output power was subjected to active and reactive
power compensation. Three phaseoutputvoltageof
320 V, 20 A was obtained. A 1kW prototype of PV
and 7 W of wind was built and tested through
simulation. The control scheme of transformer less
inverter topology was described, and its detailed
analysis was provided.
Fig 1.Block diagram of proposed system
Fig2.Full bridge transformer less inverter
3. OBJECTIVE
The objective of this Project is to provide a dynamic
formulation for the single-phase PV inverter and reveal the
origin of some of the problems discussed.
The dynamic modeling provides a powerful tool for
deterministic control-system design and system-interaction
and stability analyses of the interconnected systems.
The basic principles presented in this thesis can be used to
analyze various control practices emerging in the field of PV
inverters and other renewableenergytechnologies based on
power electronics.
The scientific contribution of thisProjectcanbesummarized
as
• Explicit formulation of photovoltaic inverter modeling.
• Effect of photovoltaic generator on a single-phase VSI-
type inverter dynamics.
• Design rule for the minimum input capacitanceofa VSI-
type photovoltaic inverter based on input-voltage-
control stability.
• Explicit formulation of the effect of multiplier-based
grid synchronization causing negative output
impedance.
• Invention and development of a current-fed semi-
quadratic buck-boost-type converter topology suited
for transformer less modular photovoltaic.
4. PROPOSED WORK
The PV module generates an electrically chargeable surface
area which faces a grounded frame. In case of such
configuration, a capacitance is formed between the PV
module and the ground. Since this capacitance occurs as an
undesirable side effect, it is referredasparasiticcapacitance.
Due to the loss of galvanic separation between the PV
module and the grid, a CM resonant circuit can be created.
An alternating CM voltage that depends on the topology
structure and control scheme, can electrify the resonant
circuit and may lead to higher ground leakage current. In
order to analyses the CM characteristics, an equivalent
circuit of the proposed topology.
In order to illustrate the CM model at switching frequency,
could be replaced for the bridge-leg. The grid is a low
frequency (50–60 Hz) voltage source;thustheimpactofgrid
on the leakage current can be neglected. The DM capacitor
Co can also be removed since it has no effect on the leakage
current.
4.1 Control of the proposed topology
In order to control the grid current, several existing control
methods such as conventional PI controller, repetitive
controller (RC), proportional resonant (PR) controller, and
deadbeat (DB) controller can be adopted due to the
capability of tracking reference signal without steady state
error.
Since the PR controller has better performance of tracking
the reference signal if compared to the normal PI and RC
controller, it is selected to control the output current of the
proposed topology. The block diagram of the PR controller
with harmonic currentcompensator,whereGc(s),Gh(s),and
Gd(s) are the transfer function of fundamental current
controller,harmoniccompensator,andinverterrespectively.
The dynamic response of the system when it is subject to
750W load to 1000W load step change. It can clearly beseen
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 06 Issue: 03 | Mar 2019 www.irjet.net p-ISSN: 2395-0072
© 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 1054
that fast and effective response under the changes of active
power reference are achieved with the proposed topology.
Therefore, it can be concluded that the proposed topology
can inject real power into utility grid with low leakage
current and low THD at output.
4.2 Verification with Real Power Injection
The proposed topology is verified with 1 kW power
injection. The experimental gate drive signals for the
proposed topology. It can be seen that the switching signals
are fully matched with the proposed PWM scheme, and the
gate drive voltages are kept constant at the desired level.
The waveforms of CM characteristics. It is clear that the
voltages V1N, V2N, V3N, and V4N are clamped at 200V
during the freewheeling period of positive and negative half
cycle. As a result, the CM voltage is kept constant at 200V for
the whole grid cycle except a small fluctuation during grid
zero crossing instant as witnessed. Consequently, the
leakage current flows through the system are well reduced.
During zero crossing instant, a small spike can be observed
due to the fluctuation of CM voltage
4.3 Report Generation
A new high efficiency transformer less topologyforgrid-tied
PV system is presented. The main advantages of the
proposed topology can be summarized as: The inherent
circuit configuration of the proposed topology does not lead
itself to the reverse recovery issues which allow utilizing
MOSFET switches even though when inject reactive power.
Therefore, without compromising the overall efficiency,
proposed topology can inject reactive power into the utility
grid. The CM voltage is kept constant at the mid-point of dc
bus voltage; as a result, low leakage current flows through
the system which is lower than the H6-type topology. PWM
dead time is not required for the proposed topology that
reduces the THD at the output.
5. SIMULATION RESULT
REFERENCES
[1] Monirul Islam, Nadia Afrin, and Saad Mekhilef, Senior
Member, IEEE “Efficient Single Phase Transformerless
Inverter for Grid-Tied PVG System With Reactive Power
Control” IEEE Transactions On Sustainable Energy,2016.
[2] M. Islam and S.Mekhilef,“H6-typetransformerlesssingle-
phase inverter for grid-tied photovoltaicsystem,”IETPower
Electron., vol. 8, pp. 636– 644, 2015.
[3] M. Islam and S. Mekhilef, “An improved transformerless
grid connected photovoltaic inverter with reduced leakage
current,” Energy Convers. Manage., vol. 88, pp. 854–862,
2014.
[4] M. Islam and S. Mekhilef, “Highefficiencytransformerless
MOSFET inverter for grid-tied photovoltaic system,”inProc.
29th Annu. IEEE Appl. Power Electron. Conf. Expo. (APEC),
2014, pp. 3356–3361.
[5] G. Bin, J. Dominic, L. Jih-Sheng, C. Chien-Liang, T. LaBella,
and C. Baifeng, “High reliability and efficiency single-phase
transformerless inverter for grid-connected photovoltaic
systems,” IEEE Trans. Power Electron., vol. 28, no. 5, pp.
2235–2245, May 2013.
[6] J. Baojian, W. Jianhua, and Z. Jianfeng, “High-efficiency
single-phase transformerless PV H6 inverter with hybrid
modulation method,” IEEE Trans. Ind. Electron., vol. 60, no.
5, pp. 2104–2115, May 2013.
[7] W. Yong and L. Rui, “Novel high-efficiency threelevel
stacked-neutral point- clamped grid-tied inverter,” IEEE
Trans. Ind. Electron., vol. 60,no. 9, pp, Sep. 2013.
[8] M. Monfared and S. Golestan, “Control strategies for
single-phase grid integration of small-scale renewable
energy sources: A review,” Renew. Sustain. Energy Rev., vol.
16, pp. 4982–4993, 2012.
[9] W. Yu, J. S. Lai, H. Qian and C. Hutchens, “Highefficiency
MOSFET inverter with H6-type configuration for
photovoltaic non-isolated AC-module applications” IEEE
Trans.Power Electron., vol. 56, no.4, pp., Apr. 2011.
[10] X. Huafeng, X. Shaojun, C. Yang, and H. Ruhai, “An
optimized transformerless photovoltaic grid-connected
International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 06 Issue: 03 | Mar 2019 www.irjet.net p-ISSN: 2395-0072
© 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 1055
inverter,” IEEE Trans. Ind. Electron., vol. 58, no. 5, pp. 1887–
1895, May 2011.
[11] S. V. Araujo, P. Zacharias, and R. Mallwitz, “Highly
efficient single-phase transformerless inverters for grid-
connected photovoltaic systems,” IEEE Trans. Ind. Electron.,
vol. 57, no. 9, pp. 3118–3128, Sep. 2010.
[12] D. P. Kaundinya, P. Balachandra, andN.H.Ravindranath,
“Grid connected versus stand-alone energy systems for
decentralized power-A review of literature,” Renew. Sust.
Energy Rev., vol. 13, pp, October 2009.

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  • 1. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 03 | Mar 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 1052 A Systematic Approach to Design Single Phase Transformer less Inverter for PVG System with Reactive Power Control Ms. Ruchi Sakhare1, Asst. Prof. Bhushra Khan2 1Student, Dept. of Electrical Engineering, Abha Gaikwad Patil College of Engineering, Maharashtra, India 2Asst. Prof. Bhushra Khan, Dept. of Electrical Engineering, Abha Gaikwad College of Engineering, Maharashtra, India ----------------------------------------------------------------------***--------------------------------------------------------------------- Abstract - There has been an increasing interest in transformer less inverter for grid-tied photovoltaic (PV) system due to low cost, high efficiency, light weight, etc. Therefore, many transformer less topologies have been proposed and verified with real power injectiononly. Recently, almost every international regulation has imposed that a definite amount of reactive power should be handled by the grid-tied PV inverter. According to the standard VDEAR-N 4105, grid-tied PV inverter of power rating below 3.68KVA, should attain power factor (PF) from 0.95 leading to 0.95 lagging. In this paper, a new high efficiency transformerless topology is proposed for grid-tied PV system with reactive power control. The new topology structure and detail operation principle with reactive power flow is described. The high frequency common mode (CM) model and the control of the proposed topology are analyzed. The inherent circuit structure of the proposed topology does not lead itself to the reverse recovery issues even when inject reactivepowerwhich allow utilizing MOSFETswitchestoboosttheoverallefficiency. The CM voltage is kept constant at midpoint of dc input voltage, results low leakage current. Finally, to validate the proposed topology, a 1 kW laboratory prototype is built and tested. The experimental results show that the proposed topology can inject reactive power into theutility gridwithout any additional current distortion and leakage current. Key Words: Common mode, converter, high efficiency, leakage current, reactive power, transformer less. 1. INTRODUCTION Due to the increasing the energy demand the new energy sources requirement is increasing day by day. Now a day’s fossil fuels are the main energy sources for generating energy but they cannot sustain for longer change. These fossil fuels give rise to the emissionofharmful gassessuchas carbon dioxide and methane gas into the atmosphere and thus creating environmental pollution. These are the non- renewable energy sources. Renewablesourcessuchas wind, hydro-electricity and solar power cooled replacefossil fuels. Wind power is currently widely used in thehillyareaswhich can compensate more energy in generation of 2000 MW of electric power. Similarly PV system had gain more attention over the years as the best renewable energy sources. Some of the advantages of PV is that it has long life, low maintenance charges, ease of installationandnoneedoffuel. Generally grid connected transformer less inverter are can be divided into two groups; single stage inverter and two stage inverter. In two stage inverter a DC to DC converter connect the PV panel converts sun light to the DC electricitywithlowoutput voltage. A DC to DC boost converter is used this DC voltage can be further converted into the AC voltage with power electronic system (Inverter). PV devices:- Several energy sources are therefore energy conversion including batteriesfuel cellsandwindgeneration each energy source is connected to inverter through specific integration technique. A PV panel creates DC power which is link to a inverter directly or through a DC to DC converter. This is decreasing the total cost. Essentially a PV cell has a semiconductor PN junction diode cell that can converts the lights into electricity. Differentcell arrangementssuchasseriesparallel and parallel –series creates a PV model that has a specific power capacity. DC-DC power converter:- DC-DC power converter are basically used in the PV system to change the outputvoltage. This converter specifically can be used either as the boost converter or buck converter or a combination of both converter may be have depending on the desired capacityor the size of the output voltage to provide appropriate input voltage for the inverter with the DC voltage stabilizationand regulation capacity. 2. METHODOLOGY  A transformer less inverter for grid connected hybrid system was simulated using MATLAB/SIMULINK tool.  This three-phase transformer inverter was capable of obtain a maximum possiblepowerfromsolarand wind module. Incremental conductance MPPT technique was used.  Therefore, the PV string canbeofdifferentelectrical parameters and working conditions. Transformer less condition of the inverter helped the system to
  • 2. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 03 | Mar 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 1053 convert maximum output power from the hybrid system to the gird by limiting pulsating power.  Leakage Current was reduced by placing LC filter across the output of the inverter. LC filter also reduced the harmonics produce at inverter output voltage.  Output power was subjected to active and reactive power compensation. Three phaseoutputvoltageof 320 V, 20 A was obtained. A 1kW prototype of PV and 7 W of wind was built and tested through simulation. The control scheme of transformer less inverter topology was described, and its detailed analysis was provided. Fig 1.Block diagram of proposed system Fig2.Full bridge transformer less inverter 3. OBJECTIVE The objective of this Project is to provide a dynamic formulation for the single-phase PV inverter and reveal the origin of some of the problems discussed. The dynamic modeling provides a powerful tool for deterministic control-system design and system-interaction and stability analyses of the interconnected systems. The basic principles presented in this thesis can be used to analyze various control practices emerging in the field of PV inverters and other renewableenergytechnologies based on power electronics. The scientific contribution of thisProjectcanbesummarized as • Explicit formulation of photovoltaic inverter modeling. • Effect of photovoltaic generator on a single-phase VSI- type inverter dynamics. • Design rule for the minimum input capacitanceofa VSI- type photovoltaic inverter based on input-voltage- control stability. • Explicit formulation of the effect of multiplier-based grid synchronization causing negative output impedance. • Invention and development of a current-fed semi- quadratic buck-boost-type converter topology suited for transformer less modular photovoltaic. 4. PROPOSED WORK The PV module generates an electrically chargeable surface area which faces a grounded frame. In case of such configuration, a capacitance is formed between the PV module and the ground. Since this capacitance occurs as an undesirable side effect, it is referredasparasiticcapacitance. Due to the loss of galvanic separation between the PV module and the grid, a CM resonant circuit can be created. An alternating CM voltage that depends on the topology structure and control scheme, can electrify the resonant circuit and may lead to higher ground leakage current. In order to analyses the CM characteristics, an equivalent circuit of the proposed topology. In order to illustrate the CM model at switching frequency, could be replaced for the bridge-leg. The grid is a low frequency (50–60 Hz) voltage source;thustheimpactofgrid on the leakage current can be neglected. The DM capacitor Co can also be removed since it has no effect on the leakage current. 4.1 Control of the proposed topology In order to control the grid current, several existing control methods such as conventional PI controller, repetitive controller (RC), proportional resonant (PR) controller, and deadbeat (DB) controller can be adopted due to the capability of tracking reference signal without steady state error. Since the PR controller has better performance of tracking the reference signal if compared to the normal PI and RC controller, it is selected to control the output current of the proposed topology. The block diagram of the PR controller with harmonic currentcompensator,whereGc(s),Gh(s),and Gd(s) are the transfer function of fundamental current controller,harmoniccompensator,andinverterrespectively. The dynamic response of the system when it is subject to 750W load to 1000W load step change. It can clearly beseen
  • 3. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 03 | Mar 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 1054 that fast and effective response under the changes of active power reference are achieved with the proposed topology. Therefore, it can be concluded that the proposed topology can inject real power into utility grid with low leakage current and low THD at output. 4.2 Verification with Real Power Injection The proposed topology is verified with 1 kW power injection. The experimental gate drive signals for the proposed topology. It can be seen that the switching signals are fully matched with the proposed PWM scheme, and the gate drive voltages are kept constant at the desired level. The waveforms of CM characteristics. It is clear that the voltages V1N, V2N, V3N, and V4N are clamped at 200V during the freewheeling period of positive and negative half cycle. As a result, the CM voltage is kept constant at 200V for the whole grid cycle except a small fluctuation during grid zero crossing instant as witnessed. Consequently, the leakage current flows through the system are well reduced. During zero crossing instant, a small spike can be observed due to the fluctuation of CM voltage 4.3 Report Generation A new high efficiency transformer less topologyforgrid-tied PV system is presented. The main advantages of the proposed topology can be summarized as: The inherent circuit configuration of the proposed topology does not lead itself to the reverse recovery issues which allow utilizing MOSFET switches even though when inject reactive power. Therefore, without compromising the overall efficiency, proposed topology can inject reactive power into the utility grid. The CM voltage is kept constant at the mid-point of dc bus voltage; as a result, low leakage current flows through the system which is lower than the H6-type topology. PWM dead time is not required for the proposed topology that reduces the THD at the output. 5. SIMULATION RESULT REFERENCES [1] Monirul Islam, Nadia Afrin, and Saad Mekhilef, Senior Member, IEEE “Efficient Single Phase Transformerless Inverter for Grid-Tied PVG System With Reactive Power Control” IEEE Transactions On Sustainable Energy,2016. [2] M. Islam and S.Mekhilef,“H6-typetransformerlesssingle- phase inverter for grid-tied photovoltaicsystem,”IETPower Electron., vol. 8, pp. 636– 644, 2015. [3] M. Islam and S. Mekhilef, “An improved transformerless grid connected photovoltaic inverter with reduced leakage current,” Energy Convers. Manage., vol. 88, pp. 854–862, 2014. [4] M. Islam and S. Mekhilef, “Highefficiencytransformerless MOSFET inverter for grid-tied photovoltaic system,”inProc. 29th Annu. IEEE Appl. Power Electron. Conf. Expo. (APEC), 2014, pp. 3356–3361. [5] G. Bin, J. Dominic, L. Jih-Sheng, C. Chien-Liang, T. LaBella, and C. Baifeng, “High reliability and efficiency single-phase transformerless inverter for grid-connected photovoltaic systems,” IEEE Trans. Power Electron., vol. 28, no. 5, pp. 2235–2245, May 2013. [6] J. Baojian, W. Jianhua, and Z. Jianfeng, “High-efficiency single-phase transformerless PV H6 inverter with hybrid modulation method,” IEEE Trans. Ind. Electron., vol. 60, no. 5, pp. 2104–2115, May 2013. [7] W. Yong and L. Rui, “Novel high-efficiency threelevel stacked-neutral point- clamped grid-tied inverter,” IEEE Trans. Ind. Electron., vol. 60,no. 9, pp, Sep. 2013. [8] M. Monfared and S. Golestan, “Control strategies for single-phase grid integration of small-scale renewable energy sources: A review,” Renew. Sustain. Energy Rev., vol. 16, pp. 4982–4993, 2012. [9] W. Yu, J. S. Lai, H. Qian and C. Hutchens, “Highefficiency MOSFET inverter with H6-type configuration for photovoltaic non-isolated AC-module applications” IEEE Trans.Power Electron., vol. 56, no.4, pp., Apr. 2011. [10] X. Huafeng, X. Shaojun, C. Yang, and H. Ruhai, “An optimized transformerless photovoltaic grid-connected
  • 4. International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056 Volume: 06 Issue: 03 | Mar 2019 www.irjet.net p-ISSN: 2395-0072 © 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 1055 inverter,” IEEE Trans. Ind. Electron., vol. 58, no. 5, pp. 1887– 1895, May 2011. [11] S. V. Araujo, P. Zacharias, and R. Mallwitz, “Highly efficient single-phase transformerless inverters for grid- connected photovoltaic systems,” IEEE Trans. Ind. Electron., vol. 57, no. 9, pp. 3118–3128, Sep. 2010. [12] D. P. Kaundinya, P. Balachandra, andN.H.Ravindranath, “Grid connected versus stand-alone energy systems for decentralized power-A review of literature,” Renew. Sust. Energy Rev., vol. 13, pp, October 2009.