An Adaptive Proportional Resonant Controller for Single Phase PV Grid Connected Inverter Based on Band-Pass Filter Technique


This paper being an adaptive proportional resonant (PR) controller for single phase grid connected inverter that modify its control parameters to grid impedance change. Forth order band bass filter is method and then combine with the adaptive system for on-line detection of any variations in the resonance frequency. The estimated frequency is then prepared by mathematical signal processing operation to identify the variations in the grid impedance. For the on–line tuning of the PR parameters, a look-up table technique is apply and its parameters are linked with the measure impedance values. Simulation results based on MATLAB environment clearly verify the effectiveness of the proposed control scheme for 2 kW grid connected inverter system.

  1. Adaptive Proportional Resonant Controller
  2. Grid Impedance Estimation
  3. LCL Filter
  4. Look-up Table



Fig. 1. Block diagram of the proposed adaptive PR controller.


Fig. 2. Simulation result of emulated grid voltage.

Fig.3. FFT analysis of grid current. (a) APR controller. (b).PR controller.

Fig. 4. Online adaptation of the APR control parameters.

Fig. 5. Grid voltage and current waveforms under changeable grid

impedance with the proposed control strategy.


 A new control strategy based on an adaptive proportional resonant (APR) controller has been grown and successfully proved on a simulated 2 kW single phase grid tide PV inverter. A fourth order Sallen-Key band pass filter tailored to the system to taking the harmonic components around the resonant frequency has been execute. data signal processing method was employed in order to provide the controller with signals compare to the variable grid impedance. A large low level of current total harmonic distortion (THD) is reach in comparison with conventional PR controller and submission with IEEE929-Standard has been show.


[1] S. Kouro, J. I. Leon, D. Vinnikov, and L. G. Franquelo, “Grid-Connected Photovoltaic Systems: An Overview of Recent Research and Emerging PV Converter Technology,” IEEE Industrial Electronics Magazine, vol. 9, pp. 47-61, 2015.

[2] “IEEE Recommended Practice for Utility Interface of Photovoltaic (PV) Systems,” in IEEE Std 929-2000, ed, 2000.

[3] “IEEE Draft Application Guide for IEEE Standard 1547, Interconnecting Distributed Resources With Electric Power Systems,” in IEEE Unapproved Draft Std P1547.2/D11, Sept 2008, ed, 2008, p. 1.

[4] H. M. El-Deeb, A. Elserougi, A. S. Abdel-Khalik, S. Ahmed, and A. M. Massoud, “An adaptive PR controller for inverter-based distribution generation with active damped LCL filter,” in 2013 7th IEEE GCC Conference and Exhibition (GCC), 2013, pp. 462-467.

[5] W. L. Chen and J. S. Lin, “One-Dimensional Optimization for Proportional-Resonant Controller Design Against the Change in Source Impedance and Solar Irradiation in PV Systems,” IEEE Transactions on Industrial Electronics, vol. 61, pp. 1845-1854, 2014.

Standalone Operation of Modified Seven-Level Packed U-Cell (MPUC) Single-Phase Inverter


In this paper the standalone operation of the modified seven-level Packed U-Cell (MPUC) inverter is given and consider. The MPUC inverter has two DC sources and six switches, which cause seven voltage levels at the output. Compared to cascaded H-bridge and neutral point clamp multilevel inverters, the MPUC inverter produce a higher number of voltage levels using fewer components. The experimental results of the MPUC prototype validate the allocate operation of the multilevel inverter handle with various load types including motor, linear, and nonlinear ones. The design considerations, including output AC voltage RMS value, switching frequency, and switch voltage rating, as well as the harmonic analysis of the output voltage waveform, are taken into account to prove the advantages of the introduced multilevel inverter.


1. Multilevel inverter
2. Packed u-cell
3. Power quality
4. Multicarrier PWM
5. Renewable energy conversion



Figure 1. Single-phase seven-level MPUC inverter in standalone mode of operation


Figure 2. Seven-level MPUC inverter output voltage and current with DC source voltages. Ch1: V1,
Ch2: V2, Ch3: Vab, Ch4: il.

Figure 3. One cycle of output voltage and gate pulses of MPUC inverter switches. Ch1: Vab, Ch2: T1
gate pulses, Ch3: T2 gate pulses, Ch4: T3 gate pulses

Figure 4. MPUC inverter switches’ voltage ratings. Ch1: Vab, Ch2: T1 voltage, Ch3: T2 voltage, Ch4:
T3 voltage. and nonlinear). The step-by-step process for connecting loads is depicted in Figure 7, which show

Fig.5. Test results when a nonlinear load is connected to the MPUC inverter.Ch1 :Vab :Ch4 :il.

Figure 6. Output voltage and current waveform of MPUC inverter when different loads are added
step by step. Ch1: Vab, Ch4: il. (A) Transient state when nonlinear load is added to the RL load (left)
and after a while a motor load is added to the system (right); (B) steady state when a nonlinear load is
added to the RL load (left) and after a while a motor load is added to the system (right).

Figure 7. Voltage and current waveform of MPUC inverter with RMS calculation for 120 V system.


In this paper a redesign PUC inverter topology has been presented and studied experimentally. The proposed MPUC inverter can produce a seven-level voltage waveform at the output with low harmonic contents. The associated switching algorithm has been create and achieve on the introduced MPUC topology with reduced switching frequency aspect. Switches’ frequencies and ratings have been investigated experimentally to validate the good dynamic performance of the proposed topology. Moreover, the comparison of MPUC to the CHB multilevel inverter showed other advantages of the proposed multilevel inverter topology, including fewer components, a lower manufacturing price, and a smaller package due to reduced filter size. Author improvement: All authors improvement equally to the work presented in this paper. Funding: This research received no external funding. competition of Interest: The authors declare no competition of interest.


1. Bose, B.K. Multi-Level Converters; Multidisciplinary Digital Publishing Institute: Basel, Switzerland, 2015.
2. Mobarrez, M.; Bhattacharya, S.; Fregosi, D. Implementation of distributed power balancing strategy with a layer of supervision in a low-voltage DC microgrid. In Proceedings of the 2017 IEEE Applied Power Electronics Conference and Exposition (APEC), Tampa, FL, USA, 26–30 March 2017; pp. 1248–1254.
3. Franquelo, L.G.; Rodriguez, J.; Leon, J.I.; Kouro, S.; Portillo, R.; Prats, M.A.M. The age of multilevel converters arrives. IEEE Ind. Electron. Mag. 2008, 2, 28–39. [CrossRef]
4. Malinowski, M.; Gopakumar, K.; Rodriguez, J.; Perez, M.A. A survey on cascaded multilevel inverters. IEEE Trans. Ind. Electron. 2010, 57, 2197–2206. [CrossRef]
5. Nabae, A.; Takahashi, I.; Akagi, H. A new neutral-point-clamped PWM inverter. IEEE Trans. Ind. Appl. 1981,5, 518–523. [CrossRef]

Single Stage PV Array Fed Speed Sensorless Vector Control of Induction Motor Drive for Water Pumping


This paper deals with a single stage solar powered speed sensorless vector controlled induction motor drive for water pumping system, which is superior to regular motor drive. The speed is supposed through supposed stator flux. The proposed system includes solar photovoltaic (PV) array, a three-phase voltage source inverter (VSI) and a motor-pump assembly.

An incremental conductance (InC) based MPPT (Maximum Power Point Tracking) algorithm is used to harness maximum power from a PV array. The smooth starting of the motor is attained by vector control of an induction motor. The want configuration is create and simulated in MATLAB/Simulink platform and the design, modeling and control of the system, are varify on an experimental prototype developed in the laboratory.

  1. Speed Sensorless Control
  2. Stator Field-Oriented Vector Control
  3. Photovoltaic (PV)
  4. InC MPPT Algorithm
  5. Induction Motor Drive (IMD)
  6. Water Pump



Fig. 1. PV fed induction motor drive configuration


Fig. 2. Starting and MPPT of PV array at 1000 W/m2

Fig. 3. Intermediate signals during starting at 1000 W/m2



Fig. 4. Simulation results during starting at 1000 W/m2 (a) Proposed drive (b) Waveforms showing sensed speed and estimated speed

Fig. 5. SPV array performance during decrease in insolation from 1000 W/m2 to 500 W/m2



Fig. 6. Dynamic performance during irradiance decrement from 1000 W/m2 to 500 W/m2 (a) Proposed drive (b) Waveforms showing sensed speed and estimated speed

Fig. 7. PV array performance on increasing insolation from 500 W/m2 to 1000 W/m2



Fig. 8. Dynamic performance during irradiance decrement from 500 W/m2 to 1000 W/m2 (a) Proposed drive (b) Waveforms showing sensed speed and estimated speed


 A single stage solar PV array fed speed sensorless vector-controlled induction motor drive has been operated subjected to different conditions and the steady state and dynamic behaviors have been found quite satisfactory and suitable for water pumping. The torque and stator flux, have been controlled individually. The motor is started smoothly. The reference speed is produce by DC link voltage controller controlling the voltage at DC link along with the speed estimated by the feed-forward term incorporating the pump affinity law. The power of PV array is maintained at maximum power point at the time of change in irradiance. This is achieved by using incremental-conductance based MPPT algorithm.

The speed PI controller has been used to control the q-axis current of the motor. Smooth operation of IMD is achieved with want torque profile for wide range of speed control. Simulation results have displayed that the controller behavior is found satisfactory under steady state and dynamic conditions of solar power change. The suitability of the drive is also verified by experimental results under various conditions and has been found quite apt for water pumping.


[1] R. Foster, M. Ghassemi and M. Cota, Solar energy: Renewable energy and the environment, CRC Press, Taylor and francis Group, Inc. 2010.

[2] M. Kolhe, J. C. Joshi and D. P. Kothari, “Performance analysis of a directly coupled photovoltaic water-pumping system”, IEEE Trans. on Energy Convers., vol. 19, no. 3, pp. 613-618, Sept. 2004.

[3] J. V. M. Caracas, G. D. C. Farias, L. F. M. Teixeira and L. A. D. S. Ribeiro, “Implementation of a high-efficiency, high-lifetime, and low-cost converter for an autonomous photovoltaic water pumping system”, IEEE Trans. Ind. Appl., vol. 50, no. 1, pp. 631-641, Jan.-Feb. 2014.

[4] R. Kumar and B. Singh, “ Buck-boost converter fed BLDC motor for solar PV array based water pumping, ” IEEE Int. Conf. Power Electron. Drives and Energy Sys. (PEDES), 2014.

[5] Zhang Songbai, Zheng Xu, Youchun Li and Yixin Ni, “Optimization of MPPT step size in stand-alone solar pumping systems,” IEEE Power Eng. Society Gen. Meeting, June 2006.

A Novel Design of Hybrid Energy Storage System for Electric Vehicles


In order to provide long distance capacity and secure the minimization of a cost function for electric vehicles, a new hybrid energy storage system for electric vehicle is create in this paper. For the hybrid energy storage system, the paper suggest an optimal control algorithm create using a Li-ion battery power dynamic limitation rule-based control based on the SOC of the super-capacitor. At the same time, the magnetic integration technology adding a second-order Bessel low-pass filter is introduced to DC-DC converters of electric vehicles. As a result, the size of battery is reduced, and the power quality of the hybrid energy storage system is increase. Finally, the efficiency of the proposed method is confirm by simulation and experiment.

  1. Hybrid energy storage system
  2. Integrated magnetic structure
  3. Electric vehicles
  4. DC-DC converter
  5. Power dynamic limitation



Fig.1 Topology of the hybrid energy storage system


(a) Power command and actual power


(b) Power of the super-capacitor and Li-ion battery

Fig.2 Simulation results of the proposed HESS

  • (a) Battery current

(b) Super-capacitor current

(c) Load current

  • (d) Load voltage

Fig.3 Simulation results of the proposed HESS applied on electric vehicles



 In this paper, a new hybrid energy storage system for electric vehicles is create based on a Li-ion battery power dynamic limitation rule-based HESS energy management and a new bi-directional DC/DC converter. The system is compared to traditional hybrid energy storage system, showing it has significant advantage of reduced volume and weight. Moreover, the ripple of output current is reduced and the life of battery is improved.


[1] Zhikang Shuai, Chao Shen, Xin Yin, Xuan Liu, John Shen, “Fault analysis of inverter-interfaced distributed generators with different control schemes,” IEEE Transactions on Power Delivery, DOI: 10. 1109/TPWRD. 2017. 2717388.

[2] Zhikang Shuai, Yingyun Sun, Z. John Shen, Wei Tian, Chunming Tu, Yan Li, Xin Yin, “Microgrid stability: classification and a  review,” Renewable and Sustainable Energy Reviews, vol.58, pp. 167-179, Feb. 2016.

[3] N. R. Tummuru, M. K. Mishra, and S. Srinivas, “Dynamic energy management of renewable grid integrated hybrid  energy storage system, ” IEEE Trans. Ind. Electron., vol. 62, no. 12, pp. 7728-7737, Dec. 2015.

[4] T. Mesbahi, N. Rizoug, F. Khenfri, P. Bartholomeus, and P. Le Moigne, “Dynamical modelling and emulation of Li-ion batteries- supercapacitors hybrid power supply for electric vehicle applications, ” IET Electr. Syst. Transp., vol.7, no.2, pp. 161-169, Nov. 2016.

[5] A. Santucci, A. Sorniotti, and C. Lekakou, “Power split strategies for hybrid energy storage systems for vehicular applications, ” J. Power Sources, vol. 258, no.14, pp. 395-407,  2014.

New Three-Phase Symmetrical Multilevel Voltage Source Inverter


This paper presents a new design and implementation of a three-phase multilevel inverter (MLI) for distributed power generation system using low frequency modulation and sinusoidal pulse width modulation (SPWM) as well. It is a modular type and it can be extended for extra number of output voltage levels by adding additional modular stages. The impact of the proposed topology is its proficiency to maximize the number of voltage levels using a reduced number of isolated dc voltage sources and electronic switches. Moreover, this paper proposes a significant factor (FC/L), which is developed to define the number of the required components per pole voltage level.

A detailed comparison based on (FC/L) is provided in order to categorize the different topologies of the MLIs addressed in the literature. In addition, a prototype has been developed and tested for various modulation indexes to verify the control technique and performance of the topology. Experimental results show a well-matching and good similarity with the simulation results.

  1. Low frequency modulation
  2. Multi-level inverter
  3. Multi-level inverter comparison factor
  4. Sinusoidal pulse-width modulation (SPWM)
  5. Symmetrical DC power sources
  6. Three-phase



Fig. 1. Proposed three-phase MLI topology.


Fig. 2. Output line-to-line voltages ( VAB,VBC , and VCA ) with low frequency (50 Hz) modulation technique. (a) Simulation.

Fig. 3. Output phase voltages ( VAN,VBN , and VCN ) with low frequency modulation technique. (a) Simulation.

Fig. 4. Inverter outputs with R-L load (VAB ,VAN , and IAN) with low frequency modulation technique. (a) Simulation.

Fig. 5. Pole voltages for scheme I, mi =0.95 and fs=2.5kHz. (a) Simulation.

Fig. 6. Line-to-line voltages for scheme I, mi =0.95 and fs=2.5kHz . (a) Simulation.

Fig. 7. Phase voltages for scheme I, mi =0.95 and fs=2.5kHz . (a) Simulation.

Fig. 8. Pole voltages for scheme II, mi =0.95 and fs=2.5kHz . (a) Simulation.

Fig. 9. Line-to-line voltages for scheme II, mi =0.95 and fs=2.5kHz  . (a) Simulation.

Fig. 10. Phase voltages for scheme II, mi =0.95 and fs=2.5kHz. (a) Simulation.

Fig. 11. Line-to-line voltage and phase voltage at for scheme I, mi =0.95 and fs=2.5kHz . (a) Simulation.

Fig. 12. Line-to-line voltage and phase voltage for scheme II, mi =0.95 and fs=2.5kHz . (a) Simulation.

Fig. 13. Inverter output voltages: (a) three phase line-to-line voltages ( VAB, VBC, and VCA ), (b) line-to-line voltage, phase voltage and the phase current under R-L load.


A new modular multilevel inverter topology using two modulation control techniques is presented. The proposed has several advantages compared with existing topologies. A lower number of components count such as isolated dc-power supplies, switching devices, electrolyte capacitors, and power diodes are required. So it exhibits the merits of high efficiency, lower cost, simplified control algorithm, smaller inverter’s foot print and increased the overall system reliability. Due to the modularity of the presented topology, it can be extended to higher stages number leads to a good performance issues such as low, low, and low and eliminating the output filter will be obtained.

Beside the low frequency modulation, two schemes are successfully applied to control the suggested . This paper also suggests a significant factor, which defines the required components to generate one voltage level across the output pole terminals. The issue related to the cost of each used component is out of scope of this paper. The system simulation model and its control algorithm are developed using PSIM and MATLAB software package tools to validate the proposed topology. A laboratory prototype has been developed and tested for various modulation indexes to verify the control techniques and performance of the topology, the similarity between the simulation and obtained experimental results was confirmed.


[1] S. J. Park, F. S. Kang, M. H. Lee, and C. U. Kim, “A new single-phase five-level PWM inverter employing a deadbeat control scheme,” IEEE Trans. Power Electron., vol. 18, no. 3, pp. 831–843, May 2003.

[2] V. G. Agelidis, D. M. Baker, W. B. Lawrance, and C. V. Nayar, “A multilevel PWM inverter topology for photovoltaic applications,” in Proc. Int. Symp. Ind. Electron., Jul. 1997, vol. 2, pp. 589–594.

[3] G. J. Su, “Multilevel DC-link inverter,” IEEE Trans. Ind. Appl., vol. 41, no. 3, pp. 848–854, May–Jun. 2005.

[4] M. Calais, L. J. Borle, and V. G. Agelidis, “Analysis of multicarrier PWM methods for a single-phase five level inverter,” in Proc. Power Electron. Specialists Conf., 2001, vol. 3, pp. 1351–1356.

[5] C. T. Pan, C. M. Lai, and Y. L. Juan, “Output current ripple-free PWM inverters,” IEEE Trans. Circuits Syst. II, Exp. Briefs., vol. 57, no. 10, pp. 823–827, Oct. 2010.

An Efficient Constant Current Controller for PV SolarPower Generator Integrated with the Grid


This paper being the detailed design and modeling of grid integrated with the Photovoltaic Solar Power Generator. As the Photovoltaic System uses the solar energy as one of the renewable energies for the electrical energy production has an huge potential. The PV system is developing very fast as compared to its counterparts of the renewable energies. The DC voltage generated by the PV system is boosted by the DC-DC Boost converter.

The utility grid is incorporated with the PV Solar Power Generator through the 3-ı PWM DC-AC inverter, whose control is provided by a constant current controller. This controller uses a 3-ı phase locked loop (PLL) for tracking the phase angle of the utility grid and reacts fast enough to the changes in load or grid connection states, as a result, it seems to be efficient in supplying to load the constant voltage without phase jump. The complete mathematical model for the grid connected PV system is developed and simulated. The results verify that the proposed system is efficient to supply the local loads.

  1. PV Solar Power Generator
  2. DC-DC Boost Converter
  3. PWM inverter
  4. PLL
  5. Constant Current Controller (CCC)



Fig.1 Switching Model of Solar Inverter


Fig.2 P-V Curve of the Solar Array

Fig. 3 V-I Curve of the Solar Array

Fig. 4 DC voltage delivered by the Boost converter

Fig. 5Inverter output voltage before filtering

Fig. 6 Inverter output voltage after filtering

Fig. 7 Load current for supplying the 2 MW load.

Fig.8 Load current for supplying the load of about 30 MW, 2 MVAr


For improving the energy efficiency and power quality problem with the increment of the world energy demand, the power generation using the renewable energy source is the only solution. There are several countries located in the tropical and temperature regions, where the direct solar density may reach up to 1000W/m2. Hence PV system is considered as a primary resource. In this paper, the detailed modeling of grid connected PV generation system is developed. The DC-DC boost converter is used to optimize the PV array output with the closed loop control for keeping the DC bus voltage to be constant.

The 2 level 3-phase inverter is converting the DC into the sinusoidal AC voltage. The control of the solar inverter is support through the constant current controller. This controller tracks the phase and frequency of the utility grid voltage using the Phase- Locked-Loop (PLL) system and generates the switching pulses for the solar inverter. Using this controller the output voltage of the solar inverter and the grid voltage are in phase. Thus the PV system can be merge to the grid. The simulation results the being in this paper to validate the grid connected PV system model and the applied control scheme.


[1] A. M. Hava, T. A. Lipo and W. L. Erdman. “Utility interface issues for line connected PWM voltage source converters: a comparative study”, Proceeding of APEC’95, Dallas (USA), pp. 125-132, March 1995.

[2] L. J. BORLE, M. S. DYMOND and C. V. NAYAR, “Development and testing of a 20 kW grid interactive photovoltaic power conditioning system in Western Australia”, IEEE Transaction, Vol. 33, No. 2, pp. 502-508, 1997.

[3] M. Calais, J. Myrzik, T. Spooner, V. Agelidis, “Inverters for single- phase grid connected photovoltaic systems – an overview”, IEEE 33rd Annual Power Electronics Specialists Conference, Volume 4, 23-27 June 2002

[4] S. K. Chung, “Phase-Locked Loop for Grid connected Three-phase Power Conversion Systems”, IEE Proceeding on Electronic Power Application, Vol. 147, No. 3, pp. 213-219, 2000.

[5] S. Rahman, “Going green: the growth of renewable energy”, IEEE Power and Energy Magazine, 16-18 Nov./Dec. 2003.

A 5-level High Efficiency Low Cost Hybrid Neutral Point Clamped Transformerless Inverter for Grid Connected Photovoltaic Application


With the increase in the level of solar energy combination into the power grid, there occur a need for highly efficient multilevel transformerless grid connected inverter which is able to inject more power into the grid. In this paper, a novel 5-level Hybrid Neutral Point Clamped transformerless  inverter topology is proposed which has no important ground leakage current.

The proposed inverter is consider in detail and its switching design to generate multilevel output is discussed. The proposed inverter is compared with some popular transformerless inverter topologies. Simulations and experiments results confirm the service and good performance of the proposed inverter.



Fig. 1. Proposed hybrid neutral point clamped inverter


Fig. 2. Inverter operation at UPF

Fig. 3. Inverter operation at 300 lag PF

Fig. 4. Inverter output for increase of modulation index from 0.45 to 0.95

Fig. 5. Inverter output for decrease of modulation index from 0.95 to 0.45

Fig. 6. Dynamic performance of inverter for increase of load

Fig. 7. Dynamic performance of inverter for decrease of load

Fig. 8. Inverter operation with chopper balancing circuit activated

Fig. 9. Inverter operation with chopper balancing circuit deactivated


 A 5-level Hybrid neutral point clamped transformerless PV grid connected inverter is presented in this paper. The main characteristics of proposed transformerless inverter are:

1) Lower stress on the grid conform inductor, thereby reducing the filtering cost and size as compared to conventional 3-level inverters like H5 and HERIC  inverter.

2) Lower cost as compared to 5L-DCMLI as the proposed inverter want less no of clamping diodes.

3) Higher power handling capacity as compared to conventional 3-level inverters.

4) Higher efficiency as compared to 5L-DCMLI and H5 inverter.

5) No common mode leakage current as the proposed inverter belongs to the family of half bridge inverters.

6) The proposed inverter is capable of trade reactive power with the grid.

Therefore, with excellent performance in eliminating the CM current, multilevel output voltage and high efficiency, the proposed inverter provides an lively alternative to the conventional transformerless grid-connected PV inverters.

Moreover, due to its perfection over the 5L-DCMLI in terms of efficiency and cost parameters, the consistency of the proposed inverter is not limited to grid connected PV inverters and it can find its way for all the applications where currently 5L-DCMLI are employed.


[1] M. Calais and V. G. Agelidis,“Multilevel converters for single-phase grid connected photovoltaic systems-an overview,” Industrial Electronics, 1998. Proceedings. ISIE ’98. IEEE International Symposium on, Pretoria, 1998, pp. 224-229 vol.1. doi: 10.1109/ISIE.1998.707781 [2] R. Teodorescu, M. Liserre et al., “Grid converters for photovoltaic and wind power systems”. John Wiley & Sons, 2011, vol. 29.

[3] E. Gubia, P. Sanchis, A. Ursua, J. Lopez, and L. Marroyo, “Ground currents in single phase transformerless photovoltaic systems”, Progress in Photovoltaics: Research and Applications, vol. 15, no. 7, pp. 629650, 2007.

[4] H. Xiao and S. Xie, “Leakage current analytical model and application in single-phase transformerless photovoltaic grid-connected inverter”, IEEE Transactions on Electromagnetic Compatibility, vol. 52, DOI 10.1109/TEMC.2010.2064169, no. 4, pp. 902913, Nov. 2010.

[5] S. Busquets-Monge, J. Rocabert, P. Rodriguez, S. Alepuz and J. Bordonau, “Multilevel Diode-Clamped Converter for Photovoltaic Generators With Independent Voltage Control of Each Solar Array”, in IEEE Transactions on Industrial Electronics, vol. 55, no. 7, pp. 2713-2723, July 2008. Doi: 10.1109/TIE.2008.924011