Fuzzy Logic Controller-based Synchronverter in Grid-connected Solar Power System with Adaptive Damping Factor*

 Abstract

In the last few years, the development of solar power systems has been rapid due to their technological maturity and cost-effectiveness. However, integrating solar power into the grid can negatively impact frequency stability, as the lack of rotating masses and inertial response can destabilize the power grid. To address this issue, a synchronverter, an inverter that mimics the operation of a synchronous generator, is crucial. It stabilizes the power grid by emulating a virtual inertia. However, a conventional proportional-integral (PI)-based synchronverter lacks an adaptive damping factor (Dp) or a digitalized smart controller to manage fast-responding solar inputs. Therefore, a novel fuzzy logic controller (FLC) framework is proposed to operate the synchronverter in a grid-connected solar power system. The FLC controls Dp in real-time, achieving a balance between speed and stability for frequency error correction based on frequency difference. The results of four case studies performed in Matlab/Simulink demonstrate that the proposed FLC-based synchronverter can stabilize the grid frequency, reducing the frequency deviation by at least 0.2 Hz (0.4%) compared to the conventional PI-based synchronverter.

Keywords

Fuzzy logic controller (FLC), synchronverter, renewable energy system (RES), grid stability, solar power system

BLOCK DIAGRAM:

                                                           Fig. 1 Power section of synchronverter

EXPECTED SIMULATION RESULTS:

                                             Fig. 2 Active power for varying resistive loads (RL)

                                        Fig. 3 Outputs of synchronverter for first case study

                                                Fig. 4 Testing environment for second case study

                                      Fig. 5 Outputs of synchronverter for second case study

                                            Fig. 6 Testing environment for third case study

                                       Fig. 7 Outputs of synchronverter for third case study

 Fig. 8 Testing environment for fourth case study

Fig. 9 Outputs of synchronverter for fourth case study

CONCLUSION:

Herein, a novel FLC-based framework was proposed to control a synchronverter in a grid- connected solar power system under dynamic weather conditions. Four case studies were simulated in Matlab/Simulink, and the results validated the ability of the proposed controller in stabilizing fg by reducing the frequency deviation by at least 0.2 Hz (0.4%), as compared with the conventional PI-based synchronverter. The performance of the FLC-based synchronverter was optimal even under sudden load changes or varying irradiances and temperatures. P was injected or absorbed whenever the frequency decreased or increased, respectively. The Dp controlled by the FLC was able to balance between transient speed and stability, whereby a larger Dp afforded a more prominent dampening effect, and vice versa.

REFERENCES:

[1] H Zsiborács, N H Baranyai, A Vincze, et al. Intermittent renewable energy sources: The role of energy storage in the European Power System of 2040. MDPI Electronics, 2019, 8(7): 729.

[2] M Z Saleheen, A A Salema, S M M Islam, et al. A target-oriented performance assessment and model development of a grid-connected solar PV (GCPV) system for a commercial building in Malaysia. Renewable Energy, 2021, 171: 371-382.

[3] Y Wang, V Silva, A Winckels. Impact of high penetration of wind and PV generation on frequency dynamics in the continental Europe interconnected system. IET Renewable Power Generation, 2014, 10(1): 10-16.

[4] F Li, C Li, K Sun, et al. Capacity configuration of hybrid CSP/PV plant for economical application of solar energy. Chinese Journal of Electrical Engineering, 2020, 6(2): 19-29.

[5] G Perveen, M Rizwan, N Goel. Comparison of intelligent modelling techniques for forecasting solar energy and its application in solar PV based energy system. IET Energy Systems Integration, 2019, 1(1): 34-51.

Modeling, Implementation and Performance Analysis of a Grid-Connected Photovoltaic/Wind Hybrid Power System

 Abstract

Modeling, Implementation and Performance Analysis of a Grid-Connected Photovoltaic/Wind Hybrid Power System Wind Hybrid System Grid-Connected PV Modeling & Analysis focuses on the dynamic modeling, design, and control strategy of a grid-connected photovoltaic (PV)/wind hybrid power system. By integrating PV stations and wind farms through a main AC-bus, the system's performance is improved. The Maximum Power Point Tracking (MPPT) technique is utilized for both PV and wind power sources to maximize the power extracted from the hybrid system, even in changing environmental conditions.

In this paragraph Using Matlab/Simulink software, the hybrid power system is modeled and simulated, and the effectiveness of the MPPT technique and control strategy is evaluated. Simulation results demonstrate the effectiveness of the MPPT technique in maximizing power extraction, and show that the hybrid power system operates at unity power factor and maintains constant grid voltage regardless of environmental conditions and injected power.

Keywords

PV; wind; hybrid system; wind turbine; DFIG; MPPT control.

Block Diagram:

Fig. 1. The system configuration of PV/wind hybrid power system.

Expected Simulation Results:

(a) Solar Irradiance.

(b) PV array voltage.

(c) PV array current.

(d) A derivative of power with respect to voltage (dPpv/dVpv).

                            Fig. 2. Performance of PV array during the variation of solar irradiance.

(a) PV DC-link Voltage.

(b) d-q axis components of injected current from PV station.

(c) Injected active and reactive power from PV station.

(d) Grid voltage and injected current from PV station.

(e) The power factor of the inverter.

(f) Injected current from PV station.

                                   Fig. 3. Performance of PV station during variation of the solar irradiance.

CONCLUSION

In this paper, a detailed dynamic modeling, design and control strategy of a grid-connected PV/wind hybrid power system has been successfully investigated. The hybrid power system consists of PV station of 1MW rating and a wind farm of 9 MW rating that are integrated through main AC-bus to inject the generated power and enhance the system performance. The incremental conductance MPPT technique is applied for the PV station to extract the maximum power during variation of the solar irradiance. On the other hand, modified MPPT technique based on mechanical power measurement is implemented to capture the maximum power from wind farm during variation of the wind speed. The effectiveness of the MPPT techniques and control strategy for the hybrid power system is evaluated during different environmental conditions such as the variations of solar irradiance and wind speed. The simulation results have proven the validity of the MPPT techniques in extraction the maximum power from hybrid power system during variation of the environmental conditions. Moreover, the hybrid power system successfully operates at unity power factor since the injected reactive power from hybrid power system is equal to zero. Furthermore, the control strategy successfully maintains the grid voltage constant regardless of the variations of environmental conditions and the injected power from the hybrid power system.

REFERENCES

[1] H. Laabidi and A. Mami, "Grid connected Wind-Photovoltaic hybrid system," in 2015 5th International Youth Conference on Energy (IYCE), pp. 1-8,2015.

[2] A. B. Oskouei, M. R. Banaei, and M. Sabahi, "Hybrid PV/wind system with quinary asymmetric inverter without increasing DC-link number," Ain Shams Engineering Journal, vol. 7, pp. 579-592, 2016.

[3] R. Benadli and A. Sellami, "Sliding mode control of a photovoltaic-wind hybrid system," in 2014 International Conference on Electrical Sciences and Technologies in Maghreb (CISTEM), pp. 1-8, 2014.

[4] A. Parida and D. Chatterjee, "Cogeneration topology for wind energy conversion system using doubly-fed induction generator," IET Power Electronics, vol. 9, pp. 1406-1415, 2016.

[5] B. Singh, S. K. Aggarwal, and T. C. Kandpal, "Performance of wind energy conversion system using a doubly fed induction generator for maximum power point tracking," in Industry Applications Society Annual Meeting (IAS), 2010 IEEE, 2010, pp. 1-

Latest Electrical projects for BTech/MTech

Electrical engineering students pursuing BTech or MTech degrees are always eager to explore the latest developments and trends in their field through practical projects. Here are some of the latest electrical projects suitable for BTech and MTech students:

1. Energy Harvesting Systems: Design and implement projects that focus on harvesting and utilizing ambient energy sources, such as solar, kinetic, or thermal energy. Explore innovative methods to convert and store these energy forms for powering low-power devices or sensor networks.
2. Electric Vehicle Charging Infrastructure: With the growing popularity of electric vehicles (EVs), develop projects related to EV charging infrastructure. Design smart charging stations, develop algorithms for intelligent charging management, and explore wireless charging technologies.
3. Grid-Connected Energy Storage: Investigate energy storage systems, such as batteries or supercapacitors, and their integration into the electrical grid. Design projects that optimize the use of energy storage for load balancing, peak shaving, or backup power supply.
4. Smart Homes and Buildings: Create projects that revolve around the concept of smart homes and buildings. Develop systems that automate energy management, enhance occupant comfort through intelligent lighting and temperature control, and integrate with IoT devices for seamless control.
5. Renewable Energy Integration and Microgrids: Focus on the integration of renewable energy sources like solar and wind into the existing power grid. Design and simulate microgrid systems that can operate in both grid-connected and islanded modes, considering energy generation, storage, and load management.
6. Cybersecurity for Smart Grids: With the increasing digitization of power systems, cybersecurity becomes crucial. Develop projects that address the challenges of securing smart grids, including intrusion detection systems, secure communication protocols, and vulnerability assessments.
7. Power Quality Monitoring and Enhancement: Explore projects related to power quality monitoring and improvement techniques. Design systems that can detect and mitigate power disturbances like harmonics, voltage sags/swells, and reactive power compensation.
8. Advanced Control Techniques for Power Electronics: Investigate advanced control algorithms for power electronic converters and drives. Develop projects that implement predictive control, model predictive control (MPC), or adaptive control techniques to improve the performance and efficiency of power electronic systems.

Active Power Filter for Power Quality in Grid Connected PV-System using an Improved Fuzzy Logic Control MPPT

 ABSTRACT

Recently, Photovoltaic (PV) systems have become one of the most significant and rapidly developing renewable energy sources worldwide. However, most grids include a power converter system based on power electronic components and several nonlinear loads that degrade power quality. This paper proposes a solution to this problem using a shunt active filter (SAPF) based on an efficiency method called the Synchronous Detection Method (SDM) to identify harmonic currents. The SAPF controller comprises an inverter that functions as a multi-functional device, interfacing the PV system with the electrical grid and eliminating harmonics generated by nonlinear loads while providing reactive power compensation. To extract maximum power from the photovoltaic system, a fuzzy logic control is proposed to address the fast irradiation change problem, which outperforms the conventional P&O algorithm. The simulation results using Matlab/Simulink show that the fuzzy logic control MPPT yields the best performance with minimal oscillation in output power. Moreover, the proposed control strategy of SAPF improves power quality in grid-connected photovoltaic systems, resulting in smaller total harmonic distortion, grid synchronization, and unity power factor.

KEYWORDS

Shunt Active Power Filter; Grid connected PV system; MPPT (P&O); Fuzzy Logic controller; power quality enhancement.

Block Diagram:

                                           Figure.1. Proposed control algorithm of SAPF.

Expected Simulation Results:

                                                                Figure.2. profile irradiation

Figure.3. Active power of PV Panel, Source and filter.

Figure.4 DC link voltage with P&O MPPT.

Figure.5. source current

Figure.6. source current FFT before filtring and after SAPF implementation.

Fig.7. source current spectrum in SAPF-PV System

Figure.8. PV current and voltage with FLC controller.

Figure.9. PV Power with FLC controller

Figure.10. DC link voltage with FLC controller.

Figure.11. source current with FLC controller.

CONCLUSION

This paper presents the simulation performance of a three-phase inverter-based multifunction PV power system with shunt active filtering capability. The simulation results show that the proposed multifunctional grid-connected PV power system is efficient for maximum PV power injection to the grid while filtering the current harmonics and compensating reactive power caused by nonlinear loads. Furthermore, a fuzzy logic controller based on P&O MPPT is applied in the PV system and compared with the conventional P&O algorithm. Under fast irradiation this FLC technique represents a good performance and increases the system efficiency. The simulation results show that the power control with multifunctional inverter is mostly achieved because in the daytime with intensive irradiation, the solar PV power system provides active power together with active power filter functionality. At night and/or during poor irradiation times, the active power required by the loads is supplied from the utility and the power quality is improving by SAPF.

REFERENCES

[1] B. Boukezata, J. P. Gaubert, A. Chaoui and M. Hachemi. “Générateur photovoltaique avec une commande directe de puissance connecté et avec adjonction de services au réseau de distribution,” Symposium de Genie Electrique EE-EPF. 2016 Grenoble

[2] A .Kalair ,N.Abas, A.R.Kalair, Z.Saleem,N.Khan. “Review of harmonic analysis, modeling and mitigation techniques”, 78 pp; 1152-1187 . 2017.

[3] M.TALI, A.Obbadi, A.Elfajri, Y.Errami. “Passive Filter for harmonics mitigation in standalone pv system for nonlinear load”, IRSEC14 ,978- 1-4799-7335-4, october 2014.

[4] B.Singh and K.Al haddad, “A review of active filter for power quality improvement”, IEEE. Vol: 46 , Issue: 5 , pp: 960 – 971.Oct1999.

[5] B.Boukezata, A.Chaoui, “Power Quality Improvement by an Active Power Filter in Grid-connected Photovoltaic systems with Optimized Direct Power Control Strategy”, Electric Power Components and Systems , vol:44, Issue :18 , pp:2036-2047, Oct 2016.

Onboard Unidirectional Automotive G2V Battery Charger using Sine Charging and its Effect on Li-ion Batteries

 ABSTRACT

The use of on-board battery chargers is common in electric and plug-in hybrid electric vehicles (EV/PHEV) for charging the battery from the utility power grid. To reduce the mass and cost of the charger while charging Li-ion batteries used in these vehicles, various cost-effective topologies are being proposed. This paper introduces two unidirectional battery charger topologies with a novel single-stage control that generates rectified sinusoidal charging currents to the battery, eliminating the need for bulky dc bus electrolytic capacitors used in conventional systems. Eliminating the electrolytic capacitors results in reduced size, mass, and cost of the charger and improved reliability. The paper presents simulations of voltage and current waveforms during normal operation and an accelerated cycle charge/discharge testing of battery cells with low-frequency current ripple to determine the impact on Li-ion battery capacity and life. The test results demonstrate the negligible impact of sine charging on Li-ion battery performance.

KEYWORDS

battery charger, sine charging, Li-ion

Schematic Diagram:

                 Fig. 1. Electrical schematic diagram of Isolated Unidirectional Charger Topology 1

Expected Simulation Results:

Fig. 2: Simulation Results of the Charger topologies with sinusoidal

                                     charging scheme (a) Topology 1 (b) Topology 2

                                      Fig. 3. Battery measured static capacity versus cycle # test results
                                                     sinusoidal charging and DC charging

                             Fig. 4. Battery capacity versus # of days test has been running to
                                               show impact of shelf life on loss of capacity

Fig. 5. Roundtrip charge discharge efficiency for 1C (16A) DC

                                  and sine charging and 1C (16A) 80% DOD DC discharge

Fig. 6. Battery HPPC resistance for an 80A, 10 second discharge

                                                 pulse at 100 and 800 cycles

Fig. 7. Battery open circuit voltage at 100 and 800 cycles

Fig. 8. Battery impedance versus frequency at 100 and 800 cycles

CONCLUSION

In battery chargers for EV/PHEVs the DC link capacitor volume can be significantly reduced by eliminating the electrolytic capacitor. This enables higher power density chargers with reduced mass, cost and improved reliability if current ripple at twice the line frequency can be tolerated by the battery. The impact of this low frequency ripple has been studied experimentally and the results support the use of the sinusoidal charging technique allowing 120Hz ripple into the battery as an alternative to DC charging. Two unidirectional battery charger topologies utilizing this sine charging technique with a single stage control have been simulated to verify the control strategy and charger performance. The first topology uses the conventional boost stage and would be more suitable for power < 1kW. As the power levels increase, the diode bridge losses significantly degrade the efficiency, so heat management might become an issue [10]. The second topology uses the bridgeless boost PFC configuration where the input diode rectifier input is replaced by two diodes and two switches. These are suitable for higher power levels >1kW due to their better efficiency. However, this topology introduces more EMI into the circuit.

REFERENCES

[1] D. Gautam, F.Musavi, M. Edington, W. Eberle, and W. G. Dunford, “An automotive on-board 3.3 kW battery charger for PHEV application,” in Proc. 7th IEEE Veh. Power Propulsion Conf., Chicago, IL,2011.

[2] W. Ruxi, F. Wang, L. Rixin, N. Puqi, R. Burgos, and D. Boroyevich, "Study of Energy Storage Capacitor Reduction for Single Phase PWM Rectifier," in Applied Power Electronics Conference and Exposition,2009. APEC 2009. Twenty-Fourth Annual IEEE, 2009, pp. 1177-1183.

[3] T. Shimizu, T. Fujita, G. Kimura, and J. Hirose, "A unity power factor PWM rectifier with DC ripple compensation," Industrial Electronics, IEEE Transactions on, vol. 44, pp. 447-455, 1997.

[4] Linlin Gu; Xinbo Ruan; Ming Xu; Kai Yao; , "Means of Eliminating Electrolytic Capacitor in AC/DC Power Supplies for LED Lightings,", Power Electronics, IEEE Transactions on, vol.24, no.5, pp.1399-1408, May 2009

[5] W. Beibei, R. Xinbo, Y. Kai, and X. Ming, "A Method of Reducing the Peak-to-Average Ratio of LED Current for Electrolytic Capacitor-Less AC-DC Drivers," Power Electronics, IEEE Transactions on, vol. 25, pp. 592-601, 2010.

Hybrid Three-Phase Transformer-Based Multilevel Inverter with Reduced Component Count

Abstract

This paper proposes a novel three-phase transformer-based multilevel inverter (MLI) topology to maximize the output voltage levels for high-power high-voltage applications while reducing component counts as compared to its transformer-based counterparts. The proposed hybrid topology is formed by connecting a three-level T-type module with full H-bridge cells through single-phase transformers. The T- type module is fixed while the full H-bridge cell can be repeated for enlarging the output voltage levels without increasing the voltage stress on switches. Key features of the proposed topology include low part count, capacitor-free, diode-free, voltage boosting, simple control, and modularity. Within the framework, a simple low-frequency pulse width modulation (LFPWM) switching scheme is used to control the output voltage, and the working principle is detailed for seven-, nine-, and N-level operation. The operability and performance of the proposed topology are numerically verified and experimentally validated at different loads. Moreover, its conversion efficiency is experimentally examined. Finally, a comparative study with existing transformer-based MLI circuits is conducted to prove its key merits.

Keywords

Cascaded-transformer multi level inverter (CTMI), DC-AC converter, hybrid multilevel inverter (MLI), multilevel inverter topology.

Circuit Diagram:

                   Figure 1. The Circuit Configuration Of The Proposed Transformer Based MLI Topology.

Expected Simulation Results:

    Figure 2. Simulation Waveforms Of The Proposed Topology When _ Is 1. (A) Pole Voltage Va0                  Synthesizing. (B) Pole Voltages Va0, Vb0, And Vc0. (C) Line Voltages Vab, Vbc, And Vca.

     Figure 3. Simulation Waveforms When _ Is 1. (A) Vab, Van, And Ian At Resistive Load. (B) Vab,                                            Van, And Ian At Resistive-Inductive Load.

         Figure 4. Simulation Waveforms When _ Is 1.5. (A) Pole Voltage Va0 Synthesizing. (B) Pole                                   Voltages Va0, Vb0, And Vc0. (C) Line Voltages Vab, Vbc, And Vca.

               Figure 5. Simulation Waveforms When _ Is 1.5. (A) Vab, Van, And Ian At Resistive Load. (B)                                        Vab, Van, And Ian At Resistive-Inductive Load.

Conclusion

This paper proposes a novel three-phase transformer-based nine-level inverter with a reduced component count, having the key features of being capacitor-, diode-free, and low counts of DC sources, switches, and transformers. The pro- posed circuit can increase the voltage level count to N levels without increasing the voltage stress across the switches, being a promising candidate for high-power high-voltage applications. Further, it has beneficial features of modularity, voltage boosting and simple structure. The working principle of the proposed topology was theoretically demonstrated, numerically verified, and experimentally validated through the in-house setup. Finally, the advantages of the proposed topology, in terms of component counts, are highlighted by a comparative study.

References

[1] P. R. Bana, K. P. Panda, R. T. Naayagi, P. Siano, and G. Panda, ``Recently developed reduced switch multilevel inverter for renewable energy integration and drives application: Topologies, comprehensive analysis and comparative evaluation,'' IEEE Access, vol. 7, pp. 54888_54909, 2019.

[2] M. Vijeh, M. Rezanejad, E. Samadaei, and K. Bertilsson, ``A general review of multilevel inverters based on main submodules: Structural point of view,'' IEEE Trans. Power Electron., vol. 34, no. 10, pp. 9479_9502, Oct. 2019.

[3] M. N. Raju, J. Sreedevi, R. P. Mandi, and K. S. Meera, ``Modular multilevel converters technology: A comprehensive study on its topologies, modelling, control and applications,'' IET Power Electron., vol. 12, no. 2, pp. 149_169, Feb. 2019.

[4] A. Salem, H. Van Khang, K. G. Robbersmyr, M. Norambuena, and J. Rodriguez, ``Voltage source multilevel inverters with reduced device count: Topological review and novel comparative factors,'' IEEE Trans. Power Electron., vol. 36, no. 3, pp. 2720_2747, Mar. 2021.

[5] H. P. Vemuganti, D. Sreenivasarao, S. K. Ganjikunta, H. M. Suryawanshi, and H. Abu-Rub, ``A survey on reduced switch count multilevel inverters,'' IEEE Open J. Ind. Electron. Soc., vol. 2, pp. 80_111, 2021.

A New Single-Source Nine-Level Quadruple Boost Inverter (NQBI) for PV Application

 Abstract

Multi-level inverters (MLIs) with switched capacitors are becoming popular due to their utilization in AC high-voltage applications as well as in the field of renewable energy. To achieve the required magnitude of output voltage, the switched capacitor (SC) technique employs a lesser number of DC sources in accordance with the voltage across the capacitor. Designing an efficient high-gain MLI with fewer sources and switches needs a rigorous effort. This paper introduces a prototype of a nine-level quadruple boost inverter (NQBI) topology powered by one solar photo-voltaic source using fewer capacitors, switches, and diodes when compared to the other SC-MLIs topology. The suggested NQB inverter produces nine levels of voltage in its output by efficiently balancing the voltages of the two capacitors. The various SC-MLIs are compared in order to highlight the benefits and drawbacks of the proposed nine-level quadruple boost inverter (NQBI) topology. To validate the efficacy of the proposed solar photovoltaic based NQBI without grid connection, detailed experimental results are presented in a laboratory setting under various test conditions.

Keywords

 NQBI, reduced switch count, switched capacitor inverter, SPWM technique.

Schematic Diagram:

Figure 1. Schematic Diagram Of Proposed Inverter Based Off-Grid Pv System With Ac Loads.

Expected Simulation Results:

Figure 2. Experimental Waveforms At Modulation Index 1 (A) Output Vol The Dc-Dc Converter, (B) Capacitor Voltage Vc1, (C) Capacitor Voltage Vc2 (D)Output Voltage And Current At Zl D 160 And (E) Output Voltage And Current At Zl D 160 C 200 Mh.

Figure 3. Experimental Waveforms At Modulation Index 0.5 (A) Output Vol The Dc-Dc Converter, (B) Capacitor Voltage Vc1, (C) Capacitor Voltage Vc2 (D) Output Voltage And Current At Zl D 80 C 200 Mh.

Figure 4. Experimental Waveforms Of (A) Output Voltage And Current Output Under Voltage Variation Of Dc -Dc Converter From 30v To 18v And (B) Output Voltage And Current Under Load Variation From Zl1 D 160 C 200 Mh To Zl2 D 80 C 200 Mh.

Conclusion

A reduced-switch, nine-level, switched-capacitor-based quadruple boost inverter topology is proposed in this paper. The NQBI is suggested for PV applications by using a solar PV panel as the only source. Though the inverter topology employs two capacitors of unequal voltage rating, the capacitor voltage equilibrium is established without employing an additional voltage balancing strategy. The comparative study shows that the proposed nine-level inverter topology has several advantages over other popular nine-level switched-capacitor inverter topologies, such as performance, total component count, and manufacturing cost. Finally, the results from the experiments show that the proposed NQB inverter-based PV system can work.

References

[1] B. P. Reddy, M. Rao A, M. Sahoo, and S. Keerthipati, ``A fault-tolerant multilevel inverter for improving the performance of a pole_phase modulated nine-phase induction motor drive,'' IEEE Trans. Ind. Electron., vol. 65, no. 2, pp. 1107_1116, Feb. 2018.

[2] E. Babaei and S. H. Hosseini, ``New cascaded multilevel inverter topology with minimum number of switches,'' Energy Convers. Manage., vol. 50, pp. 2761_2767, Nov. 2009. [Online]. Available: https://www.  sciencedirect.com/science/article/pii/S0196890409002489

[3] M. Vijeh, M. Rezanejad, E. Samadaei, and K. Bertilsson, ``A general review of multilevel inverters based on main submodules: Structural point of view,'' IEEE Trans. Power Electron., vol. 34, no. 10, pp. 9479_9502, Oct. 2019.

[4] N. Prabaharan and K. Palanisamy, ``Analysis and integration of multilevel inverter configuration with boost converters in a photovoltaic system,'' Energy Convers. Manage., vol. 128, pp. 327_342, Nov. 2016. [Online]. Available: https://www.sciencedirect.  com/science/article/pii/S0196890416308962

[5] I. Colak, E. Kabalci, and R. Bayindir, ``Review of multilevel voltage source inverter topologies and control schemes,'' Energy Convers. Man- age., vol. 52, no. 2, pp. 1114_1128, Feb. 2011. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0196890410004085