Research Article  Open Access
Efficiency Improvement of ThreePhase Cascaded HBridge Multilevel Inverters for Photovoltaic Systems
Abstract
Mediumscale photovoltaic (PV) systems using cascaded Hbridge multilevel inverters have a capability to perform individual maximum power point tracking (MPPT) for each PV panel or each small group of panels, resulting in minimization of both power losses from panel mismatch and effect of partial shading. They also provide high power quality, modularity, and possibility of eliminating dcdc boost stage and linefrequency transformer. However, each PV panel in the system is subjected to a doublelinefrequency voltage ripple at the dclink which reduces the MPPT efficiency. This paper proposes a dclink voltage ripple reduction by thirdharmonic zerosequence voltage injection for improving the MPPT efficiency. Moreover, a control method to achieve individual MPPT control of each inverter cell is also presented. The validity and effectiveness of the proposed methods were verified by computer simulation.
1. Introduction
Renewable energy technology has undergone a substantial development in the last three decades. Photovoltaic (PV) system is promising and one of the fastest growing renewable energy sources. The worldwide cumulative installed capacity of PV systems has been increasing exponentially in the last decade and recently has reached a level of 178 GW at the end of 2014 [1] due to the decreasing price per PV panel and government policies in many countries.
Generally, the PV system topologies can be categorized into four groups: (1) central inverter, (2) moduleintegrated inverter, (3) string inverter, and (4) multistring inverter [2–5]. In the central inverter topology, several PV strings (PV panels connected in series) are connected in parallel with one blocking diode per string to form a single dclink and are connected to the grid via a central inverter. This topology has a simple structure, a reliable control, and a low initial cost. However, with only one centralized maximum power point tracking (MPPT) control, the energy yield can be easily reduced by the effects of panel mismatch and partial shading. Dividing PV panels into smaller groups with individual MPPT control can mitigate the problem [6, 7]. The moduleintegrated inverter topology is another side of the spectrum. In this topology, one converter operates with only one or a few PV panels. Thus, the power loss from panel mismatch can be minimized and the effect of partial shading can be mitigated. However, the voltage amplification by either dcdc boost stage or transformer is required. The moduleintegrated inverter topology is intended for small PV systems lower than 500 W. For the string inverter topology, one PV string is connected to the grid via one inverter. Therefore, the benefit of this topology is a tradeoff between central inverter and moduleintegrated inverter topologies. Finally, the multistring inverter topology combines higher energy yield of the string inverter with low initial cost of the central inverter topology. Several PV strings, each with one dedicated dcdc converter, are connected to a central inverter. Moreover, in addition to the traditional twolevel inverters, the use of neutralpointclamped (NPC) inverter for either central inverter, string inverter, or multistring inverter topologies has also been reported [8, 9].
Recently, cascaded Hbridge multilevel inverter topology has gained interest from many researchers for PV system applications [10–20]. It is characterized by a cascade connection of several Hbridge inverters per one phase. The system topology is depicted in Figure 1 which can be either a singlephase system in Figure 1(a) or a threephase system in Figure 1(b), depending on the system power rating. A single PV panel can be directly connected to the dc side of each Hbridge inverter to implement the concept of one converter per one PV panel. This is similar to that of the moduleintegrated inverter topology. In this case, it is possible to achieve the distributed MPPT control by each Hbridge inverter individually [10, 11] that greatly optimizes the energy yield from the PV panels. The advantages of this system can be summarized as follows:(i)The MPPT can be performed individually for each PV panel to eliminate the effects of panel mismatch and partial shading, thus maximizing the energy production in contrast to the system utilizing the centralized MPPT.(ii)Due to the voltage scalability of the cascaded multilevel converter, it is possible to eliminate the dcdc boost converter stage and linefrequency transformer for voltage elevation. This can reduce the weight and cost of the PV system.(iii)The cascaded multilevel converter produces multilevel PWM output voltage waveform which has low voltage THD (Total Harmonic Distortion) and low current THD. Therefore, EMI emission and harmonic filter are minimized.(iv)Due to multiplicative effect of switching frequency, the system can achieve high output switching frequency while the device switching frequency is low. Thus, the switching power loss is low.(v)The modularity of the system enables the reduction of manufacturing cost and easy maintenance operation.
(a)
(b)
(c)
On the other hand, the system can be extended to a largecapacity PV system in which the dclink of each Hbridge inverter can be connected to several PV strings with one dedicated dcdc converter per string that is similar to the concept of multistring inverter topology [12, 13]. This kind of system can achieve a power rating of a few megawatts with the voltage rating in the mediumvoltage level. However, this paper focuses on a smaller PV system with one PV panel per one Hbridge inverter for simplifying the analysis to be presented in this paper.
Since each PV panel is directly connected to a singlephase dcac inverter, it is subjected to power fluctuation of an angular frequency of produced by the ac side of the Hbridge inverter. The power fluctuation causes voltage ripple at the terminal of the PV panel connected to the dclink capacitor. The lowfrequency ripple of the dclink voltage is significant in this topology because each cell is a singlephase inverter. This is unlike in a threephase inverter such as NPC or conventional twolevel inverter where the three phase legs share a common dclink in which the ripple frequency is higher () but much smaller in amplitude. The voltage ripple causes an output power ripple from the PV panel because the terminal voltage swings around the voltage at MPP. This power ripple makes the average output power somewhat lower than the power at MPP, thus reducing the MPPT efficiency, as described in Figure 2 [3]. Since the MPPT algorithm always drives the operating point to the MPP and the center of voltage swing is always the voltage at MPP, reducing the dclink voltage ripple in each cell can increase the average output power and the MPPT efficiency.
The dclink voltage (or current) ripple reduction methods have been proposed for some systems and applications; for example, [21] proposed a dclink ripple current reduction for paralleled threephase voltagesource converter (VSC) with interleaving (this method requires two VSCs connected in paralleled), [22] proposed a dclink voltage ripple reduction for a transformerless modular wind generator system, and [23] proposed a dclink voltage ripple minimization method for a modular VSC for HVDC power transmission. This paper presents a dclink voltage ripple reduction in each cell of the threephase cascaded Hbridge multilevel PV system by injecting the thirdharmonic zerosequence voltage to improve the MPPT efficiency. The objective of the thirdharmonic zerosequence voltage injection in this paper is different from that in [24] where it is used to increase the dclink utilization and obtain higher number of voltage levels. The method proposed in this paper does not introduce any additional circuit component. In addition, this paper also describes a control method to achieve individual MPPT control in each converter cell. The validity and effectiveness of the methods presented in this paper are verified by computer simulation.
2. Circuit Configuration of the PV System
According to Figure 1, each phase of the system is a series connection of multiple converter cells. Each converter cell consists of an Hbridge inverter and a PV panel as an isolated dc source. The dclink capacitor is installed in parallel with each PV panel as a power decoupling element for absorbing the PWM switching current produced at the dc side of each Hbridge inverter. The system is connected to the grid via aclink inductor(s) . Each Hbridge inverter is modulated with a unipolar PWM technique and produces threelevel PWM voltage. The frequency of triangular carrier signal for each cell is . When several cells are connected in series, a phaseshift PWM (PSPWM) modulation strategy is used to generate multilevel PWM voltage waveform. In this case, the number of output voltage levels becomes levels (linetoneutral), where is the number of cells per phase. The phase shift of carrier signals of the adjacent cells is [25]. Due to the multiplicative effect of switching frequency of the PSPWM, the system then achieves an output switching frequency of , while the device switching frequency is only at . This has a positive effect on the system efficiency. Moreover, both the multilevel PWM and high switching frequency characteristics have a positive effect on the harmonic performance of the system.
3. Principle of dcLink Voltage Ripple Reduction
This paper proposes the dclink voltage ripple reduction by injecting the thirdharmonic zerosequence voltage component which can reduce the dclink voltage ripple without introducing any additional circuit component. Since the thirdharmonic zerosequence voltage injection technique can be used only for threephase threewire systems, this paper focuses on the threephase cascaded Hbridge PV system as shown in Figure 1(b) only.
Considering cell depicted in Figure 3 in steadystate condition, the instantaneous power of capacitor has only ac component. Hence, by neglecting power losses of the Hbridge inverter, the instantaneous power balance can be expressed aswhere is the power flowing from the PV panel, is the power flowing to the dc side of Hbridge inverter, and is the ac component of . In this case, is much larger than because and are both ac quantities while and are both dc quantities. Hence, the instantaneous power of capacitor at the steadystate can be approximated asAn approximated expression of the ac ripple component of capacitor voltage can be calculated from the dclink capacitor power as (see Appendix)Hence, from (2) and (3), the ac ripple component of dclink voltage can be expressed aswhere is the capacitance of the dclink capacitor and is the nominal capacitor voltage. It should be noted that and are equal.
Voltage without the thirdharmonic zerosequence voltage injection is expressed aswhile with the thirdharmonic zerosequence voltage injection is expressed aswhere is the relative amplitude of the thirdharmonic voltage. By assuming that the system operates with power factor close to unity, the grid current is expressed asSubstituting (5), (6), and (7) into (4), the dclink voltage ripple component without the thirdharmonic zerosequence voltage injection is expressed aswhile the dclink voltage ripple with the thirdharmonic zerosequence voltage injection is expressed asFigure 4 shows the plots of the estimated waveforms of dclink voltage ripple and that of the dclink voltage ripple with the thirdharmonic zerosequence voltage injection when . It can be seen that injecting the thirdharmonic zerosequence voltage can reduce the amplitude of the dclink voltage ripple. Figure 5 shows the percentage of the dclink voltage ripple reduction versus obtained from the theoretical calculation using (8) and (9), for = 0 to 0.8. It shows that as increases more ripple amplitude reduction can be achieved. However, Figure 6 shows that the amplitude of is higher than 100% when is larger than 0.4 (amplitude is equal to 100% when ). Hence, the relative amplitude cannot be increased arbitrarily without bound in order to prevent the overmodulation of Hbridge inverter. The maximum possible value of depends on the modulation index of the Hbridge inverter which is a ratio between the voltage amplitude and the PV panel voltage at maximum power point . For example, when the modulation index is equal to 0.85, the amplitude of can be increased by the thirdharmonic zerosequence voltage injection up to 117% (=) before overmodulation occurs. Thus, the maximum possible value of is 0.6 according to Figure 6. Hence, the dclink voltage ripple amplitude reduction can be achieved up to 39% according to Figure 5.
4. Method for Individual MPPT Control
The principle of individual MPPT control is based on the individual control of the dclink voltage of each converter cell. By considering Figure 3, the following relation can be obtained:Hence, the dclink voltage can be controlled by controlling using the proportionalintegral (PI) controller as shown in Figure 7, considering as a disturbance. In this case, is related to aswhere is the duty cycle of the Hbridge inverter. This means that the Hbridge inverter works as a currentsource converter when seen from the dc side, where can be made proportional to by adjusting the duty cycle. Note that is an ac signal because is an ac signal while is a dc signal. Therefore, the product of and becomes a dc signal. Assuming that has a constant amplitude, the output of PI controller in Figure 7 is changed to in Figure 8, where is rms value of . This means that the dclink voltage can be controlled by adjusting the duty cycle of the Hbridge inverter. However, adjusting duty cycle will also affect the Hbridge inverter output voltage because Thus, the duty cycle of each inverter in phase (where ) cannot be adjusted arbitrarily; otherwise the summation of in phase may not be equal to , where is the voltage command for phase obtained from the grid current control. In order to simultaneously control the grid current and the individual dclink voltage, the output voltage command of each inverter must be a weighted proportion of calculated bywhere and is the rms value of the duty cycle of cell obtained from the PI controller as shown in Figure 8.
The calculation of the voltage command for each phase is based on the grid current control using the conventional voltageoriented control with current decoupling [26]. The axis current command is calculated from the summation of error signals of all cells passing through the PI controller as shown in Figure 9, while the axis current command is set to zero.
The calculation of the dclink voltage command for each cell to achieve MPPT can be done by the conventional Perturb and Observe (P&O) method, the PIbased Incremental Conductance method, or others as described in [27].
5. Simulation Results
The simulation model of the threephase cascaded Hbridge PV system in Figure 1(b) was created with four cells per phase. In this model, it is assumed that each Hbridge inverter is connected to a PV panel and a dclink capacitor at the dclink network. The parameters of the PV panel are based on the PV panel model CHSM6610P250 from Astronergy with the nominal output power of 250 W. Table 1 summarizes the parameters used in the simulation model.

5.1. Simulation Results without the ThirdHarmonic ZeroSequence Voltage Injection
Figure 10 shows the steadystate simulation results of the system in Figure 1(b) without the thirdharmonic zerosequence voltage injection. Figure 10 shows that the waveforms of the threephase voltage command ( and ) are sinusoidal with only fundamental component. The waveforms of the linetoline output voltages ( and ) are multilevel PWM voltage waveforms with 17 voltage levels. Therefore, the waveforms of the grid currents ( and ) are close to sinusoidal with small ripples and low THD. The peak amplitude of the grid current in this case is 19.2 A. The dclink voltage waveform of cell c1 contains a 100 Hz ripple of 8.2 and a small switchingfrequency ripple. The output power of PV panel of cell c1 contains a 200 Hz ripple of 25.7 and a small switchingfrequency ripple with an average output power and peak output power of 238 W and 249 W, respectively. The peak output power is the power at MPP which is equal to a product of maximum power voltage and maximum power current in Table 1 (30 V × 8.3 A). The total power produced by this system is calculated aswhere , , and are the linetoneutral grid voltages. In this case, the calculated total power is 2,856 W. Note that the converter power loss is neglected in this simulation.
5.2. Simulation Results with the ThirdHarmonic ZeroSequence Voltage Injection
Figure 11 shows the steadystate simulation results of the system in Figure 1(b) with the thirdharmonic zerosequence voltage injection (). The waveforms of threephase voltage command ( and ) are the combinations of the fundamental component and the thirdharmonic components. The waveforms of the linetoline output voltages ( and ) are multilevel PWM voltage waveforms similar to those in Figure 10. These waveforms do not contain the thirdharmonic component because the system is the threephase threewire system which cancels the zerosequence thirdharmonic components out at the output. As a result, the waveforms of the grid currents ( and ) are still close to sinusoidal with only fundamental component. The peak amplitude of the grid current in this case is increased to 19.7 A. The waveform of the dclink voltage of cell c1 contains 100 Hz and 200 Hz ripple components as predicted by (9). The amplitude of the dclink voltage ripple is decreased to 5.6 . It can be seen that the dclink voltage waveform in Figure 11 and that in Figure 4 are similar. This confirms the validity of dclink voltage ripple estimation presented in Section 3.
In Figure 11, the ripple output power waveform of PV panel of cell c1 is a multifrequency waveform. The amplitude of the power ripple is decreased to 13.6 with an average output power increased to 244.3 W. The peak power waveform remains 249 W. In this case, the total power produced by this system is 2,932 W (calculated by (14)) which is increased about 2.6% from the previous case.
5.3. Comparison of the Results
Table 2 shows the comparison of the simulation results of the two cases. It can be seen that injecting the thirdharmonic zerosequence voltages with can reduce the amplitudes of the dclink voltage ripple by 32%. The PV panel power ripple is also decreased, while the peak of power ripple remains unchanged (equal to the power at MPP). As a result, the average output power of each PV panel is increased and the total output power is also increased for the same amount. According to the simulation results, the total output power is increased about 2.6% without any additional circuit component. However, it should be noted that the percentage of the increased power also depends on the accuracy of the currentvoltage characteristics of the PV panel used in the simulation.

It should also be noted that the value of the dclink voltage ripple reduction of 32% in Table 2 is consistent with the value of about 30% in Figure 5. This means that the theoretical estimation of the dclink voltage ripple presented in Section 3 is accurate.
6. Conclusion
This paper presents a dclink voltage ripple reduction of the threephase cascaded Hbridge multilevel PV system using the thirdharmonic zerosequence voltage injection. Therefore, this method is valid only for threephase threewire systems. The injection of thirdharmonic zerosequence voltage can reduce the amplitudes of the voltage ripple and power ripple of each PV panel. As a result, the average output power of each PV panel and the total output power are increased. According to the simulation results, the dclink voltage ripple reduction is 32% when the relative amplitude of the thirdharmonic voltage is 0.4, resulting in the total power increase of 2.6% without any additional circuit component. This paper also presents a control method to achieve an individual MPPT control of each converter cell.
Appendix
Derivation of dcLink Voltage Ripple Equation
The derivation presented in this section is the same as [28] and is repeated here for completeness. The dclink voltage of each cell is equal to the dclink capacitor voltage . Denote the dclink capacitor instantaneous power by and the dclink capacitor instantaneous energy by . , and can be related asEquation (A.1) shows that can be expressed as a summation of the dc component and the ac component . From (A.1), the dclink capacitor voltage can be expressed asEquation (A.2) shows that can be expressed as a summation of dc mean voltage and the ac ripple component . The objective of the following section is to find .
Define and . Hence, from (A.2), the following equations are obtained:Next, choose a point for Taylor series expansion of which makes . Then, the following equations are obtained:The function can be approximated by Taylor series expansion around the point asBy substituting (A.4) into (A.5), the following equation is obtained:By comparing (A.6) with (A.2), the terms and can be expressed as Therefore, the ac ripple component can be calculated from the ac component of the dclink capacitor power .
Nomenclature
:  ac component of 
:  Relative amplitude of thirdharmonic voltage 
:  Capacitance of dclink capacitor 
:  Duty cycle signal of bridge cell 
:  rms value of 
:  rms duty cycle of th cell of phase 
:  Grid current of phase a 
:  Amplitude of 
:  axis current reference of the system 
:  axis current reference of the system 
:  Current of bridge cell at the dc side 
:  Current of PV panel 
:  Instantaneous power of dclink capacitor 
:  Instantaneous power of bridge cell at the ac side 
:  Instantaneous power of PV panel 
:  dclink capacitor voltage 
:  ac ripple component of dclink capacitor voltage 
:  dc mean value of dclink capacitor voltage 
:  Output voltage of bridge cell at the ac side 
:  Amplitude of 
:  Voltage of PV panel 
:  ac ripple component of PV panel voltage 
:  dc mean value of PV panel voltage 
:  Ripple component of PV panel voltage without thirdharmonic injection 
:  Ripple component of PV panel voltage with thirdharmonic injection 
:  Voltage reference of phase 
:  Reference of for th cell of phase 
:  PV panel voltage of th cell of phase 
:  Linetoneutral grid voltages 
:  Instantaneous energy of dclink capacitor 
:  dc component of 
:  ac component of 
:  Fundamental angular frequency of the system. 
Competing Interests
The authors declare that they have no competing interests.
References
 SolarPower Europe, Global Market Outlook for Solar Power 2015–2019, SolarPower Europe, Brussel, Belgium, 2015.
 J. M. A. Myrzik and M. Calais, “String and module integrated inverters for singlephase grid connected photovoltaic systems—a review,” in Proceedings of the IEEE Bologna PowerTech Conference, vol. 2, pp. 430–437, Bologna, Italy, June 2003. View at: Publisher Site  Google Scholar
 S. B. Kjaer, J. K. Pedersen, and F. Blaabjerg, “A review of singlephase gridconnected inverters for photovoltaic modules,” IEEE Transactions on Industry Applications, vol. 41, no. 5, pp. 1292–1306, 2005. View at: Publisher Site  Google Scholar
 M. Calais, J. Myrzik, T. Spooner, and V. G. Agelidis, “Inverters for singlephase grid connected photovoltaic systems—an overview,” in Proceedings of the IEEE 33rd Annual Power Electronics Specialists Conference (PESC '02), vol. 4, pp. 1995–2000, June 2002. View at: Google Scholar
 Q. Li and P. Wolfs, “A review of the single phase photovoltaic module integrated converter topologies with three different DC link configurations,” IEEE Transactions on Power Electronics, vol. 23, no. 3, pp. 1320–1333, 2008. View at: Publisher Site  Google Scholar
 N. Femia, G. Lisi, G. Petrone, G. Spagnuolo, and M. Vitelli, “Distributed maximum power point tracking of photovoltaic arrays: novel approach and system analysis,” IEEE Transactions on Industrial Electronics, vol. 55, no. 7, pp. 2610–2621, 2008. View at: Publisher Site  Google Scholar
 A. Bidram, A. Davoudi, and R. S. Balog, “Control and circuit techniques to mitigate partial shading effects in photovoltaic arrays,” IEEE Journal of Photovoltaics, vol. 2, no. 4, pp. 532–546, 2012. View at: Publisher Site  Google Scholar
 S. Alepuz, S. BusquetsMonge, J. Bordonau, J. Gago, D. González, and J. Balcells, “Interfacing renewable energy sources to the utility grid using a threelevel inverter,” IEEE Transactions on Industrial Electronics, vol. 53, no. 5, pp. 1504–1511, 2006. View at: Publisher Site  Google Scholar
 R. González, E. Gubía, J. López, and L. Marroyo, “Transformerless singlephase multilevelbased photovoltaic inverter,” IEEE Transactions on Industrial Electronics, vol. 55, no. 7, pp. 2694–2702, 2008. View at: Publisher Site  Google Scholar
 E. Villanueva, P. Correa, J. Rodriguez, and M. Pacas, “Control of a singlephase cascaded Hbridge multilevel inverter for gridconnected photovoltaic systems,” IEEE Transactions on Industrial Electronics, vol. 56, no. 11, pp. 4399–4406, 2009. View at: Publisher Site  Google Scholar
 B. Xiao, L. Hang, J. Mei, C. Riley, L. M. Tolbert, and B. Ozpineci, “Modular cascaded Hbridge multilevel PV inverter with distributed MPPT for gridconnected applications,” IEEE Transactions on Industry Applications, vol. 51, no. 2, pp. 1722–1731, 2015. View at: Publisher Site  Google Scholar
 Y. Yu, G. Konstantinou, B. Hredzak, and V. G. Agelidis, “Power balance optimization of cascaded Hbridge multilevel converters for largescale photovoltaic integration,” IEEE Transactions on Power Electronics, vol. 31, no. 2, pp. 1108–1120, 2016. View at: Publisher Site  Google Scholar
 Y. Yu, G. Konstantinou, B. Hredzak, and V. G. Agelidis, “Power balance of cascaded Hbridge multilevel converters for largescale photovoltaic integration,” IEEE Transactions on Power Electronics, vol. 31, no. 1, pp. 292–303, 2016. View at: Publisher Site  Google Scholar
 Y. Yu, G. Konstantinou, B. Hredzak, and V. G. Agelidis, “Operation of cascaded Hbridge multilevel converters for largescale photovoltaic power plants under bridge failures,” IEEE Transactions on Industrial Electronics, vol. 62, no. 11, pp. 7228–7236, 2015. View at: Publisher Site  Google Scholar
 C. D. Townsend, Y. Yu, G. Konstantinou, and V. G. Agelidis, “Cascaded Hbridge multilevel PV topology for alleviation of perphase power imbalances and reduction of second harmonic voltage ripple,” IEEE Transactions on Power Electronics, vol. 31, no. 8, pp. 5574–5586, 2016. View at: Publisher Site  Google Scholar
 J. Chavarría, D. Biel, F. Guinjoan, C. Meza, and J. J. Negroni, “Energybalance control of PV cascaded multilevel gridconnected inverters under levelshifted and phaseshifted PWMs,” IEEE Transactions on Industrial Electronics, vol. 60, no. 1, pp. 98–111, 2013. View at: Publisher Site  Google Scholar
 D. Sun, B. Ge, X. Yan et al., “Modeling, impedance design, and efficiency analysis of quasiZ source module in cascaded multilevel photovoltaic power system,” IEEE Transactions on Industrial Electronics, vol. 61, no. 11, pp. 6108–6117, 2014. View at: Publisher Site  Google Scholar
 M. Coppola, F. D. Napoli, P. Guerriero, D. Iannuzzi, S. Daliento, and A. D. Pizzo, “An FPGAbased advanced control strategy of a gridtied PV CHB inverter,” IEEE Transactions on Power Electronics, vol. 31, no. 1, pp. 806–816, 2016. View at: Publisher Site  Google Scholar
 Y. Liu, B. Ge, H. AbuRub, and F. Z. Peng, “An effective control method for threephase quasiZsource cascaded multilevel inverter based gridtie photovoltaic power system,” IEEE Transactions on Industrial Electronics, vol. 61, no. 12, pp. 6794–6802, 2014. View at: Publisher Site  Google Scholar
 C. Cecati, F. Ciancetta, and P. Siano, “A multilevel inverter for photovoltaic systems with fuzzy logic control,” IEEE Transactions on Industrial Electronics, vol. 57, no. 12, pp. 4115–4125, 2010. View at: Publisher Site  Google Scholar
 D. Zhang, F. Wang, R. Burgos, R. Lai, and D. Boroyevich, “DClink ripple current reduction for paralleled threephase voltagesource converters with interleaving,” IEEE Transactions on Power Electronics, vol. 26, no. 6, pp. 1741–1753, 2011. View at: Publisher Site  Google Scholar
 X. B. Yuan, Y. D. Li, J. Y. Chai, and J. Wang, “DClink voltage ripple reduction for a transformerless modular wind generator system,” in Proceedings of the 5th IET International Conference on Power Electronics, Machines and Drives (PEMD '10), pp. 1–6, Brighton, UK, April 2010. View at: Google Scholar
 M. Tomasini, R. Feldman, J. C. Clare, P. Wheeler, D. R. Trainer, and R. S. Whitehouse, “DClink voltage ripple minimization in a modular multilevel voltage source converter for HVDC power transmission,” in Proceedings of the 14th European Conference on Power Electronics and Applications (EPE '11), pp. 1–10, Birmingham, UK, September 2011. View at: Google Scholar
 S. K. Chattopadhyay, C. Chakraborty, and B. C. Pal, “A hybrid multilevel inverter topology with third harmonic injection for grid connected photovoltaic central inverters,” in Proceedings of the 21st IEEE International Symposium on Industrial Electronics (ISIE '12), pp. 1736–1741, Hangzhou, China, May 2012. View at: Publisher Site  Google Scholar
 B. P. McGrath and D. G. Holmes, “Multicarrier PWM strategies for multilevel inverters,” IEEE Transactions on Industrial Electronics, vol. 49, no. 4, pp. 858–867, 2002. View at: Publisher Site  Google Scholar
 L. Maharjan, S. Inoue, and H. Akagi, “A transformerless energy storage system based on a cascade multilevel PWM converter with star configuration,” IEEE Transactions on Industry Applications, vol. 44, no. 5, pp. 1621–1630, 2008. View at: Publisher Site  Google Scholar
 T. Esram and P. L. Chapman, “Comparison of photovoltaic array maximum power point tracking techniques,” IEEE Transactions on Energy Conversion, vol. 22, no. 2, pp. 439–449, 2007. View at: Publisher Site  Google Scholar
 H. Fujita, M. Hagiwara, and H. Akagi, “Power flow analysis and DCcapacitor voltage regulation for the MMCCDSCC,” IEEJ Transactions on Industry Applications, vol. 132, no. 6, pp. 659–665, 2012 (Japanese). View at: Publisher Site  Google Scholar
Copyright
Copyright © 2016 Nuntawat Thitichaiworakorn et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.