Design, Engineering and Optimization of a Grid-Tie Multicell Inverter for Energy Storage Applications
A. Ashraf Gandomi S. Saeidabadi M. Sabahi M. Babazadeh Y. Ashraf Gandomi















Shell et al.: Bare Demo of IEEEtran.cls for IEEE Transactions on Magnetics Journals



Multilevel converters have found many applications within renewable energy systems thanks to their unique capability of generating multiple voltage levels. However, these converters need multiple DC sources and the voltage balancing over capacitors for these systems is cumbersome. In this work, a new grid-tie multicell inverter with high level of safety has been designed, engineered and optimized for integrating energy storage devices to the electric grid. The multilevel converter proposed in this work is capable of maintaining the flying capacitors voltage in the desired value. The solar cells are the primary energy sources for proposed inverter where the maximum power density is obtained. Finally, the performance of the inverter and its control method simulated using PSCAD/EMTDC software package and good agreement achieved with experimental data.




Multicell inverter; Grid-tie multilevel inverter; Maximum Power Point Tracking; Flying capacitor; Energy storage devices.


Design, Engineering and Optimization of a Grid-Tie Multicell Inverter for Energy Storage Applications
    A. Ashraf Gandomi 1,
S. Saeidabadi 1,
M. Sabahi 1, 
M. Babazadeh 1, and
Y. Ashraf Gandomi 2
1Department of Electrical and Computer Engineering,
 University of Tabriz, Tabriz
2Electrochemical Energy Storage and Conversion Laboratory,
 Department of Mechanical, Aerospace and Biomedical Engineering,
 University of Tennessee, Knoxville, Tennessee, USA

Manuscript submitted August 26, 2017.
Corresponding author: A. Ashraf Gandomi (email: a.ashrafgandomi91@ms.tabrizu.ac.ir).
    December 30, 2023
=============================================================================================================================================================================================================================================================================================================================================================================================================================================================================================











§ INTRODUCTION


The application of renewable energy sources (i.e. solar wind energy) into an electric grid requires high performance energy storage devices along with various types of power electronics (i.e. rectifiers, converters and inverters). 
Figure 1 includes the schematic of a hybrid energy storage system in which a renewable energy source (here photovoltaic modules) along with an energy storage device has been implemented to the electric grid via the utilization the multilevel inverters <cit.>. 








As shown in Fig. 1, battery-based devices and hydrogen-based energy storage technologies are promising. A good review on the battery- and hydrogen-based energy storage has been provided recently <cit.>. For hydrogen based energy storage, an electrolyzer along with a polymer electrolyte membrane (PEM) fuel cells are utilized. Although being very promising, the water management for electrolyzers and PEM fuel cells remains a challenging issue to be addressed <cit.>. Also, the hydrogen gas storage technologies and infrastructure for regenerative hydrogen fuel cell systems is required to be addressed appropriately <cit.>. Several battery technologies are developed for energy storage technologies that redox flow batteries are among the most promising devices . However engineering the redox flow batteries for optimum operation requires detailed mathematical models <cit.> and experimental diagnostics <cit.>.

The application of multilevel converters for the renewable energy systems has been increased recently <cit.>. This is mostly because of high energy output (in the range of MW), high efficiency and low electromagnetic interference being offered via their application <cit.>.

Three-level converter first proposed by Nabae <cit.> and the converters with increased number of levels developed later to obtain higher levels of voltage and reduce the harmonic content of the output voltage. However, increasing the number of voltage levels results in increased system complexity and severe voltage balancing problems. Different topologies for these types of converters have been utilized including Neutral Point Clamped (NPC) and variant types of multicell inverters <cit.>. The NPC topology suffers from diode clamped and capacitor voltage balancing issues where the multicell inverters do not suffer from the same issue. Therefore, multicell inverters are promising candidates to generate increased voltage levels for high power generation applications. The multicell inverters have different types including the Cascaded Multicell (CM), Flying Capacitor Multicell (FCM) and Stacked Multicell (SM) inverters <cit.>. The FCM inverters along with the SM inverters have many unique advantages for medium voltage applications such as operation without transformer and naturally capacitor voltage balancing ability. A comparison of the different components being used with these different inverters for generating   levels had been provided in Table. I.

Table. I. comparison of different inverter’s components





The advantages of DFCM compared to conventional structures are eliminating the common point of DC sources, reducing the number of input DC sources, switches and capacitors. However, this structure is an island and in the grid-tie form of this inverter with presented control method, some difficulties arise including the power transfer from grid to input source and the possibility of discharging flying capacitors in case of connecting to the Photovoltaic (PV) cells.
In this paper a new topology for grid-tie multicell inverter has been developed. The proposed inverter has been designed based upon the DFCM inverter and accordingly shares the common advantages associated with the DFCMs including the elimination of common point of DC source, reduced number of DC sources and increased number of voltage levels. Also, the new design assures higher level of safety and via its utilization, the common problems related to the DFCMs has been eliminated (while extracting the maximum power from PV cells).





§ PROPOSED MULTILEVEL INVERTER


The proposed inverter is shown in Fig. 2. In this structure independent of the number of inverter cells and generated voltage levels, only the switches S_n and P_n in cell_n are bidirectional. The oscillations of the PV cells voltage is mostly caused by climatic oscillations. In case of low PV cells and because of the cascaded diode of PV cells would not be functional and therefore, the possibility of discharging flying capacitors or grid voltage on the PV cells increases. Discharging the grid in the positive half cycle, the negative half cycle and discharging the flying capacitors are shown in Fig. 3. According to Fig. 3, in the proposed inverter, by using only two bidirectional switches, there would be no chance of discharging the grid and the flying capacitors on the PV cells. 

Table II, includes the switching states within the proposed inverter for generating 5-level output voltage. In this table, when the switch is on, the corresponding state number is one and for the off position it is zero. Also X in this table due to modes of charging or discharging of flying capacitor C_1, is either one or zero. Based on this table, in the states 2 and 4, charging or discharging of C_1  happens naturally, while in the other states, due to value of X, C_1 can be charged. The voltage balancing algorithm of C_1 in positive half cycle is shown in Fig. 3. Based on this figure, if the measured value of voltage of capacitor C_1 is lower than its set value (v_C1), P_2 (or S_2) will be on in the state 1 (or 3). This can continues until the voltage of C_1 reaches its specified value then P_2 will be off. 
























§ PROPOSED CONTROL METHOD


In the control method, it is assumed that the inverter output current tracks the favorite sinusoidal reference current. Also as it is shown in Fig. 5, it is assumed that the proposed inverter (base on IEEE 1547 standard) does not exchange any reactive power with the grid and only active power exchanges, therefore:








    v_s(t)=V_msin(wt)





    i_r(t)=I_m.sin(wt)



Figure 6 shows five output voltage levels that have been considered for the proposed inverter. The proposed control method should be capable of injecting power from inverter to grid at different operating conditions and therefore, the maximum voltage generated through the inverter (E_1) should be greater than the grid’s maximum voltage (V_m). 






Due to generating output voltage with low Total Harmonic Distortion (THD), the values of output voltages are considered as follows:



    E_2=E_1/2,E_3=0,E_4=-E_1/2,E_5=-E_1



The grid voltage and reference current is calculated according to (4) and (5) assuming the circuit current in the constant t_k is i_s(t_k):



    v_s(t_k)=V_msin(wt_k)





    i_r(t_k)=I_msin(wt_k)



The equivalent circuits of the proposed inverter are shown in Fig. 7.





In Fig. 7, R_l and L_l are the line resistance and inductance between inverter and grid and V_0. According to Fig. 7(a):



    L_1di_s(t)/dt+R_li_s(t)=V_0+v_s(t)=V_0+V_msin(wt)



Then:



    i_s(t_k)=I_k





    i_s(t)=K_1e^-R_lt/L_l+K_2sin(wt)+K_3cos(wt)+V_0/R_l






    K_1=I_k-V_m/R_l^3+L_l^2w^2R_l+V_mL_lw/R_l^2+L_l^2w^2/e^-R_lt/L_l






    K_2=V_m/R_l^3+L_l^2w^2R_l






    K_3=-V_mL_lw/R_l^2+L_l^2w^2



In constant t_k, i_s(t_k) is measured. Control system using (8), calculates five current for a five-level output voltage of inverter during the next switching period. Therefore, for five output voltage levels, five cost functions can be written as follow:



    ΔI=|i_r)t_k+T_s)-i_s(t_k+T_s)|



From (12), proper switching state and consequently proper output voltage can be applied.
Initially, when the inverter connects to the network, the initial voltage of the capacitor is zero. At this point, no impulse current is drawn until the capacitor voltage reaches the proper value where the grid current is bypassed by S_1, S_2 and P_3 and simultaneously input source charged the capacitor by S_2 and P_2. When the capacitor voltage reaches its proper value, control method will follow their normal operation.
In Fig. 8(a) and (b), upper waveforms are inverter output voltage and the lower waveforms are the inverter output current. Based on Fig. 8(a), if the initial control method does not apply, 60% of the original period (0.012 seconds) would be required for inverter to reach its own stable performance. This situation also results in over-drawn current as high as four times of the maximum nominal current through the circuit, which potentially damages the whole circuit. However, this situation has improved in Fig. 8(b) where the response time has decreased to about 0.0005 seconds. Therefore, the inverter only requires approximately 2.5% of the original period to reach its own stable performance. Also in this case, the drawn current is within the safe range.









§ FLYING CAPACITOR VOLTAGE BALANCING METHOD

In this section, the method of capacitor voltage balancing is investigated. Based on Table II, the capacitor is discharged in the duration that output voltage equals to E/2 with positive current of circuit and output voltage equal to -E/2 with negative current of circuit. Based on the equivalent circuit of capacitor discharging states (Fig. 7(b) and (c)):



    v_s(t)=V_msin(wt)






    i_s(t)=I_msin(wt)






    v_s(t)=V_c(t)+L_ldi_L(t)/dt+R_li_s(t)






    v_c(t)=√((V_m-R_lI_m)^2+(L_lI_m)^2)sin[wt+ 
     
    arcsin(-L_lI_m/√((V_m-R_lI_m)^2+(L_lI_m)^2))]



In the equations formulated earlier ((13) to (16)),   is the grid voltage and v_c(t) is the capacitor voltage. Also i_s(t) is the circuit current that should be the sine wave because of tracking the reference sine wave.
According to Table II, unlike the case of the capacitor discharging state that was possible only in two operating modes, charging of capacitor happens in all five operating modes. When the inverter output voltage is equal to E/2 with negative current of circuit and equal to -E/2  with positive current of circuit, capacitor is charged naturally. But in the duration that output voltage is equal to E or zero, charging of capacitor is controlled by switch P_2 and within the range that output voltage is equal to -E or zero, charging of capacitor is controlled by switch S_2. The capacitor charging circuit in all five modes is shown in Fig. 7(d). In this figure, R_s is the resistance of switches per current loop, therefore the following equations for a capacitor charging state can is obtained:




    E=R_si_c(t)+v_c(t)






    i_c(t)=cdv_c(t)/dt






    v_c(t_1)=V_1






    v_c(t)=E+V_1-E/e^-t_1/R_sCe^-t/R_sC



In the (17) and (18), v_c(t) and i_c(t) are the voltage and current of capacitor respectively.
The value of R_s is very small, therefore the time of capacitor charging is short and capacitor is charged rapidly. However, capacitor discharging state is a swinging relation. Thus, capacitor voltage can be adjusted to the desired value just by controlling the charging state of capacitor voltage.





§ DETERMINATION OF CAPACITANCE OF FLYING CAPACITOR

The capacitor charging and discharging states is shown in Fig. 7(b)-(d). The value of R_s is very small, therefore the time of capacitor charging is short and capacitor’s capacitance determination is applied only for discharging state of capacitor.



    i_c=cΔV_c/Δt



Here, Δt is the time of single switching duty cycle. ΔV_c is the capacitor rated voltage drop in one switching duty cycle which is assumed five percent of capacitor rated voltage. Consequently:



    T_s=Δt






    Δv_c=%5E/2



Circuit current in Fig. 7, (i_s), is the sine wave that can be formulated as follow:



    i_s=i_msin(wt)



i_c in (21) is equal to maximum value of current in (24), I_m, and therefore (25) is utilized to calculate the capacitor’s capacitance.



    c=i_cΔt/Δv_c







§ MPPT IN THE PROPOSED INVERTER

Maximum power of PV cells in any constant is shown by P_PV. The efficiency of the system is η, the output is P_ac. Therefore:



    P_ac=ηP_pv



And:



    P_ac=V_sI_s



Here, V_s and I_s are the RMS value of grid voltage and current respectively. Therefore, if one assigns any values for P_PV and V_s, the appropriate value for I_ref capable of tracking I_s determined and this guarantees the maximum output power from solar cells.




§ VOLTAGE LOSS CALCULATION

In this section, the loss calculation has been done for the proposed topology. The loss calculation contains switches losses and capacitor losses.




 §.§ Switches losses

Mainly conduction and switching losses are calculated for switches. Every power switch contains a transistor (MOSFET) and a diode, and therefore, the instantaneous conduction loss of these elements is calculated using (28) and (29), respectively [21]:



    P_c,T(t)=[R_Ti(t)]i(t)






    P_c,D(t)=[V_D+R_Di(t)]i(t)



Where V_D is considered as forward voltage drop of the diode. R_T and R_D are equivalent resistance of the transistor and diode. At any time N_T(t) transistor and N_D(t) diodes are in current path, so the average conduction power losses can be written as:



    P_C=1/2π∫_0^2π[N_T(t)P_c,T(t)+N_D(t)P_c,D(t)]dt



The switching losses occur during turn on and turn off period of switches. For simplicity, the linear approximation of voltage and current of switches during the switching period is considered. Based on this assumption, the switching loss is calculated as follows:



    E_off,J=∫_0^t_off(v(t)i(t))dt= 
    ∫_0^t_off[(V_sw,Jt/t_off)(-I”(t-t_off/t_off)]dt=1/6V_sw,JI”t_off






    E_on,J=∫_0^t_on(v(t)i(t))dt= 
    ∫_0^t_on[(V_sw,Jt/t_on)(-I'(t-t_on/t_on)]dt=1/6V_sw,JI't_on



E_off,J and E_on,J are turn off and turn on loss of the switch J, I’’ is the current through the switch before turning off, I’ is the current through the switches after turning on and V_sw,J is the off-state voltage on the switch. The switching power loss is equal to the sum of all turns off and turns on energy losses in the fundamental frequency of the output voltage; as a result, average switching power loss can be calculated as follow:



    P_sw=f∑_J=1^N_switch(∑_k=1^N_on,JE_on,JK+∑_k=1^N_off,JE_off,JK)



f is the fundamental frequency, N_on,J and N_off,J are the number of turning on and off the J^th switch during fundamental frequency. E_on,JK is the energy loss of the J^th switch during the k^th turning on and E_off,JK is the energy loss of the J^th switch during the k^th turning off.




 §.§ Capacitor losses

The capacitor losses consist of capacitor voltage ripple losses P_rip and conduction losses P_cond. The voltage ripple of capacitor is calculated as follow:



    ΔV_rip=1/C∫_t_-^t_+i_Cdt



Where i_C, the transient current of the capacitor, equals to the line current. t_- to t_+ is the interval that the capacitor is connected in series with DC voltage sources. So, voltage ripple loss is written as follow:




    P_rip=CΔV_rip^2f



f is the frequency of the output voltage. The conduction losses can be written as follow:



    P_cond=2f∫_t_-^t_+r_Ci_C^2dt



Where r_c is the internal resistance of the capacitor. Total loss of the proposed topology is equal:



    P_loss=P_C+P_sw+P_rip+P_cond



Finally, the efficiency of converter is written as follow:



    η=P_out/P_in=P_in-P_loss/P_in



Where P_out and P_in are output power and input power of converter.




§ SIMULATION RESULTS AND EXPERIMENTAL VERIFICATION

The simulation has been done by PSCAD / EMTDC. The circuit used in the simulation and the experimental set up and the value of elements used in both of them are shown in Fig. 9 and Table III. Due to the limitation of laboratory components, DC voltage source is used instead of PV cells.









For further analysis of inverter’s performance, input DC voltage source is changing from 60 V to 65 V in 0.04 s and from 65V to 55 V in 0.06 s, the results are shown in Fig. 10. According to Fig. 10, the proposed inverter with proposed control method produces 5-level voltage and tracks the reference current properly in the variation of DC source. Also, Flying capacitor’s voltage is balanced in its specified value (half of the input DC source).





In the experimental circuit, inverter output voltage and current for 5-level output voltage is shown in Fig. 11. This figure indicates that the proposed inverter produces an output voltage waveform with 5 levels with maximum output level of 60 V. Also in this inverter, output current of approximately 2 A tracks the reference current properly that is in phase with grid voltage, therefore the proposed inverter can exchange active power with the grid. In the laboratory condition the measured output and input power are about 48 (W) and 52.8 (W), respectively. Therefore, the efficiency is equal 90.91%. Based on the efficiency calculation, it is about 91.13%. Accordingly, the computed efficiency has good accordance with the measured efficiency. Voltage and voltage ripples of flying capacitor are shown in Fig. 12. Base on Fig. 12, the voltage of flying capacitor is balanced on the desired value with 0.2 ripples.













§ CONCLUSION

In the proposed inverter compared to the structure of DFCM, independent of the inverter cell number and the number of generated voltage levels, by replacing only two unidirectional switches with two bidirectional switches, network connectivity with high safety is provided. Also, this inverter with proposed control method has unique abilities such as capacitor voltage balancing in any desired value and obtaining maximum power from PV cells. Theoretically there is no limitation for the number of flying capacitors for balancing the voltage. The proposed control method tracks maximum power point of PV cells through assuring the equal magnitude for the input and output power. Through this unique controlling methodology, the MPPT is performed just by the inverter itself. Finally, the mathematical analysis and simulation results are used to verify the operation of proposed inverter and control method.
The design, engineering and optimization procedure explained in this work provides further insight for designing multilevel inverters to be used in hybrid systems equipped with various energy storage devices (i.e. redox flow batteries and regenerative hydrogen fuel cell systems). 































ieeetran 



10

url@samestyle








gandomi2015dc
A. A. Gandomi, K. Varesi, and S. H. Hosseini, “Dc-ac buck and buck-boost
  inverters for renewable energy applications,” in Power Electronics,
  Drives Systems & Technologies Conference (PEDSTC), 2015 6th.1em plus
  0.5em minus 0.4emIEEE, 2015, pp. 77–82.

saeidabadi2017novel
S. Saeidabadi, A. A. Gandomi, and S. H. Hosseini, “A novel transformerless
  photovoltaic grid-connected current source inverter with ground leakage
  current elimination,” in Power Electronics, Drive Systems &
  Technologies Conference (PEDSTC), 2017 8th.1em plus 0.5em minus
  0.4emIEEE, 2017, pp. 61–66.

gandomi2017maximum
A. A. Gandomi, S. Saeidabadi, and M. Sabahi, “Maximum power point tracking
  control method in high gain transformer-based inverters for photovoltaic
  application,” in Power Electronics, Drive Systems & Technologies
  Conference (PEDSTC), 2017 8th.1em plus 0.5em minus 0.4emIEEE,
  2017, pp. 137–142.

pellow2015hydrogen
M. A. Pellow, C. J. Emmott, C. J. Barnhart, and S. M. Benson, “Hydrogen or
  batteries for grid storage? a net energy analysis,” Energy &
  Environmental Science, vol. 8, no. 7, pp. 1938–1952, 2015.

gandomi2013assessing
Y. A. Gandomi and M. M. Mench, “Assessing the limits of water management using
  asymmetric micro-porous layer configurations,” ECS Transactions,
  vol. 58, no. 1, pp. 1375–1382, 2013.

gandomi2016water
Y. A. Gandomi, M. Edmundson, F. Busby, and M. M. Mench, “Water management in
  polymer electrolyte fuel cells through asymmetric thermal and mass transport
  engineering of the micro-porous layers,” Journal of The
  Electrochemical Society, vol. 163, no. 8, pp. F933–F944, 2016.

zehsaz2011plastic
M. Zehsaz, F. V. Tahami, and Y. A. Gandomi, “The plastic work curvature
  criterion in evaluating gross plastic deformation for pressure vessels with
  conical heads,” in Applied Mechanics and Materials, vol. 50.1em plus 0.5em minus 0.4emTrans Tech Publ, 2011, pp. 93–99.

zehsaz2012bifurcation
M. Zehsaz, F. V. Tahami, and Y. A. Gandomi, “Bifurcation buckling of pressurized conical vessels,”
  International Journal of Advances in Engineering & Technology,
  vol. 3, no. 2, p. 108, 2012.

gandomi2014concentrated
Y. A. Gandomi, T. A. Zawodzinski, and M. M. Mench, “Concentrated solution
  model of transport in all vanadium redox flow battery membrane separator,”
  ECS Transactions, vol. 61, no. 13, pp. 23–32, 2014.

yousefzadi2016anisotropic
A. Yousefzadi Nobakht and S. Shin, “Anisotropic control of thermal transport
  in graphene/si heterostructures,” Journal of Applied Physics, vol.
  120, no. 22, p. 225111, 2016.

gandomi2016situ
Y. A. Gandomi, D. Aaron, T. Zawodzinski, and M. Mench, “In situ potential
  distribution measurement and validated model for all-vanadium redox flow
  battery,” Journal of The Electrochemical Society, vol. 163, no. 1,
  pp. A5188–A5201, 2016.

gandomi2016coupled
Y. A. Gandomi, D. Aaron, and M. Mench, “Coupled membrane transport parameters
  for ionic species in all-vanadium redox flow batteries,”
  Electrochimica Acta, vol. 218, pp. 174–190, 2016.

ashraf2017influence
Y. Ashraf Gandomi, D. S. Aaron, and M. M. Mench, “Influence of membrane
  equivalent weight and reinforcement on ionic species crossover in
  all-vanadium redox flow batteries,” Membranes, vol. 7, no. 2, p. 29,
  2017.

saeidabadi2017two
S. Saeidabadi, A. A. Gandomi, and M. Sabahi, “Two new transformer-based
  isolated seven-level inverters,” in Power Electronics, Drive Systems
  & Technologies Conference (PEDSTC), 2017 8th.1em plus 0.5em minus
  0.4emIEEE, 2017, pp. 195–200.

hosseini2015attempt
S. H. Hosseini, K. Varesi, J. F. Ardashir, A. A. Gandomi, and S. Saeidabadi,
  “An attempt to improve output voltage quality of developed multi-level
  inverter topology by increasing the number of levels,” in Electrical
  and Electronics Engineering (ELECO), 2015 9th International Conference
  on.1em plus 0.5em minus 0.4emIEEE, 2015, pp. 665–669.

gandomi2015control
A. A. Gandomi, K. Varesi, and S. H. Hosseini, “Control strategy applied on
  double flying capacitor multi-cell inverter for increasing number of
  generated voltage levels,” IET Power Electronics, vol. 8, no. 6, pp.
  887–897, 2015.

gandomi2015transformer
A. A. Gandomi, S. Saeidabadi, S. H. Hosseini, E. Babaei, and M. Sabahi,
  “Transformer-based inverter with reduced number of switches for renewable
  energy applications,” IET Power Electronics, vol. 8, no. 10, pp.
  1875–1884, 2015.

varesi2017improved
K. Varesi, A. A. Ghandomi, S. Hosseini, M. Sabahi, and E. Babaei, “An improved
  structure for multi-input high step-up dc-dc converters,” in Power
  Electronics, Drive Systems & Technologies Conference (PEDSTC), 2017
  8th.1em plus 0.5em minus 0.4emIEEE, 2017, pp. 241–246.

gandomi2017high
A. A. Gandomi, S. Saeidabadi, and S. H. Hosseini, “A high step up flying
  capacitor inverter with the voltage balancing control method,” in
  Power Electronics, Drive Systems & Technologies Conference (PEDSTC),
  2017 8th.1em plus 0.5em minus 0.4emIEEE, 2017, pp. 55–60.

saeidabadi2017new
S. Saeidabadi, A. A. Gandomi, S. H. Hosseini, M. Sabahi, and Y. A. Gandomi,
  “New improved three-phase hybrid multilevel inverter with reduced number of
  components,” IET Power Electronics, 2017.

nabae1981new
A. Nabae, I. Takahashi, and H. Akagi, “A new neutral-point-clamped pwm
  inverter,” IEEE Transactions on industry applications, no. 5, pp.
  518–523, 1981.

sadigh2013reduced
A. K. Sadigh, V. Dargahi, M. Abarzadeh, and S. Dargahi, “Reduced dc voltage
  source flying capacitor multicell multilevel inverter: analysis and
  implementation,” IET Power Electronics, vol. 7, no. 2, pp. 439–450,
  2013.

rodriguez2010survey
J. Rodriguez, S. Bernet, P. K. Steimer, and I. E. Lizama, “A survey on
  neutral-point-clamped inverters,” IEEE transactions on Industrial
  Electronics, vol. 57, no. 7, pp. 2219–2230, 2010.

banaei2013series
M. R. Banaei, M. R. J. Oskuee, and F. M. Kazemi, “Series h-bridge with stacked
  multicell inverter to quadruplicate voltage levels,” IET Power
  Electronics, vol. 6, no. 5, pp. 878–884, 2013.

mcgrath2007natural
B. P. McGrath and D. G. Holmes, “Natural current balancing of multicell
  current source converters,” in Power Electronics Specialists
  Conference, 2007. PESC 2007. IEEE.1em plus 0.5em minus 0.4emIEEE, 2007, pp. 968–974.

lezana2009fault
P. Lezana, R. Aguilera, and J. Rodríguez, “Fault detection on multicell
  converter based on output voltage frequency analysis,” IEEE
  Transactions on Industrial Electronics, vol. 56, no. 6, pp. 2275–2283,
  2009.

meynard1997modeling
T. A. Meynard, M. Fadel, and N. Aouda, “Modeling of multilevel converters,”
  IEEE transactions on industrial electronics, vol. 44, no. 3, pp.
  356–364, 1997.






































