Modeling and Analysis of Cascade Multilevel Dc-dc Boost Converter Topologies Based on H-bridge Switched Inductor

In this study investigation is done on an H-bridge switched inductor base cascade multilevel DC-DC boost converter. The proposed multilevel DC-DC boost converter topology improves the conversion efficiency of traditional topology. The proposed boost converter topology is differing from the traditional topology by the addition of switched inductor circuit. The switched inductor improved the conversion ratio gain of the boost converter circuit. The switched inductor provides a very large output voltage with different output DC levels which makes it suitable for multilevel application. Then, the mode I and mode II of operation of switched inductor are analyzed. The use of proposed switched inductor base multilevel DC-DC boost converter improved the power quality and reduced the switching frequency. The proposed DC-DC boost converter topology simulated in MATLAB/Simulink working platform and the conversion performance is evaluated. Then, the conversion performance of proposed H-bridge switched inductor based topology is compared with single level and multilevel cascade boost converter topologies.


INTRODUCTION
Now-a-days, for power conversion multilevel converters have attracted interest in power industry (Rosas-Caro et al., 2008;Lai and Peng, 1996), since; the multilevel converters already are a very important alternative in high power applications (Rodriguez et al., 2002).In almost all power conversion processes such as ac-dc, dc-ac, dc-dc and ac-dc-ac, it has been shown that multilevel converters are advantageous (Peng, 2001).Low harmonic distortion, low voltage stress, low EMI noise, low switching frequency, high efficiency, ability to operate without magnetic components are some of the advantages of multilevel converters contrary to traditional topologies (Rosas-Caro et al., 2010a;Ortuzar et al., 2006).All these advantages make multilevel converters one of the best important topics in power electronics and industrial application research and in some applications they can get modular topologies (Nilkar et al., 2011).There are several advantages for multilevel DC-DC boost converter (Samosir et al., 2011;Hwu and Yau, 2010) such as fewer components, self-voltage balancing and high voltage gain without using an extreme duty ratio and without employing a transformer (Mayo-Maldonado et al., 2011a, b;Kouro and Wu, 2009).Furthermore, without modifying the main circuit more levels can be added (Mayo-Maldonado et al., 2010a).
The multilevel converter derived from the basic types of dc-dc converters which are buck, boost (Park and Choi 2010), buck-boost, cuk, sepic and Zeta (Axelrod et al., 2008;Hwu and Yau, 2009).In the high power application, the transformer based converter is necessary, as in a power converter the voltage conversion ratio is a purpose of the modulating control signal of the active switch (Leyva-Ramos et al., 2011a).For implementing a transformer less dc-dc converter with high efficiency and high boost ratios, a number of topologies are presented (Mayo-Maldonado et al., 2010b).A multilevel converter consists of principally an array of power semiconductors and converters that produce an output voltage of stepped shape by linking its output terminals to more than one different voltage sources (Cecati et al., 2010).Neutral point clamped, flying capacitor and cascaded H-bridges multi-level structures are also included in the class of DC-DC converters (Karugaba et al., 2008).
The switched inductor multilevel boost converter is a high gain DC-DC converter to feed any applications that require high DC voltage or to feed multilevel inverter that is used in AC applications that requires low total harmonic distortions.Similarly, it can achieve high gain without increasing the duty cycle and it is the main advantage of the multilevel boost converter (Mousa et al., 2010).In the conventional converter, a very good and probably expensive driver circuit is needed; when extreme duty cycle is applied (Jiao and Luo, 2011).Only one switch is used for reducing the cost effect in multilevel DC to DC boost converter (Mousa et al., 2010).But, that increased the switching frequency of the MOSET hence, the conversion voltage is deviated from the expected level and the output voltage is affected high oscillation (Lopez et al., 2008).To achieve better dynamic performance, multi switch interleaved converters are used with small inductors and high switching frequency (Wang et al., 2011).
In literature several related works are already available which is based on multilevel DC-DC boost converters.Some of them are reviewed here.Shen et al. (2008) have proposed a multilevel dc-dc power conversion system with multiple dc sources.Very high temperature operation was possible with this magnetless system.Power loss and efficiency analysis was provided.Rosas-Caro et al. (2010b) have proposed a DC-DC converter topology.The DC-DC multilevel boost converter (MBC) was a pulse-width modulation (PWM)-based DC-DC converter.To provide different output voltages and a self-balanced voltage using only one driven switch, one inductor, diodes and capacitors for an Nx MBC, which combines the boost converter and the switched capacitor function.Mayo-Maldonado et al. (2011c) have proposed several dynamic models.The model is mainly developed for a DC-DC multilevel boost converter.Zhao et al. (2011) have proposed multilevel circuit topologies.Based on switched-capacitor and diodeclamped converters (MCT-BSD), they are called multilevel circuit topologies.Rosas-Caro et al. (2011) have presented a topological derivation of PWM DC-DC converters.The structure of the converters is very simple and provides high-voltage gain.Boost, buckboost, Cuk and SEPIC are the traditional topologies that are discussed.Nami et al. (2011) has proposed H-bridge multilevel pulse width modulation converter topology.This topology is developed based on a series connection of a high-voltage diode-clamped inverter and a lowvoltage conventional inverter.Liu et al. (2012) have proposed a cascade active-front-end converter.It was developed based on dual-boost/buck converters, since it allows regulating the power factor to control both the active and reactive powers between medium and low voltage levels.It has much enhanced system reliability compared to the traditional cascade H-bridge converter.Leyva-Ramos et al. (2011b) have proposed an average current-mode controller design methodology for an N-stage cascade boost converter.This class of converters has n-LC filters; thus, it would exhibit 2norder characteristic dynamics.The proposed scheme employs the inductor current of the input stage and the capacitor voltage of the output stage; thus, there were (n-1) capacitor voltages and (n-1) inductor currents that were not used for feedback purposes.The sensed current could also be used for one-cycle overload protection; therefore the full benefits of current-mode control were maintained.The reason is used for only a reduced set of scheme as feedback variables the system.Also, the LC filters are used to reduce the oscillation of output conversion.
The review shows that, the multilevel DC-DC converter devices have been used in switch power semiconductors at increasingly high frequencies in order to minimize harmonics and reduce passive component sizes.However, the increase in switching frequency increases the switching losses which become especially significant at high power levels.For increasing the conversion efficiency of DC-DC converter several topologies are used.The three main topologies used are the diode-clamped multilevel, capacitor-clamped multilevel and cascaded multilevel.The diode-clamped multilevel converter is relatively simple, but needs a large number of diodes to clamp the switch voltage stress.
The capacitor-clamped multilevel converter is more flexible than the diode-clamped multilevel converter, but it need large number of capacitors to clamp the voltage.Both the diode-clamped and capacitor-clamped multilevel converter have a key drawback that there are no voltage boosting feature, namely the output peak-to-peak ac voltage, which must be the same as the input dc voltage.The cascade converter is required in many isolated dc-dc converters.In this study, the multilevel cascade DC to DC boost converter with H-bridge switched inductor based topology is proposed.
In this study, a switched inductor based multilevel cascade bridge DC to DC boost converter is proposed to overcome this problem.Each bridge has one switch and the switch is connected with switched inductor, in the proposed converter.For reducing the switching frequency and improving the conversion voltage, the switch inductor is used.

PROPOSED MULTILEVEL CASCADE DC TO DC BOOST CONVERTER
The multilevel cascade dc to dc boost converter is the extension topology of single level boost converter.The use of multilevel converter is to improve the conversion ratio and efficiency of the converter.The main advantage of the multilevel topology is that the voltage conversion ratio is directly enhanced by the addition of levels.The multilevel cascade dc to dc boost converter is illustrated in Fig. 1. Figure 1, the input source of boost converter is denoted as V s .The 1 th level of the dc to dc converter inductance, diode, switch and capacitor are denoted as L 1 , D 1 , S 1 and C 1 respectively.Then, the N th level of the converter components are denoted as L n , D n , S n and C n respectively.
When the switches (S 1 , S 2 …S n ) ON in Fig. 1, the inductors L 1 , L 2 ,….L n are connected to the input and the output voltage level is resulted as the converter voltage.The voltage on the C 1 is equal to the summing up voltage on the input source and the voltage level of C 2 ..C n .Thus, it is possible to achieve high voltage gain against the duty cycle.But, when include the switched inductor circuit; the switching frequency level is limited with high gain (Liu et al., 2013).Therefore, the proposed converter is suitable for charging power in photovoltaic applications (Deivasundari et al., 2013).Moreover, the peak current of inductor is limited by switched inductor so no additional protection circuit is required (Chen, 2013).
According to the consideration of general converter operation, these converters work in the steady state with the condition of Continuous Conduction Mode (CCM).
Here, the conduction duty ratio is denoted as ˖, the switching frequency is ˦, the switching period is and the load is RL load.The input voltage and current are denoted as in V and in I respectively.The output voltage and current are V O and I O .During the conversion process, the conversion output without power loss is .
The voltage transfer ratio gain is denoted as ˙ which is described as following them: The equivalent circuit diagram on one level boost converter circuits during switch-ON and switch-OFF are illustrated in Fig. 2 as follows: The charged voltage across the capacitor C 1 is denoted as V O .The current flowing through the inductor is denoted as iL 1 .The current (iL 1 ) flowing through inductor L 1 increases with voltage V in during switch-ON period DT and decreases with voltage Hence, the ripple of the inductor current ∆˩ is expressed as follows: Then, the average current through the inductor ˩ is expressed as follow: ( ) In the above equation, the output voltage ˢ " is expressed as follows: This value is substitute in equation ( 1) and the gain equation is described as follows: Similarly, the output voltage variation ( ) is determined.That is expressed as follows: where, ˖ = The duty cycle ˦ = The frequency in Hz The above described equations are the corresponding equation of single stage DC to DC boost converter.

CASCADE MULTILEVEL DC-DC BOOST CONVERTER WITH H-BRIDGE SWITCHED INDUCTOR
Then, the multilevel cascade boost DC to DC converter with H-bridge switched inductor topology is described.Here, the purpose of the switched inductor is used to reduce the switching frequency of the converter.Hence, the power loss is reduced during conversion process, so the power quality got improved.The switched inductor provided a very large output voltage with different output DC levels which makes it suitable for multilevel application.The H-bridge switched inductor based multilevel boost converter topology is illustrated in the following Fig. 3.
For multilevel n th stage boost converter, the output voltage, the gain, current variation and the voltage variation equations are written as follows: In the proposed multilevel DC to DC boost converter model, the inductor resistance R L and the capacitor resistance ˞ are described as below: . Then, i S is the switch which used in the converter topology.i C is the i th capacitor and i L is the i th inductor.The V O and i O are the output voltage and current, respectively.
The above described switched inductor operation is same as the traditional cascade converter.But, here the switched inductor operation is only different from the nominal circuit operation.The switched inductor is operated by inductive principle which consists of two operation modes.The mode of operation of switched inductor is based on the D s1 , L and S n .The detailed description of H-bridge switched inductor is given in the following section.

Mode of operation of h-bridge switched inductor circuit:
The switched inductor simple switching dual structures, formed by either two 2-3 diodes, or two inductors and 2-3 diodes are defined.These circuit blocks can provide either a step-down of the input voltage or a step-up of it.They are inserted in classical boost converters to provide new power supplies with a steep voltage conversion ratio.As their complexity in terms of circuit elements is comparable to that of the quadratic converters, their performances (voltage ratio, stresses, efficiency) will be compared to that of available quadratic circuits.According to the conduction of inductor and diode, the mode of operation of switched inductor is categorized into two types which are illustrated in Fig. 4.

Mode I:
In mode I operation (Fig. 4a), the diodes ˖ ˖ are conducted, ˖ not conducted and also, the current flows through the both inductors.During this mode, the switches ˟ are directly conducted and the capacitor is charged indirectly.The current flows through the switched inductor (Mode I) is expressed as below: The Eq. ( 17) is the output voltage of multilevel cascade boost converter with switched inductor.Where, Mode II: In mode II operation (Fig. 4b), the diodes ˖ , ˖ are not conducted and ˖ is conducted.Then, the current flows through the both inductors.During this mode, the switches ˟ are OFF stage so, the capacitor is charged directly.The current flows through the switched inductor (Mode II) is expressed as below: The switch S n is rotated ON; the diodes D Sn-3 are furthermore rotated ON at the similar time in the suggested converter.Over through this operating state, the diodes D S1 and D S3 are offered a consecutive current path for corresponding inductors of the n th stage of the converter.On the subsequent phase, the switch S n is turned OFF, the diodes D S2 is furthermore turned ON at Fig. 5: Simulink model of H-bridge switched inductor with multilevel DC to DC boost converter topology the similar time.The diodes D S2 supply a consecutive current path for corresponding inductors of the n th stage of the converter through this operating condition; whereas in this operating condition, diodes D S1 and D S3 are rotated OFF.Hence, the operation of the multilevel cascade is the same at the final level of the converter and the resulting conversion proportion is found out.

AND DISCUSSION
The proposed H-bridge switched inductor based DC to DC boost converter topology was simulated in MATLAB/Simulink working platform.Then, the conversion performances of single level, multilevel and H-bridge switched inductor topologies are analyzed.The switching frequencies of IGBT switching voltage are analyzed by different simulation time.Also, the voltage conversion capability of the proposed topology is analyzed with conversion gain and duty cycles correspondingly.The performance of the cascade bridge circuit was tested with five level output series cascading capacitor bridges.The simulink model of Hbridge switched inductor based cascade DC to DC boost converter topology is illustrated in Fig. 5.The implementation parameters of the DC to DC boost converter model is described in Table 1 as follow.From the simulink model, the performance of inductor current, capacitor current, diode current, load voltage and switching voltage of the IGBT are examined.The performances of single level model, multilevel model and H-bridge switched inductor model are illustrated in Fig. 6 to 9 respectively.The comparison of converter voltage is illustrated in Fig. 10.Then, the gains of the single level, multilevel and Hbridge level (proposed) topologies are analyzed at different duty cycles.The duty cycle and gain are tabulated in Table 2.After that, the performance of the gain vs. duty cycle and the deviation chart are given in  Output gain of different model -------------------------------------------------------------------  The converter output voltage is obtained at the simulation time 0.01 sec.When consider the settling time and the steady state of Fig. 10, the output voltage stability of proposed converter is enhanced and the time to reach the stability level of proposed converter is less when compared to multi-level and single level topologies.Therefore, the traditional converters need stabilizing controller to maintain the stability and design of stabilizing controller is difficult.
The inductor current (I L ), capacitor current (I C ), load voltage (V ce ), diode current (I d ) and IGBT switching voltage (V R ) of the proposed topology is analyzed.When the switch is turn on, two input inductor is charging in parallel which is shown as in the inductor current characteristics.Therefore, the input current equal to 12.5 A and when IGBT turn off the input inductor connect in series that described as shown in Fig. 4b.Because of that, the input current of the circuit is decreased to half of the actual value.So, the voltage stress is reduced by the proposed topology when compared to other topologies due to the inclusion of switch inductor.The voltage stress on a switch is Figure 11a, the proposed H-bridge switched inductor topology is providing better gain when compared with other topologies.In the study, the PWM modulating frequency is selected as10kHz to analyze the performance of all topologies.Under this switching frequency, the oscillation of converter output is reduced.When varying the modulating frequency from 1kHz to 10kHz, the performance of the converter current is affected such as, inductor current, capacitor current and diode current respectively.But, the switched inductor based circuit reduces the effect of switching frequency and improves the converter current.In the switched inductor circuit, the diodes make sure the inductor and the capacitor are charged in parallel and discharged in series.The reason for improving the gain, the switching frequency effect of the converter is reduced by switched inductor which improved the conversion output.From Table 2, the conversion of the switched inductor based model how much deviated from the multilevel and single level model is analyzed.The analyzed conversion deviation is plotted in bar chart.The performance of deviation shows in Fig. 11b, the proposed switched inductor based model better than compared to single level and multilevel model.Then, the transient response of the proposed model is analyzed by changing the load value from the actual value.Under this changing condition, actual load value is reduced as 50% from 600 sec to 1200 sec and the load voltage performance is given in Fig. 12.The performance shows that, the proposed model have good settling response and reached the stead state level with less overshoot after 1200 sec.

CONCLUSION
The proposed cascade multilevel DC to DC boost converter topology with H-bridge switched inductor was implemented in MATLAB working platform.Then, the conversion performance of proposed topology was analyzed at different gain and duty cycle level.Five level series cascading circuit was used to analyze the performance of proposed topology.The conversion performance of proposed topology was compared with single level and multilevel DC-DC converter topologies.The mode of operation of switched inductor with cascade model was analyzed during switch ON and OFF condition.From the duty cycle and gain comparison, the voltage conversion of proposed topology is analyzed and compared with tradition topologies.The comparison result shows that, the proposed topology was better for DC to DC for boosting purpose without using any driving circuit.The switching frequency effect of the converter is reduced by the switched inductor circuit and so the conversion gain of the circuit is improved.Also, the stability of the converter is increased and the switching stress is reduced.In addition, the proposed model has good response and reached steady state under transient analysis.

Fig. 1 :
Fig. 1: Structure of cascade DC-DC boost converter voltage (Vs).The output voltage of C 1 is smaller than voltage through D 2 , … D n .At the same time, the negative level of voltages of C 2 , … C n is equal to the positive level value of C 1 .Hence, the total voltage across C 2 ..C n is smaller than C 1 .During the turns off condition of switches, the inductor current is closed to D 1 of all switched diodes.Throughout the switch off condition, the inductor current closes D 1 charging C 1and the output voltage level is resulted as the converter voltage.The voltage on the C 1 is equal to the summing up voltage on the input source and the voltage level of C 2 ..C n .Thus, it is possible to achieve high voltage gain against the duty cycle.But, when include the switched inductor circuit; the switching frequency level is limited with high gain(Liu et al., 2013).Therefore, the proposed converter is suitable for charging power in photovoltaic applications(Deivasundari et al., 2013).Moreover, the peak current of inductor is limited by switched inductor so no additional protection circuit is required(Chen, 2013).According to the consideration of general converter operation, these converters work in the steady state with the condition of Continuous Conduction Mode (CCM).Here, the conduction duty ratio is denoted as ˖, the switching frequency is ˦, the switching period is

Fig. 2 :
Fig. 2: Equivalent circuit of (a) switch-ON and (b) switch-OFF From the above expression, the inductor current variation ( ) 1 ε is determined.The inductor current variation is the ratio of the ripple current of the inductor ) ( 1 L i ∆ and the average current of the inductor ) ( 1 L i

Fig. 11a and
Fig.11a and b.The theoretical periodic signal with symmetric property of inductor current, capacitor current, diode current, load voltage and IGBT Switching Voltage of DC-DC converter is analyzed at the steady state points which are illustrated in Fig.6.The converter output voltage is obtained at the simulation time 0.01 sec.When consider the settling time and the steady state of Fig.10, the output voltage stability of proposed converter is enhanced and the time to reach the stability level of proposed converter is less when compared to multi-level and single level topologies.Therefore, the traditional converters need stabilizing controller to maintain the stability and design of stabilizing controller is difficult.The inductor current (I L ), capacitor current (I C ), load voltage (V ce ), diode current (I d ) and IGBT switching voltage (V R ) of the proposed topology is analyzed.When the switch is turn on, two input inductor is charging in parallel which is shown as in the inductor current characteristics.Therefore, the input current equal to 12.5 A and when IGBT turn off the input inductor connect in series that described as shown in Fig.4b.Because of that, the input current of the circuit is decreased to half of the actual value.So, the voltage stress is reduced by the proposed topology when compared to other topologies due to the inclusion of switch inductor.The voltage stress on a switch is Fig. 11: Comparison Performance of (a) Voltage gain and duty cycle and (b) Deviation of switched inductor model

Table 1 :
Implementation parameters and values

Table 2 :
Duty cycle and gain