A Transformerless High Boost DC-DC Converter

for use in Medium / High Voltage Applications

Theodore Soong, Peter Lehn

Department of Electrical and Computer Engineering

University of Toronto, 10 King's College Rd., Toronto, ON M5S 3G4. theodore.soong@mail.utoronto.ca, lehn@ecf.utoronto.ca.

Abstract- The proliferation of distributed energy resources has prompted interest in the expansion of DC power systems. One critical technological limitation that hinders this expansion is the absence of high step-down and high step-up DC converters for interconnecting DC systems. This work attempts to address the latter of these limitations.

This paper presents a new transformerless high boost DC­DC converter intended for use as an interconnect between DC systems. With a conversion ratio of 1:10, the converter offers significantly higher boost ratio than the conventional non-isolated boost converter. It is designed to operate at medium to high voltage (> lkV), and provides high voltage dc/dc gain (>5). Based on a current fed resonant topology, the design is well matched to available IGBT switch technology that enables use of relatively high switching frequencies yet accommodates the IGBTs inability to provide reverse blocking functionality. An advanced steady state model suitable for analysis of this converter is presented together with an experimental evaluation of the converter.

I. INT RODUCTION

Current DC networks are primarily two terminal High Voltage DC (HYDC) systems or distribution systems limited to specific applications like shipboard power systems [1], and telecommunications [2]. Motivation for expanding the use of DC power systems to DC distribution networks has recently been spurred by the increasing penetration of Distributed Energy Resources (DER)s such as photovoltaic (PV ) arrays, fuel cells, wind turbines, and battery energy storage systems (BESS). Connecting these resources directly to a DC grid could save an additional conversion stage, increase efficiency and potentially reduce cost [3], [4].

Development and expansion of DC networks have been hindered by several factors including DC circuit breaker limitations and a lack of efficient high gain high voltage DC­DC converters, as identified in [5], [6]. DC circuit breakers are used to protect a DC system from faults or unit failures, and the high gain DC-DC converters are used to interconnect DC networks of different voltages. The absence of efficient high gain high voltage DC-DC converters is the focus of this work.

DC-DC converters with high gain can be achieved through transformer and coupled inductor based topologies, though there are difficulties involved in creating a transformer for high voltage switching applications. Parasitic capacitance can be a large source of loss in a transformer, and a good dielectric material must be chosen to minimize losses in the parasitic

capacitance [7]. The leakage inductance of a transformer often causes voltage spikes during switching events, which can become more severe as the operating voltage rises. Many topologies exist to mitigate the effect of leakage inductance, and examples of these topologies are given in [8], [9], and [10]. All three topologies attempt to use the leakage inductance of the transformer by transferring that energy to the output or using the leakage inductance to provide soft switching. In addition, reducing the size of magnetics through higher operating frequency is hindered for higher voltage applications due to insulation requirements [11]. While use of transformers can facilitate high conversion ratios, if galvanic isolation is not necessary then a transformerless converter should be consid­ered to avoid the difficulties of high voltage transformers.

An alternative method of achieving high gain is to uti­lize resonant networks. They achieve efficient operation at high gain by reducing losses through zero voltage switching (ZVS) and/or zero current switching (ZCS). Examples of transformerless soft switching topologies are [12] and [13]. Both topologies store energy in a resonant capacitor from cycle to cycle to aid in the step-up process, and require thyristor technology (or alternate reverse blocking switches) to operate. The structure presented in [13] also offers the benefits of a modular structure. This is a desirable quality since high voltage switches are often placed in series to achieve higher blocking voltages. Thus requiring the use of passive snubbers, voltage clamps, or active gate control, which all result in loss [14].

The converter presented in this paper is a variation on the topology presented in [13], which is chosen for its transformer­less and modular topology. Figure 1 shows the single module version of the converter.

The paper proceeds as follows. Section II introduces the pro­posed topology and details its operation. Section III presents the steady state model of the converter. Section IV discusses the experiment and results, and Section V summarizes the paper in a conclusion.

II. TOPOLOGY

The proposed converter is a current fed resonant topology, which exploits the V-I characteristics of IGBTs. The converter utilizes three passive components, which are a resonant induc­tor, Lv; resonant capacitor, Cv; and the input inductor, Lin. The switches labelled SI are given identical gating signals, and

978-1-4673-2421-2/12/$31.00 ©2012 IEEE 174

- - - - - -- -------1- - --1 I fnp"t SO"Tce II Switching Mod"le Resonant I I I Capacitor

I � 1151 I i'n II 1_ + II Cn I Vi.. 1152 I II I II I

Fig. 1. Transformerless High Step-Up DC-DC Converter

2 6 7 I I I I I I

8

.. -Voal

1 I I I

iDTect t---H--/ �'I"'------t+-� ""'""1""""----"""1'"�

VCv

Sl

I I I I I - II I - Vo"e - -I-r--" I I

I

r-��--��----------�-��----�-t S2

Fig. 2. Waveforms of iLv(t), iVrect(t), VCv(t), and lin. Switching signals and converter states are also shown.

switches labelled S2 are also gated together. The combination of the H-bridge and resonant inductor is referred to as the switching module. The converter studied in this work utilizes the resonant capacitor and inductor to achieve high step-up operation. The purpose of the switching module and resonant capacitor, as labelled in Figure 1, is to control the turn "on" and "off' process of the rectifying diode.

A. Assumptions

Before discussing the converter's operation, the three as­sumptions used in analysis are listed. First, all components are assumed ideal. Second, all sources are constant over a switching period. The third assumption is that the ratio between the input inductor, Lin, and resonant inductor, Lv, should be much greater than 1, ii: > > 1, such that the input inductor can be approximated as a constant current source.

B. Operating Principle

Typical waveforms of the converter operating in steady state are shown in Figure 2. A regular switching period can be

divided into eight states. Before the start of a switching period, the resonant inductor current, i Lv (t) is non-zero. The resonant capacitor voltage, vcv(t), is at OV, and Switch S2 is "on".

State 1 [ to, td: The switching period for the converter begins with State 1 at time to. At the beginning of State 1, switch S2 is turned "off' and Sl is turned "on". This causes iLv(t) to be redirected into Cv, and both lin and iLv(t) charge Cv' VCv (t) rises from OV to Vout, and State 1 ends once VCv (t) equates to Vout.

State 2 [ tb t2]: State 2 begins when vcv(t) reaches Vout, and the rectifying diode, Drect. is forward biased. Both lin and iLv(t) then conduct through the rectifying diode to the output. For the duration of this state, Vout is applied across the resonant inductor, Lv. Thus, iLv(t) is changing at a constant rate. Figure 2 shows how the diode current is comprised of iLv(t) and lin. As iLv(t) changes, it passes the zero crossing and starts to divert lin from the rectifying diode. When i Lv (t) equates to lin, power is no longer delivered to the output, and the rectifying diode subsequently turns "off", thus ending State 2.

State 3 [ t2, t3]: The rectifying diode is no longer con­ducting at the beginning of State 3, but Cv is still charged at Vout. This applies a voltage across Lv causing its current to increase while discharging Cv. When Cv reaches OV, voltage is no longer applied to Lv, and iLv(t) stays constant. When vcv(t) reaches OV, it signifies the beginning of State 4.

State 4 [ t3, t4]: State 4 begins when vcv(t) reaches Ov. Since, no voltage is applied across Lv, vcv(t) remains at OV, and iLv(t) remains constant during this state. This state can be viewed as a hold state because the state of the resonant components are unchanging.

State 5 to State 8: State 5 begins by turning switches Sl "off', and S2 "on". This starts the process of charging C v with

lin and i Lv (t). States 5 to 8 maintain the same order of events as State 1 to 4. The difference is that i Lv (t) conducts through the opposite half of the H-bridge because iLv(t) is inverted, as shown in Figure 2.

C. Deadtime Requirement and Soft Switching

In the previous description, the converter operates the switch Sl with a 50% duty cycle, and the complementary signal is applied to S2. At the switch transitions from Sl to S2 or S2 to S 1, the resonant inductor current, hv (t), is non­zero, and should not be interrupted. Thus, negative deadtime (i.e. firing overlap) is required. A short circuit is avoided because switch transitions occur while OV is applied across the switches during State 4 and 8, as shown in Figure 3.

This topology allows the switches Sl and S2 to be turned "on" and "off' under ZVS, and the rectifying diode, Drect, to be turned "off" under ZVS. With the negative deadtime, the proposed converter is capable of providing soft switching opportunities to its switching devices, as shown in Figure 3.

The switches, Sl and S2, achieve ZVS at their turn "on" and turn "off'. Using Sl as an example, during State 8, the resonant capacitor voltage, vcv(t), is OV, and ZVS turn "on"

175

4" t---------I---------'"--

VCv

State 8 1 1 State 21 1 State 4 State 1 State 3 State 5

Fig. 3. Soft switching instances are shown on the waveforms of iLv (t), VCv (t), and iin (t). Gating signals to S I and S2 are also depicted with negative deadtime.

is guaranteed by the negative deadtime. At the end of State 4, Sl is turned "off" while vcv(t) is still OV; this achieves ZVS.

The rectifying diode, Drect, has a ZVS turn "off', which occurs at the end of State 2 when i Lv (t) has diverted the average input current, lin, from the rectifying diode and current is no longer transferred to the output. The converter then transitions to State 3 where the resonant inductor, Lv, discharges the resonant capacitor, Cv. During the transition between State 2 and 3, Lv provides a current path to extract the reverse recovery charge from the rectifying diode before discharging Cv during State 3. Thus, the rectifying diode is gradually reverse biased, and turned "off' through ZVS.

D. Control Variable

The switching frequency, fsw, is used as a control variable to control power delivery to the output. By lowering the switching frequency, the duration of the hold states, State 4 and State 8, are lengthened. In most frequency controlled converters, increasing a hold state implies that power delivered to the output is less frequent. However, this converter's hold states are used to maintain the volt-sec balance for the input inductor, Lin. A lower fsw implies a longer State 4 and State 8, which increases the average input current, lin, and an increase in the power delivered during the next period. By varying fsw, the volt-second balance can be adjusted to attain a specific lin. Therefore, these states should be referred to as the input inductor charging state instead of a holding state. This convention will be employed for the remainder of this paper.

E. Modularity

Although the primary focus of this paper is not on the modularity of the proposed converter, a brief discussion is presented in this section. To increase the voltage rating of the proposed converter, the switching module of Figure 1 would be replaced by a series string of switching modules. Ideally, any

number of switching modules could be placed in series, but the parasitic inductance between the modules and the rectifying diode increases with the number of modules. This parasitic inductance would prevent perfect voltage balance across the modules.

For the two module case, simulation shows equal voltage balancing is achievable with ideal components. If component mismatch, parasitic inductance, parasitic capacitance of IG­BTs, and switching signal delays are added to the simulation then oscillations can be observed in the voltage across the modules, but the oscillations are well bounded for a two module converter. Thus, it is possible to extend the proposed converter to two modules while maintaining voltage balance, but parasitic inductance will limit use of more than two or three modules.

III. STEADY STATE MODEL

The waveforms of the resonant inductor, Lv, and resonant capacitor, Cv, can be determined analytically while the con­verter is in steady state. Using these waveforms, an averaged model can be created, and is presented in this section.

A. Average Model

A relation between the average input inductor current and the control variable, fsw, must be found to control the output power of the converter. Using the state equations of Lv and Cv, the average model of the converter can be found using energy balance applied across the input inductor. Assuming constant input and output voltage, lIin and Vout, energy balance results in the following relation between the average input current,

lin, and the switching frequency, fsw.

lin = lIin _ rc;; Vout 4Lvfsw V Lv (1)

where Cv and Lv are the resonant capacitor and resonant inductor. For constant input and output voltages, Equation (1) determines converter's output power for a given switching frequency.

Equation (1) is verified through simulation, and the results are displayed in Table I. As the ratio of i': increases, the input inductor better approximates a current source, and the simulated lin converges upon the calculated lin. In practice, a iin ratio of 8 or greater would be used, resulting in a modest

mismatch between the calculated and simulated values of lin due to the omission of ripple in the analysis.

TABLE I SIMULATED VERIRCATION OF lin WITH DIFFERENT VALUES OF Lin, AND

Jaw. THE FOLLOWING PARAMETERS WERE USED: Vin = I OOV, Vout = I KV, Lv = 500j.LH, Cv = 0.025 j.LH.

Switching Calculated

Frequency lin 4 kHz 5.43A 2 kHz 17.92A

Simulated lin T Ratio

10 I 100 I 1000 6.26A I 5.52A I 5.45A 19.9A 18.13A 17.96A

176

VCv

Balance I I I

I I - I

,.......�� f- - - - Vout-I-I I I

'-------I'�

4 I t

State

Fig. 4. Waveforms of iLv(t), vcv(t), and iin (t) with ripple added to 4n (t).

B. Refined Model

From the previous discussion, it is apparent that the average model does not accurately calculate the input current for a practical design. Thus, a refinement to the average model was developed to enable proper sizing of components. In Figure 4, it is shown how the original ripple free input current would differ from the actual input current

By inspecting Figure 4, a refinement to the estimated average input current can be made by utilizing the ripple of the input current The original averaged input current, lin, was solved by assuming the input current, iin(t) was constant and the resonant inductor current, hv(t), intersected at lin. Instead, it can be assumed that energy balance solved for the resonant inductor's initial current at State 3, in place of lin, as depicted in Figure 4. The figure also shows that the input current ripple is determined by States 1 to 3. By assuming States 1 and 3 have minimal effect on the ripple, the initial current at State 3 can be assumed to be offset from the average input current by half the peak to peak input current ripple.

States 1 and 3 can be assumed to have minimal contribution to the ripple because they can be viewed as transition states that are caused by the switching module. The switching module's purpose is to aid in the turn "on" and turn "off' process of the rectifying diode, Drect, and States 1 and 3 would be short in duration. In comparison, State 2 is the rectifying state where energy is transferred to the output, and State 4 is the input inductor charging state required to maintain volt-sec balance across Lin. Thus, State 2 or 4 would have the largest impact on the ripple, and States 1 and 3 can be omitted from the calculation.

The resulting equation for the average input current is in quadratic form, and is given in Equation (2).

(2)

Comparison of lin Estimates 20 � lin Simulated

"""*"" lin Calculated 18 -&-lin Calculated - Refined 16

14 � �12 � � 10 �

U 8

4

3 4 5 Frequency (kHz)

6

Fig. 5. Comparison of original and refined average input current to the simulated average input current. The following parameters were used: "\lin = 100V, \fout = I kV, Lin = 5mH, Lv = 500/.iH, Cv = 0.025 /.iH.

where - - 2

a = 1 _ (Vin - Vout �) Vout Lin

b = "ilin + ( ("ilin - Vout Lv ) 2 _ 2) rc;; Vout 2Lvfsw Vout Lin V Lv

Vin rc;; -( _

) 2

C =

4Lvfsw - V Lv Vout

(3)

(4)

(5)

The final solution for the refined lin is the larger solution of the quadratic equation. The refinement to lin provides best accuracy at higher power transfers. This is because State 2 is the rectifying state, and was assumed to be much longer than States 1 and 3. Nonetheless, the refinement is of significant value since component rating is based on analysis at maximum power.

Figure 5 shows the comparison between the average model, the refined model and the simulated results for input current. Although the refined version of lin omits States 1 and 3, it offers a far better approximation to the simulated values than the average model for lin. The average model is therefore employed to offer insight into the basic relationship between converter components, due to its simplicity, but the refined version should be used in calculating component ratings.

IV. EXPERIMENT

A prototype of the proposed converter was developed and operated based on open loop control of the converter. The prototype's operation was tested at multiple input voltages with a fixed output voltage of l kV. The input voltage for the converter was provided by a DC generator when Vin was below l 30Y. For voltages above l 30V, the filtered output of a 3-phase rectifier was used. The rectifier was fed by a transformer connected to the AC grid. Both input and output voltages were supported by a capacitor bank, both sized at 4.8mF.

177

TABLE II EXPERIMENTAL COMPONENT VALUES

Converter Component Value Properties Lv 500/.lH RLv = 13.37mrl Cv 0.025/.lF RCesr = 37.6mrl Lin 5mH RLin = 18.6mrl

8S6 VI

Fig. 6. Waveforms of iLv(t), vcv(t), and iin(t) shown over multiple switching periods. Chi, Ch2, and Ch4 are VCv(t), iLv(t) and iin(t) respectively.

Experimental waveforms are shown in Figure 6 for a converter with the component values given in Table II. The traces depict the waveforms of the input inductor current, resonant inductor current, and resonant capacitor voltage while the converter operated with a il'in of 96.8V and Vout of 968V, and delivered 2.l 4kW. The average and refined models are also verified with results displayed in Table III, and were attained with the same il'in, Vout, and components used for Figure 6.

TABLE III EXPERIMENTAL lin COMPARED TO CALCULATED.

Switching Frequency (kHz) 5. 13 3.94 2.15 1.66 1. 19

I Experimental 4.5A 7.8A 19.6A 27.2A 39.4A I Average Model 3.2A 6.3A 18.0A 25.7A 38.6A I Refined Model 2.7A 5.5A 16. IA 23.IA 34.8A

A. Design Considerations and Component Sizing

1.00 47.6A 47.3A 42.7A

For the proposed converter, the input inductor, L in; resonant inductor, Lv; and, resonant capacitor, Cv require sizing. The size of Lin must be large enough to maintain the constant current source assumption of i in (t), and should be at least 8 x larger than Lv. The size of Lv can be used to determine the full load switching frequency, as evident from Equation (1). Finally, the size of Cv can be used to determine the duration of State 1, 71, which is given in Equation (6). In the setup, IGBT turn "off" losses could exist if this duration is too short, thus limiting the minimum size of Cv'

Losses can be decreased by minimizing the ratio of Cv : Lv, but increasing the size of Lv can increase the parasitic

resistances of Lv and Lin. The ratio of Cv : Lv is important because it is related to the resonant inductor current, hv(t), that circulates during the input inductor charging states, which is the longest state. During these states, iLv(t) is constant and its magnitude is given in Equation (7), which is only valid from time t3 to t4 and t7 to ts as indicated on Figure 2.

. -1 outy Lv ( V-rc:: )

71 = J LvCvsm - - rc::

. - (C;;-tLv(t) = lin + V Lv Vout

B. Efficiency

2lin + Vout y Lv (6)

(7)

The efficiency curves of the proposed converter are shown in Figure 7 and 8. Figure 7 plots the efficiency against the input current since losses are assumed to be dominated by conduction loss. Figure 8 plots the efficiency against output current to compare the efficiency curves at equal output power. For these curves, Vout was set to l kV, and none of the passive components were changed from curve to curve. As a result, components like the input inductor, Lin, and resonant inductor, Lv, may be overrated, and the conduction loss is somewhat lower than a properly rated inductor, but core loss increases due to the higher operating frequency. As expected, lower conversion ratios allow for higher efficiency, and the efficiency for this prototype typically peaks around an lin of 30A. For a step up ratio of 1: 10, a peak efficiency of 89.3% is achieved, but it is believed that efficiency improvements of several percent can be attained with optimized components.

C. Comparison of Topologies

The proposed converter should be compared with similar converters to properly assess its benefits, specifically [12] and [13]. In comparison to [12], the proposed topology is better suited for industrial applications because [12] must be interconnected to bipolar dc systems. In contrast, the proposed converter's use in HV applications is limited due to parasitic inductance, which limits modularity to two modules.

Compared to both [12] and [13], the proposed topology is better suited to the V-I characteristics of IGBTs. This allows the proposed converter to be operated at higher frequencies, which can reduce component size and cost. When compared to [13], the component that had the greatest size reduction was the resonant capacitor instead of the costlier magnetics. In addition the proposed converter would require an additional dc input inductor. Despite the additional component, the proposed topology is still able to achieve higher efficiency compared to [13] due to lower peak currents. Efficiency curves between the two converters are shown in Figure 9 where the proposed topology is referred to as the current based resonant converter, and [13] is referred to as the voltage based resonant converter. It should be noted that the voltage based resonant converter requires voltage-bidirectional two-quadrant switches. The converter implementation from [13] utilized an IGBT with

178

95

90

�85 � » u 80 " '"

'8 fE '" 75 I x

70

• 65 0

Efficiency at Different Step-Up Ratios

••

10

-+-lvI = 10 .-x-· lvI = S .3 .. · ... lvI = 5

20 30 Input Current (A)

40 50

Fig. 7. Efficiency curves for step-up ratios of 5, 8.3 and 10 plotted against input current with Vout = I kV

Efficiency at Different Step-Up Ratios 95,-----�----�----�----�----�----,

90

�85 � » � 80 <ll

'(3 fE '" 75

70

65 • 0

-+-lvI = 10 ,-x-· lvI = 8 .3 . . · ... lvI = 5

2 3 4 Output Current (A)

Fig. 8. Efficiency curves for step-up ratios of 5, 8.3 and 10 plotted against output current with Vout = lkV

a series diode as its switches, thus the measured efficiency would be higher if the converter where implemented with thyristors. The efficiency curves show that the voltage based resonant converter has a more consistent efficiency across the load range, while the current based resonant converter is able to achieve higher efficiencies at higher loads.

V. CONCLU SION

This paper has identified a need for efficient high voltage high step-up converters to interconnect DC power systems. To address this problem, a new transformerless high step-up DC/DC converter was presented. Within this paper, the opera­tion of the proposed converter was detailed and modelled. The converter was also realized as a IOOY: IkV /4kW experimental setup, and was found to fully utilize the V-I characteristics of IGBT technology. Although, application to HV systems may be limited, it is able to provide a grounded output. The converter was also shown to outperform its predecessor in efficiency and shows promise to operate at medium to high voltage and high gain as a DC interconnect.

Efficiency Comparison Between Converters 95,-----�------,_----�------,_----�,

90

80

. . . . . . � ..

.. . . . . . ... . . . . . . .. . . . . " . , . ,

-+-Voltage Based Resonant Converter . . .• . Current Based Resonant Converter 75L---��------L-----�------L-----�� o 0.2 0.4 0.6 0.8

Input Power (p.u.)

Fig. 9. Comparison of experimental efficiency between the converter of [13] and the proposed converter. The voltage-based converter operates with 'in = 115V, and Vout = 620V and the current-based converter operates with 'in = 200V, and Vout = lkV. Both have a rated input power of 5kW.

REFERENCES

[ I ] J. Ciezki and R. Ashton, " Selection and stability issues associated with a navy shipboard dc zonal electric distribution system;' Power Delivery, IEEE Transactions on, vol. 15, no. 2, pp. 665 --669, apr 2000.

[2] K. Mizuguchi, S. Muroyama, Y. Kuwata, and Y. Ohashi, "A new decentralized dc power system for telecommunications systems;' in Telecommunications Energy Conference, 1990. INTELEC '90., 12th International, oct 1990, pp. 55 --62.

[3] D. Nilsson and A. Sannino, "Efficiency analysis of low- and medium­voltage dc distribution systems;' in Power Engineering Society General Meeting, 2004. IEEE, june 2004, pp. 2315 -2321 Vo1.2 .

[4] M. Saeedifard, M. Graovac, R. Dias, and R. Iravani, "Dc power systems: Challenges and opportunities;' in Power and Energy Society General Meeting, 2010 IEEE, july 2010, pp. I -7.

[5] D. Jovcic and B. Ooi, "Developing dc transmission networks using dc transformers;' Power Delivery, IEEE Transactions on, vol. 25, no. 4, pp. 2535 -2543, oct. 2010.

[6] N. Denniston, A. Massoud, S. Ahmed, and P. Enjeti, "Multiple module high gain high voltage dc-dc transformers for offshore wind energy systems;' Industrial Electronics, IEEE Transactions on, 2010.

[7] M. Perez, C. Blanco, M. Rico, and F. Linera, "A new topology for high voltage, high frequency transformers;' in Applied Power Electronics Conference and Exposition, 1995. APEC '95. Conference Proceedings 1995., Tenth Annual, no. 0, Mar. 1995, pp. 554 -559 vol.2.

[8] W. Li, Y. Zhao, Y. Deng, and X. He, "Interleaved converter with voltage multiplier cell for high step-up and high-efficiency conversion;' Power Electronics, IEEE Transactions on, vol. 25, no. 9, pp. 2397 -2408, 2010.

[9] K. Tseng and T. Liang, "Novel high-efficiency step-up converter;' Electric Power Applications, lEE Proceedings -, vol. 15 1, no. 2, pp. 182 - 190, Mar. 2004.

[10] J.-M. Kwon and B.-H. Kwon, "High step-up active-clamp converter with input-current doubler and output-voltage doubler for fuel cell power systems," Power Electronics, IEEE Transactions on, vol. 24, no. 1, pp. 108 -115, 2009.

[11] J. Liu, L. Sheng, J. Shi, Z. Zhang, and X. He, "Design of high voltage, high power and high frequency transformer in lec resonant converter;' in Applied Power Electronics Conference and Exposition, 2009. APEC 2009. Twenty-Fourth Annual IEEE, 2009, pp. 1034 - 1038.

[12] D. Jovcic, " Step-up dc-dc converter for megawatt size applications;' Power Electronics, lET, vol. 2, no. 6, pp. 675 -685, 2009.

[13] A. Hagar, "A new family of transformerless modular dc-dc converters for high power applications;' Ph.D. dissertation, University of Toronto, 2010.

[14] R. Withanage, W. Crookes, and N. Shammas, "Novel voltage balancing technique for series connection of igbts;' in Power Electronics and Applications, 2007 European Conference on, sept. 2007, pp. I - 10.

179