Design and Control of a Bidirectional TriangularModular Multilevel DC-DC Converter

Kia Filsoof and Peter W. LehnDepartment of Electrical and Computer Engineering

University of TorontoToronto, Canada

kia.filsoof@mail.utoronto.ca, lehn@ecf.utoronto.ca

Abstract—In this paper, a novel bidirectional modular multi-level dc-dc converter is proposed. The proposed topology, namedthe Triangular Modular Multilevel dc-dc Converter (TMMC),can achieve equal power sharing among its modules over abroad range of conversion ratios. The proposed control algo-rithm provides localized control of modules which enhances theconverter’s dynamic performance and design flexibility. A 1.1kWexperimental implementation of the converter is shown to achievean efficiency of 96.3% and 98.0% in step-up and step-downmodes, respectively. The TMMC also provides multiple fixedvoltage nodes which makes it suitable as a multi-input multi-output converter.

I. INTRODUCTION

Recently, modular multilevel converters have captured theattention of the high power [1] and medium power [2]communities. Fully modular converters benefit from severaladvantages such as: (i) the ability to control the voltage andcurrent stress applied to its components through incorporationof identical modules in parallel or series, (ii) enhanced relia-bility through installation of redundant modules, (iii) reduceddesign, manufacturing, installation, and maintenance costs dueto standardization of the overall product cycle, and (iv) higherpower density due to minimized input and output currentripples through interleaving schemes. In this paper, a modularmultilevel dc-dc converter topology is developed for highpower (e.g. 1MW) applications. Examination of the topology’scapabilities shows that it may be employed as a multi-inputand/or multi-output converter, thus making variants of theconverter suitable for low power applications as well.

Several effective modular multilevel dc-dc converters havebeen proposed in literature. In reference [2], a modularmultilevel capacitor-clamped dc-dc converter (MMCCC) isproposed. The magnetic-less structure of this topology makesit well suited for automotive applications [3], [4]. The topologyalso has a bidirectional structure and may support multiplesources or loads [5]. However, due to the switched-capacitornature of this topology, a deliberate start-up procedure [6]is required to avoid current spikes. The capacitor-clampedtopology is further investigated and modified to benefit fromsoft-switching in [7], [8]. A few disadvantages associated withthe topology of [2] is that: (i) it is restricted to integer-onlyconversion ratios and (ii) its modules’ capacitors are exposedto different steady-state voltages which reduces its modularity.

Modular converters based on isolated dc-dc topologies areproposed in [9] and further investigated and modified in [10]–[13]. In applications where isolation is not a requirement,the weight, parasitics, and losses associated with transformersadd to the system complexity and limit the expandability andoperating power of such topologies.

In reference [14], a family of modular resonant dc-dcconverter topologies suited for high power applications areproposed. These topologies enable voltage sharing amongidentical modules which may be connected in series. Soft-switching is also realized with these converters. A variationto the step-up topology of [14] is proposed in [15]. Disadvan-tages with these topologies are the large size of the passivecomponents and the high peak currents.

The proposed topology, named the Triangular ModularMultilevel dc-dc Converter (TMMC) has a transformerlessstructure and does not suffer from high peak currents. Ad-ditionally, the proposed topology provides: (i) a fully modularstructure by enabling equal module power sharing at a broadrange of conversion ratios, (ii) a bidirectional structure, makingit suitable for a wide array of applications, and (iii) localizedcontrol of its modules, enhancing it dynamic performance.Moreover, the topology provides multiple fixed voltage nodeswhich may be utilized as either inputs or outputs. This qualifiesthe topology as a multiple-input, multiple-output converter andmakes it suitable as a scalable unified solution for a variety ofpower system architectures.

II. DERIVATION OF THE PROPOSED TOPOLOGY

The approach carried out to derive the proposed topology isconsidered as a contribution and is therefore briefly presented.The proposed topology was derived based on an evaluationof the power sharing capability of the topologies of [14].Topologies of [14] were used for comparison because thesetopologies were considered the most applicable transformer-less high power modular dc-dc converters at the time ofwriting. The evaluation measures how efficiently a modularconverter shares power among its modules for a given powerrating. This analysis is similar to the switch utilization of aconverter, however, for simplicity and easy visual intuition, thenumber of components required within the modules is ignored.

The topology of [14] configured as an n-level step-upconverter is shown in Fig. 1. As shown, n modules are

978-1-4673-4916-1/13/$31.00 ©2013 IEEE

Vi

Lr

Vo

D

Ii Io

module1

module2

modulen

von

von

von

Crn

Sbk Sak

SakSbkModulek

Fig. 1. Topology of [14] in step-up n-level configuration.

connected in series to support the high output voltage witheach module supporting a voltage of Vo/n. As mentionedearlier, this topology suffers from high peak input currentdue to resonance. This high peak input current, which isapproximately 1.6 (π/2) times the average input current, mustflow through all the series modules. For simplicity, selectn such that each module must withstand Vi. The resultingmodule power sharing of this converter for a given powerrating is illustrated in Fig. 2. Each module carries 1.6Ii andis rated for a voltage of Vo/n. From this figure, it is impliedthat each module within this converter must therefore be ratedat 1.6IiVi volt-amperes.

Based on the power sharing diagram of Fig. 2, a modularconverter with better power sharing capability may be sought.An apparent improvement would be the utilization of hard-switched converters which experience peak input/inductorcurrents which are approximately equal to the average inputcurrent. In addition, a topology may be sought which wouldbenefit from current sharing as well as voltage sharing throughparallel connection of its modules. The module power sharing

module 1

module 2

module 3

module n

Ii 1.6Ii

Vo = nVi

Vi

2Vi

Io

Fig. 2. Module power sharing illustration of the converter of Fig. 1 with n= Vo/Vi.

diagram of such a converter is shown in Fig. 3.If constructed optimally, each row of a modular converter

might not need to process a net current equal to the inputcurrent. For example, at the top row where a net voltage of nVi

is realized, only one module might be needed to process theoutput current, Io. Similarly, at lower rows, where a lower netvoltage is realized, more parallel modules would be requiredto process the higher current. The power sharing diagram ofsuch a topology is shown in Fig. 4. A modular dc-dc converterwith such power sharing capability has a theoretically optimalmodule utilization and is considered as a frame of referencefor derivation of the proposed topology.

As noted, a converter with a power sharing of Fig. 4would have approximately half the number of modules as thatof Fig. 3. This implies significant reduction in the requiredamount of silicon area.

III. PROPOSED CONVERTER TOPOLOGY

The proposed TMMC topology is configured as a generaln-level structure in Fig. 5. The TMMC is bidirectional suchthat the high-side voltage (VHV) and low-side voltage (VLV)may readily be used as either input or output. It is notedthat the proposed topology’s structure resembles that of thepower sharing diagram of Fig. 4. While the power sharingcapability of the TMMC is not identical to that of Fig. 4, it hasa significantly reduced silicon area requirement as comparedto the topology of [14]. Detailed discussion on this topic isoutside the scope of this paper.

As noted from TMMC’s structure in Fig. 5, there are nmodules in parallel on the first row to process the high

Ii = nIo

Vo = nVi

Vi

2Vi

Io

module [1,2]module [1,1] module [1,n]

module [2,2]module [2,1] module [2,n]

module [n,2]module [n,1] module [n,n]

Fig. 3. Power sharing of a modular converter with better power sharingcapability than that of Fig. 1.

Vo = nVi

Vi

2Vi

Io

module [2,n-1]

module [2,n-1] module [1,n]

Ii = nIo

module [2,1]

module [1,1]

module [2,2]

module [1,2]

module [n,1]

module [n-1,1] module [n-1,2]

Fig. 4. Power sharing diagram of an optimal modular dc-dc converter.

CLV[1,2]CLV[1,1]

Module[1, 1]

Module[1, 2]

CLV[1,n]

Module[1, n]

Module[2, 1]

Module[2, 2]

Module[2, n-1]

CLV[1,n-1]

Module[1, n-1]

Module[n, 1]

VHV

VLV

iLV

iHV

row 1

row 2

L[k,j]

C[k,j]

iL[k,j]

vc[k]Sb[k,j]

Sa[k,j] D[k,j]

vc[k-1]

vc[k]

Module[k, j]

vc[k-1]

vc[k]

Fig. 5. Proposed n-level TMMC and its corresponding single-module representation.

current on the low-voltage side, and at higher rows where ahigher net voltage is realized, fewer modules are connected inparallel. The low-voltage side’s parallel capacitors (CLV[k,j])are required simply for filtering reasons and are not inherentto the proposed topology’s structure.

The single module representation of TMMC’s modules isalso shown in Fig. 5 (top right). Semiconductor switchessuch as MOSFETs, IGBTs, or SiC MOSFETs may readily beutilized as the active switches. For bidirectional operation, bothswitches would be of active type. For step-up only operation,switch Sa would be of active type and switch Sb would bea diode. Conversely, for step-down only operation, switch Sa

would be a diode and switch Sb would be of active type.Switches Sa and Sb are operated in complementary of eachother.

The TMMC modules are by no means restricted to thearrangement shown in Fig. 5. Additional or fewer modulesmay be connected in parallel at any row. However, this paperis mainly focused on this right-triangular structure whichoptimally utilizes the power sharing capacity of each modulefor single-input single-output applications. This will be furtherelaborated in the following sections.

The optimal conversion ratio to operate an n-level TMMCis n+1 as the converter may easily achieve equal voltage andcurrent sharing among its modules under such configuration.An n-level TMMC may also be operated at other conversionratios and still maintain equal module power sharing. Anexception in this case would be the first row modules whichwould carry a current different than other row modules.Nevertheless, this may easily be compensated through additionor subtraction of modules on the first row.

Module[1,1]

Module[1,2]

Module[2,1]

ii

vi

CLV[1,1] CLV[1,2]

vo = vi + vC[1] + vC[2]

vC[2]

vC[1]

vo

Zload

io

Fig. 6. Two-level configuration of the TMMC in step-up mode.

The remainder of this paper is focused towards discussingthe steady-state and dynamic behavior of the TMMC. To aidwith visualization and understanding, the two-level structureis selected as the topology under analysis. All discussion isappropriately scalable to the n-level configuration.

The two-level TMMC configured in step-up mode is shownin Fig. 6. As specified, the output voltage is simply equal tothe summation of the input voltage with the first and secondrow capacitor voltages. For step-down operation, the load andthe source would simply be interchanged.

IV. PROPOSED CONTROL ALGORITHM

The proposed TMMC control algorithm provides localizedcontrol of all converter modules which enhances the dynamicperformance and overall design flexibility of the system. It alsosupports the possibility of a modular control design approach.

[k,j]

[k,j]

iL[k,j]

D[k,j]

vC[k]

iL[k,j] refPI

iL[k,j]

+_

PWM

D[k,j]’

c[k]

c[k-1]

iL[k,j] ref

current controller

c[k]

c[k-1]

Module[k, j]

control

Fig. 7. TMMC single module representation with internal current controller.

vC[1]

viCLV[1,1] CLV[1,2]

vo

PI++

_

iL[2,1] ref

iL[1,1] ref iL[1,2] ref+

vi

vC[1]

PI++

_+

vC[2]

+

+

+

+

vC[2]

vrow1 ref

vrow2 ref

Module[2,1]

control

Module[1,1]

control

Module[1,2]

control

Fig. 8. Two-level TMMC in step-up mode with corresponding control blocks.

Each module within the TMMC is controlled through aninternal current controller as represented in Fig. 7. The currentreference for each module is provided through a voltagecontroller which effectively controls the capacitor voltages ofthe corresponding module’s row.

The two-level TMMC in step-up mode with its correspond-ing voltage and current controllers is shown in Fig. 8. A volt-age controller on a given row controls the capacitor voltages ofthe particular row plus the capacitor voltages of the previousrow. By controlling the summation of the neighboring rows’capacitor voltages, an interdependency is provided within thevoltage controllers which enhances the dynamic behavior ofthe converter. The output of each voltage controller providesthe reference current for all parallel modules on the particularrow to result in equal current sharing. The reference for thevoltage controllers is set such that equal voltage sharing isachieved among all the rows for a given input voltage anddesired output voltage. It should be noted that unique voltagereferences may be provided to each row if desired, however,equal voltage and current sharing will be compromised.

V. SIMULATION AND EXPERIMENTAL RESULTS

In this section, simulation and experimental results of a two-level TMMC are discussed. The circuit parameters used in thistest are tabulated in Table I, and a snapshot of the experimentalprototype is shown in Fig 9. The prototype PCB is laid outfor a three-level TMMC, but only the two-level configurationis utilized in this work.

A. Steady-State Analysis

The two-level TMMC of Table I is simulated and ex-perimented at an output power of 1.1kW in step-up mode.The converter is operated with an input voltage of 64V at aconversion ratio of three (Vo = 192V). The results are shownin Fig. 10. It is noted that both simulation and experimentalresults are similar only with differences due to losses. Thisdifference is because the simulation model includes neitherswitching nor core losses. As expected, equal voltage andcurrent sharing is achieved between the capacitor voltagesand inductor currents, respectively. The first row inductorcurrents are slightly higher than the second row inductorcurrent because of losses in the system.

B. Efficiency Analysis

The efficiency of two-level TMMC of Table I has beenexperimentally investigated under both step-up and step-downoperations. The converter has been operated at a conversionratio of three with input voltages of 64V and 162V in step-up and step-down modes, respectively. The efficiency of theconverter has been measured at operating powers ranging from300W to 1.1kW.

The measured efficiency results are plotted in Fig. 11. Thestep-up converter’s efficiency is measured to be 96.3% at

TABLE ITWO-LEVEL TMMC SIMULATION AND EXPERIMENTAL PARAMETERS.

Parameter Value Part Number

fs 20 kHz -

L[k,j] 560 μH CWS HF5712-561M-25AH

C[k,j], CLV[k,j] 60 μF EPCOS B32678G3606K

Sa[k,j], Sb[k,j] - Infineon IPP200N25N3G

TMS320F28335

Fig. 9. Two-level TMMC experimental setup prototype.

(a) Simulation results (Vo = 192V, Pi = 1.1kW, η = 98.2%).

D[1,1], 5 V/div

iL[1,1], 10 A/div, avg = 11.3 A

iL[1,2], 10 A/div, avg = 11.5 A

iL[2,1], 10 A/div, avg = 10.9 A

time division = 10 μs/div

D[1,1], 5 V/div

vC[2], 20 V/div, avg = 64.2 V

vC[1], 20 V/div, avg = 64.3 V

(b) Experimental results (Vo = 192.5V, Pi = 1.1kW, η = 96.3%).

Fig. 10. Two-level TMMC of Table I steady-state analysis results (Vi = 64V, conversion ratio = 3).

95.5

96.0

96.5

97.0

97.5

0.28 0.48 0.63 0.81 0.96 1.06 1.1

Effic

ienc

y (%

)

Input Power (kW)

Step-Up Efficiency Results Vin = 64V, conversion ratio= 3

(a) Step-up efficiency results.

96.5

97.0

97.5

98.0

98.5

0.31 0.40 0.53 0.65 0.72 0.91 1.01 1.12

Effic

ienc

y (%

)

Input Power (kW)

Step-down Efficiency ResultsVin = 162V, conversion ratio = 3

(b) Step-down efficiency results.

Fig. 11. Experimental efficiency results of two-level TMMC of Table I in step-up (a) and step-down (b) mode.

rated power of 1.1kW. The step-down converter’s efficiencyis measured to be 98.0% at rated power.

The losses of the two-level TMMC at rated power in step-up operation are characterized and plotted in Fig. 12. Anefficiency of 96.3% is measured at this power, resulting in41W of losses. It is noted that majority of losses are due toswitching and magnetic losses.

VI. TMMC AS A MULTI-INPUT MULTI-OUTPUT

CONVERTER

Due to the TMMC’s modularity, fixed dc voltage nodesare provided above each row which may be utilized as either

inputs or outputs. This is a great advantage of the proposedtopology as it may be utilized as an overall power systemarchitecture, providing power to multiple loads at differentvoltage ratings through multiple sources at different voltageratings. The voltages at these nodes are fully controllable inthat they need not be integer multiples of the input voltagesor the neighboring rows’ capacitor voltages.

An example illustrating the application of the three-levelTMMC as a single-input multi-output converter in step-downmode is shown in Fig. 13. Arbitrary conversion ratios areselected to highlight that integer-multiple conversion ratios

45%

19%

35%

1%unknown losses

magnetic losses switching losses

conduction losses Pi = 1.1kW, Ploss = 41W,

Fig. 12. Experimental loss characterization of the two-level step-up TMMCof Table I.

Module[1,1]

Module[1,2]

Module[1,3]

Module[2,1]

Module[2,2]

Module[3,1]

CLV[1,1] CLV[1,2] CLV[1,3]

Vin

io 1

io 2

io 3

ii

Fig. 13. Three-level step-down TMMC configured as single-input, multi-output converter.

between different voltage nodes is not required. As mentionedpreviously, in step-down only applications, the modules wouldbe comprised of a low-side diode and a high-side active switch.

Another advantage which arises from this multiple-nodecapability of the TMMC is input voltage modularity which isapplicable in step-up operation (see Fig. 14). The input voltageis not restricted to be applied at the input of the first rowmodules. In applications in which the modules are rated lowerthan the input voltage, the input source may be applied to a rowabove the first row such that the modules’ capacitors do notexceed their rated voltage. This implies that the range of inputvoltages which may be applied to the TMMC may exceedthe rated voltage of available semiconductor technology in themarket. Fig. 14 demonstrates input voltage modularity of thethree-level TMMC configured as a single-input single-outputstep-up converter. The input source is in this case appliedabove the first row.

Through incorporation of multiple inputs and outputs, powerstress to modules at different rows would now vary, andtherefore, the power sharing capability of the converter undersuch applications would lead to a non-triangular structure.

[1,1] [1,2] [1,3]

[2,1] [2,2]

[3,1]

CLV[1,1] CLV[1,2] CLV[1,3]

in

loadii

io

Fig. 14. Three-level step-up TMMC demonstrating input voltage modularitythrough connection of the input source above the first row.

VII. CONCLUSION

In this work, a bidirectional modular multilevel dc-dcconverter topology and its corresponding control algorithmis proposed. The proposed TMMC converter is capable ofequal power sharing among its modules over a broad rangeof conversion ratios. The proposed control algorithm provideslocalized control of the modules which enhances the dynamicperformance and design flexibility of the converter. Applica-bility of the topology is experimentally validated through a1.1kW implementation of the two-level TMMC with measuredefficiencies of 96.3% and 98.0% in step-up and step-downoperations, respectively. The utilization of the TMMC as amulti-input multi-output converter is also proposed and brieflydiscussed.

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