Bidirectional Power Electronics for Driving Dielectric Elastomer Transducers

L. Eitzena, C. Grafa, J. Maasa

aHochschule Ostwestfalen-Lippe University of Applied Sciences Control Engineering and Mechatronic Systems, Liebigstrasse 87, 32657 Lemgo, Germany

ABSTRACT

The operation of Dielectric Elastomer Transducers typically requires high voltages in the kilovolt range and relatively low currents. Therefore, for driving Dielectric Elastomer Transducers a high voltage power electronics is necessary. For realization of energy efficient actuator and generator applications bidirectional switched-mode converter topologies should be used enabling a bidirectional energy transfer as well as a high efficiency. In this contribution a modular converter system consisting of several switched-mode converter modules featuring galvanic isolation is presented as a basic concept for realization of a high voltage power supply. Three converter topologies – bidirectional flyback, Dual Active Bridge and Isolated Bidirectional Full-Bridge converter – are investigated and suitable modulation schemes are presented, which are based on hysteretic current-mode control, enabling a high converter dynamic and limitation of the converter output current in order to prevent electrode damage. Simulation results for the proposed converter topologies are presented and experimental results for a single bidirectional flyback converter module are shown.

Keywords: bidirectional high voltage power electronics, Dielectric Electro Active Polymer

1. INTRODUCTION Dielectric Elastomer Transducers are electromechanical transducers, which can be operated as actuators (Dielectric Elastomer Actuator - DEA) as well as generators (Dielectric Elastomer Generator - DEG). Dielectric elastomers belong to the material class of Dielectric Electro Active Polymers (DEAPs) and are thin films made of elastomeric material coated with conductive and compliant electrodes representing a soft capacitor1 (the denomination DEAP device will be used for both DEA and DEG in the following). The actuation principle is based on electrostatic contraction forces, which are generated by applying electrical charge to the electrode surfaces of the DEAP. The soft, but incompressible dielectric is reduced in thickness and at the same time increased in area, describing the actuation of the material. When operated as a generator the DEAP is charged in the stretched state. During the subsequent relaxation of the flexible material the charged electrodes are shifted against the attraction forces between both electrodes and mechanical strain energy is converted to electric energy. The limited thickness of the dielectric is in the range of 30-80µm. This limitation combined with the relatively high operating field strength being in the range of 20-100V/µm leads to the need of high operating voltages for driving DEAP devices. Generator applications naturally require a high efficiency to maximize the overall energy gain and to realize a bidirectional energy transfer for feeding back harvested energy. Actuator applications can in principle be realized utilizing a power electronics only providing an unidirectional energy transfer with a dissipative element in parallel to the DEA, which allows discharging the capacitance. The dissipative element can either be passive in form of a resistor or an active discharging circuit.2 In both cases the electrical energy stored in the capacitance of the DEA is lost and converted to heat resulting in a bad actuator efficiency, whereas with a bidirectional power electronics energy can be fed back to the DC link circuit resulting in an increased actuator efficiency and reduced heat generation. Since switched-mode converters3 in general facilitate high efficiency levels and can also be realized providing a bidirectional energy transfer, suitable switched-mode converter concepts for driving Dielectric Elastomer Transducers are proposed in this contribution. ________________________________

Further author information: Lars Eitzen: E-mail: Lars.Eitzen@hs-owl.de, Telephone: +49 5261 702 119 Christian Graf: E-mail: Christian.Graf@hs-owl.de, Telephone: +49 5261 702 565 Jürgen Maas: E-mail: Juergen.Maas@hs-owl.de, Telephone: +49 5261 702 192, www.motion-ctrl.de

Electroactive Polymer Actuators and Devices (EAPAD) 2012, edited by Yoseph Bar-Cohen, Proc. of SPIE Vol. 8340, 834018 · © 2012 SPIE · CCC code: 0277-786X/12/$18 · doi: 10.1117/12.913272

Proc. of SPIE Vol. 8340 834018-1

Since, from an electrical point of view, a DEAP represents a mainly capacitive load, it will be discussed in chapter 2.1 how to feed a capacitive load. The requirements for driving DEAP devices are then stated in chapter 2.2. Subsequently, different general approaches for realization of a bidirectional high voltage switched-mode converter system are discussed and evaluated with regard to their suitability in chapter 2.3, followed by a description of the selected general converter concept, representing a modular converter system. Since the modules of the modular converter system can be realized using different types of converter modules, these are described afterwards in chapter 3.1 and chapter 3.2. Chapter 3.3 covers the discussion and selection of appropriate modulation schemes for each converter module and in chapter 3.4 the overall modulation scheme for the modular converter system and simulation results for each converter topology are given. Finally, in chapter 4, experimental results of a realized single bidirectional flyback converter module prototype driving a purely capacitive load are presented and discussed.

2. HIGH VOLTAGE CONVERTER CONCEPTS 2.1 Driving Capacitive Loads

The type of load, either inductive or capacitive as with DEAPs, defines how the load has to be fed.4 As shown for an inductive load in Figure 1a), a controlled voltage source has to be used in order to control the current through the inductance, which is described by the differential equation vL = L·diL/dt. Complementary, for driving a capacitive load, exemplified in Figure 1b), a controlled current source has to be realized, which allows to control the voltage vC according to the differential equation iC = C·dvC/dt. Since most converters are based on a voltage DC-link circuit with the impressed voltage vdS, the utilized converter has to provide current source functionality, indicated in Figure 1c).

),( iLi vLfii ==

+−

iv

Lv

LiCi ii =

ii

),( i

C

iCfv=

Ci

CL +− dPv dSv

dPi

),,(),,,( uu dSdPdPdSdPdS vvfivvfi ==

),( dSC iCfv =C

Cia) b) c) dSi

u

converter

Figure 1. a) Feeding an inductive load. b) Feeding a capacitive load. c) Converter functioning as current source.

The output current idS as well as the input current idP are controlled by setting the control vector u containing one or more control variables. Furthermore, depending on the type of converter topology, output current idS = f(vdP, vdS, u) and input current idP = f(vdP, vdS, u) can also be a function of input and output voltage vdP and vdS. Since the voltage vC = f(C, idS) can be controlled by setting the current idS, which is set by the current source converter, a superimposed voltage control can easily be realized.

2.2 Requirements for Driving DEAP Device

Most important, for efficient actuator and generator operation, the converter topology must provide a bidirectional energy transfer. This enables the feedback of harvested energy for DEG operation or the reuse of energy in case of DEA applications. As mentioned in the introduction the maximum DEAP operating voltage VDE,max can be in the range of several kilovolts, which has to be provided by the converter supplying the output voltage vdS. Furthermore, it must be possible to control the converter output voltage vdS over a range of 0 ≤ vdS≤ VDE,max, which allows to discharge the DEAP capacitance completely and by this a continuous actuation of actuators and realization of different energy harvesting cycles.5 Despite the fact that high voltage semiconductor switches with a blocking voltage of up to several kilovolts are available, these have inferior electrical characteristics in terms of switching speed and conduction losses compared to standard semiconductor switches. For this reason standard semiconductors with a maximum blocking voltage of VDS,max ≤ 1500V should be used, enabling a reasonable efficiency and reducing realization costs. Another important aspect is the ability to limit the DEAP current iDE or the converter output current idS in order to prevent electrode damage, since, although DEAP devices require high operating voltages, their electrodes are current-sensitive and only allow certain current values. Finally, the utilized converter topology has to function as a current source, as can be derived from the contents of chapter 2.1. An overview of the derived requirements is given by Table 1.

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Table 1. Requirements on the high voltage power electronics for driving DEAP devices.

ID Requirement R1 Bidirectional energy flowR2 Output voltage in kilovolt range with 0 ≤ vdS≤ VDE,maxR3 Use of standard semiconductors with VDS,max≤ 1500VR4 Limitation of DEAP current iDE or converter output current idSR5 Utilized converter topology has to be operated as current source

2.3 General Converter Concepts

There are different concepts for realizing a bidirectional high voltage power electronics based on a switched-mode converter design. The most simple approach is to use high voltage semiconductor switches such as high voltage power MOSFETs IXTH03N400 or high voltage IGBTs IXGF30N400 by the manufacturer IXYS, both semiconductor switches with a maximum blocking voltage of VDS,max = 4kV. Since standard semiconductors with considerably better electrical characteristics in terms of switching speed and conduction losses should be used, this is not a possibility. Another approach is to realize a single bidirectional converter module using several series-connected standard semiconductors to increase voltage blocking capability.6 Each high voltage switch consists of several series-connected semiconductor switches together exhibiting considerably better electrical properties than one single high voltage semiconductor switch. Choosing this approach entails the necessity of ensuring a symmetrical voltage distribution among all semiconductor switches of a high voltage switch under all switching conditions, which can be achieved with passive snubber circuits, which increase losses, or active gate control methods, which increase system complexity.7,8 Both approaches furthermore lead to large passive components such as inductors and capacitors, because large inductance and capacitance values are needed to achieve acceptable levels of output current and voltage ripple levels. Inductive elements like power chokes and transformers additionally require a high voltage isolation leading to increased parasitic effects. The third approach, which is pursued in this contribution, makes use of several bidirectional and galvanically isolated converter modules whose outputs are series-connected achieving the required high output voltage.9,10 The modular converter concept is illustrated in Figure 2.

outp

uts

seri

es-c

onne

cted

inpu

tspa

ralle

l-con

nect

ed

dSv

module 11dPv 1dSv

module kdPkv dSkv

dPv

module ndPnv dSnv

DEiEnergy transfer

)(αeR

)(αpC)(αpR

pi i

DEAPdSi

DEv

Figure 2. Modular converter concept and electrical equivalent circuit of DEAP device with lumped elements.

As depicted, the converter system consists of n identical converter modules. The index k denotes the addressed converter module with k = 1,2,…,n and n ĕ Ν. All inputs are connected in parallel, so each input voltage is vdPk = vdP. Since the module outputs are connected in series, the overall converter output voltage vdS is the sum of all converter module output voltages vdS = [vdS1, vdS2,…, vdSk,…, vdSn]. In case of an equal voltage distribution among the n converter modules, which has to be ensured by a suitable modulation scheme and/or control concept, the output voltage can be written as

n

VVvnv dS

dSkdSkdSmax,

max, =⇔⋅= . (2)

Proc. of SPIE Vol. 8340 834018-3

The voltage stress of each converter module and therefore the voltage semiconductor voltage stresses can be limited by choosing the number of converter modules n appropriately, so standard semiconductor switches can be used increasing efficiency and reducing costs. The utilized converter modules must provide galvanic isolation, otherwise input and output will be short-circuited. With regard to requirement R2 it is important that the converter topologies selected for realization of the converter modules behave as buck-boost converters. As required, this allows discharging the DEAP device completely. Figure 2 also includes an electrical equivalent circuit of a DEAP device. The variable capacitance Cp(α) describes the capacitive behavior when considering an ideal transducer. The parasitic effects are modeled by the electrode resistance Re(α) and the polymer resistance Rp(α) of the dielectric. All three parameters are a function of the contraction ratio α describing the change in geometry.5

3. CONVERTER TOPOLOGIES FOR REALIZATION OF CONVERTER MODULES Most converter topologies utilized for high voltage generation applications are flyback2,11,12,13 and full-bridge topologies.11,14,15 These are mainly dissipative applications, where an unidirectional energy flow is sufficient and therefore unidirectional converter topologies are deployed. Both converter topologies can be extended in order to realize a bidirectional energy transfer as required by R1, which is achieved by supplementing the rectifier diodes on the secondary side by additional active semiconductor switches.

3.1 Bidirectional Flyback Converter

In case of the unidirectional flyback converter this leads to the bidirectional flyback converter.12,16 The circuit diagram of the bidirectional flyback converter module number k is shown in Figure 3.

kS1

kD1

dSkv

Pki Skikw:1

kTkS2

kD2

dSkCPkv SkvdPkv mkL

dSki

mki

Figure 3. Circuit diagram of bidirectional flyback converter module number k.

The bidirectional flyback converter consists of the primary semiconductor switch S1k and the secondary semiconductor switch S2k. The two diodes D1k and D2k are connected anti-parallel to S1k and S2k functioning as rectifier diodes. The two-winding inductor Tk or flyback transformer, different from conventional high frequency transformers, is used as an energy storage element comparable to the inductor in a buck-boost converter and additionally provides galvanical isolation between primary and secondary side. Assuming an ideal flyback transformer, it can be modeled by magnetizing inductance Lmk and winding ratio wk. In order to minimize the voltage stresses of the primary and secondary semiconductor switches the winding ratio has to be chosen as wk = 1. The filter capacitance CdSk ensures an adequate output voltage ripple and stabilizes the converter module output voltage vdSk. The flyback converter is characterized by its discontinuous input and discontinuous output current. This means that the current stresses of the semiconductor switches are high and conduction losses increase unacceptably, when transferring more than about 300W. In order to prevent saturation of its magnetic core the flyback transformer gets very large at high power levels. Furthermore, the semiconductor switches are subject to relatively high voltage stresses, which requires to select semiconductor switches with relatively high blocking voltages and therefore diminished electrical characteristics. The key advantage of the bidirectional flyback converter is its simplicity. The switch control can be realized easily by using two conventional low-side drivers, because the bottom contacts of the semiconductor switches are connected to the reference ground of each converter side. Due to the low component count the flyback converter can be realized at very low costs and the natural buck-boost nature of the flyback converter allows to fully discharge the DEAP device without utilization of a special modulation scheme.

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3.2 Full-Bridge based Converter Topologies

For higher power levels a full-bridge based topology is generally utilized. The two full-bridge based converter topologies investigated in this paper are depicted in Figure 4. General advantages of these topologies are low voltage stresses of the semiconductor switches, so semiconductor switches with better electrical properties than with the flyback converter can be used, and a high flexibility considering different modulation schemes and topology configurations that are possible. Since the output current iHSk is continuous and additionally the pulse frequency at the converter output is fp = 2fsk = 2/Tsk, conduction losses and the output ripple are considerably smaller than for a flyback converter topology. Due to the large number of required semiconductors and the additional need for a high frequency transformer the costs for realization of a full-bridge based topology are considerably higher than for the flyback converter. Furthermore it should be noted that controlling the upper semiconductor switches of the full-bridge circuits requires more complex, floating driver circuitry. From a circuit point of view, the only difference between the Isolated Bidirectional Full-Bridge converter (IBFBC) 4,11,17, shown in Figure 4a), and the DAB converter18, depicted in Figure 4b), is the position of the inductance LdSk or LDABk. Each converter module consists of one primary full-bridge circuit comprising the semiconductor switches S1k…S4k and antiparallel diodes D1k…D4k and one secondary full-bridge circuit including the switches S5k…S8k and the diodes D5k…D8k coupled via the high frequency transformer Tk. Both output voltages are stabilized by the capacitance CdSk. In case of the IBFBC the inductance LdSk is placed between secondary full-bridge circuit and capacitance CdSk forming an output LC filter, while the inductance LDABk of the DAB converter is in series to the transformer Tk. For both full-bridge based topologies the transformer Tk provides galvanic isolation and the winding ratio wk represents a means for voltage matching between primary and secondary side.

DABkL

DABkiSkikS1 kD1

kS2 kD2 kS4 kD4

kS3 kD3

dPkv

HPkdPk ii =

kS5 kD5

kS6 kD6 kS8 kD8

kS7 kD7

dSkv

HSki

kv1 kv2dSkC

kw:1

kT

Pkv SkvPki

b)

SkikS1 kD1

kS2 kD2 kS4 kD4

kS3 kD3

dPkv

HPkdPk ii =

kS5 kD5

kS6 kD6 kS8 kD8

kS7 kD7

dSkv

HSki

dSkCkw:1

kT

Pkv SkvPki

dSkLa)

HSkv

Figure 4. Circuit diagrams of the two investigated full-bridge based topologies: a) IBFBC and b) DAB converter.

For charging and discharging the DEAP device with the IBFBC two separate modulations schemes have to be implemented.16 For charging the “Buck Mode” modulation scheme is utilized, during which only the primary semiconductor switches are controlled and the secondary semiconductor switches are inactive and the corresponding secondary diodes are performing as a bridge rectifier. In buck mode the IBFBC behaves as a buck converter with galvanic isolation and an additional voltage step up ratio achieved through the winding ratio wk. Given the requirement to completely discharge the DEAP device the IBFBC has to be operated as a boost converter seen from the secondary side, which is achieved via operation in “Boost Mode”. Analogous to buck mode, only the secondary semiconductor switches are controlled, while the primary full-bridge circuit serves as bridge rectifier. Since boost mode requires to switch all secondary switches simultaneously over certain switching period intervals, which is prevented by conventional half-bridge or full-bridge driver circuits, special driver circuits have to be utilized increasing costs and complexity. Furthermore additional voltage spikes on the secondary side can occur due to the current source behavior of the output inductance LdSk and the leakage inductances of the high frequency transformer, which requires an additional snubber circuit on the secondary converter side, located between secondary full-bridge circuit and inductance LdSk.

Proc. of SPIE Vol. 8340 834018-5

When operating the full-bridge based topology as a DAB converter, the parasitic leakage inductances and, if required, an additional inductance are directly used as energy transfer elements and are summed up as the inductance LDABk. The modulation scheme Phase Shift Modulation naturally provides buck-boost functionality and allows the use of standard full-bridge or half-bridge driver ICs for switch control.17 In addition Phase Shift Modulation allows low switching losses as a result of Zero Voltage Switching (ZVS) over a certain operating range, which can be extended to the whole output voltage range by controlling the current iDABk or the output current iHSk. Since the inductance LDABk is placed in series to the leakage inductances of Tk excessive voltage spikes as with the IBFBC do not occur. The main disadvantage of the DAB converter is the oscillation of reactive energy between primary and secondary side, which leads to additional conduction losses reducing efficiency. Due to the fact that the full current iDABk, also including reactive portions, has to be transferred by the transformer Tk, the winding resistances have to be kept small for minimization of conduction losses. In view of its high realization costs a full-bridge based topology is generally considered for considerably higher power outputs than 300W.

3.3 Modulation Schemes

Considering the application at hand and the derived requirements a variable frequency current-mode control scheme holds decisive advantages over conventional fixed frequency voltage-mode modulation schemes.19 The specific modulation schemes proposed for the three converter topologies are based on hysteretic current-mode control.20 This type of modulation scheme was chosen because of several reasons. In general, with hysteretic current-mode control the current through Lmk, LdSk or LDABk, depending on the topology under consideration, or the converter output current is switched between two current thresholds imin and imax, which allows limiting it independent of component tolerances. Furthermore, the proposed modulation schemes turn the respective converters into controlled current sources, whereas the control vector can be written as u = [imax, imin]. Hysteretic current-mode control, assuming a loss-less system and constant input and output voltages with vdSk = VdSk and vdPk = VdP, for the kth flyback converter stage is shown in Figure 5. The semiconductor switch states, relevant voltages and currents are shown for both supply and harvesting operation.

tskkTD skT

Pki

mkvdPV

kdSk wV /−

kSk wi

maximini

mki

01

2

1

==

k

k

DS

10

2

1

==

k

k

DSa)

0 tskkTD skT

Pki−

mkvdPV

kdSk wV /−

kSk wi−

maximini

mki−

01

1

2

==

k

k

DS

10

1

2

==

k

k

DSb)

0

Figure 5. Hysteretic current-mode control for a) supply and b) harvesting operation of bidirectional flyback converter.

During supply operation, shown in Figure 5a), the primary semiconductor switch S1k is switched on at the beginning of the switching period t = 0 initiating the conduction interval. The voltage across the magnetizing inductance is vmk = VdP resulting in a linear increase of the magnetizing current imk, which equals the primary current iPk, starting from imk = imin. Due to the opposite winding directions of primary and secondary winding of Tk the secondary Diode D2k blocks and the secondary current iSk = 0. When iPk = imax at t = DkTsk. with the duty cycle Dk and the switching period Tsk, the semiconductor switch S1k is switched off, the blocking interval begins and the energy stored in the magnetizing inductance Lmk is transferred to the secondary side in terms of the current iSk via the secondary diode D2k. The output voltage vdSk = VdSk is reflected to the primary side resulting in the linear decrease of the magnetizing and secondary current with imk = iSk·wk. As soon as imk = imin at t = Tsk a new switching interval begins. Analogous to supply operation, harvesting operation, shown in Figure 5b), can be reconstructed. The difference is that S2k is switched on instead of S1k during the conduction interval and D1k on the primary side functions as rectifier during the blocking interval.

Proc. of SPIE Vol. 8340 834018-6

The arithmetic average value of the secondary current, indicated by a horizontal bar above its symbol, is determined by integration over one switching period Tsk. As can be seen from (3) the arithmetic average of iSk is a function of input and output voltage VdP and VdSk and the current thresholds imax and imin.

)()(2

)(1minmax ii

VwVVdtti

Ti

dSkkdPk

dPkT

tSk

SkSk

Sk

off

+⋅+

=⋅= ∫ (3)

The proposed control scheme allows limiting the maximum output current as well as directly setting the average output current of each flyback converter module by adjusting the two current thresholds imax and imin accordingly. In order to reduce the switching frequency and switching losses and to eliminate one control variable for simplification imin should be set to imin = 0, so the magnetizing current is switched between imax and zero. Assuming imax and imin to be constant it can also be deduced from (3) that the average output current and thus the system dynamic of the flyback converter decreases with increasing output voltage vdSk. Compared to voltage-mode control with a fixed switching frequency fsk = 1/Tsk = const, indicated by the duty cycle Dk, with current-mode control not only the maximum output current can directly be limited but also a higher dynamic is achieved, since the conduction interval is initiated as soon as the magnetizing current reaches the corresponding current threshold. The same facts hold true for switch control of the IBFBC using buck and boost mode based on hysteretic current-mode control. The relevant control signals, voltage and current waveforms for buck and boost mode are shown in Figure 6. As with the flyback converter a loss-less system and a constant input and output voltage are assumed.

kS5

kS6

kS7

kS8

t

HSki−

HPki−

Ski−

kS1

kS2

kS3kS4

Skv dPkVw±

dSv dPkVw+

tskT

HSki

HPki

SkiLdskv

dSkV−

maximini

skT

a) b)

maximini

1 2 3 4 1 2 3 4

12t 23t 34t0 0 12t 23t 34t

dSkdPk VVw −+

Figure 6. Buck and boost mode ( a) and b) ) for IBFBC on basis of hysteretic current-mode control.

For buck mode operation the IBFBC is controlled according to Figure 6a). The primary semiconductor switches S1k to S4k are controlled in push-pull manner, while the secondary full-bridge is inactive, passively functioning as bridge rectifier. During buck mode at t = 0 a positive voltage is applied to the transformer Tk by activating the switches S1k and S4k in interval 1. The resulting positive voltage at the secondary full-bridge vHSk = wkVdP side leads to iSk = iHSk with a positive slope taking the path via D5k and D8k starting from the lower threshold iHSk(t = 0) = imin. At the beginning of the freewheeling interval 2 at t = t12, when iHSk = imax, S1k and S4k are switched off. The current iHSk flows either through D5k and D6k or D7k and D8k and the voltage vHSk becomes vHSk = 0, which leads to a negative voltage across the inductance vLdSk = -VdSk. As soon as iHSk = imin the voltage at the primary side of the transformer vPk is inverted by activation of S2k and S3k at the beginning of interval 3 at t = t23. The resulting negative voltage vSk = -VdP·wk at the secondary transformer side is rectified and the current -iSk = iHSk is flowing through D6k and D7k. The switching period ends with the freewheeling interval 4 with iHSk = imax at t = t34, during which the current flows either through D5k and D6k or D7k or D8k. The current iHSk falls linearly until iHSk = imin at t = Tsk and a new switching period begins. For boost mode operation the IBFBC is controlled according to Figure 6b). Only the secondary semiconductor switches S5k to S8k are controlled while the primary full-bridge is inactive and is passively functioning as bridge rectifier. During

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boost mode, at the start of interval 1 at t = 0 and iHSk = imin, a negative current iHSk is made possible by short-circuiting the secondary full-bridge circuit achieved by activation of the switches S5k to S8k. This leads to a decreasing current iHSk, since vLdSk = -VdSk. When iHSk = imax at t = t12 the semiconductor switches S5k and S8k are deactivated and the current iHSk is applied to the transformer Tk via S6k and S7k during interval 2. The resulting primary transformer current iPk is rectified by the diodes D2k and D3k. As vLdSk = wkVdPk – VdSk is positive iHSk is decreasing in magnitude. At the beginning of interval 3 at t = t23 the secondary full-bridge circuit is again short circuited by S5k to S8k, leading to a negative slope of iHSk until iHSk = imax. During interval 4, initiated by iHSk = imax at t = t34 the semiconductor switches S6k and S7k are switched off and the current iHSk is conducted by S5k and S8k. The current iHSk = iSk, exhibiting a positive slope due to vdSk = wkVdP – VdSk, is applied to the transformer Tk and rectification is realized by D1k and D4k on the primary side. When iHSk = imin a new switching period begins. In accordance to the earlier discussion of the flyback converter the average output current can be expressed as a function of the switching thresholds imax and imin.

2

)()(1 minmax

0

iidttiT

iSkT

HSkSk

HSk+

=⋅= ∫ (4)

As can be seen from (4), the average value of iHSk depends only linearly on the two current thresholds imax and imin. Due to the linearity the IBFBC is easier to control than the flyback converter. Assuming imax and imin to be constant, the arithmetic average value of iHSk stays constant over the whole output voltage range. As with the flyback converter the lower current threshold can be set to imin = 0, facilitating reduced switching losses. Since the IBFBC represents a buck converter with an additional voltage boost ratio wk, the output voltage vdSk must fulfill the equation vdSk ≤ wk·VdSk in order to ensure proper operation. A possible DAB modulation scheme for the DAB converter, shown in Figure 7, also enabling limitation of the converter output current, is based on Phase Shift Modulation, which originally is a fixed frequency modulation scheme indicated by the duty cycle Dk.

tsT

kk SS 41 ,kk SS 32 ,kk SS 85 ,kk SS 76 ,

DABkv

2/sT

DABki

HPki

HSki

t2/sT

dSkdP VV '++

dSkdP VV '+−dSkdP VV '−−

dSkdP VV '−+

maxi+maxia ⋅+

maxi−

0 0

a) b)

sT

skkTD

skkTD

k

k

SS

7

6

k

k

DD

8

5

k

k

DD

8

5

k

k

SS

8

5

k

k

DD

7

6

k

k

DD

7

6

k

k

DD

7

6

k

k

DD

4

1

k

k

SS

4

1

k

k

DD

3

2

k

k

SS

3

2

k

k

SS

3

2

k

k

DD

4

1

k

k

SS

4

1

k

k

SS

7

6

k

k

SS

4

1

k

k

DD

8

5

kSS

8

5

k

k

SS

8

5

k

k

DD

7

6

k

k

SS

7

6

k

k

SS

7

6

k

k

SS

7

6

k

k

DD

3

2

k

k

DD

3

2

k

k

DD

4

1

k

k

DD

4

1

k

k

SS

4

1

k

k

SS

4

1

k

k

SS

3

2

k

k

DD

3

2

k

k

SS

3

2

k

k

DD

8

5

kSS

8

5

maxia ⋅−

1 2 3 4 5 6 1 2 3 4 5 612t 23t 34t 45t 56t

Figure 7. Buck and boost mode ( a) and b) ) for DAB converter based on hysteretic current-mode control.

The original Phase Shift Modulation scheme is based on controlling the phase shift DkTsk between the primary and secondary full-bridge. For Dk > 0 energy is fed to the load, while for Dk < 0 energy is fed back to the DC link circuit. Since Phase Shift Modulation does not enable direct limitation of the output current and the saturation of the Transformer Tk is difficult to prevent for dynamical changes of the output voltage vdSk, it is extended by controlling the

Proc. of SPIE Vol. 8340 834018-8

output current iHSk or iDABk between certain current thresholds. Compared to the original Phase Shift Modulation scheme, the extended Phase Shift Modulation scheme ensures low switching losses over the complete output voltage range, because ZVS is enforced by control of the current according to the switching thresholds with iSk = imax, iSk = a·imax, iSk = -imax and iSk=-a·imax with 0 ≤ a ≤ 1 and imax > 0. The commutation under ZVS conditions from diode to semiconductor switch is indicated by circles encircling the commutation event. For the depicted modulation scheme the voltage vdSk has to fulfill vdS < wkVdP as well. The switching period Tsk can be divided into six intervals. During interval 1 of buck mode, shown in Figure 7a), beginning at t = 0 the primary pair S1k/S4k and the secondary pair S6k/S7k are switched on. The voltage across the inductance LDABk is at a maximum with vDABk = VdP+V’dSk = VdP + wkVdSk. As a result the current iDABk increases with a positive slope, the current iHPk is positive and iHSk is of opposite polarity. At the instant iSk = +a·imax/wk at t = t12 the semiconductor switches S5k/S8k and S6k/S7k are toggled and interval 2 begins. The voltage vDABk is reduced but still positive with vDABk = VdP – wk·VdSk, so the slope of iDABk is reduced, but still positive. Since S6k and S7k are off, the current iSk = iDABk/wk commutates to the diodes D5k and D8k and iHSk is positive during interval 2. As soon as iSk = imax/wk at t = t23 interval 3 is initiated by toggling the pairs S1k/S4k and S2k/S3k. The current iDABk, enforced by LDABk stays positive, but commutates to D2k and D3k because S1k/S4k are off, so iHPk changes polarity from positive to negative. During interval 3 and 4 no change of the semiconductor switch control states occurs and the negative voltage across the inductance is vDABk = -VdP - wk·VdSk leading to a negative slope of iDABk. At the transition between interval 3 and 4 at t = t34, when iHPk and iHSk change polarity, the currents iPk and iSk smoothly commutate from D2k/D3k and D5k/D8k to S2k/S3k and S5k/S8k, while both semiconductor switch pairs are switched on under the forward voltage drop of the antiparallel diodes causing negligible switching losses. The current waveforms during interval 4, 5 and 6 are equal to interval 1, 2 and 3, only the voltage vDABk and the current iDABk are inverted. Boost mode operation of the DAB converter is shown in Figure 7b). Again assuming a loss-less system and constant input and output voltage, the arithmetic average of the output current iHSk for buck and boost mode is obtained by integration over one switching period Tsk and is equal to

⎩⎨⎧

−=+=

⋅⋅−⋅⋅

⋅−⋅=⋅= ∫ .harvesting1

andsupply 1with

)(2)1()(1

max

2

0 bb

iVaVw

VabdttiT

idSdPk

dPT

HSkSk

HSk

Sk

(6)

3.4 Modulation Schemes for Modular Converter Concepts

Considering the control of the modular converter system an appropriate overall modulation scheme has to be utilized ensuring a symmetrical voltage distribution between the n converter modules. The simulation results for the modular flyback converter system are shown in Figure 8.

0 2 4 6 8 10 12 14 16-101

time in ms

i Pk, i

Sk in

A

4 4.05 4.1 4.15-101

time in ms

i Pk, i

Sk in

A

12 12.05 12.1 12.15-101

time in ms

iP1, iS1 iP2, iS2 iP3, iS3 iP4, iS4 iP5, iS5

0 5 10 150

0.2

0.4

0.6

time in ms

v dSk in

kV

vdS1

vdS2

vdS3

vdS4

vdS50 5 10 15

0

1

2

3

time in ms

v dS in

kV

vdS

supply operation

harvesting operation

Figure 8. Simulation results for modular converter system with synchronously triggered flyback converter modules.

The simulations were performed for a DEAP capacitance Cp = 0.5µF, a polymer resistance Rp = 1MΩ and an electrode resistance Re = 10Ω. For control of the modular flyback converter system all present modules are triggered synchronously depending on the primary and secondary current of one flyback converter module. The simulation of the

Proc. of SPIE Vol. 8340 834018-9

modular flyback converter system was performed for wk = 1, imax = 1A, imin = 0, the magnetizing inductances Lm1 = 9.4mH, Lm2 = 9.2mH, Lm3 = 10.7mH, Lm4 = 9.2mH, Lm5 = 9.7mH, which were deliberately chosen to be unequal, CdSk = 0.17µF, VdP = 325V and n = 5 modules for supply and harvesting operation. The simulation results show an adequate voltage distribution among the flyback converter modules achieved for synchronous control of the flyback converter modules. As predicted the dynamic of the converter decreases with increasing output voltage. In order to achieve voltage balance among the DAB converter module outputs each module is triggered separately depending on the secondary current iSk. As a result the average output currents for all DAB converter modules are equal. The module output currents iHSk = [iHS1 , iHS2 , iHS3], the module output voltages vdSk and the output voltage vdS of the modular converter system with n = 3 modules are shown in Figure 9 for supply and harvesting operation.

0 5 10 15 20 25 30 35-0.2

00.2

time in ms

i HSk

in A

iHS1

iHS2

iHS3

5 5.02 5.04 5.06 5.08 5.1-0.2

0

0.2

time in ms

i HSk

in A

25 25.05 25.1-0.2

0

0.2

time in ms

i HSk

in A

iHS1

iHS2

iHS3

0 10 20 300

0.5

1

time in ms

v dSk in

kV

vdS1

vdS2

vdS3

0 10 20 300

1

2

3

time in ms

v dS in

kV

udS

supply operationharvesting operation

Figure 9. Simulation results for modular DAB converter system with separately triggerd DAB converter modules.

The simulation was performed with CdSk = 0.6µF, LDAB1 = 7.7mH, LDAB2 = 7.3mH, LDAB3 = 6.8mH, wk = 4, imax = 1A and a = 0.5. In contrast to the flyback converter topology the dynamic of the DAB converter system increases with increasing voltage. As with the DAB converter the modules of the modular IBFBC converter system have to be triggered separately depending on iHSk as well, as the simulation results for LdS1 = 10.2mH, LdS2 = 9.2mH, LdS3 = 10.7mH, CdS1 to CdS3 = 0.6µF and wk = 4 in Figure 10 show. The converter dynamic is independent of the output voltage level.

0 5 10 15 20 25 30 35-0.2

00.2

time in ms

i HSk

in A

iHS1

iHS2

iHS3

7.5 7.505 7.51 7.515 7.52 7.525-0.2

0

0.2

time in ms

i HSk

in A

25 25.005 25.01 25.015 25.02 25.025-0.2

0

0.2

time in ms

iHS1

iHS2

iHS3

0 10 20 300

0.5

1

time in ms

v dSk in

kV

vdS1

vdS2

vdS3

0 5 10 15 20 25 30 350

1

2

3

time in ms

v dS in

kV

vdS

supply operation

harvesting operation

Figure 10. Simulation results for modular IBFBC system with separately triggered converter modules.

Proc. of SPIE Vol. 8340 834018-10

4. EXPERIMENTAL RESULTS The measurement results for a first experimental prototype of a bidirectional flyback converter module driving a capacitor with a capacitance of Cp = 0.47µF are shown in Figure 10. The primary and secondary current iP and iS, the output voltage vdS and the relevant gate control voltages vGS1 and vGS2 for supply operation from vdS = 0V to vdS = 400V are shown in Figure 11a), while harvesting operation from vdS = 400V to vdS = 0V is depicted in Figure 11b). The DC link voltage was vdS = 60V, the magnetizing inductance of the flyback converter was Lm = 19mH with wk = 1.

a) b)

0 1 2 3 4 5 60

2

time in ms

v GS1

in V

0

0.5

i P, iS in

A

0.2 0.4 0.6 0.8 1 1.2 1.40

0.5

time in ms

i P, iS in

A

0

200

400

v dS in

V

0 1 2 30

2

time in ms

v GS2

in V

-0.6

-0.4

-0.2

0

0.2 0.4 0.6 0.8 1-0.6-0.4-0.2

0

time in ms

iPiS

0

200

400

Figure 11. Primary and secondary current, output voltage and gate control voltages for a) supply and b) harvesting

operation of bidirectional flyback converter.

Control of the semiconductor switches S1 and S2 was realized using a real-time operating system with an operating frequency of 100kHz. The measurements for supply operation were taken for the reference current thresholds i*max = 0.5A and i*min = 0A. The converter dynamics reflected by the experimental results are consistent with (3), exhibiting a diminished dynamic at high output voltages. In addition, the peak values of the secondary current are increasingly degraded caused by the finite commutation time of the magnetizing current from primary to secondary side and the faster decrease of the secondary current at high output voltages. As can be seen a variable switching frequency results from the implemented hysteretic current-mode control scheme, whereas the switching frequency increases with increasing output voltage. The measurement results during harvesting operation were captured for i*max = −0.4A and i*min = 0A.

5. CONCLUSION In this contribution a modular switched-mode converter concept for bidirectional operation of DEAP devices was presented, which allows the use of standard semiconductor switches enabling a high level of efficiency, smaller passive components and a high flexibility due to modularity. For realization of the individual converter modules the bidirectional flyback converter and two full-bridge circuit based topologies, DAB converter and IBFBC, were investigated. For each converter topology a modulation scheme based on hysteretic current-mode control was proposed facilitating direct limitation of the converter output current, current source operation of the respective converter modules, simplified converter dynamics regarding control and a higher converter dynamic compared to a fixed frequency modulation scheme. Simulation results for the proposed modulation schemes for the modular converter system were presented for each converter topology, exhibiting a symmetrical voltage distribution among the individual converter modules. The feasibility of hysteretic current-mode control for a single bidirectional flyback converter module driving a capacitive load was proven by an experimental prototype operated in supply and harvesting operation.

Proc. of SPIE Vol. 8340 834018-11

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