DC-DC Converter for charging and dischargingsuper-capacitors used in electric hybrid cars.

Čeřovský Zd. Pavelka Vl.Czech Technical University Prague, Faculty of electrical Engineering

Technicka 2, CVUT FEL K314CZ 16627 Prague 6, Czech Republic

Tel. ++420 224 352 157 Fax: ++420 233 339 972e-mail: cerovsky@fel.cvut.cz

e-mail: pavelkv@fel.cvut.cz

Keywords:

Hybrid vehicles, Emerging technologies, Automotive components, DC power supplies, Test bench

Abstract:Experimental working stand for electric and hybrid car drive research was projected in the ResearchCentre JB at the Technical University in Prague. Super capacitors are implemented. They are able toaccept the kinetic energy during breaking the vehicle and regenerate it during next speeding up. Thepower at which the energy can be transferred via DC-DC converter is studied in this paper. It islimited by the duty factor of the DC – DC converter and by the resistance R in the converter circuitmainly. The ratio of the super capacitor and intermediate traction circuit voltages and the inductivityof the inductance in the DC – DC converter influence the maximum power at which the energy can betransferred via DC-DC converter too but not so drastically.

1 Introduction.

The history of electric surface transportation is a history of successful electric component developmentin electric locomotives. Demands of this electric drives branch have contributed to the electricalengineering progress a lot. Electric car and hybrid electric car stood in the shadow of electric railwayrush development for a long time. But new technologies in electrical engineering refresh repeatedlythe interest of researchers, engineers and producers.

The fuel-cells and super-capacitors are in present time the most promising new technologies. Thesuper-capacitors are not capable to store sufficient energy comparable with fuel tank or electricbatteries but nevertheless they are able to accept the energy during breaking the vehicle and regenerateit during next speeding up. The dynamic of super capacitors is high. Special problems occur onexperimental working stand on the DC-DC converter connecting the super-capacitor with the DCintermediate-circuit of traction converters. The reasonable voltage of super-capacitors is rather lowand the voltage to which the energy should be regenerated may be rather high. They are somelimitations for the DC-DC converter power transfer between super capacitor and intermediate tractionconverter.

2 Experimental working stand description

Experimental working stand was projected in the Research Centre JB at the Technical University inPrague. The scheme is depicted in Fig.1. The internal consumption engine ICE is simulated by acontrolled electric ac motor ACM1 supplied by the power converter EC1. Rotor of specialsynchronous permanent magnet generator SGPM is firmly coupled with the ACM1 shaft. Stator is

firmly coupled with car wheels and rotates with the speed proportional to the car velocity. On thisshaft is inserted traction motor TM. Generator SGPM and traction motor TM are electricallyconnected through EC3 power electronic converter set. Traction resistance is simulated with controlledac motor ACM2 supplied by the power converter EC2. A super capacitor is connected with powerconverter set EC3 by a DC-DC converter. It acts as an energy buffer.

2.1 Parameters of the experimental set

The output of both ACM1 and ACM2 motors is the same 7.5 kW, 3 x 400 V, 0 – 6000 min-1,maximum torque 31 Nm.

The output of the special permanent magnet synchronous generator SGPM with rotating stator androtor is 5 kW, 4000 min-1, maximum speed 6000 min-1, 267 Hz, 400 V.

The output of the traction motor TM is 3 kW, 1420 min-1, max speed 6000 min-1, 400 V.

The super capacitor capacity is 100F, full charged voltage 56V, maximum current 400 A.

2.2 Description of the function

During start of the car when ACM2 speed is zero the ACM1 torque is transmitted via SGPMsynchronous generator air gap to the SGPM stator. Conventional fixed stator would fasten this torqueby the foot but “electric split device” SGPM transmits it to the output shaft and adds it to the traction

motor TM torque. When the ACM2 shaft isturning then SGPM torque transfers

mechanical power that increases with output shaft speed. Traction motor power decreases becauseSGPM differential speed decreases too. Power and losses in electric machines fall and powertransmission efficiency increases. Electric power splitting generator SGPM supplies the traction motorvia EC3 converter. When stator SGPM speed is near to the rotor SGPM speed the clutch ELM willswitch on and power transmission from ACM1 to ACM2 takes place on a pure mechanical way.

SUPER CAPACITOR With DC-DC converter

EC2EC1

Fig.2. Test room view

U1 C1

L R

C2 U2

T1

T2

Fig.3. Scheme of the DC-DC converter

D1

D2

i1

i2

3 Mathematical model of the DC-DC converterThe scheme of the DC-DC converter is on the Fig.3.We want to analyse the energy transfer from the super-capacitor C2 (the voltage of which is rather

low) into the capacitor C1 (thevoltage of which is rather high).The aim is to find what output canbe transferred at what voltage ratioU2/U1 and how it is influenced byinductance L and resistance R andby different duty factors. Weassume in the first state idealtransistors with zero switchingtime. Later on we introduce the

real transistor properties with real switching time.

3.1 Ideal transistors.Two current shapes can occur. In the first case current i2 is un-interrupted, in the second case it isinterrupted. Both cases are depicted in the Fig. 4.

Let us denote:

RL

=τ

factordutyTT

z on ==

frequencyT

f 1=

Tp is time when i1 reaches the value zero

τ

τfzp

eUU

UUT−

−

−−=

21

21ln

zmez is the minimal duty factor at whichcurrent i2 is un-interrupted

1

2111

ln1U

feUU

fzmez

−−−

+=τ

τ

Imin is the minimal value of un-interrupted current i2 pulsation.

τ

τ

f

fz

e

eRU

RUI 1

1

12min

1

1−

−−

−

−−=

Imax is the maximal value of i2 pulsation.

ττ

τ

ττfz

fz

f

ffz

eIeRU

e

eeRU

RUI

−−

−

−−

+

−=

−

−−= min

21

1

12max 1

1zmax is duty factor for the wanted Imax

iT

2

i1

i2

Current i2 is un-interrupted.(continuous)

iT

i1

Tpi2

Current i2isinterrupted

Fig.4. Possible current shapes

−−=

2

maxmax 1ln

URI

fz p τ for interrupted i2

−

−

−+−=

−ττ f

n eURIU

fz1

1

max2max 111ln for un-interrupted i2.

ICAV is average current value from or into appropriate capacitor( )R

UUfTzUI p

AVpC122

2

−+= for interrupted current from super-capacitor C2

( )R

zUUI AVnC−−

=112

2 for continuous current from super-capacitor C2

RUUfTeI

RUUfI p

T

AVpC

p

21max

211 1 −

−

−

+

−=

−ττ for interrupted current into the

capacitor C1

( )RUUzeI

RUUfI f

z

AVnC21

1

max21

1 11 −−−

−

+

−=

−−

ττ for continuous current into capacitor C1

PC2 is output power from the capacitor C2 222 UIP AVCC =PC1 is input power into the capacitor C1 111 UIP AVCC =

3.2 Real transistorsReal transistor cannot switch on and off immediately. How is the real transistor simulated is shown onthe Fig.5.

The switching off time consistsof delay time tsv, voltage risetime tv, rapid drop and tailingtime ti1 and ti2. The process takestogether approximately 10µs.The time at which the transistorT2 should be off is at switchingfrequency 5kHz and duty factor0.9T 20µs. We shall see that thefeatures of transistor areimportant.

4 Results of simulation.Calculations were made for ideal and real transistor.

4.1 Ideal transistor calculation.

4.1.1 Influence of duty factor.

In Fig. 6. are depicted efficiency η, power P1AV which is pumped from the capacitor C2 into C1 duringswitching period as function of duty factor z. Parameters for which the calculation holds are:

Switch off

Switch on

iT

uT

iT

uT

tsv tv ti1 ti2 tsz tz tu1 tu2

Fig.5. Switch off and switch on transistor characteristics

Switching frequency f=10kHz,U1=400V, U2=56V (dash curve),U2= 33V(full curve), L=0,9mH,R=0,15Ω.From the Imax curve follows thatat low duty factor the Imax growsslowly because the current i2 isinterrupted. Therefore thepumped power is low. Startingfrom the point at which thecurrent begins to be continuousP1AV grows and reaches itsmaximum at some special dutyfactor value “zPmax”. Theconditions for power pumpingare worse when the capacitor C2

voltage is low. Also the efficiency of the energy transfer is worse.

The influence of capacitor C2 voltage U2 on the power transfer is depicted on Fig. 7, where the voltageU1 =400V was hold constant and the voltage U2 changes. It can be seen that the power at which theenergy can be pumped from the capacitor C2 and transferred into the capacitor C1 is limited.

At our test bank the maximum C2 voltage is 56V and the power transfer from the super-capacitor C 2 islimited to 5.2kW. For the test bank with machinery power of 3kW it is quite enough. This factinfluences the control strategy for the optimal use of super capacitor on a hybrid vehicle. The strategyhas to balance the energy flow under changing conditions of different drive demands. This task liesoutside of the aim of this paper.

4.1.2 Influence of resistance R.It can be seen from Fig.6 that there is aspecial factor duty “zPmax” at which thepower input into the intermediate circuit is atits maximum. At higher “zPmax” the poweroutput from the super-capacitor growsfurther but the power input into theintermediate circuit begins to fall down. It ispossible to prove that the power input intothe intermediate circuit is at its maximumwhen the power transfer efficiency is 50%. Itholds for average current values:

5.022

11

2

1 =⋅⋅

≅UIUI

PP

AV

AV

AV

AV

It is evident that the power transfermaximum takes place at un-interruptedcurrent only. When we assume that the timeconstant is high (τ>>T) then the current timecourse during different transistor switchingmode is linear. For average current valuesthen holds:

( )zII AVAV −= 121

Fig.6. Energy pumping from the super-capacitor havingU2=56V, resp.33V by ideal transistor.

0.85 0.9 0.95 10

100

200

300

400Cerpani energie ze superkondenzatoru

z [-]

Imax

P1AV

η

U2=33VU2=56V

U1=400Vf=10kHzL=0.9mHR=0.15Ω

0

20

40

60

80

100

0

4

8

12

16P [kW] I [A]

η [%]

Energy transfer from C2 into C1

0,0

50,0

100,0

150,0

200,0

250,0

0,0 50,0 100,0 150,0 200,0 250,0

Voltage U2

Pum

ped

pow

er P

1

Fig. 7. Power transfer from the super capacitorinto the intermediate circuit by ideal transistoras function of super-capacitor voltage

Introducing this equation into the previous one where z equals z Pmax we get

( )5.0

1

2

1max =⋅−

UUzP

For the average current value I2AV holds

( )R

UUzI AV21

21 −⋅−

=

For the maximum power input into the intermediate circuit we get using last three equations:

( )( ) ( )

RU

R

UUUzR

UUzzUIUP P

P

PAVAV 4

21

21

112

22

222

max21max

max

2111 −=

−⋅∗=−

−⋅−∗

−==

We can do following conclusion:Maximum power that can be pumped from the super-capacitor into the intermediate circuit does notdepend on the intermediate circuit voltage. It depends only on the super-capacitor voltage and on thecircuit resistance. Fig.8 shows the maximum possible transferred power for different circuit resistancesR against the super-capacitor voltage. Let us stress on this place that this result holds for idealtransistor with switching time zero. In next paragraph the influence of real transistor will be studied.

0

24

68

10

1214

1618

20

0 10 20 30 40 50 60 70

Super-Capaciter Voltage

Max

imum

tran

sfer

red

pow

er P

1

R=0,05R=0,1R=0,15

4.1.3 Influence of the inductance L.

Assuming ideal transistors with zero switching time the maximum power that can be pumped from thesuper-capacitor into the intermediate circuit does not depend on the circuit inductance.

Fig. 8. Maximum possible transferred power for different circuitresistances R.

4.2 Real transistor calculation

Mathematical model of the realtransistor is based on transistorcharacteristics in the Fig. 5.

Two important features, different fromthe previous case, when zero switchingtime of transistor was assumed, are:The first one is loss in transistor duringswitching on and off. The second one isthe fact that the real switching timeproduces in the real inductance realvoltage only.

The difference between ideal transistortheory and real transistor theory isshown in Fig.9. Three C2capacitor voltages 56V, 40V and 30Vwere taken in account. Dashed curvesare results of ideal transistor theory and

full curves of real transistor theory. Thecapacitor C1 voltage was 400V for allthree cases. It is seen that the realtransistor diminishes the transferredpower.

The comparison of the maximum powerthat can be transferred from the supercapacitor into the intermediate circuit isdepicted in Fig.10. The maximum powerdepends not only on the super capacitorvoltage U2 but also on the intermediatecircuit voltage U1 , which is in oursimulation represented by the capacitorC1 voltage

5 Conclusion

Super-Capacitor is a high dynamic device able to store energy for later use during driving on hybridelectric vehicles. With respect to the DC-DC converter and used transistors the power transfer betweensuper capacitor and intermediate DC circuit is limited by resistance between super-capacitor andtraction intermediate circuit. Further more it is influenced by ratio of super capacitor and intermediatecircuit voltages. The lower resistance is advantageous not only for the power transfer dynamic but alsofor the high transfer efficiency. The inductivity of the inductance influences the current pulsation. Theinductance selection has to be a compromise between low resistance and low current pulsation

0.85 0.9 0.95 10

1

2

3

4

5

6

z [-]

P1A

V [k

W]

30V

40V

56V

U1=400V f=10kHz L=0.9mH R=0.15Ω

Fig.9. Energy pumping from the super-capacitorhaving U2=56V, 40V .33V by ideal and real transistor.

0 10 20 30 40 50 600

1

2

3

4

5

6

U2 [V]

P1

[kW

]

ideal

real

f=10kHz L=0.9mH R=0.15Ω

U1=400V

U1=100V

Fig. 10. Power transfer from the super capacitor intothe intermediate circuit by ideal or real transistor asfunction of super-capacitor voltage

demand. There is a special duty factor of the DC-DC converter at which the transferred power is at itsmaximum.

The comparison between ideal transistor and real transistor can reveal following results for realtransistor:

1. The maximum transferred power is limited by the circuit resistance R2. The maximum transferred power is influenced by the intermediate circuit voltage.3. The maximum transferred power takes place at higher duty factor for real transistor then for

ideal transistor.4. There is a maximum duty factor that cannot be raised up because of blanking time of the

transistor in the DC-DC converter. The real maximum duty factor is lower then 1

6 Reference list1. Mohan N., Undeland T.M., Robbins W.P.: Power electronics, John Willey and Sons 1989.2. Westbrook M.H.: The electric and hybrid-electric car, Society of Automotive Erngineers,

ISBN 0 7680 0897 2, 2001.3. Denton T.: Automobile Electrical and Electronic Systems, SAE International ISBN 0 340

73195 8.4. Čeřovský Z., Flígl S., Hanuš P., Mindl P.:Hybrid drives and hybrid energy transfer (in Czech),

Proceedings of XXVII Electric drive Conference Plzen 2001, P.73-78, ISBN 80-02-01434-0