three-phase unity power factor

Three-Phase Unity Power Factor AC/DC Converter (PFC) with Dual Isolated DC/DC Converter for a Battery Charger J. Herminjard

EPE '99 - Lausanne P. 1

Three-Phase Unity Power Factor AC/DC Converter (PFC) with DualIsolated DC/DC Converter for a Battery Charger

J. Herminjard, EIVD-LEP, CH-1401 Yverdon,e-mail: [email protected] ; URL: http://www.eivd.ch

Phone: +41(0)244 232 272 / Fax: +41(0)244 250 050C. Zimmermann, EPFL-DE-LEI, CH-1015 LausanneR. Monnier, R+D Leclanché SA, CH-1401 Yverdon

Acknowledgement

This development was supported by “Fonds pour Projets et Etudes de l’Economie Electrique” of“l’Union des Centrales Suisses d’Electricité PSEL” and by the commission RDP of the ”ChambreRomande d’Energie Electrique RDP-CREE”. We thank these organisations for their generous support.

Keywords

Battery charger, Control, Converter circuits, DSP, Efficiency, Harmonics, High frequency powerconverters, Power factor correction, Power Quality, Simulation, Three phase systems

Abstract

In this article the development and realization of a 8 kW battery charger with Power Factor Correction(PFC) is described. The converter consists of two parts: The first part is an AC/DC converter based ona “VIENNA” topology with a controlled output voltage of 700V and midpoint connection [1],[2]. Thesecond part consists of two DC/DC converters with galvanic isolation and parallel outputs. The outputcurrent and voltage can be controlled in the ranges 0-28A and 0-280V.

1 Introduction

The increasing number of electric vehicles demands battery chargers with high efficiency, lowharmonic distortion of the mains current and reduced weight and volume. For this reason two highschools and a battery manufacturer have realized a battery charger prototype of 8 kW with unitypower factor and three-phase sinusoidal currents.Figure 1.1 shows the principal parts of the realized installation. The “VIENNA” topology [1], [2] waschosen for the realization of the AC/DC converter, due to the possibility of having two controlledintermediate voltages with only three controlled semiconductors. This part was developed andrealized in the Laboratory of Power Electronics (Professor C. Yechouroun) of EIVD (Ecoled'Ingénieurs du canton de Vaud) in Yverdon-les-Bains.The two DC/DC switched mode converters use planar transformers working at 30kHz to generate anisolated rectified output current for the battery. This part was realized in the Laboratory of IndustrialElectronics (Professor A. Rufer) at the Swiss Federal Institute of Technology Lausanne (EPFL) withhelp of the industrial partner Leclanché SA, Yverdon-les-Bains.

Fig. 1.1 : Global scheme of the installation



2 AC/DC Converter "VIENNA"

2.1 Circuit

The AC/DC Converter “VIENNA” is shown in Figure 2.1. This circuit draws three-phase sinusoidalcurrents in phase with the mains voltage 400V/50Hz and produces two controllable intermediatevoltages Uz1 and Uz2 at 350V each. The control of the input currents can be made only if the sum ofthe two output voltages is higher than the peak line-to-line main voltage.

Fig. 2.1 : AC/DC Converter “VIENNA”

2.2 Intermediate DC voltage control

The control of the two intermediate DC voltages must follow their references and maintain sinusoidalcurrent consumption in phase with the three mains. In our application the two voltage references areidentical.

2.2.1 Control circuit

Figure 2.2 represents the proposed circuit for the control of the two intermediate voltages.

Fig. 2.2 : Intermediate voltage control circuit

Studying the behaviour of the “VIENNA” converter (Fig. 2.1) we can find the two following facts:



• The load current i+ of capacitor C1 is provided by the sum of all positive main currents, if thecorresponding transistor is turned off.

• The load current i- of capacitor C2 is provided by the sum of all negative main currents, if thecorresponding transistor is turned off.

Let’s suppose that the output of the voltage control for uz1 gives the reference ic+ and uz1 is below its

reference. The voltage control (block no. 1 in Figure 2.2) will react and increase the reference for thecurrent i+ which is provided by the sum of all positive main currents, but only if the correspondingtransistors are turned off. We know that, for increasing the main current the transistor should beturned on most of the time, but this leads to a decreasing current i+. This is contradictory to thedesired control supposed before. To resolve this problem, we simply interchanged the two currentreferences given by the two voltage regulators (block no. 1).The block no. 2 gives only the negative parts of the three-phase references which are in phase withtheir main voltages, and the block no. 3 gives the three-phase references for the positive parts. Takingthe sum of the outputs of these two blocks leads to a three-phase sinusoidal reference for the threephase current regulators (block no. 4). These regulators are tolerance band current controllers andallow the AC/DC converter to draw the correct currents from the mains. The commands of thetransistors depend on the signs of the line voltage ui, therefor a logic block no. 5 must be added withthe functional behaviour resumed by (2.1) and (2.2).

−<+>

=hiiif1

hiiif0'd

cm

cmi i = 1,2,3 (2.1)

<≥

=0uif'dinv

0uif'dd

ii

iii i = 1,2,3 (2.2)

where h represents the hysteresis of the current control.

2.2.2 Transfer function

Considering that the input power of the converter is equal to the output power, the following equationin p.u. (2.3) can be derived :

112

3i

ui

z

⋅⋅

=+ (2.3)

with:nnn I

I

I

I

I

Ii 3211 === ;

n

zz U

Uu 1

1 =

Un = nominal effective main voltage; In = nominal effective main current

For small variations of the current i1 and supposing that uz1 remains almost constant during this time itis possible to write:

1iKi i ∆⋅=∆ + (2.4)

where

czi u

K12

3

⋅=

We express the variation of the voltage uz1 in equation (2.5)+⋅= cz i

sTsu

1)(1 (2.5)

with the time constant of the load: T = RnC ; n

nn I

UR =



2.2.3 Calculation of the voltage control parameters

Figure 2.3 shows the block diagram of one of the two PI control loops to obtain an intermediate DCvoltage.

Fig. 2.3 : Block diagram of the voltage control

In this figure we distinguish the voltage regulator (block no. 1), the simplified transfer function of theclosed loop of the current control modelled by a small time constant Tp (block no. 2), block no. 3represents the factor between input and output current (expression 2.4) and finally the transferfunction of the load (block no. 4). ∆ich represents the variation of the load current.

The parameters Tn and Ti were determined according to [3]:

pi

n

T

T

T

T

⋅=

2 ;

T

TT

pi

2

8=

Tp is a small time constant modelling the current control, and T = RnC is the time constant of the load.

2.3 Simulation and measurements

The simulation allows to verify if the theoretical developments correspond in a sufficient exactmanner with the measurements [4].

2.3.1 Drawn main currents

Figure 2.4a shows the simulation of the three currents drawn from the 400V main in stationaryoperation and symmetrical load of 2 x 4kW. The measures in Figure 2.4b are made for an outputpower of 5,5 kW.

0

0 1 0 2 0

t [ m s ]

0

0 . 5

1 . 0

1 . 5

- 0 . 5

- 1 . 0

- 1 . 5

i 1 , 2 , 3 [ p . u . ]

(a) Simulation (b) Measurement

Fig. 2.4 : Waveforms of the three phase currents drawn from the main



2.3.2 Step response of the voltage control loop

Figure 2.5a shows the behaviour of the voltage uz1 after a step of its reference. Figure 2.5b representsthe variation of the voltage uz1 after a sudden load reduction of 50%.

The simulation parameters are: R1,2 = 35 [Ω] C1,2 = 1 [mF]Tn = 2 [ms] Ti = 400 [us]

...

(a) reference step (b) load step

Fig. 2.5 : Voltage control

The measurements in Figure 2.6 show the step response of the output voltage.

Fig. 2.6 : Output voltage response of the AC/DC converter to a voltage reference stepfrom 1,6 to 1,7 p.u.

2.4 Conclusions

This research has permitted to develop an original voltage control, which allows even non-symmetrical output voltages and loads. Note that for our application a symmetrical voltage isrequested. The results of simulations and measurements confirmed the validity of the proposedcontrol for the AC/DC converter. The obtained efficiency of this converter is high (η = 0,96).



3 DC/DC Converter

3.1 Description of the DC/DC converter with two shifted channels

The 8kW DC/DC converter (Fig. 3.1) must be able to supply 280V at 28A continuously in order tocharge the batteries. The use of a two stage converter, where the inputs of the inverters are connectedin series and the outputs of the rectifiers in parallel, allows :• The reduction by a factor of 2 of the breakdown voltage of the semiconductors• Less electromagnetic emissions (EMI)• A reduction of the current ripple iL by addition of the two currents iL1 and iL2, shifted by 180°.

Fig. 3.1 Basic circuit structure of the DC/DC converter with voltage and current waveforms

The switching frequency, fixed at 30kHz in order to match planar transformers available on themarket today, allows a substantial reduction of the volume and weight of the converter’s passiveelements. Such a high frequency has further the advantage of being inaudible. Ultra rapid IGBT of the4th generation are used for the inverters (IRG4PC50UD, VCES=600V,VCE(on)=1,65V, IC=27A, TO-247).

Since the two inverters are driven with a phase shift of 90° (Fig. 3.1), the two currents applied to thetwo transformers are also shifted by 90°. The pulsating frequency of 30kHz becomes 60kHz after therectifier, and the shift between the ripples of the two currents iL1 et iL2 is now 180°. The addition ofthese two signals will reduce the current ripple of iL, which has now a frequency of 120 kHz. Thismethod of running the converter minimises the required value of the filter capacitor C.Theoretically, in normal operation the value of the two voltages ud1δ et ud2δ will depend linearly on thepulse width δ (Fig. 3.1) between 0 and π, according to the formula

πδ

δ ⋅⋅=1

21z1d

N

NUU (3.1)

On the other hand, for small loads, the current ripple in the inductor L1 is bigger than the currentcontinuously demanded by the load. This will lead to a discontinuous-conduction mode and the output

fp = 30 kHz 60 kHz 120 kHz

Uout

Uz2

up1

ωt

ud1δ

ωt

iL1

ωt ωt

i

up2

ωt

ud2δ

ωt

iL2

ωt

iLiL1

iL2

ud1δ

ud2δ

L1

L2N1 : N2

26 : 21

RDC1

RDC2 C

0 π/2 π 3π/2 0 π/2 π 3π/2

δUZ1

ic

iout

up1

up2

Uz1

0 π/2 π 3π/2 0 π/2 π 3π/2



voltage will be higher than would be calculated by (3.1). Moreover the circuit will loose its integralbehaviour [5]. In reality, the output voltage of the non controlled converter depends on the internalresistance and the load. This internal resistance consists of the resistances of the transformer as seenfrom the transformer’s secondary side and the resistance of the filter inductor. The internal resistanceof one converter is

Ω=Ω+Ω=+= 058,002,0038,0RRR 1L1cc1DC (3.2)

The total internal resistance RDC of the two converters in parallel is 29mΩ. The resulting voltage dropacross the converter is very low, therefore one can consider this converter as an ideal voltage source.

3.2 Control requirements of the battery

The charging principle of lead-acid batteries is based on current and voltage limitation as shown in thegraph below. Obviously, regulation of the current and voltage is necessary.

Fig. 3.2 : Relation between current and voltage during charging

The current of each DC/DC converter connected in parallel is controlled separately. For the firstconverter (Fig. 3.3), the control parameters are calculated by the pseudo-continuous model. Then, theparameters are applied to the second.

Fig. 3.3 : System to control represented by the first DC/DC converter with its load

3.2.1 Current control

From the electric circuit of Figure 3.3 follow the two formulas here below:

∫

−−= dtR2

U

C

2

b

bout1Lout

uiu (3.3)

out1L

11DC1L1d dt

dLR u

iiu ++⋅=δ (3.4)

Combining these equations and applying the Laplace transform gives:

CsR1

R2)s(IsL)s(IR)s(I)s(U

b

b1L1L1L1DC1L1d +

⋅+⋅+⋅=δ (3.5)

From (3.5) the transfer function can be derived:

I, U

t

Uc

IcBat

Constant charge curent Constant charge voltage

2,44V/element

2outi

Uz1 ud1δ

L1

2

C

2Rb

uout

Voltage source controlled by δiL1

δ1

RDC1

Ub

ic/2



1DCb

b1

2

1DC

1b

1DCb

1DC

b

1DCb1d

1Li

RR2

RCLs

R

LCR

RR2

Rs1

CsR1

RR2

1

)s(U

)s(I)s(G

+⋅⋅+

+⋅

+⋅+

+⋅

+==

δ(3.6)

One can find a resonant circuit where the damping depends on the load resistance. In our case thisresistance is Rb, the internal resistance of the battery. The used lead-acid battery has a nominal voltageUb of 180V and a low internal resistance Rb of about 1Ω. Numerical simulations with Simplorer

have shown that with our electric values (RDC1 = 58mΩ ; C = 110µF) the step response of the currentiL1 after an input voltage step ud1δ is rapid and not oscillating. So this system can be approximated by asimple RL circuit if the time constant of RbC is very low versus the time constant composed by L1,RDC1 and 2Rb. In this case the transfer function (3.6) can be approximated by

1Lsisi

sT1

1K)s(G

+⋅≅ (3.7)

The degree of our system to control is now reduced to one and has a dominant time constant TL1

calculated in (3.8), which depends on the internal resistance of the converter and the battery.

1DCb

11L

RR2

LT

+= (3.8)

The gain depends also on these two resistances

1DCbsi

RR2

1K

+= (3.9)

The dimensioning of the current controller GRi(s) is made in a classical manner. Since the degree ofthe system is one we chose a PI controller with the following transfer function:

ii

niRi

sT

sT1)s(G

+= (3.10)

With the time constant Tni of the current regulator we compensate the time constant of the system TL1.The integration time constant of the regulator is obtained by:

pEiiii TK2T = (3.11)

Here Ki is the total system gain resulting from the driver Kcmi and from the system Ksi :

sicmii KKK = (3.12)

The time constant TpEi, is the sum of all small time constants in the control loop including the timeconstant related to the PWM-Modulator, the sampling time constant of the controller and also the timeconstant of the measurement [6].In closed loop, this current control circuit has a transfer function which can be replaced by anequivalent time constant Tei.

pEiei T2T = (3.13)

3.2.2 Voltage control

The voltage regulator Gru(s) superposes the two current controllers. Its output value, limited to themaximum battery charging current IcBat, gives the two current references iL1c and iL2c (Fig. 3.4). Whenthe output voltage Uout reaches the value of Uc the current references will decrease slowly until itreaches the value of leakage current of the battery.The output voltage changes very slowly because the system to control Gsu(s) is a battery without anydynamical requirements. That is why the voltage regulator is an integrator with a large time constant.



3.2.3 The complete control circuit

Figure 3.4 shows the functional scheme of the closed loop control circuits. We consider only smallvariations around a stable operating point. Thus the constant battery voltage Ub is not shown.The input of the voltage regulator GRu(s) is the error between the voltage reference uoutc and the outputvoltage uout , and the output is the current reference divided into the two equal values of iL1c and iL2c.The two internal current regulators GRi1(s) and GRi2(s) work in parallel, and they control iL1 and iL2

respectively.

Fig. 3.4 Complete control circuit with voltage and current control

3.3 Measure of the output current step response

To verify the correct behaviour of the controlled system we apply on the reference a current step of2 A. The following measurement (Fig. 3.5) shows a response time of 700µs for the current iout.

Fig. 3.5 : Step response of the output current iout

3.4 Conclusions

The model for the current controller was correct and the calculated parameters can be used. Furtherthe output current and voltage ripple are very low. The use of this DC/DC converter topology satisfiesthe demands of high efficiency (η= 0.93) and low weight.

0 10.02.0 4.0 6.0 8.010.00

15.00

11.00

12.00

13.00

14.00

iout [A]

t [ms]

∆uoutc ∆uout∆iout

∆iL2

∆iL1

∆ud2δ

∆ud1δ

∆ucm2

∆ucm1

-

-

-

+

+

∆iL1c

∆iL2c

½

GRi1(s) Gcm1(s) Gsi1(s)

Gsi2(s)

Gsu(s)

Gcm2(s)GRi2(s)

GRu(s)



4 Realized battery charger prototype

Figure 4.1 shows the realized battery charger prototype, consisting of a three phase unity power factorAC/DC converter (PFC) and a dual isolated DC/DC switched mode converter. The control of eachconverter is made by easily programmable floating point DSP cards with fast A/D converters and afast link to a host PC in order to have online measurement and supervision possibilities. Thereferences for battery charge current and voltage can also be modified any time by potentiometers onthe front panel. On the DSP card, a large FPGA circuit is used, in which the modulation functions areimplemented [7].

Fig. 4.1 : Prototype of a three-phase unity power factor AC/DC converter (PFC )with dual DC/DC converter for a battery charger

The AC/DC converter draws a sinusoidal current in phase with the main voltage of 400V and theoutput of the DC/DC converter is fully controllable in current and voltage up to 28A and 280V. Theefficiency of the installation reaches η = 0,90.

References

1. J.W. Kolar, F.C. Zach: A Novel Three-Phase Tree-Switch Tree Level Unity Power Factor PWM Rectifier,Proceedings of the 28th Power Conference, Nürnberg, Germany, June 28-30. pp. 125-138 (1994)

2. J.W. Kolar, U. Drofenik, F.C. Zach, DC Link Voltage Balancing of a Three-Phase/Switch/Level PWM(VIENNA) Rectifier by Modified Hysteresis Input Current Control, Proceedings of the Power ConversonConference, pp. 443-465 (June 1995)

3. H. Bühler, Electronique de réglage et de commande, Traité d'Electricité, Presses polytechniques romandes,Lausanne 1987

4. SIMEC. Simplorer 4.0. http://www.simec.com

5. N. Mohan, T. M. Undeland, W.P.Robbins, Power Electronics : converters, applications, and design, JohnWiley & Sons, Inc. (1995)

6. H. Bühler, Réglage des systèmes d’électronique de puissance, Volume 1, Presses polytechniques romandes,Lausanne 1997

7. Sharc DSP for Power Electronic Applications: http://leiwww.epfl.ch/sharc

three-phase unity power factor

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