interleaved buck converter aplied to high power hid lamp supplying desig modeling and control

8/21/2019 Interleaved Buck Converter Aplied to High Power Hid Lamp Supplying Desig Modeling and Control

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INTERLEVE BUK ONVERTER LIE TO HIGH OWER HI LULYING: EIGN OELING N ONTROL

Andrea C Schiler, Dougla Pai,Alexandre Camo, Marco A Dalla Coa

schittler@ieeeorg, douglaspappis@gmailcom,alex3075318@gmailcom, marcodc@gedreufsmbr

J Maco Alono

marcos@uniovies

Federal niversity of Santa Maria - FSM Electrical Engineer Post-Graduation Program - PPGEE

Electronic Ballast Research Group - GEDRE

niversidad de Oviedo DEECS Tecnologa Electrnica

Campus de Viesques sn, Edificio 3, 3304Gijn, Spain Av Roraima, n 1000 97 105-900 Santa Maria, RS, Brazil

b As the output current levels of power converters

increases, interleaved topologies become widely used. A wellknown topology is the interleaved buck converter (IBC), whichpresents as main characteristic a low ripple output currentsource behavior. Due to HID lamp voltage source characteristicsand their acoustic resonance issue, it is necessary to drive themwith nearly constant current with a square-wave shape.Therefore, a buck-interleaved converter can be advantageous for supplying high power HID lamps. The goal of this paper is aproposal of an electronic ballast based on a two-cell buckinterleaved converter for high power HID lamps, with currentcontrol loop, voltage sensing and constant power. A DC modelased on averaged state-space technique is derived for theballast, as well as an AC model based on sma-signaldisturbances. The results are veried experimentally andthrough simulation in Matlab/Simulink and PSIM sowares.

x Electronic ballast, high power HID lamps,interleaved buck converter, modeling, state-space averagingtechnique.

NTRDUCTIN

The use of power converters is increasing in several areas,

such as electric cars, portable electronic devices and

electronic ballasts [] As the output current levels increase in

these converters, a configuration with parallel converters or

cells of a same converter can be applied []

Commonly applied from medium to high power levels,

current sharing among converter cells or among converters

enables losses reduction in magnetic cores and

semicondctos, once the cet levels e lwe 3]

Another characteristic is the output current ripple reduction,

which consequently lowers the output capacitor of the

converter

Regarding to that, an interleaved topology can be applied

to high power high-intensity discharge (HD) lamp supplying

These lamps present a voltage source characteristic [4],

which requires the ballast to present an output stage as a

current source Mainly, the applied ballast might present an

output current nearly constant, with nominal current ripple of

5% maximum, because of the acoustic resonance phenomena

This work was partially co-sponsored by the Brazilian andSpanish govements under research grants CAPES/DGU/5267,CEEE-D and PHB2010-0145-PC.

[5] Moreover, the parallel output capacitor has to be below a

maximum value to assure converter stability, as presented in[6], due to the lamp negative incremental impedance

t is important to highlight that HD lamp electronic ballast

manufacturers present products up to a maximum power of

only 400 W (eg Philips, OSRAM, TridonicATCO), although

electromagnetic ballasts present disadvantages as low

eiciency, audible noise, icker and reduction of the lamp

lifetime [7] that are emphasized at the high power range

The simple substitution of electromagnetic by electronic

bllasts llows for impleentti of intelligent featres as

self-tests and insertion of communication networks (DAL,

wireless, etc), which have been becoming essential for actual

lighting consumers market

For designing such ballast, a single-cell converter might

present some issues, as high current levels at the

semiconductors and magnetic cores, increasing conducting

and switching losses Also, a relatively increased size output

capacitor may be applied to reduce output current ripple

Considering the presented characteristics, a buckinterleaved converter becomes suitable to be applied for high

power HD lamps supplying, not only for the simple design but also for its inherent output current source characteristic

Besides, the ballast should present PFC (power factor

correction) and PC (power and/or current control) stages, as it

is shown in Fig 1 PFC stage design will not be covered by

this proposal, being assumed as a constant DC voltagesource

Focusing on the lamp current, Fig shows a typical

configuration for HD lamps supplying [7] t presents two

main stages: power andor current control, represented by the

constant current source; and inversion stage, applied to avoid the lamp early aging by electrophoresis [8] For the sake of

_ _

-

H

P C _

L_

al

_

p

_

Fig. 1. HID ballast characteristics block diagram

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simplification, the starter circuit has not been shown in the

figure

-

t

Fig. 2. HI lamp supplying configuration with current control and inverter

From a control point of view, ballast reactive elements have a dynamic behavior and together with the lamp dynamics can bring the system to instability [8] Therefore, aclosed-loop system is required and based on an interleaved

topology a high power HD lamp electronic ballast can be proposed

The main goal of this paper is to present a two-cell BC

operating in continuous conduction mode (CCM) applied to

high power HD lamps supplying The converter operates

with two current loops, a voltage sensing and constant power

Converter design, modeling will be presented and confirmed

by experimental results and the control loop will be verified

through simulation

Sectin resents the BC details f oeration nd

modeling; section introduces the discharge lamp model

and frequency analysis Section V contains some

experimental results n section V, topics conceing the final

version of this paper are described Finally, some conclusions

are presented in section V

WCELL NTERLEAVED BU

A two-cell buck-interleaved converter is shown in Fig 3The time intervals, AC model and transfer functions are derived at the follow subsections

Fig. 3. Two-cell buck-iterleaved

, ,

A. Time intervals

f 7

As started in [] , for the output current ripple

minimization, the gate signals delay angle 8 can be

calculated as shown in (1)

360=

nc Where: n number of cells

(1)

The time intervals are divided as they can be seen in Fig

4 There, each time interval can be observed, as so the

inductor currents (i e i2) and gate signals ( for S and 2

for S2)' n Fig 5 the equivalent circuits for each time interval

are shown

:

I ;

<h

I

V

T1 � T �

D� T �

Ts

Fig. 4. Inductors L1 and L2 currents theoretical waveforms; MSFETs S 1and S2 gate signals

• Time interval n this interval (Fig 5 (a)) the MOSFETs S e S are

tued on t can be observed that the load current is shared in

two circuits: SL-load e S-L-load, charging the two

inductors The diodes D and D are reversed biased

• Time interval 2Here (Fig 5 (b)), the switch S is still on and switch S is

tued off The diode D is directly biased and enables the

discharge of the energy stored at inductor L

•Time interval 3This interval is equal to interval , as it can be observed

based on ig 4 The switch is turned on and the switch S

is still on

'"D

J)

(a) (b) Fig. 5. Time intervals for the two-cell buck-interleaved: (a) T and T3; (b) T2; (c) T4

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• Time interval 4 At this interval (ig 5 (c)) the switch S is tued o and

the switch S remains turned on The diode D is directly

polarized and enables the discharge of the energy stored atinductor

B. AC model and Transfer function

Considering a system with the state matrix as x and theinput matrix as u, the statespace representation is given by() [14]

x=A+Buy=C +Eu

Where: A dynamic matrix;

B input matrix;

C output matrix;

E direct transfer matrix

()

Based on [9], the small-signal AC model can be derived

from the state-space DC model and the steady state

equilibrium point (X) The DC model can be calculated based

on the matrices derived from the time intervals of the

converter, in the way shown in (3) As the two-cell buck

interleaved presents four time intervals, the DC model will

present the sum of four terms, as it can be seen in (3)

2. 2 2

A=I Tk A k B =I Tk ·B k C=I Tk,C k (3)

kl kl kl

Where: A" B" Ck state-space matrices that identify each time interval operation;

Tk respective time for each stage of operation

The steady state operation point is calculated as (4) [9]

(4)

Where: input vector

The AC model is calculated based on the steady state

equilibrium point and on the addition of small disturbances

(small-signal) at the system input vector Equation (5) gives

the relationship between DC model, equilibrium vector, input

vector and AC model

A p=A

B � [B (� ( - ) mA ')X+ (� ( - ) 'H B ') u] (5)

C p =C

Where: Ap Bp Cp small-signal derived state-space

matrices

The two-cell buck-interleaved AC model including

inductor conducting resistance (RL' switches conducting

resistance (Rdsol and diodes drop voltage is presented in

(6) Converter modeling is based on state-space matrix

[i Ll i L2 v oVand input matrix [ vdf1 vdf2V

( RL + Rdso Dc) 11

01

( RL + Rdso Dc) 1A - 0 p 1 2

1 1 1Co Co Co (6)

1 11 1 0B - 1 1 p

2 20 0 0

The transfer function (T) can be obtained from (7) [9]

G ( s )=C p .s I-A pr1 .Bp (7)

A general T for the two-cell buck-interleaved converter

of inductor current by duty-cycle is shown in (8) The

following terms are compressed in the T for a better

visualization:

• a1= -Rdso ILl + Y - df;• a2 = -RdsoIL2 + Y - df;• = RL + Rdso Dc;• eq = parallel assocatn of the converter

interleaved inductors

C. Converter design

The converter design is based on a 400 W lamp, which the

model will be presented in section A

or a buck converter, the duty-cycle can be calculated as

shown in (9)

(9)

The inductors current ripple can be calculated as being

twice the required output current ripple Regarding to that,

the inductors can be calculated as shown in (10) Note that

the inductors and the respective current ripples are considered

equal

(8)

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. - ) = m D1

!i L · c ·

Where: T switching period;

iL inductor current ripple

STEM NALSIS

(10)

The discharge lamps model has been consolidated by

many authors [8], [10], [11], [1] n [8] the lamp is included

in the TF based on the principle that the converter can be

modeled as a constant current source dependent on the lamp

voltage and duty-cycle, once it is operating at the

discontinuous conduction mode (DCM)

n this paper, another approach is made, based on lamp

and ballast dynamics isolation, considering the control loop

faster than any load variation t means that each dynamic can

be considered independent from the otherA. am Mode!

As presented in [10] , the discharge lamps present a

different response at steady-state and at a small-signal

disturbance The steady-state model can be approximated by

a resistance and the dynamic model is presented at (11)

(s - z)ZL p( S ) = k s + p

(11)

he lamp dynamic mode proposed in [10] has beenadapted for simulation by [11] and it is based on theequivalent circuit shown in Fig 6

p ModeFig. 6. im

ti

n

; ;ei

d p

t

e

d fr�

i

]

n this paper, the lamp model was obtained by analyzing the lamp response against an input voltage step This methodwas proposed in [8] Lamp response and model obtained from

that are shown in Fig 7 and the derived parameters are shownn he be I.

TABL IAM AAT (400W)

arameter Value 13.531 Qz 3.95 1 krad/s

p

15.36 krad/s

B. Ballast secications

The two-cell buck-interleaved converter operating in

continuous conduction mode (CCM) was designed with a

f 7

switching frequency of 40 kHz The Bode diagram that

characterizes the inductor cuent over the duty-cycle (TF

presented in (8» is shown in Fig 8

Even though the converter presents stability without acompensator, a control loop should be inserted to prevent

changes at the load in case of any variation

By Nyquist theorem, a system is enabled to reproducesignals until half of the sampling frequency Commonly, the

crossover frequency ) is chosen at a lower decade of the

switching frequency ) n this case, is chosen to be close

to the lamp model pole There are two reasons for this: first,

the analyzed converter is a well-known plant and second, for

the sake of dynamics, the lamp pole is not as significant as

the right-plane zero

2

4.8

6

�4

>

38

6

�

3.4 =

-

:

_

_

0 0.2 03 04 6 7 8 9

Fig. 7. Lamp response and model obtained

ode agra

Inf, P 946 de a 783e4 radsec3

�" .C ·1

3

" -5€

9

'

1

reuey ad/sec)

Fig. 8. Inductor current by dutycycle frequency response

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Control oo

1) Design

The compensator must present steady-state null error andmaintain the phase margin of the system at least 60° For that, the proportional-integral (PI) compensator can be applied andits TF is shown in (1)

(1)

The two-cell buck-interleaved has been simulated using

two current control loops, one for each interleaved cell A

voltage sensing loop was added to generate the lamp current

reference, so the lamp power is maintained constant

The block diagram that illustrates the current/power

control loop of the complete system is presented in Fig 9

(sensors and modulators gains are considered unitary) and the blocks description is shown as follows:

• Ci(s) - Compensator TF for current loop 1;• Ci2(s) - Compensator TF for current loop 1 ;• G() - System TF, relation between inductor

L current and duty-cycle;• G2() - System TF, relation between inductor

L2 current and duty-cycle;• P - Lamp power

Based on the system evaluation, values found for the PI

compensator coeicients are K 06166 and 1396

krad/s

The Bode diagram of the open loop transfer functionincluding the PI controller is presented in Fig 10

Fig. 9. Closed loop block diagram

2) Simulation Results

PSIM soware was used to simulate the circuit withcurrent loop and the lamp model The c design values areshown at table II The simulated circuit is shown in Fig 11,including the lamp simulation model extracted from [8] andadapted to PSIM

Boe Diagram

G = In. Pm = 110 deg (at 14e+04 ad/sec)6

4

20

i 00

�-20

-0

30

i OLTF

60

� 9

20

10'

10

Fequency (ad/sec)

Fig. 10. Frequency response of the open loop transfer function

TABLE IIIMUATION AN OTOT AAMTE V

Y 400Y() OOYP () 400W

C 220 nF 7.5

R 5Q

;

40kHz:hS SPA08N80C3

HFA5PB60

Figure 1 presents the results for lamp current (upside

waveform); inductors currents (middle waveforms) and the

input voltage in the downside graphic with a 50V step at 10

ms In Fig 13 it can be seen that the lamp power is

v maintained constant ater the input voltage step

IV XPERIMENAL ESULTS

A 400W two-cell c prototype was built with

components shown in table II Figure 14 shows the gate

signals for the switches used on the converter In Fig 15 both

inductors currents are presented and a comparison between an

inductor current and the lamp current is shown in Fig 16 It

can be seen the ripple reduction for the inductor current to the total (lamp) current Finally Fig 17 illustrates the input

current (which is, for the c the sum of both switches

currents) and the voltage stress in one switch Converter

measured overall efficiency is 985%

It can be observed in Fig 17 a certain dierence of current

levels between each cell, consequently on the inductors That

can occur due to inherent non-linearities and components

tolerances, being difficult to prevent Such unbalance can

lead to instability and/or chokes saturation Therefore, it can

be concluded that it required current regulation of each cell,

rather than only controlling the output current

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S,

0R"v

v_

L

c.

Gain:

Lamp simulatonmodel

f 7

2

P

Fig. . Circuit simulation model including lamp equivalent circuit

Fig. 12. Lamp and inductors current�; input voltage with a 50V step at 10 ms

Tek E,c Acion 21.0MHz· Filt d Rurdos

100V 100V ElIo)'

380 f480V 3733kHZ

Fig. 14. Gate signals for two-cells!BC at open loop operation (OV/div;

O/div)ePVi 20MH F1. d Rudo

. . . . . . . . . . . . . . . . . . . - .

'" ,! I ,! I ' : I ,! I ! I

-

. . . . . . . . . . . . . . . . -

tOA El tOA EI2o.o)' 1860 f500A <10H

Fig. 16. Lamp (up waveform) and inductor current (down waveform) (div;20/div)

oonTia)

Fig. 13. Lamp power -50 V step at input voltage at 10 ms

TekV

. . . . . . . . . . . . . .

. . . . . . . . . . . . _

. . . . . . . . . . . . . . . -

[

1.00

A tO A E0O=) :4

f-224 A

230MH Fil d do

<10H

Fig. 15. Inductors currents for two-cells !BC at open loop operation (div;

20s/div)TekV .50MH Fi1 d Rdo

200A El 200V E10.0) 2620 f800V <10H

Fig. 17. Input current (upside) and r voltage stress for two-cells!BC openloop operation (2div; 200V/div; Os/div)

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v. NCLUSIN

This pape pesented an electonic ballast fo supplying

high powe HD lamps based upon a two-cell CCM buck

inteleaved convete fo cuent/powe contol nvesionstage has been implemented via odinay full-bidge and a

PFC stage is assumed

t can be concluded that the inteleaved buck convete is

an excellent option fo designing an electonic ballast due to

its inheent output low ipple cuent souce as well as its

suitability fo high powe ballast applications Moe

impotantly, it has to be highlighted that only electomagnetic

ballasts ae cuently available on the maket fo this ange of

lamp powe

Moeove, such convete pesents the advantage of being

exible in tems of powe level, as the numbe of cells can be

inceased fo a highe lamp powe, keeping the same

functionality Besides, inteleaved topologies can bing

advantages as smalle size, in compaison with a single-cell

convete fo the same powe and high eiciency, 985% in

the pesented convete

The ballast has been analyzed fom a contol point of

view Based upon the aveage state-space technique, DC and

AC models fo the two-cell inteleaved buck convete can be

obtained consideing most of the impotant paasitic

elements

This guaantees theoy and pactical match, impoving

eliability of the feedback contol loop Fo obtaining the

system model, HD lamp has been consideed as a esistance,

once its impedance chaacteistics ae compensated by thecontol loop

Feedback contol loop has been also pesented in the pape

Fo ovecoming the HD lamp negative incemental

impedance, two cuent loops have been successfully

included, one fo each inducto cuent This avoids the

complexity of adding the lamp small-signal AC model to the

convete model Lamp voltage sensing loop has been added

fo the lamp powe setting

n summay, it can be concluded that this pape pesented

a complete poposal fo a high powe HD lamps electonic

ballast design, with its most impotant pats being descibed

in detail

NCS

[1] Shud, M A, Khaaz, A, Ashu, A S, Shate, M,

Benyoussef, "A study of modeling and simulation fo

inteleaved buck convete 1st Powe Electonic & Dive

Systems Technologies Confeence, PEDSTC 010

[] Mao, H, Yao, L, Wang, C, Bataseh, "Analysis of

inducto cuent shaing in nonisolated and isolated

mutiphase DC-DC convetes EEE Tansactions on

ndustial Electonics, v 54, no 6, pp 3379-3388, Decembe,

007

[3] Wang, J B, Chuang, S "A study of the inteleaved

buck deived convetes EEE nteational Confeence on

ndustial Technology, CT 006

[4] Made, D Ho, P "A dynamic model fo the electicalchaacteistics of uoescent lamps EEE ndusty

Applications Society Annual Meeting, AS 199

[5] Dalla Costa, M A, Alonso, J M, Gaca, J, Cadesn,

J, Rico-Secades, M "Acoustic esonance chaactetization of

low-wattage metal-halide lamps unde low-fequency squae

wavefom opeation EEE Tansactions on Powe

Electonics, v , n 3, pp 7 35743, May 007

[6] Machesan, T B, Cevi, M, Kisten, A L, Campos, A,

Pado, R N "Analysis of the output capacito and lamp

voltage invesion fo the bidiectional fyback convete

EEE ndusty Applications Society, AS 008[7 ] Shen, M, Qian, Z Peng, F Z "Design of a two-stage

low-fequency squae-wave electonic ballast fo HD lamps EEE Tansactions on ndusty Applications, v 39, n

, pp 4-430, Mach/Apil, 003

[8] Alonso, J M, Dalla Costa, M A, Cadesn, J, Matn

Ramos, J A, Gaca-Gaca, J "Small-signal modeling of

dischage lamps though step esponse and its application to

low-fequency squae-wavefom electonic ballasts EEE

Tansactions on Powe Electonics, v , n 3, pp 744-75,

May 007

9] Eickson, R W, Maksimovic, D "Fundamentals of

Powe Electonics Book, nd edition, 001

[10] Deng, E, Cuk, S "Negative incemental impedance and

stability of fuoescent lamps EEE Applied Powe Electonics Confeence and Exposition, AEC 1997

Ben-Yaakov, S, Shvatsas, M, Gozman, S "Statics and

dynamics of uoescent lamps opeating at high fequency:

Modeling and simulation EEE Tansactions on ndusty

Applications, v 38, n 6, pp 1486-149,

Novembe/Decembe, 00

[11] Glozman, S, Ben-Yaakov, S "Dynamic inteaction

analysis of HF ballasts and uoescent lamps based on

envelope simulation EEE Tansactions on ndusty

Applications, v 37 , n 5, pp 153 1-1536, Septembe/Octobe,

001

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interleaved buck converter aplied to high power hid lamp supplying desig modeling and control

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