Symmetrical Power Supply for 42 V Automotive Applications

giantsneckspiffyElectronics - Devices

Oct 13, 2013 (3 years and 9 months ago)

70 views

FACTA UNIVERSITATIS (NI
?
S)
SER.:ELEC.ENERG.vol.17,December 2004,365-376
Symmetrical Power Supply for 42 V Automotive
Applications
Roberto Giral,Javier Calvente,Ramon Leyva
Abdelali El Aroudi,Goce Arsov,and Luis Mart´nez-Salamero
Abstract:The Positive Channel Two Input Two Output (PCTITO) converter is a third
order MIMODC-to-DCunidirectional and non-isolated switching converter that is de-
rived fromthe non-inverting buck-boost converter.Negative and Dual Channel TITO
converters are also presented.In steady state one of the PCTITO outputs is positive
while the other is negative.Although the outputs could be regulated to provide dif-
ferent absolute values,an interesting application of the new converters is to provide
symmetrical outputs (i.e.,

15 V) to supply balanced loads.Since the absolute value
of the outputs could be greater or smaller than the input voltage,the PCTITO con-
verter will be suitable for present 14 V (from 9 to 16 V) or for future 42 V (from
30 to 50 V) automotive voltage distribution buses.To regulate the outputs,two in-
phase equal-switching frequency PWM-based multivariable control loops have been
designed.The closed-loop systemmust provide lowaudiosusceptibility and good line
and load regulation at both outputs.In addition,the common mode voltage between
the two outputs that could appear in unbalanced load operation has to be minimized.
With these general guidelines,several control parameter adjustments have been con-
sidered,validated using an averaged model of the system,and tested by simulation.
Keywords:MIMO,PWMdc-dc switching converter,symmetrical output regulator,
automotive 42V PowerNet.
Manuscript received June 22,2004.An earlier version of this paper was presented at the Third
Triennial International Conference on Aplied Automatic Systems,AAS’03,September.18-22,3003,
Ohrid,Republic of Macedonia.
R.Giral,J.Calvente,R.Leyva,A.El Aroudi,and L.Mart?nez-Salamero are with Universi-
tat Rovira i Virgili,Escola T?ecnica Superior d’Enginyeria,Departament d’Enginyeria Electr?onica,
El?ectrica i Autom?atica,Campus Sescelades,Av.Pa¤?sos Catalans 26,43007 Tarragona,Spain;(e-
mail:rgiral@etse.urv.es).G.Arsov are with SS Cyril and Methodius University,Faculty of
Electrical Engineering,Institute of Electronics,P.O.Box 574,1000 Skopje,Republic of Macedonia
(e-mail:g.arsov@ieee.org).
365
366 R.Giraletal.:
1 Introduction
The automotive industry is experiencing an electronic revolution.To provide ef-
ciently enough electric power to supply the increasing number of electric and
electronic loads that cars are going to incorporate,car manufacturers are consid-
ering to substitute the actual 14 V alternator-12 V battery set.In the short term,
one of the solutions the automotive industry is going to adopt considers to raise the
DC nominal voltage of the system (42 V PowerNet).According to ISO/CD 21848
draft [1] discussed in SAE2002 Congress,the supply voltage range for 42 Vsystem
devices will be very wide [30 V,48 V].
In this context,as it happens in current vehicles,there will be loads that require
to be supplied by symmetrical voltages like

15 V.There are a large number of so-
lutions,even commercially available,that could provide multiple outputs and that
could be congured for symmetrical voltages.Some solutions use several stages
[2],while others use two separate (isolated or non-isolated) regulators.Other so-
lutions are dual channel and require two unregulated symmetrical input voltages
[3].
Fig.1.The Positive Channel Two Input Two Output (PCTITO) DC-DC
switching converter.
When the loads are also symmetrical,like in the power supply of some class
AB or class D audio ampliers [4],the Positive Channel Two Input Two Output
(PCTITO) unidirectional regulator of Fig.1 could be an interesting solution for
automotive 42 V applications in which isolation among input and outputs is not
required.The PCTITO regulator is a third order MIMO (Multiple Input Multiple
Output) non-isolated dc-dc switching converter that can be derived form a non-
inverting buck-boost converter [5].In fact,instead of connecting the ground node
to the middle output point (Mnode),if the ground is connected to the bottom (B)
node,and switches are simultaneously activated,the converter structure is identical
to the non-inverting buck-boost.On the other hand,if the ground node is connected
to the top node (T) instead of node M,switch Bis superuous and the systemstruc-
SymmetricalPowerSupplyfor42VAutomotiveApplications 367
ture becomes a buck-boost cell.
Fig.2.The Dual Channel (DCTITO) converter.
Fig.2 shows the Dual Channel TITO (DCTITO),a third order converter that
presents a structure very similar to the ve order dual channel resonant buck-boost
converter presented in [3] being,in fact,a dual channel buck-boost converter.If the
positive input of the DCTITOis made zero,the Negative Channel NCTITOwill be
obtained.In al the TITO converters (DC,PC and NC) there are Two control Inputs
(S
A
,S
B
) and Two voltage Outputs (v
P
,v
N
).
The application of different control laws to the two MOSFET of the TITO
structures will permit,in principle,to regulate independently the converter output
voltages,one positive and one negative,to obtain absolute values greater (step-up)
or smaller (step-down) than the input (or inputs).
In Section 2,the PCTITO circuit is analyzed using an averaged model of the
switches (MOSFETs and diodes).Ageneral control strategy is proposed in Section
3,where several adjustment procedures of the control coefcients are studied by
means of simulations.Finally,some conclusions and proposals for future works
are presented.
2 Time-Averaged Circuit in Open Loop
Substituting the converter MOSFETs and diodes by their time-averaged models
in the form of controlled sources permits to obtain the time-averaged equivalent
circuit model [6] of the PCTITO converter shown in Fig.3,where d
A
and d
B
are
the duty cycles of S
A
and S
B
,respectively.The current i and the voltages v
P
and v
N
are the time-averaged state variables of the circuit.Note that v
N
has been dened
to be positive.
Considering ideal components (without losses,ideal switches),the averaged
368 R.Giraletal.:
system can be described by the following equations in matrix form:
x

A x

Bv
g

(1)
where
x


i v
P
v
N

T

(2)
and
A



0
d
B

1
L
d
A

1
L
1

d
B
C
P

1
R
P
C
P
0
1

d
A
C
P
0

1
R
N
C
N



B



d
A
L
00


(3)
Fig.3.Time-averaged equivalent circuit model of the PCTITO con-
verter.
Let us assume that,around equilibrium,the averaged systemvariables are con-
stituted of a steady-state part plus a small-signal component in the form
i

I


i v
P

V
P

v
P
;v
N

V
N

v
N
v
g

V
g

v
g
;d
A

D
A


d
A
;d
B

D
B


d
B

(4)
where d
A
and d
B
are the two control inputs.The steady-state operating point of the
state variables in open loop is
I

V
g
D
A

1

D
B

2
R
P


1

D
A

2
R
N

V
P


1

D
B

R
P
I

V
N


1

D
A

R
N
I

(5)
Since 0

D
A

1 and 0

D
B

1,all three steady-state values are positive,
and equal (symmetrical) output voltages can be provided.Considering equal loads
(R
P
=R
N
=R),the expressions of the steady-state output voltages become indepen-
dent of load R.In this case,controlling both switches with the same duty-cycle
(D
A
=D
B
=D) results in equal steady-state output voltages.
V
P

V
N

D

1

D

V
g
2

(6)
SymmetricalPowerSupplyfor42VAutomotiveApplications 369
In symmetrical operation,the sum of V
P
and V
N
of (6) yields the same result
of the single-output non-inverting buck-boost of ([5]) as expected.In the general
case,since no losses have been considered,combining (5) and (7) it can be seen
that the steady-state input power is equal to the power delivered to the resistive
loads.
P
in

V
g
D
A
I

P
out

V
2
P
R
P

V
2
N
R
N

(7)
Dening the enlarged small signal input vector of (8) the time-averaged system
can be linearized around its equilibrium point as in (9)-(12).
u


v
g

d
A

d
B

T

(8)
x

A
L
x

B
L
u

(9)
Matrices A
L
and B
L
are
A
L



0
D
B

1
L
D
A

1
L
1

D
B
C
P

1
R
P
C
P
0
1

D
A
C
P
0

1
R
N
C
N


(10)
B
L



D
A
L
B
12
V
g
L
B
13
V
g
L
0 0 B
23
V
g
C
P
0 B
32
V
g
C
N
0


(11)
with the following dimensionless parameters
B
12


1

D
B

2
R
P


1

D
A

R
N

1

D
B

2
R
P


1

D
A

2
R
N
B
13


1

D
B

D
A
R
P

1

D
B

2
R
P


1

D
A

2
R
N
B
23

B
32


D
A

1

D
B

2
R
P


1

D
A

2
R
N

(12)
Previous expressions could be easily simplied assuming equal loads R
P
=R
N
=R.
Further reasonable simplication considers equal output capacitors (C
P
=C
N
=C).
370 R.Giraletal.:
3 Control Strategies
From the small signal equations at the end of previous section,it is possible to ob-
tain different transfer functions in the Laplace domain that could be used to design
small signal control strategies.
The intended PCTITO application is to provide an automotive symmetrical
power supply.EMC automotive directives make desirable that both switches op-
erate at the same switching frequency,therefore a pulse width modulation (PWM)
based control scheme is preferred.However sliding mode or other hysteretic based
schemes are also easily applicable.
Considering the wide margin and possible noise at the input voltage (42 V
PowerNet) of the converter,line regulation and audiosusceptibility become impor-
tant aspects to be taken into account in the control design which,in principle,will
have a common voltage reference for both outputs.In addition,although the nomi-
nal operation considers balanced operation (symmetrical output voltages and equal
loads),the converter must be able to operate to some extent in unbalanced load
modes,therefore load regulation at both outputs will have to be taken into ac-
count.Finally,related with all the previous subjects,cross regulation effects are
also important.Probably,for supplying high quality symmetrical output voltages,
the common mode voltage of the outputs has to be kept as small as possible in the
case of input voltage and/or load changes.
A general view of the system,that includes the PCTITO converter and the
block diagram of a multivariable PWMcontrol scheme,is depicted in Fig 4.The
control circuit will provide two pulse width modulated digital control signals S
A
and S
B
.The right bottom box in the gure corresponds to the two required PWM
modulators.The gure shows a simplied version of them that omits RS ip-ops
normally used to prevent multiple commutations in one cycle.Aleading-edge saw-
tooth signal with the desired amplitude and frequency is used to generate both con-
trol signals by comparing it with the corresponding control law signals.The use of
a common sawtooth signal will cause simultaneous switch-on of both MOSFETS.
Zero and unity duty cycles are not allowed,they are avoided by limiting the signals
entering the PWMcomparison blocks between 5%and 95%of the sawtooth signal
amplitude (usually normalized to unity).
The multivariable control strategies that have been considered are symmetrical
in structure.Since buck-boost structures have been shown to exhibit right half-
plane zeroes,it is expected that the inclusion of the inductor current in the control
law will improve the stability margins.
The duty cycles of the switches in the open loop system description of (1)-(3)
have to be substituted by the general expressions for d
A
and d
B
shown in (13).
SymmetricalPowerSupplyfor42VAutomotiveApplications 371
Fig.4.PWMmultivariable control scheme for the PCTITO.
d
A

K
IA

i

K
VAP

PI
P

K
VAN

PI
N
d
B

K
IB

i

K
VBP

PI
P

K
VBN

PI
N

(13)
where PI
P
and PI
N
are the outputs of two proportional-integral blocks of the Pos-
itive and Negative error voltages with respect to a common reference V
R
,respec-
tively.K
IA
and K
IB
are respectively the coefcients of the inductor current feedback
for switches A and B (peak current mode control).Accordingly,K
VAP
and K
VBP
are the A and B coefcients for the PI
P
voltage term,and K
VAN
and K
VBN
the cor-
responding coefcients for the PI
N
contribution.Fig.4 shows that two PI blocks
with time constants T
VP
and T
VN
have been considered.
PI
P

die
P

ie
P
T
VP
PI
N

die
N

ie
N
T
VP
die
P

v
R

v
P
die
N

v
R

v
N

(14)
Since ie
P
and ie
N
in (14) are the integrals of the corresponding error voltages
die
P
and die
N
,the dimension of the closed-loop system has been enlarged up to
ve.In this case ie
P
and ie
N
are two additional state variables that have to be added
to the previous ones:i,v
P
and v
N
.The closed-loop state variable vector is (15).
After linearizing the system,the A
L
and B
L
matrices of the closed loop system
372 R.Giraletal.:
description in the form of (9) could be obtained again but they are too large to be
included here.
x


i v
P
v
N
ie
P
ie
N

T

(15)
It has to be pointed out that,in order to get information about the closed-
loop system response to load perturbations,the equations of the output voltage
derivatives have been modied to include two small signal current sources.Each
one of the newinputs is connected in parallel with the corresponding resistive load.
The u vector for the closed loop system is (16).Also the open loop duty cycles
are no more inputs to the system and should be replaced by the voltage reference
which has been assumed to be the same for both output voltages (v
RP
= v
RN
= v
R
=
V
R

v
R
)
u


v
g

i
OP

i
ON
v
R

T

(16)
The steady-state closed loop equilibrium point for the converter variables will
be
V
P

V
N

V
R
I


R
P

R
N

V
R

R
P
V
g
R
P
R
N

V
R
V
g

(17)
There are eight control coefcients and the integrals of the error voltages in
closed-loop depend on them in a complex form,therefore the corresponding ex-
pressions have been omitted.Instead,it is more useful to include the steady-state
values for the duty cycles,D
A
and D
B
,of both switches (18).Both duty cycles
are equal if the loads are balanced.For unbalanced loads,although D
A
is always
between zero and one,D
B
could become negative for certain values of the voltage
reference smaller than the input voltage if R
P
is also smaller than R
N
.In practice,
this will imply that the control for S
B
could be saturated and that,depending on
the mentioned parameters,the system with unbalanced loads could not always be
regulated as desired.This also suggests that a worst case for checking the effect of
load perturbations could be found for R
N
larger than R
P
D
A


R
P

R
N

V
R

R
P

R
N

V
R

R
P
V
g
D
B


R
P

R
N

V
R


R
P

R
N

V
g

R
P

R
N

V
R

R
P
V
g

(18)
SymmetricalPowerSupplyfor42VAutomotiveApplications 373
3.1 Design example
In order to verify the theoretical analysis,an example with several control possibil-
ities has been designed.The nominal converter parameters have been determined
as follows:
An input voltage of V
g
=42 V accordingly to the PowerNet specications.Ar-
bitrarily,an output voltage reference of V
R
=15 V has been xed.The nominal
output power will be 150 W,which implies an average input current of about 3.6
A and,in balanced load operation,R
P
=R
N
=3 Ω.Steady-state duty-cycles (18)
are about 41.7%.With a switching frequency of 50 kHz (T=20 ms),L

40 mH
and considering simultaneous turn-on of the MOSFETS,the inductor peak-to-peak
current ripple will be 8.75 A over a mean value (17) of about 8.6 A.Since the
peak-to-peak ripple is smaller than 200% of the mean value,the inductor continu-
ous conduction mode operation (CCM) is ensured.Taking C
P
=C
N

500mF,the
voltage ripple will be about 83 mV in each capacitor (166 mV over the 30 V sum
of V
P
and V
N
,0.55%).
Once the plant parameters have been chosen,we have to determine the values
of the control coefcients.First,assuming nominal operation,we can consider
that the contribution of the voltage terms in the control loop is much slower than
the inductor current contribution.We will choose the K
IA
and K
IB
coefcients to
ensure that the slope of the current contribution to the control signal during the
off MOSFET conduction subinterval (m
2
) is approximately equal to the slope of
the sawtooth signal m
a
(compensating ramp criteria to provide deadbeat control
behaviour and to avoid subharmonics,see chapter 12 of [5].In our case,the slope
of the compensating ramp is m
a
=50 V/ms and K
IA
= K
IB
= 80 mV/A,which gives
a slope of about 60 V/ms for the current contribution (maximum current slope
2

V
R
/L;L=40 mH).Higher values of V
R
could require smaller values for the K
I
terms.It is recommended that 0

5

m
2

m
a

m
2
.
As an intuitive approach to adjust the voltage term coefcients,we have ini-
tially considered several assumptions that provide symmetrical expressions of the
control laws.Namely,PI time-constants have been considered to be equal (T
VP
= T
VN
= T
V
).The proportional coefcients of the direct terms have also been
assumed to be equal (K
VAP
= K
VBN
= K
V
),while the proportional coefcients cor-
responding to the crossed terms have been made zero (K
VAN
= K
VBP
= 0).From
the characteristic polynomial of the system,it can be shown that

0

058

K
V

15

603.Aset of root loci taking K
V
as a family parameter,K
V

(0.5,1,1.5,2),
and varying T
V
continuously between 100 ms and 500 ms shows that all the system
poles could be made real and negative for K
V

1.5.Taking K
V
= 1.5 and T
V
=150
ms,the two dominant poles are smaller than z =

1/T
V

corner f requency

-6.7
374 R.Giraletal.:
krad/s.For a nal value of T
V
=220 ms and K
V
=1,the dominant poles are still
real-negative (corner frequency of about -7.2 krad/s).With the obtained set of pa-
rameters,several PSIMsimulations have been carried out.
Fig.5 shows the simulated waveforms of the output voltages v
P
and -v
N
of
the regulator.The (a) arrows point out the small overshoots that appear at start-up
fromzero initial conditions for the nominal 42 Vinput,3 Ωbalanced load case.The
reference voltage raises from 0 to 15 V in 1 ms.At point (b) there is a step change
in the input voltage that goes from 42 V to 30 V.A +1 ampere step perturbation
in the positive output is applied at t=5 ms (c).Finally,from 7 ms to 7.5 ms,the
reference voltage rises from15 V to 18 V (d).
Fig.5.Simulated output voltages of the regulator.(a) start-up for
nominal conditions.(b) input voltage step change from 42 V to
30 V.(c) unbalanced load change:+1 A step at i
OP
(Fig.4).(d)
reference change from15 V to 18 V.
Fig.6 shows the ripple amplitude for different operating points.In the 2 to 3
ms interval the ripples are in agreement with the expected 83 mVpp in each output
for nominal operation.A detailed exploration of the interval (not shown) reveals
that both output ripple waveforms are in phase and exhibit a peak-to-peak ripple of
83.4 mV.In the interval 3 ms-5 ms,the step change in the input voltage from 42
V to 30 V at 3 ms causes an undershoot of about 150 mV in both v
P
and v
N
.The
duration of the transient is about 600 ms,which is consistent with the dominant
poles (

4 times the time constant).The ripple amplitude in steady state is about
100 mV.The duration of the transients caused by the +1 A step change at 5 ms
(c) is slightly shorter than the corresponding duration at (b).The main effect of
the change is that the load becomes unbalanced and this causes the increase of the
common mode voltage as it can be seen in Fig.7.The unbalance in the loads
breaks the symmetry observed in the transients.
SymmetricalPowerSupplyfor42VAutomotiveApplications 375
Fig.6.Detail of the simulated output wave-
forms of Fig.5 showing ripples.
Fig.7.Common mode voltage between positive
and negative outputs corresponding to Figs.5
and 6.
Fig.8.Detail of the simulated output wave-
forms for K
VAP
=K
VBN
=3,K
VAN
=K
VBP
=

1.
Fig.9.Common mode voltage between positive
and negative outputs corresponding to Fig.8.
Other parameter adjustments are possible.Considering again symmetrical co-
efcients,Figs.8 and 9 show the results corresponding to simulations in which the
K
V
parameters have been adjusted to K
VAP
=K
VBN
=3,K
VAN
=K
VBP

1.All the
results have been slightly improved with these coefcients.
4 Conclusions and Future Works
The PCTITO is a two-input two-output DC-DC switching converter that has been
controlled to provide two symmetrical outputs from a positive input voltage in the
42 V PowerNet automotive standard range (30 - 50 V).Although the main results
have been obtained by means of computer simulations,some theoretical analyses
have been performed.The system has been modelled in open loop.Steady-state
expressions for the state variables and a small signal time-domain averaged model
have been presented.A general full state feedback control strategy yields a system
376 R.Giraletal.:
with symmetrical output voltages with excellent line and load regulation.Good
audiosusceptibility and acceptable response to load changes are also obtained for
two different sets of control coefcients.With balanced loads,the common mode
voltage is completely eliminated and kept very small for unbalanced loads.
Future studies will address some theoretical aspects like the justication of the
control parameters adjustment.Experimental verication will be also carried out.
Acknowledgments
This work was supported by the Spanish Ministerio de Ciencia y Tecnologa under
Grant TIC2000-1019-C02-02.
References
[1] W.Bremer,Standardization of the 42V PowerNet,(Chairman-ISO
TC22/SC3/WG14).In 42-Volt Executive Panel, in SAE World Congress,2002.
[Online].Available:http://www.sae.org/42volt/
[2] Y.Xi and P.Jain,A forward converter topology with independent and precisely regu-
lated multiple outputs, IEEE Trans.on Power Electronics,vol.18,2003.
[3] J.Hamar and I.Nagy,Asymmetrical operation of dual channel resonant DC-DC con-
verters, IEEE Trans.on Power Electronics,vol.18,pp.8394,2003.
[4] A.Ginart,R.Bass,W.Leach,and T.Habetler,Analysis of the class AD audio am-
plier including hysteresis effects, IEEE Trans.on Power Electronics,vol.18,pp.
679685,2003.
[5] R.Erickson and D.Maksimovic,Fundamentals of Power Electronics.Kluwer Aca-
demic Publishers,2001.
[6] E.V.Dijk,H.Spruijt,D.O'Sullivan,and J.Klaassens,PWM-switch modeling of
DC-DC converters, IEEE Trans.on Power Electronics,vol.16,pp.659665,Jan.
1995.