Philippe BARRADE, Alain BOUSCAYROL, Philippe DELARUE ... · Philippe BARRADE, Alain BOUSCAYROL,...

EMR’11 Lausanne July 2011

Joint Summer School EMR’11 “Energetic Macroscopic Representation”

Philippe BARRADE, Alain BOUSCAYROL, Philippe DELARUE,Walter LHOMME

EMR’11, Lausanne, July 2011 2

• Introduction

• Input filter oscillations – Structure and conventional control scheme – From oscillations rejection to instabilities

• Merged control – Objectives and tuning parameters – Merged control loops – Modeling and sizing rules – Input filter stability

• Experimental validation – Stability abacus – Results

• Conclusion

- Content -


• General frame – DC/DC or 3 phases DC/AC converters – Feeding from a DC source via a 2nd order low pass filter

• Depending on the control of the converter – Some input filter oscillations can occur – In extreme cases, instabilities can be observed

• Depending on the operating point – Reference output power, DC feeding voltage

• Main goal – Allow the input filter stabilization by the appropriate control of the converter

• Obtained from an Energetic Macroscopic Representation (EMR)

- Outline -


• Structure and conventional control scheme – Example of a battery charger – Simplified control

• A resistor R is needed to damp the input filter • The input filter oscillations impact on the output current if not taken into

account by the control of the converter

- Input filter oscillations -


• From oscillations rejection to instabilities (1) – The control must enable the regulation of the input current, by rejecting the

input filter oscillations • Use of an Energetic Macroscopic Representation (EMR), leading to an

inversion based control identification



• From oscillations rejection to instabilities (2) – The input filter oscillations are now rejected

• The input filter becomes unstable • The input filter oscillations still impact on the output current

ripple

€

0 = IeδUc +UcδIe ⇒ Zd =δUcδIe

= −UcIe

= −Uc

2

Po

€

Po =Uc Ie

By rejecting the input filter oscillations, the converter absorbs an average constant power:

This makes the converter to behave as a negative impedance which loads the input filter:

Zd versus R defines the unstability conditions of the input filter:

• function of the operating point Po



• Objectives and tuning parameters – 2 solutions for the input filter stabilization

• Adapt the value of the damping resistor • Stabilization by the correct control of the converter

– Control for the input filter stabilization

• Only 1 tuning parameter (D) for two objectives – Regulation of the input current – Stabilization of the input filter

- Merged control -


• Merged control loop – One defines 2 independant control loops (one per objective)

• 2 duty cycles are then defined – Du for the input filter stabilization loop – Di for the output current control

• The two duty cycles are merged to obtain the required duty cycle D – Weightning factor kw

€

D = kwDu + 1 − kw( )Di

- Merged control -


• Modeling and sizing rules (1) – Open loop average model

– Duty cycles definition

€

CU•c =

1RUe −Uc( ) + Il − DIs

L I•l =Ue −Uc

Ls I•s = DUc −Uso

€

Du =Ie _ refIs

=1Is

−kp Ue −Uc( ) + Il +1RUe −Uc( )

⎛

⎝ ⎜

⎞

⎠ ⎟

Di =Us _ refUc

- Merged control -


• Modeling and sizing rules (2) – Closed loop average model

• Linearization along a given operating point

€

U•c

I•l

I•s

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥

= A.UcIlIs

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

+ BUe

Us _ ref

⎡

⎣ ⎢

⎤

⎦ ⎥

€

A =

kw −1RC

−kwk pC

+Po 1− kw( )CUe

21− kwC

−Uso 1− kw( )CUe

−1L

0 0

kwLs

UsoUe

+UeIso

k p −1R

⎛

⎝ ⎜

⎞

⎠ ⎟

⎛

⎝ ⎜

⎞

⎠ ⎟

UekwLsIso

−UsokwLsIso

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

€

B =

1C

1R−kwR

+ kwk p⎛

⎝ ⎜

⎞

⎠ ⎟ −

Iso 1− kw( )CUe

1L

0

kwUeLsIso

1R− k p

⎛

⎝ ⎜

⎞

⎠ ⎟ −

UsoLsUe

1− kwLs

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥ ⎥

- Merged control -


• Modeling and sizing rules (3) – Stability analysis

• Considering the transfer function

• Focusing on its denominator

– The coefficients are functions of » Main parameters (L,C,R, etc…) » Operating point (Ue, Uso, Is_ref=Iso)

– Dominant poles only are considered » Equivalent 2nd order system: oscillation frequency (ωn) and

damping (ζ)

€

Fs (s) =Uc (s)Iso (s)

€

D(s) = a0s4 + a1s

3 + a2s2 + a3s + a4

- Merged control -


• Input filter stability (1) – Defined by the weightning factor kw – Defined by the input filter stabilization control loop

• Simple proportional controler kp

12

System unstable for kw=0 and kw≥1

Is_ref=Iso=50A

System stable in the zones (I) and (II)

Zone (I) of a great interest: • Allow the required stabilization • Enable to set the dynamic behavior

- Merged control -


• Input filter stability (2) – Results for 2 different dynamic properties:

• ζ=0.1 (kp=1, kw=0.36) • ζ=0.7 (kp=1, kw=0.89)

- Merged control -


• Experimental validation has been performed at L2EP, from calculations made at LEI

• Topology of theinput filter is an LC filter, taking into account the coil series resistance – Needs in identifying stability conditions for this new topology (@20A)

- Experimental validation -


• Experimental results – For various values of kw

- Experimental validation -


• An new and original method for the stabilization of input filter has been proposed

• This method has been identified thanks to an energetic macroscopic representation – Allows the identification of efficients control structures

• The model of the system and its control has shown: – The control structure based on an inversion method leads to the

effective input filter stabilization – One can moreover adjust the dynamic behavior

- Conclusion -


• [1] R.D. Middlebrook, S. Cuk, “A general unified approach to modelling switching converters power stages”, IEEE PESC Rec. pp 18-34, 1976.

• [2] R.D. Middlebrook, “Input filter considerations in design and application of switching regulators”, IEEE Industry Applications annual meeting, 1976

• [3] P. Barrade, “Comportement dynamique des ensembles filter-convertisseur”, PhD thesism Institut National Polytechnique de Toulouse, France, 1997.

• [4] F. Barruel, N. Retiere, J. Schanen, A Caisley, “Stability approach for vehicles DC power network: application to aircraft on-board system”, Power Electronics Specialists Conference, PESC’05, pp 1163-1169, june 16th, 2005.

• [5] X.G. Feng, J.J. Liu, F.C. Lee, “Impedance specifications for stable DC distributed power systems”, IEEE Transactions on Power Electronics, vol. 17, pp. 157-162, 2002.

• [6] Ph. Delarue, A. Bouscayrol, A. Tounzi, X. Guillaud, G. Lancigu, “Modelling, control and simulation of an overall wind energy conversion system", Renewable Energy, vol. 28, no. 8, pp. 1159-1324, July 2003.

• [7] K. Chen, A. Bouscayrol, W. Lhomme, "Energetic macroscopic representation and inversion-based control: application to an electric vehicle with an electrical differential", Journal of Asian Electric Vehicles, Vol. 6, N°. 1, pages. 1097-1102, 6-2008.

- References -

Philippe BARRADE, Alain BOUSCAYROL, Philippe DELARUE ... · Philippe BARRADE, Alain BOUSCAYROL,...

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