UPC UNIVERSITAT POLITECNICA DE CATALUNYA ENERGY PROCESSING BY MEANS OF POWER GYRATORS By ANGEL CID-PASTOR B. Eng. Rovira i Virgili University, Tarragona, Spain, 1999 M. Eng. Rovira i Virgili University, Tarragona, Spain, 2002 D.E.A. Institut National des Sciences Appliquées, Toulouse, France 2003 THESIS Submitted as a partial fulfillment of the requirements for the degree of Doctor of Philosophy in Electronics Engineering in the Department of Electronics Engineering of the Technical University of Catalonia (UPC) at Barcelona, 2005 Thesis Supervisor: LUIS MARTINEZ-SALAMERO Barcelona, Spain Als meus pares, Angel i Pilar A la meua companya Laura i ACKNOWLEDGEMENT (In Catalan) En primer lloc, vull expressar la meua gratitud a Luis Martinez Salamero, director d’aquesta tesi, pels seus consells, orientació, per tot el que he après treballant al seu costat i per la seua generositat. Gràcies també a Francesc Guinjoan Gispert membre del Department d’Enginyeria Electrònica de la Universitat Politècnica de Catalunya per la tutoria d’aquesta tesi. Igualment, gràcies a Corinne Alonso del Laboratoire d’Analyse et d’Architecture des Systèmes de Toulouse i a Jean Alzieu i Guy Schweitz d’Electricité de France R&D per permetre’m realitzar aquest treball de recerca en les millors condicions. Destacaré aquí la professionalitat de tots els professors del Departament d’Enginyeria Electrònica Elèctrica i Automàtica de l’Escola Tècnica Superior d’Enginyeria de l’Universitat Rovira i Virgili que m’han proporcionat els coneixements necessaris per dur a terme aquesta tesi. Un record especial per als membres del Grup d’Automàtica i Electrònica Industrial de l’ETSE-URV amb els quals vaig tenir la sort de treballar com a tècnic de laboratori entre els anys 1999 i 2002. Vull agrair l’ajuda i col·laboració que m’han ofert Bruno Estibals, Alain Salles i Fairid Boudjellal i el recolzament de tots els companys del LAAS-CNRS. A tots, moltes gràcies. ii TABLE OF CONTENTS 1 INTRODUCTION...................................................................................................................1 2 SYNTHESIS OF POWER GYRATORS................................................................................5 2.1 Introduction .....................................................................................................................6 2.2 Power gyrator definition..................................................................................................7 2.2.1 Power gyrator of type G ..........................................................................................8 2.2.1.1 Power gyrator of type G with variable switching frequency ..............................8 2.2.1.2 Power gyrator of type G with constant switching frequency............................20 2.2.1.3 Other types of G-gyrators..................................................................................28 2.2.2 Power gyrator of type R ........................................................................................38 2.2.2.1 Power gyrator of type R with variable switching frequency.............................40 2.2.2.2 Power gyrator of type R with constant switching frequency ............................44 2.3 Semigyrator definition...................................................................................................46 2.3.1 Semigyrator of type G ...........................................................................................46 2.3.1.1 Semigyrator of type G with variable switching frequency ...............................47 2.3.1.2 Semigyrator of type G with constant switching frequency...............................51 2.3.2 Semigyrator of type R ...........................................................................................52 2.3.2.1 Semigyrator of type R with variable switching frequency................................53 2.3.2.2 Semigyrator of type R with constant switching frequency ...............................57 2.4 Conclusion.....................................................................................................................59 3 REALIZATION OF ELECTRONIC FUNCTIONS IN ENERGY PROCESSING BY MEANS OF GYRATORS............................................................................................................ 63 3.1 Introduction..................................................................................................................... 64 3.2 Addition of currents........................................................................................................64 3.2.1 G-gyrators paralleling with current distribution policy ........................................ 67 3.2.1.1 Democratic current sharing............................................................................... 68 3.2.1.2 Master-slave current distribution ...................................................................... 70 3.3 Combining v-i and i-v conversion .................................................................................. 71 3.4 Impedance matching....................................................................................................... 75 3.4.1 Impedance matching by means of a dc transformer ............................................. 75 3.4.2 Impedance matching by means of a dc gyrator .................................................... 77 3.4.2.1 G-gyrator-based maximum power point tracking of a PV array ...................... 79 3.4.2.1.1 Experimental results.................................................................................... 83 3.4.2.2 MPPT by means of gyrators of type G with controlled input current .............. 85 3.4.2.3 MPPT by means of gyrators of type R.............................................................. 87 3.5 Conclusion ...................................................................................................................... 91 iii TABLE OF CONTENTS ( Continued ) 4 VOLTAGE REGULATION BY MEANS OF GYRATORS............................................. 93 4.1 Introduction .............................................................................................................. 94 4.2 Voltage regulation by means of a single G-gyrator.................................................... 94 4.2.1 Switching regulator dynamic model .................................................................. 96 4.2.2 Circuit realization of the voltage control loop...................................................100 4.2.3 Simulated and experimental results ..................................................................101 4.3 Voltage regulation based on paralleled gyrators .......................................................103 4.3.1 Dynamic model of the current loop ..................................................................105 4.3.2 Dynamic model of the n-paralleled gyrators.....................................................106 4.3.3 Stability analysis for democratic sharing ..........................................................107 4.3.4 Simulation and experimental results.................................................................109 4.4 Conclusions .............................................................................................................113 5 CONCLUSION AND FUTURE WORK .........................................................................115 6 REFERENCES................................................................................................................121 7 APPENDIX A.................................................................................................................124 8 APPENDIX B .................................................................................................................128 9 APPENDIX C .................................................................................................................130 10 APPENDIX D .............................................................................................................132 iv LISTE OF TABLES TABLE I. COMPARISON OF CONTROL LAWS FOR POWER GYRATORS ................61 TABLE II. MEASURED EFFICIENCY OF POWER GYRATORS .....................................61 v LIST OF FIGURES Fig. 2.1 Representation of a power gyrator of type G as a two-port 6 Fig. 2.2 Representation of a power gyrator of type R as a two port 6 Fig. 2.3 Voltage-current conversion by means of a G-gyrator 8 Fig. 2.4 Current-voltage conversion by means of a R-gyrator 8 Fig. 2.5 Block diagram of a dc-to-dc switching regulator operating in sliding-mode with G-gyrator characteristics. 9 Fig. 2.6 Fourth order converters with non-pulsating input and output currents a) buck converter with input filter b) boost converter with output filter c) Cuk converter d) Cuk converter with galvanic isolation 10 Fig. 2.7 Damping network connected in parallel with capacitor C1 13 Fig. 2.8 Practical implementation of a BIF-converter-based G-gyrator L1 =12 µH, L2=35 µH, C1 = 12 -1 µF , C2 = 6.6 µF Cd = 100 µF, Rd = 2.2 Ω, La = 22 µH Ra = 1.2 Ω, g = 0.5 Ω R=1 Ω 14 Fig. 2.9 Damping network connected in series with inductor L1 15 Fig. 2.10 Simulated behaviour of the BIF converter-based G-gyrator with variable switching frequency during start-up 15 Fig. 2.11 Experimental behavior of the BIF converter-based G-gyrator with variable switching frequency during start-up 16 Fig. 2.12 Simulated behavior of the BIF converter-based G-gyrator in sliding-mode for a pulsating input voltage. 16 Fig. 2.13 Experimental behavior of the BIF converter-based G-gyrator in sliding-mode