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Multiobjective Optimization for Parameter Extraction of Power Electronics Devices

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Multiobjective Optimization for Parameter Extraction of Power Electronics Devices POLITECNICO DI MILANO Scuola di Ingegneria dei Sistemi Corso di Laurea Specialistica in Ingegneria Matematica Multiobjective Optimization For Parameter Extraction Of Power Electronics Devices Relatore: Prof. Maurizio VERRI Correlatore: Prof. Riccardo SACCO Correlatore: Dr. Ivica STEVANOVIC Correlatore: Dr. Marco BELLINI Tesi di laurea di: Daniele PRADA Matr. 711741 Anno Accademico 2011–2012 Daniele Prada: Multiobjective optimization for parameter extraction of power electronics devices, Laurea Specialistica in Ingegneria Matematica, © December 2012 PREFACE This work stems from my internship in the Power Electronics Integration and Semi- conductor groups of the Automation Devices department at ABB Switzerland Ltd, Corporate Research, Dättwil. From February 1st to October 31st , 2011, I have been working as a trainee on the subject “Parameter extraction for power electronics de- vices”. This work was part of the research project “IGBT modeling and parameter extraction”. Starting from an idea of my two ABB’s supervisors, Ivica Stevanovich and Marco Bellini, I studied and developed from scratch a multi-objective opti- mization approach. Such an approach was so effective that a paper appeared on the subject in the “Proceedings of the IEEE Bipolar/BiCMOS Circuits and Technol- ogy Meeting, 2011”, entitled “Improved Lumped Charge Model for High Voltage Power Diode and Automated Extraction Procedure” [5]. I am presently in the pro- cess of writing some further papers on this subject in collaboration with some ABB’s engineers [82]. This thesis is organized as follows. Chapter 1 introduces the procedure of auto- matic parameter extraction for power semiconductor devices. At first, an introduc- tion to the field of power electronics and the basic principles that govern a power diode operation are presented. Then, the different types of diode models used in circuit simulators are categorized and briefly explained. Among the whole spec- trum of diode models, three are selected as a case study: Lauritzen model [68], Ma model [75] and Extended Lauritzen model [5, 82]. The latter diode model represents an original contribution of my thesis and has been published in the paper co-authored with Marco Bellini and Ivica Stevanovic and mentioned above. Finally, parameter extraction and refinement using a formal optimization procedure are described. At the end of this chapter, the multi-objective optimization approach for parameter extraction is briefly introduced. Chapter 2 presents multiobjective programming and some of the nomenclature used in successive chapters. The different solution techniques for multiobjective optimization problems are classified. Some of these techniques, like the weighted sum method, are deeply described in order to show their potential drawbacks when dealing with parameter extraction problems. In Chapter 3, evolutionary algorithms for solving multiobjective problems are discussed. I chose and implemented this particular class of solution techniques to develop a parameter extraction methodology that is potentially general enough to be applicable to all classes of models and devices. First, the Covariance Ma- trix Adaptation Evolution Strategy (CMA-ES) is described, as it was employed to optimize a single device output characteristic at a time. Then, multi-objective evo- lutionary algorithms (MOEA) are extensively described. Emphasis is put on the algorithms that I implemented during the internship. Finally, some methodologies for statistical performance assessment of stochastic multiobjective optimizers are reviewed. Material covered in this chapter is the heart of this work and represents the state of the art in the multi-objective nonlinear nonconvex optimization context. A substantial part of the described techniques and algorithms is an innovative contribution of this thesis. iii In Chapter 4 I discuss two test cases where the automated parameter extraction procedure based on MOEAs was used. Our results show that MOEAs are promis- ing candidates to deal with parameter extraction of power semiconductor devices. In Chapter 5 some conclusions are drawn and my view of current and future research directions is illustrated. Appendix A provides a quick overview of the structure of the software for pa- rameter extraction developed during the internship. Appendix B gives the complete code of three YAML files for designing a single objective optimization, a multiobjective optimization and a MOEA comparison, in this order. PREFAZIONE Questa tesi è il risultato dell’esperienza di tirocinio da me svolta presso ABB Swi- tzerland Ltd, Corporate Research, Dättwil, dal 1 Febbraio al 31 Ottobre, 2011. L’ar- gomento del tirocinio era “estrazione parametrica per dispositivi elettronici di po- tenza”, e faceva parte del progetto di ricerca “estrazione parametrica e modellizza- zione dell’IGBT”. Partendo da un suggerimento dei miei due supervisori in ABB, Ivica Stevanovich e Marco Bellini, ho studiato e sviluppato da zero un’innovativa procedura di estrazione basata su algoritmi di ottimizzazione multiobiettivo. Tale procedura si è rivelata talmente efficace che alcuni dei risultati di questo studio sono stati pubblicati su un articolo comparso in “Proceedings of the IEEE Bipola- r/BiCMOS Circuits and Technology Meeting, 2011”, dal titolo “Improved Lumped Charge Model for High Voltage Power Diode and Automated Extraction Procedu- re” [5]. Al momento, sto scrivendo un altro articolo sul medesimo argomento, in collaborazione con alcuni ingegneri di ABB [82]. La tesi è strutturata come segue. Il Capitolo 1 introduce la procedura di estra- zione parametrica per modelli di dispositivi elettronici di potenza. Dopo un’in- troduzione generale all’elettronica di potenza, vengono richiamati i concetti fon- damentali alla base del funzionamento di un diodo di potenza. Segue una breve classificazione dei diversi modelli di diodo utilizzabili in simulazioni circuitali al computer. Viene approfondito lo studio di tre particolari modelli, da me impiegati durante il tirocinio in ABB: il modello Lauritzen [68], il modello Ma [75] e il model- lo Lauritzen esteso [5, 82]. L’ultimo di questi modelli rappresenta un contributo originale della mia tesi ed è stato pubblicato nell’articolo scritto in collaborazione con Marco Bellini e Ivica Stevanovic e menzionato precedentemente. Infine, viene descritta la procedura di estrazione ed ottimizzazione parametrica per modelli di dispositivi elettronici. A conclusione del capitolo, viene brevemente introdotta la procedura di estrazione parametrica basata su algoritmi evolutivi multi-obiettivo. Il Capitolo 2 illustra alcuni concetti chiave della programmazione multiobietti- vo e una parte della notazione utilizzata nei capitoli successivi. Viene fornita una possibile classificazione degli algoritmi per la risoluzione di problemi multiobietti- vo. Alcuni metodi tra i più comunemente impiegati vengono descritti a fondo per aiutare il lettore a comprendere le ragioni per cui tali metodi non sono stati da me utilizzati nella procedura di estrazione parametrica. iv Il Capitolo 3 discute la classe degli algoritmi evolutivi per l’ottimizzazione mul- tiobiettivo. La procedura di estrazione parametrica da me sviluppata si basa su questo tipo di algoritmi ed è sufficientemente generale per poter essere applicata a qualsiasi modello a parametri concentrati di un dispositivo elettronico. Inizial- mente viene introdotto il metodo CMA-ES, un particolare algoritmo evolutivo uti- lizzato per ottimizzare una o più curve caratteristiche di un dispositivo di potenza alla volta. Segue un’ampia trattazione sugli algoritmi evolutivi multiobiettivo. Un rilievo particolare è dato ai metodi da me implementati durante il tirocinio in ABB. L’ultimo paragrafo richiama alcune tecniche statistiche per il confronto di algorit- mi di ottimizzazione stocastici. Il materiale discusso in questo capitolo rappresenta il cuore del lavoro di ricerca da me svolto e rispecchia lo stato dell’arte nel contesto dell’otti- mizzazione multi-obiettivo non lineare non convessa. Una parte sostanziale delle tecniche e degli algoritmi descritti costituisce un contributo innovativo della mia tesi al problema dell’estrazione parametrica. Nel Capitolo 4 sono presentati due esempi di estrazione parametrica basata su algoritmi evolutivi multiobiettivo. I risultati suggeriscono che tali algoritmi con- sentono di raggiungere un buon accordo tra il modello di un dispositivo e i dati sperimentali. Nel Capitolo 5 vengono tratte alcune conclusioni sull’efficacia degli algoritmi evolutivi multiobiettivo per l’estrazione parametrica e vengono proposte possibili linee di ricerca future. L’AppendiceA riporta una descrizione sintetica della struttura del software per l’estrazione parametrica sviluppato durante il tirocinio in ABB. Nell’AppendiceB è riportato il codice completo di tre file YAML impiegati nel- l’ambito di un’ottimizzazione a singolo obiettivo, di un’ottimizzazione multiobiet- tivo e di un confronto fra algoritmi evolutivi multiobiettivo. v CONTENTS 1 modeling of power semiconductor devices1 1.1 Overview of Power Semiconductor Devices . 1 1.1.1 Semiconductor Devices . 3 1.1.2 Power semiconductor devices . 4 1.2 Power Semiconductor Diode Basics . 8 1.2.1 Review of Basic p-n Diode Characteristics . 8 1.2.2 Construction and Characteristics of Power Diodes . 12 1.3 Why Simulate? . 20 1.4 Classification of Models . 20 1.5 The Lumped-Charge Modeling Approach . 22 1.5.1 Basics Concepts . 22 1.5.2 Diode models . 23 1.6 Parameter extraction . 38 1.6.1 Step 1: initial parameter estimation
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