# Dealing with unpredictability and heterogeneity: contributions to modelling and control of renewable and multi-source energy conversion systems

Antoneta Iuliana Bratcu

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Antoneta Iuliana Bratcu. Dealing with unpredictability and heterogeneity: contributions to modelling and control of renewable and multi-source energy conversion systems. Automatic. Université Grenoble Alpes (UGA); ED n°220: Électronique, électrotechnique, automatique, traitement du signal, 2022. tel-03887544

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# HABILITATION À DIRIGER LA RECHERCHE

Pour obtenir le diplôme

## DE L'UNIVERSITÉ GRENOBLE ALPES

Spécialité : **Automatique-Productique**

Arrêté ministériel : 25 mai 2016

Présentée par

**Antoneta Iuliana BRATCU**

préparée au sein de Grenoble Image Parole Signal Automatique Laboratoire (GIPSA-lab)

dans l'École Doctorale Électronique, Électrotechnique, Automatique et Traitement du Signal (EEATS)

# Dealing with unpredictability and heterogeneity: contributions to modelling and control of renewable and multi-source energy conversion systems

Thèse soutenue publiquement le **18 novembre 2022**, devant le jury composé de :

**Mme. Mara TANELLI**

Professeure, Politecnico di Milano, Milan, Italie, Présidente

**Mme. Jing SUN**

Professeure, Université de Michigan, Ann Arbor, Michigan, États Unis, Rapporteur

**M. Leopoldo GARCIÁ FRANQUELO**

Professeur, Université de Séville, Séville, Espagne, Rapporteur

**M. Guillaume SANDOU**

Professeur, CentraleSupélec, Université Paris-Saclay, Gif-sur-Yvette, France, Rapporteur

**M. Gilney DAMM**

Directeur de recherche, Université Gustave Eiffel, Marne-la-Vallée, France, Examinateur

**M. Malek GHANES**

Professeur, Centrale Nantes, Nantes, France, Examinateur

**M. Daniel HISSEL**

Professeur, Université de Franche-Comté, Belfort, France, Examinateur

**M. Seddik BACHA**

Professeur, Université Grenoble Alpes, Grenoble, France, Examinateur

**M. Olivier SENAME**

Professeur, Grenoble INP, Grenoble, France, Examinateur

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Acknowledgments

The following lines aim at simply saying "*Thank you!*" to all the wonderful people I have had the chance to meet and learn from.

My amazing teachers, my inspiring mentors... my brilliant colleagues... my sparkling, warm and devoted friends... here, in France, and there, in Romania. Together with my either constant companions, or episodic or hazardous, yet meaningful meetings, we are all in a great adventure of knowledge... and I am grateful for that.

I wish I could thank Professor Emil CEANGĂ in person, but this is no longer possible. Professor CEANGĂ was the first one having taught me about signals and systems, some thirty years ago now, at "Dunărea de Jos" University of Galați, in Romania. Later, I was lucky to work with him. I have done my best to write this memoir in respectful memory of his teachings.

I cannot finish without loving and grateful thoughts for my parents, who have always supported me through the endeavours of my life. My wonderful mother has recently passed away. She would have been happy to learn that I am now able to defend my habilitation thesis. I guess that these lines help me to somehow accept my guilt and payback for a cruel disobedience and stupid incomprehension... because, after all, I was such a normal child.
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# Contents

## 1 Introduction 3

1.1 Why this memoir? 3

1.2 Curriculum Vitae 4

1.3 Research activity overview 6

1.3.1 Before having joined GIPSA-lab (1995 – 2011, in Romania and during post-doctoral fellowships in France) 6

1.3.2 After having joined GIPSA-lab (2011 to date) 7

1.3.3 Short overview of most significant five publications 8

1.4 Supervision of doctoral and post-doctoral works 9

1.5 Technology transfer projects and industrial collaborations 11

1.6 Research management and related activities 12

1.7 Initiated academic collaborations 14

1.8 Evaluation activities 14

1.9 Impact and recognition 15

1.10 Scientific publications 1996–2001 16

1.11 Scientific publications 2002–2022 17

## 2 Necessity and motivation of the proposed scientific approach 27

2.1 Control-oriented characterization of renewable energy conversion systems (RECS) 27

2.2 Control approach to exploit complementarity within multi-source/hybrid electrical energy systems (MSES) 30

2.3 Hardware-in-the-loop simulation (HILS) as systematic method of experimental validation 34

2.4 Heterogeneity and stochasticity of energy-communication interaction in smart grids 39

## 3 Mitigating unpredictability of renewable energy conversion systems (RECS) by optimal control methods 45

3.1 From control objectives to formal control approaches 45

3.2 Optimal control of wind energy conversion systems (WECS) 50

3.2.1 Frequency-separation-based optimal control of WECS 52

3.2.2 Sliding-mode control of WECS for multi-purpose optimization 57

3.2.3 Wind turbulence employed as searching signal in MPPT for WECS 61

3.3 Control of micro-hydro energy conversion systems (miHECS) 64

3.3.1 Direct active power control of a cross-flow-water-turbine (CFWT)-based miHECS 66

3.3.2 Supervision of smooth switching between operating modes of miHECS 68
<table>
  <tbody>
    <tr>
      <td>3.3.3</td>
      <td>Master-slave synchronized operation of miHECS for structural loads alleviation</td>
      <td>71</td>
    </tr>
    <tr>
      <td>3.4</td>
      <td>Power optimization control approaches for photovoltaic (PV) systems</td>
      <td>75</td>
    </tr>
    <tr>
      <td>3.4.1</td>
      <td>Extremum-seeking control (ESC)-based MPPT for photovoltaic (PV) systems</td>
      <td>77</td>
    </tr>
    <tr>
      <td>3.4.2</td>
      <td>MPPT-degraded operation of some particular grid-connected PV topologies</td>
      <td>80</td>
    </tr>
    <tr>
      <td>3.4.3</td>
      <td>Intrinsic sinusoidal ripple used as searching signal in ESC-based MPPT for grid-connected PV systems</td>
      <td>84</td>
    </tr>
    <tr>
      <td>3.5</td>
      <td>Summary of contributions and conclusion</td>
      <td>89</td>
    </tr>
    <tr>
      <td>4</td>
      <td>Exploiting heterogeneity of multi-source energy systems (MSES) in a robust control approach</td>
      <td>93</td>
    </tr>
    <tr>
      <td>4.1</td>
      <td>Formal foundations and mathematical tools</td>
      <td>94</td>
    </tr>
    <tr>
      <td>4.2</td>
      <td>Design of robust Power Management Systems (PMSs) for multi-storage systems</td>
      <td>97</td>
    </tr>
    <tr>
      <td>4.2.1</td>
      <td>Robust PMS design for a three-storage DC power supply microgrid on board of an electric vehicle</td>
      <td>99</td>
    </tr>
    <tr>
      <td>4.2.2</td>
      <td>HILS-assessed PMS real-time performance</td>
      <td>103</td>
    </tr>
    <tr>
      <td>4.2.3</td>
      <td>Some results of embedding robust PMSs in general-purpose microcontrollers</td>
      <td>104</td>
    </tr>
    <tr>
      <td>4.3</td>
      <td>Robust PMS design for frequency and voltage regulation in multi-source AC microgrids</td>
      <td>106</td>
    </tr>
    <tr>
      <td>4.3.1</td>
      <td>Frequency-regulation PMS for an ultracapacitor-based AC microgrid: robust control design and PHILS validation</td>
      <td>107</td>
    </tr>
    <tr>
      <td>4.3.2</td>
      <td>Voltage-regulation PMS for an ultracapacitor-based AC microgrid: robust control design and numerical simulation validation</td>
      <td>112</td>
    </tr>
    <tr>
      <td>4.3.3</td>
      <td>Frequency-regulation PMS for a battery-ultracapacitor AC microgrid: some results of microcontroller embedding</td>
      <td>115</td>
    </tr>
    <tr>
      <td>4.4</td>
      <td>Summary of contributions and conclusion</td>
      <td>117</td>
    </tr>
    <tr>
      <td>5</td>
      <td>Perspectives and scientific project</td>
      <td>119</td>
    </tr>
    <tr>
      <td>5.1</td>
      <td>Towards a comprehensive co-design approach for modern microgrids</td>
      <td>119</td>
    </tr>
    <tr>
      <td>5.1.1</td>
      <td>Generic robust PMS design for multi-source microgrids</td>
      <td>119</td>
    </tr>
    <tr>
      <td>5.1.2</td>
      <td>Effective estimation methods of storage state of health</td>
      <td>120</td>
    </tr>
    <tr>
      <td>5.1.3</td>
      <td>Towards formalizing microgrids co-design</td>
      <td>121</td>
    </tr>
    <tr>
      <td>5.2</td>
      <td>Control of particular topologies of power electronic converters</td>
      <td>121</td>
    </tr>
    <tr>
      <td>5.3</td>
      <td>Control-purpose modelling of energy-communication interaction in smart grids</td>
      <td>122</td>
    </tr>
    <tr>
      <td colspan="2">Bibliography</td>
      <td>125</td>
    </tr>
  </tbody>
</table>
# Chapter 1

# Introduction

## 1.1 Why this memoir?

The exercise of writing this HDR (*Habilitation à Diriger des Recherches*) memoir has some quite "prosaic" original motivations: indeed, it is required in the French system, in order to be authorized to conduct research activities, that is, to supervise Ph.D. theses. Therefore, it is a priori about a rather "administrative" reporting.

However, as personal perceptions are subjective by definition, each researcher can take the liberty of performing this "have to" her/his way. This is why I decided to use this task as an opportunity to look back at my research career with some questions in mind: here is what I have done because it was interesting and motivating to me – but was it significant and useful in a larger sense? Are the contributions reported here really meaningful?

In other words, an exercise of delivering an honest, objective, self-critical and relativized analysis of one's past research activity, subsequently accompanied by a projection into the future, to answer a legitimate question: and now what? What comes next?

While in my case it was not quite obvious to summarize roughly the last twenty years of my career, I have done my best to write this memoir such that it contains at least some partial answers to the above questions. The reported activity mainly concerns **optimal and robust control approaches for electrical energy conversion systems – characterized by a large penetration of renewables and presence of storage units** – with strong emphasis of the associated **application** aspects: **real-time preliminary validation, processor-unit embedding and real-world testing**. Focus is on different types of renewables – wind, photovoltaic and micro-hydro – and then on (hybrid) storage power management within multi-source systems and microgrids.

Apart from their steady societal and ecological interest – which have lastly rendered them "*en vogue*" from both scientific and research funding opportunity viewpoints – these dynamical systems are challenging in view of at least two of their features: *unpredictability* and *heterogeneity*. A constant idea was adopted throughout the approaches summarized here: to transform these *challenges*, as much as possible, in *opportunities* for control design.

This memoir is organized as follows. In the remainder of this first chapter a description of my career evolution is given, before introducing in a rather informal manner the necessity and motivation of the proposed scientific approach (Chapter 2). The following two chapters summarize the core of my contributions, with focus on the optimal control of renewable energy conversion systems (Chapter 3) and then on Power Management System robust design for multi-source electrical energy systems and microgrids (Chapter 4). Once the summarizing effort accomplished, the concluding Chapter 5 aims at identifying some research directions worthy to pursue.
## 1.2 Curriculum Vitae

### General information

* Last name: BRATCU

* Given names: Antoneta Iuliana

* Birth date and place: January 13th 1972 at Galați (Romania)

* E-mails: antoneta.bratcu@gipsa-lab.fr, gipsa-lab.grenoble-inp.fr, grenoble-inp.fr

### University degrees

* **2001:** Ph.D. degree in *Control Systems and Informatics (Automatique et Informatique)*, University of Franche-Comté, Besançon, France – with honors (mention « **très honorable** »)

- Title: *Systematic determination of precedence graphs and assembly line balancing* (in French: *Détermination systématique des graphes de précédence et équilibrage des lignes d'assemblage*)

- Assessment Committee:

- Guy JUANOLE (Professor at University of Toulouse), president

- Jean-Paul BOURRIÈRES (Professor at University of Bordeaux 1), rapporteur

- Bernard DESCOTES-GENON (Professor at "Joseph Fourier" University, Grenoble), rapporteur

- Alain BOURJAULT (Professor at Ecole Nationale Supérieure de Mécanique et Microtechniques – EN-SMM, Besançon), examiner

- Abdellah EL MOUDNI (Professor at University of Technology of Belfort-Montbéliard – UTBM, Belfort), examiner

- Gérard VALLET (Engineer at ADEPA), examiner

- Jean-Michel HENRIOUD (Professor at University of Franche-Comté, Besançon), thesis supervisor

- Viorel MÎNZU (Professor at "Dunărea de Jos" University of Galați, Romania), thesis supervisor

* **1998:** Bachelor Economist, *International Transactions*, "Dunărea de Jos" University of Galați (Romania), Faculty of Economical and Administration Sciences

* **1996:** Master in Engineering, *Power Electronics and Advanced Control Systems for Energy Conversion*, "Dunărea de Jos" University of Galați (Romania), Faculty of Electrical Engineering

* **1995:** Bachelor Engineer, *Control Systems and Industrial Informatics*, "Dunărea de Jos" University of Galați (Romania), Faculty of Electrical Engineering

### Functions

Since September 2011: Associate Professor, CNU (Conseil National des Universités) 61 Section (*Control systems, informatics and signal processing*).

* **2011 – 2016:** Tenured position on **CNRS – Grenoble INP Chair "Modelling and control of dynamical systems with applications to smart grids"**

* **Establishment (teaching affiliation):** École Nationale Supérieure de l'Eau, l'Énergie et l'Environnement (ENSE³ – Grenoble INP), Grenoble (France)

* **Laboratory (research affiliation):** Grenoble Image Speech Signal Automatic Control Laboratory (GIPSA-lab), UMR (Unité Mixte de Recherche) CNRS 5216

### Teaching service and responsibilities

* Teaching service

- **2011 – 2016:** **64 hours ETD / year** while on **CNRS – Grenoble INP Chair**

* Control systems for electrical energy (lectures, computer sessions – 2nd year of *Engineering of electrical energy* specialty (*Ingénierie de l'Energie Electrique* – IEE), ENSE³ / Grenoble INP)

* Modelling and control of power electronic converters (computer sessions – 2nd year IEE ENSE³)

* Design and control of electrical grids (project – 1st year ENSE³)
- since 2016 to date : **192 hours ETD / year**

* Control systems for electrical energy (lectures, computer sessions, practical sessions – 2nd year IEE ENSE³)

* Modelling and control of power electronic converters (computer sessions – 2nd year IEE ENSE³)

* Design and control of electrical grids (project – 1st year ENSE³)

* Control and regulation (practical sessions – 1st year *Electrical and power engineering* (*Génie électrique et énergétique* – GEE) apprenticeship specialty ENSE³)

* Control and numerical regulation (lectures, computer sessions – 2nd year apprenticeship GEE ENSE³)

* Optimization in electrical power systems (computer sessions – 3rd year IEE, 3rd year *Energy systems and markets* (*Systèmes énergétiques et marchés* – SEM) specialty and international master *Smart grids and buildings*, ENSE³)

- **tutoring** of 2 students in final diploma project and 1 student in apprenticeship (in average per year)

- since 2015 **coordination of the teaching unit** "Control systems for electrical engineering", 2nd year IEE ENSE³

- since 2019 **coordination of the integrating project unit**, 3rd year of *Control Engineering and Intelligent Systems* (*Automatique et Systèmes Intelligents* – ASI), ENSE³

* Administrative responsibility at GIPSA-lab

- 2012 – 2018: **Coordinator of local organization of Grenoble Summer School of Automatic Control** – annual scientific event hosted by GIPSA-lab, having Ph.D. students as main audience, on a different topic each year

* 1995 – 2011: teaching and research staff at "Dunărea de Jos" University of Galați (Romania), Faculty of Electrical Engineering

- 1995 – 2000: Teaching Assistant (308 hours/year, practical sessions only)

* Basics of control systems

* Numerical methods

* Modelling and simulation of dynamical systems

- 2000 – 2005: Lecturer (308 hours/year, lectures and practical sessions)

* Basics of control systems

* Numerical methods

* Modelling and simulation of dynamical systems

- 2005 – 2011: Associate Professor (224 hours/year, lectures and practical sessions)

* Real-time models for electromechanical conversion

* Microprocessors

* Theory of dynamical systems

* Administrative responsibility at "Dunărea de Jos" University of Galați

- 2003 – 2011: Secretary of Galați Territorial Section of *Romanian Society of Automatic Control and Technical Informatics* (SRAIT)

**Research**

* December 2007 – December 2009: **post-doctoral fellowship** with Grenoble Electrical Engineering Laboratory (G2ELab) / Grenoble Institute of Technology (Grenoble INP), while Associate Professor at "Dunărea de Jos" University of Galați (Romania), Faculty of Electrical Engineering

* October 2004 – May 2005: **post-doctoral fellowship** granted by the Agence Universitaire de la Francophonie (A.U.F.) with École Nationale Supérieure des Mines de Saint Étienne (ENSM.SE), Industrial Engineering and Informatics Center (G2I)
* December 2001 – December 2002: **post-doctoral fellowship** granted by Regional Council of Champagne-Ardenne Region with University of Technology of Troyes (UTT), Optimization of Industrial Systems Laboratory (LOSI)

* November 1996 – July 2001: **Ph.D. student** at Laboratoire d'Automatique de Besançon (LAB), while Teaching Assistant and then Lecturer at "Dunărea de Jos" University of Galați (Romania), Faculty of Electrical Engineering

### National (Romanian) distinction

* 2007 IN HOC SIGNO VINCES PRIZE, *Engineering Sciences* Section, of National Academic Scientific Research Council (C.N.C.S.I.S.), granted to Ph.D. holders younger than 35 years, for outstanding research activity

## 1.3 Research activity overview

Overview of my research activity is presented below as decomposed into **two chronologically-succcessive parts**, in coherence with the evolution of my career.

### 1.3.1 Before having joined GIPSA-lab (1995 – 2011, in Romania and during post-doctoral fellowships in France)

My research activity during this period can globally be described as developing and applying **dynamic optimization techniques**, both **continuous** and **discrete**, for industrial systems control. To this end, systematic procedures aiming at extremizing objectives expressed by functions or functionals defined over either continuous or discrete spaces, are employed as mathematical tools. Numerical implementation of such procedures is achieved by means of dedicated software tools.

There are two main classes of industrial systems targeted as applications, namely:

- systems requiring use of *discrete* (combinatorial) *optimization methods*: design, optimization and reconfiguration of production systems, such as assembly lines and transfer lines;

- systems requiring application of *continuous optimization methods*, namely *multi-criteria optimal control of renewable energy conversion systems* – such as *wind, photovoltaic, micro-hydro* – going towards implementation of supervision and energy/power optimal management strategies, possibly supposing coupling with combinatorial optimization methods.

Modelling and solving of problems of the first class of systems rely on either exact or heuristic methods such as dynamical programming, branch-and-bound algorithms (e.g., in C++ implementations), constrained linear-integer programming (e.g., with C++ and ILOG as software tools), logical programming with constraints (e.g., with PROLOG as software tool).

As regards problems of the second class, their development supposes extensive use of software environments dedicated to analysis and design of continuous dynamical systems, such as MATLAB® /Simulink®.

In the case of *renewable energy conversion systems*, mathematical statement of the multi-criteria optimization is specific to each conversion technology, but in all cases *maximization of conversion efficiency* is aimed at. As it is in general about nonlinear dynamical systems, design methods may include some *linear* ones (e.g., deterministic and stochastic LQ design), but most of them are specifically *nonlinear* (e.g., sliding mode, feedback linearization, Extremum Seeking Control, etc.).

It is the second class of systems my research interest has been focused on during following years; therefore, this is detailed below.

Implementation and exploitation of **renewable energy conversion systems** challenges control engineering practitioners first of all because of the discontinuity, unpredictability and randomness of the primary resource, but also because of the nonlinearity of their static power curves.

For **grid integration** of such systems, the control approach is indispensable in order to solve the generally **Maximum Power Point Tracking (MPPT)** problem – taking account of a strongly variable, *a priori* unknown
or at least either difficult-, or expensive-to-measure(estimate) resource – as well as the "smooth" integration into the grid, which must allow disturbance rejection coming from both sides and also weakly-distorted, good-quality sinusoidal current injection into the grid.

In the case of autonomous (stand-alone, islanded) AC systems or microgrids, as these are not connected to the strong (infinite-power) grid, control objectives mainly deal with ensuring voltage and frequency regulation despite of load variations, which always requires advanced, generally nonlinear, control methods and tools.

My research experience in this domain concerns the **wind, photovoltaic and micro-hydro energy conversion systems**.

Design of minimal-knowledge-based MPPT optimal control laws was one of the main goals, while envisaging an as easy as possible real-world implementation, robust at both parameter and modelling uncertainties. This goal naturally supposes design of appropriate pulse-width-modulation (PWM)-based modelling and control of the ubiquitous DC/AC and AC/AC power electronic converters, acting as actuators in this context.

I also have experience with real-time validation of such control laws, namely on dedicated test benches implementing the whole conversion chain, including the grid connection. To this end, Hardware-in-the-loop simulation (HILS) techniques were extensively used and an original systematic design of a HILS system in a general case was proposed.

As regards effective applications, wind and micro-hydro systems were here concerned, whose operation is based on three-phase rotating electrical machines coupled with the primary energy sources, in this case, the turbines. From a control viewpoint, the role of machines is to impose the steady-state operating point to the turbines, which further enables the possibility of controlling them according to the goal. To this end, a suitable modelling and identification approach is obviously necessary.

### 1.3.2 After having joined GIPSA-lab (2011 to date)

At Grenoble Images Speech Signal and Control Laboratory (GIPSA-lab, UMR CNRS 5216), I joined the Linear Systems and Robustness (Systèmes Linéaires et Robustesse – SLR) team, within the Control Systems Department. This team was carrying out theoretical, methodological and applied research, towards novel structural, algebraic, robust, optimization-based approaches of analysis, observation, identification and control of dynamical systems. Having solid skills in modelling, identification, observation and control of linear systems, SLR team was focusing on taking into account the modelling uncertainties and various disturbances into the control or estimation design.

My arrival in 2011 as an Associate Professor on a tenured position on CNRS – Grenoble INP Chair "Modelling and control of dynamical systems with applications to smart grids" had the role of enhancing SLR potential on the electrical energy topic, thus giving me the opportunity of diversifying my research topics.

Evolution of my research topics has continued after GIPSA-lab restructuring at the beginning of 2020, when I joined the newly created MODUS (Modelling and Optimal Decision for Uncertain Systems) team, within the Control Systems and Diagnostic Pole. MODUS team is committed to bring its skills and know-how at bridging the gap between advanced control and its real-world application in a broad regard. To this end, the employed methods will aim at complementing classical approaches – such as Lyapunov-based or optimal control – by data-driven and learning-based methods to take account of uncertainties and big data issues, very frequently occurring in nowadays real-world systems.

Since my arrival at GIPSA-lab, my research work has been developed along with several directions.

One of these directions is the design of robust and linear parameter-varying (LPV) optimal control methods for coordination inside of multi-source electrical systems supplying irregular loads, for both embedded applications – such as supply systems on board of electric vehicles – or stationary applications – such as different microgrid use cases, requiring formulation of different control objectives, respectively. The dynamic specialization of sources – within identifiable frequency ranges placed around the so-called characteristic frequency – is here taken into account in order to minimize their exploitation stress and prolong their lifetimes. In this case, the control problem can be cast into a robust disturbance rejection formalism, such as the $H_\infty$ framework.

This was the topic of the 2012–2015 Ph.D. thesis of Waleed NWESATY (defended in 2015) – where a three-source
system has been considered – as well as of a technology pre-transfer project funded by Institut Carnot Logiciels et Systèmes Intelligents (LSI) and of its continuation towards effective transfer with Linksium Grenoble Alpes Technology Transfer Office (TTO). A rapid-prototyping demonstrator was conceived and built at GIPSA-lab for test and validation purpose, in order to advance the technology readiness level (TRL) of the proposed solution. In the context of the technology transfer, two software licenses and a know-how procedure are in progress to protect the intellectual rights.

In the same framework is also placed the design of a **multi-variable robust control of microgrids with strong penetration of renewable energy sources and storage units**. This was the core topic of the Ph.D. thesis of Quang-Linh LAM, run in collaboration with Grenoble Electrical Engineering Laboratory (G2ELab) during 2014–2017, defended in 2018. Both *frequency* and *voltage control and stability* of stand-alone microgrids were addressed. Use of $H_\infty$ framework allowed a **comprehensive control design methodology** being proposed, as well as a thorough robustness analysis – in relation with some strongly varying parameters, such as the storage unit state of charge – both of which were validated on a real-time **Power Hardware-in-the-Loop (PHIL)** dedicated test bench at G2ELab.

Another research direction is represented by the **control of renewable energy conversion systems**, which I continued to work on, also continuing to develop my well-established collaboration with G2ELab. Namely, topics related to **operation optimization** of wind, photovoltaic and micro-hydro systems, but also to their **grid integration**, were approached in this context, which largely rely upon **power electronic converter control**. In the framework of this collaboration, validations were primarily achieved on PHIL real-time benches. In addition, in the specific case of **micro-hydro** energy conversion systems, the effective assessment was advanced by tests on a **real-world prototype**, involving complementary skills and control implementation know-how. This topic issued several journal articles during this period.

In relation with control approaches, optimization approaches were also developed, aiming at **optimizing the decision making process for smart grids evolving under uncertainties**. Energy-cluster-based modelling at different aggregation levels – e.g. of a building, a quarter or a region – as well as **agent-based optimization** were used to this end. Integration of electric vehicles into the grid (V2G) for ancillary service purposes was formulated and solved as an optimization problem. These issues were the core topic of **Smart Energy** research project granted by Grenoble Institute of Technology (Grenoble INP)) during 2012–2014, in which I co-supervised two six-month post-doctoral fellows, Salam HAJJAR and Julian FERNANDEZ, respectively.

A recent research interest is focused on the **modelling of smart grids as cyber-physical systems**, for control purposes. In smart grids co-existence of the energy grid and the communication network is fundamental. Hence, **modelling of interactions between the energy layer and the communication one** is here a challenging issue, specific to smart grids, because of the need to conciliate in a certain manner – and ideally within a single model, if at all possible – two systems of different natures: the **continuous-time-driven** dynamics of the energy grid and the **discrete-event-driven** dynamics of the superposed communication network.

This has recently been identified as a challenging research topic in the academic Grenoble area and made the object of the 2016–2019 Ph.D. thesis of Ronak FEIZIMIRKHANI (defended in March 2020), co-supervised in collaboration with G2ELab, funded in the context of **CY-PHY-GRID** research project granted by **AGIR** (Alpes Grenoble Innovation et Recherche) funding scheme of Grenoble Alpes University. In this thesis **ARMA models of GOOSE** (Generic Object-Oriented Substation Event) **traffic** of the standard **IEC 61850** are developed. Also, **estimation of maximum delay in smart grids with proprietary (known) architecture** was validated on an intelligent substation test bench available at G2ELab. Results are useful for smart grid supervision operators.

### 1.3.3 Short overview of most significant five publications

* *Journal articles*

1. A.I. Bratcu, I. Munteanu, S. Bacha, D. Picault, B. Raison (2011). Cascaded DC-DC converter photovoltaic systems: power optimization issues. *IEEE Transactions on Industrial Electronics*, 58(2), 403–411.
– article in top 1% most highly cited between 2011 and 2015 in ISI Thomson Web of Science
This article is one of the first having proposed application of *Extremum Seeking Control* (ESC) to
*photovoltaic* (PV) conversion systems. A novel energy conversion configuration is here also proposed,
together with specific methods of harvesting the maximum power.

2. I. Munteanu, A.I. Bratcu (2015). MPPT for grid-connected photovoltaic systems using ripple-based extremum seeking control: analysis and control design issues. *Solar Energy*, 111, 30–42.

This article presents a detailed systemic analysis of implementing the *Maximum Power Point Tracking* (MPPT) for PV systems by means of Extremum Seeking Control (ESC). This is an on-line optimum tracking, when this optimum moves in an *a priori* unknown manner as a consequence of solar irradiance variation. A *systematic ESC control design procedure* is proposed.

3. W. Nwesaty, A.I. Bratcu, O. Sename (2016). Power sources coordination through multivariable LPV/Hinf control with application to multi-source electric vehicles. *IET Control Theory and Applications*, 10(16), 2049–2059.

In this article the problem of *coordinating several storage units, of different technologies*, which compose
a multi-source system – *e.g.*, a microgrid containing batteries, supercapacitors and fuel cells – in a
way such that to respect their *dynamic specialization* and thus to preserve at most their reliability
and lifetime. This problem of dynamic (frequency) separation of sources’ operation is approached in a
well-posed formal framework, namely, that of *robust control for linear parameter-varying (LPV) systems*.

• Books

1. I. Munteanu, A.I. Bratcu, N.A. Cutululis, E. Ceangă (2008). *Optimal control of wind energy systems – Towards a global approach*. Advances in Industrial Control Series, Springer, London, U.K. ISBN 978-1-84800-079-7, 283 pages.

In this monograph one of the most promising advanced control methods of wind energy conversion
systems are detailed: optimal LQ control, sliding mode control, feedback linearizing control. Hardware-
in-the-loop simulation (HILS) results obtained on dedicated test benches are discussed, which enhance
the opportunity and pertinence of applying the proposed methods.

2. S. Bacha, I. Munteanu, A.I. Bratcu (2013). *Power Electronic Converters Modelling and Control – With Case Studies*. Advanced Textbooks in Control and Signal Processing Series, Springer, London, U.K. ISBN 978-1-4471-5478-5, 454 pages.

This book is an *advanced textbook* targeting mainly a Ph.D.-student audience working with electrical energy conversion systems, where power electronic converters are indispensable. These converters exhibit strongly nonlinear dynamic behaviour, very fast and also hybrid dynamics, as well as parameter variance. Hence, they propose multiple challenges to control designers.

This book is composed of *two parts* covering *twelve chapters* in total: a first part (first five chapters) dedicated to *analysis (modelling) methods* and a second part (next seven chapters) focused on the *synthesis (control design)*, detailing both classical and advanced control methods for power converters. Representative case studies are presented from a pedagogical perspective. Problems with solution, as well as problems proposed for solving are provided at the end of each chapter.

Some chapters of this book serve as support for the teaching unit "Power Electronics II – Modelling and control of power electronic converters" of the *Engineering of electrical energy* specialty at École Nationale Supérieure de l'Éau, l'Énergie et l'Environnement (ENSE³ – Grenoble INP).

1.4 Supervision of doctoral and post-doctoral works

Publications issued within different supervised Ph.D. theses and post-doctoral works can be found in the list of scientific publications (Section 1.11). Names of the different supervised Ph.D. students and post-doctoral fellows appear in magenta in that list.
<table><caption>Table 1.1: Ph.D. students co-supervised at GIPSA-lab and the corresponding supervision shares.</caption><thead><tr><th></th><th>Ph.D. student</th><th>Time interval</th><th>Supervision share</th></tr></thead><tbody><tr><td>1</td><td>Ronak FEIZIMIRKHANI</td><td>2016–2020</td><td>65%</td></tr><tr><td>2</td><td>Quang-Linh LAM</td><td>2014–2018</td><td>50%</td></tr><tr><td>3</td><td>Waleed NWESATY</td><td>2012–2015</td><td>75%</td></tr><tr><td>4</td><td>Adrian FLORESCU</td><td>2009–2012</td><td>25%</td></tr></tbody></table>

Table 1.1 offers an inverse-chronological-order synthetic view of the four Ph.D. theses I co-supervised since I have joined GIPSA-lab in 2011, at 215% aggregated supervision share. Next, the supervised doctoral and post-doctoral works are enumerated.

## Defended Ph.D. theses

1. **Ronak FEIZIMIRKHANI** (Doctoral School in Electronics, Electrotechnics, Automatic Control and Signal Processing (École Doctorale en Electronique, Electrotechnique, Automatique et Traitement du Signal – EEATS); funding in the context of CY-PHY-GRID research project granted by AGIR (Alpes Grenoble Innovation et Recherche) funding scheme of Grenoble Alpes University, November 2016 – October 2019; **defended on March 4th 2020)**, supervision share **65%**; supervisor Professor Yvon BÉSANGER (G2Elab)
*Modelling and analysis of smart grids as cyber-physical systems*
https://tel.archives-ouvertes.fr/tel-03285450/

R. Feizimirkhani has had a two-year postdoctoral position (2020 – 2022) with the project *Analysis of delays in interoperable smart grids* (Analyse des retarDs dans les smArt Grids InterOpérables – ADAGIO), funded by Institut Carnot Énergies du futur. At the present, she is an R&D engineer with Atos in Grenoble, France.

2. **Quang-Linh LAM** (EEATS Doctoral School; funding by French Ministry, October 2014 – September 2017; **defended on January 17th 2018**), supervision share **50 %**; supervisor Professor Delphine RIU (G2Elab)
*Advanced control of microgrids for frequency and voltage stability: robust control co-design and real-time validation*
https://tel.archives-ouvertes.fr/tel-01836292/document

At the present Q.-L. Lam works as an Assistant Lecturer – Researcher with Polytechnic School of Danang in Vietnam.

3. **Waleed NWESATY** (EEATS Doctoral School; funding by French Ministry, October 2012 – September 2015; **defended on October 22nd 2015**), supervision share **75%**; supervisor Professor Olivier SENAME (GIPSA-lab)
*LPV/H<sub>∞</sub> control design of on-board energy management systems for electric vehicles*
https://hal.archives-ouvertes.fr/tel-01237735/

At the present, W. Nwesaty is a project leader of hardware/software electronic systems with Cémios, Rhône-Alpes Region, France.

4. **Adrian FLORESCU** (EEATS Doctoral School; funding by French Ministry, October 2009 – September 2012; **defended on November 19th 2012**), supervision share **25%**; supervisor Professor Seddik BACHA (G2Elab)
*Optimized energy flow management on board of electric vehicles*
https://tel.archives-ouvertes.fr/tel-00798937v1/document

At the present, A. Florescu is an R&D engineer with Safran Electrical & Power, Ile-de-France, France.

## Ph.D. theses co-supervised at “Dunărea de Jos” University of Galați (Romania)

Until 2013 in Romania only Full Professors could officially supervise Ph.D. thesis. Co-supervision activity below is reported based on letters provided by the official supervisor.

1. **Iulian MUNTEANU** (2002 – 2006, funding by doctoral contract), supervision share **50%**; supervisor Prof. Emil CEANGĂ
*Contributions to the optimal control of wind energy conversion systems*
www.etc.ugal.ro/imunteanu/phd_disertation.pdf
I. Munteanu was an R&D engineer with GIPSA-lab, having worked between 2017 and 2020 on K-INF technology transfer project funded by the Technology Transfer Office (Société d'Accélération du Transfert Technologique – SATT) Linksium Grenoble Alpes.

2. **Adriana SCARLAT** (2009 – 2012, funding by doctoral contract), supervision share **30%**, namely between 2010 and 2011; supervisor Prof. Emil CEANGĂ
   *Advanced control of wind energy conversion systems*

(in Romanian: *Sisteme avansate de conducere a proceselor de conversie a energiei eoliene*)

http://www.gup.ugal.ro/guppress/index.php/test/catalog/book/402

At the present, A. Scarlat Burlibaşa is an Associate Professor with the Department of Control Systems and Electrical Engineering at the Faculty of Control Systems, Computers, Electrical and Electronic Engineering of “Dunărea de Jos” University of Galați (Romania).

**Post-doctoral fellows**

1. **Ronak FEIZIMIRKHANI** (September 2020 – August 2022, funding in the context of *Analyse des retarDs dans des smArt Grids InterOpérables – ADAGIO* research project granted by Institut Carnot Énergies du Futur), supervision share **25 %**
   *Communication delay estimation in interoperable smart grids*

At the present, R. Feizimirkhani is an R&D engineer with Atos in Grenoble, France.

2. **Julian Alberto FERNANDEZ** (June – November 2014, funding in the context of *Smart Energy* research project granted by Grenoble Institute of Technology (Grenoble INP)), supervision share **50 %**
   *Decision optimization under uncertainty in smart grids – optimal grid integration of electric vehicles*

After having passed the period from 2016 until 2021 in the British Columbia region in Canada, while employed as a post-doctoral fellow with the University of Victoria, then as a research scientist with the Clean Energy Research Center and as a project manager with the University of British Columbia, J.A. Fernandez is now working as a senior consultant with WSP in Vancouver, Canada.

3. **Salam HAJJAR** (July – December 2014, funding in the context of *Smart Energy* research project granted by Grenoble INP), supervision share **50 %**
   *Decision optimization under uncertainty in smart grids by means of collaborative multi-agent strategies*

After having passed four years as an Assistant Professor at Marshall University / College of Electrical and Computer Engineering in Huntington, West Virginia, S. Hajjar is presently an Assistant Professor at West Virginia University, Beckley, West Virginia, U.S.A.

**1.5 Technology transfer projects and industrial collaborations**

1. **July – October 2020: Expertise report** for *Faiveley Transport (Wabtec Group) (12 000 Euros)*, dealing with the design and implementation of a control solution for a Katium-power-converter-based Li-ion battery charger for railway applications.

2. **April 2017 – April 2018: Leader of technology pre-transfer project K-INF: Embedded real-time PMS for multi-source electrical energy systems (Système embarqué de gestion temps réel des systèmes d'énergie multi-sources)** funded by Institut Carnot *Logiciels et Systèmes Intelligents* (LSI)
   – objective: technology readiness level (TRL) advancement of a robust coordination Power Management System (PMS) solution for multi-source electrical systems with application to electrical vehicles' on-board supply systems

– technology transfer of the results obtained during W. Nwesaty's Ph.D. thesis (*LPV/H<sub>∞</sub> control design of on-board energy management systems for electric vehicles*), targeting a possible further funding by Linksium Grenoble Alpes Technology Transfer Office (TTO) (Société d'Accélération du Transfert Technologique – SATT)

– duration: 12 months

– budget: **72 000 Euros** (out of which one Senior R&D engineer)
3. **October 2018 – March 2020: Leader of technology transfer project K-INF: Robust PMS for multi-source electrical energy systems** (Gestionnaire d'énergie robuste embarqué des systèmes multi-sources) funded by Linksium Grenoble Alpes TTO (pursuing the above-listed K-INF **technology pre-transfer project** in the use case of frequency regulation in microgrids with renewable energy sources and hybrid storage units)

- technology transfer objective: either **licensing** to an existing enterprise, or **start-up** creation

- duration: 18 months

- budget: **183 561 Euros** (out of which one Senior R&D engineer)

https://www.k-inf.fr

4. **October – December 2014: Expertise report for Schneider Electric (10 000 Euros)**, dealing with an improved control solution of a kVA-rated three-phase generation system containing a storage unit (battery).

## Participations at international technology exhibitions and fairs

**Goal:** showcasing K-INF technology and demonstrator.

1. 2018 *Global Industrie / Smart Industrie*, March 27–30 2018, Paris Nord Villepinte, France;

2. 2018 *European Utility Week*, November 6–8 2018, Vienna, Austria;

3. 2019 *European Utility Week / Initiate! Hub*, November 12–14 2019, Paris Expo Porte de Versailles, France;

4. 2020 *Forum 5i (Innovation – Industrie – Inclusion – Investissement – International) / Technological showcase*, September 29 2020, World Trade Center Grenoble, France

https://www.pocmedia.fr/forum-5i-une-vitrine-pour-les-chercheurs-entrepreneurs/

# 1.6 Research management and related activities

## Research projects

1. **2022 – 2023: Leader** of the exploratory research project

*Partial-derivative-model-based estimation of battery state of health parameters (PaDeSoH)*

funded by the national **IDEX** (*Investissements d'avenir*) programme (ANR-15-IDEX-02) through local **IRGA** (*Initiatives de Recherche à Grenoble Alpes*) funding scheme

- comprising twelve-month post-doctoral fellow funding (**75 000 Euros**)

2. **2016 – 2019: Leader** of *Alpes Grenoble Innovation et Recherche (AGIR)* 2016 project, funded by Grenoble INP

*Modelling and analysis of smart grids as cyber-physical systems (CY-PHY-GRID)*

- comprising three-year Ph.D. thesis funding (Ronak FEIZIMIRKHANI) + 3 500 Euros accompanying funding

3. **June – November 2015: Leader of CNRS Exploratory Project**

*Modelling and analysis of smart grids as cyber-physical systems for decentralized control purpose (CYBERGRID)*

- partners: 2 research laboratories from Grenoble area: GIPSA-lab and G2ELab

- budget: **11 000 Euros** (travel, master internships and small equipment)

- results of this project allowed further collaboration funding within the framework of the above-listed 2016 AGIR project

http://www.cellulenergie.cnrs.fr/2015-Appel-a-Projets-Exploratoires-de-la-Cellule-Energie-du-CNRS

4. **2013 – 2017: Member of ANR Progelec project** (42 months)

*Photovoltaic units integrated into electrical grids with distributed storage (PhotovoltAIques integRés aux réseAux électriques avec stockages DIStribuEs – PARADISE)*

- partners: 5 research laboratories and 3 SMEs as industrial partners

- budget: **1 900 565 Euros** in total (out of which 758 480 Euros funded by ANR), out of which **167 725 Euros** for GIPSA-lab

https://anr.fr/fr/projets-finances-et-impact/projets-finances/projet/funded/project/anr-13-prge-0007/?tx_anrprojects_funded%5Bcontroller%5D=Funded&cHash=21f68bca02f63561937f882bc23f4574

http://www.gipsa-lab.fr/projet/PARADISE/accueil.html
5. **2012 – 2014: GIPSA-lab responsible** in the structuring project **Smart Energy** funded by Grenoble INP in the framework of *Support of Excellence and Innovation* (Soutien à l'Excellence et à l'Innovation – SEI) scheme

– partners: 4 research laboratories from Grenoble area: Grenoble Electrical Engineering Laboratory (G2ELab), Sciences for Design, Optimization and Production Laboratory (Laboratoire des Sciences pour la Conception, l'Optimisation et la Production de Grenoble – G-SCOP), Grenoble Informatics Laboratory (Laboratoire d'Informatique de Grenoble – LIG), GIPSA-lab

– funding of 2 six-month post-doctoral fellowships at GIPSA-lab (J.A. Fernandez and S. Hajjar)
http://www.grenoble-inp.fr/grenoble-in-press/pour-une-gestion-intelligente-de-l-energie-567122.kjsp

**Submitted applications**

* **2022: Participation to proposal writing of Horizon Europe European Innovation Council (EIC) PathFinder Challenge project application**

*Supercapacitor and Battery Hybrid Energy Storage System for Improved Energy Storage – SuperBESS*

– topic HORIZON-EIC-2022-PATHFINDERCHALLENGES-01-02 (Mid to long term and systems integrated energy storage)

– call identifier HORIZON-EIC-2022-PATHFINDERCHALLENGES-01

– project coordinators: Vasco da Gama Colab Energy Storage Associaçao (Portugal)

– three-partner consortium: Vasco da Gama Colab / Portugal, Grenoble INP / France, SINTEF Energi AS / Norway

**Participation to research projects applications**

1. **2020: Participation to proposal writing of H2020 RIA (Research and Innovation Actions) European project application**

*STadium storAGE: Multi-use hybrid battery storage for application in nearly net zero energy football stadium*

– **STAGE**

– topic LC-BAT-9-2020

– call identifier H2020-LC-BAT-2019-2020 (*Building a Low-Carbon Climate-Resilient Future Next-Generation Batteries*)

– project coordinators: Badenova Warmeplus GMBH & Co. KG, Franhofer Institute for Solar Energy Systems (Germany)

– nine-partner consortium: 1 academic institution (Grenoble INP / France), 2 research institutes (Franhofer Institute / Germany, Austrian Institute of Technology / Austria), 2 large industrial groups (Badenova Warmeplus / Germany, ABB Power Grids S.p.a. / Italy), 4 SMEs (Skeleton Technologies / Estonia, Visblue Aps / Denmark, Fundacion Tekniker / Spain, R2M Solution / Spain)

which was favourably evaluated (total score **13 out of 15** for three criteria: "Excellence" 4.5/5, "Impact" 3.5/5, "Quality and efficiency of the implementation" 5/5), but not funded within the given budgetary limits;

2. **2014: Participation to proposal writing of H2020 RIA European project application**

*Energy Optimal Design of 3-wheels Pedelec – EO3BIKE*

– topic GV-5-2014

– call identifier H2020-GV-2014

– project coordinator: Grenoble INP / GIPSA-lab (Prof. Olivier SENAME)

– eleven-partner consortium: 3 academic institutions (Grenoble INP / France, Politecnico di Milano / Italy, Technische Universiteit Delft / The Netherlands), 2 local authorities (Isère County / France, Authority for Transport / Malta), 2 centers (European Center for Information and Communication Technologies / Germany, Centre de Ressources et d'Innovation Mobilité Handicap (CEREMH) / France), 4 SMEs (Soben / France, Zehus S.R.L. / Italy, EBL Gmbh / Germany, Klaxon Mobility S.R.L. / Italy)

which was favourably evaluated (total score **12 out of 15** for three criteria: "Excellence", "Impact", "Quality and efficiency of the implementation"), but not funded within the given budgetary limits (first-ranked not funded application).
## 1.7 Initiated academic collaborations

1. September 2016: Kick-off of a collaboration on control of modular multi-level power electronic converters (MMCs) with Prof. Remus TEODORESCU of Department of Energy Technology / Aalborg University / Denmark

- article co-authoring

2. October 2015: One-week visit at Department of Sustainable Electrical Energy / Delft University / The Netherlands, in the group of smart grids led by Prof. Peter PALENSKY, in the context of CYBERGRID Exploratory Project funded by the Energy Cell of CNRS

- presentation of on-going work on modelling of energy-communication interactions in the smart grids

3. 2014 – 2015: Kick-off of collaboration with Systems and Transportation Laboratory (Laboratoire Systèmes et Transports – SET) of University of Technology of Belfort-Montbéliard (UTBM) / France

- coordinated control of multi-source electrical energy systems, with application to microgrids - in particular, on-board supply systems of electric vehicles

- first goal: real-time validation of the at-that-time-on-going Ph.D. work of W. Nwesaty (LPV/Hinf control design of on-board energy management systems for electric vehicles) during April 2015

- collaboration pursued with publication of an article in *IEEE Transactions on Control Systems Technology*

## 1.8 Evaluation activities

### Ph.D. assessment committees

1. 2023 (date to be established): Quentin HILPERT – *Modélisation et détermination des stratégies de conditionnement de puissance pour des réseaux de puissance répartis pour des applications embarquées aéronautiques et spatiales* – supervised by Prof. Stéphane CAUX, Plasma and Energy Conversion Laboratory (LAPLACE – Laboratoire Plasma et Conversion d'Énergie) / Toulouse Institute of Technology (INPT), Toulouse, France. EDSYS (Systems) Doctoral School

- member

2. December 15 2022: Lucas MOLINA BARROS – *Supervisory Control of Reconfigurable HVDC grids* – supervised by Prof. Laurent PIÉTRAC, SIGMA Clermont, and Assoc. Prof. Emil DUMITRESCU, Ampère Laboratory / INSA Lyon, France. ED160 (Electronics, Electrotechnics and Control) Doctoral School

- member

3. November 25 2022: Grégoire LE GOFF – *Scalable Control Allocation Methods for the Modular Multilevel Converter from Modelling to Real Time Implementation* – supervised by Prof. Maurice FADEL, Plasma and Energy Conversion Laboratory (LAPLACE – Laboratoire Plasma et Conversion d'Énergie) / Toulouse Institute of Technology (INPT), Toulouse, France. GEETS (Electrical Engineering, Electronics, Telecommunications and Health) Doctoral School

- member

4. January 29 2021: Yankai XING – *Control of direct current connections (HVDC) for the damping of inter-area oscillations* – supervised by Prof. Bogdan MARINESCU, Laboratory of Digital Sciences of Nantes (LS2N – Laboratoire des Sciences du Numérique de Nantes) / École Centrale Nantes, France. MATHSTIC (Mathematics and Information and Communications Science and Technology) Doctoral School

- member
https://www.ls2n.fr/event/soutenance-de-these-de-xing-yankai-equipe-dsg/

5. September 27 2019: Saber LAAMIRI – *Commande des systèmes électriques : machines synchrones et convertisseurs multi-niveaux* – supervised by Prof. Malek GHANES, Laboratory of Digital Sciences of Nantes (LS2N – Laboratoire des Sciences du Numérique de Nantes) / École Centrale Nantes, France. MATHSTIC Doctoral School (Mathematics and Information and Communications Science and Technology)

- member
https://www.ls2n.fr/event/soutenance-de-these-de-saber-laarimi-equipe-commande/
6. November 28 **2016**: Rasmus PEDERSEN – *Power Management and Voltage Control using Distributed Resources* – supervised by Prof. Rafael WISNIEWSKI and Assoc. Prof. Christoffer SLOTH, Aalborg University (Denmark) / Department of Electronic Systems
– rapporteur
http://www.aau.dk/arrangementer/vis/phd-defence-by-rasmus-pedersen--power-management-and-voltage-control-using-distributed-resources-.cid293919

7. August 23 **2016**: Lóránd BEDE – *Advanced and Robust Control of Grid Connected Converters* – supervised by Assoc. Prof. Tamas KEREKES and Prof. Remus TEODORESCU, Aalborg University (Denmark) / Department of Energy Technology
– rapporteur
http://www.en.tek-nat.aau.dk/news-events/show-event/phd-defence-by-lorand-bede-on-advanced-and-robust-grid-control-of-power-converters cid260286

## Peer-to-peer evaluation of research projects

1. **2019**: Scientific evaluation of a *Strategic Research Initiatives* (*Initiatives de Recherche Stratégique* – IRS) project, in the framework of *Excellence Initiatives* (IDEX) national funding schemes

2. **2014**: Scientific evaluation of an *ANR Young Researcher* (*Jeunes Chercheuses Jeunes Chercheurs* – JCJC), in the framework of 2014 ANR Call for Generic Proposals

3. **2014**: Scientific evaluation of an *Individual Research Grant*, The Israel Science Foundation (ISF)

4. **2012**: Member of the *European Working Group on Electricity Grids*: Exercise Defining a SET-Plan European Energy Education and Training Initiative
– objective: drafting recommandations in order to improve the European educational offer in electrical grids

## Peer-to-peer review

Reviewer of:

– approx. 4–5 journal submissions per year: *IEEE Transactions on Control Systems Technology*, *IEEE Transactions on Industrial Electronics*, *IEEE Transactions on Vehicular Technology*, *IET Renewable Power Generation*, *ISA Transactions*, *etc.*;

– approx. 2–3 conference submissions per year: *American Control Conference* (ACC), *Mediterranean Conference on Control and Automation* (MED), *IFAC World Congresses* and *IFAC Symposia/Conferences/Workshops*, *etc.*

## 1.9 Impact and recognition

On a **national** level, I am member of:

* CNU (*Conseil National des Universités*): substitute member starting from 2020, Section 61 (*Control systems, informatics and signal processing*);

* Modelling and Control of Dynamic Systems (GdR MACS) – more specifically, *Electrical Systems Control* (CSE) and *Intelligent Grids and Electrical Systems* (RSEI) workgroups
http://gdr-macs.cnrs.fr/membres/antoneta-iuliana-bratcu;

* Club of Teachers and Researchers in Electronics, Electrotechnics and Control Systems (Club des Enseignants et des Chercheurs en Electronique, Electrotechnique et Automatique – Club EEA).

<table><caption>Table 1.2: Citations' number and Hirsch indices in mostly used scientometric databases (December 2022).</caption><thead><tr><th></th><th>Web of Science</th><th>Scopus</th><th>Google Scholar</th></tr></thead><tbody><tr><td>Total citations</td><td>1267</td><td>1601</td><td>4024</td></tr><tr><td>Self-citations excluded</td><td>1201</td><td>1505</td><td></td></tr><tr><td>h-index<br>(without self-citations)</td><td>14<br>(14)</td><td>17<br>(16)</td><td>24</td></tr></tbody></table>

*Symposium on Industrial Electronics* – ISIE 2023

In terms of **international** recognition, I can mention:

* membership of IFAC Technical Committee 6.3 Power and Energy Systems (since 2017)
https://tc.ifac-control.org/6/3/members;

* IPC member of 11th IFAC Symposium on Control of Power and Energy Systems – CPES 2022
https://cpes2021.com/en/commitees;

* member of *Control Systems Technical Track Program Committee* at the 32nd *IEEE International*
https://2023.ieee-isie.org/technical-technical tracks/tt-06-control-systems/;

* Technical Associate Editor at *2023 IFAC World Congress*
  https://www.ifac2023.org/about/pc/

* elevation to the IEEE Senior Member grade in 2018;

* IPC member of *International Conference on System Theory, Control and Computing* – ICSTCC
  https://icstcc.ugal.ro/2022/index.php/committees/international-program-committee

Table 1.2 gives a synthetic view of my publications' impact in terms of number of citations and scientific Hirsch indices. Other information about my scientific performance can be found at:
https://exaly.com/author/5703917/antoneta-iuliana-bratcu/rankings

## 1.10 Scientific publications 1996–2001

* *During the Ph.D. thesis*

My Ph.D. thesis, *Systematic determination of precedence graphs and assembly line balancing* (in French: *Détermination systématique des graphes de précédence et équilibrage des lignes d'assemblage*), defended in July 2001 at Université de Franche-Comté, Besançon, France, is a contribution to a global approach of rational design of assembly systems, organized into two main parts.

https://tel.archives-ouvertes.fr/tel-00258992

More precisely, its first part is dedicated to the generation of precedence graphs to be used in assembly line balancing. The existence of a *structural property* – called property Π – is proved to be *necessary and sufficient to ensure the equivalence between a set of assembly sequences and a single precedence graph*. Based upon this property, two algorithms are proposed for systematic generation of precedence graphs.

The second part is dedicated to the analysis of *self-balancing assembly systems*, whose design avoids solving an assembly line balancing classical problem. It is sufficient that such systems satisfy a simple technological constraint of placing the (human) operators on the line – from slowest to fastest – for spontaneously obtaining the optimal balancing. The sufficient condition for self-balancing – the "well-ordering" – is proved using stability criteria of discrete-time dynamical systems.

This thesis issued the publications listed below.

### Book chapters

1. J.M. Henrioud, A. Bratcu (1999). Algorithm for generating the precedence graphs in assembly systems. In: *Software and Hardware Engineering for the 21st Century* (Ed. Nikos E. Mastorakis), pp. 44–49. World Scientific Engineering Society Press. ISBN 960-8052-06-8.

2. V. Mînzu, A. Bratcu (1999). Precedence graphs generation using assembly sequences. In: *Software and Hardware Engineering for the 21st Century* (Ed. Nikos E. Mastorakis), pp. 122–127. World Scientific Engineering Society Press. ISBN 960-8052-06-8.

### Articles in international journals without impact factor

1. A. Bratcu, V. Mînzu (2001). Self-balancing manufacturing systems regarded as hybrid dynamical systems. *Control Engineering and Applied Informatics* – Romanian Society of Control Engineering and Technical Informatics (SRAIT), 3(3), 11–16.

2. V. Mînzu, A. Bratcu (2000). Some results on the modelling of TSS manufacturing lines. *Annals of "Dunărea de Jos" University of Galați*, III (*Electrotechnics, Electronics, Automatic Control, Informatics*), 40–47. http://www.ann.ugal.ro/eeai/index.html.

3. V. Mînzu, D. Cernega, A. Bratcu (1998). A stochastic algorithm for treating the precedence constraints in discrete optimization problems. *Annals of "Dunărea de Jos" University of Galați*, III, 46–51. http://www.ann.ugal.ro/eeai/index.html.

### Articles in proceedings of IFAC and IEEE conferences

1. A. Bratcu, V. Mînzu (2001). Modelling and analysis of self-balancing manufacturing lines as hybrid dynamic systems. In: *Procs. of the 9th IFAC Symposium on Large Scale Systems: Theory & Applications – LSS 2001*, Bucharest, Romania, July 18–20 2001, pp. 37–42.
2. A. Bratcu, J.-M. Henrioud, V. Mînzu (2001). A look at self-balancing manufacturing lines through theory of hybrid dynamical systems. In: *Procs. of the 2001 IEEE International Symposium on Assembly and Task Planning – ISATP 2001*, Fukuoka, Japan, May 28–29 2001, pp. 375–380.

3. A. Bratcu, V. Mînzu (1999). A simulation study of self-balancing production lines. In: *Procs. of the 1999 IEEE International Conference on Intelligent Engineering Systems – INES 1999*, Stará Lesná, Slovakia, November 1–3 1999, pp. 165–170.

4. V. Mînzu, A. Bratcu, J.-M. Henrioud (1999). Construction of the precedence graphs equivalent to a given set of assembly sequences. In: *Procs. of the IEEE International Symposium on Assembly and Task Planning – ISATP 1999*, Porto, Portugal, July 21–24 1999, pp. 14–19.

**Articles in proceedings of other international conferences**

1. A. Bratcu (1999). Nonlinear modelling of a self-balancing production line. In: *Procs. of the 11th European Simulation Symposium – ESS 1999*, Erlangen, Germany, October 26–28 1999, pp. 481–483.

2. A. Bratcu, V. Mînzu, J.-M. Henrioud (1999). Equivalence between a given set of assembly sequences and a set of precedence graphs. In: *Procs. of the 12th International Conference on Control Systems and Computer Science – CSCS 12*, Bucharest, Romania, May 26–28 1999, pp. 295–300.

* *Other collaborations* during the same period issued the following publications:

**Articles in international journals without impact factor**

1. A. Bratcu, I. Bivol (1996). A control algorithm for an asynchronous machine imposing speed evolution. *Annals of "Dunărea de Jos" University of Galaţi*, III, 23–27. http://www.ann.ugal.ro/eeai/index.html.

**Articles in proceedings of IFAC conferences**

1. D. Cernega, A. Bratcu (1998). Design of a discrete event based supervisor for continuous processes. In: *Procs. of the 8th IFAC/IFORS/IMACS/IFIP Symposium on Large Scale Systems: Theory & Applications – LSS 1998*, Patras, Greece, July 15–17 1998, pp. 59–64.

2. C. Tudorie, V. Ariton, A. Bratcu (1998). Knowledge-based decision and conversation in a hybrid diagnosis system. In: *Procs. of the 8th IFAC/IFORS/IMACS/IFIP Symposium on Large Scale Systems: Theory & Applications – LSS 1998*, Patras, Greece, July 15–17 1998, pp. 51–54.

**1.11 Scientific publications 2002–2022**

Names of the different supervised Ph.D. students and post-doctoral fellows, as well as Master students, appear in **magenta** in the list below.

**Books**

1. S. Bacha, I. Munteanu, A.I. Bratcu (2013). *Power Electronic Converters Modelling and Control – With Case Studies*. Advanced Textbooks in Control and Signal Processing Series, Springer, London, U.K. ISBN 978-1-4471-5478-5, 454 pages.

2. I. Munteanu, A.I. Bratcu, N.A. Cutululis, E. Ceangă (2008). *Optimal control of wind energy systems – Towards a global approach*. Advances in Industrial Control Series, Springer, London, U.K. ISBN 978-1-84800-079-7, 283 pages.

3. A.I. Bratcu, A. Filipescu (2004). *Numerical methods used in analysis of dynamical systems* (in Romanian: *Metode numerice utilizate în analiza sistemelor – aplicații*). MatrixRom, Bucharest, Romania. ISBN 973-685-828-6, 142 pages.

4. E. Ceangă, I. Munteanu, A. Bratcu, M. Culea (2001). *Signals, circuits and systems. 1st Part: Signal analysis* (in Romanian: *Semnale, circuite și sisteme. Partea I: Analiza semnalelor*). Academica, Galați, Romania. ISBN 973-8316-16-2, 201 pages.

**Book chapters**

1. I. Munteanu, A.I. Bratcu, E. Ceangă (2013). Low-power wind energy conversion systems: generation configurations and control objectives. In: *Handbook of Wind Power Systems* (Eds. P. Pardalos et al.), pp. 773–803. Springer, London, U.K. ISBN 978-3-642-41080-2.
2. I. Munteanu, A.I. Bratcu, S. Bacha, D. Roye (2010). Real-time physical simulation of wind energy conversion systems. In: *Wind Power* (Ed. S.M. Muyeen), pp. 233–258. IN-TECH. ISBN 978-953-7619-81-7.

3. S. Belmokhtar, A.I. Bratcu, A. Dolgui (2006). Modular machining line design and reconfiguration: some optimization methods. In: *Manufacturing the Future: Concepts-Technologies-Visions* (Eds. V. Kordic, A. Lazinica, M. Merdan), ch. 5 (pp. 125–152). pro literatur Verlag, Mammendorf, Germany. ISBN 3-86611-198-3.

4. D.C. Cernega, A.I. Bratcu, A. Şerbencu (2005). Discrete event supervision for communication protocol conversion. In: *Intelligent Systems at the Service of Mankind II* (Eds. W. Elmenreich, J. Tenreiro Machado, I. J. Rudas), pp. 227–238. UBooks Verlag, Augsburg, Germany. ISBN 3-86608-052-2.

## International patents

1. A.M. Andreica, S. Bacha, A.I. Bratcu, J. Guiraud, I. Munteanu, D. Roye (Grenoble Institute of Technology, Electricité de France) (2009). *Hydraulic turbomachine for recovering and converting kinetic energy of water currents into electricity, has regulation units electrically regulating power from generator to ensure that shaft rotates at same speed relative to another shaft*. Patent WO2010020735-A1, FR2935159-A1.

## APP (Agence pour la Protection des Programmes – Software Protection Agency) software and know-how patent applications – alphabetical order of authors

1. A.I. Bratcu, I. Munteanu, J.-M.W. Nwesaty, O. Sename (2018). *K-INF Multi-source management system robust design*. Grenoble Institute of Technology, Grenoble Alpes University. APP software application, RT2018013, version 1.1 May 2018.

2. A.I. Bratcu, I. Munteanu (2019). *K-INF Multi-storage energy management system robust design for frequency regulation in AC microgrids*. Grenoble Institute of Technology, CNRS, Grenoble Alpes University. APP software application.

3. A.I. Bratcu, I. Munteanu (2020). *Design procedure of a robust multi-storage energy management for frequency regulation in AC microgrids*. Grenoble Institute of Technology, CNRS, Grenoble Alpes University. *Know-how patent application*.

## Articles in international journals with impact factor

1. Q-L. Lam, D. Riu, A.I. Bratcu, A. Labonne, C. Boudinet (2022). Power hardware-in-the-loop validation of primary frequency robust control in stand-alone microgrids with storage units. *Electrical Engineering* (Springer). To appear, DOI: 10.1007/s00202-022-01666-6.

2. R. Feizimirkhani, A.I. Bratcu, Y. Bésanger, A. Labonne, T. Braconnier (2021). A methodology for the evaluation of the message transmission delay over IEC 61850 communication network – a real-time HV/MV substation case study. *Sustainable Energy, Grids and Networks*, 28, art. no. 100555.

3. Q-L. Lam, A.I. Bratcu, D. Riu (2021). Multi-variable $H_\infty$ control approach for voltage ancillary service in autonomous microgrids: design and sensitivity analysis. *IEEE Access*, 9, 140212–140234.

4. J.-M.W. Nwesaty, A.I. Bratcu, A. Ravey, D. Bouquain, O. Sename (2020). Robust energy management system for multi-source DC energy systems – real-time setup and validation. *IEEE Transactions on Control Systems Technology*, 28(6), 2591–2599.

5. Q.L. Lam, A.I. Bratcu, C. Boudinet, M. Thomas, A. Labonne, D. Riu (2020). Primary frequency $H_\infty$ control in stand-alone microgrids with storage units: a robustness analysis confirmed by real-time experiments. *International Journal of Electrical Power and Energy Systems*, 115, art. no. 105507.

6. M. Hauck, A. Rumeau, A.I. Bratcu, S. Bacha, I. Munteanu, D. Roye (2018). Identification and control of a river-current-turbine generator – application to a full-scale prototype. *IEEE Transactions on Sustainable Energy*, 9(3), 1365–1374.

7. W. Nwesaty, A.I. Bratcu, O. Sename (2016). Power sources coordination through multivariable LPV/$H_\infty$ control with application to multi-source electric vehicles. *IET Control Theory and Applications*, 10(16), 2049–2059.
8. A. Florescu, A.I. Bratcu, I. Munteanu, A. Rumeau, S. Bacha (2015). LQG optimal control applied to on-board energy management system of all-electric vehicles. *IEEE Transactions on Control Systems Technology*, 23(4), 1427-1439.

9. A. Florescu, S. Bacha, I. Munteanu, A.I. Bratcu, A. Rumeau (2015). Adaptive frequency-separation-based energy management system for electric vehicles. *Journal of Power Sources*, 280, 410-421.

10. I. Munteanu, A.I. Bratcu (2015). MPPT for grid-connected photovoltaic systems using ripple-based extremum seeking control: analysis and control design issues. *Solar Energy*, 111, 30-42.

11. A. Burlibaşa, I. Munteanu, A.I. Bratcu (2014). Unitary power control strategy for low-power wind energy conversion system using active speed stall control for full-load regime. *IET Renewable Power Generation*, 8(6), 696-706.

12. C. Vlad, A.I. Bratcu, I. Munteanu, S. Epure (2014). Real-time replication of a stand-alone wind energy conversion system: error analysis. *International Journal of Electrical Power and Energy Systems*, 55, 562-571.

13. O. Crăciun, A. Florescu, I. Munteanu, A.I. Bratcu, S. Bacha, D. Radu (2014). Hardware-in-the-loop simulation applied to protection devices testing. *International Journal of Electrical Power and Energy Systems*, 54, 55-64.

14. A. Burlibaşa, I. Munteanu, A.I. Bratcu (2012). Control law design of a low-power wind energy system using active speed stall techniques. *Control Engineering and Applied Informatics* – Romanian Society of Control Engineering and Technical Informatics (SRAIT), 14(3), 15-24.

15. M. Vallet, I. Munteanu, A.I. Bratcu, S. Bacha, D. Roye (2012). Synchronized control of cross-flow-water-turbine-based twin towers. *Renewable Energy*, 48, 382-391.

16. M. Andreica Vallet, S. Bacha, I. Munteanu, A.I. Bratcu, D. Roye (2011). Management and control of operating regimes of cross-flow water turbines. *IEEE Transactions on Industrial Electronics*, 58(5), 1866-1876.

17. M. Hauck, I. Munteanu, A.I. Bratcu, S. Bacha, D. Roye (2011). Operation of grid-connected cross-flow water turbines in the stall region by direct power control. *IEEE Transactions on Industrial Electronics*, 58(4), 1132-1140.

18. A.I. Bratcu, I. Munteanu, S. Bacha, D. Picault, B. Raison (2011). Cascaded DC-DC converter photovoltaic systems: power optimization issues. *IEEE Transactions on Industrial Electronics*, 58(2), 403-411.

19. I. Munteanu, A.I. Bratcu, M. Andreica, S. Bacha, D. Roye, J. Guiraud (2010). A new method of real-time physical simulation of prime movers used in energy conversion chain. *Simulation Modelling Practice and Theory*, 18(9), 1342-1354.

20. I. Munteanu, A.I. Bratcu, S. Bacha, D. Roye, J. Guiraud (2010). Hardware-in-the-loop-based simulator for a class of variable-speed wind energy conversion systems: design and performance assessment. *IEEE Transactions on Energy Conversion*, 25(2), 564-576.

21. C. Vlad, I. Munteanu, A.I. Bratcu, E. Ceangă (2010). Output power maximization of low-power wind energy conversion systems revisited: possible control solutions. *Energy Conversion and Management*, 51(2), 305-310.

22. C. Vlad, I. Munteanu, A.I. Bratcu, E. Ceangă (2009). Anticipative control of low-power wind energy conversion systems for optimal power regime. *Control Engineering and Applied Informatics* – Romanian Society of Control Engineering and Technical Informatics (SRAIT), 11(4), 26-35.

23. I. Munteanu, A.I. Bratcu, E. Ceangă (2009). Wind turbulence used as searching signal for MPPT in variable-speed wind energy conversion systems. *Renewable Energy*, 34(1), 322-327.

24. A.I. Bratcu, A. Dolgui (2009). Some new perspectives in the analysis and simulation of bucket brigades (self-balancing production lines). *International Journal of Production Research*, Special Issue *Cutting Edge of French Community of Production Research*, 47(2), 369-387.

25. A.I. Bratcu, I. Munteanu, S. Bacha, B. Raison (2008). Maximum power point tracking of grid-connected photovoltaic arrays by using extremum seeking control. *Control Engineering and Applied Informatics* – Romanian Society of Control Engineering and Technical Informatics (SRAIT), 10(4), 3-12.
26. I. Munteanu, S. Bacha, A.I. Bratcu, J. Guiraud, D. Roye (2008). Energy-reliability optimization of wind energy conversion systems by sliding mode control. *IEEE Transactions on Energy Conversion*, 23(3), 975-985.

27. I. Munteanu, N.A. Cutululis, A.I. Bratcu, E. Ceangă (2005). Optimization of variable speed wind power systems based on a LQG approach. *Control Engineering Practice*, 13(7), 903-912.

28. A.I. Bratcu, A. Dolgui (2005). A survey of the self-balancing production lines ("bucket brigades"). *Journal of Intelligent Manufacturing*, 16(2), 139-158.

29. B. Rekiek, A. Dolgui, A. Delchambre, A. Bratcu (2002). State of art of optimization methods for assembly line design. *Annual Reviews in Control*, 26(2), 163-174.

### Under-review submissions

* Q-L. Lam, D. Riu, A.I. Bratcu (2022). Frequency Robust Control Application in Islanded Microgrids Considering Parametric Uncertainties and Distinct Photovoltaic Penetration Rate Scenarios. Submitted to *Iranian Journal of Science and Technology – Transactions of Electrical Engineering* (Springer).

### Articles in international journals without impact factor

1. S. Hajjar, A.I. Bratcu, A. Hably (2015). A day-ahead centralized unit commitment algorithm for a multi-agent smart grid. *Annals of Computer Science and Information Systems* – Polish Information Processing Society, 6, 265-271, on-line: http://dx.doi.org/10.15439/2015F227.

2. A. Scarlat, I. Munteanu, A.I. Bratcu, E. Ceangă (2010). Use of a configurable torque-speed dependence for power maximization of squirrel-cage-induction-generator-based wind energy conversion system. *Bulletin of the Polytechnic Institute of Iași – Automatic Control and Computer Science Section*, LVI(LX)(4), 41-60.

3. C. Vlad, I. Munteanu, A.I. Bratcu, E. Ceangă (2008). Optimal control in energy conversion of small wind power systems with permanent-magnet synchronous generators. *WSEAS Transactions on Systems and Control*, 3(7), 644-653.

4. I. Munteanu, S. Bacha, A.I. Bratcu, J. Guiraud, D. Roye (2007). Conception systématique des simulateurs temps réel hardware-in-the-loop – Application aux systèmes de conversion éolienne. *Journal Européen des Systèmes Automatisés* – Hermès-Lavoisier, 41(9-10), 1139-1164.

5. A.I. Bratcu, A. Dolgui (2007). Une généralisation du Modèle Normatif des lignes auto-équilibrées (« bucket brigades »). *Journal Européen des Systèmes Automatisés* – Hermès-Lavoisier, 41(3-4), 287-309.

6. I. Munteanu, N.A. Cutululis, A. Bratcu, E. Ceangă (2006). Using a nonlinear controller to optimize a variable speed wind power system. *Journal of Electrical Engineering*, 6(4), on-line: http://www.jee.ro/index.php/jee/article/view/WW1151314467W449faa23f2738.

### Articles in proceedings of IFAC and IEEE conferences
IFAC

1. R. Ghassani, A.I. Bratcu, R. Teodorescu (2022). Genetic algorithm applied to state-feedback control design of grid and circulating current in modular multilevel converters. In: *Procs. of the 11th IFAC Symposium on Control of Power and Energy Systems – CPES 2022*, virtual, June 21–23 2022.

2. A.I. Bratcu, R. Teodorescu (2020). State-feedback control of grid and circulating current in modular multilevel converters. In: *Procs. of the 21st IFAC World Congress*, Berlin, Germany, July 12–17 2020. IFAC-PapersOnLine, 53(2), 12396-12401.

3. R. Feizimirkhani, A.I. Bratcu, Y. Bésanger (2018). Time-series modelling of IEC 61850 GOOSE communication traffic between IEDs in smart grids – a parametric analysis. In: *Procs. of the 10th IFAC Symposium on Control of Power and Energy Systems – CPES 2018*, Tokyo, Japan, September 4–6 2018. IFAC-PapersOnLine, 51(28), 444-449.
4. Q.L. Lam, A.I. Bratcu, D. Riu (2016). Robustness analysis of primary frequency H-inf control in stand-alone microgrids with storage units. In: *Procs. of the 2016 IFAC Workshop on Control of Transmission and Distribution Smart Grids – CTDSG 2016*, Prague, Czech Republic, October 11–13 2016. IFAC-PapersOnLine, 49(27), 123–128.

5. W. Nwesaty, A.I. Bratcu, O. Sename (2015). Reduced-order LPV controller for coordination of power sources within multi-source energy systems. In: *Procs. of the 8th IFAC Symposium on Robust Control Design – ROCOND 2015*, Bratislava, Slovakia, July 8–11 2015. IFAC-PapersOnLine, 48(14), 132–137.

6. W. Nwesaty, A.I. Bratcu, O. Sename (2014). MIMO Hinf control for power source coordination – application to energy management systems of electric vehicles. In: *Procs. of 19th IFAC World Congress 2014*, Cape Town, South Africa, August 2014, pp. 3905–3911.

7. A. Florescu, A.I. Bratcu, I. Munteanu, S. Bacha (2012). Energy management system within electric vehicles using ultracapacitors: an LQG-optimal-control-based solution. In: *Procs. of the 15th IFAC Workshop on Control Applications of Optimization – CAO 2012*, Rimini, Italy, September 2012, pp. 229–234.

8. A.I. Bratcu, D.C. Cernega, I. Munteanu (2006). Supervisory control of grid connected wind power systems to guarantee safe operation. In: *Procs. of the 3rd IFAC Workshop on Discrete-Event System Design – DESDes 2006*, Rydzyna, Poland, September 26-28 2006, pp. 117–122.

9. I. Munteanu, A.I. Bratcu, N.A. Cutululis, E. Ceangă (2005). A two loop optimal control of flexible drive train variable speed wind power systems. In: *IFAC Proceedings Volumes – Procs. of the 16th Triennial IFAC World Congress*, 38(1), 344–349.

10. A.I. Bratcu, D. Dulman, I. Munteanu, A. Dolgui (2004). Optimal motion planning of cooperative mobile robots in 2D environments. In: *Procs. of the 3rd IFAC Conference on Management and Control of Production and Logistics – MCPL 2004*, Santiago, Chile, November 3–5 2004, pp. 223–228.

11. I. Munteanu, A.I. Bratcu, L. Frangu (2004). Nonlinear control for stationary optimization of wind power systems. In: *Procs. of the IFAC Workshop on Automatic Systems for Building the Infrastructure in the Developing Countries – DECOM-TT 2004*, Bansko, Bulgaria, October 3–5 2004, pp. 195–200.

12. A.I. Bratcu, A. Dolgui (2003). Synergy, Collaboration and Self-Balancing in Production Systems – The Bucket Brigades. In: *Procs. of the IFAC Workshop Intelligent Assembly and Disassembly – IAD 2003*, Bucharest, Romania, October 9–11 2003, pp. 78–83.

13. I. Munteanu, E. Ceangă, N.A. Cutululis, A. Bratcu (2003). Linear quadratic optimization of variable speed wind power systems. In: *Procs. of the IFAC Workshop on Control Application of Optimisation – CAO 2003*, Visegrad, Hungary, June 30 – July 2 2003, pp. 162–167.

14. B. Rekiek, A. Delchambre, A. Dolgui, A. Bratcu (2002). Assembly line design: a survey. In: *Plenary Papers, Survey Papers and Milestones of the 15th Triennial IFAC World Congress*, Barcelona, Spain, July 21–26 2002, pp. 131–142.

15. A. Bratcu (2002). On the modelling of bucket brigades. In: *IFAC Proceedings Volumes – Procs. of the 15th Triennial IFAC World Congress*, 35, 97–102.

### Under-review submissions

* I. Munteanu, A.I. Bratcu (2022). HILS-based demonstrator for real-time validation of robust control strategies: an electric vehicle application case. Submitted to *2023 IFAC World Congress*, Yokohama, Japan.

### IEEE

1. R. Feizimirkhani, V.H. Nguyen, Y. Bésanger, Q.T. Tran, A.I. Bratcu, A. Labonne, T. Braconnier (2021). Application of Long Short-Term Memory (LSTM) neural network for the estimation of communication network delay in smart grid applications. In: *Procs. of 2021 IEEE International Conference on Environment and Electrical Engineering and 2021 IEEE Industrial and Commercial Power Systems Europe – EEEIC/I&CPS Europe 2021*, Bari, Italy, September 7–10 2021, pp. 1–6.
2. A.I. Bratcu, F. Ihuel, A. Contrepois (2021). Two-level state-space-based control strategy of Katium-power-converter-based Li-ion battery charger for railway applications. In: *Procs. of the 23rd European Conference on Power Electronics and Applications – EPE ECCE 2021*, Ghent, Belgium, September 6–10 2021, pp. 1–9.

3. A.I. Bratcu, F. Ihuel, A. Contrepois (2021). Katium-power-converter-based Li-ion battery charger for railway applications: control-oriented modelling. In: *Procs. of the 2021 IEEE Conference on Control Technology and Applications – IEEE CCTA 2021*, San Diego, California, U.S.A., August 9–11 2021, pp. 583–588.

4. M. Almeida Barbosa, K. Gül, A.I. Bratcu, I. Munteanu (2019). Management of a photovoltaic-battery-based microgrid in a prosumer context. In: *Procs. of the 6th International Symposium on Electrical and Electronics Engineering – ISEE 2019*, Galați, Romania, October 18–20 2019, pp. 1–6.

5. R. Feizimirkhani, A.I. Bratcu, Y. Bésanger, A. Labonne, T. Braconnier (2019). Modeling of IEC 61850 GOOSE substation communication traffic using ARMA model. In: *Procs. of the 2019 IEEE PES Innovative Smart Grid Technologies – ISGT-Europe 2019*, Bucharest, Romania, September 29 – October 2 2019, pp. 1–5.

6. R. Rezvani, A.I. Bratcu. Robust control of a single-ended primary-inductor converter (SEPIC) (2017). In: *Procs. of the 5th International Symposium on Electrical and Electronics Engineering – ISEE 2017*, Galați, Romania, October 20–22 2017, pp. 1–6.

7. T. Peirelinck, A.I. Bratcu, Y. Bésanger (2016). Impact of IEC 61850 GOOSE communication quality on decentralized reactive power control in smart distribution grids – a co-simulation study. In: *Procs. of the 2016 IEEE Electrical Power and Energy Conference – EPEC 2016*, Ottawa, Canada, October 12–14 2016, pp. 1–6.

8. Q.L. Lam, A.I. Bratcu, D. Riu (2016). Systematic multi-variable H-infinity control design for primary frequency regulation in stand-alone microgrids with high penetration of renewable energy sources. In: *Procs. of the 15th European Control Conference – ECC 2016*, Aalborg, Denmark, June 29 – July 1st 2016, pp. 1794–1799.

9. E. Sharma, A.I. Bratcu, C. Chiculiță, Y. Bésanger (2015). Co-simulation of a low-voltage utility grid controlled over IEC 61850 protocol. In: *Procs. of the IEEE 5th International Conference on Electric Utility Deregulation and Restructuring and Power Technologies – DRPT 2015*, Changsha, China, November 26–29 2015, pp. 2365–2372.

10. A.I. Bratcu, V. Aulagnier (2015). Control of energy storage systems for three-phase applications. In: *Procs. of the 19th International Conference on System Theory, Control and Computing – ICSTCC 2015*, Cheile Grădiștei – Fundata Resort, Romania, October 14–16 2015, pp. 666–672.

11. J.A. Fernandez, A. Hably, A.I. Bratcu (2015). Assessing the economic profit of a vehicle-to-grid strategy for current unbalance minimization. In: *Procs. of 2015 IEEE International Conference on Industrial Technology – ICIT 2015*, Seville, Spain, March 17–19 2015, pp. 2628–2635.

12. Q.-L. Lam, D. Riu, A.I. Bratcu, J. Mongkoltanatas (2015). Multi-variable H-infinity robust control applied to primary frequency regulation in micro-grids with large integration of photovoltaic energy source. In: *Procs. of the 2015 IEEE International Conference on Industrial Technology – ICIT 2015*, Seville, Spain, March 17–19 2015, pp. 2921–2928.

13. W. Nwesaty, A.I. Bratcu, O. Sename (2014). Optimal frequency separation of power sources by multivariable LPV/H<sub>∞</sub> control: application to on-board energy management systems of electric vehicles. In: *Procs. of 2014 IEEE 53rd Annual Conference on Decision and Control – CDC 2014*, Los Angeles, California, U.S.A., December 15–17 2014, pp. 5636–5641.

14. W. Nwesaty, A.I. Bratcu, O. Sename (2014). LPV control for power source coordination – application to electric vehicles energy management systems. In: *Procs. of the 13th European Control Conference – ECC 2014*, Strasbourg, France, June 25–27 2014, pp. 2649–2654.
15. A. Florescu, S. Bacha, A. Rumeau, I. Munteanu, A.I. Bratcu (2013). PHIL simulation for validating power management strategies in all-electric vehicles. In: *Procs. of the 15th European Conference on Power Electronics and Applications – EPE 2013-ECCE Europe*, Lille, France, September 2–6 2013, pp. 1–6.

16. W. Nwesaty, A.I. Bratcu, A. Hably (2013). Extremum seeking control techniques applied to photovoltaic systems with multimodal power curves. In: *Procs. of International Conference on Renewable Energy Research and Applications – ICRERA 2013*, Madrid, Spain, October 20–23 2013, pp. 85–90.

17. M. Hauck, A. Rumeau, I. Munteanu, A.I. Bratcu, S. Bacha, D. Roye, A. Hably (2012). A 1:1 prototype of power generation system based upon cross-flow water turbines. In: *Procs. of the IEEE International Symposium on Industrial Electronics 2012 – ISIE 2012*, Hangzhou, China, May 28–31 2012, pp. 1414–1418.

18. A. Florescu, S. Bacha, I. Munteanu, A.I. Bratcu, A. Rumeau (2012). Results concerning ultracapacitor-based energy management strategy within electric vehicle. In: *Procs. of the 16th International Conference on System Theory, Control and Computing – ICSTCC 2012*, Sinaia, Romania, October 12–14 2012, pp. 1–7.

19. A. Florescu, S. Bacha, I. Munteanu, A.I. Bratcu (2012). Frequency-separation-based energy management control strategy of power flows within electric vehicles using ultracapacitors. In: *Procs. of the 38th Annual Conference of IEEE Industrial Electronics Society – IECON 2012*, Montreal, Canada, October 25–28 2012, pp. 2957–2964.

20. O. Crăciun, A. Florescu, I. Munteanu, S. Bacha, A.I. Bratcu, D. Radu (2011). Protection devices testing based on power-hardware-in-the-loop simulation. In: *Procs. of the 37th Annual Conference of IEEE Industrial Electronics Society – IECON 2011*, Melbourne, Australia, November 7–10 2011, pp. 3736–3741.

21. A. Scarlat, I. Munteanu, A.I. Bratcu, E. Ceangă (2010). Stability analysis for an improved power optimization method applied to a wind energy conversion system. In: *Procs. of the 3rd International Symposium on Electrical and Electronics Engineering – ISEE 2010*, Galaţi, Romania, September 16–18 2010, pp. 187–192.

22. O. Crăciun, A. Florescu, S. Bacha, I. Munteanu, A. I. Bratcu (2010). Hardware-in-the-loop testing of PV control systems using RT-Lab simulator. In: *Procs. of 14th International Power Electronics and Motion Control Conference – EPE-PEMC 2010*, Ohrid, Macedonia, September 6–8 2010, pp. S2-1–S2-6.

23. M. Andreica, S. Bacha, D. Roye, I. Munteanu, A.I. Bratcu, J. Guiraud (2009). Cross-flow water turbines control under grid disturbances. In: *Procs. of IEEE PowerTech 2009*, Bucharest, Romania, June 28 – July 2 2009, pp. 1–6.

24. A.I. Bratcu, I. Munteanu, S. Bacha, D. Picault, B. Raison (2009). Power optimization strategy for cascaded DC-DC converter architectures of photovoltaic modules. In: *Procs. of the IEEE International Conference on Industrial Technology – ICIT 2009*, Churchill, Victoria, Australia, February 10–13 2009, pp. 1–8.

25. M. Andreica, S. Bacha, D. Roye, I. Munteanu, A.I. Bratcu, J. Guiraud (2009). Stand-alone operation of cross-flow water turbines. In: *Procs. of the IEEE International Conference on Industrial Technology – ICIT 2009*, Churchill, Victoria, Australia, February 10–13 2009, pp. 1–6.

26. A.I. Bratcu, I. Munteanu, E. Ceangă (2008). Optimal control of wind energy conversion systems: from energy optimization to multi-purpose criteria – a short survey. In: *Procs. of the 16th IEEE Mediterranean Conference on Control and Automation – MED 2008*, Ajaccio, France, June 25–27 2008, pp. 759–766.

27. A.I. Bratcu, I. Munteanu, E. Ceangă, S. Epure (2007). Energetic optimization of variable speed wind energy conversion systems by extremum seeking control. In: *Procs. of the IEEE Region 8 EUROCON 2007 International Conference on Computer as a Tool*, Warsaw, Poland, September 9–12 2007, pp. 2536–2541.

28. A.I. Bratcu, I. Munteanu, D.C. Cernega, M. Culea (2007). Safe and optimal operation of grid connected wind power systems by supervisory control. In: *Procs. of the IEEE Region 8 EUROCON 2007 International Conference on Computer as a Tool*, Warsaw, Poland, September 9–12 2007, pp. 2542–2549.

29. I. Munteanu, J. Guiraud, D. Roye, S. Bacha, A.I. Bratcu (2006). Sliding mode energy-reliability optimization of a variable speed wind power system. In: *Procs. of the 9th IEEE Workshop on Variable Structure Systems – VSS 2006*, Alghero Italy, June 5–7 2006, pp. 92–97.
30. A.I. Bratcu, A. Dolgui, S. Belmokhtar (2005). Reconfigurable transfer lines cost optimization – a linear programming approach. In: *Procs. of the 10th IEEE International Conference on Emerging Technologies and Factory Automation – ETFA 2005*, Catania, Italy, September 19–22 2005, pp. 625–632.

31. A.I. Bratcu (2004). A heuristic to minimize the equipment cost for large transfer lines with operations parallelization. In: *Procs. of the IEEE Conference on Intelligent Engineering Systems – INES 2004*, Cluj-Napoca, Romania, September 19–21 2004, pp. 579–583.

32. D.C. Cernega, A.I. Bratcu (2004). Communication protocol conversion solved by discrete event supervision. In: *Procs. of the IEEE Conference on Intelligent Engineering Systems – INES 2004*, Cluj-Napoca, Romania, September 19–21 2004, pp. 339–343.

33. A.I. Bratcu, L. Makdessian, A. Dolgui (2003). Minimisation of equipment cost for transfer lines with blocks of parallel tasks. In: *Procs. of the 5th IEEE International Symposium on Assembly and Task Planning – ISATP 2003*, Besançon, France, July 9–11 2003, pp. 109–114.

## Articles in proceedings of other international conferences

1. Q.-L. Lam, A.I. Bratcu, D. Riu (2018). Voltage regulation in stand-alone microgrids with storage units: a multi-variable H-infinity control approach. In: *Procs. of CIRED Workshop 2018 on Microgrids and local energy communities*, Ljubljana, Slovenia, June 7–8 2018, paper 0511 (4 pages).

2. A. Scarlat, I. Munteanu, A.I. Bratcu, E. Ceangă (2011). Control and management of high-power wind energy conversion system operating regimes: towards aerodynamic-compliant energy performance. In: *Procs. of the 18th International Conference on Control Systems and Computer Science – CSCS 2011*, Bucharest, Romania, May 24–27 2011, 8 pages.

3. A. Scarlat, I. Munteanu, A.I. Bratcu, E. Ceangă (2010). Improved power optimization method for squirrel-cage-induction-generator-based wind energy conversion systems. In: *Procs. of the 14th International Conference on System Theory and Control – ICSTCC 2010*, Sinaia, Romania, October 17–19 2010, pp. 491–496.

4. C. Vlad, I. Munteanu, A.I. Bratcu, E. Ceangă (2008). A peak power tracker for low-power permanent-magnet-synchronous-generator-based wind energy conversion systems. In: *Procs. of the 12th WSEAS International Conference on Systems*, Heraklion, Greece, July 22–24 2008, pp. 407–412.

5. N.A. Cutululis, H. Bindner, I. Munteanu, A. Bratcu, E. Ceangă, P. Soerensen (2006). LQ optimal control of wind turbines in hybrid power systems. In: *Procs. of the European Wind Energy Conference – EWEC 2006*, Athens, Greece, February 27 – March 2 2006.

6. A.I. Bratcu, D. Dulman, I. Munteanu (2005). A two level optimal control structure for cooperative robot systems. In: *Procs. of the 14th International Workshop on Robotics in Alpe-Adria-Danube Region – RAAD 2005*, Bucharest, Romania, May 26–28 2005, pp. 268–273.

7. A.I. Bratcu, I. Munteanu, D. Dulman (2005). Maximum power point tracking for wind power systems: a minimal knowledge approach. In: *Procs. of the 15th International Conference on Control Systems and Computer Science – CSCS 2005*, Bucharest, Romania, May 25–27 2005.

8. I. Munteanu, N.A. Cutululis, A. Bratcu, E. Ceangă (2004). Using a nonlinear controller to optimize a variable speed wind power system. In: *Procs. of the 9th International Conference on Optimization of Electrical and Electronic Equipments (IEEE sponsored) – OPTIM 2004*, Braşov, Romania, May 20–23 2004, pp. 303–311.

9. A. Bratcu, A. Dolgui, L. Makdessian, F. Yalaoui (2002). Balancing and optimal cost resource planning of production lines with blocks of parallel tasks. In: *Procs. of the 1st CIRP (U.K.) International Seminar on Digital Enterprise Technology – DET 2002*, Durham, U.K., September 16–17 2002, pp. 159–162.

## Francophone conferences

1. A.I. Bratcu, I. Munteanu, D.C. Cernega (2006). Modélisation à évènements discrets d'un système éolien à vitesse variable en vue de la commande supervisée. In: *Actes de la 6-ième Conférence Francophone de Modélisation et Simulation – MOSIM 2006*, Rabat, Maroc, April 3–5 2006. Lavoisier, CD-ROM, ISBN 2-7430-0893-8.
2. I. Munteanu, J. Guiraud, S. Bacha, D. Roye, A.I. Bratcu (2006). Méthodologie de simulation temps reel hardware-in-the-loop – application aux systèmes éoliens. In: *Actes de la 6-ième Conférence Francophone de Modélisation et Simulation – MOSIM 2006*, Rabat, Maroc, April 3–5 2006. Lavoisier, CD-ROM, ISBN 2-7430-0893-8.

3. A.I. Bratcu, A. Dolgui (2003). Lignes auto-equilibrées : nouveau concept, analyse et modélisation. In: *Revue des Systèmes* (Lavoisier), hors série/4-ième Colloque Francophone sur la Modélisation des Systèmes Réactifs – *MSR 2003*, pp. 195-209.

4. A.I. Bratcu, A. Dolgui (2003). Une relaxation du Modèle Normatif des lignes de production auto-équilibrées (« bucket brigades »). *Actes de la 4-ième Conférence Francophone de Modélisation et Simulation – MOSIM 2003*, Toulouse, France, April 23–25 2003, SCS European Publishing House, pp. 262–269.

## Articles in proceedings of national conferences (France)

1. Q.L. Lam, A.I. Bratcu, D. Riu (2016). Frequency robust control in stand-alone microgrids with PV sources: design and sensitivity analysis. In: *Actes du 2-ième Symposium de Génie Électrique – SGE 2016*, Grenoble, France, June 7–9 2016, 8 pages.
<figure><img src="image_5.png" /></figure>
# Chapter 2

# Necessity and motivation of the proposed scientific approach

## 2.1 Control-oriented characterization of renewable energy conversion systems (RECS)

In order to fix ideas and for justifying necessity of our approach and well positionning our contributions related to control of renewable energy conversion systems (RECS), we will start in a *system* context, namely by considering a generic global block diagram of a *microgrid* built around a RECS based on a generic primary energy converter, as presented in Fig. 2.1. The microgrid concept dates back to some twenty years ago (for a comprehensive presentation, see, for example [1]); its interest from both research and economical viewpoints has constantly increased since then. The microgrid in Fig. 2.1 is equipped with a generic storage and power electronic interfaces playing the role of actuators for control.

The *primary energy converter* is led by the uncontrollable, random and intermittent variations of the natural resource involved, whose *non electrical* energy is converted into *electrical* energy to be further conveyed to what is generically identified in Fig. 2.1 as the "Electrical AC grid". This converter can, for example, be either a rotating prime mover coupled with a rotating electrical machine in the case of wind energy or micro-hydro conversion systems, or photovoltaic (PV) panels obeying the photoelectric effect principle.

The two power electronic interfaces – grid-side and primary-converter-side, respectively – are coupled in a way such as to materialize an intermediary DC bus, thus enabling what is commonly called a *back-to-back structure*. Existence of this DC bus allows a generic storage being inserted – but also a more complex DC microgrid in the general case – with the role of compensating for the renewable source intermittency. The *primary-converter-side power electronic interface* is typically a converter with voltage-boost function, allowing to obtain an output DC-bus voltage at a higher level than the input one; it is by means of controlling this interface that one imposes the operating point of the primary energy converter. As regards the *grid-side power electronic interface*, this is typically an inverter, in charge with grid variables control (e.g., injection of sinusoidal currents into the grid).

Different operation modes of such energy conversion system may be defined, essentially depending of the connection nature to the AC grid [2]–[4]. Thus, two main operating modes exist, namely *grid forming* – when the generation part of the system is connected to a small-power microgrid (experienced as a load) – and *grid*
<figure><img src="image_6.png" /><figcaption>Figure 2.1: Generic global block diagram of a renewable-energy-based microgrid as generation system with generic storage, featuring back-to-back connection of power electronic converters by means of a common DC bus.</figcaption></figure>

**following** – when the generation system is connected to the strong utility (infinite-power) grid. The two modes are directly translated in terms of control objectives of the *grid power electronic interface* – generically and globally indicated on the figure as "Grid control" – thus:

* in the *grid-forming* mode the main objective is to maintain the output (*load*) voltage (*V*) and frequency (*f*) constant – this is why this mode is also called the *Vf* mode. The resulted microgrid operates in the so-called *off-grid* mode because it is not connected to the main, strong grid – this is also called *autonomous* or *stand-alone* operation [5], [6]. In this mode the role of the "Primary energy converter control" is:

- either *to maintain the DC-bus voltage as constant*, if the storage system is absent,

- or *to impose the operating point of the renewable source (primary energy converter) if the storage system is present and equipped of some local energy/power management system able to ensure a constant DC-bus voltage – a battery management system (BMS) is a typical example*;

* in the *grid-following (grid-connected or on-grid)* mode the main objective consists in controlling levels of output (*grid*) active and reactive power (*P* and *Q*, respectively), thus allowing participation of the renewable-energy-based system to *ancillary services* – this is why this mode is also called the *PQ mode* [7], [8]. In this mode two cases may appear:

- either the demanded power, *P*\*, is less than the renewable source's maximum power, *P*<sub>RENEmax</sub>: *P*\* < *P*<sub>RENEmax</sub>.

The required power level, *P*\*, can only be guaranteed if a storage system is present. In this case the renewable source becomes *dispatchable* due to presence of storage, which ensures that DC-bus voltage to be constant. Therefore, the role of the "Primary energy converter control" is *to impose the operating point of the renewable source*;
- or the renewable source is **not dispatchable** because there is no storage system, and then it is required to provide the maximum power available in the resource: $P^* = P_{RENEmax}$.

In this case the DC-bus voltage is maintained constant by the "Grid control", that is, at inverter level, whereas the "Primary energy converter control" imposes the maximum operating point of the renewable source. A Maximum Power Point Tracking (MPPT) control must then be put in place, in order to track a priori unknown renewable resource variations, whom available maximum power, $P_{RENEmax}$, actually depends on – see, for example, [9], [10], for MPPT statement and basic implementation in the case of wind turbines.

Therefore, MPPT is a focal control problem, intriguingly challenging mainly because the maximum power point changes with the resource in a generally unknown and unpredictable manner. Indeed, primary renewable energy converters are characterized by **unimodal power curves** for a given renewable resource level. Two examples are suggested in Fig. 2.1:

* of a **PV** system: the PV pannel power, *P*, **unimodal** dependence on PV pannel voltage, *V*, plotted for different **solar irradiance** levels;

* of a **wind energy conversion system** (WECS): the power coefficient, $C_p$, **unimodal** dependence on wind turbine's blade pitch angle, $\beta$, and on tip speed ratio, $\lambda$, which in turn depends on the **wind speed** and also on the turbine rotational speed. The power harvested from wind depends on $C_p$, which expresses the wind turbine efficiency.

The power coefficient is defined for any rotating prime mover (another example are water turbines). In the case of rotating prime movers the **variable-speed operation** [11] is a concept enabling MPPT implementation.

The locus of all maximum power points is called the **Optimal Regimes Characteristic** (ORC). Irrespective of the primary energy converter nature, MPPT strategies may in a first place be based on *a priori* sufficient knowledge of maximum power points (and the ORC), namely obtained from an as complete as possible *off-line* identification of static power characteristics. However, it may be necessary that such identification to be resumed after some time, because of parameters' deviations over time in relation with their nominal (rated) values.

But, in most of cases, ORC exact description is not known. **Control challenge is then formulated as being able to track the renewable energy variations in real time, based on minimal knowledge about the system, in particular, about the ORC.** Contributions having come as a possible response to this control challenge of **MPPT for RECS** are summarized in Chapter 3 of this memoir and concern:

* both **ORC-good-knowledge-case**, namely state-of-the-art, conventional MPPT implementations – in Section 3.3 for water-turbine-based (micro-hydro) systems,

* and also **ORC-minimal-knowledge-case**, namely by using **Extremum Seeking Control (ESC)** techniques [12], [13] in two versions:

- by **inducing exogenous periodic disturbances** into the system in order to identify direction towards the maximum power point, therefore, its position – in Section 3.4 for PV systems;

- by **using disturbances already existing in the system**:

* in Section 3.2 in the case of WECS, where wind speed turbulence component (modelled as a coloured noise) is used as excitation signal in ESC,

* and in Section 3.4 for some particular – meanwhile largely used – grid-connected PV system configurations, where the sinusoidal ripple of some variables is used as excitation signal in ESC.

Implementation of **an energy-reliability trade-off by optimal control techniques for WECS** is another topic summarized in Chapter 3, which is dedicated to control of all types of RECS. It is about configuring the best trade-off between two antagonistic demands: **maximizing the power** harvested from wind by tracking the ORC irrespective of the wind speed variations, **meanwhile minimizing efforts** for doing that, which leads in turn at mechanical fatigue reduction, thus preserving reliability. Contributions reported in Section 3.2 concern two control methods used to this end:
* a frequency-separation-based formulation of mixed-criteria dynamic optimization, further allowing to cast the high-frequency-related subproblem into the Linear Quadratic Gaussian (LQG) control formalism,

* and Sliding Mode (SM) control, based upon defining a wind-speed-varying switching surface,

with the remark that the same general formal approaches can be applied (possibly with adaptations) to any rotating-prime-mover-based RECS.

Finally, some of the contributions in Chapter 3, namely in Section 3.3, concern a larger viewpoint, with application to water-turbine-based (micro-hydro) energy conversion systems, such as:

* direct active power control, referring to grid-connected (otherwise said, *PQ*) operation, where possibility of operating a RECS as a *dispatchable* power generation system *despite absence of a storage unit* is investigated;

* designing some proper management of "smooth" switching between the two modes – *Vf* and *PQ* – as a renewable generation system like the one in Fig. 2.1 may be required to switch between the grid-forming (*stand-alone*) and the grid-following (*grid-connected*) modes;

* and also synchronization of two rotating-prime-mover-based RECS for some global purpose, e.g., alleviating mechanical efforts inside of a master-slave configuration.

## 2.2 Control approach to exploit complementarity within multi-source/hybrid electrical energy systems (MSES)

Decision of integrating energy sources of different types and technologies must obviously be based on the conclusion that these sources behave better together than each alone. Thus, existence of the *complementarity between the sources* is here exploited as a first good premise, whereas their *coordinated* – possibly *optimal* with regard to some well-defined criterion – *behaviour can only be guaranteed by control action* [14]–[16].

<figure><img src="image_7.png" /><figcaption>Figure 2.2: General configuration of a microgrid with classical and renewable sources and different types of storage, coupled in parallel on a common DC link, supplying both AC and DC loads.

Such a microgrid can operate in either grid-forming (stand-alone) or grid-connected mode, as previously explained in Section 2.1. In either case, sources' power flows are managed by a *Power Management System (PMS)*, which embeds the control algorithm ensuring proper coordination of sources in view of a</figcaption></figure>

Configuration of a generic multi-source-based microgrid as in Fig. 2.2 is considered; partial configurations of this one are also illustrative. It is equipped of *classical* – Diesel generator, thermal generator – as well as *renewable sources* – solar panels, wind turbine – of *storage units* of diverse technologies – batteries, supercapacitors (ultracapacitors), fuel cells – and also of (possibly both) AC and DC loads.
common goal. Power flow management exhibits faster dynamics than those controlled at the level of an *Energy Management System (EMS)*, thus PMS are placed nearer to the plant and lower in a possible multiple-layer control hierarchy. In particular, the PMS is the one implementing the effective coordination between sources in the sense of taking profit of their complementarity.

*In this context notion of complementarity between two power source technologies refers specifically to their respective dynamic abilities in providing energy in a longer or a shorter term.* Hence, complementarity supposes different variation speeds of the provided energy, thus different response times. It is therefore its *dynamic* substrate that enables complementarity to justify and meanwhile be exploited for control and coordination purposes.

*Dynamic specialization* of sources is best represented by Ragone plot [17], whose a quite complete version is resumed here in Fig. 2.3, where *dynamic specialization range* of each storage source can be identified through the relation between its *energy density* (*specific energy*) and its *power density* (*specific power*). A large span of storage technologies is illustrated:

* from *high-specific-energy* storage sources, such as fuel cells – able to provide energy in a long term, otherwise called "energy sources" for this reason, so specialized in the *low-frequency* range when talking about energy variations –

* to the *high-specific-power* sources, such as ultracapacitors (supercapacitors) – able to provide energy very quickly, otherwise called "power sources", so specialized in the *high-frequency* range,

with different electrochemical storage (e.g., batteries) or mechanical storage (e.g., flywheels) technologies being placed in between.

<figure><img src="image_8.png" /><figcaption>Figure 2.3: Ragone plot: dynamic specialization of different source/storage technologies.</figcaption></figure>

Notion of *characteristic (own) frequency of a source* was introduced to quantify more precisely its dynamic specialization range:

$$f_p = \frac{\rho_p}{\rho_e}, \qquad (2.1)$$

where $\rho_p$ is the power density, measured in W/kg and read on the abscissa of Ragone plot, and $\rho_e$ is the energy density, measured in J/kg and represented on the ordinate. Fig. 2.4 presents characteristic frequency values for some of the main storage technologies.

It is thus clear that a given source behaves best when exploited in its specialization range – i.e., when variation spectrum of the power demand is placed *around its characteristic frequency* – because its *reliability* and *lifetime* are best ensured this way. Reliability requirements may impose

the decision to suitably complement – otherwise said, to *hybridize* – a high-energy-density source, also identified as *main source*, by a high-power-density one, identified as *auxiliary source*, in order to protect the first from possible damages due to unappropriate exploitation outside its specialization range. Two classes of indicators for hybridization are important in a first place for initial sizing and rating the hybrid source/storage system:

* *power potential of hybridization (PPH)*: based on the possibility of reducing the main source's size – in terms of rated power, weight, cost, etc. – due to the presence of the auxiliary one

* *energy potential of hybridization (EEH)*: based on taking into account variation spectrum of load power and also regularity of charging/discharging cycles of the main source if this is a storage one.

In such a hybrid tandem the auxiliary source will supply the high-magnitude fast variations of power demand, which the main source is not specialized to supply. Note that the simple decision to put together these two types
<figure><img src="image_9.png" /><figcaption>Figure 2.4: Characterization of main storage technologies by their characteristic frequencies.</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Figure 2.5: Simplified block diagram of a hybrid two-storage-unit supply system in a stand-alone microgrid.</figcaption></figure>

of sources is not sufficient to guarantee their *realiability-aware operation*, a multi-source PMS must also be designed to appropriately coordinate them – this action supposes, irrespective of the method employed, that sources be *dynamically separated*. We will then talk about dynamic separation or, equivalently, *frequency separation* of sources. Moreover, in order to exhaust all optimization possibilities, *PMS design may already be considered in the phase of initial system sizing* – this kind of approach is called *system-control co-design*.

To further fix ideas, a partial version of the generic microgrid in Fig. 2.2 is considered, namely in the form of a *hybrid two-storage-unit* supply system, materializing a stand-alone microgrid. Simplified block diagram in Fig. 2.5 shows both sources, the main one and the auxiliary one, coupled in parallel to a common DC link by means of two-quadrant converters ensuring their bidirectionality (charging/discharging) and further interacting with a load/source. Roles of the two-quadrant converters can, for example, be ensured by synchronous buck converters.

A *battery-ultracapacitor* supply system on board of an electric vehicle (EV) is a typical instance in this regard, which originally motivated the approach detailed here. This motivation – based on collaboration with Ph.D. student Adrian FLORESCU, co-supervised by Professor Seddik BACHA and myself, and post-doctoral fellow Iulian MUNTEANU, with the help of R&D engineer Axel RUMEAU – is developed next and issued the two main journal publications below:

* A. Florescu, S. Bacha, I. Munteanu, A.I. Bratcu, A. Rumeau (2015). Adaptive frequency-separation-based energy management system for electric vehicles. *Journal of Power Sources*, 280, 410–421.

* A. Florescu, A.I. Bratcu, I. Munteanu, A. Rumeau, S. Bacha (2015). LQG optimal control applied to on-board energy management system of all-electric vehicles. *IEEE Transactions on Control Systems Technology*, 23(4), 1427–1439.

The most intuitive implementation of a frequency-separation PMS for the hybrid system in Fig. 2.5 is by means of a *frequency splitter* – composed of a low-pass filter and a high-pass filter having the same folding frequency, $1/T$ – which dispatches the low-frequency and high-frequency components of power demand towards the main and auxiliary sources, respectively. Having initially been presented in our conference paper [18], this idea subsequently evolved towards an *adaptive* version of this control strategy, implemented in a classical, widely-used two-level structure, resumed here in Fig. 2.6 [19]:

* the upper-level control mainly implements the DC-link voltage regulation, but also a control loop in charge with maintaining auxiliary source (AS)'s state of charge (SoC) – otherwise said, its voltage – within admissible limits; the frequency splitter, whose folding frequency is rendered adjustable by means of an adaptive strategy, is also embedded here;

* the lower-level control concerns control loops of the two sources' currents.

The idea of rendering variable the separation frequency allows adapting solicitation of the two sources while taking into account additional constraints related to AS SoC and load requirements (charge/discharge) at a given moment. Thus, flexibility is added by allowing the main source (MS) taking over the role of AS if ever the AS SoC does not any longer allow its operation as a peak-power source.

The obtained results suggested to go beyond empirical-rule-based adaptive dynamic-separation PMS for hybrid systems based on differently, complementarily specialized sources. Idea of using an *optimal control framework* thus appeared, having initially been proposed in our conference paper [20].
<figure><img src="image_11.png" /><figcaption>Figure 2.6: Adaptive-frequency-splitting-based two-level PMS: the lower-level control concerns both the main source (MS) and the auxiliary source (AS) current loops, whereas the upper-level control consists of the DC-link voltage control [19].</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Figure 2.7: General power flow configuration and optimal-control-based PMS for the class of two-DC-DC-source power system supply described in Fig. 2.5, used for off-grid applications [21].</figcaption></figure>

Fig. 2.7 details the principle of an optimal-control-based PMS for the same class of two-storage-unit multi-source system like the one in Fig. 2.5. It is assumed that MS current is controlled in order to ensure DC link voltage regulation, despite stochastic and *a priori* unknown variations of reversible load's power (current), by means of a two-loop control structure whose outer closed loop represents the plant – identified by the block "Plant" in Fig. 2.7 – for the subsequent control design approach. The aim is to cast the problem into an *optimal stochastic-disturbance-rejection formalism*, as presented in our journal paper [21].

To this end, the block "Plant" is modeled as a family of linearized (linear parameter varying) systems in
variations – obtained by high-pass filtering (HPF) – around operating points corresponding to different mean values of load current. Further formalization is based on the idea that **the AS together with its converter plays the role of an actuator for the "Plant"**, able to reject high-frequency disturbances represented by load current variations. In this way, designing an adjustable trade-off between MS's current variations and AS's current variations can be straightforwardly expressed as a trade-off between performance and control effort.

To conclude, the block "Optimal control" in Fig. 2.7 contains the result of an **LQG optimal control problem** coupled with a **gain scheduling strategy** to cover the whole range of load variations. Thus, the two power sources are controlled to share the stochastically-variable reversible load according to their respective dynamic specialization ranges.

Note that the relation between the "Plant" (MS and DC link) closed-loop bandwidth and the HPF folding frequency is the most important degree of freedom in the dynamic-separation-based PMS design, as it should practically follow the relation between the respective characteristic frequencies of the two sources.

The idea of associating an optimization index to the dynamic separation of sources depending on their dynamic specializations, i.e., their respective characteristic frequencies, leads naturally to the possibility of **generalizing the optimal approach for an arbitrary number of sources, n**. Note that stating an LQG problem in the above-mentioned form for an *n*-source hybrid system is not any longer effective; introduction of more degrees of freedom in the design is necessary. In this context, approaching PMS design by using *weighting functions* within an *H∞ robust control design* allows sufficient flexibility in suitably conditioning the sources' dynamic closed-loop behaviour, in addition to *guaranteeing robustness in stability and performance*. Further combination with *Linear Parameter Varying (LPV) techniques* – e.g., in a *polytopic approach*, thus generalizing gain scheduling methods – ensures extending domain of well performance.

Following these ideas, contributions summarized in Chapter 4 concern developments around $H_\infty$ and LPV methods, exploited for well-performing multi-source PMS design with guaranteed performance. Two class of applications are illustrated for purpose of effectiveness validation, namely:

* in Section 4.2 *generalization of PMS design guidelines for n-source generation systems* is detailed, then validated in the case of three-source ($n=3$) DC microgrids on board of all-electric multi-storage vehicles;

* design of robust PMS for frequency and voltage regulation in stand-alone AC microgrids is presented and validated in Section 4.3 in the context of using ultracapacitors as fast storage units.

## 2.3 Hardware-in-the-loop simulation (HILS) as systematic method of experimental validation

Scientific results and developments around this topic originate in the exposure I had benefited from to work that Professor Emil CEANGĂ carried out in the mid-1990s at "Dunărea de Jos" University of Galați in Romania. Indeed, articles [22]–[24], issued from his collaboration with a team from Université du Havre in France, are among the first ones dealing with replicability of renewable-energy-conversion governing phenomena under controlled conditions.

Unpredictability of operating conditions of different renewable-energy sources and the associated significant risks render very difficult *in situ* preliminary experimental validation of control laws. The **hardware-in-the-loop simulation (HILS)** principle is nowadays widely employed for rapid prototyping, as recognized of full effectiveness. In this way, replicable experiments can repetitively be carried out in laboratory conditions on dedicated test rigs.

Generally speaking, the HILS concept consists in the closed-loop connection of both physical and software parts, in order to replicate in laboratory (controlled, customizable) conditions the dynamic behaviour of an industrial process or system. The software part results from modelling those parts of the real system which will be *simulated* – because it is to expensive and/or dangerous to use the *real* parts – whereas the physical part is taken as it is from that system.

Since its definition and introduction at the beginning of the 1990s for developing and testing control structures for mechanical equipments [25] – HILS applications in the automotive industry using the MATLAB®/Simulink®
<figure><img src="image_13.png" /><figcaption>Figure 2.8: Representation of the interaction between the investigated physical system (IPS) and the emulated physical system (EPS) within the basic physical system (BPS) [29].</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Figure 2.9: Real-time physical simulator (RTPS) within a general HILS structure [29].</figcaption></figure>

software on a dSPACE™ development kit date back to 1996 [26], [27] – HILS concept has increasingly been used – in particular, for control law rapid prototyping – being now involved in other modern concepts such as, for example, the *digital twin*.

Based on concepts, terminology and methodological aspects first introduced in [23], then partially used in [24] and [28], a systematic design method of HIL simulators resulted when I was with the group led by Professor Emil CEANGĂ at "Dunărea de Jos" University of Galați, namely within the collaboration with Ph.D. students Iulian MUNTEANU and Nicolaos Antonio CUTULULIS, as the seventh chapter of our 2008 Springer monograph:

* I. Munteanu, A.I. Bratcu, N.A. Cutululis, E. Ceangă (2008). *Optimal control of wind energy systems – Towards a global approach*. Advances in Industrial Control Series. Springer, London. ISBN 978-1-84800-079-7, 283 pages.

Let a *basic physical system* (BPS) be considered, for which a generic control problem is formulated. A HIL simulator is aimed at cost-effectively and safely replicating the BPS dynamic behaviour, for as realistic as possible closed-loop deterministic experiments under customizable conditions.

HILS structures basic idea relies upon assuming that the BPS can be naturally divided into two interacting subsystems, namely a first subsystem – for which closed-loop experiments are very expensive and deterministic experiments are almost impossible – and a second subsystem, undertaking the control action. Thus, it is the first subsystem whose behaviour must be replaced by a physical simulator; it is called an *emulated physical system* (EPS), whereas the second subsystem exists in the HIL simulator exactly as it is in the BPS. Being the object of study, the second subsystem is called an *investigated physical system* (IPS).

The interaction EP-IPS supposes a power transfer between them and is characterized by a pair of *interaction variables*, further denoted as $z_1$ and $z_2$. Having assumed that the "active" participant – i.e., able of providing energy – is the EPS, with the IPS being the energy absorber, the interaction, as experienced by the EPS, is depicted in Fig. 2.8. The physical nature of the interaction variables depends on BPS in a biunique manner. Being the cause variable, $z_1$'s variation initiates the energy imbalance; $z_2$ is the response variable. Product of thusly defined interaction variables has always power dimension.

The EPS is replaced by a *real-time physical simulator* (RTPS), which must offer the "natural" environment for IPS and must replicate the models of the EPS and of the interaction EPS-IPS, in order for the resulted HIL simulator to approximate the BPS dynamics. Basically, the RTPS must *physically* provide one of the interaction variables based on the *measure* of the other one and on the EPS model. A tracking loop at the output of the RTPS – called the *effector* (EFT) – is in charge with this task; the controlled variable is called *driving variable* and the other one, *response variable*. The EFT reference is established by the *real-time software simulator* (RTSS), according to a model of the EPS, referred to as EPSM. Fig. 2.9 details the RTPS structure for the simplified case when the interaction variables are scalars.

There are two main ways of choosing the generic driving and response variables, namely:
1. if the variable chosen as driving variable is an output/state of the BPS, then it is an effect variable ($z_2$), so the model implemented in the RTSS is strictly causal and is obtained directly from the EPS model;

2. if the variable chosen as driving variable is a cause variable ($z_1$), then the model implemented in the RTSS is non-causal and is fed by a measure of the effect, $z_2$.

Both cases have drawbacks: quite slow dynamic in the first case, need of computing time derivatives – thus noise increasing – in the second case. Some other remarks can also be made. First, as the IPS is generally "active", it induces in BPS variations of potential energy, so its influence on the RTPS should not be neglected. Also, Fig. 2.9 shows that the response variable is affected by the transducer dynamic (described by vector field $S$) and the driving variable by the effector dynamic (described by vector field $E$). Therefore, these variables have actually slightly modified instantaneous values, thus affecting the HILS emulation accuracy.

The above remarks lead to formulating the *basic reproducibility conditions*, which must be met for the EPS to be successfully replaced by the RTPS:

* computation inside the RTSS must be sufficiently faster than the dynamic of the EPS (real-time condition);

* the EFT dynamic must be faster than that of the EPS (the tracking loop is sufficiently fast);

* the passband of the transducers must be sufficiently large.

As a conclusion to the above conceptualization approach, a *seven-step systematic design procedure of HIL systems* is provided in [29] as an operational tool. A comprehensive application of this procedure for designing a PMSG-based WECS real-time physical simulator is reported in our book chapter [30].

Effectiveness of a real-time simulator is judged upon its performance against the mathematical model to replicate – in other words, what is *mathematically* modeled is compared to what is *physically* obtained on the simulator. In particular, the *simulator's capability of replicating the desired time and frequency response*, for an as large as possible frequency domain, is of crucial importance.

With respect to this issue, two main publications can be cited, whose results are synthetically discussed next. In both works the considered configuration is that of a *permanent-magnet-synchronous-generator (PMSG)-based wind energy conversion system (WECS)*, in a *grid-connected* case in the first work, while in the second work a *stand-alone (off-grid)* operation is studied.

As regards how the HIL simulator is built in each of the two cases, another difference exists between the two case studies, namely regarding the choice of the driving variable: it is about a *torque-driven* simulator in the first case and about a *rotational-speed-driven* one in the second case. Both time- and frequency-domain performance of the respective real-time simulator are thoroughly assessed in both works. Analysis of real-time replication errors finally allows some remarks when the two cases are compared one against the other, as it can be concluded next.

1. I. Munteanu, A.I. Bratcu, S. Bacha, D. Roye, J. Guiraud (2010). Hardware-in-the-loop-based simulator for a class of variable-speed wind energy conversion systems: design and performance assessment. *IEEE Transactions on Energy Conversion*, 25(2), 564–576,

which discusses the results obtained by experimenting on the multi-functional test rig at Grenoble Electrical Engineering Laboratory (G2ELab), during my post-doctoral 2008–2009 internship, within collaboration with post-doctoral fellow Iulian MUNTEANU, Professors Daniel ROYE and Seddik BACHA, with the precious help of R&D engineer Joël GUIRAUD.

In this work, a complete grid-connected generation chain employing a horizontal-axis fixed-pitch three-bladed rotor PMSG-based WECS is chosen as example for the step-by-step illustration of the HIL simulator design procedure.

Fig. 2.10 offers an overall synthetic view of how the HIL simulator is built, starting from the WECS configuration as a basic physical system (BPS) in Fig. 2.10a). Identification of both emulated and investigated physical systems (EPS and IPS, respectively), as well as interaction between the two, is also suggested in this first part of the figure.
<figure><img src="image_15.png" /><figcaption>Figure 2.10: Structure of a grid-connected PMSG-based WECS from the viewpoint of the HIL simulator design procedure [31]: a) emphasizing interaction between EPS and IPS within the BPS; b) emphasizing interaction between EFT and RTSS within the RTPS that replaces the EPS.</figcaption></figure>

Fig. 2.10b) further shows how the EPS is replaced by a real-time physical simulator (RTPS) and presents details about structures of both effector (EFT) and real-time software simulator (RTSS) within the RTPS. As also indicated in this second part of the figure, interaction between EFT and RTSS is here based on having chosen the *rotational speed*, $\Omega_R$ – an *effect variable* – as *driving variable*; therefore, the model implemented in the RTSS is *strictly causal*. The *response variable* is then the *electromagnetic torque*, $\Gamma_E$, a *cause variable*. The imposed torque value, $\Gamma_E^*$, serves as a reference to the EFT; therefore, the EFT is in this case *torque driven* within the RTPS.

Fig. 2.11 offers a glimpse of **HIL simulator frequency-domain accuracy**. Thus, the simulator's frequency response was measured by applying variable-frequency exogenous sinusoidal variations around a typical steady-state point – here, an operating point close to the maximum power point was established, which is characterized by an average wind speed – here, about 8 m/s.

The two parts of Fig. 2.11 are dedicated to results on the two input-to-output transfer channels, respectively – that is, from the *wind speed* (*disturbance input*) to *rotational speed* (Fig. 2.11a)), and from *electromagnetic torque* (*control input*) to *rotational speed* (Fig. 2.11b)), respectively.
<figure><img src="image_16.png" /><figcaption>Figure 2.11: Bode plots allowing to evaluate the errors associated to real-time replication in the frequency domain [31]: a) disturbance-to-output transfer channel; b) control-input-to-output transfer channel.</figcaption></figure>

Bode plots in Fig. 2.11a) are shown along with a typical spectral density of the wind turbulence, with most of the energy located between 0.1 and 1 rad/s [44]. Simulation errors are negligible for almost the whole frequency range considered, which totally includes the wind speed spectrum, thus suggesting that the simulator fully succeeds in replicating the real system in response to the wind speed variations.

Fig. 2.11b) indicates that replication errors with respect to the electromagnetic torque are slightly larger than those on the disturbance-to-output channel, especially the gain errors. This fact is however not critical, since the error is almost constant (3 dB) over the whole frequency range of interest, so easy to compensate by control action. The electromagnetic torque dynamic is controllable and it must essentially follow the dynamic of the main disturbance, i.e., of the wind turbulence, where the high-frequency variations are usually not present, for reasons of minimizing the fatigue loads [44]. The replication error is thus relevant in the same frequency range as in the case of wind turbulence.

2. C. Vlad, A.I. Bratcu, I. Munteanu, S. Epure (2014). Real-time replication of a stand-alone wind energy conversion system: error analysis. *International Journal of Electrical Power and Energy Systems*, 55, 562–571,

which presents the results issued from experiments on the dedicated test rig at “Dunărea de Jos” University of Galați in Romania, within collaboration with Romanian colleagues Ciprian VLAD and Silviu EPURE.

In this case, the investigated physical system (IPS) consists of a variable-speed PMSG-based stand-alone WECS supplying a wide range DC load by means of a diode bridge rectifier and a DC-DC step-down converter. Unlike in the first above-discussed case, the second choice of the driving variable was made here – thus, a *speed-driven* real-time physical simulator (RTPS) is built, with the *a priori* drawback of a reduced bandwidth [29]. This drawback was significantly alleviated by embedding into the real-time software simulator (RTSS) a feed-forward compensation of the inherent physical disturbance produced by the generator torque variations.

The block diagram of the HIL structure is presented in Fig. 2.12, where the different parts and the interaction between them can directly be identified. This time, it is the *electromagnetic torque*, $T_G$ – a cause variable – that is chosen as *driving variable*; its estimation based on sensing the current value, $I_R$, is here preferred to a more expensive solution employing a torque transducer. It results further that the rotational speed, $\Omega$ – an effect variable – plays here the role of response variable, so the effector within the RTPS is driven by the rotational speed imposed value, $\Omega^*$ (it is said that it is *speed driven*). RTSS is implemented on a dSPACE™ rapid prototyping system identified as DS1103 in Fig. 2.12.
<figure><img src="image_17.png" /><figcaption>Figure 2.12: HIL simulator design applied to a stand-alone PMSG-based WECS: emphasizing interaction between IPS and RTPS [32].</figcaption></figure>

Like in the first HIL simulation case presented before, the *simulator frequency-domain accuracy* was analyzed for a frequency range larger than two decades. To this end, small-amplitude variable-frequency sinusoidal variations of its exogenous signals, the wind speed and the load current reference, were applied around a typical operating point. Fig. 2.13 exhibits the Bode plots for both input-to-output channels.

The replication accuracy on each transfer channel is assessed in relation to the frequency spectrum of its respective exogenous signal. For the *first* channel – corresponding to *disturbance* influence on output – very good simulation quality is revealed in the frequency range of interest (Fig. 2.13 (a) and (b)): the maximum gain error is below 1 dB and is placed within the bandwidth, whereas phase lag errors are negligible. Both gain error and phase lag error increase with the frequency. Very good simulation quality can also be concluded on the *second* channel – corresponding to *control input* influence on output – in the frequency range of the load current reference variations (Fig. 2.13 (c) and (d)), with replication errors being here slightly more visible than on the first transfer channel. Gain errors of around 1 dB can be viewed along the whole frequency range of interest and phase lag errors are placed around 2°.

Having now a *concluding look* at the two above-presented HIL simulation case studies, one can note that the theoretically-predicted worse dynamic replication accuracy of a speed-driven simulator vs. that of a torque-driven one [29] can be outperformed by *appropriately enhancing the software part* to accomodate compensation strategies of different negative influences. Indeed, Figs. 2.11 and 2.13 sustain the idea that *quite similar performance* of the two is possible to obtain.

## 2.4 Heterogeneity and stochasticity of energy-communication interaction in smart grids

Always within the topic of grid and microgrid technology, we now put the focus on what renders them "smart". Information and Communication Technologies (ICT) are key concepts having enabled in the last years the digitalization revolution. In particular, what is today called as the *energy transition* – roughly described by the transition from fossil-based and centralized to renewable-based and decentralized energy production, but also by new manners of consuming this energy – is largely due to the growing intelligence of the nowadays power distribution grids.

One of the definitory features of the emerging concept of "*smart grid*" suposses that different entities – production units, loads, circuit breakers, power stations, etc. – can communicate with each other and exchange information
<figure><img src="image_18.png" /><figcaption>Figure 2.13: Real-time simulation performance in the frequency domain – simulator *vs.* linearized model Bode plots obtained around average wind speed of about 7 m/s chosen as typical operating point [32]: (a) and (b) wind-speed-to-rotational-speed transfer channel; (c) and (d) load-current-reference-to-rotational-speed channel.</figcaption></figure>

by means of a communication network that overlays – or it is integrated into – the energy network. Imbrication between these two networks becomes increasingly important, leading to concepts such as *critical infrastructures*. Governing phenomena have non-unitary character – multi-domain, multi-physics – and take place at different time scales (multi-scale); this is a real challenge for stating a unitary modelling and control paradigm.

New communication protocol standards have especially been defined for the smart grids [33]–[35]; among them, the **IEC-61850 standard** is nowadays one of the most used. Irrespective of the protocol used, the information flow through a communication network generally exhibits **variable delays** potentially responsible for unstable – or at least degraded – behaviour of the power system. Moreover, certain asynchronous events – erroneous transmissions, collisions, loss of data packets, *etc.* – may also take place. Thus, a smart grid in interaction with its communication network exhibits **hybrid dynamics**. The energy grids have already been analyzed as complex interconnected systems and modelled as hybrid dynamic systems in a systematic context allowing to study their structural properties such as the stability [36]. Recent works have envisaged more general methods for modelling the communication protocols for large-scale systems [37].

Modelling of smart grids as cyber-physical systems has become quite recently a topic of interest within our research. The smart grids considered here rely upon distributed Intelligent Electronic Devices (IEDs) equipped, among others, with sophisticated communication functions to perform supervision, protection and control. As the performance of the underlying communication network can affect power grid operation, focus was put on obtaining a modeling method for its Quality of Service (QoS) analysis.

In this context, a methodology of evaluation of the maximum message transmission delay using an analytical model based on *Network Calculus Theorem* can be cited here as main result. This methodology is proposed and validated on a smart-grid communication network implemented on a real reduced-scale HV/MV smart
substation test bench equipped with a real-time IEC-61850-traffic generator within a cooperative load-shedding scenario. Thus, to fix ideas, but without losing generality, the chosen substation real-time scenario – whose schematics is depicted in Figure 2.14 – includes three communicating IEDs participating in a common task of load shedding, while two other IEDs are added to generate background, perturbation traffic, for generalization purposes.

<figure><img src="image_19.png" /><figcaption>Figure 2.14: Reduced-scale laboratory distribution grid with smart substation implementing a three-IED-based load shedding scenario – residential load is the less prioritary [38]. Any arriving data flow needs a guaranty to be served at each port, so it is upper-bounded by an arrival curve and lower-bounded by a service curve [39].</figcaption></figure>

The arrival curve defines constraints on the traffic flow arriving at a port; thus, variations of function $F(t)$ are supposed to be upper-bounded by an increasing function $\alpha(t)$, named arrival curve [40]:

$$F(t) - F(s) \leq \alpha(t-s), \forall s \leq t. \qquad (2.2)$$

One of the most used arrival curves is the so-called $(\sigma, \rho)$-model proposed in [41], which is a simple linear model:

$$\alpha(t) = \sigma + \rho t, \qquad (2.3)$$

where $\sigma$ signifies the burstiness of the flow in bits and $\rho$ represents an upper bound on the long-term average rate of the traffic flow in bits/s.

<figure><img src="image_20.png" /><figcaption>Figure 2.15: Determining arrival curve parameters by identifying the upper-bound linear curve of cumulative function $F(t)$ – illustration for first flow at first port, corresponding to scenario in Fig. 2.14 [38].</figcaption></figure>

Effective determination of these two parameters results from linear curve fitting of the upper bound of measured cumulative function $F(t)$ for each flow, as shown in Fig. 2.15 as an example for the first flow passing through the first port in the considered load-shedding scenario.

The service curve is a function of time defining lower bounds on the services provided by ports during a defined time interval. The rate-latency $\beta(t)$ model is a widely used service curve model represented by a linear function as

$$\beta(t) = R[t - T]^+, \qquad (2.4)$$
where $[x]^+$ denotes the $\max\{x, 0\}$, $R$ signifies the transmission rate in bits/s and $T$ represents the latency in seconds [40]. It is said that a flow receives $\beta_{R,T}$ as a service curve when that flow is served by the rate of $R$ in $T$ time after its arrival at the service system. If there is only one flow passing through a port, $R$ and $T$ are taken from the port (switch or router) datasheet. If there is more than one flow, then datasheet values are penalized to reflect influence of the other flows – exact penalizing formulae depend on the adopted queue-scheduling policy, that is, either First Input First Output (FIFO) or Priority Queuing (PQ) [42].

Network calculus is developed in the min-plus algebra, according to which the message transmission delay for each flow $j$ passing through each port $i$ is upper-bounded by a quantity depending on the characteristics of its arrival curve, i.e., $\sigma_j$, and the received service from that port, i.e., $T_i$ and $R_i$:

$$D_{i,j} \le h(\alpha_j, \beta_i) = T_i + \frac{\sigma_j}{R_i} \qquad (2.5)$$

Further, estimation of maximum transmission delay relies upon building several matrix-form models – physical connection model, logical connection model, source model and service model [43] – in relation with the digraph representation of the network, supposed completely known, then by using these models to obtain the message distribution matrix for each flow $j$, $S_j$. Information within $S_j$ matrix is then used for maximum delay estimation of each traffic flow, based on corroborating estimations of form (2.5).

The proposed methodology – synthesized in Figure 2.16 – is therefore essentially an identification-based one, i.e., consisting in fitting objectively measured data on models with known structure. Here $D$ is the number of data flows passing through a number $P$ of service stations (switches or routers). First, the arrival curve is fitted over the measured flows by means of an identification process resulting in the $(\rho, \sigma)$-model, as illustrated in Fig. 2.15. Then, message distribution is modeled and the maximum delay is estimated for each flow receiving services at each port. To evaluate the estimation effectiveness, estimated values are compared against delays measured objectively by a network analyzer – in this case, Wireshark. Comparison shows very satisfactory estimation errors (within 10%).

<figure><img src="image_21.png" /><figcaption>Figure 2.16: Major-step flowchart of the proposed identification-based methodology of maximum communication delay estimation for networks with completely known configuration [38].</figcaption></figure>

The analytical-method-based maximum delay estimation proves reliable; however, it is limited to the cases with a completely known network structure, which is the case of the proprietary networks. If a priori knowledge about
the communication network is not available, some other estimation approach should be envisaged.

These results were obtained within the collaboration with Ph.D. student Ronak FEIZIMIRKHANI, working under the co-supervision of Professor Yvon BÉSANGER and myself, with the help of R&D engineers Antoine LABONNE and Thierry BRACONNIER, and are presented in the journal article below, as main concluding publication result:

* R. Feizimirkhani, A.I. Bratcu, Y. Bésanger, A. Labonne, T. Braconnier (2021). A methodology for the evaluation of the message transmission delay over IEC 61850 communication network – a real-time HV/MV substation case study. *Sustainable Energy, Grids and Networks*, 28, art. no. 100555.

While this method is independent of the communication protocol, the IEC 61850 protocol serves to illustrate its effectiveness. The method is applied on a pre-sampled traffic data, i.e., off-line. On-line application of this method on a sliding *T*-width time window on an *a-priori*-not-known, possibly evolving network, would give a time evolution of the maximum delay. Such information may further be used with machine-learning algorithms to predict delay upper bounds. In addition, more complex scenarios such as inter-substation communication with faults, modern QoS strategies (e.g., Priority Queuing) and dynamic networks (e.g., delay optimal routing) or some message characteristics such as variable-length data, on-line flow studies while they are generated by different sources with different flow rates are interesting to be analyzed.

This topic is presently under *ongoing exploration*, in particular during the post-doctoral internship of Ronak FEIZIMIRKHANI. Its average-term further development makes the object of prospective research directions, as detailed in Chapter 5, Section 5.3.
<figure><img src="image_22.png" /></figure>
# Chapter 3

## Mitigating unpredictability of renewable energy conversion systems (RECS) by optimal control methods

This chapter attempts offering an overall view of our main research contributions in solving control problems for renewable energy conversion systems (RECS), usually involving multi-criteria dynamic optimization, expressed in terms of sometimes sophisticated trade-offs to take account of antagonistic objectives and complex constraints. The different mathematical formulations and solving approaches employed to this end are overviewed in the introductory Section 3.1.

The reporting made here roughly covers a ten-year time span (2003–2013), with some publications slightly exceeding this period. Most of the results had been obtained before having joined GIPSA-lab in Grenoble, namely during a part (2003–2011) of my time at “Dunărea de Jos” University of Galați in Romania and my postdoctoral fellowship at G2ELab in Grenoble (2008–2009). Sections 3.2, 3.3 and 3.4 are each dedicated to an instance of RECS, namely, to wind energy conversion systems, micro-hydro – i.e., water-turbine-based – energy conversion systems and photovoltaic systems, respectively.

Some useful insights are aimed at in the concluding Section 3.5.

### 3.1 From control objectives to formal control approaches

This section aims at pointing out the main steps to take on the way from formulation of control objectives – in terms specific to each RECS technology – to mathematical modelling and then identification of most appropriate formal control approaches to employ. Two classes of RECS are here considered, which are distinguished by the presence – and absence, respectively – of moving mechanical parts. Thus, the first class is based on a mechanical-to-electrical conversion, involving rotating turbines as prime movers – more precisely, wind energy conversion systems (WECS) and micro-hydro energy conversion systems (miHECS) are those which our contributions are focused on. The other RECS class consists of the photovoltaic (PV) systems.

In order to fix ideas and further justify our global vision, some basic definitions and concepts characterizing the wind-turbine-based RECS (WECS) are briefly introduced, that also apply to water-turbine-based RECS (miHECS). Indeed, the analogy between these two types of RECS is very pertinent, being originated in the analogy
between the two primary flowing resources, the wind and the water, respectively.

Performance of a wind turbine is generally characterized by means of its non-dimensional characteristic performance curves [44]. Thus, the tip speed ratio, $\lambda$, and the power coefficient, $C_p$ – already qualitatively recalled in Section 2.1 of this memoir – are essential notions for expressing the aerodynamic performance of a wind turbine.

The tip speed ratio is the ratio between the peripheral blade speed and the wind speed:

$$ \lambda = \frac{R \cdot \Omega_l}{v}, \qquad (3.1) $$

with $R$ being the blade length, $\Omega_l$ being the low-speed shaft rotational speed and $v$ being the wind speed.

The non-dimensional power coefficient, $C_p$, describes the power extraction efficiency of a wind turbine. Theoretical maximum of $C_p(\lambda)$, obtained by assuming perfect blade design, equals 0.59 and is called the *Betz limit*. For control purposes, an useful remark is that curve $C_p(\lambda)$ is **unimodal** – Fig. 3.1 presents an instance of this curve, namely for a typical two-bladed wind turbine – meaning that the power conversion efficiency has a well determined maximum for a specific tip speed ratio, denoted by $\lambda_{opt}$. The torque coefficient, denoted by $C_r$ and defined as:

$$ C_{\Gamma}(\lambda) = \frac{C_p(\lambda)}{\lambda}, \qquad (3.2) $$

is an additional variable that characterizes the wind torque, $\Gamma_{wt}$.

<figure><img src="image_23.png" /><figcaption>Figure 3.1: Unimodal allure of a wind turbine’s power coefficient, $C_p$, as function of its tip speed ratio, $\lambda$ [44].</figcaption></figure>

<figure><img src="image_24.png" /><figcaption>Figure 3.2: Wind power versus wind speed characteristic, with identification of main control objectives for each operating region.</figcaption></figure>

The wind-harvested power by a wind turbine rotating in air of density $\rho$ is expressed as [44]:

$$ P_{wt} = \frac{1}{2} \cdot \rho \cdot \pi R^2 \cdot v^3 \cdot C_p(\lambda), \qquad (3.3) $$

that allows concluding that the captured power characteristic, $P_{wt}(\Omega_l)$, at constant wind velocity, has the same unimodal allure as the power coefficient in Fig. 3.1. Therefore, the turbine rotor outputs non-negligible mechanical power if rotating in an intermediary speed range, which depends on the wind speed.

Fig. 3.2 presents the different operating regions of a wind turbine, in relation with the wind speed. A wind turbine operates, with different dynamics, from the cut-in wind speed (usually 3–4 m/s, for modern wind turbines) to the cut-out wind speed (around 25 m/s). The wind power varies proportionally with the wind speed cubed – according to (3.3) – until it reaches the wind turbine rated power corresponding to the rated wind velocity. The wind turbine operation range is thus splitted in two: below the rated (also called **partial-load region**) and **full-load region** (between the rated and the cut-out wind speed). As also indicated in Fig. 3.2, while in partial load the control objective is wind power maximization, in full load the captured power must be **limited to the rated** by control action to avoid mechanical damage.
Our contributions focus on the *optimal control of WECS in partial-load region* – more generally, on the *optimal control of rotating-turbine-based RECS* – so it is this topic that will be detailed next. Roughly speaking, the aim is the *Maximum Power Point Tracking* (MPPT) – as anticipated in Section 2.1 – possibly included either in a more complex optimization objective to suitably express some desired trade-off, or in a multi-level control/supervising structure to take account of additional constraints.

To further fix ideas, the turbines considered here have *fixed pitch*, therefore, the MPPT is enabled by the concept of *variable-speed operation* [11]. It is mainly about *hill-climbing* methods, *perturb-and-observe* (PO)-based methods – among which *extremum seeking control* (ESC) – *linear quaudratic gaussian* (LQG) and *sliding mode* control. Some of the control approaches employed for WECS were also applied for miHECS, as presented next within this chapter. Note also that, while application of LQG and sliding mode control was particularly adapted to the first class of RECS (i.e., with moving parts), hill-climbing and ESC are examples of application to both classes of RECS considered here – in particular, for implementing the MPPT for PV systems, whose unimodal allure of curves of output-power-*vs*.-*voltage has already been recalled in Fig. 2.1 in Section 2.1.

As regards WECS power limitation in full-load region (i.e., for high winds), a comprehensive overview – including both passive and active control – is given in the fourth chapter of our monograph [29].

The above introduction of maximizing the wind-harvested power in WECS serves as an illustrative case able to suggest generalizations for formulating the MPPT under a more general form. Such an MPPT formalization would be applicable – with adaptations – to practically any class of RECS, as they are all characterized by unimodal power conversion efficiency curves. Under some conditions, these curves can be multimodal – such as for PV system configurations under partially-shaded conditions – and in this case further extensions and adaptations may apply [45]–[47].

Next, presentation of **MPPT** under a form generally applicable to all **RECS** is aimed at.

**MPPT** is difficult to put in place when **precise information about RECS unimodal efficiency curves is not available**, which is almost always the case in practice. That is, neither the abscissa, nor the ordinate of the maximum efficiency curve is known – moreover, both of them vary with the primary resource – *i.e.*, with either the wind/water speed for WECS/miHECS, or the solar irradiance level for the PV systems – which, in addition, is usually difficult and/or expensive to measure. Thus, a method of "primary resource tracking" should be implemented, able to ensure operation at maximum power irrespective of resource variations. It is about tracking the **Optimal Regimes Characteristic** (ORC), defined as the locus of all maximum power points. Figs. 3.3 a) and b) present the ORC allure of a fixed-pitch WECS in the wind-power-*versus*-rotational-speed plane, and of a PV system in the PV-power-*versus*-voltage plane, respectively. In particular, Fig. 3.3b) illustrates a case where the peak power locus does not correspond to a function, but to a curve.

The basic idea of MPPT is that, given a certain value of the primary resource, to adjust the reference of the independent variable – *i.e.*, the abscissa – such that to maximize the dependent variable, *i.e.*, the power. Next, let the abscissa be generically denoted as *x*. In order to establish whether its reference must be either increased or decreased, it is necessary to estimate the current position of the operating point in relation to the maximum of the power curve. This can be done in two main ways, as follows.

<figure><img src="image_25.png" /><figcaption>Figure 3.3: Example of locus of maximum power points on the power curve of a RECS, materializing the ORC when the primary resource varies: a) case of a fixed-pitch WECS; b) case of a PV system.</figcaption></figure>
* The abscissa reference is modified by a variation $\Delta x$, the corresponding change in the captured power, $\Delta P_{harvested}$, being determined in order to estimate the value $\partial P_{harvested}/\partial x$. The sign of this value indicates the position of the operating point in relation to the maximum of characteristic $P_{harvested}(x)$. If the abscissa reference is adjusted in ramp with a slope proportional to this derivative, then the system evolves to the optimum, where $\partial P_{harvested}/\partial x = 0$.

This MPPT principle is illustrated in Fig. 3.4, where four decision cases are identified, depending on the actual operating point position in relation to the maximum on the power curve, under a form suggesting the action of climbing a hill. Then, based on the relation $\frac{\partial P_{harvested}}{\partial x} = \frac{dP_{harvested}}{dt} / \frac{dx}{dt}$, the decision rules can be inferred as shown in Table 3.1.

<figure><img src="image_26.png" /><figcaption>Figure 3.4: Illustration of the hill-climbing decision process in MPPT.</figcaption></figure>

<table><caption>Table 3.1: Basic logic decision rules of MPPT, inferred from Fig. 3.4.</caption><thead><tr><th>dP<sub>harvested</sub>/dt</th><th>&lt; 0</th><th>&gt; 0</th></tr></thead><tbody><tr><th>&lt; 0</th><td>x ↗ - case I</td><td>x ↘ - case II</td></tr><tr><th>&gt; 0</th><td>x ↘ - case III</td><td>x ↗ - case IV</td></tr></tbody></table>

* A **probing signal is added** to the current $x$ reference; this signal is a slowly variable sinusoid, whose amplitude does not significantly affect the system operation, but still produces a detectable response in the harvested power evolution. The operating point position in relation to the maximum is then obtained by comparing the phase lag of the probing sinusoid and that of the sinusoidal component of active power. If the phase lag is zero/$\pi$, then the current operating point is placed on the ascending/descending part of $P_{harvested}(x)$; therefore, the slope of the $x$ reference must increase/decrease in order for the operating point to approach the maximum. Around the maximum, the probing signal does not produce any detectable response, hence the abscissa reference does not any longer have to change.

The above simplified presentation of MPPT techniques assumes negligible influence of factors like the high-frequency variations of the primary resource or some system unmodelled or parasitic dynamics.

The second version of MPPT led to formalising the *Extremum Seeking Control* (ESC) approach, which relies upon finding the extremum of some unimodal hard-to-model dynamics based on the plant's response to some sinusoidal probing signals [48], [12], [13].

<figure><img src="image_27.png" /><figcaption>Figure 3.5: Explanation of the ESC principle [12].</figcaption></figure>

Fig. 3.5 [12] explains the ESC principle by means of a closed-loop block diagram. The ESC controller performs a modulation/demodulation operation and its output has a harmonic component called the probing signal. The role of the washout filter is to separate the high-frequency components of the plant output. After demodulation and integration, the average component of the control input is obtained, which is further summed up with the probing signal and fed back to the plant. Fig. 3.5 depicts the case of a plant containing a dynamic described by a generic unimodal function denoted by $f(x)$, which has a maximum at $x_{opt}$. It is assumed that the argument of function $f$ has two components: an average one, $\bar{x}$, and a harmonic probing component, of amplitude $a$.
Consider then the Taylor series of this function around its maximum, $f(x_{opt})$, with $\tilde{x} = x_{opt} - \bar{x}$ denoting the optimum searching error. As the integrator constant, $k$, and the excitation amplitude, $a$, are positive and the function $f$ is concave in its extremum – i.e., $f''(x_{opt})$ is negative – based on the diagram shown above, it results that the search error gradient is negative [13]:

$$ \frac{d\tilde{x}}{dt} = \frac{k \cdot a^2 \cdot f''(x_{opt})}{4} \cdot \tilde{x}, \qquad (3.4) $$

thus corresponding to a convergent searching process. The excitation frequency, $\omega$, must be sufficiently large to ensure closed-loop stability; the washout filter parameter, $h$, depends on this frequency [13].

<figure><img src="image_28.png" /><figcaption>Figure 3.6: Application of ESC principle illustrated on the unimodal power conversion efficiency curve of a generic RECS.</figcaption></figure>

Further insights can be formulated if considering the unimodal power conversion efficiency curve of a RECS, as in Fig. 3.6 – e.g., power coefficient in the case of rotating turbines, power-versus-voltage curve in the case of PV systems, etc. The same generic notations $f(x)$ are preserved next for this curve. Consider a hypothetical $\omega$-frequency sinusoidal variation of the variable $x$ with a sufficiently small amplitude $a$. Depending on the position of the operating point on the slope of the efficiency curve, the $f(x)$ variation will be sinusoidal, in phase with the $x$ variation for the ascending part and out of phase (with a phase lag of $\pi$) for the descending part (the intermodulation components for small $a$ being neglected). It follows that the integrator input, $d\tilde{x}/dt$, will toggle its sign as the operating point moves from a side to the other of the $f$ optimum, and, assuming equal slopes of the $f(x)$ curve, its value – and consequently the search direction – varies as in:

$$ \frac{d\tilde{x}}{dt} = \pm k \cdot b \cdot \sin^2(\omega t) \qquad (3.5) $$

Equation (3.5) guarantees that the operating point will move to the optimal position with a speed of convergence depending proportionally on $k$ and $a$ and inverse proportionally on $\omega$ [13].

Applicaton of ESC in its above-described standard form appears to be almost naturally suited for RECS, especially when there are no moving parts. Indeed, while ESC techniques prove to be easily applicable, without great inconvenients, for example, to PV systems, injection of an artificial sinusoidal probing signal has some drawbacks when rotating turbines are involved. For example, in the case of WECS, given that the plant is naturally excited by a random signal, namely the wind, it would be difficult to separate the response to the probing sinusoid from the total output signal, which appears as random too. The solution would be to increase the signal magnitude and/or to use filters. However, large signals may induce supplementary mechanical loads, whereas filters provide delayed feedback information.

The idea of avoiding adding supplementary excitation led to formulate a new form of ESC, that of using the already existing perturbation, which is present as a result of the stochastic nature of the primary resource. For example, in the case of WECS, this already-in disturbance is the wind speed turbulence. In this case, the modulation process is naturally achieved by means of (nonharmonic) high-frequency wind variations.

As detailed in Section 3.2, the wind speed turbulence used as searching signal within ESC ensures good performance, provided that information about system state is poor.

The same idea – of using already-in disturbances as probing (searching) signals – can be generally applied to RECS. For example, for some particular classes of grid-connected PV systems it is possible to put into evidence that certain signals contain sinusoidal components, which can be used as already existing searching signals in ESC algorithms. Contributions on application of this new ESC version, as well as of standard ESC for maximizing the power captured by PV systems, are detailed in Section 3.4.
**Remark:** Direct imposing of the optimal operating point position is a specific MPPT method for rotating prime movers – such as wind and water turbines – widely used in practice, especially for medium- and high-power turbines.

<figure><img src="image_29.png" /><figcaption>Figure 3.7: Two manners of implementing MPPT for rotating prime movers by directly imposing the optimal operating point position [29].</figcaption></figure>

This method represents a rather static viewpoint, based on forcing the turbine rotor to operate in partial load at maximum power, corresponding to the instantaneous primary resource flow speed. Equivalently, this means imposing to the electrical generator the electromagnetic torque corresponding to the maximum power available in the resource. The turbine works at maximum efficiency when turning at optimal tip speed ratio, $\lambda_{opt}$, so the maximum power, $P_{harvested_{max}}$, is proportional to the generator rotational speed cubed, denoted by $\Omega_h$ in Fig. 3.7, where the index "h" stands for high-speed shaft:

$$P_{harvested_{max}} = \frac{0.5\pi\rho R^5 C_{popt}}{\underbrace{\lambda_{opt}^3 \cdot i^3}_{k_G}} \cdot \Omega_h^3 = k_G \cdot \Omega_h^3 \quad (3.6)$$

In (3.6) $C_{popt} = C_p(\lambda_{opt})$ and "i" denotes the ratio of the drive train multiplier between the low-speed shaft – the one driven by the resource flow – and the high-speed shaft, that of the generator; $\rho$ is the resource (air/water) mass density and $R$ is the turbine radius, i.e., the length of its blades. Fig. 3.7 makes appear proportionality coefficient $k_G$ and indicates two manners of implementing this kind of MPPT: a) by imposing the generator torque reference, $\Gamma_G^*$, computed based on the generator rotational speed measure, $\Omega_h$:

$$\Gamma_G^* = \frac{P_{harvested_{max}}}{\Omega_h} = \frac{0.5\pi\rho R^5 C_{popt}}{\lambda_{opt}^3 \cdot i^3} \cdot \Omega_h^2 = k_G \cdot \Omega_h^2 \quad (3.7)$$

and b) by imposing a power reference, $P^*$, and using a PI controller to modify the generator mechanical characteristic and further obtain the torque reference, $\Gamma_G^*$. Conversion efficiency, $\eta^*$, may also be present in $P^*$ computation.

As the control structure allows tracking the primary resource flow speed within admissible limits of mechanical loads, this method can only be used under slow variations of the resource, thus achieving a static optimization. For turbulent conditions, filtering is necessary, along with using compliant PI parameters, to ensure sufficiently slow closed-loop dynamics. This method is strongly sensitive to parameter variations.

While remaining focused on **rotating-prime-mover-based RECS**, the necessity of achieving power maximization along with reasonable mechanical loads – in a reliability-aware context, of fatigue loads reduction for prolonging the RECS service time – led to idea of properly sizing a so-called **energy-reliability trade-off**, expressed as an optimality criterion. Next section is dedicated to some of the contributions we proposed by following this idea, for the specific case of wind energy conversion systems (WECS).

## 3.2 Optimal control of wind energy conversion systems (WECS)

Placing the *harvested power maximization* within a *sustainable* approach renders mandatory to also take into account reliability issues related to the WECS mechanical structure, that is, *minimizing intensity of loads*, responsible on a long term of fatigue phenomena. A *multi-purpose optimization* is achieved in this way.

To fix ideas and introduce main concepts, symbols and notations, the general configuration of a horizontal-axis-turbine-based WECS is depicted in Fig. 3.8 in two versions, fundamentally differentiated from the point of view of power flow control, enabled by means of the AC/DC/AC – also called *back-to-back* – power electronic topology.
<figure><img src="image_30.png" /><figcaption>Figure 3.8: General configuration of a WECS based on a horizontal-axis turbine and different generators: a) SCIG/PMSG; b) DFIG [29].</figcaption></figure>

Thus, Fig. 3.8a) presents the case based on either a squirrel-cage induction generator (SCIG) or a permanent-magnet synchronous generator (PMSG) – in this case the AC-AC converter is stator grid-connected and rated at the generator’s power level. In Fig. 3.8b) a doubly-fed induction generator (DFIG) is employed – in this case, it is the rotor that is interfaced with the grid by means of the power electronic converter, so only part of the generated power is transferred to the grid. From a system viewpoint, the conversion chain consists into four interacting main components : the aerodynamic subsystem (AS) – $S_1$ and the electromagnetic subsystem (EMS) – $S_2$, interacting by means of the drive train (mechanical transmission) – $S_3$, whereas $S_4$ denotes the grid interface.

<figure><img src="image_31.png" /><figcaption>Figure 3.9: Schematics of a WECS rigid drive train [29].</figcaption></figure>

<figure><img src="image_32.png" /><figcaption>Figure 3.10: Schematics of a WECS flexible drive train [29].</figcaption></figure>

The drive train is single (fixed) multiplying ratio, denoted by *i*, of efficiency *η*, either *rigid* (Fig. 3.9) or *flexible* (Fig. 3.10). Within the drive train, LSS and HSS denote low- and high-speed shafts, respectively, with $\Omega_l$ and $\Omega_h$ being the rotational speed of the LSS and HSS, respectively. Figs. 3.9 and 3.10 make appear equivalent inertias $J_l$ and $J_h$, which depend on wind turbine axis inertia, $J_{wt}$, and generator inertia, $J_g$, as well as wind turbine torque, $\Gamma_{wt}$, and generator torque, $\Gamma_G$. For the flexible case – where LSS and HSS are elastically coupled by means of a spring of stiffness $K_s$ and damping $B_s$ – a new internal torque $\Gamma$ is rendered visible.

The action of two control subsystems is suggested on Fig. 3.8: ensuring the variable-speed operation (exerted on $S_1$, $S_2$ and $S_3$) and respectively controlling the power transfer at grid imposed parameters (exerted on $S_4$).

Contributions briefed within this section were obtained within the collaboration with Ph.D. student Iulian MUNTEANU, working under the supervision of Professor Emil CEANGĂ at “Dunărea de Jos” University of Galați, Romania, and under the supervision of Professors Daniel ROYE and Seddik BACHA during his 2005 doctoral internship at G2ELab in Grenoble, France. They are as follows.

* A first control approach starts from formulating an optimal control problem with mixed criteria, whose central idea consists in applying the frequency separation principle – widely used in control systems –
in an original manner, adapted to WECS particularities and needs. Thus, it is shown that the two above-mentioned antagonistic requirements can be expressed within two distinct dynamic (frequency) domains; hence, a two-time-scale WECS dynamic is identified, driven by the **seasonal** (in *low* frequency) and the **turbulence** (in **high** frequency) component of the wind speed, respectively.

In the **high-frequency domain**, the two antagonistic objectives are cast into an **LQG problem**. The resulting **control structure** has the merit of being **desensitized to WECS parameter variations**, thus rendering unnecessary adaptive structures. Main results are resumed in Subsection 3.2.1; they were published in:

I. Munteanu, N.A. Cutululis, A.I. Bratcu, E. Ceangă (2005). Optimization of variable speed wind power systems based on a LQG approach. *Control Engineering Practice*, 13(7), 903–912.

Moreover, this vision can be generalized to **all the main WECS control objectives** – such as, for example, those related to electric power conditioning – as they **can be treated as pairs of antagonistic goals taking place into two separable frequency domains, respectively** – this idea is detailed as a global conclusion of our monograph [29].

* A second solution employs **sliding mode control** techniques: captured power maximization is guaranteed by operating the wind turbine on an **adaptive sliding surface**, whose position in relation to the *Optimal Regimes Characteristic* (ORC) defines the sought-for energy-reliability trade-off. Main results are synthesized in Subsection 3.2.2; they were reported in:

I. Munteanu, S. Bacha, A.I. Bratcu, J. Guiraud, D. Roye (2008). Energy-reliability optimization of wind energy conversion systems by sliding mode control. *IEEE Transactions on Energy Conversion*, 23(3), 975–985.

* A third, **ESC-based**, solution takes profit of the fact that the **searching signal** is already present in the system excitation: it is about the **turbulence component of the wind speed**, modelled as a pseudo-random signal. The information about the actual operating point position in relation to the maximum power point is decided upon the phase lag between the captured power signal and turbine rotational speed signal. This approach is resumed in Subsection 3.2.3 – details can be found in:

I. Munteanu, A.I. Bratcu, E. Ceangă (2009). Wind turbulence used as searching signal for MPPT in variable-speed wind energy conversion systems. *Renewable Energy*, 34(1), 322–327.

### 3.2.1 Frequency-separation-based optimal control of WECS

Fig. 3.11 gives a glimpse of how WECS dynamics can be split into two distinct frequency domains, respectively corresponding to the two spectral ranges identified in the wind speed dynamics: a low-frequency dynamic due to the **seasonal** (long-term, **low-frequency**) component of the wind velocity, $v_s$, and a fast, **high-frequency** dynamic in response to the action of the **turbulent** wind velocity, $v_t$. In Fig. 3.11 $S(f)$ is the wind speed power spectral density in Van der Hoven's large-band (six-decade) wind speed model [44].

The low-frequency component, $v_s$, determines the average position of the operating point on the wind turbine characteristic – this position is subject to slow, low-frequency dynamics, considering that their spectrum is entirely placed inside the turbine bandwidth – and the turbulence component, $\Delta v = v - v_s \equiv v_t$, excites the high-frequency dynamics by generating high-frequency variations around this point. Hence, the evolution of WECS measurable variables (i.e., generator rotational speed, $\Omega_h$), is the superposition of some slow dynamics (SD) and some turbulent dynamics (TD), as suggested in Fig. 3.11. Thus, the idea of separately compensating the two dynamics [49], by designing a two-loop control structure, naturally resulted. Based on using the measured system output, $\Omega_h$, and measured total wind speed, $v$, as feedback information, the two loops use estimated values of $v_s$ and $v_t$, respectively.

The electromagnetic subsystem (EMS, identified as $S_2$ in Fig. 3.8) is torque controlled, so it can be treated as a first-order element providing electromagnetic torque much faster than the drive train's dynamic.
<figure><img src="image_33.png" /><figcaption>Figure 3.11: Intuitive illustration of the frequency separation of WECS dynamics [29].</figcaption></figure>

Because the torque variations induced by the seasonal wind component, $v_s$, are negligible, the SD-related optimization problem may be reduced to $\lambda_{opt}$ tracking. In contrast, the mechanical fatigue due to the turbulence wind component, $v_t$, is significant, so the TD-related optimization problem may be cast into an LQG dynamic optimization. Two control loops result in this way: a low-frequency loop (**LFL**), using $v_s$ within a steady-state optimal controller (**tip speed controller** – TSC) to ensure steady-state operation on the ORC and a high-frequency loop (**HFL**), using $v_t$ within an **LQG controller**, for dynamic optimization of the linearized system’s behaviour around this point.

*Therefore, choice of the frequency limit between what is considered SD and TD, respectively, is crucial in ultimately trading off the power optimization against the mechanical stress alleviation.*

Note also that, as the initial, global optimization problem was split into two sub-problems, each of which is intended to be solved to optimality, then the solution obtained by aggregating the two separate solutions is in general **sub-optimal**. Its closeness to the ideal, optimal solution depends again upon **how sharply the two wind dynamics can be separated**.

<figure><img src="image_34.png" /><figcaption>Figure 3.12: Block diagram suggesting implementation of frequency separation principle by means of a two-loop control structure [49].</figcaption></figure>

Next, any variable $x$ from the system is decomposed into two components: a steady-state one, denoted by $\bar{x}$, and a high-frequency one, representing variations around the steady-state value, $\Delta x = x - \bar{x}$, with $\bar{\Delta x} = \Delta x/\bar{x}$ being the normalized variations.

The steady-state value, $\bar{x}$, belongs to the LFL and the normalized variation, $\bar{\Delta x}$, is treated within the HFL. The block diagram of the frequency-separation-based two-loop optimal control structure – referred to in the following by its acronym, **2LFSP** [49], [29] – is shown in Fig. 3.12. $\bar{\Omega}_h$ and $\bar{\Delta\Omega}_h$ are fed back into the LFL and the HFL, respectively, to further provide each a torque reference component, $\bar{\Gamma}_G$ and $\bar{\Delta\Gamma}_G$ respectively. The total torque reference to be fed into

the electromagnetic subsystem is the sum $\Gamma_G^* = \bar{\Gamma}_G + \Delta\Gamma_G$, with $\Delta\Gamma_G = \bar{\Delta\Gamma}_G \cdot \bar{\Gamma}_G$. The slow dynamics also embeds the dynamic of the associated exogenous signal, $v_s$, while $\Delta v = v - v_s \equiv v_t$ is embedded in the turbulent dynamics.

The steady-state optimization aimed at in the **LFL** can be ensured by tracking the low rotational speed corresponding to $\lambda_{opt}$, $\Omega_{lopt} = v_s \cdot \lambda_{opt}/R$, enabled by variable-speed operation. A tip speed controller (**TSC** in Fig. 3.12) is used for this purpose, whose reference is computed based upon $v_s$. A classical PI and an on-off controller are two possible versions of such a controller.

The **PI control** loop can be either a torque, speed or active power loop, with an action equivalent to imposing a
generator torque reference given by (3.7), which is often called the **K·Ω² law** [11], [44], [50], [51]. As regards the **on-off controller**, this consists in zeroing the difference $\sigma(t) = \lambda_{opt} - \bar{\lambda}(t)$, where $\bar{\lambda}(t)$ is computed with the seasonal, low-frequency wind speed component, $v_s$, and a measure of low-speed shaft rotational speed, $\Omega_l$ [52], [53]:

$$ \overline{\lambda(t)} = \frac{R \cdot \Omega_l}{v_s} \qquad (3.8) $$

As mentioned before, the role of the **HFL** is to alleviate the mechanical stress induced by exclusively aiming at maximizing the harvested power within the LFL. To this end, the HFL control problem is cast into an LQ Gaussian optimization problem defined on the linearized model around the maximum-power steady-state operating point – as ensured by the LFL – with an energy-reliability trade-off performance index of the form [54]:

$$ I = \underbrace{E\{\alpha \cdot [\lambda(t) - \lambda_{opt}]^2\}}_{I_1 \text{ - power maximization}} + \underbrace{E\{\Delta\Gamma_G^2(t)\}}_{I_2 \text{ - mechanical effort minimization}} \rightarrow \min, \qquad (3.9) $$

where $E\{\cdot\}$ is the statistical average symbol. Parameters of the linearized model depend on the operating point, that is, on the low-frequency wind speed, $v_s$. It is especially the case of the **torque parameter**, $\gamma$, which depends significantly on $v_s$ through the tip speed ratio $\bar{\lambda}(t)$ given by (3.8) [54]:

$$ \gamma = \gamma(\overline{\lambda(t)}) = \frac{C'_{p}(\overline{\lambda(t)}) \cdot \overline{\lambda(t)}}{C_{p}(\overline{\lambda(t)})} - 1, \qquad (3.10) $$

where $C'_{p}(\lambda) = dC_{p}(\lambda)/d\lambda$. The gain-scheduling control solution proposed in [54] was supposing the exact knowledge on how parameters, especially $\gamma$, depend on the operating point. Or, this is practically never the case, as the information about $C_{p}(\lambda)$ is often poor or difficult to obtain. **The combined action of the two control loops inside the 2LFSP practically desensitizes the system in relation to the static operating point, by cancelling the variation of the torque parameter, $\gamma$, vs. the tip speed, $\lambda$.** Indeed, if the system is maintained by the LFL around the maximum-power steady-state point, irrespective of the wind speed, then $C'_{p}(\lambda_{opt}) \approx 0$; therefore, according to (3.10), $\gamma$ is maintained around:

$$ \gamma(\lambda_{opt}) \approx -1 \qquad (3.11) $$

To fix ideas, the case of a **rigidly-coupled induction-generator-based low-power WECS** is chosen next to particularize application of 2LFSP control strategy [49]; in [55] application of 2LFSP to **flexibly-coupled WECS** is presented. Based on slow and turbulent WECS dynamics modelling, the control design methods of LFL and HFL are briefed, respectively. Effectiveness of the combined action of the two control loops is illustrated by some real-time (on-line) simulations carried out on an electromechanical WECS simulator.

**WECS slow (low-frequency) dynamics model** is obtained by tangent linearization of the mechanical interaction around an operating point. Thus, using notations introduced in Fig. 3.9, the first-order transfer function from the generator torque, $\overline{\Gamma}_G$, to $\overline{\Omega}_h$, the HSS rotational speed, results as:

$$ H_{\overline{\Gamma}_G \to \overline{\Omega}_h} = - \frac{i^2 / K_{wt}}{(i \cdot J_h) / K_{wt} \cdot s + 1}, \qquad (3.12) $$

where $J_h$ is the HSS inertia, $i$ is the speed multiplier ratio and $K_{wt}$ is the absolute value of the slope of the wind-turbine-torque-vs.-LSS-speed curve, $\Gamma_{wt}(\Omega_l)$, in the chosen operating point. As stable operating points are placed on the descending part of the $\Gamma_{wt}(\Omega_l)$ curve, then $K_{wt}$ is defined by: $K_{wt} = \left| \frac{\partial \Gamma_{wt}}{\partial \Omega_l} \right| = - \frac{\partial \Gamma_{wt}}{\partial \Omega_l}$.

Based on (3.12) – which indicates a linear system variant with the operating point, so ultimately with $v_s$ – the **LFL tip speed controller** – TSC in Fig. 3.12 – can result as a PI controller, tuned, for example, according to the empirical Ziegler-Nichols procedure [56]. In any case, tuning of TSC parameters is not critical, because the low-frequency wind speed, $v_s$, varies much more slowly comparatively to the WECS dynamics.
**WECS turbulent (high-frequency) dynamics model** results as a linearized-in-normalized-variations model, namely obtained by considering as state variables the normalized variation of the low rotational speed around its steady-state value, $\overline{\Delta\Omega_l}$, and the normalized variation of the wind torque around its average value, $\overline{\Delta\Gamma_{wt}}$. The normalized wind speed variation, $\overline{\Delta v(t)}$, is here modelled as a pseudorandom process yielded by passing a white noise, $e(t)$, through a first-order shaping filter:

$$ \dot{\overline{\Delta v(t)}} = \frac{1}{T_w} \cdot (e(t) - \overline{\Delta v(t)}), \qquad (3.13) $$

where $T_w = L_t/v_s$ is the filter time constant, with $L_t$ being the turbulence length, which is usually found empirically for a given wind site. Equation (3.13) results as a simplified adaptation of the non-integer-shaping-filter-based wind turbulence model in [57].

WECS high-frequency model can thus be put into the form of a linear system, having $\mathbf{x}(t) = [\overline{\Delta\Omega_l(t)} \quad \overline{\Delta\Gamma_{wt}(t)}]^T$ as state vector, $u(t) = \overline{\Delta\Gamma_G(t)}$ as control input, $e(t)$ as disturbance input and $z(t) = \overline{\Delta\lambda(t)}$ as output:

$$ \left\{ \begin{aligned} \dot{\mathbf{x}} &= \underbrace{\begin{bmatrix} 0 & 1 \\ \frac{\gamma}{T_w} & \frac{\gamma}{J_T} - \frac{1}{T_w} \end{bmatrix}}_{\mathbf{A}} \cdot \mathbf{x} + \underbrace{\begin{bmatrix} -\frac{1}{J_T} \\ -\frac{\gamma}{J_T} \end{bmatrix}}_{\mathbf{B}} \cdot u + \underbrace{\begin{bmatrix} 0 \\ \frac{2-\gamma}{T_w} \end{bmatrix}}_{\mathbf{L}} \cdot e \\ z &= \underbrace{\begin{bmatrix} \frac{2}{(2-\gamma)} & -\frac{1}{(2-\gamma)} \end{bmatrix}}_{\mathbf{C}} \cdot \mathbf{x}, \end{aligned} \right. \qquad (3.14) $$

where $J_T = \frac{\overline{\Omega_l} \cdot J_l}{\overline{\Gamma_{wt}}} = \frac{\overline{\Omega_h} \cdot J_h}{\overline{\Gamma_{wt}}}$ has dimensions of time constant and the different matrices can be identified: the state matrix A, the input matrix B, the exogenous disturbance matrix L and the output matrix C.

Performance index in (3.9) is adapted to model (3.14) such as to express an LQG problem. Thus, the first component, $I_1$, corresponding to **captured power maximization** or, otherwise said, to **maintaining the system around $\lambda_{opt}$**, results as a quadratic form of the state vector:

$$ I_1 = E\{\overline{\Delta\lambda}^2(t)\} = E\{\mathbf{x}^T(t) \cdot \mathbf{C}_{\alpha}^T \mathbf{C}_{\alpha} \cdot \mathbf{x}(t)\} \rightarrow \min, \qquad (3.15) $$

with matrix C defined in (3.14) and matrix $\mathbf{C}_{\alpha} = \sqrt{\alpha} \cdot \mathbf{C}$. The second component, $I_2$, corresponding to **mechanical (control) effort minimization**, results as:

$$ I_2 = E\{\overline{\Delta\Gamma_G^2}(t)\} = E\{u^T(t) \cdot \mathbf{R} \cdot u(t)\} \rightarrow \min, \qquad (3.16) $$

with matrix R = 1. By summing up (3.15) and (3.16) the global index I is obtained:

$$ I = E\left\{ \mathbf{x}^T(t) \cdot \underbrace{\mathbf{C}_{\alpha}^T \mathbf{C}_{\alpha}}_{\mathbf{Q}} \cdot \mathbf{x}(t) + u^T(t) \cdot \mathbf{R} \cdot u(t) \right\} \rightarrow \min, \qquad (3.17) $$

Provided that the LFL is working properly, the parameters of the turbulent dynamic are time invariant; hence, the stated LQG dynamic optimization problem is also time invariant. LQG controller existence and uniqueness are guaranteed if the open-loop system meets a well-known set of structural properties, among which the controllability of $(\mathbf{A}, \mathbf{B})$ matrix pair [58]. The solution of this problem is the generator torque control input normalized variation obtained as full-state feedback:

$$ u(t) = \overline{\Delta\Gamma_G(t)} = -\mathbf{K} \cdot \mathbf{x}(t), \qquad (3.18) $$

where the feedback vector gain $\mathbf{K} = \mathbf{R}^{-1} \cdot \mathbf{B}^T \cdot \mathbf{S}$ is computed based on the unique, symmetric and positive semi-definite matrix solution $\mathbf{S}$ of the Riccati algebraic matrix equation:
$$S \cdot A + A^T \cdot S + C_{\alpha}^T \cdot C_{\alpha} - S \cdot B \cdot R^{-1} \cdot B^T \cdot S = 0 \quad (3.19)$$

<figure><img src="image_35.png" /><figcaption>Figure 3.13: 2LFSP applied to a rigidly-coupled WECS: implementation of LFL and HFL and their combined action [49], [29].</figcaption></figure>

Implementation details of both LFL and HFL, as well as the interaction between them, can be viewed in the block diagram in Fig. 3.13. The low-frequency component, $v_s$, is usually obtained by low-pass filtering the signal $v(t)$ provided by the anemometer; e.g., a fourth-order Butterworth low-pass filter having the cut-off frequency at most equal with the WECS bandwidth may be used for this goal [49]. Estimation of the low-frequency wind speed may be improved by prediction [59], [29].

Some representative real-time simulation results – resumed from [49] – are next presented to illustrate the inter-conditioned operation of the LFL and HFL into the same optimal control structure for a low-power (6 kW) variable-speed fixed-pitch rigid-drive-train induction-generator-based WECS. To this end, a small-scale WECS electromechanical simulator, conceived based upon the HILS

concept (see Section 2.3 in Chapter 2), having the generator rotational speed, $\Omega_h$, as driving variable [24], was employed. Both PI-controller-based and on-off-controller-based LFL implementations were tested, but only results with the PI-controller-based one are summarized here.

Time evolutions of some relevant variables are presented, which suggest the role of tuning parameter $\alpha$ in the HFL (the weighting coefficient of index (3.9)) in trading-off the closeness of the operating point to the optimal one and the mechanical load intensity induced by the torque variations, with LFL PI controller parameters being constant.

The LFL is excited by the low-frequency component of the wind speed, $v_s$ (Fig. 3.14a)), taking values in the usual range, from 4 to 10 m/s; here, $v_s$ results as the output of a fourth-order Butterworth low-pass filter – the LPF in Fig. 3.13 – with 0.1 Hz as cut-off frequency. Fig. 3.14b) shows that the LFL ensures operation on the ORC, corresponding to the tip speed of $\lambda_{opt}$; indeed, torque parameter $\gamma$ – which is strongly dependent of $\lambda$, according to (3.10) – exhibits in this figure reasonably small variations around the value $\gamma(\lambda_{opt}) = -1$. The amplitude of these variations depends on $v_s$, which is the output of the separating filter.

Concerning the HFL, the variables of interest are normalized variations around the optimal operating point ensured by the LFL, i.e., that of the tip speed ratio, $z(t) = \overline{\Delta\lambda(t)}$, and that of the generator torque, which is the control input, $u(t) = \overline{\Delta\Gamma_G(t)}$. Maximum variations of the operating point can reasonably be considered within ±20% around the optimal values. For each value of $\alpha$ among the several tested, the state feedback vector gain, $K$, was computed based upon the model's parameters obtained for $v_s$ in the middle of its variation range.

The suggested qualitative interpretation of results in Fig. 3.15 confirms expectations, that is, the amplitude of the tip speed ratio normalized variation, $\overline{\Delta\lambda}$, decreases with the value of $\alpha$, while that of the electromagnetic torque, $\overline{\Delta\Gamma_G}$, increases. Indeed, large $\alpha$ values correspond to interest placed on maximizing control performance, to the detriment of control effort.
<figure><img src="image_36.png" /><figcaption>Figure 3.14: 2LFSP real-time simulation results [49]: effectiveness of the PI-controller-based LFL.</figcaption></figure>

<figure><img src="image_37.png" /><figcaption>Figure 3.16: 2LFSP real-time simulation results [49]: tracking of the ORC thanks to the combined action of LFL and HFL.</figcaption></figure>

for small $\alpha$ (Figs. 3.16a) and c)), these variations are significantly larger than those for large $\alpha$ (Figs. 3.16b and d)) and increase as the wind speed increases.

These variations are both placed within the band of ±20% around zero, meaning that the unnormalized values are oscillating around the operating point with the same amplitude.

Fig. 3.16 shows the combined functioning of the two loops, the operating point variations around the ORC for four values of $\alpha$. As expected,

### 3.2.2 Sliding-mode control of WECS for multi-purpose optimization

Variable structure control (VSC) is particularly effective for variable-speed WECS control, being naturally suited for implementation by the already existing high-frequency-switching power electronics and intrinsically robust to disturbances and parametric uncertainties, thus making unnecessary a precise knowledge of the system [60]–[62]. The increased mechanical stress due to chattering is here the main drawback; however, various methods are available to alleviate it.

The main general difficulty about the VSC design concerns the definition of a sliding surface with guaranteed properties of attractiveness and stability [63], [64]. Flexibility of the sliding-mode approach can be raised by adopting *combined switching surfaces*, with multiple degrees of freedom, in order to allow *multi-criteria optimization* – in our case, the focus remains on captured power maximization along with minimization of the electromagnetic torque variations, responsible of inducing fatigue phenomena.

In this context, the contribution briefed here is resumed from [65] and deals with a sliding-mode approach for tracking the power optimum of a WECS. The design is based on *systematic computation of the sliding surface*
from imposing a desired reduced-order dynamics, which further allows the turbine operation being adjusted to be more or less close to the ORC, according to a desired trade-off between the generator torque (control input) ripple and the optimum tracking. A *multipurpose (energy-reliability) optimization* is achieved in this way.

To fix ideas, a *variable-speed rigid-drive-train doubly-fed-induction-generator (DFIG)-based WECS* is here the chosen configuration – see Fig. 3.8b) and Fig. 3.9. The variable-speed regime is achieved by *generator torque vector control* ensuring a first-order closed-loop dynamic – from torque reference, $\Gamma_G^*$, to effective torque, $\Gamma_G$ – of $T_G$ time constant [66]–[68]. The same Van der Hoven’s limited-frequency wind speed model – with a low-frequency component and a turbulence component – is adopted. The power coefficient curve, $C_p$, is considered known, the structural dynamics are negligible and a constant conversion global efficiency for the whole wind speed domain is assumed.

By coupling the single-mass model of the high-speed shaft (HSS) [69] (see notations in Fig. 3.9) with that of the controlled generator torque, a second-order nonlinear state model is obtained, which is already in the *regular form* required by the VSC design [63]:

$$ \underbrace{\begin{bmatrix} \dot{\Omega}_h \\ \dot{\Gamma}_G \end{bmatrix}}_{\mathbf{x}} = \underbrace{\begin{bmatrix} \frac{\Gamma_{wt}(\Omega_h \cdot i, v)}{i \cdot J_t} - \frac{\Gamma_G}{J_t} \\ -\frac{\Gamma_G}{T_G} \end{bmatrix}}_{f(\mathbf{x}, t)} + \underbrace{\begin{bmatrix} 0 \\ \frac{1}{T_G} \end{bmatrix}}_{\mathbf{B}(\mathbf{x}, t)} \underbrace{\cdot \Gamma_G^*}_{u}, \quad (3.20) $$

where $J_t = J_{wt}/i^2$. Based upon (3.20), the goal is to find a sliding surface allowing operation more or less close to the ORC, implicitly requiring an antagonistic sizing of the control effort. Thus, a *wind-speed-dependent sliding surface* is sought for, whose image in the $(\Omega_l, P_{wt})$ plane must have a nonempty intersection with the ORC for each value of the wind speed and also an adjustable slope for tuning the sliding-mode dynamics – see also Fig. 3.17b), further presented, which is illustrative in this regard.

The sliding-mode dynamic may be imposed as equivalent to a linear one:

$$ \dot{\Omega}_h = \frac{\Gamma_{wt}(\Omega_h \cdot i, v)}{i \cdot J_t} - \frac{\Gamma_G}{J_t} = \begin{bmatrix} a_1 & a_2 \end{bmatrix} \cdot \begin{bmatrix} \Omega_h \\ \Gamma_G \end{bmatrix}, \quad (3.21) $$

where $a_1$ and $a_2$ correspond to the adjustable first-order dynamic on the sliding surface. After some algebra, the *sliding surface* results as a function of the state vector variable:

$$ \sigma \begin{pmatrix} \mathbf{x} = \begin{bmatrix} \Omega_h & \Gamma_G \end{bmatrix}^T \end{pmatrix} = a_1 \cdot J_t \cdot \Omega_h + a_2 \cdot J_t \cdot \Gamma_G - J_t \cdot \dot{\Omega}_h, \quad (3.22) $$

thus also depending on the derivative of a state variable, $\dot{\Omega}_h$, which is particularly embarrassing for the real-time implementation, as it increases high-frequency noises. Instead, this derivative can be estimated in practice by using a suitably chosen first-order high-pass filter.

Parameter $a_1$ represents the time constant of the sliding-mode dynamics – resulted from imposing the convergence speed to the sliding-mode regime – whereas choice of $a_2$ imposes the steady-state regime; in this way, the equilibrium on the sliding surface may be fully described. In our case, provided that power maximization is of interest, the equilibrium point is set to the optimal one, that is, on the ORC.

The two components of the *sliding-mode control law*: the *equivalent control input*, $u_{eq}$, and the *on-off* component, $u_N$, must now be computed. The *equivalent control input* has torque dimensions (N·m) and is obtained as:

$$ u_{eq} = \Gamma_G - \frac{T_G}{(1 + a_2 J_t)} \cdot (a_1 J_t \Omega_h + a_2 J_t \Gamma_G) \cdot (a_1 - A(\lambda, v)), \quad (3.23) $$

where $A(\lambda, v) = \frac{K \cdot v \cdot R^2}{i^2} \cdot \frac{C'_p(\lambda)\lambda - C_p(\lambda)}{\lambda^2}$, with $K = 0.5\pi\rho R^2$ considered as invariant and $C'_p(\lambda)$ being the derivative of the power coefficient in relation to $\lambda$.