Contribution aux systèmes renouvelables connectés en réseau : contrôle, analyse de la stabilité et fiabilité

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Contribution aux systèmes renouvelables connectés en réseau : contrôle, analyse de la stabilité et fiabilité

Ivano Forrisi

To cite this version:

Ivano Forrisi. Contribution aux systèmes renouvelables connectés en réseau : contrôle, analyse

de la stabilité et fiabilité. Energie électrique. Université de Lorraine, 2016. Français. �NNT :

2016LORR0345�. �tel-01757068�

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UNIVERSIT´ E DE LORRAINE

Ecole Doctorale ”Informatique Automatique ´ ´ Electronique- ´ Electrotechnique Mathmatiques”

D´ epartement de Formation Doctorale ” ´ Electronique- ´ Electrotechnique”

TH` ESE

pr´ esent´ ee ` a

L’UNIVERSIT´ E DE LORRAINE

En vue de l’obtention du

DOCTORAT DE L’UNIVERSIT ´ E DE LORRAINE Sp´ ecialit´ e : G´ enie ´ Electrique

par

Ivano FORRISI

Contribution to renewable systems grid connected:

control, stability analysis and reliability

Soutenue publiquement le 2 d´ ecembre 2016 devant le jury compos´ e de : Pr´ esident Delphine RIU Prof. - Grenoble INP, G2Elab Rapporteurs Mohamed BENBOUZID Prof. - Universit´ e de Brest

Micka¨ el HILAIRET Prof. - Universit´ e de Franche-Comt´ e Examinateurs Babak NAHID-MOBARAKEH Prof. - Universit´ e de Lorraine

Serge PIERFEDERICI Prof. - Universit´ e de Lorraine Giovanni SPAGNUOLO Prof. - University of Salerno Nicolae BRINZEI MdC - Universit´ e de Lorraine

Th` ese pr´ epar´ ee au Groupe de Recherche en ´ Electrotechnique et ´ Electronique de Nancy

Site de l’ENSEM - EA N

4366

Contents

R´ esum´ e 5

General Introduction 11

1 Thesis Context- Presentation of PV-GRID connected systems 13

1.1 Introduction . . . . 13

1.2 PV conversion . . . . 14

1.2.1 Distributed-MPPT: architecture and topologies . . . . 16

1.2.2 Solar cells and solar panel: electrical model . . . . 19

1.2.3 PV array modeling behavior verification . . . . 21

1.2.4 MPPT solutions: basic concepts . . . . 23

Classical MPPT solutions . . . . 23

1.2.5 DMPPT with two photovoltaic sources/ constraints . . . . 24

1.3 2-Level inverter . . . . 26

1.3.1 Pulse-Width Modulation . . . . 26

1.3.2 Three-phase 2-Level inverter . . . . 27

1.4 Neutral Point Clamped inverter . . . . 28

1.5 Neutral Point Piloted inverter . . . . 29

1.6 Modulation strategies for the NPC inverter . . . . 30

1.6.1 Phase Shifted PWM (PS-PWM) . . . . 30

1.6.2 Phase Opposition Disposition PWM (POD-PWM) . . . . 31

1.6.3 Alternative Phase Opposition Disposition PWM (APOD-PWM) . 31 1.7 LCL output filter design . . . . 32

1.8 Conclusions . . . . 34

2 Renewable Source-Grid connected Neutral Point Clamped inverter 35 2.1 Introduction . . . . 35

2.2 Comparison between classical inverter and NPC . . . . 35

2.2.1 Power losses in both configurations . . . . 36

2.2.2 Comparison between classical inverter and NPC in matching mode 37 2.3 Indirect Sliding Control (ISC): DC/DC and DC/AC converter . . . . 38

2.3.1 ISC of DC/DC boost converter . . . . 38

2.3.2 ISC of DC/AC converter . . . . 39

2.4 Flatness-based Control . . . . 39

2.5 Dc voltages balancing . . . . 40

2.5.1 Voltages balancing algorithm . . . . 41

2.5.2 Average Model of the clamping current . . . . 42

2.5.3 Poles tracking and parameter selection . . . . 44

2.5.4 Model improvement in a given operating range for input powers P

and P

. . . . 45

2.5.5 Simulation and experimental results . . . . 46

2

2.5.6 Conclusions . . . . 50

2.6 LCL output filter and control . . . . 51

2.6.1 L filter design . . . . 51

2.6.2 LC filter design . . . . 51

2.6.3 LCL filter . . . . 52

2.6.4 Flatness-based Control . . . . 54

2.6.5 Passivity-based Control . . . . 56

Port Hamiltonian systems . . . . 57

PCHD: control design . . . . 58

IDA-PCB: control design . . . . 61

Improving model with parameters estimator . . . . 62

2.6.6 Simulation results: Flatness-based Control vs Passivity-based Con- trol . . . . 65

2.6.7 Experimental results and simulations of the THD: Flatness-based Control vs Passivity-based Control . . . . 70

2.6.8 Flatness vs Passivity: conclusions . . . . 77

3 Large Signal Stability analysis 78 3.1 Introduction . . . . 78

3.2 Nonlinear systems and Lyapunov stability . . . . 78

3.2.1 Definition of Lyapunov stability . . . . 79

3.2.2 Tagaki-Sugeno multi-models . . . . 80

3.2.3 Application of TS approach to model a PFC-LCL filter system . . 81

3.3 Higher-Order Singular Value Decomposition (HOSVD) . . . . 83

3.3.1 Singular value decomposition theory . . . . 83

3.3.2 Application of HOSVD to model a PFC-LCL filter system . . . . 86

3.3.3 Estimation of the domain of attraction . . . . 88

3.4 Application to the NPC inverter including voltage balancing . . . . 90

3.4.1 Large signal stability analysis with fast voltage control loop . . . 91

Takagi-Sugeno model . . . . 92

HOSVD model . . . . 93

3.4.2 Large signal stability analysis taking into account the voltage con- trol loop dynamic . . . . 94

3.5 Conclusion . . . . 98

4 Availability comparison between 2-Level and multilevel inverters 99 4.1 Introduction . . . . 99

4.2 Reliability definitions . . . 100

4.2.1 Mean Time Between Failures and Mean Time To Failure . . . 101

4.2.2 Accelerated Life Testing . . . 101

4.2.3 Availability and repair . . . 102

4.3 Electronic components reliability . . . 103

4.3.1 IGBT failure rate . . . 103

4.3.2 Power diode failure rate . . . 104

4.3.3 Failure rate under lifetime and heat cycle . . . 104

4.4 Markov Chains and degraded modes . . . 105

4.4.1 Degraded modes of the NPC inverter . . . 106

4.4.2 Degraded modes of the NPP inverter . . . 108

4.4.3 Multi-Phase Markov models . . . 109

4.5 Inverter availability assesment using Markov chain model . . . 111 4.6 Conclusions . . . 114

General Conclusion 115

Bibliography 117

Appendix 126

A Input voltages balancing 5-Level NPC 127

B Markov chains details 129

C Matlab code for matrix A in large signal stability analysis 131

D Published papers 135

Summary 136

R´ esum´ e

Cette th` ese a pour but l’analyse d’un syst` eme photovoltaque connect´ e au r´ eseau ´ electrique en prenant en compte le contrˆ ole, l’ ´ etude de la stabilit´ e et la fiabilit´ e(Fig 1). Un ond- uleur de type 2-Niveau (Fig. 2) a ´ et´ e compar´ e avec un onduleur multi-niveaux appel´ e Neutral Point Clamped. Les avantages et d´ esavantage de chaque topologie ont ´ et´ e analys´ e en consid´ erant l’efficacit´ e ´ energ´ etique, l’optimisation de l’injection de l’´ energie sur le r´ eseau ´ electrique et la fiabilit´ e du systme. Pour le contrˆ ole du courant de sor- tie de l’onduleur, ont ´ et´ e propos´ ees deux solutions : un contrˆ ole bas´ e sur la th´ eorie de la platitude et un contrˆ ole par passivit´ e. Ces deux diff´ erents contrˆ oles sont compar´ es par rapport ´ a la robustesse, la complexit´ e et le nombre de capteurs utilis´ es. Il a ´ et´ e montr´ e que les deux contrˆ oles sont capables de g´ erer la probl´ ematique de la r´ esonance du filtre LCL. Pour augmenter l’efficacit´ e de l’algorithme MPPT dans une configura- tion Distributed-MPPT avec la connexion en s´ erie des deux sorties des convertisseurs boost, une nouvelle technique a ´ et´ e propos´ e pour l’´ equilibrage des tension d’entr´ ee d’un onduleur NPC. En utilisant un outil appel´ e TPtool, un ´ etude de la stabilit´ e large sig- nal par ”Higher-Order-Singular-Value-Decomposition” a ´ et´ e pr´ esent´ e et compar´ e avec une m´ ethode bas´ ee sur les mod` eles Takagi-Sugeno pour des systmes non-lin´ eaires. Fi- nalement, l’onduleur 2-Niveaux est compar´ e avec deux multi-niveaux diff´ erents (NPP et NPC) en termes de disponibilit´ e, en prenant en compte les niveaux de redondance des convertisseurs. Pour analyser la disponibilit´ e, a ´ et´ e consid´ er´ ee la th´ eorie des chaines de Markov et pour l’impl´ ementation, le logiciel GRIF a ´ et´ e utilis´ e.

Figure 1: PV-GRID connected system

Lobjectif de cette th` ese est de pr´ esenter et mod´ eliser une strat´ egie pour ´ equilibrer les tensions ´ a lentr´ ee dun onduleur de type NPC en modifiant uniquement la strat´ egie de contrˆ ole de londuleur. En consid´ erant lavantage du DMPPT par rapport au CMPPT, on se concentre sur la probl´ ematique li´ ee aux d´ es´ equilibres des tensions dans le cas dun

5

d´ es´ equilibre entre les puissances dentr´ ee. les contraintes que doivent respecter lalgo- rithme MPPT ont ´ et´ e d´ efinies. La contrainte la plus importante est li´ ee aux limites de la tension de sortie de chaque boost. Ainsi, lorsquon a un d´ es´ equilibre de puissance, un d´ es´ equilibre des tensions de sortie des convertisseurs boost apparait. En pr´ esence dun d´ es´ equilibre, il n’est plus possible de r´ ecup´ erer la puissance maximum de chaque panneaux solaires. Dans la configuration classique avec un onduleur 2-niveaux (Fig. 2) , il est impossible d’´ equilibrer les deux tensions dentr´ ee, tandis que dans la configuration propos´ ee (Fig. 3) il est possible d’avoir l’´ equilibre grˆ ace ´ a la pr´ esence du courant Io (Fig.

4).

Figure 2: Configuration Onduleur classique 2-Niveaux

Figure 3: Configuration Onduleur classique 3-Niveaux

Dans la litt´ erature, il existe d´ ej´ a des ´ etudes sur la probl´ ematique d’´ equilibrage des deux tensions d’entr´ ee mais jamais en consid´ erant que le d´ es´ equilibre est d ´ a un d´ es´ equilibre des puissances dentr´ ee (notre cas) mais plutt ´ a des imperfections de l’onduleur, ou ´ a un d´ es´ equilibre entre les charges triphas´ ees. La d´ efinition dun nouveau mod` ele bas´ e sur le courant Io prenant en compte les variables ct´ e DC (origine du d´ es´ equilibre) a per- mis d’´ etudier la dynamique d’´ equilibrage du systme. Une ´ etude de l’efficacit´ e ´ energ´ etique

6

a ´ et´ e r´ ealis´ ee dans cette thse. Dans le but de pouvoir obtenir le maximum de puissance des deux sources PV, deux architectures de puissances sont consid´ er´ ees. La premi` ere associe un onduleur classique ´ a chaque source PV et la seconde utilise un seul onduleur NPC. L’onduleur NPC pr´ esente de plus un THD en tension de sortie plus faible qu’un onduleur classique et donc permet de diminuer la taille du filtre r´ eseau.

De plus, la tension aux bornes des composants semi-conducteurs est la moiti´ e de celle impos´ ee avec un VSI classique 2-niveaux. Ceci permet d’am´ eliorer la fiabilit´ e du syst` eme global. Une strat´ egie de type ”Indirect Sliding Mode” a ´ et´ e utilis´ ee pour le contrˆ ole des courants de sortir de londuleur NPC et des courants dentr´ ee des convertisseurs boost.

Pour la r´ egulation de la tension Vdc un contrˆ ole bas´ e sˆ ur la platitude a ´ et´ e impl´ ement´ e.

une comparaison entre l’onduleur classique 2-niveaux et londuleur NPC 3-niveaux par rapport ´ a lefficacit´ e ´ energ´ etique est pr´ esent´ ee, sans consid´ erer le filtre de sortie. Il est r´ esent´ e lalgorithme d’´ equilibrage propos´ e et on d´ etaille le mod` ele utilis´ e pour le courant de clamping Io. L´ equilibrage des tensions dentr´ ee est possible jusqu’´ a une diff´ erence de puissance DeltaP=35%.. Les r´ esultats exp´ erimentaux obtenus sur un banc r´ ealis´ e au laboratoire valident les r´ esultats de simulations obtenus.

Figure 4: Mod´ elisation pour le courant Io

Figure 5: MLI modifi´ ee pour l’algorithme d’´ equilibrage

Pour la validation des mod` eles et l’efficacit´ e de l’algorithme d´ equilibrage propos´ e, nous avons utilis´ e Matlab/Simulink. Pour les convertisseurs DC/DC on a utilis´ e des

7

composants Semikron SKM50GB123D et pour l’onduleur SK20MLI066. En outre, on a utilis´ es cinq capteur de courant et six capteur de tension. Sur la Fig. 7 est repr´ esent´ e le banc de test utilis´ e. Sur les Figs.8-9 sont pr´ esent´ ees respectivement les simulations et les r´ esultats sur le banc dans le cas o´ u on a une variation de puissance du 23% et sans utiliser l’algorithme d’´ equilibrage. ur les Figs.10-11 on a une variation de 35%

et on utilise cette fois l’algorithme d’´ equilibrage propos´ e. On voit que les simulations (Figs.8-9) refl` etent bien la r´ ealit´ e (Figs.10-11).

Figure 6: Comparaison entre le mod` ele instantan´ e et le mod` ele moyen

Figure 7: Test bench

8

Figure 8: ´ Equilibrage OFF: tensions d’entr´ e de l’onduleur et une des courants

Figure 9: ´ Equilibrage ON: tensions d’entr´ e de l’onduleur et une des courants

Figure 10: ´ Equilibrage OFF(test): tensions d’entr´ e de l’onduleur et une des courants

9

Figure 11: ´ Equilibrage ON (test): tensions d’entr´ e de l’onduleur et une des courants

10

General Introduction

In this work a PV-grid connected system is studied. The focus is put on a multilevel inverter to connect to main grid. The connection of the inverter with the main AC grid is realized through a three-phase interconnection filter.

Renewable energy is nowadays one of the most important energy source above all for environmental reasons. In last decades, giant steps have been taken in order to improve the global efficiency of photovoltaic fields. To increase the global photovoltaic efficiency, several issues should be taken into account:

• efficiency of the solar cells (new technologies and materials)

• efficiency of the power converters (DC/DC, DC/AC, filters, etc)

• effectiveness of Maximum Power Point Tracking (MPPT) techniques

In this thesis, we are interested in the second and third points. In addition, we pro- pose to compare candidate topologies regarding reliability of the power converters.

The main advantage of photovoltaic energy for grid-connected systems is related to the fact that power plant could be close to grid reducing transmission losses. The most important disadvantage of this type of energy source is its intermittence, which leads flicker effects to the main grid or involve the use of storage devices in case of embedded or autonomous applications.

In this work, the chain PV-grid is analyzed in terms of power design, control, stability analysis and reliability. For the stability issue in grid-connected systems, two approaches can be used to analyze stability properties of the system. The first one, widely used by engineers, is based on small signal modeling and eigenvalues analysis. The main draw- back of such a method is to limit the analysis to small variations around an operating point for states and input variables. To avoid this constraint we propose to investigate large signal stability analysis methods.

For the reliability assessment, the reliability of the multilevel converters is often con- sidered a strong weakness in literature. For this reason we are interested in comparing classical 2-Level inverters with an alternative solution using only one multilevel inverter.

Therefore, this manuscript is organized as follows:

• The first chapter is the presentation of this work. In this part, different configura- tion for the injection of the photovoltaic energy to grid are presented. To introduce

11

our study on the MPPT, classical MPPT solutions are presented, analyzing the constraints and literature research. A brief overview of the 2-Level classical con- figurations and the multilevel inverters is introduced. Finally, in order to present the issue of the output filter design and control, an LCL filter is studied.

• In the second chapter an efficiency comparison between power architectures con- stituted with 2-Level classical inverters and a Neutral Point Clamped inverter is presented. The problem of the photovoltaic power mismatch and its consequences are analyzed and a novel technique of input voltages balancing of the Neutral Point Clamped inverter is introduced. Several control techniques are presented in this part, such as: Indirect Sliding Mode Control, Flatness-Based Control, Passivity- Based Control.

• The third part deals with large signal stability analysis. After a short introduction on the Lyapunov theory, Takagi-Sugeno approach and Higher-Order Singular Value Decomposition (HOSVD) are discussed and compared for two examples including nonlinear and strongly nonlinear systems.

• The last chapter deals with the reliability of the power systems. The aim of this work is to introduce the tools allowing reliability analysis applied to power elec- tronic systems. The failure rate of system components is determinated considering the operating conditions. The proposed modeling of the system is based on stochas- tic processes like that continuous time Markov chains taking into account not only the failures but also the possibility to repair. Finally, we will compare different inverter topologies (2-Level classical inverter, NPC and Neutral Point Piloted ) in terms of their availability.

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Chapter 1

Thesis Context- Presentation of PV-GRID connected systems

1.1 Introduction

The aim of this PhD thesis is to analyze a PV-GRID connected system (Fig. 1.1) in terms of power design, control, stability and reliability. During the last three years, the PhD thesis has been led in the Groupe de Recherche en ´ Electrotechnique et ´ Electronique de Nancy (GREEN), in France. The core of the issue is the choice of the inverter topology for increasing the reliability and for the optimization of the energy injection.

For this reason, in the next paragraphs different configurations in order to inject the energy are introduced. Among renewable energy power generation applications, grid- connected photovoltaic inverter systems have been given a high recognition during the last decades [1]. In the past few years, the multilevel technologies for grid-connected PV inverter systems have drawn more interests. The advantages of the multilevel topologies with respect to the classical 2-Level inverter are related above all to the THD (Total Har- monic Distortion), and obviously the volume and cost of the output filter, but as shown in Chapter 4, the availability of these topologies can be improved in some particular sit- uation. Weakness are essentially the number of semiconductors used and, accordingly, the cost of the power converter.

Figure 1.1: PV-GRID connected system

This chapter gives the state-of-art of PV-GRID connected system considering stan- dard configurations based on classical 2-Level inverter. In order to introduce the second

13

CHAPTER 1. THESIS CONTEXT- PRESENTATION OF PV-GRID CONNECTED SYSTEMS

chapter of this thesis, a brief review of the power mismatching issues and the dc-dc boost converter in this chapter are presented. The operating of 2-Level and multilevel invert- ers is analyzed and in details different PWM strategies for the Neutral Point Clamped inverter are presented. In last decades, a LCL output filter is often used in order to decrease size, cost and total harmonic distortion(THD) [2]. However, the resonance of the LCL filters challenge the stability of the current control loop [3]. On the dc-side, under uncertain characteristics of the PV source impedance (e.g., number of PV mod- ules connected and/or uncertainty in source circuit parameters), the stability might be violated due to equivalent source/load impedance mismatch [4]. In order to manage the stability issues, large stability analysis is given and in this chapter a brief recapitulation of the existing method are presented. The reliability issue which is a baffling factor in PV system acts as a tough obstacle on spreading this technology [5]. Generally, the inverter is responsible for the majority of failures in PV systems. Field test data has demonstrated the solar panels which actually are the most reliable part of the PV sys- tem can perform very well for more than 25 years [6]. For this reason, considering the introduction of a non-standard configuration for PV-GRID connected systems, a reliabil- ity comparison between classical 2-Level inverter and multilevel inverters (NPC [7] and NPP [8]) is given. In this chapter, some example of the reliability analysis in electronics applications are presented.

1.2 PV conversion

Up to few years ago, large-scale power plants represented the majority of the Photo- voltaic (PV) systems installed all around the world. Such plants were able to generate hundreds of kilowatts or even some megawatts because they paved large even grounds with thousands of panels, all of the same type and with the same orientation towards the Sun. This kind of installation required specific solutions for power conversion, so that the effort was concentrated in developing high performance inverters, usually equipped with only one DC input at which the Maximum Power Point Tracking (MPPT) algorithm operated. The latter did not have to face uncommon problems: the central inverter was easily able to draw the PV strings and the whole field towards the Maximum Power Point (MPP) of a power vs. voltage curve that was a scaled-up version of that one of any PV panel of the field. This quiet condition was due to the fact that all the panels received the same irradiation level and were equally oriented. Effects due to clouds, determining a partial shading of the PV field, were neglected, especially when the occurrence of such a condition was not frequent and when the clouds transition was expected to be very fast. Possible different orientation of the PV panels, due to ground unevenness and mis- takes in the installation, was considered as a minor issue. Additionally, theft problems and issues related to the monitoring of the power production of the PV field were not afforded systematically, with significant consequences on the plant productivity. In fact, some stops in the energy production of the whole plant, or of a part of it, were required for maintenance or repairing. Last, but not least, issues related to safety were a minor problem, because the access to the area of the PV plant was open to authorized and skilled personnel only. More recently, multi-string inverters have been proposed on the market, their main feature being two or more DC inputs, each one equipped with its own MPPT controller. Such a feature allowed to divide the PV field in subsections, each one potentially working in different operating conditions, and to ensure the maximum power from each one of them. In case of shadowing, or installation with a different orientation with respect to the Sun of some panels, a power drop affected only the string in which

14

CHAPTER 1. THESIS CONTEXT- PRESENTATION OF PV-GRID CONNECTED SYSTEMS

such panels were connected, without any effect on the parts of the PV field connected to the other DC inputs of the inverter. Such a solution also allowed to have different sections of the PV field made of different types of panels, the only forethought being the series connection in the same string of panels of the same peak power and open circuit voltage.

Figure 1.2: String of two series connected Kyocera KC120 modules

Fig. 1.2 qualitatively shows the effects of the series connection of PV modules sub- jected to different irradiances. With the same working conditions, the current vs. voltage curve of the string is a scaled up version, in terms of voltages, of the curve of a single module. Instead, the series connection of modules working in different conditions gives rise to multiple variations in the slope of the curve and, consequently, in multiple peaks of different heights in the power vs. voltage curve of the array. Details about the pos- sible modifications in the curve shape can be found in [9]. Multi-string inverters have mitigated the effect of the so called mismatching events in the case of large PV fields but not in the case of small power installations. Moreover, they have not been help- ful in solving the problem of substituting few damaged PV panels, after some years of operation, in the plant building. The unavailability of panels with characteristics that are close to those ones of the original panels in the PV field determines the stop in the power production of the power plant, or at least of a part of it; in fact the substitution of the damaged panels with similar, but not exactly the same panels, determines a mis- matching effect, in the string including different types of panels, even if they all operate under the same irradiation level. An increased need of flexibility in the electrical de- sign of the PV field has been also required by the increased interest in PV applications in urban contexts. These require a relatively small number of panels, but they may have many different orientations with respect to the Sun and/or shadowing effects can irregularly affect them. Last but not least, because of convection effects due to wind or different installation supports, they can work at more or less different temperatures.

Such a mismatch is due to the installation of the panels on more than one faade of a building and to the shadows produced by obstacles, trees, chimneys, poles and so on.

Since the use of any multi-string inverter would require too many series connected panels

per each DC input, because some hundreds of volts must be reached, the mismatching

effect would be unacceptable. The solution that has been recently proposed in literature

and, slightly after, put on the market by some producers is the so-called Distributed

MPPT (DMPPT). Such a term was firstly introduced in [10] and nowadays it is the

CHAPTER 1. THESIS CONTEXT- PRESENTATION OF PV-GRID CONNECTED SYSTEMS

synonym of MPPT control dedicated to a single PV panel. This goal can be obtained by means of two different tools. The first, and older, one is the adoption of one DC/DC converter per PV module, so that the dedicated converter, whose output terminals are connected in series or in parallel with those ones of the converters dedicated to the other panels, runs the MPPT. This solution requires a careful choice of the DC/DC converter topology and control, depending on the chosen electrical connection and on the maximum stresses the switching devices can be subjected to. The second solution is especially aimed at grid connected PV systems and it is based on the adoption of a DC/AC converter (micro-inverter) per PV panel. In this case the micro-inverter output terminals are straightforwardly connected to the grid, so that the circuit has to take charge for the significant boosting of the low DC voltage at the panel terminals up to the peak voltage value at the AC mains. In many cases, and especially when the DC/AC converter involves a DC link followed by a PWM inverting stage, a DC/DC converter with a high voltage conversion ratio is needed for boosting up the PV panel voltage by 10- 15 times. Up to now, any DC/DC converter having such a feature has the drawback of a low efficiency, so that the main limitation of the most flexible DMPPT solution, that is the panel dedicated inverter, is the quite low conversion efficiency. Another solution to the mismatching effect is currently available on the market. It consists of a switching box that takes at its input the couples of cables coming from each PV module in the field. The couple of its own output terminals is connected at the inverter input port.

The switching box performs a periodic reconfiguration of the PV field by arranging the PV modules connection in order to maximize the power produced by the whole field.

The switching box consists of a large number of power switches, realized in a proper way so that a high reliability is ensured, and a digital control unit that takes the decisions about the reconfiguration. A similar approach is presented in [11]. All the mentioned solutions have among the main features the increased safety in case of fire, because of the capability of reducing the risk of hazards for firemen. The automatic module shutdown is included in many products. Firefighters shut off power but this means that the central inverter is shut off. Unfortunately, the DC of hundreds of volts is still present and this poses risks to firefighters, especially when they cut through roofs and walls because it could result in chopping through live wires.

1.2.1 Distributed-MPPT: architecture and topologies

The first grid-connected PV systems put in service were made of strings of PV modules which were connected in parallel and fed a central DC/AC inverter, as shown in Fig.

1.3. The function of such a central inverter, besides that one of converting DC power to

grid-compliant AC power, was also that one of carrying out the tracking of the MPP of

the Power vs. Voltage (P-V) characteristic of the whole field. In other words, the central

inverter was responsible of the Field Maximum Power Point Tracking (FMPPT). It is

well known that, in case of mismatch (due to clouds, shadows, dirtiness, manufacturing

tolerances, aging, different orientation of parts of the PV field in the so called Building

Integrated Photovoltaic Systems etc.), the P-V characteristic of the PV field exhibits

more than one peak, due to the presence of bypass diodes, and MPPT algorithms can

fail [12]- [13]. The failure of such MPPT algorithms is due to the fact that they are

not able to avoid that the operating point of the PV source may remain trapped in

the neighborhood of a relative maximum power point instead that close to the absolute

maximum power point. Moreover, even when FMPPT is able to catch the absolute

maximum power of the mismatched PV field, such a power is lower than the sum of the

CHAPTER 1. THESIS CONTEXT- PRESENTATION OF PV-GRID CONNECTED SYSTEMS

available maximum powers that the mismatched modules are able to provide.

Figure 1.3: Grid-connected PV system with FMPPT

Distributed Maximum Power Point Tracking (DMPPT) allows to overcome the draw- backs associated to mismatching phenomena. Two different DMPPT approaches can be adopted. The first one is based on the adoption of one microinverter per PV module converting DC power to grid-compliant AC power. Another approach is instead based on the use of a module dedicated DC/DC converter carrying out the MPPT for each module, shown in Fig. 1.4 and central inverters.

The DMPPT architecture shown in Fig. 1.5 instead requires DC/DC converters characterized by two contrasting requirements: a high voltage conversion ratio (e.g. from 20-30 V to 350-450 V) and a high conversion efficiency. Up to now, only one company, the eIQ Energy, markets a device (Parallux Vboost) which has been developed for such a kind of architecture.

Usually, in commercial PV modules, each bypass diode is connected in parallel to a string

of up to 18-20 PV cells. Therefore, since a PV module is equipped with more than one

bypass diode, if the module is not uniformly shadowed but, as an example, only one cell

is covered by snow or dirt, then the power versus voltage characteristic of the whole PV

module may exhibit multiple peaks. In such a case, the MPPT controller of the dc/dc

converter associated to such a PV module can lead to a suboptimal operating condition

since no MPPT technique is able to correctly face the presence of multiple peaks in

the power versus voltage PV characteristic. Therefore, it is worth noting that DMPPT

is fully effective only if each PV module is equipped with as many dc/dc converters

as bypass diodes. In particular, one dc/dc converter should be inserted in place of

each bypass diode. However, in order to grant the functionality of the rest of the PV

system also when a dc/dc converter is turned off or damaged, a bypass diode should

be connected at the output of each dc/dc converter. Indeed, depending on the adopted

dc/dc converter topology and on the type of chosen switching components, the addition

of a bypass diode at the output of each dc/dc converter may not be necessary. As an

example, if the standard boost topology is chosen and the active switch of the boost

converter is a MOSFET, the bypass function is ensured by the presence of the boost

CHAPTER 1. THESIS CONTEXT- PRESENTATION OF PV-GRID CONNECTED SYSTEMS

Figure 1.4: Grid-connected PV system with DMPPT. Approach based on the adoption of MPPT DC/DC converters with the output ports connected in series

output diode and of the body diode of the MOSFET itself. Instead, if the synchronous

version of the boost topology is chosen, the bypass function is ensured by the presence of

the body diodes of the two MOSFETS or by the presence of the external diode which is

generally added in antiparallel to each MOSFET in order to increase the overall efficiency

of the power stage. Another important aspect to discuss is indeed just related to the

power stage efficiency. In fact, one drawback of DMPPT applications is represented by

the fact that DMPPT is able to ensure higher energy efficiency than FMPPT, in presence

of mismatching phenomena, only if the efficiency of the power stage of MPPT DC/DC

converters is enough high [14]. In fact, in ideal, uniform operating conditions, the overall

efficiency of a PV system with FMPPT is expected to be greater than that one of the

same system operating with DMPPT since this last includes additional dc/dc conversion

stages. Indeed, DMPPT does not necessarily require two dc-dc stages; e.g., in the case of

the commercial device SolarEdge, the strategy of the company is based on the adoption of

a dc/dc stage dedicated to each PV module and on the use of a single dc/ac stage for the

whole array. Nevertheless, if a commercial PV inverter is adopted, it usually contains two

conversion stages: a dc/dc and a dc/ac stage. In such a case DMPPT requires the flow

of energy from the PV modules to the grid through three different conversion stages: two

dc/dc stages and one dc/ac stage. Therefore high efficiency is a mandatory requirement

for the dc/dc converters to be adopted in DMPPT PV applications; indeed efficiency is

the starting point of the design process of the power stage of the SCPVMs. Such a design

involves not only decisions concerning the topology of the dc/dc converter, the type of

power components, the value of the output voltage, the value of the switching frequency

but also, the time varying characteristics of the PV sources. In fact, the peculiarity of

DMPPT PV applications is just represented by the fact that the operating point of the

SCPVMs is not constant but it is continuously changing. So that it is not possible to

identify a single reference operating condition to be taken into account in the design

CHAPTER 1. THESIS CONTEXT- PRESENTATION OF PV-GRID CONNECTED SYSTEMS

process. In particular the profile of the efficiency of the dc/dc MPPT converter must be optimized on the basis of the power profile of the PV source which in turn depends on the weather conditions characterizing the installation site [14]. In addition, it is worth noting that the set of design constraints characterizing grid-connected and stand alone DMPPT PV applications are not coincident. In particular the optimization of a dc/dc converter dedicated to stand alone DMPPT PV applications requires to keep into account, in addition to what has been already listed above, also the efficiency of the charge/discharge processes of the batteries, their lifetime, and the shape of the profile of the power required by the load. The second drawback of DMPPT PV applications is represented by the fact that conditions exist in which also the DMPPT approach does not allow the working of each PV module of the field in its MPP. This is due to constraints associated to the more or less limited voltage conversion ratio of the adopted DC/DC converters, to the finite voltage and current ratings of devices used in the power stage of SCPVMs and/or due to a non optimal value of the bulk inverter voltage.

Figure 1.5: Grid-connected PV system with DMPPT. Approach based on the adoption of MPPT DC/DC converters with the output ports connected in parallel

In Chapter 2 of this thesis, the using of a multilevel inverter in a configuration DMPPT-DC/DC converters with the output ports connected in series is adopted. In order to explain the advantage of this topology with respect to a classical configuration based on a 2-Level inverter, let us to give an example considering two different PV connected to a 2-Level inverter through dc/dc boost converters. In the newt paragraphs they will be presented a simple MPPT with one photovoltaic sources before to introduce the MPPT for two different sources and to consider what happen when a mismatch is present between the spources.

1.2.2 Solar cells and solar panel: electrical model

The theory of solar cells explains the process by which light energy in photons is con-

verted into electric current when the photons strike a suitable semiconductor device.

CHAPTER 1. THESIS CONTEXT- PRESENTATION OF PV-GRID CONNECTED SYSTEMS

The theoretical studies are of practical use because they predict the fundamental limits of solar cell, and give guidance on the phenomena that contribute to losses and solar cell efficiency [15]. The principle of a solar cell operation [16] is shown in Fig. 1.6.

Figure 1.6: Solar cell operation

In three steps we explain how the energy of a photon is converted in electricity [17]:

• Photons in sunlight hit the solar panel and are absorbed by semi-conducting ma- terials

• Electrons (negatively charged) are knocked loose from their atoms as they are excited. Due to their special structure and the materials in solar cells, the electrons are only allowed to move in a single direction. The electronic structure of the materials is very important for the process to work, and often silicon incorporating small amounts of boron or phosphorus is used in different layers

• An array of solar cells converts solar energy into a usable amount of direct current (DC) electricity

Although the current is reasonable, the voltage is too small for most applications [18].

To produce useful dc voltages, the cells are connected togheter in series and encapsulated into modules. A module typically contains 28 to 36 cells in series, to generate a dc output voltage of 12V in standard illumination conditions. The 12V modules can be used singly, or connected in parallel and series into an array with a larger current and voltage output, according to the power demanded by the application. Cells within a module are integrated with bypass and blocking diodes in order to avoid the complete loss of power which would result if one cell in the series failed.

A solar cell and a solar module PV are modeled as a current source because it supplies a constant current over a wide range of voltages with in parallel a p-n junction diode.

In order to consider the non-ideal effects, a parallel and series resistances are added as shown in Fig. 1.7.

where G is the irradiation level in (W/m

), T

is the temperature. Therefore, the

photovoltaic current I

is given by the eq. 1.1:

CHAPTER 1. THESIS CONTEXT- PRESENTATION OF PV-GRID CONNECTED SYSTEMS

Figure 1.7: Equivalent circuit of a PV source

I

= I

− I

e

Vpv+RsIpv

Vt

− 1

− V

+ R

I

R

(1.1)

The current I

is the current source and it is observed that it is linearly dependant with the temperature and irradiation [19]:

I

= G K

(T

− T

) + I

(1.2)

where T

= 25C, K

is a coefficient of temperature dependency and I

is the short-circuit current under standard test conditions (1000W/m

).

I

is the diode inverse saturation current, V

is a voltage taking into account of the PV source temperature and diode ideal factor α and this voltage is calculated by 1.3

V

= αk

T

q (1.3)

where k

is the Boltzmann’s constant and q the charge of the electron. The resis- tances values are present on datasheet and they depend on temperature and irradiation level. Actually, the resistance R

has more influence that R

.

1.2.3 PV array modeling behavior verification

First, the static behavior of the modeled PV panel is verified under different uniform conditions. In Fig. 1.8, it can be observed that the simulated panel behavior is in accordance with theoretical expected behavior. It has to be underline again that no experimental validation will be proposed since it would have required measurement of the irradiation and temperature which were not available on the used test bench.

Our aim was to have a model presenting similar behavior as observed in practice

while the PV source is under non-uniform conditions. An array constituted with 6 PV

panels as simulated in Fig. 1.8 is proposed for verifying the behaviour under non-uniform

conditions. The considered interconnection scheme is shown in Fig. 1.9 (”3p2s” con-

figuration), with protection diodes and considered conditions for each individual panel

of the array. It has to be noticed that it was chosen to independently model each PV

CHAPTER 1. THESIS CONTEXT- PRESENTATION OF PV-GRID CONNECTED SYSTEMS

Figure 1.8: Simulated PV panel static characteristic under different uniform conditions array and protection diodes. However, as done in [20], by-pass diode can directly be integrated in the model thanks to the Lambert function(not explain in this thesis).

Figure 1.9: PV array ”3p2s” under non-uniform conditions (cond1 : 1000W.m

, 25

C, - cond2 : 500W.m

, 10

C)

In Fig. 1.10, the simulated static characteristic corresponding to the array shown in

Fig. 1.9 is given. As expected, as two different irradiation conditions are considered, the

resulting characteristic presents two distinct power maximum. This behavior has been

observed to be conform to experimental behavior under non-uniform conditions. Then

the PV model is validated and could be used for simulating the MPPT which are going

to be treated thereafter.

CHAPTER 1. THESIS CONTEXT- PRESENTATION OF PV-GRID CONNECTED SYSTEMS

Figure 1.10: Simulated static characteristic under non-uniform conditions for the array

”3p2s”)

1.2.4 MPPT solutions: basic concepts

From the behaviour of the photovoltaic source characteristics under uniform and non- uniform irradiation conditions, one important problematic of the use of photovoltaic sources is easily understandable. This problematic comes from the presence of a max- imum of power on the characteristic. To optimize the functioning, the global power optimum must be followed, which is not trivial since the characteristic curve is not known during time as it varies with respect to irradiation and temperature. The opti- mum power research is often called Maximum Power Point Tracking (MPPT).

Maximum Power Point Tracking thematic has been largely studied and many solu- tions have been proposed. Number of papers on the subject has grown considerably through the last decades and remains strong. A non-exhaustive review of MPPT tech- nique is proposed in [21]. In this paper, the authors listed more than 90 paper published from 1968 to 2005 among which at least 19 distinct methods have been introduced.

There, the two most commonly used MPPT algorithm are presented and some solution for non-uniform irradiation conditions are reviewed.

Classical MPPT solutions

Among hundreds of MPPT algorithm which can be found through the literature, two particular techniques largely distinguish especially because of their simplicity of imple- mentation:

• Perturbation and Observation (P&O):

This first method is the most used, especially on industrial applications. It works by applying perturbation on the PV operating voltage or current in order to in- crease the power. The perturbation can also directly been applied on the associated converter duty cycle (this method being also called Hill-climbing in the literature).

One of the main particularity of this technique is that even when converged it stays

oscillations around the maximum. Among articles discussing on this technique, ref-

erence [22] can be distinguished. In this paper, the authors gives mathematical

CHAPTER 1. THESIS CONTEXT- PRESENTATION OF PV-GRID CONNECTED SYSTEMS

analysis enabling to optimize the two parameters of the P&O algorithm, i.e. its time and perturbation steps (duty cycle of an associated boost converter in [22]).

When optimized following the method proposed in [22], the P&O MPPT converges precisely on the maximum with good behaviour under transient conditions (veri- fied for fast variation on the irradiation).

• Incremental Conductance (IncCond):

This second technique is based on the observation of the power derivative and uses the fact that the PV characteristic slope is zero at the maximum. Even if this technique is known to be more efficient than the P&O under fast variations on the conditions and has the advantage to stabilize without residual oscillations, this second technique remains less used than the P&O.

Many improvements on those two techniques can be found through the literature as for example in [23], [24], [25], and so forth... Some can also found more advanced methods as proposed in [26], presenting better results under fast variations on the irradiation and temperature condition. However, every of those methods may felt under non-uniform conditions when power characteristic present multiple maxima.

1.2.5 DMPPT with two photovoltaic sources/ constraints

Let us consider the system with two different power sources shown in Fig. 1.11, where the total power is calculated as follows:

P

=

2

X

i=1

P

=

2

X

i=1

V

I

=

2

X

i=1

V

f(V

) (1.4)

It is worth noting that, in presence of mismatching it is not always possible to achieve the MPP of the overall system by simply tracking the MPP of each PV module [10]. In principle, only step-updown converters with unitary efficiency would be able to allow it.

Figure 1.11: DMPPT-DC/DC converters with the output ports connected in series: two photovoltaic sources

Due to the series connection of the boost output ports, the voltages V

and V

are

calculated as follows:

CHAPTER 1. THESIS CONTEXT- PRESENTATION OF PV-GRID CONNECTED SYSTEMS

V

= V

P

P

(1.5)

where V

= V

+ V

is the inverter input voltage.

Equation 1.5 highlights that the dc/dc output voltage can vary in a wide range due to possible imbalances among powers delivered by modules. Considering tha particular case of P

= V

I

' 0 (totally shadowed) and P

= V

I

6= 0, then V

' 0 and V

= V

.

However, the output voltage in a boost converter corresponds to the maximum voltage across the switches and the output capacitor. In order to prevent the output voltage of one or more dc/dc from exceeding a given maximum value V

, an output-voltage limitation technique must be adopted by means of a suitable duty-cycle limitation func- tion [10].

Figure 1.12: DMPPT-DC/DC converters with the output ports connected to the Neutral Point Clamped inverter: two photovoltaic sources

The output-voltage limitation constraint is:

V

< V

(1.6)

where V

is the rated voltage drain-source of the MOSFET used for the boost converter (or collector-emitter for a transistor).

This is not the only constraint, but the output voltage is limited by the dc/dc topology used, for example in this case, the dc/dc output voltage has to be higher than the PV output voltage V

:

V

> V

(1.7)

The global MPPT adopted in several techniques tries to solve this problem of con-

straints and to increase the MPP range of feasibility [10]. Another technique is explained

in [27] where PSO theory is used in order to optimize the global MPPT algorithm in this

CHAPTER 1. THESIS CONTEXT- PRESENTATION OF PV-GRID CONNECTED SYSTEMS

configuration. As explained in Chapter 2 of this thesis, it is possible to change inverter topology in order to balance the output voltage of the boost converter and to solve the problem of the output voltages constraints. Moreover, if the dc/dc output voltages are balanced by the inverter, independent MPPT is achievable for every power sources. In Fig. 1.12 the configuration proposed in this thesis is shown and the details are explained in Chapter 2.

To be noted that in this configuration the dc/dc ouput ports are not really in series connected, because of the presence of the ”neutral point” of the inverter. This charac- teristic is the crucial point in order to balance the dc/dc output voltages. The equations 1.5 are valid only in mismatch operating mode and this is an advantage in order to delete the constraints on the dc/dc output voltages (Chapter 2 for details).

1.3 2-Level inverter

Power inverters are systems converting electrical energy from the DC form into the AC one. The purpose of DC/AC power inverter is to take DC power supplied and transform it into an AC voltage power source, such as for emulation of the power available at an ordinary household electrical outlet. In this paragraph it is briefly explained the operating of a classical 2-Level inverter and the relative pwm strategy often used.

1.3.1 Pulse-Width Modulation

In electronic power converters and motors, PWM is used extensively as a mean of pow- ering alternating current (AC) devices with an available direct current (DC) source.

Variation of duty cycle in the PWM signal to provide a DC voltage across the load in a specific pattern will appear to the load as an AC signal, or can control the speed of motors that would otherwise run only at full speed or off. This is further explained in this section. The pattern at which the duty cycle of a PWM signal varies can be created through simple analog components, a digital micro-controller, or specific PWM integrated circuits. Analog PWM control requires the generation of both reference and carrier signals that feed into a comparator which creates the output waveform based on the difference between the signals [28]. The reference signal is sinusoidal and at the frequency of the desired output signal, while the carrier signal is often either a saw tooth or triangular wave at a frequency significantly higher than the reference one. When the carrier signal exceeds the reference, the comparator output signal is at one state, and when the reference is at a higher voltage, the output is at its second state [28]. In the next figure is shown the process, for a single-phase, for three-phase it is the same but with three sinusoidal reference voltages shifted by 120. Let us define the amplitude (m

) and frequency (m

) ratio as follows:

( m

=

c

m

=

m

(1.8)

The amplitude ratio must be less than and m

>> 1 for a good design [29].

CHAPTER 1. THESIS CONTEXT- PRESENTATION OF PV-GRID CONNECTED SYSTEMS

Figure 1.13: Pulse-Width Modulation single-phase and output voltage

Figure 1.14: 2-Level inverter

1.3.2 Three-phase 2-Level inverter

Three phase inverter is used to provide adjustable frequency power for industrial appli- cations. Three phase inverter is more common than single phase inverters. DC supply for three phase inverters is taken from a battery or usually from a rectifier. In industrial application, VSI is mostly used, because a wide range of speed control is possible. Three phase VSI is operated at two modes:

• 180 degree mode operation

• 120 degree mode operation

In 180 degree mode of operation three switches conduct at one cycle, each IGBT is

operated at 60 degree delay angle. In this mode of operation, one can easily get the

pure sine wave using a filter. So it is otherwise called as a quasi square wave mode or

CHAPTER 1. THESIS CONTEXT- PRESENTATION OF PV-GRID CONNECTED SYSTEMS

switched mode (Ned Mohan et al 2009). In 120 degree mode operation is pair of switch conduct at 120 degree delay angle. In this mode a shoot through fault occurs. Often the dc source is the output of a rectifier, a battery or the output of a boost converter (usually in photovoltaic applications). In table 1.1 is summarized the operating of the 2-Level inverter in terms of output voltages related to the switching states.

Table 1.1: Switching states of a 2-Level three-phase inverter S

S

S

S

S

S

V

V

V

ON ON OFF OFF OFF ON V

0 −V

ON ON ON OFF OFF OFF 0 V

−V

OFF ON ON ON OFF OFF −V

V

0

OFF OFF ON ON ON OFF −V

0 V

OFF OFF OFF ON ON ON 0 −V

V

ON OFF OFF OFF ON ON V

−V

0

ON OFF ON OFF ON OFF 0 0 0

OFF ON OFF ON OFF ON 0 0 0

1.4 Neutral Point Clamped inverter

The three-level neutral-point-clamped voltage source inverter was introduced by Nabae in 1981 [30] and it is popular in the energy conversion systems dedicated to systems employing wind and solar energies. In Fig.2.2 the main circuit of the NPC-PWM in- verter is shown, where the

0

indicates the neutral point with respect to the dc source;

(S

, S

), (S

, S

), (S

, S

), are the main transistors operating as switches for the PWM; (S

, S

), (S

, S

), (S

, S

), are auxiliary transistors to clamp the output terminal potential to the neutral point potential, together with (D

...D

). The anti- parallel diodes on every switch are called D

...D

To be noted that (a, b, c) are referred respectively to the first, second and third leg. In Table 1.2 shows the output voltage level in different combinations of switch and current (considering the first leg as reference, I = i

):

Table 1.2: Switching states of a NPC inverter

Sign of current Switch ON Switch with current Output voltage I > 0 S

, S

S

, S

I < 0 S

, S

D

, D

I > 0 S

, S

D

, S

0 I < 0 S

, S

S

, D

0 I > 0 S

, S

D

, D

−

I < 0 S

, S

S

, S

−

The inverter Neutral Point Clamped has three different levels, so that the output voltage in every leg has three voltage levels (the classic inverter output voltage has

,

−

).

Let us define the conversion functions f

as follows:

CHAPTER 1. THESIS CONTEXT- PRESENTATION OF PV-GRID CONNECTED SYSTEMS

Figure 1.15: Neutral Point Clamped inverter

f

=

( 1, if the i

switch of the k

leg is OFF

0, otherwise (1.9)

The output voltages referred to the point

0

are:



 

 

V

= (f

f

− f

f

)

V

= (f

f

− f

f

)

V

= (f

f

− f

f

)

(1.10)

Finally, the output voltages referred to the point

N

are:



 V

V

V



 =





2 −1 −1

−1 2 −1

−1 −1 2



 =



 V

V

V



 (1.11)

1.5 Neutral Point Piloted inverter

The Neutral Point Piloted, introduced by J.Holtz in 1977 [31], is very similar to the NPC but in some situation it is possible to reduce the power losses as presented by V.Guennegues et al. in [32]. The converter topology is shown in Fig.1.16 is a 3-Level inverter that can increase the efficiency with respect to the NPC topology. The NPP is composed of six active switches (IGBTs) and six diodes per leg. The median branch semiconductors are tumbled series connected in order to create a bidirectional switch.

The voltage stress distribution depends on the switches state. In Table 1.3 are synthe-

sized the diffrent states of this topology, considering V

as output voltage reference:

CHAPTER 1. THESIS CONTEXT- PRESENTATION OF PV-GRID CONNECTED SYSTEMS

Table 1.3: Switching states of a NPP inverter V

S

S

S

S

S

S

Vdc

2

ON ON ON OFF OFF OFF

0 OFF OFF ON OFF OFF ON

−Vdc

2

OFF OFF OFF ON ON ON

Figure 1.16: Neutral Point Piloted inverter

The switching voltage of vertical IGBTs is divided by two in comparison with the conventional NPC topology. This way it is possible to double the switching frequency for a given current. The improvement of the inverter output waveform reduces the size of the filter with respect to the NPC [32].

1.6 Modulation strategies for the NPC inverter

There are three important different types of PWM , changing the carriers. In an inverter multilevel we dont have only one carrier but (N-1) carriers, where N is the number of levels (in this case N=3). So we have two carriers and we can choose different triangular carriers as:

• Phase shifted carriers PWM

• Phase disposition carriers PWM

• Phase opposition disposition carriers PWM

1.6.1 Phase Shifted PWM (PS-PWM)

The number of carriers in multilevel inverters is equal to N-1, where N is the inverter level number. Therefore in our case there will be two carrier for the 3-Level NPC, as shown in Fig.1.17.

The carriers are shifted by half-period because we have a 3-level inverter, but in

general , the formula for shifting, is

so that 180 in the case N = 3. When the

CHAPTER 1. THESIS CONTEXT- PRESENTATION OF PV-GRID CONNECTED SYSTEMS

Figure 1.17: Phase Shifted PWM

reference signal is greater than the signal of the Carrier

, than the switch S

is in state ON and the switch S

is in state OFF. When the reference signal is greater than the Carrier

, the switch S

is in state ON and the switch S

is in state OFF.

1.6.2 Phase Opposition Disposition PWM (POD-PWM)

In this case the carriers are opposite in amplitude and with the same phase. This modulation is very different from the Phase Shifted, because the intermediate switches (S

and S

) are always in state ON or always in state OFF for one half-period of the reference signal Fig. 1.18.

Figure 1.18: Phase Opposition Disposition PWM

When the reference is greater than Carrier

, the switch S

is in state ON and the switch S

is in state OFF. When the reference is greater than Carrier

, the switch S

is ON and the switch S

is in state OFF and therefore the reference is always greater than the Carrier

in the first half-period (S

always ON, S

always OFF). In the second half-period it is the opposite.

1.6.3 Alternative Phase Opposition Disposition PWM (APOD- PWM)

This modulation is similar to previous one, because the carriers are opposite in amplitude

and, in addition, they have an opposite phase too [33], as shown in the Fig. 1.19.

CHAPTER 1. THESIS CONTEXT- PRESENTATION OF PV-GRID CONNECTED SYSTEMS

Figure 1.19: Alternative Phase Opposition Disposition PWM

1.7 LCL output filter design

Several characteristics must be considered in designing a LCL filter, such as current rip- ple, filter size and switching ripple attenuation. The reactive power requirements may cause a resonance of the capacitor interacting with the grid [34]- [35]. Actually, pas- sive or active damping must be added by including a resistor in series with the capacitor.

Figure 1.20: LCL ideal filter

In this thesis, as explained in Chapter 2, we apply a flatness-based control in order to manage the resonance of the LCL filter without a damping addition. Let us consider the definition of the base impedance (Z

) and the base capacitance (C

) [34]:

( Z

=

n

C

=

gZb

(1.12)

where E

is the line-to-line voltage, P

is the rated active power and ω

is the grid pulsation.

Considering a maximum power factor variation seen by the grid of 5%, it means that the capacitance of the LCL filter C

is equal to 0.05C

. The maximum current ripple at the output of DC/AC inverter is given by:

∆I

= 2V

3L

(1 − m) mT

(1.13)

where V

is the inverter input voltage, m is the inverter modulation factor and T

is the switching period. The mawimum peak to peak current is when m = 0.5, therefore

CHAPTER 1. THESIS CONTEXT- PRESENTATION OF PV-GRID CONNECTED SYSTEMS

the equation 1.13 becomes:

∆I

= V

6f

L

(1.14)

where f

=

sw

is the switching frequency.

If we consider a 10% ripple of the rated inverter output current, then I

=

√ 2 3Vph

, where V

is the phase-to-phase inverter output voltage.

Actually, the aim is to reduce the ripple to the grid side of 20% with respect to the output inverter side. In order to calculate the ripple reduction, the LCL filter equiv- alent circuit is initially analyzed considering the inverter as a current source for each harmonic frequency. Equations 1.15 and 1.16 relate the harmonic current generated by the inverter with the one injected in the grid:

i

(h)

i

(h) = 1

|1 + r [1 − L

C

ω

x]| = k

(1.15)

L

= q

k_a²

+ 1

C

ω

(1.16)

where, k

is the desired attenuation, x is the ratio between C

and C

, and r is the ratio between the inductance grid side and inverter side:

n x =

b

r =

1

(1.17)

Plotting the results for several values of r helps in evaluating the transfer func- tion of the filter at a particular resonant frequency, depending on the nominal grid impedance [36].

The resonance of this filter is defined by the equation 1.18:

ω

=

s L

+ L

L

L

C

(1.18)

CHAPTER 1. THESIS CONTEXT- PRESENTATION OF PV-GRID CONNECTED SYSTEMS

1.8 Conclusions

In this thesis the problems related to the optimization of the solar energy conversion is faced. When we talk of the PV grid connected system or other solar applications, it is important to study the complete chain in order to optimize the power conversion. For this reason in this first chapter, an overview of the different DMPPT systems and the different possible inverter topologies are given. The introduction of a DMPPT-DC/DC converters with the output ports connected in series with two photovoltaic sources is presented, that’s because in this thesis the same configuration is analyzed considering a variant: a multilevel inverter. A 3-Level three-phase Neutral Point Clamped is take into account and in this chapter I presented three different PWM techniques in order to command the three-phase converter. Another topology called Neutral Point Piloted is presented because of it is possible to increase the availability of the system (as it will be presented in Chapter 4).

Moreover, the design of a LCL filter is presented, because in a lot of application grid- connected we are in presence of a LCL filter. The presence of the LCL filter is due to two different reasons:

• to reduce the size of the filter and to decrease the cost and the THD

• side effect: it is due the line inductance if we are far to the grid connection point (this situation is detailed in Chapter 2)

The LCL filter introduces some problems of resonance and stability of the inverter

output control. For this reason, the study of non-linear systems is important in necessary

in order to ensure the proper operation.