ΕΘΝΙΚΟ ΜΕΤΣΟΒΙΟ ΠΟΛΥΤΕΧΝΕΙΟ ΣΧΟΛΗ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ ΚΑΙ ΜΗΧΑΝΙΚΩΝ ΥΠΟΛΟΓΙΣΤΩΝ ΤΟΜΕΑΣ ΤΕΧΝΟΛΟΓΙΑΣ ΠΛΗΡΟΦΟΡΙΚΗΣ ΚΑΙ ΥΠΟΛΟΓΙΣΤΩΝ

Matlab/SPICE modeling and high-level high level control design for the photovoltaic system ∆ΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ Μαρία-Ηρώ Γ. Μπάκα

Επιβλέπων:

Σούντρης ∆ηµήτριος Επ.Καθηγήτης Επ Καθηγήτης Ε.Μ.Π. ΕΜΠ

Αθήνα, Μάιος, 2010

2

ΕΘΝΙΚΌ ΜΕΤΣΌΒΙΟ ΠΟΛΥΤΕΧΝΕΊΟ ΣΧΟΛΉ ΗΛΕΚΤΡΟΛΌΓΩΝ ΜΗΧΑΝΙΚΏΝ ΚΑΙ ΜΗΧΑΝΙΚΏΝ ΥΠΟΛΟΓΙΣΤΏΝ ΤΟΜΈΑΣ ΤΕΧΝΟΛΟΓΊΑΣ ΠΛΗΡΟΦΟΡΊΚΗΣ

ΚΑΙ

ΥΠΟΛΟΓΙΣΤΏΝ

Matlab/SPICE modeling and high-level control design for the photovoltaic system ΔΙΠΛΩΜΑΤΙΚΗ ΕΡΓΑΣΙΑ Μαρία-Ηρώ Γ. Μπάκα

Επιβλέπων: Σούντρης Δημήτριος Επ.Καθηγήτης Ε.Μ.Π.

Εγκρίθηκε από την τριμελή εξεταστική επιτροπή την 19η Μαΐου 2010.

............................ ............................

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Σούντρης Δημήτριος Κιαμάλ Ζ. Πεκμεστζή Επ. Καθηγητης Ε.Μ.Π. Καθηγητής Ε.Μ.Π.

Κιαμάλ Πεκμεστζή Καθηγητης Ε.Μ.Π.

Σταύρος Παπαθανασίου Επ. Καθηγητής Ε.Μ.Π.

Αθήνα, Μάιος, 2010 3

................................... Μαρία-Ηρώ Γ. Μπάκα ∆ιπλωµατούχος Ηλεκτρολόγος Μηχανικός και Μηχανικός Υπολογιστών Ε.Μ.Π.

Copyright © Μαρία-Ηρώ Γ. Μπάκα, 2010 Με επιφύλαξη παντός δικαιώµατος. All rights reserved.

Απαγορεύεται η αντιγραφή, αποθήκευση και διανοµή της παρούσας εργασίας, εξ ολοκλήρου ή τµήµατος αυτής, για εµπορικό σκοπό. Επιτρέπεται η ανατύπωση, αποθήκευση και διανοµή για σκοπό µη κερδοσκοπικό, εκπαιδευτικής ή ερευνητικής φύσης, υπό την προϋπόθεση να αναφέρεται η πηγή προέλευσης και να διατηρείται το παρόν µήνυµα. Ερωτήµατα που αφορούν τη χρήση της εργασίας για κερδοσκοπικό σκοπό πρέπει να απευθύνονται προς τον συγγραφέα. Οι απόψεις και τα συµπεράσµατα που περιέχονται σε αυτό το έγγραφο εκφράζουν τον συγγραφέα και δεν πρέπει να ερµηνευθεί ότι αντιπροσωπεύουν τις επίσηµες θέσεις του Εθνικού Μετσόβιου Πολυτεχνείου.

4

Abstract Photovoltaic solar panels provide a very attractive solution for future clean energy provision on site. Today's panels provide a relatively high eciency under optimal conditions and when they are newly fabricated.

However,

when external temperature, radiation angle and radiation concentration conditions are varying, the power uctuates quite heavily. Moreover, aging effects do play a signicant role on both the panels and the converter of the solar energy system.

These eects heavily depend on the context whithin

which the panels are used and on the type of technology employed. In this thesis the existing literature on the time-dependent and variation eects is reviewed. Modeling and analysis of the module and the controller are carried out in order to examine the improvement of the overall eciency of the solar panel system. The existing congurations of the grid connection systems and their problems are explored.

It is proposed to distribute the

conversion stages inside the module to eectively reduce the problems that today's photovoltaic systems face. Moreover, a knob-controlled conguration of the module and the intra-module converters is examined. A global controller is proposed for selecting the conguration on the system at run-time in order to improve the system's eciency. The control method is based on the concept of system scenarios. Potential congurations and dierent use-case scenarios are analyzed, under dynamic operating conditions.

The purpose

of this analysis is the establishment of a roadmap for future work on actual counter measure development, where the eciency over the entire life time of a solar system will be highly improved, with minimal hardware modications.

KEYWORDS:

Control Photovoltaic System, MPPT, Module Topology,

System Scenarios, Modeling Solar System

6

Contents 1 Introduction

11

1.1

Context and Motivation

. . . . . . . . . . . . . . . . . . . . .

11

1.2

Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

1.3

Structure of the Thesis . . . . . . . . . . . . . . . . . . . . . .

12

2 State of the Art 2.1

Solar Cell

13

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

2.1.1

Temperature Dependence

. . . . . . . . . . . . . . . .

17

2.1.2

Irradiation Dependence . . . . . . . . . . . . . . . . . .

18

2.1.3

Transient Model . . . . . . . . . . . . . . . . . . . . . .

18

2.2

Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

2.3

Control

24

2.4

Limitations of the State of the Art

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Solar Cell

29

31

3.1

Spice Modeling

. . . . . . . . . . . . . . . . . . . . . . . . . .

31

3.2

Solar Cell Parameters . . . . . . . . . . . . . . . . . . . . . . .

36

3.3

Irradiation Input

38

. . . . . . . . . . . . . . . . . . . . . . . . .

4 Solar Module

41

4.1

Proposed Interconnect Model

. . . . . . . . . . . . . . . . . .

41

4.2

Matlab Model . . . . . . . . . . . . . . . . . . . . . . . . . . .

42

4.3

Instantiation of the Module

. . . . . . . . . . . . . . . . . . .

43

4.4

Experimental Results . . . . . . . . . . . . . . . . . . . . . . .

45

4.5

HFSS

46

4.6

Thermal Model

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 System Control

51

55 7

6 Conclusions

57

8

List of Figures 2.1

Ideal circuit of a solar cell

2.2

I-V characteristic of a solar cell

. . . . . . . . . . . . . . . . . . . .

2.3

P-V characteristic of a solar cell . . . . . . . . . . . . . . . . .

15

2.4

Series Resistance Components . . . . . . . . . . . . . . . . . .

17

2.5

Temperature Eects

18

2.6

Irradiation Eects . . . . . . . . . . . . . . . . . . . . . . . . .

19

2.7

AC equivalent of a solar cell

. . . . . . . . . . . . . . . . . . .

20

2.8

Cross section of a module

. . . . . . . . . . . . . . . . . . . .

21

2.9

A module of 6x9 with all the cells connected in series

. . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . .

14 14

. . . . .

21

. . . . . . . . . . . . . . . . . . . . . . .

22

2.11 State of the art topology of the module . . . . . . . . . . . . .

24

2.10 Photovoltaic System

2.12 Blocking diodes . . . . . . . . . . . . . . . . . . . . . . . . . .

25

2.13 Bypass diodes . . . . . . . . . . . . . . . . . . . . . . . . . . .

26

2.14 State of the art system including the MPPT . . . . . . . . . .

28

3.1

Equivalent electrical circuit of the solar cell

. . . . . . . . . .

31

3.2

Circuit of the cell implemented in SPICE . . . . . . . . . . . .

32

3.3

Spice subcircuit of a cell

3.4

Eects of the series resistance

. . . . . . . . . . . . . . . . . .

3.5

Eects of the shunt resistance

. . . . . . . . . . . . . . . . . .

37

3.6

Eects of the recombination diode . . . . . . . . . . . . . . . .

37

3.7

Irradiance Calculation

. . . . . . . . . . . . . . . . . . . . . .

38

4.1

Wires

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

4.2

Transient response of the module

. . . . . . . . . . . . . . . .

46

4.3

Transient response of the module, time delay . . . . . . . . . .

47

4.4

Transient response of the module, voltage uctuation 1

. . . .

48

4.5

Top view and cross section of a cell within a module . . . . . .

49

4.6

Top view of a module . . . . . . . . . . . . . . . . . . . . . . .

49

. . . . . . . . . . . . . . . . . . . . .

9

33 36

10

4.7

3D model of the module in HFSS

. . . . . . . . . . . . . . . .

50

4.8

3D model of the module in HFSS

. . . . . . . . . . . . . . . .

51

4.9

3D model of the module in HFSS

. . . . . . . . . . . . . . . .

52

4.10 Direction of temperature transmission in the module 4.11 Equivalent thermal circuit

. . . . .

52

. . . . . . . . . . . . . . . . . . . .

54

Chapter 1 Introduction 1.1

Context and Motivation

This thesis is developed and completed in imec in Belgium. Imec is a nanoelectronics and nano-technology center and one of the elds of its research is energy and especially photovoltaics. The objectives of this thesis belong to the research activities of the photovoltaics (PV) group of imec.

Apart

from the research in improving the eciency and reducing the cost of the solar cell, the overall eciency of the photovoltaic system is a eld of great interest. The eciency of the solar system is reduced during dynamic conditions by time-dependent eects. The eciency of today's power circuits is high, although the overall eciency is strongly aected from varying factors such as partial shading. In rooftop applications these problems become more eminent and the congurations that are used in today's systems are not facing these problems eectively at the run-time. The MPP tracker is central for a large number of modules, making the module mismatching a crucial factor. Even when the control is decentralized at the module level, the eciency is further reduced and reliability issues make these congurations inecient.

1.2

Ob jectives

This thesis is focused on the cell and module level of the photovoltaic system and the high-level control of the system. The objectives of this thesis are the following:

11

12

CHAPTER 1.

INTRODUCTION

1. the exploration of the key parameters for the design of an ecient photovoltaic system. 2. the analysis of the problems that the topologies of centralized control impose. 3. the modeling and the simulation of the modules under dynamic conditions. 4. to suggest a knob-controlled conguration that faces eectively the problem that the current and the output power are limited, because of the series connection of the modules and of the cells inside the module. 5. Propose a controller, which will decide at run-time the conguration of the system, in order to improve the average eciency. 6. Create global control at the module level, which will not be based on individual local MPP trackers, as research papers are recently proposing to do.

1.3

Structure of the Thesis

The chapters are organized based on these objectives. In chapter 2, the literature of the basic parameters that aect the eciency of the photovoltaic system are reviewed. The state of the art conguration of the system is presented and the problems of this conguration is explained. In chapter 3, the solar cell model is examined and modeled.

The exitation of the system is

analyzed in this chapter as well. In chapter 4, the knob-controlled conguration of the solar module is suggested. Possible topologies are presented and analyzed.

A parameterized matlab function is proposed to instantiate the

module and simulations are done in hspice. In chapter 5, the global setup of the proposed photovoltaic system is described, including the global controller, the monitors and the knobs of the system.

The concept of system

scenarios and the proposed control method are analyzed and illustrated on the solar system.

Finally, three dierent congurations of the system are

simulated under two dierent irradiation scenarios.

Chapter 2 State of the Art A photovoltaic system generates electricity by the direct conversion of the sun's radiation into electricity. It is a modular system because it is built out of several pieces or elements which have to be scaled up to build larger systems or scaled down in order to build smaller systems. The main elements of the system are the solar cells which convert the sun's energy into electricity. The cells are packaged and connected in a suitable form in order to connect with the electronic equipment. The electronic equipment is required to interface the system and it is chighly dependent on the application for which the photovoltaic system is utilized [1]. The electronic equipment can be:

•

a storage element in stand alone system

•

the grid in grid connection systems

•

AC or DC loads by suitable DC/DC converters or DC-AC inverters

2.1

Solar Cell

The basic structure of the photovoltaic system is the solar cell. A solar cell is an electronic device which directly converts sunlight to electricity.

The

ideal operation of the solar cell is described by an electrical equivalent model consisting of a current source connected in parallel with a diode. The I-V characteristic (gure 2.2) of a solar cell shows the potential steady-state operation points of the cell and is dened by the following equation:

13

14

CHAPTER 2.

STATE OF THE ART

Figure 2.1: Ideal circuit of a solar cell

Figure 2.2: I-V characteristic of a solar cell

2.1.

15

SOLAR CELL

V I = I sc − I o(e V T − 1) ,where Io is the saturation current of the diode. From gure 2.3, it can be seen that there is an optimum operating point where the cell generates maximum power. This point is referred to as the Maximum Power Point (MPP).

Figure 2.3: P-V characteristic of a solar cell The main parameters that are used to describe and dene the solar cell operation are:

•

Isc, short-circuit current, which in the ideal case is equal to the photogenerated current. In the gure, it is represented by the intersection of the I-V curve with the current axis

•

Voc, open-circuit voltage, which mainly depends on the saturation current of the diode. In the gure, it is represented by the intersection of the I-V curve with the voltage axis

V oc= V T ln(1 +

I sc ) Io

16

CHAPTER 2.

•

STATE OF THE ART

FF, ll factor which is dened as the ratio of the maximum power from the solar cell to the product of Voc and Isc

FF =

Pmax Im Vm = Isc Voc Isc Voc

The parameters of the cell are dependent on the technology and the materials used to manufacture the cell. In the case of the short-circuit density, the area of the cell is important since both the amperage of the photogenerated current and the saturation current are computed through the corresponding densities.

I sc = AJ sc I o = AJo where A is the area of the solar cell and Jsc and Jo are the current densities. In practice, the observed curve produced by a solar cell diers from the IV charcteristic of the ideal model. In order to better reproduce the output of a solar cell, additional components are added which represent the losses. The losses are both linear and non-linear. Alternate non-ohmic current paths in parallel with the intrinsic solar cell are simulated by the addition of a second diode, while a series and a shunt resistance are used for the ohmic losses. The addition of the non-ideal components is shown in gure[] and leads to the following characteristic [2].

I = I ph − I o1(e

V + IRs kB T

− 1) − I o2(e

V + IRs kB T

IRs − 1) − V + Rsh

The presence of the shunt resistance mainly represents manufacturing defects which provide alternate linear paths for the photogenerated current, rather than poor solar cell design [3]. The total series resistor in state of the art modeling is composed by three separate kinds of resistances as depicted in gure 2.4 [4]. 1. the resistance caused by the movement of current through the emitter and base of the solar cell, R2 and R3 2. the contact resistance between the metal contact and the silicon, R1 and R4 3. the resistance of the top and rear metal contacts, R5 and R6

2.1.

17

SOLAR CELL

Figure 2.4: Series Resistance Components

2.1.1

Temperature Dependence

The operating temperature has a strong eect on the electrical response of the solar cell [1]. Based on the electrical elements which are used to describe the electrical behavior of the cell and their temperature dependence, the eect on the main parameters can be analyzed.

The saturation current density

of a diode has a strong dependency on temperature.

Also the electrical

properties of materials, mainly the resistivity, which are used to compute the resistors included in the cell model, are a function of the surrounding temperature. Changes of the operating temperature have a strong impact on the open-circuit voltage and in turn on the ll factor which is a function of the open-circuit voltage. The short-circuit current undergoes small changes according to the temperature, since the resistances of the cell are temperature dependent. In addition photon absorption depends on temperature, and this leads to a thermal dependence of the photogenerated current and thus of the short-circuit current [5].

18

CHAPTER 2.

STATE OF THE ART

Figure 2.5: Temperature Eects

2.1.2

Irradiation Dependence

The function of the solar cell is directly related to the sunlight and the irradiation level. The short-circuit current is a superposition of the photogenerated current and the dark current produced by the diode [1]. The photogenerated current is considered to be proportional to the irradiation level, while the dark current density of a diode is independent of illumination. The actual dependence is of the form (alpha*Irrad-oset_loss), where the oset_loss is considered to be relatively small and is neglected. It is evident that the short-circuit current uctuates according to the falling irradiation and the open-circuit voltage changes slightly as the point that the two currents compensate is shifted.

2.1.3

Transient Model

The above description of the solar cell corresponds to a steady-state behavior of the system.

As the operating conditions of the system dynamically

change, the cell eventually shifts to a dierent operation point of an I-V curve. The change is not instantaneous. The time delay and the uctuation can be represented by capacitors. In literature, two kinds of capacitances are mentioned [6]:

•

diusion capacitance, CD , which represents the charge storage in the depletion layer

2.2.

19

MODULE

Figure 2.6: Irradiation Eects

•

transition capacitance, CT , which is attributed to the existence of defect and interface states

Studies which concentrate on the transient response of solar cells, use mainly an ac equivalent electrical circuit where the eect of the p-n junction is shown by capacitors while the diodes are absent (gure 2.7). Experiments and measurements of the transient response of solar cells have been performed using as input sinusoidal signals, square wave signals, or a short pulse. The conclusions drawn call for dependency of the electrical elements of the ac model on voltage and frequency. The public information is very limited and not sucient to perform a transient analysis of the cell in real-time conditions [7].

2.2

Module

The power produced by a single solar cell is dependent on the technology of the cell and its area. Namely the short-circuit current is around 8A while the open circuit voltage is 0.6V. The purpose of a photovoltaic system is to be connected with the public grid and to provide power. An increase of the area of the cell leads to a larger short-circuit current while the open-circuit voltage is independent of the area and remains the same. Thus, in order to make such a connection, it is necessary to increase the power output of the solar cells by interconnecting them.

20

CHAPTER 2.

STATE OF THE ART

Figure 2.7: AC equivalent of a solar cell

Solar cells are electrically connected and packaged in modules. Besides the necessity of having higher voltages and larger currents, the reasons which lead to the encapsulation of cells within modules are:

•

protection of the cells and their interconnecting wires from the typically harsh environment in which they are used

•

protection of the user from electrical shock

•

creation of an automated process which is cheaper in higher volumes

Most modules consist of a transparent top surface, an encapsulant, a rear layer and a frame around the outer edge. In most modules, the top surface is glass, the encapsulant is EVA (Ethyl Vinyl Acetate) and the rear layer is Tedlar (gure 2.8) [3]. Typically the number of cells connected in a module is 6x6 or 6x9 or 6x12. In industry, all the cells within the module are uniformly connected in series(gure 2.9). Considering a typical module size of 54 cells connected in series, the voltage produced by a fully illuminated module is around 30V. This voltage is not high enough to be connected to the grid. Several modules are connected both in series and in parallel, forming a solar panel or array, to further increase the power. The solar panel is directly connected to a central converter (DC/DC conversion and DC/AC conversion) which both implies the operating voltage to the panel and stabilizes the voltage of the system to be connected to the public grid(gure 2.10)].

2.2.

21

MODULE

Figure 2.8: Cross section of a module

Figure 2.9: A module of 6x9 with all the cells connected in series

22

CHAPTER 2.

STATE OF THE ART

Figure 2.10: Photovoltaic System

Research studies have considered localization of the dc/dc conversion, by applying a dc/dc converter to each module while the dc/dc conversion remains central. In other cases the cells in a module are divided to substrings. All the cells in a substring are connected in series, each substring has its own dc/dc converter and the substrings may be connected in series or in parallel. The last case can be considered as equivalent to the localization of the dc/dc conversion with smaller modules. In general the cells can be either connected in series or in parallel. In series connections, there is a build-up of the voltage, while in parallel connections there is a build-up of the current.

Since interconnected cells do not have

identical electrical properties or do not operate under the same conditions there are mismatch losses. Mismatch eects may occur either in the shortcircuit current or in the open-circuit voltage and may be caused by shading, degradation, dierent production and other factors [3]. In series connection an open-circuit voltage mismatch leads to a reduction of the overall power which is caused by the reduced generation of power by the poor cell. The current is unaected, while the total voltage across the string can be found by adding up the voltages produced by each cell. In the case of a short-circuit current mismatch the total current accumulating from the cells is limited to the lowest current produced by a cell in the conguration. Depending on the operating point of the module and the degree of mismatch, a drastic impact on the PV module can occur. The excess current produced

2.2.

23

MODULE

by the good cells forward biases causing the reverse bias of the poor cells in short-circuit operation conditions. This eect causes large power dissipation on the bad cells which leads to a phenomenon called hot-spot heating. Overall, in a series connected conguration with current mismatch, severe power reductions are experienced if the poor cell produces less current than the maximum power current of the good cells.

If combined bad and good

celss operate at short circuit or low voltages, the high power dissipation in the poor cell may cause irreversible damage to the module. The destructive eects of hot-spot heating may be circumvented through the use of a bypass diode. A bypass diode is connected in parallel, but with opposite polarity, to a solar cell as shown below. Under normal operation, each solar cell will be forward biased and therefore the bypass diode will be reverse biased and will eectively be an open circuit.

However, if a solar

cell is reverse biased due to a short-circuit current mismatch between several series connected cells, then the bypass diode conducts, thereby allowing the current from the good solar cells to ow in the external circuit rather than forward biasing each good cell. The maximum reverse bias across the poor cell is reduced to about a single diode drop, thus limiting the current and preventing hot-spot heating.In industry, two bypass diodes are placed in the module, as more diodes would increase the cost of the module (gure 2.11). In state of the art it is mentioned that the modules are not connected fully in series to form the panel. A combination of series and parallel connections of the modules is used to increase both the current and the voltage. There is no reference on parallel connection in the cell level. In parallel connection, short-circuit current mismatch has a minor eect on the operation of the cells, while open-circuit voltage mismatch leads to a lower total operating voltage and potentionally the bad cells may act as a load. In order to prevent current ow through the string of lower-voltage cells, blocking diodes are used. The use of blocking diodes also prevents the panel to act as a load of the grid or the battery during night time. Each string of modules which is to be connected in parallel has its own blocking diode (gure 2.12). The blocking diode on the shaded module prevents the current ow from the parallel module into the shaded one. The diodes which are used in the photovoltaic system are not ideal. They consume power and heat up, which means that when their operation is not needed they reduce the total eciency of the system. In parallel connection of the modules, the bypass diodes which are placed across the modules are connected in parallel as well (gure 2.13). A short-circuit current mismatch

24

CHAPTER 2.

STATE OF THE ART

Figure 2.11: State of the art topology of the module

of the modules will cause the excess current to ow through a diode, thereby heating the diode. Heating of the diode reduces the saturation current and the eective resistance. If the current ow increases due to further shading, the diodes could burn out allowing damage to the modules to occur.

2.3

Control

In order to connect the photovoltaic system to the public grid, the modules are electrically interconnected to form the panel.

The panel is connected

to the central converter which is directly connected to the public grid. The purpose of the control is to have maximum generation of power from the system. Achievement of maximum eciency requires constant operation of the cells on the Maximum Power Point. Under dynamic operating conditions, the Maximum Power Point is uctuating, and for this reason a Maximum Power Point Tracker is used to nd and maintain the maximum output power point.

The tracker does this by the use of monitors and knobs.

Monitors

are online measurements of relevant system characteristics, while knobs are

2.3.

25

CONTROL

Figure 2.12: Blocking diodes

26

CHAPTER 2.

Figure 2.13: Bypass diodes

STATE OF THE ART

2.3.

27

CONTROL

run-time or on-time controllable parameters.The monitors are the power, the voltage or the current of the system while the controllable parameters are usually the voltage or the current of the module. In order to locate the MPP of the array various algorithms have been presented [8].

•

Perturb & Observe/Hill Climbing: In these algorithms the operating voltage of the array is perturbated and the power is monitored. According to the perturbation and the change of power (positive, negative) the MPP is reached. These methods mainly fail under rapidly changing conditions.

•

Constant Voltage and Current: The near linear relationship between VM P P and Voc, IM P P and Isc under varying irradiance and temperature levels is the base of these methods.

By monitoring the open-circuit

voltage or the short-circuit current, the optimum voltage is chosen. Monitoring in this case means the interruption of the operation of the module, or the use of a pilot cell.

•

Incremental Conductance: The derivative of the power with respect to the voltage at the MPP equals to zero. This leads to the conclusion that the instananeous conductance and the incremental conductance must be equal in magnitude and opposite in sign when the MPP is reached.

dP dV

=

d(V I) dV

=I +V

dI dV

=0

at the MPP and

− VI =

dI dV

The main knob of the system is the operating voltage of the array which is controlled by altering the duty cycle of the converter. The converter has two stages of conversion: 1. dc/dc conversion 2. dc/ac conversion The port of the dc/dc converter which is toward the grid has a xed voltage, so a change of the duty cycle of the converter leads to a dierent operating voltage of the panelnd eventually, of each module and each cell. The duty cycle changes according to the location of the MPP which is provided to the controller by the MPP tracker.

In state of the art, both the monitors

28

CHAPTER 2.

STATE OF THE ART

and knobs of the system are situated in the converter as can be depicted in gure 2.14. the only voltage controlled is the operating voltage of the panel. The current algorithms consider uniformity of the panel, as the only voltage controlled is the operating voltage of the panel. This means that a connection of N cells in series and M cells in parallel is treated as a single cell, which has the same form of I-V characteristic as one cell. The short-circuit current of that cell is M times the short-circuit of one cell and the open-circuit voltage is N times the open-circuit voltage of one cell. As the operating conditions of the cells are not always the same and the cells are not identical, the I-V characteristic of the panel will dier from the one considered. Thus, the MPP of the panel will not satisfy the equations in which the existing algorithms are based on and the MPP will not be reached.

Figure 2.14: State of the art system including the MPPT More complex algorithms have been studied in research level for locating the Maximum Power Point, as neural networks, while other Maximum Power Point Tracking Techniques include array reconguration . This means that the PV arrays are arranged in dierent series and parallel combinations such that the resulting MPPs meet specic load requirements.

This method is

time consuming and tracking MPP in real time is not obvious [9]. As mentioned in a previous section, in research there is consideration of localization of the dc/dc conversion. These recent research patents suggest

2.4.

LIMITATIONS OF THE STATE OF THE ART

29

that a local dc/dc converter should be used for each module or substring of cells. This enables an independent search of the MPP for a smaller number of cells. Each dc/dc converter is controlled by a dierent MPP tracker which may result to a dierent optimum duty cycle and a dierent operation voltage of each module/substring. Unifomity is assumed in the level where the dc/dc converters are connected. The decisions of the duty-cycle of the local dc/dc converters are based on local monitors. The decisions are independent as the converters do not interact and are not connected to a global controller.

2.4

Limitations of the State of the Art

As transient simulation is required in order to study and simulate the solar system, the absence of a transient model is considered a serious limitation of existing literature. From the cell point of view, there is no sucient electrical equivalent model which shows the transient eects under dynamic operating conditions. There are very limited studies on the thermal eects, while a thermal model has never been studied. As referred in section 2.1, the intramodule connections are not completely distinguished from the cell model. Concerning the module, simulations are mainly made without including all the intramodule wire connections. The eect of the surrounding materials on the function of the cells has been neglected and again transients eects have not been studied. The conguration of the module is static resulting to a signicant loss in case of a single severely degraded cell. On the control level, concerning both industrial and research developments, there is a limited amount of monitors and knobs which are located mainly in the central converter. This type of monitor considers a uniformity among the modules and the cells, which results to only a small imrovement of the global eciency as analyzed in section 2.3. In industry, all the monitors are situated in the central converter, while the only knob is the duty cycle of the dc/dc converter. The algorithms used to control the knob of the system are reactive and do not look ahead or use any prediction. They are either "current state" or purely history based. In research, localization of the converters takes into account that the system is not uniform and that there should be some distribution of the control. Although there is a study on having a Maximun Power Point tracker for each module or substrings, there is no interaction of the distributed convert-

30

CHAPTER 2.

STATE OF THE ART

ers, so there is a loss of the global optimization. The algorithms currrently studied in research, although more complex than those in industry, are still not proactive. So the prediction of the future evolution of the system is not really considered yet.

This evolution should especially try to predict the

relatively fast changing temperature and shading/irridiation conditions over the short-time future.

Chapter 3 Solar Cell The solar cell is the basic structure of the photovoltaic system. In order to simulate the solar module, it is necessary to have an equivalent electrical circuit of the cell. The present Thesis focuses on the modeling of silicon solar cells. Every cell in the module is considered to potentionally have dierent operating conditions. For that reason, irradiation is not considered uniform in the module, but each cell is excited individually.

3.1

Spice Modeling

The basic model used for the simulation of the cell is the steady-state electrical equivalent described in the state of the art chapter with the addition of a capacitance to introduce the transient eects. The simulation tool used was HSPICE. The circuit which was implemented in spice code is shown in the following gure.

Figure 3.1: Equivalent electrical circuit of the solar cell

31

32

CHAPTER 3.

SOLAR CELL

As mentioned before, the amperage of the photogenerated current is proportional to the irradiation level falling on the cell. The dependence of the current source is represented by a voltage-controlled current source.

Two

voltages are used to control the value of the current generated. One voltage is the intensity of irradiation which may be altered by shading and the other is the maximum potential current produced, which is dependent on the location, the weather conditions, the given inclination angle and orientation of the panel. Although the irradiation falling on the cells is eventually the product of the two voltages, the dierent time constants and the data available led to such a separation.

Figure 3.2: Circuit of the cell implemented in SPICE In order to simulate a solar module, the circuit of the solar cell is replicated a few times, as the cell is the basic component of the photovoltaic system.

The successive use of the cell model leads to the implementation

of the cell as a subcircuit, which allows reuse without redening internal nodes and elements of the cell cicuit. A subcircuit in spice encapsulates the components and electrical connections by considering the node numbers for internal use only, while global are only the nodes needed for connection with the external circuit [1].

In order to create an instantiation of a cell, four

external nodes have to be dened, as shown in the following gure. Nodes number 302 and 333 are connected to the voltages which represent the irradiation input, while nodes 300 and 303 are the two terminals of the solar cell. The electrical components, diodes, resistors and capacitors, are described and placed within the subcircuit but their value depends on the parame-

3.1.

33

SPICE MODELING

Figure 3.3: Spice subcircuit of a cell

ters of each instantiation, allowing creation of cells with dierent electrical properties and operation conditions. The parameters used are:

•

the length and width of the solar cell, which inuence the value of all the elements

•

the saturation current density of the two diodes

•

the series and shunt resistance in

•

the capacitance in nF/cm

•

the operating temperature

Ωcm2

2

The spice code of the cell, which shows the dependence of the values on the parameters is the following:

.subckt solar_cell 300 303 302 333 length=0 width=0 j0=0 j02=0 rs=0 rsh=0 c_junction_nominal=0 temp=0 girrad 300 301 cur='(v(333))*v(302)*length*width d1 301 300 diode .model diode d (is='j0*length*width',eg=1.17) d2 301 300 diode2 .model diode2 d (is='j02*length*width',n=2) rs 301 303 'rs/(length*width)' rsh 301 300 'rsh/(length*width)' ct 301 300 'c_junction_nominal*length*width'

34

CHAPTER 3.

SOLAR CELL

.ends solar_cell

All the parameters are computed according to the area of the cell, while temperature dependence in this model concerns the operation of the diodes where the dependence is a built-in function in spice. The main issues of this research study on the cell level are within the objectives stated in the introduction. The simulation of the module under dynamic conditions requires an equivalent electrical cell model which includes transient behavior. In order to include transient analysis to the cell model the following are needed.

1. separation of all metallization from the electrical equivalent of the cell, in order to have a distributed model and have a separate thermal analysis for each material 2. combination of the steady-state model and the transient model, in order to simulate the transient response of the cell under dynamic conditions 3. use of dynamic parameters so that the charcteristic that is produced by the simulation is more accurate and corresponds to the actual operation of the cell

Separation of Metallization As seen on the model described above, the values of the parameters correspond to a cell of a square centimeter area, and according to the length and width of each cell the actual parameters are calculated in spice. Apart from the front and rear contact metal, the layers of the cell are uniform which allows a distribution of the cell model. The metallization used as a contact on the front size of the cell cannot be uniform as light has to come through in order to have absorption of photons by the semiconductor. Inevitably part of the cell area is covered and the active area is reduced. As mentioned in the previous chapter, the resistance of this metallization is included in the series resistance of the cell, which prohibits a separate analysis of the interaction of the metal contacts and wires of the module. The rear contact of the cell is not uniform in order to have less metal in the module.

Another reason

for the division of the series resistance into its individual components is the independent inuence of temperature on each one of the components. While

3.1.

35

SPICE MODELING

the reason which this separation is needed is described here, the eort made wiil be analyzed in the next chapter.

Combination of Steady-State and Transient Model In order to have an real evalutation of the gain of the control applied on the system, a model which shows the transient behavior of the cell is required. As mentioned earlier, several studies focus on the transient response and the ac parameters of the cells.

The values which are found in literature

cannot be used directly, as they refer to dierent types of cells, produced by dierent technologies which may not be respective to the chracteristics of the diodes and the resistors used here. Values from the literature may be used as initial values for the capacitors and be callibrated to converge and to t the measured response of the cell. Lack of measurements made this calibration impossible.

Dynamic Parameters The term dynamic parameters should be distinguished from the thermal dependence of the solar cell parameters. The elements used in ac analysis are two capacitors (diusion and dynamic capacitance), the shunt and series resistances and a resistor which substitutes the diode. The diusion capacitance is a function of the operating voltage and frequency, while the transition capacitance and the dynamic resistance of the diode depend only on the operating voltage. There was an eort of including the voltage dependence of the capacitance in the spice model. The equation describing the voltage dependence of the capacitance is the following:

q s ( NA ND ) C = A 2(Vbiq−V j ) NA +ND ,where A is the cell area, q is the elementary charge, permittivity of the semiconductor,

Vbi

voltage applied to the capacitor and is

s

is the electrical

is the built-in potential,

(V − IRs ),

Vj

is the

V and I are the voltage

Rs is the series resistance, NA is the acceptor impurity concentration and ND is the donor impurity concentration

and current of the cell respectively, [10].

Taking a nomimal capacitance value for a nominal voltage, the voltage dependent capacitance can be computed by the two nominal values and the

36

CHAPTER 3.

SOLAR CELL

actual voltage applied. This dependence was modeled in spice as a voltage dependent capacitor. This caused functional problems of the spice simulation, so at the end it was neglected. The main reason for errors is expected to be due to the static value of these parameters.

3.2

Solar Cell Parameters

The values of the parameters of the solar cell depend on the technology used to produce the cell. This thesis focuses on the silicon solar cells, so the values mentioned refer to this specic type of solar cells. It is important to point out the eect of the dierent values of the parameters on the I-V characteristic of the cell, at equivalent values of irradiance and temperature, and the need of accurate values in the analysis. Ideally, as can be deduced from the circuit of the ideal cell, the series resistance and the saturation current of the recombination diode of the cell is zero, while the shunt resistance is innite. As the series resistance increases, the value of the short-circuit current and the ll factor are severely reduced. In practice the series resistance is kept low by proper design of the cell (gure 3.4).

Figure 3.4: Eects of the series resistance Decrease of the shunt resistance may also lead to a degradation of the performance of the cell. It must be clear though that only very small parralel resistances will cause a signicant modication of the open-circuit voltage (gure 3.5). The open-circuit voltage is also degraded when the recombination diode becomes important. The result indicates that when the recombination diode

3.2.

37

SOLAR CELL PARAMETERS

Figure 3.5: Eects of the shunt resistance

dominates, the characteristic is also heavily degraded, both in the opencircuit voltage and in the FF. The short-circuit current remains practically constant (gure 3.6).

Figure 3.6: Eects of the recombination diode The simulation concerns a square silicon solar cell of an area of 15.6x15.6 2 cm . The values used were provided by IMEC and are as follows:

2

•

series resistance, rs=500mΩcm

•

2 shunt resistance, rsh=500Ωcm

•

characteristics of the diusion diode

 

saturation curent density, jo=9.7E-13A/cm ideality factor, n=1

2

38

CHAPTER 3.

•

SOLAR CELL

characteristics of the recombination diode



saturation curent density, jo2=4E-8A/cm



ideality factor, n=2

2

The value of the capacitance was taken from literature [11] and the value 2 was C=35nF/cm . The above values were used as default in the subcircuit written in SPICE. .subckt solar_cell 300 303 302 333 length=15.6 width=15.6 j0=9.7e-13 j02=4e-8 rs=500m rsh=500 c_junctionn ominal

3.3

= 35n

Irradiation Input

The two inputs required for the simulation of the cell are the potential photogenerated current density and the intensity of the illumination. In order to have a simulation which corresponds to real time behavior of the system, irradiation data were necessary. The available data [12] contain information on the horizontal global irradiance, the direct normal irradiance, the diuse horizontal irradiance, but also measurements of the air temperature, the relative humidity and other atmospheric conditions. From these measurements and the use of a software program called SMARTS the spectral irradiance can be extracted.

The spectral irradiance is the power received by a unit 2 µm [1].

surface area in a wavelength dierential dλ and the units are W/m

Figure 3.7: Irradiance Calculation

This form of the irradiation data is not yet suitable to be used as input for the spice simulation and further computations are needed. An excel le was provided from the solar cell group in IMEC which transformed the spectral irradiance to potential current up to specic wavelengths. The semiconductor used in this case is silicon, which absorbs photons up to 1300µm, so the current was calculated up to this wavelength.

3.3.

IRRADIATION INPUT

39

In order to reuse as much information as possible, the location chosen was Phoeinix Arizona and the irradiation data was provided for every hour of the 15th of each month. The les of the spectral irradiance were used as an input for a matlab le and the output was a matrix containing the potential photogenerated current density of each hour. The time constants of a solar cell are denetely smaller than an hour. As other sources available have more ne-grained information, a combination of measurements was used to further dene the input. Assuming that the intensity of the irradiation aects all wavelengths equally, the potential current is proportional to the level of the global irradiance. Measurements from another location were used to compute a factor of illumination change within a ve minute interval. This factor was used to compute the potential current with a ve minute step. The main cause of the shading of the solar cells are the clouds. The cloud movement may be quite rapid and is the smallest time constant which is imposed on the cell. The movement of the clouds is considered to be in some occasions in the range of milliseconds. As no real data was found with such a small time step between the measurements, the second voltage source can be used to create this uctuation of irradiance. The time step of the pulse and the amplitude represent the speed of the cloud and the level of shading respectively. If no shadows are considered, a xed voltage is imposed, where the amplitude again represents the level of shading.

40

CHAPTER 3.

SOLAR CELL

Chapter 4 Solar Module As referred in the state of the art chapter, the topology of the module used in industry is static.

The static topology is designed based on the worst

operating conditions and the controller, which uses an algorithm for tracking the MPP, considers uniform electrical characteristics on the level which it is connected.

The main idea of the proposed module is having a dynamic

conguration of the system, hence introducing knob-controlled topology and local DC/DC converters. The topology and the knob positions will be determined on run-time by the controller using the concept of system scenarios. The controller in this case is global, so each local dc/dc converter which is connected optimizes the output of a series connection of cells, but interacts with the other converters through this controller. Each scenario corresponds to a set of dierent congurations of the module, leading to an improvement of the system's eciency under dynamic conditions.

4.1

Proposed Interconnect Model

The parameters that were studied and may be altered on run-time, are the position of bypass diodes, the interconnection of the cells, the number of the local dc/dc converters and the connection of the dc/dc converters. The main problem on the state of the art interconnection of the cells within the module is the allowance of signicance loss of power in the case of mismatch eects. The module that is proposed may allow dynamic connection of cells in series or in parallel. The way the cells are connected will be decided by the proposed controller on run-time according to the operating conditions of

41

42

CHAPTER 4.

SOLAR MODULE

the system. For more information please refer to the commitee version of the text.

4.2

Matlab Model

The purpose of the matlab model is to generate as an output a spice le which represents the module topology in a specic situation.

The code is

fully parameterized and according to the value of the input parameters an instantiation of the module is created. The matlab function that is used to produce the spice le is generate_module and has the following form:

generate_module(X, Y, N, M, D, N D, S, IR, M ON, HOU R) The parameters X and Y are the geometric characteristics of the module. The value of X is the number of cells that t in the length of the module, that is the number of cells in a column. The value of Y respectively is the number of cells which t in the width of the module, that is the number of cells in a row. Both values must be integers, and the value of Y is further restricted to be an even number as mentioned in the previous section. The parameters N and M determine the size of the substrings and the number of strings respectively. The value of N is the number of cells connected in series in each substring, so according to the static placement of the cells it must be a multiple of X. As M is the number of substrings in the module, the following relation should be valid in every instantiation of the module:

X ∗Y =N ∗M where both sides of the equation are equal with the total number of cells of the module. Parameter D is a matrix of boolean numbers with dimensions XxY and each element of the matrix corresponds to a single cell of the module. If an array element is unity, it means that there is a bypass diode across that cell, while a zero element value means that there is no diode. Parameter ND is also a matrix, which represents the location of the bypass diodes between neighboring cells, with dimensions (Y div 2)x(X+1).

The congurations which

involve non-neighboring connected columns to form the substrings, or direct connection of the substrings for use of a common converter, require the use of the S parameter. The approach that is used is rstly creates intermediate

4.3.

INSTANTIATION OF THE MODULE

43

substrings of neighboring columns and secondly, according to the elements of the S vector interconnects these intermediate substrings (section 4.1.1). The dimensions of the vector depend on the conguration which is instatiated. The last three parameters account for information of the irradiation input. IR is a XxY matrix in which each elements represent a cell. The values that are allowed are in the closed set [0,1]. The value of each element indicates the amount of illumination of a cell. A zero value indicates a fully shaded cell, where a value of unity means a fully iluminated cell. Intermediate values are interpreted as partial shading. The parameters MON and HOUR are the month and hour of the simulation respectively. They are used internally in the matlab le so that the potential current density of a cell is computed. The matlab function described above, creates a spice le which contains information about the formulation of the substrings in a module. The connections with the local dc/dc converters in not included in this phase.

4.3

Instantiation of the Module

In the spice le created by matlab, the connections between the cells are not ideal. The wires used for interconnection cause a loss of power through their resistance and interaction between them indicates the presence of a capacitance along the cell. The interconnection of the cells is shown in gure 4.1. As mentioned in the previous chapter, there was an eort of a separate analysis of the metallization of the module and the cell model. The module was simulated in a software program called HFSS (section 4.5) , but the results are not yet in a form that can be used. In order to have an estimation of the eect of the wires, a rough computation of the resistance and capacitance was carried out. As the cells are placed very close to one another, the metal layers of each cell are considered to interact with the neighboring cells. This reason led to a distinction of the cells that are placed in the inner part of the module and the cells along the edges of the module. A further renement was made for the cells at the edge of the module, as the cells which are placed along the edges which are vertical to the connections do not always have direct electrical connectection, while the cells on the edge parallel to the connections are connected with metal wires. All metal connections of the module are implemented in spice as subcircuits.

Three dierent subcircuits were written for each of the three cases

stated above. The equations used to calculate the resistance and the capac-

44

CHAPTER 4.

SOLAR MODULE

Figure 4.1: Wires

itance of the wires are

C=

di WL tdi

R=

ρL HW

where the capacitance is modeled by the parallel-plate capacitor model, area capacitance, and the resistance is computed by the resistance of a rectangular conductor. In the above equations, W and L, are respectively the width and length of the wire, H is the thickness of the wire and the dielectric layer.

The parameters

di

and

ρ

tdi

is the thickness of

are the permittivity of the

dielectric layer and the resistivity of the metal wire respectively [15]. The three subcircuits which were implemented in spice are:

.subckt parasitics_wires_calculate 1 2 3 4 resistance=0 capacitance=0 .subckt parasitics_wire_edges_along_calculate 1 2 resistance=0 .subckt parasitics_wire_edges_vertical_connect_calculate 1 2 resistance=0

4.4.

45

EXPERIMENTAL RESULTS

As can be seen, the subcircuit dened for the cells placed in the middle of the module, connects four cells. As cells interact with the neighboring cells on both sides, each cell is connected in two instances of the par-

asitics_wires_calculate circuit. For this reason, the resistance, which was calculated for the wire connection of the cells, is multiplied by two, so that the resistance of the parallel connection of the two resistors equals the total resistance computed. The same value of resistance was assigned to the par-

asitics_wire_edges_along_calculate circuit, which refers to the cells along the connections. The resistance of the wires which connect neighboring cells diers since the geometry of the metal diers. The capacitance that was calculated was directly placed across the cell and is not included in any subcircuit.

The capacitance of the neighboring

wires in this phase is neglected and is set to a zero value. The values of the resistors and the capacitors are

•

in the middle of the module and along the connections, resistance=0.0105

•

vertical connections, resistance=0.0193

•

capacitor across the cell, capacitance=0.323n

4.4

Experimental Results

The main experimental results, at this level, concern the transient response of the module. The transient behavior can be found in the cell's capacitance and in the wires of the module. The simulation was excited by an irradiation source, implemented in spice by a voltage source, the value of which changed every 5 minutes in an hour. The response of the module is shown in gure 4.2. As can be seen, the voltage of the module follows the excitation with almost no delay. The spice transient simulation is not continuous and involves a determination of a time step. In each step, spice is performing a dc analysis using the initial conditions of the capacitors. A simulation of one hour duration does not allow a small enough time step to show the delay of the solar module. Reducing the duration of the simulation and the time step, the voltage delay and uctuation can be seen (gures 4.3 and 4.4. The time constants which describe the module are relatively small compared to the frequency of the excitation.

46

CHAPTER 4.

SOLAR MODULE

Figure 4.2: Transient response of the module

4.5

HFSS

HFSS is a simulation tool for 3D full-wave electromagnetic eld simulation, which provides E- and H-elds, currents, S-parameters and near and far radiated eld results.

As an engineering tool its automated solution process

requires the users to just specify geometry, material properties and the desired output.

HFFS will automatically generate an appropriate, ecient

and accurate mesh for solving the problem using the proven nite element method, so that the physics denes the mesh and not the mesh dene the physics [16]. The desired output from HFSS is the scaterring matrix of the module either in a touchstone le, which can be directly included in the hspice netlist, either in a matrix form, so that the R,L and C values may be extracted from the S-parameters [17]. The simulation of the module in HFSS required the creation of a 3D model of the solar module.

In order to determine all the parameters which were

needed for the 3D model, 2D views of the cell and the module were drawn. Since the output should be as close to reality as possible, all the layers of the module are included in the model. The dimensions of the various elements

4.5.

HFSS

Figure 4.3: Transient response of the module, time delay

47

48

CHAPTER 4.

SOLAR MODULE

Figure 4.4: Transient response of the module, voltage uctuation 1

4.5.

49

HFSS

are shown in gures 4.1,4.5 and 4.6.

Figure 4.5: Top view and cross section of a cell within a module

Figure 4.6: Top view of a module The module considered is of typical size, with 9 cells in each row and

50

CHAPTER 4.

6 colums.

SOLAR MODULE

The dimensions of this module, and mainly the ratio of the di-

mensions in the xy plane to those in the z axis, are beyond the simulation capability of HFSS. In order to overcome this diculty, the module size was reduced to 2x2 and some characteristic views are shown in gure 4.7 The model, apart from the basic structure, is fully described by parameters which allow reuse in case of dierent dimensions of elements. The whole body of the cell in this model is silicon and is not divided in a n- and p-type region, as the simulation is focused on the metal parts of the module and for that purpose uniformity is acceptable.

Figure 4.7: 3D model of the module in HFSS The frequencies in which the solar module is operating are in the range of Hertz and Kilohertz and HFSS is mainly used for high-frequency simulations. Low frequency stimuli combined with the ratio of the dimensions of the module made the mesh denition extremely demanding in memory usage. In order to enable the simulation, the model was further reduced to the size of a single cell.

The nal output of HFSS was a 2-port touchstone le of

a cell dened with a symmetry boundary. Some intermediate results of the electric eld of the cell are shown in gures 4.8 and 4.9. In this gure, part

4.6.

51

THERMAL MODEL

of the metallization is present, and the model is half of a cell.

Figure 4.8: 3D model of the module in HFSS

4.6

Thermal Model

In literature, although studies which focus on the temperature dependence of the solar cell were found [18], no thermal equivalent, while in the module level there is no reference. The temperature is transmitted in all directions, and may be analyzed by analytical equations . If the trasmission is considered to be in one dimension, the system can be solved with the use of partial dierential equations [19]. In the module, the temperature transmission was considered to be vertical to its layers as shown in gure 4.10. The layers of the module were considered uniform and the computation of the thermal resistance and capacitance was based on the following equations:

l Rth = Ak Cth = ρcV ol

52

CHAPTER 4.

SOLAR MODULE

Figure 4.9: 3D model of the module in HFSS

Figure 4.10: Direction of temperature transmission in the module

4.6.

53

THERMAL MODEL

,where l the thickness of the layer, A the area of the layer, k the thermal conductivity,

ρ the density of the material, c the thermal capacitance and Vol

the volume of the layer. The resistors are connected between the junctions of the layers, while the capacitance is calculated for the midpoint of the layer. In order to have the same nodes, the capacitance is divided and placed in the junctions as well. The steady-state behavior of the system is described by the matrix equation:

[G][T ] = [P ] , while the transient state follows:

] + [G][T ] = [P ] [C][ dT dt , where G is the conductance matrix, C the capacitance matrix, T the temperature vector and P the vector of power input. The thermal equivalent of the solar module with one dimension temperature transmission is of the form shown in gure 4.11. This circuit should be coupled with the electrical equivalent in order to have thermal dependence of the module. Coupling the two systems is likely to be possible in spice, but running parallel simulations could prove to be more ecient. Due to limited time and lack of information on the thermal properties of the materials of the module, further thermal analysis is left for future work.

54

CHAPTER 4.

SOLAR MODULE

Figure 4.11: Equivalent thermal circuit

Chapter 5 System Control As stated earlier, the operation of the photovoltaic system is dynamic in nature. In chapter 4, a knob-controlled conguration of the module is introduced, in order to exploit the dynamic nature of the system. The selection of the conguration is made by the controller at run-time.

The controller

introduces an overhead in the system. This overhead cost consists of the addition of the hardware of the controller and of the energy consumed while it is being active. These two cost components are compensated by integrating the controller in the module and by reducing the frequency of active control. The proposed control method is based on the concept of system scenarios which is analyzed in the second section of this chapter. In the rst section, the global setup of the system is described. For more information please refer to the commitee version of the text.

55

56

CHAPTER 5.

SYSTEM CONTROL

Chapter 6 Conclusions Photovoltaic power systems have received much attention during the last years. The research is expanded in many elds of interest, starting from the PV cell tecnologies to the equipment that is used to transfer the power to the grid. This thesis adresses the problems that exist in today's connection of the PV generators with the existing congurations in order to transfer the energy to the grid. Also a novel conguration of the connection between the solar modules and the electronic equipment is presented, which solves the problems eectively, introducing individuality inside the module and also reducing the possible drawbacks that today's systems have. In the rst chapter, the fundamental principles of the operation of the solar system are analyzed.

The existing conguration of the system is re-

viewed and the reasons why this topology is not ecient are explained. In the second chapter the cell model is described.

Transient eects are inro-

duced in the equivalent electrical circuit, while the excitation is based on real data information.

The third chapter deals with the solar module.

A

new solar module that allows changeable congurations based on run-time decisions is suggested and a fully distributed intra-module conversion is proposed. The knob-controlled topologies are described and the matlab function used to instantiate the module is presented. Modeling of the metallization of the module is discussed and computation of the wire parasitics are made. The results of the transient simulations of the module are presented. From the simulations it is evident that the delay of the module is in the range of ns. This indicates, that rapid irradiation and temperature changes aect the module operation. A crude thermal model of the module is also introduced. In the fourth chapter, the global setup of the proposed photovoltaic sys-

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CHAPTER 6.

CONCLUSIONS

tem is described. A global controller is used, which is based on the system scenario concept. The methodology of this concept is explained and its illustration on the photovoltaic system is described. Two dierent scenarios of partial shading are simulated in dierent congurations. The comparison of the eciency of those congurations illustrate the optimization that can be achieved by a knob-controlled conguration. The maximum power produced by a dynamic conguration of the module is shown that may be 30% more than the power generated by the state of the art conguration.

Future Work As this thesis has shown, today's photovoltaic grid connection systems suer from reduced eciency. In rooftop applications where during the design of the system is not possible to avoid partial shading or the same orientation on each module, the time-variant eects become the most important factor. This thesis suggests the distribution of the conversion inside the module. The transient simulation of the module needs to be further studied and rened. In the cell level dynamic parameters should be used. Further analysis of the impact of the metallization of the module is required and exploitation of the HFSS results. A thermal equivalent model must be developed both in cell and module level. Coupling of the thermal and the electrical model is necessary for the transient behavior of the system. The coupling of the thermal and electrical model would allow other excitations apart from irradiance, as temperature and humidity. Future works invloves the extention of the matlab le to include the connection of the dc/dc converters.

The switches that are used for dynamic

conguration of the module topology are in this thesis ideal, and should be replaced with non-ideal devices. More knobs can be possible introduced in the topology of the module. More proacdtive control schemes that exploit future look ahead predictions may be studied. The proposed control method may be further dened for the photovoltaic system.

More RTS should be

examined and more congurations should be simulated. The calibration step should be added in the system scneario framework, especially for the aging and reliabiity context. Finally the development of a real-time distributed tracking system and the implementation of a controller for run-time decisions based on the conditions must be studied.

Bibliography [1] Castaner and Silvestre, "Modeling Photovoltaic Systems using Pspice", John Wiley, 2002. [2] Tom Markvart and Luis Castaner, "Practical Handbook of Photovoltaics: Fundamentals and Applications", John Wiley, 2002. [3] Christiana Honsberg and Stuart Bowden, "Photovoltaics CDROM", http://pvcdrom.pveducation.org/ [4] A.Goetzberg, J.Knobloch, B.Vob, "Crystalline Silicon Solar Cells", John Wiley,1998. [5] Y.Tsuno1, Y. Hishikawa1 and K.Kurokawa, "Temperature and Irradiance Dependence of the I-V Curves of Various Kinds of Solar Cells", 15th International Photovoltaic Science Engineering Conference, 2005. [6] J.Bousek, A.Poruba, "Precise Evaluation of Fast Transients in Testing of Silicon Solar Cells", 22nd European Photovoltaic Solar Energy Conference, September 2007. [7] J.Thongpron,

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[10] C.Monokroussos, R.Gottschalg, A.N.Tiwari, G.Friesen, D.Chianese and S.Mau, "The Eects of Solar Cell Capacitance on Calibration Accuracy when Using a Flash Simulator", IEEE, 2006. [11] T.Pernau, P.Fath, E.Bucher, "Phase-sensitive LBIC Analysis". [12] http://www.nrel.gov/rredc/solar_resource.html [13] S.V.Gheorghita,

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