Electrical Faults Modeling of the Photovoltaic Generator

(1)

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Electrical Faults Modeling of the Photovoltaic Generator

Wail Rezgui, Leïla-Hayet Mouss, Nadia Kinza Mouss, Mohamed Djamel Mouss, Yassine Amirat, Mohamed Benbouzid

To cite this version:

Wail Rezgui, Leïla-Hayet Mouss, Nadia Kinza Mouss, Mohamed Djamel Mouss, Yassine Amirat, et al.. Electrical Faults Modeling of the Photovoltaic Generator. International Review on Modelling and Simulations, 2014, 7 (2), pp.245-257. �hal-01017387�

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Electrical faults modeling of the photovoltaic generator

Wail Rezgui¹, Leïla-Hayet Mouss¹, Kinza Nadia Mouss¹

Mohamed Djamel Mouss¹, Yassine Amirat² and Mohamed Benbouzid³

Abstract– In this paper, we presented a new methodology for the mathematical modeling of the photovoltaic generator’s characteristics based on known electrical laws. This proposed new methodology in this work consists of a three new algorithms, each one presents the characteristic of the cell, group of cells, module, string and generator, when one or more of its components : cells, bypass diodes and blocking diodes subjected to these types of defaults: reversed polarity, open circuit, short circuit or impedance. The three new algorithms obtained can facilitate the prediction for the prognosis or the detection for the diagnosis of these photovoltaic generator’s defaults.

Keywords: photovoltaic generator, I-V characteristic, modeling, simulation, reversed polarity, open circuit, impedance and short circuit faults.

Nomenclature

PV = Photovoltaic generator.

String = Photovoltaic string.

Module = Photovoltaic module.

Group = Photovoltaic group.

Cell = Photovoltaic cell.

nc: ncg / ncp = Cell number: good / defective.

ng: ngg / ngp = Group number: good / defective.

nm: nmg / nmp= Module number: good / defective.

ns: nsg / nsp = String number: good / defective.

nfg / nfp = Good / defective generator.

N_Cells = Number of cells in each group.

N_Groups = Number of groups in each module.

N_Modules = Number of modules in each string.

N_Strings = Number of strings in each generator.

V = Voltage.

I = Current.

P = Power.

I_Bypass = Bypass current.

VCell_imposed = Voltage imposed.

VCell_Open-circuit = Cell open circuit voltage.

ICell_Short-circuit = Cell short circuit current.

phi = Sunlight.

phi_SC = Sunlight standard condition.

iphSC = Photo current standard condition.

t_nf = Normal functioning temperature.

tc_SC = Cell temperature standard condition.

at = Ambient temperature.

R_s = Cell series resistance.

R_sh = Cell shunt resistance.

I₀ = Reverse saturation current of the diode.

dtv = Diode thermal voltage.

Alpha = Temperature coefficient of the short- circuit current.

I. Introduction

The productivity of photovoltaic generators is based on two main factors [1-3]: solar radiation energy which is captured by the generator and direct electrical energy resulting from the conversion of the solar radiation energy by the photovoltaic phenomena. So, the degradation of these two factors means the presence of a problem at the generator.

Practically, the existence of electrical defects on this type of systems can reduce its productivity, among of the major faults known in the field of its diagnosis [4-11]: the short circuit, open circuit, impedance and finally reversed polarity faults. So, these defects can reduce the power produced by the PV generator by the change of its current, voltage, resistance, temperature and sunlight. For this and with the rising costs of photovoltaic generators, it is better to predict and maintain the faulty components before its unavailability.

The paper’s objective is the development of a model able to predict the abnormal situations of the PV generator functioning [12-22]. Our contribution presented in this paper is to propose a new methodology for modeling the photovoltaic generator, based 1) on the mathematical modeling of the IV characteristic of its faulty components which can be: cells, bypass diodes and blocking diodes, for objective to study the functioning of these faulty elements itself, and 2) this new methodology based also on the mathematical modeling of the IV characteristic of the generator’s groupings, which can grouped these faulty elements: cell, cells’ group, module, string and finally the PV generator, for objective to study the influence of these faulty components on the functioning of these groupings.

(3)

II. Modeling the photovoltaic generator in normal functioning

Fig1. Electrical block diagram of a photovoltaic generator in its normal functioning Modeling of the PV generator in its proper

functioning presented in this work, is for objective to make a comparison of the results thereafter, between the normal case and the abnormal cases, this comparison may facilitate the detection of any defect can degrade the productivity of a photovoltaic generator.

To test the performance of the mathematical models presented in this article, we used a generator figure1 consists of five parallel strings, each terminated with a blocking diode and contain five photovoltaic modules in series, where each module is formed with two groups of photovoltaic cells, and finally each group contains eighteen cells regrouped by one bypass diode.

Because, we have used in the modeling of the generator’s cells the “a diode model, so the mathematical modeling of the I-V characteristic of the generator in the normal function is

 

, , , , , , , ,

, , , ,

_

2

0

2 0 0 .8

n fp

C elln cg n g g n m g n sg n fg s C elln cg n g g n m g n sg n fg

n cg n g g n m g n sg n f

P V M o d u les G ro u p s C ells C ell im p o sed

P V S trin g s

n f

S C

S C S C

S C

V R I

d tv

C ell

I N N N V

V N

a lp h a t

p h i p h i

ip h a lp h a a t tc

p h i p h i

I e V

 

   

 

 



 

 



 



, , , ,

0 g s C elln cg n g g n m g n sg n fg

sh

R I

I R





 

 

 

 

   

  

 



(1)

Figure2 shows the IV characteristic and the power of a good photovoltaic generator.

0 10 20 30 40 50 60 70 80 90

0 500 1000

power (W)

voltage (V)

0 10 20 30 40 50 60 70 80 900

10 20

current (A)

power of a good generator IV of a good generator

Fig2. Power and IV of a good PV generator

III. Modeling the photovoltaic generator in malfunctioning

III.1. Cell defects

III.1.1. At the level of the PV cell a) For the reversed polarity default A cell reversed polarity provides

, , , , , , , ,

n cp n g p n m p n sp n fp n cg n g p n m p n sp n fp

C ell C ell

V V

I I

  

 

 (2)

b) For the open circuit default

Because the cell is presented as a generator, so his characteristic when subjected to the open circuit default is

(4)

, , , ,

_

0

n cp n g p n m p n sp n fp

C ell C ell o p en circu it

C ell

V V

I

 

 



(3)

c) For the impedance default

A cell is subjected to the impedance fault if

, , , , , , , , , , ,

, , , , 0

n cp n g p n m p n sp n fp n cp n g p n m p n sp n fp n g p n m p n sp n fp

C ell C ell G ro u p

C ell

V Z I

I

  

 

 (4)

d) For the short circuit default

A photovoltaic cell is short circuited if

, , , ,

, , , , _

0

n cp n g p n m p n sp n fp C ell

C ell C ell S h o rt circu it

V

I I _

 

 



(5)

III.1.2. At the level of the PV group a) For the reversed polarity default

The faulty PV group’s voltage contains cells reversed polarity is

 

, , , , , , , , , , ,

1 C ells

ngp nm p nsp nfp nc ncp ngp nm p nsp nfp nc ncp ngp nm p nsp nfp

N

G roup C ell C ell

nc

V V V

 



   ⁽⁶⁾

But the group’s current is dependent to its voltage, for that, if its voltage is positive

, , , , , , ,

ngp nm p nsp nfp nc ngp nm p nsp nfp

G roup C ell

I I (7)

Where, the good and defective cells supplied the same currents values.

Else – if the voltage of this group is negative–, then

, , , , , , , , , ,

ngp nm p nsp nfp nc ngp nm p nsp nfp ngp nm p nsp nfp

G roup C ell B ypass

I I I (8)

The existence of a single cell open circuit in a faulty photovoltaic group can cut the circulation of its current, so its characteristic is

, , ,

, , , , , ,

n g p n m p n sp n fp _

n g p n m p n sp n fp n g p n m p n sp n fp

G ro u p C ells C ell O p en circu it

G ro u p B yp a ss

V N V

I I

  

 



(9)

If the faulty group contains defective cells impedances, contains also at least one good cell, so the current flowing between its cells is not null, and by the voltages in series addition law

, , ,

, , , ,

, , , , , , , ,

1 n g p n m p n sp n fp

C ells

n c n cp n g p n m p n sp n fp

n c n cp n g p n m p n sp n fp n c n cp n g p n m p n sp n fp G ro u p

N C ell

n c C ell C ell

V

Z I



 



  

 

  

 

 (10)

If the group’s voltage is positive, then consequently it contains at least one good cell, and by the currents in series addition law

, , , , , , ,

ngp nm p nsp nfp nc ncp ngp nm p nsp nfp

G roup C ell

I I

  (11)

But if the group’s voltage is negative and it contains at least one good cell, so by the currents in series addition law

, , , , , , , , , ,

ngp nm p nsp nfp nc ncp ngp nm p nsp nfp ngp nm p nsp nfp

G roup C ell B ypass

I I I

   (12)

The last situation, where the entire group’s cells are impedances, so the current choose the easy way

, , ,

, , , , , ,

0

n g p n m p n sp n fp

n g p n m p n sp n fp n g p n m p n sp n fp G ro u p

G ro u p B yp a ss

V

I I

 

 

 (13)

The IV characteristic of a faulty PV group contains defective cells short circuit is dependent on the number of its good cells existing. If it contains at least one cell is good

, , , , , , ,

1 C ells

n g p n m p n sp n fp n c n cp n g p n m p n sp n fp

n g p n m p n sp n fp n cg n g p n m p n sp n fp N

G ro u p C ell

n c

G ro u p C ell

V V

I I

 

 



 



 (14)

By cons, – all the group’s cells are defective– and by the nodes law:

, , ,

, , , _ , , ,

0

n g p n m p n sp n fp

n g p n m p n sp n fp n g p n m p n sp n fp

G ro u p

G ro u p C ell sh o rt circu it B yp a ss

V

I I _ I

 

  



(15)

III.1.3. At the level of the PV module a) For the reversed polarity default

So the faulty module's voltage contains cells reversed polarity is

 

, ,

, , , , , , , ,

1 1

n m p n sp n fp

G ro u p s C ells

n c n cp n g n m p n sp n fp n c n cp n g n m p n sp n fp M o d u le

N N

C ell C ell

n g n c

V

V V

 

 



   ⁽¹⁶⁾

But the module’s current is dependent to the voltages of each one of its groups, so if it contains at least one group with a positive voltage

If group ng’=1: N_Groups where Vgroup_ng’>0:

, , , ', , ,

nm p nsp nfp nc ngng nm p nsp nfp

M odule C ell

I I

  (17) Else and by the currents in series addition law and the nodes law

, , , , , , , , ,

nm p nsp nfp nc ng nm p nsp nfp ng nm p nsp nfp

M odule C ell B ypass

I I I (18)

The IV characteristic of the faulty module depends on the number of its faulty groups existing, so if it contains at least one good group

(5)

 

, ,

, , , ,

,

, , , , ,

1 1

_ _

m in 1 n m p n sp n fp

n c n gn g p n m p n sp n fp

n m p n sp

G ro u p s

n m p n sp n fp n g n m p n sp n fp

M o d u le

N N

C ell

n g n c

G ro u p s d efective C ells C ell o p en circu it N

M o d u le n g G ro u p

V

N N V

I I

  





 

   

   

   

  

    

 

 





(19)

Otherwise,

, ,

, , , , ,

n m p n sp n fp _

n m p n sp n fp n g p n m p n sp n fp

M o d u le G ro u p s C ells C ell O p en circu it

M o d u le B yp a ss

V N N V

I I

   

 



(20)

The module’s voltage contains at least one good cell is dependent to the voltages provided by its good and defective cells

If  nc = 1: NCells of ฀ ng = 1: N_Groups’, Icellnc,ng,nmp,nsp,nfp≠0

, ,

, , , ,

, , , , , , , ,

1 1

n m p n sp n fp

n c n cp n g n m p n sp n fp

n c n cp n g n m p n sp n fp n c n cp n g n m p n sp n fp M o d u le

N N

C ell

n g n c C ell C ell

V

Z I

 

 

 



 

 

  

 

  ⁽²¹⁾

N_Groups’: Number of groups where each one contains at least one cell is good.

But the module’s current where it has at least one cell is good and by the currents in series addition law

 

, , m in ^{G ro u p s}1 , , ,

N

M odule ng G roup

I  _ I (22)

By const, if all the module’s cells are defective then:

฀nc =1:N_Cells of ฀ ng=1:N_Groups, Icellnc,ng,nmp,nsp,nfp=0

, ,

, , , , ,

0

n m p n sp n fp

M o d u le

M o d u le B yp a ss

V

I I

 

 

 (23)

The faulty module’s characteristic, where it has at least one good cell

 

, , , , , ,

1 1

n m p n sp n fp n c n cp n g n m p n sp n fp

n m p n sp n fp n cg n g n m p n sp n fp

N N

M o d u le C ell

n g n c

M o d u le C ell

V V

I I

  

 



 



  (24)

But if all its cells are defectives then

, ,

, , _ , , ,

0

n m p n sp n fp

n m p n sp n fp n g p n m p n sp n fp

M o d u le

M o d u le C ell S h o rt circu it B yp a ss

V

I I _ I

 

  



(25)

III.1.4. At the level of the PV string a) For the reversed polarity default

The string's voltage is equal by the voltages in series addition law

, , , ,

,

, , , ,

1 1 1

G ro u p s

M o d u les C ells

n c n cp n g n m n sp n fp n sp n fp

n c n cp n g n m n sp n fp

N N N

C ell S trin g

n m n g n c C ell

V V

V



   

 

 

      (26) And the string’s current is equal by the currents in series addition law

 

, m in ^{M odules}1 m in ^{G roups}1 , , ,

nsp nfp ng nm nsp nfp

N N

String nm ng G roup

I  _ _ I (27)

The string’s characteristic if it contains at least one good group

 

,

, , , ,

,

, ,

1 1

1

_ _

1 1

m in m in

n sp n fp

M o d u les

n c n gn g p n m n sp n fp

n m n sp

G ro u p s M o d u les

n sp n fp n g n

S trin g

N N

N C ell

n g n c

n m

G ro u p s D efective C ells C ell O p en circu it N N

S trin g n m n g G ro u p

V

N N V

I I

  





 



   

   

   

 

    

 



  

 



m n sp n fp^, ^,













(28)

Otherwise:

,

_

0

n sp n fp

S trin g M o d u les G ro u p s C ells C ell O p en circu it

S trin g

V N N N V

I

    

 

 (29)

And this is the problem, it is true that this default increases the voltage and even gives the maximum which is our objective, but he canceled outright the current and thus also the power.

Also the IV characteristic of the string is depended on the number of its good and defective cells, so if it contains at least one good cell then

If nc = 1 : N_Cells of ฀ ng = 1:N_Groups’ of ฀ nm =1:

N_Modules, Icellnc,ng,nm,nsp,nfp ≠ 0

, , , ,

,

, , , ,

, ,

1 1

m in m in

n c n cp n g n m n sp n fp G ro u p s

n c n cp n g n m n sp n fp n sp n fp

n c n cp n g n m n sp n fp

n sp n fp n g

C ell

N N N

C ell S trin g

n m n g n c

C ell N N

S trin g n m n g G ro u p

V V Z

I

I I









 

 

 

 

 

  



  



n m n sp n fp^, ^,









  

  



(30)

N_Groups’: Number of groups where each one contains at least one cell is good.

By cons, if all string’s cells are impedances then:

฀ nc = 1 : NCells of ฀ ng = 1 : NGroups of ฀ nm = 1 : N_Modules, Icellnc,ng,nm,nsp,nfp = 0

,

0 0

n sp n fp

n sp n fp S trin g

S trin g

V I

 

 



(31)

At the string, the difference between its current and its voltage must remarkable because its current is remaining

(6)

constant, by against its voltage increases by increasing the number of its cells. So, the IV characteristic of a faulty string contains at least one good cell

 

, , , , ,

1 1

G ro u p s

n sp n fp n c n cp n g n m n sp n fp

n sp n fp n cg n g n m n sp n fp

N N N

S trin g C ell

n m n g n c

S trin g C ell

V V

I I

  

 



 



   (32)

Otherwise – all its cells are short circuited–:

,

, _

0

n sp n fp

n sp n fp S trin g

S trin g C ell S h o rt circu it

V

I I _

 

 



(33)

III.1.5. At the level of the PV generator a) For the reversed polarity default

Because this default can reduce the voltage of the string, then the faulty generator's voltage is dependent to its faulty strings’ voltages only, but the generator's current is dependent to its good and defective strings



^,



, , , ,

1

1 1 1

1 1

m in

m in m in

S trin g s

n fp n s n sp n fp

G ro u p s

n c n cp n g n m n s n sp n fp S trin g s

n c n cp n g n m n s n sp n fp

n fp N

P V n s S trin g

N N N

C ell N

n s

n m n g n c C ell

N N

P V n m n g

V V

V V I



 

 



  

 



  

  

   



  

 



^, ^, ^,



1 S trin g s

n g n m n s n fp N

G ro u p n s

I











  

  

 

(34)

The IV characteristic of the faulty generator is determined by the IV characteristics of its strings, so its current is dependent to its good and faulty strings which contain at least one good group and by the currents in parallel addition law

, , , ,

nfp nc ngg nm ns nfp

P V Strings C ell

I N _I (35) Where N_strings’: strings contain at least one good group.

And its voltage is dependent to its good strings, so if it contains at least one good string (because they have the most minimal voltage)

, , , ,

nfp ncg ngg nm g nsg nfp

P V M odules G roups C ells C ell

V N N N V (36)

Otherwise:



^,



, , , ,

, 1

1 1

1

1 _

_

m in

S trin g s

n c n gn g p n m n s n sp n fp M o d u le

S trin g s

n m n s n sp N

N N

C ell

N n g n c

N n s

n m G ro u p s D efective

C ells C ell o p en circu it

V V

V N

N V



 



 





 

 

 

  

 

   

    

 

s  

 

 

 

 ⁽³⁷⁾

The faulty generator’s voltage is dependent to its faulty strings’ voltages; because if it contains a good string, sure its voltage is greater, by cons the generator’s current is dependent to its strings contained at least one cell is good.

If  nc=1:N_Cells of  ng=1:N_Groups’ of  nm=1: N_Modules of

 ns=1:N_Strings, Icellnc,ng,nm,ns,nfp≠0



^,



, , , ,

1

1 1

m in

S trin g s

n c n cp n g n m n s n sp n fp G ro u p s

S trin g s

n c n cp n g n m n s n sp n fp N

C ell

N N N

N

C ell n s

n m n g n c

C ell

V V

V Z

I



 



 

 



 



  

  

   

  



  

 

, , , ,

_

, , ,

_

1 1

1

m in m in

n fp

n cg n g g n m g n sg n fp

S trin g s D efective

n g n m n s n fp P V

S trin g s G o o d C ell N

N N

n m n g G ro u p

n s

I

N I

  I





 

 

  

 

 



 

 

 

 

   

     

  

 

(38)

Where: N_Groups’: Number of groups where each one contains at least one cell is good.

But if all the cells of this faulty generator are impedances, so the generator’s characteristics become

0 0

n fp

n fp P V

P V

V I

 

 



(39)

Faulty generator’s voltage depends on the number of its good and defective strings, and even the number of the good cells existing in each one of its faulty strings.But the generator’s current is dependent to its good and faulty strings which contain at least one good cell:

 

,

, , , ,

1

1 1

_

m in

S trin g s

G ro u p s

S trin g s

n cg n g n m n s n fp n fp

N

N N N

N

n s C ell

n m n g n c

S trin g s C ell P V

S trin g s C ell S h o rt circu it

V V

V

N I

I

N I



 



  



 



 

 

 

  

 

  

  









 



(40)

Where:

N_Strings’: Number of strings contains at least one good cell.

N_{Strings’’}: Number of strings all its cells are defective.

III.2. Bypass diode defects

III.2.1. At the level of the PV group a) For the reversed polarity default

As the bypass diode is reversed polarity, it can create a short circuit default at the level of its group