1 1 Materials for Energy Applications Group, Department of Mechanical Engineering, University of Western Macedonia, Kozani , 50100, Materials for Energy Applications Group, Department of Mechanical Engineering, University of Western Macedonia, Kozani , 50100, GreeceGreece

22 Environmental Research Laboratory, Institute of Nuclear Technology & Radiation Protection, NCSR “ Demokritos ” Environmental Research Laboratory, Institute of Nuclear Technology & Radiation Protection, NCSR “ Demokritos ”

Athens, 15310, Greece Athens, 15310, Greece

C. Mpounta 1,*1,*, S.S Makridis 1,2 , E.I Gkanas1,2, A.Z. Sarris 11, O.K. Romanou 11, A.K Stubos1,2

Development of a photovoltaic array model for use in power electronics simulation Development of a photovoltaic array model for use in power electronics simulation studies: Case studies using MATLAB/SIMULINKstudies: Case studies using MATLAB/SIMULINK

ResultsSolarex MSX60 - 60 Watt Nominal maximum Power , 36 Series connected Polycrystalline Silicon cells

a. Temperature Dependence of the model b. Irradiation Dependence of the model c. Diode Quality Factor Dependence

1.Matlab MSX-60 model I - V curves for various temperatures.

(G = 1 Sun, T = 0, 25, 50 & 75°C)

2.Matlab MSX-60 model P - V curves for various temperatures.

(G = 1 Sun, T = 0, 25, 50 & 75°C)

3.Matlab MSX-60 model I - V curves for various irradiation levels.

(G = 0.25, 0.5, 0.75, 1 Sun, T = 25°C)

4.Matlab MSX-60 model P - V curves for various irradiation levels.

(G = 0.25, 0.5, 0.75, 1 Sun, T = 25°C)

6.Matlab MSX-60 model I - V curves for various Rs values (G = 1 Sun, T = 25°C, Rs = 0, 8m, 16mΩ)

5.Matlab MSX-60 model I - V curves for various diode quality factors.

(G = 1 Sun, T = 25°C, n = 1, 1.25, 1.5, 1.75 & 2)

d. Series Resistance Dependence

Sunpower A300 Solar Panel - 300 Watt Nominal maximum Power , 96 Series connected Monocrystalline Silicon cells

Conclusions

Matlab Sunpower A300 model I - V curves for various temperatures.

(G = 1 Sun, T = 0, 25, 50 & 75°C)

I. The module’s cells temperature increase causes a slight rise to the model’s short circuit current Ιsc, from 3.80 to 3.92 [A] (3%), whereas the open circuit voltage Voc, shows a noticeable reduction. These changes result in the alteration of the characteristic I-V curves form, giving to the curve’s “knee” a more rounded form. Curves peak points represent the maximum module’s output power in both Figs.1&2. Therefore the growing roundness of the “knee” catalytic affects both the Pm and the total outcome power of the module, that radically decreases.

II. The rising values of the ambient irradiation, maintaining constant cell temperature, lead to a directly proportional and significant Ιsc and Pm increase, whereas the Voc is slightly affected (Figs.3&4).

Circuit diagram of the PV model

III. Series resistance Rs, represents the internal losses due to the current flow and gives a more accurate shape between the Pm point and Voc. As shown in Fig.6, increasing values of Rs cause significant output power losses. Shunt resistance Rsh, which is in parallel with the diode, was neglected, so that the diode quality factor, n stays set to 1.2, achieving the best curve match. It is noted that for an ideal cell Rs = Rsh = 0. IV. The chosen model, is of moderate complexity and was enhanced in accuracy by adding: temperature dependence of the diode saturation current Io, temperature dependence of the photo current IL and Rs. The net current of the cell is the difference of the photocurrent, IL and the normal diode current Io.

I. The cell’s performance characteristic I – V curve follows the general module’s curves form, since the module consists of a number (96) of series connected cells. If each cell’s net output current, in every temperature and irradiation level, is multiplied with the total cells number the result will be the module’s total net current.

a. Temperature Dependence of the model

II. In the case where a number of cells does not work properly (e.g. due to manufacturing failure) when connected to a module, the output power and module’s net current would be significantly decreased compared to the normal expected values. Therefore it is very important to test in advance the cells individual characteristics in order to reassure their correct operation out and in a module as a whole. The directly proportional relation between cell and module shows that the failure of one cell in a module can cause serious module malfunctions.

1.1. Overall the program’s execution results show a distinct match to both manufacturers published curves and electrical characteristics, simulating accurately their Overall the program’s execution results show a distinct match to both manufacturers published curves and electrical characteristics, simulating accurately their expected performance. That also allows the extraction of more curves reflecting the model’s performance when more complex variables are added under different expected performance. That also allows the extraction of more curves reflecting the model’s performance when more complex variables are added under different conditions.conditions.

2.2. Modules perform when connected in an array, the same way as cells in a module. This sequence creates an analysis pattern that indicates that macroscopic efficient Modules perform when connected in an array, the same way as cells in a module. This sequence creates an analysis pattern that indicates that macroscopic efficient operation is the result of microscopic efficient operation.operation is the result of microscopic efficient operation.

3.3. The series connection of the cells in a module as long as the series connection of the modules in an array is always preferable for permitting a simpler and easy to The series connection of the cells in a module as long as the series connection of the modules in an array is always preferable for permitting a simpler and easy to control operation. control operation.

References : A. Hansen, P. Lars, H. Hansen and H. Bindner. “Models for a Stand-Alone PV System”. Risø National Laboratory, Roskilde, December 2000, G. Walker, "Evaluating MPPT converter topologies using a MATLAB PV model," Journal of Electrical & Electronics Engineering, Australia, J. A. Gow, C. D. Manning “Development of a photovoltaic array model for use in power electronics simulation studies,” IEE Proceedings on Electric Power Applications, Model of Photovoltaic Module in Matlab™ - Francisco M. González - Longatt

2.Matlab Sunpower A300 model P - V curves for various temperatures.

(G = 1 Sun, T = 0, 25, 50 & 75°C)

(*xrysoula.mpounta@windowslive.com)

Materials for Energy Applications GroupMaterials for Energy Applications Group

The electrical behavior of a solar cell individually and hence this of a photovoltaic module and array in total, is reflected and determined by the variation of their typical electrical parameters as shown on their characteristic curves (I-V and P-V). Each cell’s/module’s electric circuit is modeled in order to create an electrically equivalent (ideal) model based on discrete electrical components whose behavior is known. This equivalent model is used in simulation studies, utilizing the existing standard equations concerning its typical parameters through a specialized program such as MatLab/Simulink. In this work the PV module that was initially chosen for modeling is the Solarex MSX60. The module’s model was implemented using a Matlab program which calculates the module’s net current Ia [Α], using its typical parameters: Short Circuit current-Isc, Open Circuit voltage-Voc ,and the variables module Voltage[V], Irradiation[Suns] and module cells Temperature[oC]. The model allows the extraction of two directly related results with one calculation, since the module’s and each cell’s current match. Although convenient, this direct correlation between the cells’ and module’s current is not always desirable in PV systems analysis. Therefore a second PV module, Sunpower A300 Solar Panel, was also modeled using a slightly modified version of the former Matlab program. In the second case the program calculates the cell’s net current I a [Α], using its typical parameters and variables. All the variable’s values needed to set for complete and accurate program calculation were provided in the manufacturer’s data. The results of the program’s execution for both cases are shown below.