Module |  |  |  |

| To view the Module page, click Module on the main window's navigation menu. Note that for the Module page to be available, the technology option in the Technology and Market window must be Photovoltaics - SAM Performance Models. The Module page allows you to choose a module performance model from four options, choose or enter module parameters, and view module characteristics.

The photovoltaic module performance models calculate the hourly DC electrical output of a single module based on the hourly total incident solar radiation (plane-of-array irradiance) calculated by the Climate model. The photovoltaic array output depends on the number of modules and the pre-inverter derate factor specified on the Array page. Solar Advisor passes the array's hourly DC power output to the inverter model, whose characteristics are on the Inverter page.

Note. In addition to the number of modules and derate factors, the input variables on the Array page specify the array orientation and tracking, and the method used to calculate total incident radiation.

There are four options available for modeling PV modules:

• | Simple Efficiency Module

• | CEC Performance Model

• | Sandia PV Array Performance Model

• | Concentrating PV Module

Each model uses a different algorithm to predict module performance. In general, if you are modeling a system that uses a particular brand and type of flat-plate PV module, you should first look for the module in the Sandia database, and then in the CEC database. If you do not find the module in either database, or are not modeling a particular brand of module, then use the single-point efficiency model.

For concentrating photovoltaic (CPV) modules, use the Concentrating PV Module model unless you are modeling the Entech 22x module, in which case you can choose the module from the database in the Sandia model.

To specify a photovoltaic module model:

1. | Choose the model name from the list.

2. | For the Sandia or CEC models, choose a module from the database of available models.

For the Simple Efficiency Model and Concentrating PV Module, enter module characteristics.

Choosing the Best Flat-plate Model for your Analysis

This section briefly describes each model and provides guidelines for choosing the best model to meet the goals of your analysis. Each model is described in more detail in the "About" sections below.

There are three flat-plate PV performance models available in the current version of Solar Advisor:

• | The Simple Efficiency Module model is a simple representation of module performance that requires you to provide the module area, conversion efficiency, structure, and a temperature coefficient.

• | The Sandia PV Array Performance Model calculates hourly efficiency values based on field measurements of deployed systems using data from a database of commercially-available modules. The Sandia model tends to produce more accurate predictions of module performance than both the CEC model and Simple Efficiency model. However, because of the time and effort required to make the field measurements, the Sandia module database is less up-to-date than the CEC database.

• | The California Energy Commission (CEC) Performance Model predicts module performance based on a database of module characteristics determined from module ratings. Like the Sandia model, the CEC model calculates hourly efficiency values, and allows you to select from a list of a commercially-available modules. Because the model coefficients can be generated quickly by the CEC using standard module specifications such as those provided by module manufacturers, the module database is more up-to-date than the Sandia database. The CEC model predictions are more accurate than the Simple Efficiency model, but less accurate than the Sandia model, particularly for thin-film modules.

Because the Sandia model is the most accurate of the three models, it should be your first choice when choosing between the models. If you are investigating a module that is not included in the Sandia database, you can either choose a different module in the database with similar characteristics, or see if the model is in the CEC database. If you do not find your module in either the Sandia or CEC databases, choose the single-point efficiency model. Some types of analyses that require sensitivity or parametric analyses are best performed with the single-point efficiency model.

Table 13. Summary of guidelines for choosing a photovoltaic module performance model.

Use this model... | ...if your analysis involves... | Comments
Sandia Model based on field test data. | estimates of module performance for crystalline or thin-film modules, or to model the Entech 22x concentrating photovoltaic module. | If your module is in both the Sandia and CEC lists, use the Sandia model.
CEC Model based on module ratings. | estimates of module performance for crystalline-silicon modules or for new modules recently available on the market. | Use the CEC model when your analysis involves a particular module that is not available in the Sandia database.
Simple Efficiency Module Simple constant efficiency model with temperature correction. | sensitivity or parametric studies on module efficiency or temperature coefficients. | Use the Simple Efficiency model for modules not included in either the Sandia or CEC model database, or to model a system using a particular size of module where the make and model is not important.
Concentrating PV Module Simple constant efficiency model. | Modeling concentrating photovoltaic modules. | See Modeling Concentrating Photovoltaic (CPV) Modules for details.

Modeling Thin-film Modules

For modules based on thin-film cell technology, including amorphous silicon, copper indium diselenide (CIS), cadmium telluride (CdTe), and heterojunction with intrinsic thin layer (HIT), the CEC and single-point efficiency models do not adequately represent module performance at low-light levels. Because the Sandia model is based on field measurements, it provides a more reliable prediction of thin-film module performance, but its results for thin-film modules have only been validated at the module level, not at the system level.

For best results, if you are modeling a thin-film module, look for the module in the Sandia database. If the module is not available in the Sandia database, you may want to use a module from the database with similar characteristics to the one you are modeling. Use the table below to help identify the thin-film modules in the Sandia database.

Table 14. Thin-film module manufacturers and model numbers available in the Sandia module database.

Cell Type | Manufacturer | Model Series or Number
amorphous tandem junction (2-a-Si) | Solarex | MST
amorphous silicon triple junction (3-a-Si) | Uni-Solar | PVL, SHR, US, USF
cadmium telluride (CdTe) | BP Solar | BP980, BP990
First Solar | FS
copper indium diselenide (CIS) | Shell Solar | ST
Siemens Solar | ST
amorphous silicon heterojunction (HIT-Si) | Sanyo | HIP

Modeling Concentrating Photovoltaic (CPV) Modules

For CPV modules, other than the Entech 22X Concentrator module, use the Concentrating PV Module option. This model uses a simple algorithm that calculates the module's hourly DC output by multiplying the hourly direct normal component of the solar radiation data in the weather file by the module's area and efficiency as specified on the Module page.

If you are modeling the Entech 22X Concentrator (c-Si), you can use the Sandia PV Array Performance model instead of the Simple Efficiency model. The Entech module is modeled using a set of coefficients determined by analyzing field test measurements. To use the Entech module, choose the Sandia model option and select the Entech 22X Concentrator [1994] module from the list of available modules. The Entech module is a special case in the Sandia module database, and its coefficients have been selected to allow it to be modeled using global radiation data.

To use the single-point efficiency CPV model:

1. | On the Module page, choose Concentrating PV Module.

2. | Enter the module's total collector area in square meters.

3. | In the Radiation Level and Efficiency Table, enter an efficiency value for each of up to five incident beam radiation reference values in increasing order. To enter fewer than five efficiency values, you must include five radiation values, but you can assign the same efficiency value to more than one radiation value. For example, to represent a module with 20% constant efficiency, you could assign the value 20.0 to each of the five radiation values 200, 400, 600, 850, 1000.

Concentrating PV Module Characteristics
Variable | Description | Units
Area | The module collector area in square meters. | m 2
Rated Power | The module's rated maximum DC power at the reference radiation value indicated in the efficiency table below. Solar Advisor uses this value to calculate the array cost shown on the PV System Costs page, but not in simulation calculations. The rated module power is the product of the reference radiation, reference efficiency and area. | W DC

Radiation Level and Efficiency Table
Variable | Description | Units
Radiation | The incident beam radiation level at which the given efficiency value applies. | W/m 2
Efficiency | The module conversion efficiency at a given radiation level used in the hourly simulations to convert incident normal solar radiation to DC electrical output. | %
Reference | Indicates which value to use for the reference calculations. |

The module's hourly DC output is the product of the hour's direct normal solar radiation from the weather file as defined on the Climate page, collector area, and module efficiency from the Module page:

Where,

P mp,CPVModule (WDC) | The module's average DC electric output for the hour.
E DirectNormal (W/m 2) | The direct normal solar radiation from weather processor.
A Collector (m 2) | The collector area in square meters.
η Module | The module's conversion efficiency at the incident beam radiation for the current hour, extrapolated from the efficiency curve defined by the table on the Module page.

About the Sandia PV Array Performance Model

The Sandia PV Array Performance Model uses an algorithm and a database of commercially available modules developed at Sandia National Laboratory. To use the model, you simply select a module or array from the Module Name list.

The Sandia model is described in King et al, 2004. Photovoltaic Array Performance Model. Sandia National Laboratories. SAND2004-3535. http://www.osti.gov/bridge/product.biblio.jsp?query_id=0&page=0&osti_id=919131

To use the Sandia photovoltaic model:

1. | On the Module page, choose Sandia PV Array Performance Model.

2. | Choose a module from the list of available modules. Solar Advisor displays the module's characteristics and model coefficients for your reference.

The first several items in the Sandia database are arrays instead of single modules. The arrays are indicated by the word "Array" in the name, which also includes the number of modules and the module type. When you use an array from the database, you should set the Pre-Inverter derate factor on the Array page to zero.

If you are modeling a module not included in the database and want to use the Sandia model, you can try to find a module with similar characteristics to your module's specifications.

The Sandia model consists of a set of equations that provide values for five points on a module's I-V curve. The equations involve a set of coefficients that have been empirically determined based on field measurements taken from modules installed in real, operating photovoltaic systems. The Sandia database consists of a set of manufacturer specification and measured data for each module and array in the database.

Solar Advisor does not track voltage and current levels in the system and assumes that the array operates at its maximum power point.

The Sandia Module Library Parameters

When you select a module from the Sandia database on the Module page, Solar Advisor displays module's parameters for your reference. You can see the complete set of parameters in the Module library by using Solar Advisor's library editor.

The Sandia module library includes parameters for modules that have been tested by Sandia National Laboratory. Manufacturers wishing to add their modules to the Sandia database should contact Sandia National Laboratory directly. Because the parameters involve data from field measurements, it is not possible to generate parameters from manufacturer specifications.

The tables below describe the parameters in the Sandia module library, which are explained in more detail in the King 2004 reference cited above.

Module Characteristics
Parameter | Description | Units
Maximum Power (P_mp) | The module (or array's) rated power. Equal to the product of the maximum power voltage and maximum power current. | W DC
Maximum Power Voltage (V_mp) | Maximum power voltage under reference conditions. | V
Maximum Power Current (I_mp) | Maximum power current under reference conditions. Defines the maximum power point on the module's I-V curve. | A
Open Circuit Voltage (V_oc) | Open circuit voltage under reference conditions. Defines the open circuit point on the module's I-V curve. | V
Short Circuit Current (I_sc) | Short circuit current under reference conditions. Defines the short circuit point on the module's I-V curve. | A
Cell Area (A_c) | The total cell area: Includes all cells in the module, but does not include space between cells. This value should be less than the module area. Equal to the area of a single cell multiplied by the number of cells | m 2
Material | Cell material | --
Number of Cells (N_c) | Number of cells per module, equal to the product of Series Cells and Parallel Cells under Additional Parameters (see below). | --

Additional Parameters
Parameter | Description | Units
Material | Cell material. Multi-crystalline silicon is mc-Si, single-crystal silicon is c-Si. See the table above for thin-film cell material abbreviations. | --
Series Cells | Number of cells in series per cell string. | --
Parallel Cells | Number of cell strings in parallel. | --
BVoco | Open circuit temperature coefficient | V/°C
MBVoc | Coefficient representing dependence of Bvoco on irradiance. Typically zero. | V/°C
Vintage | Year field measurement data were collected. | year
BVmpo | Temperature coefficient at module Vmp under reference conditions | V/°C
MBVmp | Coefficient representing dependence of Bvmpo on irradiance. Typically zero. | V/°C
AImp | Normalized maximum power temperature coefficient, calculated by dividing alpha by Isco. | 1/°C
AIsc | Normalized short circuit temperature coefficient, calculated by dividing alpha by Isco | 1/°C
N | Empirically determined factor, also called the "diode factor." | --
dTC | Temperature difference between the cell and module back surface under reference conditions. | °C
FD | Fraction of diffuse irradiance used by module. For flat-plate modules, FD=1; for CPV modules, FD=0; and for low-concentration modules, 0 < FD < 1. | --
Ixo | Current at module open circuit voltage of Voc / 2 under reference conditions. Defines one of the five points on the module's I-V curve. | --
Ixxo | Current at module open circuit voltage of (Voc + Vmp) / 2under reference conditions.Defines one of the five points on the module's I-V curve. | --

A, B, C Coefficients
Parameter | Description | Units
A0-4 | Empirically determined coefficients used in polynomial representation of solar spectral effects of daily air mass variation on Isc. | --
B1-5 | Empirically determined coefficients used in polynomial representation of optical effects of the angle of incidence (AOI) on Isc. |
C0-5 | Empirically determined performance coefficients that relate Imp, Ix, and Ixx to effective irradiance. | --
a, b | Empirically-determined coefficients used in temperature correction calculations. | --

About the CEC Performance Model

The California Energy Commission (CEC) Performance Model uses the University of Wisconsin-Madison Solar Energy Laboratory's five-parameter model with a database of module parameters maintained by the California Energy Commission (CEC) for the California Solar Initiative. To use the model, you simply choose a module name from the CEC Module list.

The five-parameter model is described in brief in De Soto 2003, "Improvement and Validation of a Model for Photovoltaic Array Performance," Solar 2003 Conference Proceedings, American Solar Energy Society.

A more detailed description can be found in De Soto 2004, Improvement and Validation of a Model for Photovoltaic Array Performance, Master of Science Thesis, University of Wisconsin-Madison. http://sel.me.wisc.edu/theses/desoto04.zip.

For information about the CEC list of eligible photovoltaic modules, see http://www.gosolarcalifornia.org/equipment/pvmodule.html.

To use the CEC photovoltaic model:

1. | On the Module page, choose CEC Performance Model.

2. | Choose a module from the list of available modules. Solar Advisor displays the model's characteristics and model coefficients for your reference.

The modules in the list are from Solar Advisor's CEC module library, which is described in more detail below.

Note. To make sure that you have the latest CEC module library, on the Help menu, click Check for updates. Solar Advisor will connect to NREL servers on the Internet and, if a more recent version of the library is available, automatically update your current library. Updating the library only affects the standard CEC module library, and will not affect any modules you may have added to the library.

The five-parameter model calculates a module's current and voltage under a range of solar resource conditions (represented by an I-V curve) using an equivalent electrical circuit whose electrical properties can be determined from a set of five parameters. These five parameters, in turn, are determined from standard reference condition data provided by either the module manufacturer or an independent testing laboratory, such as the Arizona State University Photovoltaic Testing Laboratory.

Solar Advisor does not track voltage and current levels in the system and assumes that the array operates at its maximum power point.

The CEC Module Library Parameters

When you select a module from the CEC database on the Module page, Solar Advisor displays module's parameters for your reference. You can see the complete set of parameters in the Module library by using Solar Advisor's library editor.

The CEC module library contains a set of module parameters for modules included in the CEC's database of eligible photovoltaic modules. Manufacturers wishing to add their modules to the CEC database should contact the CEC directly.

If you would like to add a module to the CEC module library in your copy of Solar Advisor, please contact us at solar.advisor.support@nrel.gov. If you can provide us with a list of the module's specifications as shown on the Module page under Module Characteristics, we may be able to create a set of coefficients for you to use. We provide this service on a case-by-case basis, and cannot guarantee the quality of the coefficients we generate.

The parameters in the CEC module library include:

• | A set of module characteristics at standard test conditions, which may be provided by either the module manufacturer or by an independent testing laboratory.

• | A set of additional parameters used in the model's equivalent circuit to calculate the module's I-V curve.

• | Reference inputs required to generate the calculated model parameters.

Module Characteristics
Parameter | Description | Units
Maximum Power (P_mp) | The module rated power. Equal to the product of the maximum power voltage and maximum power current. | W DC
Maximum Power Voltage (V_mp) | Reference maximum power voltage at STC. | V
Maximum Power Current (I_mp) | Reference maximum power current at STC. | A
Open Circuit Voltage (V_oc_ref) | Reference open circuit voltage at STC. | V
Short Circuit Current (I_sc_ref) | Reference short circuit current at STC. | A
Cell Area (A_c) | Total cell area, equivalent to the product of the number of cells per module and the area of a single cell. The cell area should be less than the module area. | m 2
Number of Cells (N_s) | Total number of cells per module. | --
Short Circuit Temp. Coeff (Alpha_sc) | Maximum current temperature coefficient. | %/°C
Open Circuit Temp. Coeff. (Beta_oc) | Maximum voltage temperature coefficient. | %/°C
Max. Power Temp. Coeff. (Gamma_r) | Maximum power temperature coefficient from module specifications. | %/°C

Additional Parameters
Parameter | Description | Units
T_noct | NOCT temperature. | °C
A_ref | Modified ideality factor at reference conditions. | --
I_l_ref | Light current at reference conditions. | A
I_o_ref | Diode reverse saturation current. | A
R_s | Series resistance. | Ohm
R_sh_ref | Shunt resistance. | Ohm
Adjust | An adjustment factor used in the coefficient generator to verify that the calculated Gamma_r value is equal to the Gamma_r value in the module specifications. |
Gamma_r | Maximum power temperature coefficient calculated by the coefficient generator. | %/°C
Source | The source of manufacturer data used to generate the coefficients. | --

Reference Inputs
Parameter | Description | Units
T_amb_noct | NOCT ambient temperature. Default value is 25 °C. | °C
T_refC |  | %
FFV_wind | Wind speed adjustment factor to account for wind shear. Default value is 0.51 for arrays mounted at ground level or up to 22 feet (6.7 m) above the ground, and 0.61 for arrays mounted higher than 22 feet (6.7 m) above the ground. | --
I_noct | NOCT incident solar radiation. Default value is 800 W/m 2. | W/m 2
I_ref |  | W/m 2
tau_alpha |  | --
kL |  | --
eta_mppt | A derating factor to account for inverter losses at the array's maximum power point. The default value is one because inverter losses are handled separately by the inverter performance model. | --
e_g |  | eV

About the Simple Efficiency Model for Flat-plate Modules

The flat-plate photovoltaic single-point efficiency model calculates the module's hourly DC output assuming that the module efficiency is fixed, regardless of the amount of solar radiation incident on the module. The model makes an adjustment for cell temperature, assuming that it is mounted on an open rack that allows air to flow over the back of the module.

The model calculates the DC power output of a single module using the equations described below.

To use the single-point efficiency flat-plate model:

1. | On the Module page, choose Simple Efficiency Module.

2. | Enter a temperature coefficient.

This is the number typically reported on manufacturer specification sheets as the maximum power coefficient. See the table below for sample values for different cell types.

3. | Choose a module structure from the three available options (displayed as front material / cell / back material).

Module manufacturers typically include a description of the front material, and frame or back material in a mechanical characteristics section of module specification sheets.

4. | Enter the module's total cell area in square meters, equivalent to the product of the cell area and number of cells.

5. | In the Radiation Level and Efficiency Table, enter an efficiency value for each of up to five incident beam radiation reference values in increasing order. To enter fewer than five efficiency values, you must include five radiation values, but you can assign the same efficiency value to more than one radiation value. For example, to represent a module with 13.5% constant efficiency, you could assign the value 13.5 to each of the five radiation values 200, 400, 600, 850, 1000.

Characteristics The module characteristics define the module's capacity, efficiency, and thermal characteristics.
Variable | Description | Units
Power | The module's rated maximum DC power at the reference radiation indicated in the table below. Solar Advisor uses this value to calculate the array cost on the PV System Costs page, but not in simulation calculations. The module power is the product of the reference radiation, reference efficiency and area. | W DC
Temperature Coefficient (Pmax) | The rated maximum-power temperature coefficient as specified in the module's technical specifications. | %/°C
Module Structure | The module's front and back materials (front material/cell/back material) used in the temperature correction algorithm. The model assumes that modules are mounted on an open rack that allows air to flow freely over the back of the module. | --
Area | The module collector area in square meters. To calculate the area for a given module power rating at a given reference radiation level, divide the power rating by the module efficiency and radiation level. For example, a 100 W module with 13.5% efficiency at 1000 W/m 2 requires an area of 100 W / (0.135 × 1000 W/m 2) = 0.74074 m 2. | m 2

Radiation Level and Efficiency Table
Variable | Description | Units
Radiation | The incident global (beam and diffuse) radiation level at which the given efficiency value applies. | W/m 2
Efficiency | The module conversion efficiency at a given radiation level used in the hourly simulations to convert incident normal solar radiation to DC electrical output. | %
Reference | Indicates which value to use for the reference calculations. |

Table 15. Sample temperature coefficient values for different cell types based on an informal survey of manufacturer module specifications.

Cell Type | Maximum Power Temperature Coefficient (%/°C)
Monocrystalline Silicon | -0.49
Polycrystalline Silicon | -0.49
Amorphous Silicon | -0.24
Amorphous Silicon Triple Junction | -0.21
Copper Indium Gallium DiSelenide (CIGS) | -0.45
Cadmium Telluride (CdTe) | -0.25

For each hour of the year, the flat-plate single-point efficiency model calculates the module DC output as the product of the total incident radiation, module area, and temperature correction factor:

Where,

E TotalIncident (W/m 2) | Total incident radiation from the Climate model.
A Module (m 2) | The module area in square meters.
F TempCorr | Temperature correction factor, described below.

The temperature correction factor algorithm is the same one used for Solar Advisor's implementation of the Sandia model, and is described in detail in King et al, 2004. Photovoltaic Array Performance Model. Sandia National Laboratories. SAND2004-3535. http://www.osti.gov/bridge/product.biblio.jsp?query_id=0&page=0&osti_id=919131.

First, the model calculates the module back temperature T Back:

The cell temperature T cell is:

The temperature correction factor F TempCorr is:

Where,

E TotalIncident (W/m 2) | The total incident solar radiation from weather processor.
E 0 (W/m 2) | The reference total incident radiation at STC
T ref (25°C) | The reference temperature at STC
γ (%/°C) | The maximum power temperature coefficient from Module page
a, b | Empirically-determined coefficients for the T back equation. Based on the temperature correction approach used for the Sandia model. determined by the Module Structure option on the Module page and the values in the table below.
ΔT 0 (3°C) | Temperature difference between the cell and module back surface at STC irradiance of 1000 W/m2. This value is for flat-plate modules in an open rack mount.
v Wind (m/s) | Hourly wind speed from the weather file.
T Ambient (°C) | Hourly ambient temperature from weather file.

Table 16. Empirically-determined a and b coefficients for each of the three Module Structure options available on the Module page.

Module Structure (from Module page) | a | b
Glass/cell/polymer | -3.56 | -0.0750
Glass/cell/glass | -3.47 | -0.0594
Polymer/cell/steel | -3.58 | -0.113