# The Photovoltaic Energy Calculation Engineering Essay

3353 words (13 pages) Essay

1st Jan 1970 Engineering Reference this

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We used the program PVSYST in order to calculate accurately the output of our photovoltaic installation. PVSYST was the only program we had access to and it is a very widely known industrial program for sizing and designing photovoltaic systems. We used the most up to date version of 5.0.6.

## Procedure

First from the main menu above we choose project design and we select the stand alone system because ours is not connected with an existing grid (i.e. electrical generator)

In order to create a project in PVSYST, here is the Eco-friendly bulk carrier, we have to define:

The project name, which will identify the project in the file list in our data library.

The geographical location.

The hourly Meteo file, which is given from the program.

A geographical site is defined by:

its name, country, and world region,

its geographical co-ordinates: latitude, longitude, altitude and time-zone,

Monthly meteorological data.

To be used in the simulation, the minimum meteorological data include:

the monthly Global horizontal irradiation

Monthly averages of the ambient temperature.

Meteo values are displayed and easily defined on the screen. It is to be noted that for the verification of rather "uncertain" data, the clearness index Kt is also displayable, which is the irradiation actually received on earth, normalised to extra-terrestrial irradiation in monthly values. The monthly average of Kt should usually lie between about Kt = 0.25 and Kt = 0.75 at any place (PVSYST defaults). Monthly meteo values can be used as a basis for the generation of synthetic daily data.

Then we generate a graph for the specific site (i.e. Broome):

Where, the blue line is the clear day model (irradiation values with clear sky).

The above graph shows us graphically the irradiation sum per month (diffuse and global) with daily change values.

The Clearness Index Kt for Broome:

We can see that the values range from 0.25 to 0.75

The ambient temperature changes through the year.

The above graphs were generated by the program from the below table:

Also it is interesting to show the solar path at Broome or what is the solar height with respect of the plane through the day in order to understand how the sun moves from east to west. The graph also shows some landmark dates (denoted as 1 to 7) where the sun changes height:

Our next step to the program is to find the albedo Coefficient:

The albedo coefficient is the fraction of global incident irradiation reflected by the ground in front of a tilted plane. This effect takes place during the reversal computation of the horizontal irradiation onto a tilted plane. The albedo "seen" by the plane is of course null for a horizontal plane, and increases with tilt.

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Find out moreIn the project definition, the albedo values can be adjusted each month in order to take any possible snow-cover into consideration. The value usually admitted in the urban localities is of the order of 0.14 to 0.22, and can go up till 0.8 for a snow-cover. Ideally, the best value is obtained by a direct measurement on the site. But in practice, except for vertical planes, this value does not take on any great importance as the albedo component is relatively weak in the incident global irradiation (this contribution can be visualised in the results of the simulation). The following table gives some usual values for the albedo:

We used the 0.35 value of the Albedo coefficient because it matches on our material.

After defining the above values through the program we proceeded to the orientation of our PV plane. Our project consist a fixed tilted plane (The plane tilt is defined as the angle between the plane and the horizontal), because we considered placing the panels at the hatches due to the fact that they would be exposed all day to the sun's radiation. PVs are placed onto the hatches of the ship with zero tilt (Azimuth is zero as well because it doesn't affect the global on collector plane output. In northern hemisphere, the plane azimuth is defined as the angle between south and collector plane. In southern hemisphere, the plane azimuth is defined as the angle between north and collector plane).

As the program calculated, our loss with respect to an optimum orientation is 3.8% and the available irradiation on this tilted plane is 2370kWh/m2

We also considered using various configurations of panels as to maximise the output per m2 before choosing the above configuration. The below configurations was rejected due to the sun is changing place constantly throughout the day and the ship's movement reinforces the situation, we decided that the best configuration was the above due to sturdy design (one panel placed along the hatch), high efficiency (sun always hit the panel at any time) and simple installation.

Using two panels on each hatch half, tilted for 25o each having an output of 2445 kWh/m2 and the loss to an optimum orientation is 0.7%. Sun hit the panels only east and west when the ship goes north. (Highest efficiency, complex design, not easy installation).

Using two panels on each half, tilted for above 25o the output is greatly decreased and we have great loss to an optimum orientation.

The next step is to calculate the near shadings effect or shading. Near shadings are partial shadings which affect only a part of the field. The shaded part changes during the day and over the seasons. We call shading factor the ratio of the illuminated part to the total area of the field, or inversely shading loss is its complement.

Through the construction/perspective tool we created a model of the ship from the ship's particulars with the PVs installed on it in order to calculate the shading loss we have in various positions of the ship:

The real effect of partial shadings on the electrical production of the PV field is non-linear, and depends on the interconnections between the modules. In the PV array, the current of each cell string is limited by the current of the worst cell in the series. That is, when one only cell is shaded the entire string is strongly affected (which has also dramatic effects on the I/V(current/voltage) characteristics of the whole array). Even with by-pass protection diodes, this string does not participate more than slightly in the production of the PV array. This phenomenon is too complex to be treated in great detail . Nevertheless, the program provides a simplified method, giving the possibility of partitioning the field into rectangles, each of which supposed to represent a string of modules in series. Then it calculates a "Shading factor according to strings", stating that as soon as a string is hit by a shadow, the entire string (rectangle) is considered as electrically unproductive. Although not perfect, this approach should give an upper limit for the real shading loss evaluation. In practice, one often observe that (except for regular arrangements like sheds), this upper limit is not so far from the lower limit (that is, the linear loss).

And the losses percentage due to shading in any sun height.

After we define the natural parameters, we proceeded to the system consumption during a month in the specific site (BROOME). We cannot apply the maximum load 669.64 kW because it is the 100% and it is impossible to achieve it, but we apply an acceptable amount of about 20% of the max output which is 140Kw as a fixed load for 12 hours.

After that we proceed to battery set and module selection:

Where:

LOL "Loss-of-load" probability

This value is the probability that the user's needs cannot be supplied (i.e. the time fraction when the battery is disconnected due to the "Low charge" regulator security). It may be understood as the complement of the "Solar fraction" (although it is described in terms of time rather than energy). During the sizing process, the LOL requirement allows for determining the PV array size needed, for a given battery capacity. Here the default program value is 5% which is acceptable.

Autonomy and battery sizing:

In the Presizing process, the proposed battery pack capacity is determined according to the required autonomy of the system, given in days.

The autonomy is defined as the time during which the load can be met with the battery alone, without any solar inputs, starting of course from a "full charged" battery state. With non-constant loads (seasonal or monthly definition, weekly use), this is accounted as the worst case over the year. The calculation takes the minimum state of charge (SOC) disconnecting threshold, and the battery "energy efficiency" into account.

For our project we decided that 4 days is enough autonomy for our ship.

Battery Voltage Choice

In a stand-alone PV system with direct coupling to the user (without inverter), the battery voltage determines the distribution voltage. As now many DC appliances can be found as well in 24V as in 12V, this choice should be made according to system and/or appliance power, as well as the extension of the planned distribution grid to minimise the ohmic wiring losses.

This choice should be done from the early planning of an installation, since the existing appliance voltage usually cannot be changed, and voltage translators will be expensive and not 100% efficient.

The rated distribution values could be chosen according to the following criteria (inverter supposed directly connected on the battery pack):

12V: little systems for lighting and TV: Appliance max power < 300 W Corresponding current 25 A- Inverter: about < 1 kW

24V: medium size, with fridge and little appliances, or wiring extension to more than 10 m. Appliance max power < 1000 W. Corresponding current 42 A- Inverter : about < 5 kW

48V: special industrial or agricultural use Appliance max power < 3kW Corresponding current 62 A -Inverter : about < 15 kW

Higher powers require either high DC voltages (special appliances) or AC feeding through inverter. Here we choose 440V

The module which we choose was the highest output monocrystalline silicon module in the program database, from SunPower company, constructed in 2009 the specifications of the module are:

The batteries specification ,model and Manufaturer:

Continuing: below is a brief sketch of the system

The battery operating temperature was set to a fixed value of 20oC and the program let us use a default regulator with a DC-DC converter which specs are above.

Array Losses

Array losses in PVSYST program:

Array loss parameters are initially set to reasonable default values by the program, so that modifications only need to be performed during a second step of the system study.

PVSYST treats in detail the following loss types in a PV array:

Thermal losses

Ohmic wiring losses

Module quality losses

Mismatch losses

Incidence angle (IAM) losses.

In the simulation results, the effect of each loss will be available in hourly, daily or monthly values. They may be visualized on the Loss diagram.

## Array Thermal losses

## Thermal Model

The thermal behaviour of the field - which strongly influences the electrical performances - is determined by a thermal balance between ambient temperature and cell's heating up due to incident irradiance:

U · (Tcell - Tamb) = Alpha · Ginc · (1 - Effic)

Where Alpha is the absorption coefficient of solar irradiation, and Effic is the PV efficiency (related to the module area), i.e. the removed energy from the module. The usual value of the Absorption coefficient Alpha is 0.9.

When possible, the PV efficiency is calculated according to the operating conditions of the module. Otherwise it is taken as 10%.

The thermal behaviour is characterised by a thermal loss factor designed here by U (formerly called K-value), which can be splitted into a constant component Uc and a factor proportional to the wind velocity Uv:

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View our servicesU = Uc + Uv · v (U in [W/m²·k], v = wind velocity in [m/s]).

These factors depend on the mounting mode of the modules.

For free circulation, this coefficient refers to both faces, i.e. twice the area of the module. If the back of the modules is more or less thermally insulated, this should be lowered, theoretically up to half the value (i.e. the back side doesn't participate anymore to thermal transfer).

## Determination of the parameters

The determination of the parameters Uc and Uv is indeed a big question. We have some reliable measured data for free mounted arrays, but there is a severe lack of information when the modules are integrated. What value should be chosen according to the air duct sizes under the modules, and the length of the air path?

One can observe that the heat capacity of the air is very low. Even with large air vents, the flowing air under the modules may quickly attain the equilibrium with the modules temperature at the end of the duct, leading to no heat exchange at all. Therefore for the top of the array the U value may be the fully insulated U-value; you can have big differences between the regions of the array near the air input, and at the output. The program doesn't take this inhomogeneity of the array temperature into account.

On the other hand, the use of the wind dependence is very difficult. On one hand the knowing of the wind velocity is extremely rare. On the other hand the "meteo" wind velocity (taken at 10 meter height) is not representative of the temperature at the array level (there may be a factor of 2 between them). In this respect the Uv value is obviously not the same for these two definitions of the wind velocity.

Default and proposed values

The default value is fixed for free-standing arrays, as:

Uc = 29 W/m²·k, Uv = 0 W/m²·k / m/s

If you have fully insulated arrays, this should be halved:

Uc = 15 W/m²·k, Uv = 0 W/m²·k / m/s

These values suppose an average wind velocity of around 1.5 m/sec at the collectors level. In very windy regions (larger average wind velocities), you can increase the values; but we cannot say by which amount in a reliable way.

NOCT Values

Some practicians - and most of PV module's catalogues - usually specify the NOCT coefficient ("Nominal Operating Collector Temperature"), which is the temperature attained by the PV modules without back coverage under the standard operating conditions defined as:

Irradiation = 800 W/m², Tamb=20°C, Wind velocity = 1 m/s, Open Circuit.

The NOCT factor is related to loss factor U by the thermal balance (from the expression of the top Alpha · 800 W/m² · (1 - 0) = (Uc + Uv · 1m/s) · (NOCT - 20°C).

In the definition dialog, the user may define either the U factors or the NOCT. The program immediately gives the equivalence (using Alpha=0.9 and Effic = 10%, without wind dependence).

## Ohmic wiring losses

## Ohmic Loss Ratio

The Ohmic Loss ratio is referred to the PV array at standard conditions (1000 W/m², 25°C), It is the ratio of the wiring ohmic loss Pwir = Rwir * Isc² compared to the nominal power Pnom(array) = Rarray * Isc² (SC= short circuit).

## Where:

Rarray = Vmp / Imp at Standard Test Conditions (STC)

Rwir = global wiring resistance of the full system.

This is computed for a given sub-array as the resistance of all strings wires in parallel, in series with the cables from the intermediate connexion box on the roof to the inverter input. The global wiring resistance Rwir is obtained by putting all the sub-array wiring resistances in parallel.

## Use in the simulation

The "Global wiring resistance" value finally used during the simulation may be defined here: as an Ohmic Loss ratio (the default value is 1.5% at STC) or given explicitly in mOhm.

## Wire diameter optimisation and Wiring Resistance

Wire sections are determined by the maximum allowable current and the ohmic resistance. Here the proposed diameters are automatically limited to the minimum allowable section, according to the European standards for isolated wires mounted in apparent mounting ducts.

Now for a given global loss target (at STC, i.e. maximum operating current), the best section choice is determined by the program in order to minimise:

The global copper mass,

The ohmic losses behave in a quadratic way with the array current (Ploss = R · I²), so that the ratio diminishes linearly with the output current. Therefore the average wiring losses are much lower during the whole running year.

Metal resistivity

The resistivity of wiring metals is strongly dependent on the temperature, which can widely vary due to dissipating currents.

For pure metal, one has:

Copper: Rho = 1.68 E-8 * (1 + 0.0068 * Temp [°C]) [Ohm·m]

Default value: Temp = 50°C => 22 mOhm·mm²/m

Aluminium: Rho = 2.7 E-8 * (1 + 0.0043 * Temp [°C]) [Ohm·m] Default value: Temp = 50°C => 33 mOhm·mm²/m

We use copper which have minimum resistivity.

## Module quality losses / mismatch

## Module quality loss

It is well-known that most of PV modules series don't match the manufacturer nominal specifications. Up to now, this was one of the greater uncertainties in the PV system performance evaluation.

Now, with "guaranteed" power statements and increasing availability of independent expertise, the situation seems going toward some clarification. Module series are sold with a given tolerance, and actual powers usually lie under the nominal specified power, but stay in the tolerance.

We decided that the program default was acceptable.

## Array mismatch loss

Losses due to "mismatch" are related to the fact that the real modules in the array do not strictly present the same I/V characteristics. The graph below helps for visualising the realistic behaviour of such an array, with a random distribution of the characteristics of short-circuit current for each module.

This allows for the quantification of power-loss at the maximum power point, as well as of current-loss when working at fixed voltage. (MPP= maximum power point)

## Array incidence loss (IAM)

The incidence effect (the designated term is IAM, for "Incidence Angle Modifier") corresponds to the weakening of the irradiation really reaching the PV cells' surface, with respect to irradiation under normal incidence. In principle, this loss obeys Fresnel's Laws, (They describe the behaviour of light when moving between media of differing refractive indices. The reflection of light that the equations predict is known as Fresnel reflection), concerning transmission and reflections on the protective layer (the glass), and on the cell's surface. In practice, it is often approached using a parameterisation called "ASHRAE" (as it has become a standard in this American norm), depending on one only parameter bo:

FIAM = 1 - bo · (1/cos i - 1), with i = incidence angle on the plane.

For single-glazed thermal solar modules, the usually accepted value for bo is of the order of 0.1. But in a PV module, the lower interface, in contact with the cell, presents a high refraction index and our specific measurements on real crystalline modules actually indicate a value of bo = 0.05.

We used the program PVSYST in order to calculate accurately the output of our photovoltaic installation. PVSYST was the only program we had access to and it is a very widely known industrial program for sizing and designing photovoltaic systems. We used the most up to date version of 5.0.6.

## Procedure

First from the main menu above we choose project design and we select the stand alone system because ours is not connected with an existing grid (i.e. electrical generator)

In order to create a project in PVSYST, here is the Eco-friendly bulk carrier, we have to define:

The project name, which will identify the project in the file list in our data library.

The geographical location.

The hourly Meteo file, which is given from the program.

A geographical site is defined by:

its name, country, and world region,

its geographical co-ordinates: latitude, longitude, altitude and time-zone,

Monthly meteorological data.

To be used in the simulation, the minimum meteorological data include:

the monthly Global horizontal irradiation

Monthly averages of the ambient temperature.

Meteo values are displayed and easily defined on the screen. It is to be noted that for the verification of rather "uncertain" data, the clearness index Kt is also displayable, which is the irradiation actually received on earth, normalised to extra-terrestrial irradiation in monthly values. The monthly average of Kt should usually lie between about Kt = 0.25 and Kt = 0.75 at any place (PVSYST defaults). Monthly meteo values can be used as a basis for the generation of synthetic daily data.

Then we generate a graph for the specific site (i.e. Broome):

Where, the blue line is the clear day model (irradiation values with clear sky).

The above graph shows us graphically the irradiation sum per month (diffuse and global) with daily change values.

The Clearness Index Kt for Broome:

We can see that the values range from 0.25 to 0.75

The ambient temperature changes through the year.

The above graphs were generated by the program from the below table:

Also it is interesting to show the solar path at Broome or what is the solar height with respect of the plane through the day in order to understand how the sun moves from east to west. The graph also shows some landmark dates (denoted as 1 to 7) where the sun changes height:

Our next step to the program is to find the albedo Coefficient:

The albedo coefficient is the fraction of global incident irradiation reflected by the ground in front of a tilted plane. This effect takes place during the reversal computation of the horizontal irradiation onto a tilted plane. The albedo "seen" by the plane is of course null for a horizontal plane, and increases with tilt.

In the project definition, the albedo values can be adjusted each month in order to take any possible snow-cover into consideration. The value usually admitted in the urban localities is of the order of 0.14 to 0.22, and can go up till 0.8 for a snow-cover. Ideally, the best value is obtained by a direct measurement on the site. But in practice, except for vertical planes, this value does not take on any great importance as the albedo component is relatively weak in the incident global irradiation (this contribution can be visualised in the results of the simulation). The following table gives some usual values for the albedo:

We used the 0.35 value of the Albedo coefficient because it matches on our material.

After defining the above values through the program we proceeded to the orientation of our PV plane. Our project consist a fixed tilted plane (The plane tilt is defined as the angle between the plane and the horizontal), because we considered placing the panels at the hatches due to the fact that they would be exposed all day to the sun's radiation. PVs are placed onto the hatches of the ship with zero tilt (Azimuth is zero as well because it doesn't affect the global on collector plane output. In northern hemisphere, the plane azimuth is defined as the angle between south and collector plane. In southern hemisphere, the plane azimuth is defined as the angle between north and collector plane).

As the program calculated, our loss with respect to an optimum orientation is 3.8% and the available irradiation on this tilted plane is 2370kWh/m2

We also considered using various configurations of panels as to maximise the output per m2 before choosing the above configuration. The below configurations was rejected due to the sun is changing place constantly throughout the day and the ship's movement reinforces the situation, we decided that the best configuration was the above due to sturdy design (one panel placed along the hatch), high efficiency (sun always hit the panel at any time) and simple installation.

Using two panels on each hatch half, tilted for 25o each having an output of 2445 kWh/m2 and the loss to an optimum orientation is 0.7%. Sun hit the panels only east and west when the ship goes north. (Highest efficiency, complex design, not easy installation).

Using two panels on each half, tilted for above 25o the output is greatly decreased and we have great loss to an optimum orientation.

The next step is to calculate the near shadings effect or shading. Near shadings are partial shadings which affect only a part of the field. The shaded part changes during the day and over the seasons. We call shading factor the ratio of the illuminated part to the total area of the field, or inversely shading loss is its complement.

Through the construction/perspective tool we created a model of the ship from the ship's particulars with the PVs installed on it in order to calculate the shading loss we have in various positions of the ship:

The real effect of partial shadings on the electrical production of the PV field is non-linear, and depends on the interconnections between the modules. In the PV array, the current of each cell string is limited by the current of the worst cell in the series. That is, when one only cell is shaded the entire string is strongly affected (which has also dramatic effects on the I/V(current/voltage) characteristics of the whole array). Even with by-pass protection diodes, this string does not participate more than slightly in the production of the PV array. This phenomenon is too complex to be treated in great detail . Nevertheless, the program provides a simplified method, giving the possibility of partitioning the field into rectangles, each of which supposed to represent a string of modules in series. Then it calculates a "Shading factor according to strings", stating that as soon as a string is hit by a shadow, the entire string (rectangle) is considered as electrically unproductive. Although not perfect, this approach should give an upper limit for the real shading loss evaluation. In practice, one often observe that (except for regular arrangements like sheds), this upper limit is not so far from the lower limit (that is, the linear loss).

And the losses percentage due to shading in any sun height.

After we define the natural parameters, we proceeded to the system consumption during a month in the specific site (BROOME). We cannot apply the maximum load 669.64 kW because it is the 100% and it is impossible to achieve it, but we apply an acceptable amount of about 20% of the max output which is 140Kw as a fixed load for 12 hours.

After that we proceed to battery set and module selection:

Where:

LOL "Loss-of-load" probability

This value is the probability that the user's needs cannot be supplied (i.e. the time fraction when the battery is disconnected due to the "Low charge" regulator security). It may be understood as the complement of the "Solar fraction" (although it is described in terms of time rather than energy). During the sizing process, the LOL requirement allows for determining the PV array size needed, for a given battery capacity. Here the default program value is 5% which is acceptable.

Autonomy and battery sizing:

In the Presizing process, the proposed battery pack capacity is determined according to the required autonomy of the system, given in days.

The autonomy is defined as the time during which the load can be met with the battery alone, without any solar inputs, starting of course from a "full charged" battery state. With non-constant loads (seasonal or monthly definition, weekly use), this is accounted as the worst case over the year. The calculation takes the minimum state of charge (SOC) disconnecting threshold, and the battery "energy efficiency" into account.

For our project we decided that 4 days is enough autonomy for our ship.

Battery Voltage Choice

In a stand-alone PV system with direct coupling to the user (without inverter), the battery voltage determines the distribution voltage. As now many DC appliances can be found as well in 24V as in 12V, this choice should be made according to system and/or appliance power, as well as the extension of the planned distribution grid to minimise the ohmic wiring losses.

This choice should be done from the early planning of an installation, since the existing appliance voltage usually cannot be changed, and voltage translators will be expensive and not 100% efficient.

The rated distribution values could be chosen according to the following criteria (inverter supposed directly connected on the battery pack):

12V: little systems for lighting and TV: Appliance max power < 300 W Corresponding current 25 A- Inverter: about < 1 kW

24V: medium size, with fridge and little appliances, or wiring extension to more than 10 m. Appliance max power < 1000 W. Corresponding current 42 A- Inverter : about < 5 kW

48V: special industrial or agricultural use Appliance max power < 3kW Corresponding current 62 A -Inverter : about < 15 kW

Higher powers require either high DC voltages (special appliances) or AC feeding through inverter. Here we choose 440V

The module which we choose was the highest output monocrystalline silicon module in the program database, from SunPower company, constructed in 2009 the specifications of the module are:

The batteries specification ,model and Manufaturer:

Continuing: below is a brief sketch of the system

The battery operating temperature was set to a fixed value of 20oC and the program let us use a default regulator with a DC-DC converter which specs are above.

Array Losses

Array losses in PVSYST program:

Array loss parameters are initially set to reasonable default values by the program, so that modifications only need to be performed during a second step of the system study.

PVSYST treats in detail the following loss types in a PV array:

Thermal losses

Ohmic wiring losses

Module quality losses

Mismatch losses

Incidence angle (IAM) losses.

In the simulation results, the effect of each loss will be available in hourly, daily or monthly values. They may be visualized on the Loss diagram.

## Array Thermal losses

## Thermal Model

The thermal behaviour of the field - which strongly influences the electrical performances - is determined by a thermal balance between ambient temperature and cell's heating up due to incident irradiance:

U · (Tcell - Tamb) = Alpha · Ginc · (1 - Effic)

Where Alpha is the absorption coefficient of solar irradiation, and Effic is the PV efficiency (related to the module area), i.e. the removed energy from the module. The usual value of the Absorption coefficient Alpha is 0.9.

When possible, the PV efficiency is calculated according to the operating conditions of the module. Otherwise it is taken as 10%.

The thermal behaviour is characterised by a thermal loss factor designed here by U (formerly called K-value), which can be splitted into a constant component Uc and a factor proportional to the wind velocity Uv:

U = Uc + Uv · v (U in [W/m²·k], v = wind velocity in [m/s]).

These factors depend on the mounting mode of the modules.

For free circulation, this coefficient refers to both faces, i.e. twice the area of the module. If the back of the modules is more or less thermally insulated, this should be lowered, theoretically up to half the value (i.e. the back side doesn't participate anymore to thermal transfer).

## Determination of the parameters

The determination of the parameters Uc and Uv is indeed a big question. We have some reliable measured data for free mounted arrays, but there is a severe lack of information when the modules are integrated. What value should be chosen according to the air duct sizes under the modules, and the length of the air path?

One can observe that the heat capacity of the air is very low. Even with large air vents, the flowing air under the modules may quickly attain the equilibrium with the modules temperature at the end of the duct, leading to no heat exchange at all. Therefore for the top of the array the U value may be the fully insulated U-value; you can have big differences between the regions of the array near the air input, and at the output. The program doesn't take this inhomogeneity of the array temperature into account.

On the other hand, the use of the wind dependence is very difficult. On one hand the knowing of the wind velocity is extremely rare. On the other hand the "meteo" wind velocity (taken at 10 meter height) is not representative of the temperature at the array level (there may be a factor of 2 between them). In this respect the Uv value is obviously not the same for these two definitions of the wind velocity.

Default and proposed values

The default value is fixed for free-standing arrays, as:

Uc = 29 W/m²·k, Uv = 0 W/m²·k / m/s

If you have fully insulated arrays, this should be halved:

Uc = 15 W/m²·k, Uv = 0 W/m²·k / m/s

These values suppose an average wind velocity of around 1.5 m/sec at the collectors level. In very windy regions (larger average wind velocities), you can increase the values; but we cannot say by which amount in a reliable way.

NOCT Values

Some practicians - and most of PV module's catalogues - usually specify the NOCT coefficient ("Nominal Operating Collector Temperature"), which is the temperature attained by the PV modules without back coverage under the standard operating conditions defined as:

Irradiation = 800 W/m², Tamb=20°C, Wind velocity = 1 m/s, Open Circuit.

The NOCT factor is related to loss factor U by the thermal balance (from the expression of the top Alpha · 800 W/m² · (1 - 0) = (Uc + Uv · 1m/s) · (NOCT - 20°C).

In the definition dialog, the user may define either the U factors or the NOCT. The program immediately gives the equivalence (using Alpha=0.9 and Effic = 10%, without wind dependence).

## Ohmic wiring losses

## Ohmic Loss Ratio

The Ohmic Loss ratio is referred to the PV array at standard conditions (1000 W/m², 25°C), It is the ratio of the wiring ohmic loss Pwir = Rwir * Isc² compared to the nominal power Pnom(array) = Rarray * Isc² (SC= short circuit).

## Where:

Rarray = Vmp / Imp at Standard Test Conditions (STC)

Rwir = global wiring resistance of the full system.

This is computed for a given sub-array as the resistance of all strings wires in parallel, in series with the cables from the intermediate connexion box on the roof to the inverter input. The global wiring resistance Rwir is obtained by putting all the sub-array wiring resistances in parallel.

## Use in the simulation

The "Global wiring resistance" value finally used during the simulation may be defined here: as an Ohmic Loss ratio (the default value is 1.5% at STC) or given explicitly in mOhm.

## Wire diameter optimisation and Wiring Resistance

Wire sections are determined by the maximum allowable current and the ohmic resistance. Here the proposed diameters are automatically limited to the minimum allowable section, according to the European standards for isolated wires mounted in apparent mounting ducts.

Now for a given global loss target (at STC, i.e. maximum operating current), the best section choice is determined by the program in order to minimise:

The global copper mass,

The ohmic losses behave in a quadratic way with the array current (Ploss = R · I²), so that the ratio diminishes linearly with the output current. Therefore the average wiring losses are much lower during the whole running year.

Metal resistivity

The resistivity of wiring metals is strongly dependent on the temperature, which can widely vary due to dissipating currents.

For pure metal, one has:

Copper: Rho = 1.68 E-8 * (1 + 0.0068 * Temp [°C]) [Ohm·m]

Default value: Temp = 50°C => 22 mOhm·mm²/m

Aluminium: Rho = 2.7 E-8 * (1 + 0.0043 * Temp [°C]) [Ohm·m] Default value: Temp = 50°C => 33 mOhm·mm²/m

We use copper which have minimum resistivity.

## Module quality losses / mismatch

## Module quality loss

It is well-known that most of PV modules series don't match the manufacturer nominal specifications. Up to now, this was one of the greater uncertainties in the PV system performance evaluation.

Now, with "guaranteed" power statements and increasing availability of independent expertise, the situation seems going toward some clarification. Module series are sold with a given tolerance, and actual powers usually lie under the nominal specified power, but stay in the tolerance.

We decided that the program default was acceptable.

## Array mismatch loss

Losses due to "mismatch" are related to the fact that the real modules in the array do not strictly present the same I/V characteristics. The graph below helps for visualising the realistic behaviour of such an array, with a random distribution of the characteristics of short-circuit current for each module.

This allows for the quantification of power-loss at the maximum power point, as well as of current-loss when working at fixed voltage. (MPP= maximum power point)

## Array incidence loss (IAM)

The incidence effect (the designated term is IAM, for "Incidence Angle Modifier") corresponds to the weakening of the irradiation really reaching the PV cells' surface, with respect to irradiation under normal incidence. In principle, this loss obeys Fresnel's Laws, (They describe the behaviour of light when moving between media of differing refractive indices. The reflection of light that the equations predict is known as Fresnel reflection), concerning transmission and reflections on the protective layer (the glass), and on the cell's surface. In practice, it is often approached using a parameterisation called "ASHRAE" (as it has become a standard in this American norm), depending on one only parameter bo:

FIAM = 1 - bo · (1/cos i - 1), with i = incidence angle on the plane.

For single-glazed thermal solar modules, the usually accepted value for bo is of the order of 0.1. But in a PV module, the lower interface, in contact with the cell, presents a high refraction index and our specific measurements on real crystalline modules actually indicate a value of bo = 0.05.

## Final Report for Broome for January

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