4.1. Application Description
In order to appraise the to be included panels operation, considering the theoretically studied parameters, an application available on the Finite Element tool, that illustrates the operation at an user-specified location of a Si solar cell, will be used. It is highly dependant on user specified parameters, such as the altitude, location and cell’s attributes, to characterize the cell performance, making it a good fitting to the case study. To handle the different types of inputs, the application combines two different modules, being them Ray Optics and Semiconductor.
For the concerning Ray Optics module, the Geometrical Optics interface is used to model, for a predefined position, the received irradiance through the day, at a specific date. It is based on the ray tracing algorithm that simulates the path of light, starting from the receiver object until the source. This module does not consider the scattering of the radiation by atmosphere particles and molecules, therefore, the direct radiation received by the solar cell from sunlight is the total radiation. The model measures the intensity of the directly incident radiation as a function of the following parameters: altitude above sea level, air mass and angle of incidence and reference irradiance. The reference irradiance is the only constant and will be here adapted to the average yearly value at Pêro Pinheiro, being it about 4400 .
Semiconductor’s module is used to compute the cell characteristics based on the Gauss law. To better define the conditions several interfaces are adopted, which resort to input design parameters provided by the user, naming the cell temperature, the shunt and series resistances and the azimuth and tilt angles. The used geometric model is a 1D PN junction with the anode and cathode modeled as thin ohmic contacts deposited on the emitter and base side, correspondingly. To model the solar cell the Semiconductor module will interact with the Ray Optics, in order to obtain the spectral irradiance, which will be subsequently used to determine the generation rate. In its turn, the generation rate depends on the absorption coefficient and the photon generation rate. Counterbalancing the complexity of the equations, some valid assumptions are made: the spectral irradiance is approximated through sun’s blackbody spectrum at temperature 5777 and the anode is assumed as having the reflectance equal to one due to a perfect antireflecting coating.
With the objective of extracting the solar cell characteristics, namely the maximum power point—constituted by the voltage at maximum power
and the current at maximum power
—the short circuit current
and the open circuit voltage
, the application will generate the cell parameter correspondent I-V and P-V curves. The efficiency
will be calculated, with resource to Equation (
10), where
corresponds to the fill factor, given by the expression in Equation (
11) and
is the incident power, defined by
, being
A the solar cell area.
4.2. Solar Cell Simulations
Starting to define the sunlight properties for the Ray Optics Computations, there was a need to specify both the zone coordinates, the date and the altitude. For the coordinates the Pêro Pinheiro zone is considered, with value (38.861077, −9.320995). To the date, the winter and summer solstice of 2019 were used, as they contrast with the shortest and longest light hours. Finally, for the altitudes, bearing in mind the variation of the irradiation and wind velocity with it, the maximum (2000 ) and the minimum (200 ) will be taken into account.
To characterize the cell properties, the cell temperature, the shunt and series resistances and the azimuth and tilt angles were detailed. The cell temperature will be calculated with resource to Equation (
7), where the non-constant values, like
and
will depend on the considered altitude, thus, will be further specified on the respective simulation. For the solar cell series and shunt resistances, good commercial values are 1000
for the first and
, which, according to the cell area of 25
, will have the final values of 4000
and 2
.
Commonly, the azimuth is defined as the angle between the object and the meridian of the location, however, the program was made with the south hemisphere in mind, intrinsically making the azimuth referent to north and defined as positive to east. A detailed measurement of the cell azimuth angle is not feasible, for the UAV can fly in every direction, therefore, the simulations will be made with the maximum and minimum values. For the last property, particularly the tilt angle, the cruise flight angles are chosen, due to the reduced time the vehicle spends climbing. As a result, the angle of 3 is used for the wings and 90 for the booms. The azimuth and tilt angles are the only parameters that exhibit a difference, amidst the booms’ and wings’ solar cells. For the booms there is even a further distinction in the azimuth angle between sides of the same boom, being this the reason for separate simulations for wings and booms. The maximization and minimization of these parameters is made for the wings, seeing that for its position and extension they will produce higher output energy.
Opening with the simulations for the maximum values, the date 21 June 2019 was used, corresponding to summer solstice, the day with more light hours of the year, together with an altitude of 2000
, being based in a cell temperature of
(
), obtained with
, predetermined
and wind velocity of
. The UAV has an AOA of 3
which corresponds to a tilt of
, as such, its favored direction of flight to minimize the incident angle will be north, which equals an azimuth of 0
. These values originated
Figure 8 where the direct irradiance received by the cell on the wings’ surface can be seen. For every sunlight incident simulation the values are only displayed since the sun rises until the sun sets. If a value is not present for the sunlight incident angle, the direct irradiance is programmed to be assumed as zero.
The UAV in context has two booms with a right side and a left side each. To simulate this situation, different azimuth angles were used for the faces with distinct faces, always with a tilt angle of 90
. When the vehicle is flying north, each boom has a side facing east and another facing west. To emulate the east faces, an azimuth angle of 90
is used, generating the direct irradiance in
Figure 9. By facing east with a 90
tilt, it is natural for the cell to only receive light in the morning and early afternoon hours and even then due to its angles the irradiance values will be lower than the wings’ ones.
A rotation of 180
from the east faces azimuth angle is used to generate the west ones, which count with an azimuth of 270
. The corresponding graphic for the direct irradiance can be observed in
Figure 10. Due to its azimuth and tilt angles’ values, the west side booms only start to receive light in the afternoon, almost right when it ends for its counterparts.
The last simulations are made with the objective to produce the minimum values possible, so that a complete range of the output energy is made. For the date, the winter solstice, 22 December 2019, the shortest day of the year, was chosen, together with an altitude of 200 . The cell temperature, was calculated, having the value of , obtained with , predetermined 388 and a wind velocity of .
For the minimum values, it was considered a UAV flying in south direction (azimuth of 180
) with a tilt angle of
. These values were behind the creation of
Figure 11 where the irradiance received by wings’ surface cell can be seen. Comparing to the wing’s last results, a clear reduction of both the active hours and received irradiance can be seen, which will have major implications on the output energy the cell can produce.
There is no need to distinguish the maximum and minimum value simulations in terms of booms’ angles. So, bearing that in mind, the east faces will still have an azimuth of 90
and the same value for the tilt angle, generating the direct irradiance graphic illustrated in
Figure 12.
Considering the already explained 270
azimuth angle, together with the
tilt angle, the graphics for the direct irradiance can be subsequently observed in
Figure 13, for the west side of the booms. Again, with the 180
discrepancy from the east faces, the sunlight will only focus on these cells by early afternoon, more specifically, at 2 pm.
All these previously illustrated and described graphics concerned the external variables that, although they may affect the energy output the cell will have, by means of the reduction of the irradiance, they do not condition or influence the cell internal operation and subsequently its efficiency. Of the constant parameters heretofore characterized only the series resistance, the shunt resistance and the cell temperature have an impact in the cell efficiency.
Varying the load resistance
, the application obtained the I-V and P-V curves illustrated in
Figure 14 and
Figure 15, from where the maximum power point,
and
were extracted. The efficiency was determined with the referred parameters and the provided solar cell area of 25
(50
long ×
narrow), obtaining a value of
%, based on Equation (
10).
The previously computed I-V and P-V curves were determined for one isolated solar cell, with 25 (50 × ) of area. In order to ascertain the total output power, the number of cells that fit in the UAV considered structures need to be calculated. Each wing has a total length of 1009 and a width of 278 —excluding the aileron—where, a line of 20 cells can be made at length and column 556 at width, composing a total of 11,120 cells, that conceive a singular wing panel. For one face of the boom, the length is 503 and the width 45 , therefore, a line of 11 cells and a column of 90 cells can be made, forming a panel of 990 cells.
With the number of cells of each panel calculated, the connections are shaped, thus, permitting the settlement of the voltage and current values. It was decided with the number of cells in mind, to associate the column cells in parallel, with the link between different columns being a series connection, both for the wings and boom’s faces. These connections will show its effects in the current and voltage, as expected, with the parallel bonds augmenting the current in each point proportionally to the number of lines and the series bonds having the same effect on the voltage, which will increase proportionally to the number of columns. Being constituted by series and parallel connections of the already presented silicon solar cell, the panels have merely an increase in the voltages and currents, nonetheless counting with the same characteristics. On that manner, the efficiency maintains itself the same as the single photovoltaic cell, cutting the need to make any further calculations.
To have an estimation of the generation of the solar panels for 40 (UAV’s time of flight), considering the maximum and minimum presented cases, the direct irradiance graphics were analysed in order to find the 40 period with maximum irradiance. The “brute force” method was used, and with resource to it, it was concluded that the maximum production was from 13 h 30 min to 14 h 10 min, where both the boom’s sides panels were producing energy and the irradiance incident on the wings reached its peak. Having the wings the highest area, it was natural that its production would be more important to the results. As aforementioned, the UAV usually flies between 10 and 16 , so, this extreme hours were also taken into account. To calculate the total direct irradiance received by the panels over the considered times, the area of the concerning part of the graphics was determined, using a linear regression, a valid approximation due to the reduced period of time in consideration.
With the irradiance, the efficiency and the area of the panels, the generation—the product of the three—was calculated. For the longest summer day, having the unmanned vehicle a 0 azimuth angle and tilt angle, mimicking the best conditions, the produced energy for a flight at 10 am is , at the maximum hour production are obtained and 40 before 16 pm is . Emulating the worst conditions, the shortest winter day with the UAV flying in a 180 azimuth and the same tilt angle, the produced energy was at 10 am, at the maximum hour production and at 15 : 20 pm.
As aforementioned, the unmanned vehicle uses two batteries, one for the motor and the other for the “payload”. Both are Li-Po with of nominal voltage, being the contrast in the number of batteries. Due to the motor higher consumption, its battery is composed by 10 cells connected in series with a 10 capacity, while the battery for the components counts with a reduced number of 3 cells, likewise connected in series, with a 5 capacity. In total, the motor battery has an energy stored of , while the other has 370 . The system UAV plus payload will need to stop either by the run out of the motor battery or the run out of the components battery, although this do not mean both the batteries will always be discharged. The consumption of energy highly depends on the payload height, mission, and type of flight, however, for the payload battery, the medium consumption is usually inferior to 2 —which with the 5 capacity can last up to two and a half hours—indicating that the time of flight is shortened by the discharging of the motor battery. In this case the appropriate decision is to connect all the solar panels only to the motor battery, so that the maximum time of flight can be achieved. Knowing the motor drains up a 370 battery in 40 , the calculations of the augmented time of flight with the solar panels, for each case, is simple. On the ideal summer day, the panels can give the unmanned aerial vehicle an extra time of flight between 3 (the minimum produced at 10 am) and 7 min 30 s (the maximum energy produced by the panels). For the worst winter day, the values are much more discouraging, varying between 35 and 2 min 19 s.