Accepted Manuscript Transmittance optimization of solar array encapsulant for high-altitude airship
Weiyu Zhu, Huafei Du, Lanchuan Zhang, Yuanming Xu, Jun Li PII:
S0960-1481(18)30263-5
DOI:
10.1016/j.renene.2018.02.111
Reference:
RENE 9842
To appear in:
Renewable Energy
Received Date:
12 September 2017
Revised Date:
19 December 2017
Accepted Date:
24 February 2018
Please cite this article as: Weiyu Zhu, Huafei Du, Lanchuan Zhang, Yuanming Xu, Jun Li, Transmittance optimization of solar array encapsulant for high-altitude airship, Renewable Energy (2018), doi: 10.1016/j.renene.2018.02.111
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ACCEPTED MANUSCRIPT
Transmittance optimization of solar array encapsulant for
1
high-altitude airship
2 3
Weiyu Zhu a, Huafei Du a, Lanchuan Zhang a, Yuanming Xu a, Jun Li b*
4
a School
of Aeronautic Science and Engineering, Beihang University, 37 Xueyuan Road, Beijing
5
100191, PR China
6
b School
of Aeronautics and Astronautics, Central South University, Changsha 410083, PR China
7 8
Abstract
9
The efficiency of solar cell is a critical problem to the energy management of high-altitude airship.
10
Excessive temperature and solar radiation intensity of solar cell will reduce the cell efficiency. The
11
main purpose of this study is to increase the energy output of solar array through optimizing
12
transmittance of solar array encapsulant. The thermal and heat transfer models of solar array were
13
considered during the investigation of the effect of transmittance on output performance of solar array.
14
And the optimization model of transmittance is presented to obtain the optimum transmittance in
15
different working conditions for the first time. The feasibility of the numerical model is verified by
16
comparison with experimental data of the temperature of solar array during a day. The results indicate
17
that the output performance of solar array is variable under different transmittances and the optimum
18
transmittance of solar array is changing with the working latitude and date. The simulation results show
19
that the maximum increase of output energy can reach up to 0.5 MJ on summer solstice. The
20
optimization study provides both theoretical and practical support for choosing optimal encapsulant
21
materials in the preparation stage of high-altitude airship.
22
Key words:
23
Optimum transmittance; Solar array; Energy; High-altitude airship; Thermal effect Nomenclature A
=
the area, m2
c
=
specific heat capacity
D
=
the maximum diameter of airship, m
* Corresponding authors at: School of Aeronautics and Astronautics, Central South University, Changsha 410083, PR China. E-mail address:
[email protected] (J. Li). 1
ACCEPTED MANUSCRIPT Etotal = = G = ne
the total energy output of solar array per day, J
hfree
free convection heat transfer coefficient
=
the vector of gravity direction normal vector of a element
hforce =
force convection heat transfer coefficient
Id
=
the direct solar irradiance, W/m 2
If
scattered radiation, W/m 2
ks
= =
ke
=
thermal conductivity of airship envelope
kair l
= =
atmospheric thermal conductivity the axial coordinate of the profile of airship, m
L
=
total length of the airship, m
m
=
the masses, kg
=
the vector of solar direct radiation
=
the normal vector of the element i
ns ni
thermal conductivity of solar array
Nuair =
the free convection Nusselt number
P
=
device specific parameters related to the type of solar cell
Q
=
total radiation on solar array, W
Qpow =
output power of solar array, W
QT
=
the heat power of solar array, W
QS
=
solar incident radiation, W
QE
=
radiation from the earth, W
Qinf
=
infrared radiation heat loss, W
Qcon
=
convective and conductive heat transfer loss, W
Qd
=
solar direct radiation, W
Qf
=
diffuse radiation, W
Qsun2 =
incident radiation to the solar cell layer, W
r
=
the equivalent rotary radius of airship, m
re
=
the solar reflectivity
ts
=
the thickness of solar array, m
te
=
the thickness of airship envelope, m
τ
=
time, s
Ts,i
=
the temperature of solar array element, K
Tatm
=
the temperature of atmosphere, K
µair
=
atmospheric dynamic viscosity, m/s
w
=
the relative velocity between the airship and the flowing air, m/s
=
the solar absorptivity of solar array
ele
=
the rotation angle of the generatrix, degrees
=
solar elevation angle, degrees
i
=
the included angle between the normal vector of the element and the vector of gravity
direction
i
=
the included angle between the normal vector of the element and the vector of solar 2
ACCEPTED MANUSCRIPT irradiation, degrees
=
the infrared reflectivity of solar array
i
=
Stefan–Boltzmann constant value, = 5.67e-8 W/(m2·K4)
=
view factor to the sky
SC
=
conversion efficiency of solar cell
=
the transmittance of encapsulant material
24 25
1. Introduction
26
As significant potential in the areas of telecommunications, Navigation system and Earth observation
27
sciences, the researches of high-altitude airships have developed rapidly [1-3]. But the challenge of
28
energy supply is a significant limitation to the requirement of long-endurance missions [4]. The flight
29
of high-altitude airship depends almost on solar power during the day, the energy consumption of
30
onboard devices and payload also come from solar array [5, 6]. Therefore, the interest of solar array
31
has grown immensely in the study of energy management of high-altitude airship.
32
In the past decades, the researches about feasibility and viability of solar array used in high-altitude
33
airship have been carried out. Knaupp et al. [7] investigated the high-altitude airship persistence
34
through exploring solar regenerative and non-regenerative power systems and listed several
35
advantageous features of solar powered airship. Naito et al. [8] studied power system requirements of
36
high-altitude airship and the feasibility of the solar power system for the airship. Colozza et al. [9]
37
identified the feasibility of a high-altitude airship combining environmental conditions and state of the
38
power and propulsion technologies.
39
Based on the researches of scholars, it is certain that solar array on the airship can provide enough
40
energy to drive the vehicle. But the performance of solar array is influenced by complex thermal
41
environment during the operation process of high-altitude airship [10]. To investigate the effect of the
42
output performance of solar array, the thermal performances of high-altitude airship were analyzed
43
first by some researchers. Wang and Yang [11] presented an effective and economical approach to
44
analyze thermal state of stratospheric airship considering environmental thermal sources. In that study,
45
a novel computational model for analyzing the airship’s transient thermal performance under different
46
environmental conditions was also developed. Wang and Liu [12] achieved temperature distributing
47
situations of airship taking into account some influential factors such as solar radiation and wind speed 3
ACCEPTED MANUSCRIPT 48
through numerical simulation. Li and Xia [13] conducted experimental investigation of the thermal
49
characteristics of airships and the transient temperature distributions of hull, the results show that solar
50
radiation and airflow have significant influences on the airship envelope temperature.
51
Depending on the efforts have been made on the thermal conditions of high-altitude airship, the
52
thermal characteristic and output performance of solar array on the airship were discussed in a recent
53
study. Wang and Song [14] presented a computation method for solar radiation on solar array of high-
54
altitude airship, and studied the effect of the airship’s attitude on the performance of its energy system.
55
Li et al. [15, 16] investigated the thermal performance of stratospheric airship and the output
56
performance of solar panel with thermal effect through a simplified numerical model. Li and Lv [17]
57
compared the output performance of solar array on stratospheric airship with and without thermal
58
effect, and mentioned the effects of the transmittance of solar array encapsulant on output performance
59
of solar array. It can be seen that these investigations studying various influence factors of the output
60
performance of solar array are propitious to improve the energy management of high-altitude airship in
61
different working conditions. To reduce the required area of solar array of high-altitude airship, Garg et
62
al. [18] proposed an optimization method by maximizing the energy produced per unit square meter of
63
the solar array. Li and Lv [19] obtained the minimum area of solar array on high-altitude airship under
64
the premise of enough output power and analyses the change of minimum area in different effect
65
factors. Except by optimizing the areas of solar array on airship, the solar energy management can also
66
be improved by selecting the suitable component of solar array.
67
Although these investigations involving optimizing the areas of solar array are valuable to
68
improve solar energy management of high-altitude airship, the method of optimizing the transmittance
69
of solar array encapsulant to promote output energy do not receive enough attention. Encapsulant
70
material in a Photovoltaic module is an essential component used for providing protection of cells from
71
moisture, foreign impurities and mechanical damage. In addition, Notteand Polino et al. [20]
72
investigated the influence of encapsulation material and method on the optical and electrical
73
performances of flexible polymer solar cells. Hasan and Arif [21] developed structural, thermal and
74
electrical model to determine efficiency and life of PV module for different encapsulant materials and
75
selected the optimum material based on its properties including light transmittance. Based on these 4
ACCEPTED MANUSCRIPT 76
researches, it can be seen that the encapsulant material was often required to possess certain desirable
77
characteristics high transmittance of light [22]. But considering the effect of temperature and solar
78
radiation intensity of solar cell, the output performance of solar array may not be improved by solely
79
increasing the transmittance of solar array encapsulant. As we known, the energy input of solar cell is
80
proportional to the incident solar irradiation [23-25], but the enhancement of incident solar irradiation
81
will result in the increase of the solar cell temperature, and the photoelectric conversion efficiency of
82
solar cell may be correspondingly decreased [26]. Meanwhile, Khan et al. [27] investigated the effect
83
of solar irradiation intensity on the photoelectric conversion efficiency of a silicon solar cell, theoretical
84
and experimental results indicated that excessive illumination intensity may lead to the decrease of
85
efficiency of cell. Therefore, the transmittance of solar array encapsulant is not always proportional to
86
the energy output, and there is the best balance point between them. The optimization of transmittance
87
of solar array encapsulant is necessary to choose the most appropriate encapsulant to improve the
88
output energy of solar array of high-altitude airship.
89
The aim of this paper is to guide the material selection of solar array encapsulant to obtain maximum
90
output energy of solar array of high-altitude airship by optimizing the transmittance of solar array
91
encapsulant under different working conditions. Based on the thermal model and heat transfer model of
92
solar array laying on the back of high-altitude airship, the variations of temperature and energy output
93
of solar array with the change of transmittance of solar array encapsulant are discussed. In order to
94
calculate the optimum transmittance of encapsulant of solar array, the optimization model of
95
transmittance of solar array encapsulant is built. Finally, the effects of wind velocity of environment
96
and working date and latitude on the optimum transmittance are also analyzed.
97 98
2. Methodology 2.1
Thermal model of solar array
99
Solar array is symmetrically laid on the back of airship. The geometric model of airship is a
100
rotational body, and its profile is decided by a specific quadratic curve. To simplify computation, it is
101
assumed that the deformation of airship profile owing to workload and the change of environment are
102
neglected and solar array is perfectly aligned with the curvature of the surface of airship. The diagram
103
of solar array laying airship is shown in Fig. 1. The profile equation of airship is given as 5
ACCEPTED MANUSCRIPT r f l
104
0lL
(1)
105
where l is axial coordinate, r is equivalent rotary radius and L is the length of airship. To analyze the
106
total area of solar array, solar array is divided into a number of elements. An area element i of solar
107
array could be calculated by
108
dAi f l d dl 1 f (l )
109
where A is area, θ is the rotation angle of the generatrix along the circumferential direction, ,
110
. Sun
Qinf
(2)
Airship
QS Solar
array
g gas Liftin Inner
Qcon
Inner
ne
S
air
i
air Ballonet
QE
i G
111
An solar array unit
112
Fig. 1 Schematic diagram of the high-altitude airship and solar array.
113
Airship working in the high-altitude atmosphere is exposure to complicated thermal environment. As
114
shown in Fig. 1, the thermal environment of solar array of airship can be simplified as three parts:
115
incident solar radiation from sun and earth; infrared radiation, convective and conductive heat loss; and
116
electric energy and heat energy storing in solar array [15, 28]. The heat-balance equation of a solar
117
array element may be expressed as
118
dQ pow dQT dQS dQE dQinf dQcon
119
where Qpow is output power of solar array, QT is the heat power of solar array, QS is solar incident
120
radiation, QE is radiation from the earth, Qinf is infrared radiation heat loss, Qcon is convective and
121
conductive heat transfer loss.
122
The incident solar radiation of an element dQS includes solar direct radiation dQd 6
(3)
and diffuse
ACCEPTED MANUSCRIPT 123
radiation dQ f , it can be defined as dQS dQd dQ f
124
I d cos i dAi dQd 0
125
(4)
0 ij 2 ij 2
(5)
126
dQ f I f (0.5 0.5cosi )dA
127
where is the solar absorptivity of solar array, I d is the direct solar radiation intensity and I f is the
128
diffuse solar radiation intensity. As shown in Fig. 1, i is the included angle between the element
129
normal ne and the solar irradiation S , and i is the included angle between the cell element normal
130
and the gravity direction G [10, 28].
131 132
(6)
The radiation from the Earth dQE is given by 0.5 re I d sin ele I f 1 cosi dAij 0 i 2 dQE 0 i 2
(7)
133
where re is the reflectivity that can be approximately adopted as 0.18 for clear sky and 0.57 for
134
overcast sky [29], and ele is solar elevation angle. The infrared radiation heat loss to external
135
atmosphere can be shown as
136
4 dQinf [(Ts4,i Tatm )i ]dAi
137
where is infrared reflectivity of solar array, is Stefan–Boltzmann constant value of 5.67e-8
138
W/(m2·K4), i is view factor to the sky [30], Ts ,i and Tatm is the temperature of solar array element i
139
and atmosphere. The convection and conductive heat loss can be defined as [31]
(8)
140
dQcon dQconv d Qcond
(9)
141
dQconv ( h 3free h 3forced )1/3 (Ts ,i Tatm )dAi
(10)
142
d Qcond (Ts ,i Te ) / (t s / k s te / k e )dAi
(11)
143
where t is thickness, k is thermal conductivity, and the subscript e means airship envelope. The
144
convection heat transfer coefficient includes two kinds: free and force, it can be defined respectively as
h free
145
146 147
h force
k air Nuair D
v D k air (2 0.41 w D air
(12) 0.55
)
(13)
where k air is atmospheric thermal conductivity, Nuair is the free convection Nusselt number [32], D is 7
ACCEPTED MANUSCRIPT 148 149
the diameter of airship, vw is the wind velocity, and air is atmospheric dynamic viscosity [33]. 2.2
Heat transfer Model
150
In the previous studies, solar array used in the airship hull was divided into three layers: the first
151
layer covers glass and encapsulant which is often seen as transparent to solar radiation; the second
152
layer consists of the solar cells and electric interconnections; and the third layer is the substrate [15,
153
34]. However, as shown in Table 1, the transmittance of encapsulant material defined as may not
154
reach 100 % and it is variable when the material of encapsulant is different.
Encapsulant film
Solar cell panel
155 156
Fig. 2 Sample diagram of thin film solar cell.
157
Table 1 The transmittance of encapsulant material of solar array [22]. Encapsulant material
Transmittance /%
EVA (Ethylene-vinyl Acetate
>91
PVB (Polyvinyl butyral) Copolymer)[35]
94
TPU (Thermoplastic Poly-urethane)
93.5
PDMS
94.5
FEP
95
Parafilm Epoxy res
88
Flexoskin Epoxy resin Epoxy Resin
85 >82
158
In this paper, the effect of heat insulation structure of solar array is not considered. As shown in Fig.
159
3, the mechanism of heat transfer of the solar array may be described as follows: The first layer
160
transmits a large part of solar flux to be absorbed by the solar cells layer. Another part of solar flux is
161
reflected to the outer space [15, 34]. The first layer conducts heat to the atmosphere and solar cell. And
162
the solar cell layer conducts heat to the substrates layer; the substrate layer conducts heat to airship
163
envelope or thermal insulation layer connecting airship and solar array.
8
ACCEPTED MANUSCRIPT
dQcon
dQS
dQinf
dQT1
Encapsulant Material
dQ1,2
dQsun2
Solar Cell
dQele, dQT2
dQ2,3 Substrate Layer
dQT3
dQ3,e
164 165
Fig. 3 Heat transfer mechanism of the solar array.
166
The mechanism of the heat transfer of the solar array is given by the following differential time-
167
dependent equations: ms1cs1dT1 dQS dQsun 2 dQinf dQ1,2 dQcon
168 169
(14)
where Qsun 2 is incident radiation to the solar cell layer, which can also be defined as
170
dQsun 2 dQS
(15)
171
ms 2 cs 2 dT2 dQsun 2 dQ1,2 dQ2,3 dQele
(16)
172
ms 3cs 3 dT3 dQ2,3 dQ3,e
(17)
174
dQ1,2 dAs (T1 T2 ) / t1 / k1 t2 / k 2
(18)
175
dQ2,3 dAs (T2 T3 ) / t2 / k 2 t3 / k3
(19)
176
dQ3,e dAs (T3 Te ) / t3 / k3 te / k e
(20)
173
177 178
where
Therefore, the output power of a solar cell element can be given by dQpow sc dQsun 2 sc dQS
(21)
179
where is transmittance of encapsulant of solar array, and sc is conversion efficiency of solar
180
cells [36]. The empirical correlations for the efficiency as a function of cell temperature, irradiance and
181
air mass were derived by several scholars [37]. A five-parameter correlation could be developed for the
182
Kyocera module, which allows the efficiency to be described as a function of the cell temperature,
183
irradiance and air mass in the entire measured range via Eq.(22):
184
I P2 I T AM sc P1 P3 1 P4 s ,i P5 I 0 I 0 T0 AM 0
185
where P1 ,P2, P3, P4 and P5 are device specific parameters which are related to the type of solar cell, I is 9
(22)
ACCEPTED MANUSCRIPT 186
the sum of direct solar radiation intensity and the diffuse solar radiation intensity, I0 is 1000 W/m2 , T0
187
is the standard temperature of 25 ℃, AM is air mass and AM0 is the standard air mass of 1.5.
188
2.3
Optimization model of transmittance
189
According to Eq.(15), the incident irradiance to solar cell can be increased by improving the
190
transmittance of solar array encapsulant, but the temperature of solar cell will rise and the efficiency
191
may be correspondingly decreased. In case of constant areal density and restricted weight, the needed
192
areas of solar array are unchanged. The objective of the optimization model is to receive the maximum
193
energy output by adjusting the transmittance. The optimization problem is defined as follows:
194 195
max ：
Etotal Etotal I , T , = dQpow d i 1
(23)
subject to
0.5 0.95
196
(24)
197
where Etotal is the total energy output of solar array per day, is time. As we known, under
198
different working condition, the solar array will receive unequal solar radiation, and the solar array
199
encapsulant may not an optimum value to output power. It is worthy to develop the optimization model
200
to get more energy output and corresponding transmittance of solar array encapsulant. Optimization
201
problems are solved using artificial bee colony (ABC) algorithm which is an optimization algorithm
202
based on the intelligent foraging behavior of honey bee swarm [38, 39]. ABC algorithm has similar
203
performance to that of other optimization algorithms, although it has less control parameters making
204
ABC algorithm more efficient in optimizing multi-modal and multi-dimensional problems[40, 41]. Fig.
205
4 shows the flowchart of solving the transmittance optimization by using an artificial bee colony
206
algorithm. And the overall flow chart of optimum transmittance calculation is shown in Fig. 5. The
207
steps of artificial bee colony algorithm can be clustered as follow:
208 209
(1) Generate initialize population: Giving the random range of transmittance of solar array in a certain environmental parameters;
210
(2) Employed bees: Evaluating the efficiency of these transmittances;
211
(3) Onlooker bees: Evaluating the output energy per day of these transmittances, and determining the
212 213
optimum transmittance of the certain range; (4) scout bees: Carrying out random search when solution is abandoned; 10
ACCEPTED MANUSCRIPT 214
(5) Repeat steps 2 to 5 until the maximum number of cycle is reached. Generate initial population
selection
Produce new solutions for employed bees Efficiency
NO
Are there abandoned solutions?
Evaluate the efficiency of solar array YES
Produce new solutions for scout bees
selection
Produce new solution for on looker bees
YES
Output energy
215 216
Max cycle number? NO
Evaluate the output energy per day of solar array
Stop
Fig. 4 Flow chart of solving the transmittance optimization by using an ABC algorithm. Start Transmittance of solar array encapsulant
Solar irradiation intensity
Input solar energy
217 218 219
Efficiency of solar cell
Temperature of solar cell
Output energy
Maximum output energy
End
Optimium transmittance
Fig. 5 Flow chart of optimum transmittance calculation.
3. Result and Analysis
220
According to the above theoretical model, a MATLAB problem is built to calculate the total energy
221
output of solar array and the optimum transmittance of solar array encapsulant. The design parameters
222
of airship in the program are listed in
223 224
Table 2. Table 2 Design parameters of airship.
11
ACCEPTED MANUSCRIPT
225
3.1
226
Parameters
Value
Length, m
220
Diameter of maximum section, m
54
Area, m2
33,000
Area of solar array, m2
5500
Volume, m3
380,000
Working altitude, km
20,000
Year
2015
Experimental verification
3.1.1 Experiment setup
227
To validate thermal model of solar array, the experimental study to measure the temperature of solar
228
array laying on the airship was done in the Academy of Opto-electronics of Chinese Academy of
229
Science in Beijing. The latitude of the location and the test date are 40°N and October 15th. The
230
ambient temperature fluctuates in the range of 10-30 ℃ during the test time. The schematic diagram
231
of experimental set-up is shown in Fig. 6. This test system mainly includes a solar array with length of
232
1.5 m and breadth of 1 m, a small-scale airship with diameter of l m and the length of 3 m, several
233
thermocouples, a temperature patrol instrument and a computer to process the temperature data. b) a) Thermocouple
Solar cell
Encapsulant film Solar array
Airship Airship
Computer
234 235
d)
c)
Thermocouple
Temperature patrol instrument
Temperature patrol instrument
Solar array
Fig. 6 Ground test setup: Schematic diagram of test circuit a) Two solar array which have different encapsulant
236
materials were laid on a small airship; b) Temperature patrol instrument; c) A thermocouple was installed on a solar
237
array element.
12
ACCEPTED MANUSCRIPT 238
3.1.2 Verification for the numerical model
239
The validity of the numerical model is verified by comparing the calculated values with the ground
240
experimental results by us and the 25m-long high-altitude Airship experimental data which is
241
performed by Kenya Harada [42]. These time history of the max temperature of solar array are shown
242
in Fig. 7, it can be seen that the calculated and experimental values by Kenya yield a good
243
correspondence with deviations below 3.7%, particularly at 16:00 with deviations below 0.1%, and the
244
ground experimental data which displayed the temperature history from 10:00 am to 3:00 pm was close
245
to the calculated result. Therefore, the numerical model to calculate the temperature of solar array in
246
this paper can be acceptable to the engineering applications.
340
(a)
330
Caculated K.HARADA_measured
Caculated Ground experiment
325
Temperatue (K)
Temperatue (K)
320
(b)
300
280
320
315
260 310
240 22:00
247
08:00
13:00
18:00
23:00
10:48
04:00
12:00
13:12
14:24
Local time (Hrs)
Local time (Hrs)
248 249
03:00
Fig. 7 Comparison of calculation of the thermal model with experimental data.
3.2
Effect analysis
250
The dependence of the solar cell efficiency on temperature described by Anthony J. Colozza [36] is
251
used in this paper. It can be assumed that the solar cell efficiency is inversely proportional to the
252
temperature. The maximum temperature of solar array as a function of encapsulant transmittance in the
253
summer solstice latitude 23°N is shown in Fig. 8. It can be found that the increase of transmittance will
254
result in obviously raising of the temperature, which may cause the decrease of efficiency of solar cell.
255
Therefore, it is feasible to improve the negative effect of high temperature on efficiency of solar cell
256
through altering the transmittance.
13
ACCEPTED MANUSCRIPT 360
Maximum temperature (K)
340
320
300
280
260 0
4
8
12
16
20
24
Time (Hrs)
257 258
Fig. 8 The maximum temperature of solar array.
259
From Fig. 9, it can be seen that the greater transmittance of solar array encapsulant is, the stronger
260
illumination intensity will be, and the maximum illumination intensity is up to 1200 W/m2. Fig. 10
261
shows the experimental result of the efficiency of the cell against intensity of illumination at the solar
262
cell temperature of 25 ℃ by Khan et al. [27] and the numerical result according to Eq.(22) by
263
Kyocera [37]. The solar module selected in this paper is Khan Module. With the increase of
264
illumination intensity, the efficiency of solar cell initially increased and stayed steady. The efficiency
265
then decreased when the illumination intensity is up to 850 W/m2. Therefore, the efficiency of solar
266
cell may be decreased when the transmittance of solar array encapsulant is increasing due to the
267
increase of the solar illumination intensity during the day. 1400
2
Illumination intensity (W/m )
1200 1000 800 600 400 200 0 0
268 269
4
8
12
16
20
24
Time (Hrs)
Fig. 9 The change of the intensity of illumination during a day.
14
ACCEPTED MANUSCRIPT 20
Khan Module Kyocera Module 18
Efficiency (%)
16
14
12
10 0
270
200
400
600
800
1000
1200
1400
1600
1800
2
Illumination intensity (W/m )
271
Fig. 10 The efficiency of the cell against intensity of illumination at 25 ℃.
272
Fig. 11 and Fig. 12 illustrate the total energy output of solar array in one day with the increase of
273
transmittance under different working dates and latitudes. From Fig. 11, it can be seen that the energy
274
output trends which are first ascended and then descended are similar at latitude 15°N and 45°N, but
275
due to the different solar radiation intensity, the transmittances of the output energy peak are 0.82 and
276
0.86 respectively. And as result of longer solar irradiation time at latitude 45°N on summer solstice, the
277
output energy at latitude 15°N is lower than that at 45°N. As shown in Fig. 12, there are no clear
278
turning points within the range of transmittance on winter solstice. The total energy output is increased
279
with the increase of transmittance, and the energy output at latitude 15°N is higher than that at 45°N,
280
which is different from the result on summer solstice day. It can also be seen that the total energy
281
output of solar array on summer solstice is much higher than that on winter solstice. The reason is that
282
the incident illumination intensity on summer solstice day is stronger[43]. In addition, on summer
283
solstice day, the difference of output energy between the optimal transmittance and maximum
284
transmittance approximately reaches 0.5 MJ at latitude 15°N, thus it is worthy to optimize
285
transmittance to receive more energy output.
15
ACCEPTED MANUSCRIPT 7
1.5x10
15°N 45°N
7
Total Energy output Per day (J)
1.4x10
Optimum transmittance
7
1.3x10
7
1.2x10
7
1.1x10
7
1.0x10
0.5
286 287
0.6
0.7
0.8
0.9
1.0
Transmittance of solar array
Fig. 11 Effects of transmittance on total energy output on summer solstice day 7
1.3x10
7
1.2x10
15°N 45°N
Total Energy output Per day (J)
7
1.1x10
Optimum transmittance
7
1.0x10
6
9.0x10
6
8.0x10
6
7.0x10
6
6.0x10
6
5.0x10
6
4.0x10
0.5
0.6
0.7
0.8
0.9
1.0
288 289
Fig. 12 Effects of transmittance on total energy output on winter solstice day
290
Since flowing air can take away a part of the heat radiated by the solar array, the wind velocity can
291
also influence the temperature of solar array [13]. Effects of transmittance on total energy output under
292
different wind velocity are shown in Fig. 13. The working date and latitude of airship are set to summer
293
solstice and 15°N respectively. And the greater wind velocity is, the more energy output will be.
294
Moreover, it can also be observed that the transmittances of maximum output have slight variation with
295
the increase of wind velocity. Whereas there are some errors of transmittance in the manufacturing
296
process of encapsulant materials, the effect of wind velocity on optimum transmittance may be
297
neglected.
Transmittance of solar array
16
ACCEPTED MANUSCRIPT 7
1.25x10
vw=0m/s vw=20m/s
7
Total Energy output Per day (J)
1.20x10
vw=40m/s
Optimum transmittance 7
1.15x10
7
1.10x10
7
1.05x10
7
1.00x10
0.5
298 299 300
0.6
0.7
0.8
0.9
1.0
Transmittance of solar array
Fig. 13 Effects of transmittance on total energy output under different wind velocity.
3.3
The optimum transmittance
301
As the above analysis results show, the energy output of solar array the optimum transmittance of
302
solar array encapsulant can be turned by various work conditions. Therefore, the effects of different
303
dates and latitudes on optimum transmittance should be discussed.
304
Fig. 14 shows comparison result of the optimum transmittance of solar array encapsulant on summer
305
solstice and winter solstice as the function of working latitude. On summer solstice day, as the change
306
trend of the intensity of solar irradiation is first enhanced then weaken with the increase of latitude, the
307
optimum transmittance is first decreased then increased. And the minimum optimum transmittance
308
which is located between latitude 20°N to 30°N is about 0.81. It can also be seen that the maximum
309
difference of optimum transmittance at various working latitude is up to 0.1. But on winter solstice day,
310
with the increase of working latitude, the intensity of solar irradiation is weaken with the increase of
311
latitude, so the change curve of the optimum transmittance is increased firstly and then maintained
312
steady after reaching the maximum value, and the latitude of turning point is about 10°N. It can be
313
interpreted that the solar illumination incident on solar array is descended with the increase of latitude
314
on winter solstice [44]. When the latitude is higher than 20°N, solar illumination intensity is not very
315
strong at the maximum transmittance of solar array encapsulant, so the decrease of efficiency is not
316
remarkable. And it may be an ideal way to increase energy output through raising transmittance of
317
solar array encapsulant, when the working latitude is higher than 10°N on winter solstice.
17
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0.96 0.94
Summer solstice day Winter solstice day
Optimal Transmittance
0.92 0.90 0.88 0.86 0.84 0.82 0.80 0
10
20
318
30
40
50
Latitude (°)
319
Fig. 14 Effects of latitude on optimum transmittance of solar array.
320
As shown in Fig. 15, the relationship between optimum transmittance and working date at 15°N and
321
45°N is presented. At the middle months of a year, the intensity of solar irradiation is first enhanced
322
then weakened, and the date of the strongest radiation intensity is near June 1st, so the optimal
323
transmittance is reduced first and then increased and the lowest optimum transmittance is also near
324
June 1st. The maximum difference of optimum transmittance on different working date is about 0.14 at
325
15°N, and because the airship at 15°N may receive stronger solar illumination intensity than at 45°N
326
throughout a year, the lowest value of optimum transmittance at 45°N is 0.87, which is larger than that
327
of 15°N. 15°N 45°N
0.96 0.94
Optimal Transmittance
0.92 0.90 0.88 0.86 0.84 0.82 0.80 0.78 01-Feb
01-Apr
01-Jun
01-Aug
01-Oct
01-Dec
328 329
Fig. 15 Effects of working date on optimum transmittance of solar array.
330
In fact, in the practical working process of high-altitude, the encapsulant material of solar array
331
cannot be changed, and the working hour of high-altitude airship is more than one month, so the
332
transmittance of solar array encapsulant is fixed in that time. And taking into account of the fabrication
333
error of solar array encapsulant, the optimum transmittance can be regarded as the same under some
Working Date
18
ACCEPTED MANUSCRIPT 334
different conditions. For example, the difference of optimum transmittance from May 1st to Sep 1st is
335
not more than 0.02 at 15°N, so the optimum transmittance in these days can be considered to be a same
336
value, 0.82. And when the working date of the high-altitude airship working at 15°N is May 1st to Sep
337
1st, the solar array encapsulant is suggested to select transmittance of 0.82.
338
3.4
Selection of encapsulant material
339
As a result of the diversity of transmittance of solar array encapsulant, the output energy of solar
340
array is affected with the different encapsulant materials. According to the above optimization results,
341
it can be seen that the optimum transmittance is largely determined by working date and latitude, and
342
the different encapsulant materials often have different transmittance, so the selection of encapsulant
343
material of solar cell should be based on the optimization results. The preferable encapsulant materials
344
of solar array under some typical dates and latitudes are listed in Table 3.
345
Table 3 The transmittance of encapsulant material of solar array.
Working date
Working latitude
Spring solstice Summer solstice
>95 Transmittance/%
Suggested Encapsulant material FEP; PDMS
82
Epoxy Resin; Flexoskin
Autumn solstice
91
EVA
Winter solstice
>95
FEP
0
91
EVA;
30
81
Epoxy Resin; Flexoskin
45
86
Parafilm
Summer solstice
346
Optimum
15
4. Conclusion
347
The efficiency of solar cell plays a significant role in improving the output performance of solar
348
array of high-altitude airship. The temperature and incident radiation intensity of solar cell, which are
349
the key influencing factors to the efficiency of solar cell, can be increased with the rise of transmittance
350
of solar array. In this paper, In order to enhance energy output through achieving the balance between
351
efficiency and radiation input, the optimum transmittance has been calculated by the ABC optimization
352
algorithm.
353
The optimization results indicated that the working latitude and date of airship are significant factors
354
to the optimum transmittance of encapsulant of solar array. On summer solstice, the energy output with 19
ACCEPTED MANUSCRIPT 355
the optimal transmittance can approximately increase up to 0.5 MJ at latitude 15°N. On winter solstice
356
day, when the latitude is higher than 10°N, it is helpful for improving energy output to increase the
357
transmittance as large as possible. The effect of working date on optimum transmittance of encapsulant
358
of solar array is different at high and low latitude. At the higher latitude, 45°N, the optimum
359
transmittance in these dates from Sep 1st to Mar 1st the next year keep the maximum value of 0.95. At
360
the latitude 15°N, the optimum transmittance in these days from Apr 1st to Sep 1st can be considered to
361
be a same value, 0.82. The optimization results are conducive to improve the output performance of
362
solar array by choosing the most suitable encapsulant of solar array under different working conditions.
363
However, this work still has certain limitations. In reality, the working hours of long-endurance
364
airship are often up to one year, but the optimum value for the transmittance of the solar array that can
365
work through the whole year is not investigated in this paper. In addition, to simplify the computation,
366
different parts of temperature of solar array laid on the airship have been assumed to be the same, but
367
in fact, the layout parameters of solar array may affect the temperature distinction of different parts of
368
solar array. Therefore, future work is focused on investigating optimization results for whole year and
369
the effect of temperature distinction of different parts of airship.
370
Acknowledgments
371
This work was supported by the National Natural Science Foundation of China under Grant No.
372
51307004.
373
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Highlights
The thermal and heat transfer models of solar array of high-altitude airship are established.
The optimization model of transmittance of solar array encapsulant is presented.
The feasibility of the numerical model is verified by comparison with experimental data.
The energy output of solar array of high-altitude airship is improved through optimizing the transmittance of solar array encapsulant.
The effect of working condition on the optimum transmittance of solar array encapsulant is analyzed.
