Geostationary Communication Satellite Solar Array Optimization Using Gravitation Search Algorithm

Oukil, Souad; Boudjemai, Abdelmadjid

doi:10.5028/jatm.v12.1165

Souad Oukil ^**Correspondence author: soukil@cds.asal.dz

Agence Spatiale Algérienne - Centre de Développement des Satellites - Département d’Ingénierie des Satellites - Oran - Algeria.

http://orcid.org/0000-0002-4677-0890

Abdelmadjid Boudjemai

Agence Spatiale Algérienne - Centre de Développement des Satellites - Département de Recherche en Mécanique Spatiale - Oran, Algeria.

http://orcid.org/0000-0001-8916-0040

*Correspondence author: soukil@cds.asal.dz

Section Editor: Alison Moraes

AUTHOR’S CONTRIBUTION

Conceptualization: Oukil S and Boudjemai A; Methodology: Oukil S and Boudjemai A; Investigation: Oukil S and Boudjemai A; Writing - Original Draft: Oukil S; Writing - Review and Editing: Oukil S and Boudjemai A.

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Figure 1
Deployed wing of the solar array.

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Figure 2
Morozov and Lopatin (2011)Morozov EV, Lopatin AV (2011). Design and analysis of the composite lattice frame of a spacecraft solar array. Compos Struct 93(7):1640-1648. https://doi.org/10.1016/j.compstruct.2010.12.007
https://doi.org/10.1016/j.compstruct.201... stowed wing of the solar array. Courtesy of ISS-Reshetnev Company.

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Figure 3
Five different equivalent circuit models. (a) Single diode; (b) Single diode with one resistor; (c) single diode with two resistors; (d) double diode with two resistors; (e) triple diode with two resistors.

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Figure 4
Solar array architecture.

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Figure 5
Multiobjective GSA algorithm flowchart.

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Figure 6
Gravitational forces between particles concept.

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Figure 7
TJ GaAs cell’s I-V curve characteristics trough the mission life.

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Figure 8
TJ GaAs cell’s P-V curve characteristics trough the mission life.

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Figure 9
Design variable I, V and P in relation to the iteration numbers at BOL at T = 28 °C without degradation.

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Figure 10
Design variable I, V, P, N_p and N_s in relation to the iteration numbers at BOL at T = 28 °C with degradation.

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Figure 11
Design variable I, V, P, N_p and N_s in relation to the iteration numbers at EOL at T = 28 °C with degradation.

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Figure 12
Design variable I, V, P and T in relation to the iteration numbers at BOL in solstice season at T = 39 °C.

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Figure 13
Design variable I, V, P and T in relation to the iteration numbers at BOL in equinox season at T = 49 °C.

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Figure 14
Design variable I, V, P and T in relation to the iteration numbers at EOL in solstice season at T = 42 °C.

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Figure 15
Design variable I, V, P and T in relation to the iteration numbers at EOL in equinox season at T = 52 °C.

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Figure 16
Convergence characteristics of GSA and GA.

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Table 1
Comparison of the related work references.

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Table 2
Electrical power requirements of the solar panel.

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Table 3
Triple junction gallium arsenide (TJ GaAs) main characteristics at BOL at 28 ºC.

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Table 4
Degradation factors at BOL and EOL.

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Table 5
Range of parameters.

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Table 6
TJ-GaAs cell's main characteristics at BOL and EOL.

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Table 7
TJ-GaAs cells work point.

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Table 8
Solar array general design.

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Table 9
GSA Control parameters values.

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Table 10
Solar array power generation at BOL and EOL.

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Table 11
Solar array power generation at BOL and EOL at solstice and equinox season.

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Table 12
Solar array power requirements and all calculated values at BOL and EOL.

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Table 13
Solar array power margin at BOL.

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Reference	Author	Algorithm	Advantages	Disadvantages
*Wei et al. (2011)*Wei H, Cong J, Lingyun X, Deyun S (2011) Extracting solar cell model parameters based on chaos particle swarm algorithm. Paper presented 2011 International Conference on Electric Information and Control Engineering. IEEE; Wuhan, China. https://doi.org/10.1109/ICEICE.2011.5777246 https://doi.org/10.1109/ICEICE.2011.5777...	H. Wei	Proposed a chaotic particle swarm optimization algorithm (CPSO) for extracting solar cell model parameters.	It can reduce the influence of experimental data measurement accuracy.	It sometimes easily gets trapped in a local optimum and the convergence rate decreases considerably in the later period of evolution.
*El-Naggar et al. (2012)*El-Naggar KM, AlRashidi MR, AlHajri MF, Al-Othman AK (2012) Simulated annealing algorithm for photovoltaic parameters identification. Sol Energy 86(1):266-274. https://doi.org/10.1016/j.solener.2011.09.032 https://doi.org/10.1016/j.solener.2011.0...	KM. El-Naggar	Proposed a simulated annealing (SA) based approach for optimal estimation of solar cell model parameters.	It was used to solve a transcendental function that governs the current-voltage relationship of a solar cell, as no direct general analytical solution exists.	Repeatedly annealing with a schedule is very slow, especially if the cost function is expensive to compute.
Harrag and Messalti (2017)Harrag A, Messalti S (2017) Three, five and seven PV model parameters extraction using PSO. Energy Procedia 119:767-774. https://doi.org/10.1016/j.egypro.2017.07.104 https://doi.org/10.1016/j.egypro.2017.07...	A. Harrag	Proposed a particle swarm optimization technique for the characterization of the equivalent electrical model of photovoltaic cell.	It has fast convergence towards an optimum, is simple to compute, easy to implement.	When reaching a near optimal solution, the algorithm stops optimizing and the accuracy that the algorithm can achieve is limited.
*Chegaar et al. (2003)*Chegaar M, Ouennoughi Z, Guechi F, Langueur H (2003) Determination of solar cells parameters under illuminated conditions. Journal of Electron Devices 2:17-21.	M. Chegaar	Proposed the vertical optimization method, the analytical five-point method, and their methods for extracting solar cell parameters of the single diode lumped circuit model.	It does not require a priori knowledge of the parameters.	In the case of the module, the calculated saturation current is far higher than that obtained numerically and it does not give all the parameters simultaneously.
*Xiao et al. (2006)*Xiao W, Lind MGJ, Dunford WG, Capel A (2006) Real-time identification of optimal operating points in photovoltaic power systems. IEEE Trans Ind Electron 53(4):1017-1026. https://doi.org/10.1109/TIE.2006.878355 https://doi.org/10.1109/TIE.2006.878355...	W. Xiao	Proposed a method of real-time estimation uses polynomials to demonstrate the power-voltage relationship of PV panels.	It implements the recursive least-squares method and Newton-Raphson method to identify the voltage of the optimal operating point.	In several cases, this method is found to be highly unstable for poor initial guess.
*Huld et al. (2010)*Huld T, Gottschalg R, Beyer HG, Topič M (2010) Mapping the performance of PV modules, effects of module type and data averaging. Sol Energy 84(2):324-338. https://doi.org/10.1016/j.solener.2009.12.002 https://doi.org/10.1016/j.solener.2009.1...	T. Huld	Proposed to mapping the performance of PV modules, effects of module type and data averaging to estimate the energy yield of photovoltaic modules.	Data of arbitrary locations in a large geographical area was used.	It takes more time to run simulations compared to other methods.
*Easwarakhanthan et al. (1986)*Easwarakhanthan T, Bottin J, Bouhouch I, Boutrit C (1986) Nonlinear minimization algorithm for determining the solar cell parameters with microcomputers. J Sol Energy 4(1):1-12. https://doi.org/10.1080/01425918608909835 https://doi.org/10.1080/0142591860890983...	T. Easwarakhanthan	Proposed a nonlinear least-squares optimization algorithm based on the Newton model modified with Levenberg parameter, for the extraction of solar cell parameters from the experimental data.	The program allows an in situ theoretical modeling of solar cells in laboratories when incorporated into microcomputer-based data acquisition software.	For flat functions (i.e. smooth functions with derivatives that vanish at a certain point), the algorithm can get lost in parameter space. In some cases, the algorithm can be very slow to converge.
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Ishaque and Salam (2011)Ishaque K, Salam Z (2011) An improved modeling method to determine the model parameters of photovoltaic (PV) modules using differential evolution (DE). Sol Energy 85(9):2349-2359. https://doi.org/10.1016/j.solener.2011.06.025 https://doi.org/10.1016/j.solener.2011.0...	K. Ishaque	Proposed an improved modeling approach using differential evolution method to determine the model parameters of photovoltaic modules.	It gives superior results for any irradiance and temperature variations and can be useful for PV simulator developers.	It can create a problem of a slow convergence and it also easily falls into the local optimum.
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Park and Choi (2017)Ortiz-Conde A, Sánchez FJG, Muci J (2006) New method to extract the model parameters of solar cells from the explicit analytic solutions of their illuminated I-V characteristics. Sol Energy Mater Sol Cells 90(3):352-361. https://doi.org/10.1016/j.solmat.2005.04.023 https://doi.org/10.1016/j.solmat.2005.04...	J-Y. Park	Proposed a new simulation model for PV panels using online datasheet parameter tuning.	Not only applied to the other simulation programs but also used as the PV simulation engine in PV hardware simulators.	It needs much more computational time.
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		Solstice (SS)	Equinox (EQX)
BOL	Requirements (W)	2098	2369
EOL	Requirements (W)	1913	2155

V_mp (V)	V_oc (V)	I_mp (A/cm²)	I_sc (A/cm²)	dI_sc/dT (mA/cm²/K)	dI_mp/dT (mA/cm²/K)	dV_mp/dT (mV/ºC)	dV_oc/dT (mV/ºC)	Cell Area (cm²)
2.277	2.565	0.016	0.0168	0.01	0.009	-6.01	-6	26

	TJ-GaAs cell
	BOL	BOL with degradation	EOL With degradation
V_mp (V)	2.277	2.277	2.254
V_oc (V)	2.565	2.565	2.539
I_mp (A/cm²)	0.016	0.016	0.014
I_sc (A/cm²)	0.0168	0.0161	0.0148
dI_sc/dT (mA/ cm²/K)	0.01	0.01	0.014
dI_mp/dT (mA/ cm²/K)	0.009	0.009	0.012
dV_mp/dT (mV/ ºC)	-6.01	-6.01	-6.9
dV_oc/dT (mV/ ºC)	-6	-6	-6.5
Work Temperature (ºC)	28	28	28
Cell Area (cm²)	26	26	26

	I _op	V _op
BOL	0.3407	2.1631
EOL	0.2981	2.1415

Number of sections	16
Number of strings	6
Number of cells per string	30

Number of agents (N)	200
Max iterations (Max_it)	200
Parameters values used for algorithm	G₀=100, α=10
Mass	Random
Velocity	Random
Acceleration	Random
Position of agents	Random
Distance between agents in search space	Random

Design variable	BOL	BOL with degradation	EOL with degradation
I_sc (A/cm²)	0.0168	0.016134	0.014880
I_mp (A/cm²)	0.016	0.016	0.014756
V_mp (V)	2.277	2.277	2.25423
V_oc (V)	2.565	2.565	2.53935
Np (Cells)	100	99	99
Ns (Cells)	30	28	27
I (A)	37.43	37.14	33.94
V (V)	64.37	64.77	64.98
P (W)	2409.34	2405.80	2205.40
T (ºC)	28	28	28

	BOL		EOL
	SS	EQX	SS	EQX
Temperature	39 ºC	49 ºC	42 ºC	52 ºC
P (W)	2123.35	2398.53	1937.80	2182.46
I (A)	32.79	37.02	29.90	33.68
V (V)	64.77	64.77	64.79	64.79

		SS	EQX
BOL	Requirements (W)	2098	2369
BOL	Bus power (W)	2123	2398
EOL	Requirements (W)	1913	2155
EOL	Bus power (W)	1937	2182

				Power margin (%)
BOL	SS	Requirements (W)	2098	1.19
	SS	Bus power (W)	2123	1.19
	EQX	Requirements (W)	2369	1.22
	EQX	Bus power (W)	2398	1.22
EOL	SS	Requirements (W)	1913	1.25
	SS	Bus power (W)	1937	1.25
	EQX	Requirements (W)	2155	1.25
	EQX	Bus power (W)	2182	1.25

I = I_{pv} - I_{01} [\exp (\frac{V + {IR}_{s}}{N_{a 1} V_{T}}) - 1] - I_{02} [\exp (\frac{V + {IR}_{s}}{N_{a 2} V_{T}}) - 1] - \frac{V + {IR}_{s}}{R_{sh}}

I = I_{pv} - I_{01} [\exp (\frac{V + {IR}_{s}}{N_{a 1} V_{T}}) - 1] - I_{02} [\exp (\frac{V + {IR}_{s}}{N_{a 2} V_{T}}) - 1] - I_{03} [\exp (\frac{V + {IR}_{s}}{N_{a 3} V_{T}}) - 1] - \frac{V + {IR}_{s}}{R_{sh}}

P = V_{op} I_{sc} (T, R) A_{cell} N_{p} ⟨1 - A_{3} (T, R) \{e^{[\frac{V_{op}}{A_{4} V_{oc} (T, R) N_{s}}]} - 1\}⟩ K_{CG} K_{CM} K_{PC} {(1 - D / Y)}^{t} (SIV)

[1] *Correspondence author: soukil@cds.asal.dz

Degradation factors at BOL	Affecting I_SC	Assembly mismatch loss	0.98
		Coverglass coating	0.98
		Total	0.96
Degradation factors at EOL	Current Factors	Coverglass charge particles	0.99
		Ultraviolet rays	0.97
		Propellant contamination	0.98
		Micrometeoroid damage	0.98
		Total	0.92
	Voltage Factors	Coverglass charge particles	0.99
	Voltage Factors	Total	0.99

N_s (cells)	25 ≤ N_s ≤ 35
N_P (cells)	85 ≤ N_p ≤ 110
V_op (V)	60 ≤ V_op ≤ 67
I_op (A)	I_opmin ≤ I_op ≤ I_opmax
Temperature T (ºC)	Case of solstice season	BOL	37 ≤ T ≤ 40
		EOL	40 ≤ T ≤ 44
	Case of equinox season	BOL	48 ≤ T ≤ 51
		EOL	50 ≤ T ≤ 54

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Geostationary Communication Satellite Solar Array Optimization Using Gravitation Search Algorithm

ABSTRACT: