Geostationary Communication Satellite Solar Array Optimization Using Gravitation Search Algorithm

The growing demand for satellite communications with high subsystems reliability and the increasing complexity of satellite power subsystems that use large deployable solar panels and appropriate electronics modules, with increasing embedded satellite payloads, are needs that make a difficult task even more difficult. Therefore, effective optimization techniques are required to help engineers and decision makers configure satellite power subsystems well in terms of performance and reliability. One of the important requirements in each space mission is the design of a system to provide uninterruptible energy with desired quality and quantity. The satellite power subsystem project must satisfy its demand for electricity during the mission. To obtain this electrical energy, it is necessary to calculate the required area of the satellite structure for the installation of solar panels. Also, the number of strings, serial cells in each string and the size of the cells (Kimber and Gleeson 1988; Kimber and Goodbody 1994) must be defined in the design of each solar panel. As mentioned, the design of a solar array on a specific space mission is based on the mission requirements. Solar cells are still the most suitable energy source in space missions. The behavior of solar cells is strongly related to environmental conditions (Castañer and Silvestre 2002; Luque and Hegedus 2003). https://doi.org/10.5028/jatm.v12.1165 ORIGINAL PAPER


INTRODUCTION
The growing demand for satellite communications with high subsystems reliability and the increasing complexity of satellite power subsystems that use large deployable solar panels and appropriate electronics modules, with increasing embedded satellite payloads, are needs that make a difficult task even more difficult. Therefore, effective optimization techniques are required to help engineers and decision makers configure satellite power subsystems well in terms of performance and reliability.
One of the important requirements in each space mission is the design of a system to provide uninterruptible energy with desired quality and quantity. The satellite power subsystem project must satisfy its demand for electricity during the mission.
To obtain this electrical energy, it is necessary to calculate the required area of the satellite structure for the installation of solar panels. Also, the number of strings, serial cells in each string and the size of the cells (Kimber and Gleeson 1988;Kimber and Goodbody 1994) must be defined in the design of each solar panel. As mentioned, the design of a solar array on a specific space mission is based on the mission requirements. Solar cells are still the most suitable energy source in space missions. The behavior of solar cells is strongly related to environmental conditions (Castañer and Silvestre 2002;Luque and Hegedus 2003). https://doi.org/10.5028/jatm.v12.1165 ORIGINAL PAPER Degradation is an important factor in space missions, which, compared to terrestrial applications, has direct effects on the performance of solar cells. Taking into account the mentioned factor, the generated power of a solar array can be estimated more accurately in space missions before launch or during the mission (Taherbaneh et al. 2011).
The production of solar energy necessary to supply large satellites with high power demand is ensured by the deployment of large solar panels with highly reliable mechanisms, also robust distribution and conditioning electronics, and finally a powerful energy storage system. To meet these requirements, the use of optimization tools has become an essential area to solve many problems encountered in the space industry. In fact, during the last few years, a very rapid growth of works using optimization methods has been observed.
Multiobjective optimization is a very active field of research because the economic and industrial risks are enormous. Multiobjective optimization methods provide the designer with a set of solutions corresponding to as many compromises between the different antagonistic objectives of the problem.
In this work, a gravitational search algorithm (GSA) was introduced in order to estimate the solar panel parameters of the single diode model for several cases, based on the experience gained from first Algerian geostationary communication satellite Alcomsat-1 project.
The paper deals with the extraction of the parameters of a photovoltaic (PV) module of geostationary satellite, using multiobjective functions taking into account the solstice (SS) and equinox (EQX) periods during temperature operation, as well as in the case of the degradation effect in order to achieve the overall minimum solution in a very short time with very good accuracy. The results of the simulation show that the GSA algorithm has achieved the best efficiency for modeling the photovoltaic cell as well as the PV module of a geostationary satellite.

RELATED WORK
Several researchers have proposed to identify the different parameters affecting the characteristics of the power system by applying several optimization methods, namely deterministic and heuristic methods (Wei et al. 2011;El-Naggar et al. 2012;Harrag and Messalti 2017). A comparative study of four methods to extract solar cell parameters from the single diode lumped circuit model was carried out by Chegaar et al. (2003). Other study has been developed by Xiao et al. (2006) based on the application of the real-time estimation method that uses polynomials to demonstrate the power-voltage relationship of photovoltaic panels and by the implementation of the recursive least squares method and the Newton-Raphson method, in order to identify the optimal operating point voltage. A mathematical model has been developed for the energy performance of PV modules, which depends on the irradiance in the plane and the temperature of the module (Huld et al. 2010).
Other studies have been based on the use of different methods and techniques. A particular study was carried out by researchers applying the nonlinear least squares optimization algorithm and which established the modified Newton model with the Levenberg parameter was applied for the extraction of the five parameters of solar cell illuminated from experimental data (Easwarakhanthan et al. 1986). Ortiz-Conde et al. (2006) have used a new method based on the computation of the cocontent function from the exact and explicit analytical solutions of the characteristics of the illuminated current voltage (I-V). As for the research conducted for AlRashidi et al. (2011), an application of a new model search optimization technique has been employed to estimate parameters of a solar cell and a PV module. Ishaque and Salam (2011) used a method based on differential evolution, which consists of simultaneously calculating all the parameters of a photovoltaic module at different levels of irradiance and temperature with an experiment of three PV modules of different types (multicrystalline, monocrystalline and thin film). In photovoltaic (PV) generation system, to obtain the maximum available energy from PV source using highly efficient power conditioning system is an important issue because the characteristic of real PV panel is always changing with dynamic irradiance and temperature conditions (Cubas et al. 2014;Park and Choi 2017). Derick et al. (2017) applied the wind driven optimization technique to identify solar PV parameters. The precision and convergence time of the proposed method are compared to several other algorithms.
Other researchers have proposed an extension of the gravitational research algorithm (GSA) to multiobjective optimization problems and its application in various fields, including the power system. Ghasemi et al. (2013) discuss the design of multimachine power system stabilizers using a fuzzy GSA. Mondal et al. (2013) solve the multiobjective economic emission load dispatch problem considering wind power penetration. Tian et al. (2014) discuss the multiobjective optimization of short-term hydrothermal scheduling using a nondominated sorting GSA with chaotic mutation. Bhattacharya and Roy (2012) have applied an efficient and reliable heuristic technique inspired by swarm behaviors and GSA algorithm for solution of multiobjective optimal power flow (OPF) problems.
The comparison of the related work references, are summarized in Table 1. 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) 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) 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) 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) 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) 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) 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.

GEOSTATIONARY COMMUNICATION SATELLITE ELECTRICAL POWER SUBSYSTEM REQUIREMENTS
The required concept for power distribution unit and management is essentially determined by the electrical power subsystem architecture. State-of-the-art power distribution unit and management concepts use either regulated or nonregulated primary power buses, or, in a combination of both methods, a semiregulated and hybrid power supply system.
The primary power of the spacecraft, in most cases generated by a solar array, will be fed into the main power bus of the electrical power subsystem by direct or indirect energy transfer, when necessary to cover the bus power demand. Power transfer from the solar array to the main bus by direct energy transfer corresponding to the amount of power necessary to satisfy the bus power demand will be achieved by regulation methods (Ley et al. 2009).
The solar array consists of two identical wings extending symmetrically from the north and south sidewalls of the satellite, for a better symmetrical momentum. The rigid solar array consists of numerous solar cells mounted on a base substrate made of aluminum honeycomb with face sheets made of fiber composite. The objective of this fiber sheets aims to reduce the weight.
As shown in Fig. 1, each wing is made of one yoke and two panels connected by hinges and close cable loops.   Figure 2 shows that the wings are stowed against the south and north side walls of the spacecraft by hold and release mechanism during launch. After the spacecraft separation from the launch vehicle, the hold-down pins are cut off and the solar array is deployed by the springs integrated in the hinges. The mechanical and electrical interfaces to the satellite are made at the solar array drive assembly (SADA) on the satellite sidewall. The SADA slowly rotates the wing to track the sun while the satellite maintains Earth pointing. The design of a solar array in a specific space mission is based on the mission requirements. Table 2 provides the required electrical specifications of the solar panel for the beginning of life (BOL) and the end of life (EOL) of the mission at solstice and equinox season. Note that the desired solar array power shall be higher than the values indicated in Table 2. To select the appropriate solar cells, the following parameters are very important: required electrical power, solar cell technology, resistance against orbital radiations and operating temperature range. Considering all the above parameters, the cells shall be of the triple junction gallium arsenide (TJ GaAs) manufacturing type with cell area of 26 cm², measured at 28 °C, as shown in Table 3. Table 3. Triple junction gallium arsenide (TJ GaAs) main characteristics at BOL at 28 °C.

SOLAR ARRAY POWER REQUIREMENTS AND DEGRADATION FACTORS
The required power for the satellite during the mission is obtained from the power consumption of all satellite subsystems, such as attitude and orbit control subsystem (AOCS), on board data handling subsystem (OBDH), telemetry, command and ranging subsystem (TC&R), propulsion, thermal control, etc., including, the harness loss, battery charging and power condition unit (PCU) consumption.
In this paper, the highest power demand at the EOL is 2200 W at equinox. This will be the power requirement used to calculate and determine the power generated by the solar arrays at the BOL. The power needed at BOL was 2337.5 W.
The degradation factors, which used to calculate the output power, are listed in Table 4. At the BOL, the degradation factors are mainly caused by external factors, such as assembly mismatch loses or some performance reductions due to the coating of the cover glass. At the end of the mission life, there are several factors that affect the performance of a regular solar cell; these factors could affect the voltage or current characteristics of the cells, and are mainly related to space environmental factors across the mission life cycle.  a) The single diode model In Fig. 3a, the equation to relate the output current, I, to the output voltage, V, is given by Eq. 1: (1) where I pv is the photocurrent delivered by the constant current source, I 0 is the reverse saturation current corresponding to the diode, where k is the Boltzmann constant, T the temperature expressed in Kelvin, and q is the electron charge), a is the ideality factor that takes into account the deviation of the diodes from the Shockley diffusion theory, and N is the number of series-connected cells in the photovoltaic system to be analyzed (obviously, N = 1 in case of a single cell) (Cubas et al. 2017).
b) The single diode with one resistor model. The main equation of Fig. 3b is given by Eq. 2: (2) Where R s is the series resistor.
c) The single diode with two resistor model The main equation of the model in Fig. 3c is given by Eq. 3: ( Where R sh is the shunt resistor. In the triple diode model, the first diode would contribute the diode current (I D1 ) due to diffusion and recombination in the quasi neutral regions of the emitter and bulk regions with N a1 = 1, and the second diode would contribute the diode current (I D2 ) due to recombination in the space charge region with N a2 = 2. The purpose of adding a third diode in parallel to the two diodes is to consider contribution of the diode current component (I D3 ), due to recombination in the defect regions, grain sites, etc. The ideality factor N a3 , of the third diode is to be estimated along with other parameters of the model and is predicted to be varying between 2 and 5 depending on the local factors (Steingrube et al. 2011;Khanna et al. 2015).

SELECTED MODEL
An analytical approach is introduced to investigate the electrical behavior of solar panels. It considers all effective parameters in designing solar arrays for space applications.
In order to reduce complexity, single diode model is selected for modeling the solar cell. Figure 3c shows the equivalent circuit of one-diode model of a solar cell. This model, used by several researchers, have been used for the simulation. The use of this single diode model to describe the static I-V characteristic has been widely considered, it has been successfully used to fit experimental data and offers good compromise between approximation precision and simplicity (Bouzidi et al. 2012;Lotsch et al. 2005).
The current-voltage characteristic of the model is also based on Eq. 3 and is represented by Eqs. 6-8: Once the variables V mp , V oc , I mp and I sc have been supplemented with the corresponding temperature coefficients and the radiation dependent on the remaining factors R as shown in the following example for A 1 (Eqs. 9-12), one obtains the temperature and radiation dependent I-V characteristic of the solar array (Ley et al. 2009): (9) (10) where T is cell temperature and T 0 cell normal temperature 28 °C.
Eq. 13 and Eq.14, which depends on temperature, are given by: (14) Figure 4 shows that solar cells on the array are segmented in many strings connected in parallel. The following relations (Eqs. 15-16) approximately hold true with a suitable margin in the array segmentation. The margin varies as the design progresses from the conceptual stage to the final design (Ley et al. 2009). The equation for the I-V characteristic may then be written as Eq. 17: The I-V characteristic of a cell irradiated with a certain dose of 1 MeV is achieved by applying the remaining factors K on the cell data (Taherbaneh et al. 2011) (Eqs. 18-21).
The generated electrical power of the array for summer solstice after 15 years of in-orbit operation and respecting the degradation factors is calculated as follows (Eq. 22) (Ley et al. 2009): where P: generated electrical power, I op is operational current, V op is operational voltage, K CG is cell cover glass loss factor, K CM is cell mismatch loss factor, K PC is parameter calibration loss factor, D is degradation, Y is year, t is satellite life and SIV is seasonal solar intensity variations. Note that Eqs. 6 and 22 are used in the expression of objective functions for simulation in the GSA algorithm. The main parameters to optimize in this study using the multiobjective GSA algorithm are mainly the following: number of cells in serial (N s ), number of cells in parallel (N p ), bus current I op , bus voltage (V op ), bus power (P) and temperature (T). All these constitute the individual position of several masses that represent a complete solution set. The initial positions of each agent should be randomly selected while satisfying different equality and inequality constraints of the geostationary communication satellite solar array optimization.

A MULTIOBJECTIVE GRAVITATIONAL SEARCH ALGORITHM
In solving optimization problems with a large search space, conventional optimization algorithms do not provide an appropriate solution, as the search space increases exponentially with the size of the problem, thus solving problems exact techniques (such as exhaustive search) are not practical.
In this paper, the studied algorithm called gravitational search algorithm (GSA) is based on the law of gravity and the notion of interactions between point masses. The GSA algorithm uses the theory of Newtonian physics and its search agents are a collection of masses. Gravitational force is a way of transferring information between different masses, as any other algorithm based on a population (Esmat et al. 2009;Ghalambaz et al. 2011;Chatterjee et al. 2010;Khajehzadeh and Eslami 2012;Siddique and Adeli 2016;Ghazali et al. 2017).
The multiobjective GSA algorithm is shown in Fig. 5. Every mass accelerates along a resulting force from neighboring masses. The agents are considered objects and their performance is measured by their masses. All these objects attract each other by the force of gravity, and this force causes a global movement of all objects towards objects with heavier masses. Therefore, the masses cooperate by using a direct form of communication, by the gravitational force. The heavy masses -which correspond to the good solutions -move more slowly than the lighter ones, which guarantees the exploitation step of the algorithm (Bohat and Arya 2018). Create the initial population randomly of group 1 In GSA, each mass (agent) has four specifications: position, inertial mass, active gravitational mass, and passive gravitational.

Define initial parameters
The mass position and its gravitational and inertial masses are determined using an objective function. In other words, each mass presents a solution, and the algorithm is navigated by correctly adjusting gravity and mass of inertia. Over time, the masses are expected to be attracted by the heavier mass (Oliveira et al. 2018). As shown in Fig. 6 where M i is the gravitational mass related to agent i; M i is the gravitational mass related to agent j; ε is small constant; R ij is the Euclidean distance between the two agents i and j; G 0 is the initial value of G; T is the total number of iterations and α is the parameter.
The acceleration of the agent i at time t and in direction d th , is given by Eq. 24, where M ij is the inertial mass of the i th agent (Bohat and Arya 2018).
The position of every agent is defined as: Where X 1 j the position of i th agent is in n th dimension, N is number of agents in the search space and dim is prespecified dimension of the problem (Bohat and Arya 2018).
The fitness evaluation of current population of agents performed through considered objective function followed by the calculation of masses of all agents as shown in Eq. 26 and 27: where: M i (t) is the gravitational mass related to agent I at iteration t; fitness (X k j ) is the evaluation function of the X k j ; best k is the the maximum fitness values among the solutions for k th objective; worst k is the the minimum fitness values among the solutions for k th objective and m is the number of objectives functions.
For a minimization problem, the best k (t) and worst k (t) are defined in Eqs. 28 and 29:

MULTIOBJECTIVES FUNCTIONS
The employment of the GSA algorithm follows a very simple iterative technique to minimize an objectives function, given by P and I. The details of this objectives function will be explained later. The design variables are represented by P and I (Eqs. 30 and 31). where: To apply the GSA, random values are taken for the design variables within the following ranges. These ranges were chosen based on the minimum size constraints and maximum area constraints, in addition to general observation and intuition about the final design's optimal geometry. Table 5 shows the optimal design parameters with variable design parameters.

RESULTS AND DISCUSSION
Several simulations and analytical calculations have been performed to determine the optimal parameters of the geostationary satellite solar array.
In order to determine the number of cells in parallel and in series, the number of the solar panel sections, and the number of panels needed in the solar array, numerous aspects must take into account the power of the satellite at end of life as well as the various degradation factors caused by the space environment. This first step in designing a solar array is to find the power consumption at the beginning of life. The second step, the V-I characteristics curve in three cases, at the BOL, at BOL with degradation and at EOL with the degradation factors was defined. The same assumption was made for the P-V characteristics curve. For these calculations, some assumptions were taken. The working point of the solar cells at the EOL, at the BOL and the voltage of the solar arrays were assumed.
Also, the interest of this study is to predict the power generation of the geostationary satellite solar array, which subject to space environment and under a number of practical constraints and other cases both solstice (SS) and equinox season (EQX), in order to extract the desired performance parameters using multiobjective functions.

POWER REQUIREMENTS AND DEGRADATION FACTORS CALCULATION
In fact, the degradation factors presented in Table 4 are used in the TJ GaAs cell characteristic, which makes it possible to calculate the characteristics of a solar cell, at the BOL and EOL. The main characteristics of a TJ GaAs solar cell, at the BOL and EOL including the degradation factors effects, which used to calculate the total output power, are shown in Table 6.
In order to define the number of solar cells and panels needed for the solar array, there are some considerations that were defined in this paper, such as 64 V is the solar array voltage, the number of sections on the sequential switching shunt regulator is 16, the working point of the solar cell at BOL and EOL was taken at the 95% of the maximum work point. Table 7 shows the TJ GaAs Cells Work Point.

TJ GAAS CELL'S I VS V CHARACTERISTICS
The V-I and P-V characteristics curves in three cases, at the BOL, at BOL with degradation due to assembly and cover glass and at EOL with the degradation factors, as shown in Fig. 7

Number of sections 16
Number of strings 6

OPTIMAL VALUE OF SOLAR POWER GENERATION USING GSA ALGORITHM
Simulations have been made using the GSA algorithm to analyze different parameters of geostationary communication satellite subsystem solar array. The value of gravitational search algorithm control parameters is given in Table 9. The optimal solutions are obtained after 200 iterations and this after several runs. The optimization process has maximized the power generated, represented by the objective or fitness function P, by satisfying the design criteria. The best performing design was saved for each successive starting population to converge on the optimum values. Figs. 9 to 15, show, this fact by displaying the optimum value of the objective function. The results have been displayed for the following iterations and the optimum values obtained by the GSA algorithm have been described in the Tables 10 and 11.

Mass Random
Velocity Random Acceleration Random

Position of agents Random
Distance between agents in search space Random  Tables 10 and 11 shows that the design parameters such as the number of cells and temperature mainly affect the value of power generated by solar panel. The solar array current at BOL was 2.283 A per section and 64 V voltage level. Table 10 shows the output power characteristics of the satellite solar array at 28 °C, at BOL without and with degradation and at EOL. The analytical result of power at EOL (T = 28 °C) is 2386.20 W and from the results obtained in Table 10 and after optimization, the total power at EOL is decreased by181 W, one can prove that the relative error is about 8.20% of the total power. The proposed design, fulfil with all the requirements established for the primary power source defined at the beginning of the paper. According to the results of the simulation in which all the degradation factors of the electrical behavior of the solar panel are taken into consideration during the BOL and EOL, it is found that the requirements of the mission P, V and I are fulfilled, when the satellite meets different environmental conditions, as shown in Table 11. Table 12 shows that the designed solar panels satisfy mission power requirements as defined in Table 2.

CONCLUSION
In this research, design of a solar array and its necessary considerations for a space mission were presented. The designed solar array, which should supply the required power for the mentioned mission, was consisted of two equal solar panels. Each panel consisted of six strings, which were made of thirty series triple-junction GaAs solar cells.
In this paper, the GSA was proposed to optimize simultaneously multiple objectives functions for solving the geostationary solar array problem. Optimal operation of a power system is one of the most important aspects of the power subsystem. The GSA optimization algorithm is used as a tool for the extraction of the solar array parameters in which all the degradation factors of the electrical behavior of the solar panel are taken into consideration during the BOL and EOL. As it was shown, the effectiveness of the suggested algorithm verified on several test cases (on solstice and equinox seasons).
It was observed from the results that the optimization process is highly essential to achieve a better design with better performance parameters for the geostationary solar array.
The results show that the design parameters such as the number of cells in serial, number of cells in parallel and temperature, mainly affect the value of power generated by solar panel at EOL. However, the total power of the optimized system is decreased by 181 W (i.e., 8.20% of the total power). The corresponding of optimized value of current and voltage generated by solar panel were found at 33.94 A and 64.98 V, respectively. The degradation and output power characteristics of the solar panels were calculated for different temperature values. The active surface area is 26 cm². The maximum power point is at 0.94 W.
The results are in full accordance with the mission requirements either in beginning or in end of life. The degradation and output power characteristics of the solar panels were calculated for different temperature values. Therefore, the power prediction of the designed solar array for the mentioned satellite completely satisfies its mission requirements.

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.