Iranian (Iranica) Journal of Energy & Environment Modeling of Maximum Solar Power Tracking by Genetic Algorithm Method

This paper presents a model of solar cell by using MATLAB SIMULINK. P-V, I-V and P-I characteristics were studied for various values of irradiance at constant temperature. Genetic Algorithm (GA) was used for maximum power point tracking (MPPT) of Photovoltaic (PV) system using the direct control method. The main objective of this paper is to find out the optimal angle, which is used for the positional control of solar module and optimal power tracking. The principle of GAs is searching for the maximum of fitness function and not for the minimum of power derivation; this gives more stability and minimize oscillation of output power around the maximum power point (MPP). The main contribution of the proposed scheme is the elimination of PI control loop which normally exists to manipulate the duty cycle. Simulation results indicate that the proposed controller outperforms the others method for all type of environmental conditions. doi 10.5829/ijee.2021.12.02.03


INTRODUCTION 1
The necessity of energy is heightening gradually. Nowa-days we mostly use the conventional energy sources like coal, natural gases, gasoline, fossil fuels, oil, nuclear energy etc to meet this increasing demand. But, these non-renewable resources are rapidly diminishing day after day. The rising energy demand and also the alarming depletion rate of the principal energy resources occasion increase the price of natural combustible energy resources. Moreover, the uninterrupted use of fossil fuels has affected drastically the environment diminishing the ecosphere and cumulatively summating to global warming. Hence, we had to think about the renewable energy sources like water, sunlight, wind, tide, biomass, geothermal heat etc. These sources are limitless , sustainable, regenerative and very clean. Out of different kind of renewable energy sources, the sun is an endless source of energy that can easily be converted into other types of energy such as thermal, electrical and chemical [1].
It is the most readily available and prominent source of energy with its huge consistency around the world. Solar energy is clean, non-polluting, incurring no fuel *Corresponding Author Email: drmjamiati@gmail.com (M. Jamiati) costs, needing fiddling maintenance, noiseless and sustainable source of energy with an enhanced service life and eminent reliability. Our focus falls on solar PV systems in this paper. Photovoltaic technology is the science of converting sunlight into electricity [2]. Therefore, this is conditional in many countries putting in place stimulating schemes to help solar energy in the next decades so that investment costs to be reduced [3].
The purpose of this paper is to increase the efficiency of the PV systems through using Maximum Power Point Tracking (MPPT), by which the solar module can generate maximu m amount of power at any time. To obtain the maximu m power, PV system is normally equipped with maximu m power point (MPP) tracker in conjunction with the power converter. Many MPP tracking techniques have been proposed in recent years. Among these methods, hill climbing (HC) [4] and Perturbation and Observation (P&O) [5] are the most extensively used algorithms due to the simplicity and ease of implementation.
HC is the perturbation in the duty cycle of the power converter, whereas P&O method is the perturbation in the operating voltage of the PV array. A major drawback of P&O is that the system oscillates consistently around the MPP, which wastes a considerable amount of power fro m the PV source. Another popular approach is the Incremental Conductance method. This works based on incrementally comparing the ratio of derivative of conductance with the instantaneous conductance. The increment size determines how fast the MPP is tracked. Fast tracking can be achieved with larger increments at the cost of accuracy. Furthermore oscillation around the MPP may still occur [4][5][6][7].

MODELING OF SOLAR CELL
To model a single solar cell, we need a current, a diode and two resistors. As we use only one diode here, the model is known as a single diode model. This cell can generally be modeled by connecting the inverted diode in parallel with the current source. The diode has its own shunt and series resistance. Here the part of the cell including current source and the diode is assumed to be ideal. When the cell is subjected to sunlight, direct current is generated and it varies linearly with incoming solar radiation. Figure 1 shows an electrical circuit for the single diode model of a solar cell [4,5].
From the above circuit, the characteristics equation of single diode model of solar cell can be written as: where, I is Output current of the PV Cell. Iph is Current of the DC Current Source i.e. the Photon generated current. Id is Diode Current. Ish is Current through the Shunt Resistance.
We know the DC current source as well as the photon generated current is actually the short circuit current but the solar irradiation has an effect on this. Thus it can be written in terms of irradiance, nominal irradiance and the short circuit current of the cell. So we can write: where, Ir is Actual Irradiation in Watts per square Meter, Ir0 is Nominal Irradiation in Watts per square Meter and Isc is Short Circuit Current in Amperes. Next we concentrate on the diode current. The diode equation is a non-linear mathematical equation which depends on many important factors. The equation can be written as Equation (3).

Figure 1.
Single-diode model of the theoretical photovoltaic cell [5] (3) where, Is is the reverse saturation or leakage current of the diode, q is the electron charge [1.60217646×10 -19 C], k is the Boltzmann constant [1.3806503×10 -23 J/K], T [K] is the temperature of the p-n junction, and a is the diode ideality constant which is generally assumed as 1.2. Now the voltage across the diode can be written in terms of output voltage & current, series resistance and the ideality factor of the diode. The equation is stated as follows: This time, the value of the reverse saturation current is we can find out with the help of the a few important factors. The expression is as follows: Here Voc is the Open Circuit Voltage of the cell. Thereafter, we focus on the current through the shunt resistance. The expression of this current is very simple and can be written in terms of output voltage and current of the solar cell and the shunt and series resistance. The expression is: So, we can now write the full expression of the output current of the cell using all the sub-equations as follows: Here if we put the constant values of k, q and a as mentioned earlier, the expression can be re-written as: We now express the above equation using MATLAB SIMULINK blocks. All the simulation work in this paper was performed using MATLAB SIMULINK 7.10 with their toolboxes. To study the P-V, V-I and P-I characteristics at variable irradiance through our model, we take the KD 240GH P series module, in which 60 cells are connected in series. Table 1 summarized which gives the datasheet parameters for the module KD 240GH P series at irradiance 1000W/m 2 & Temperature at 25°C [8]. A repeating sequence is taken as a voltage source, temperature and is kept constant at 25°C and irradiance is varied between 100 Watts per square meter to 1000 Watts per square meters by 10 steps.

SIMULINK MODEL OF SOLAR CELL
The MATLAB SIMULINK model of a single solar cell is shown in Figure 2.

CHARACTERISTIC CURVES
We see the effects of varying solar irradiation in the P-V, I-V and P-I curves shown below. In each case we study that with an increase in the irradiation, the parameters of y-axis of all the curves increased. The maximu m power point also increases with an increase in solar irradiation . As the irradiation increases, more sunlight incidents into the solar cell and the electrons are supplied with more  [9] excitation energy and the mobility of electrons is increased. That causes additional amount of power generation for the same value of voltage. Figure 3 illustrates the power generation with respect to voltage and power flux (W/m 2 ) for the PV panel. There are maximu m power generation at certain value of the voltage while increasing the power flux. Figure 4 depicts power with respect to voltage while Figure 5 shows power generation with respect to electrical current.

Trcking
In all the curves shown above we see that initially the value of y-axis parameter increases, but after a certain  In order to we can compare result of our purpose method with result of other methods [10,11], in simulation we used of the MSX-60 PV MODULE at 25 o C, A.M1.5, 1000 w/m 2 . Table 2 summarized the parameter of the PV module.
We know that, partial shading condition significantly changes the characteristics of a PV array. Figure 6 shows a typical partial shading condition. In this example, three shading patterns, i.e. λ=1, λ=0.65, λ=0.5 and λ=0.25 are applied to the PV array. Figure 7 shows the resulting I V and P V curves for the shading pattern demonstrated in Figure 6 for constant λ=1.
It is clearly shown that in shading condition that described in before, if modules have not MPPT system,

Algorithm (GA)
GA has been used for optimizing the parameters of the control system that are complex and difficult to solve by conventional optimization methods. GA maintains a set of candidate solutions called population and repeatedly modifies them. At each step, the GA selects individuals from the current population to be parents and uses them to produce the children for the next generation. Candidate solutions are usually represented as strings of fixed length, called chromosomes. A fitness or objective function is used to reflect the goodness of each member of the population. Given a random initial population, GA operates in cycles called generations, as follows:  Each member of the population is evaluated using a fitness function.  The population undergoes reproduction in a number of iterations. One or more parents are chosen stochastically, but strings with higher fitness values have higher probability of contributing an offspring.  Genetic operators, such as crossover and mutation, are applied to parents to produce offspring.  The offspring are inserted into the population and the process is repeated The computational flow chart of the GA optimization approach followed in the present paper is shown in Figure 8.

Optimization technique
In this paper, in order to receive maximu m power of PV panels, firstly we used GA to find the MPP (find operating point) and then to find optimal angle of panels in during day, proportional with position of sun in sky. The MATLAB/SIMULINK model of the example solar cell shown in Figure 2 is developed using Equations (1) to (8).
The developed MATLAB/SIMULINK model of a PV array with MPPT controller and buck-boost converter is shown in Figure 9. Figure 9 shows the PV system used in this work, in which the simulation of a PV system involving a buckboost DC-DC converter (with a MPPT controller). The PV modules are MSX60 configured in a 4×2 array.
The buck-boost converter is selected due to the availability of wide input window. Moreover, it satisfactorily follows the PV array's MPP at all times, regardless of the cell temperature, the solar insulation, and the connected load [12]. The converter is design in continuous current mode with the followin g specifications: C1 = 470 μF, C2 = 220 μF, L = 1.5 mH, and 20-kHz switching frequency. Three types of environmental conditions are conducted. In the first condition, the PV array receives the uniform insolation of λ=1 ( Figure 6) before it is changes to partially shaded condition. After, a step change of uniform insolation (λ=1) is applied to PV array.
In the second condition starts shadow, the I-V and P-V curves change the shape as the environment changes from uniform insolation to partially shaded condition. Consequently, the operating point shifts from A to B, as shown in Figure 7. In other words, Program started with initial population (initial solution). These solutions consist of purpose amount for variables d and α. d is variable that control operating rat of converter, Thereupon control the operating point. And α is the angle of panel from east toward west. In order to find optimal angle before run the program, we should set the o'clock in input data. In next step should initial solution evaluation to given the fitness of candidate solution. The ob jective function is evaluated for each individual by simulatin g the system dynamic model considering purpose mount for α and d. The objective function is the output power of module. The range of d is between 0.01-0.99 and α is between 0-180 o . Then apply other step of GA operators, consist of selection, crossover and mutation.
In order to preservation best member, Mutation not operate on this member.
Good solutions are selected, and by means of the GA operators, new and better solutions are achieved. This procedure continues until a desired termination criterion is achieved. Although the chances of GA giving a local optimal solution are very few, sometimes getting a suboptimal solution is also possible. While applying GA , a number of parameters are required to be specified. An appropriate choice of these parameters affects the speed of convergence of the algorithm. For different problems, it is possible that the same parameters for GA do not give the best solution, and so these can be changed according to the situation. For the very first execution of the program, a wider solution space can be given and after getting the solution one can shorten the solution space nearer to the values obtained in the previous iteration. Optimization is terminated by the pre specified number of generations. The best individual of the final generation is the solution.
For the third environmental condition, similar to condition 1, the PV array receives the uniform insulation (λ=1).

SIMULATION RESULTS
In order to show the effectiveness of the proposed model of PV system with MPPT simultaneous tuning the controller parameters in the way presented in this paper. To evaluate the performance of the proposed simultaneous design, approach the response with the proposed d compared with the response without MPPT. The response without the MPPT (no control) is shown with solid line with legend N. MPPT (Figure 10), The responses with MPPT (with GA) is shown with legend W. MPPT with dotted line ( Figure  11). It is clear, that the power of panel with MPPT increased.

CONCLUSION
In this paper, a Genetic Algorithm (GA) with the capability of control direct duty cycle is used to track the maximu m power point of PV system. Also this algorith m used to find best angle of modules to receive maximu m power. A PV system, designed in MATLAB Simulin k was used for the validation, in which a dc-dc buck-boost converter was used as a MPP tracker. The performance of proposed controller is compared with conventional HC method. Results reveal that the proposed method totally outperforms that HC method in terms of tracking speed and steady state oscillations.