Modeling and Control Maximum Power Point Tracking of an Autonomous Photovoltaic System Using Artificial Intelligence

Despite investigative efforts seen in the literature, the maximum power point tracking remains again a crucial problem in photovoltaic system (PV) connected to the power grid. In this paper, a new maximum power point tracking technique which is our contribution to the resolution of this problem is treated. We proposed a hybrid controller of maximum power point tracking based on artificial neural networks. This hybrid controller is composed of two neural networks. The first network has two inputs and two outputs: the inputs are solar irradiation and ambient temperature and the outputs are the reference output voltage and current corresponding at the maximum power point. The second network has two inputs and one output: the inputs use the outputs of the first network and the output will be the periodic cycle which controls the DC/DC converter. The training step of neural networks requires two modes: the offline mode and the online mode. The data necessary for the training are collected from a very large number of real- time measurements of the PV module. The performance of the proposed method is analyzed under different operating conditions using the Matlab/Simulink simulation tool. A comparative study between the proposed method and the perturbation and observation approach was presented.

for achieving the efficiency demanded involve the use of advanced semiconductor materials, intelligent control systems and PV technologies without loss of power. As shown in Figure 1, better monitoring, forecasting and communication technologies will also be crucial for the siting of future grid-connected PV systems.
The downside to solar power generation is that the power generation is not constant throughout the day, as it changes with climatic conditions [1]. In addition, the conversion efficiency of solar energy to electric energy is very low which is only in the order of 9% to 17% in low irradiation regions [2]. Despite its simple shape, the operating point oscillates around the MPP (Maximum Power Point) which causes energy loss and long tracking time. In addition, depending on variations in climatic conditions (solar irradiation and ambient temperature), the operating point moves on another curve [3]. This leads to failures in MPP monitoring, as for example, the algorithm is unable to identify the source of disturbance from voltage variation or weather conditions. The perturbation and observation (P&O) technique also requires a control process system (such as software), which makes it challenging to integrate it into the PV panel [4]. An incremental conductance (InC) MPPT algorithm improving the P&O technique is presented in [5]. A modification of this InC algorithm, employing a dynamic adaptation of the number of steps during the tracking process is proposed [6]. In [7], it has demonstrated through experimental tests that the P&O and InC methods have similar performance under static and dynamic conditions. The voltage-constant and current-constant methods also require a voltage and current sensor respectively for their implementation, but the periodic interruption of the operation of the PV source to measure the no-load voltage and the short-circuit current results loss of energy [8]. Using artificial intelligence techniques, the accuracy of predicting voltage and current at the PPM is strongly affected by the accuracy of estimating the temperature of PV modules, which affects the values of Vt and Is [9]. The implementation of digital techniques is complex and given the complexity of the calculations of the voltage or current MPP, a microcontroller or a DSP unit is necessary for the realization of such an MPPT system. In addition, the response time of the MPP tracking algorithm is relatively low [10]. To avoid the use of a derivative to perform the MPPT process, is affected by the accuracy of the measurements of the correlation function c(t) [11] [12]. The Maximum Seek Control (ESC) method which has a self-optimization strategy, operates on a similar basic principle that RCC MPPT, it has the disadvantage that for its realization in the PV power processing system, the development of a relatively complex control circuit is necessary [13] [14].
Despite investigative efforts seen in the literature the maximum power point tracking still remains a crucial problem in the grid connected PV system.
In this work, we propose a hybrid MPPT controller based on the artificial neural network to improve the failures mentioned above. The hybrid MPPT is composed of two neural networks, the first network has two inputs and two outputs; inputs are solar irradiation and ambient temperature and outputs are reference output voltage and current. The second network has two inputs and one output; the inputs use the outputs of the first network and the output will be the periodic cycle which controls the DC/DC converter ( Figure 14). The data necessary for the generation of the RNA (Artificial Neuron Network) model are obtained from the series of measurements. The networks are developed in two modes: the offline mode to obtain the optimal structure, activation function and learning algorithm of neural networks and the online mode where these optimal RNA MPPT controllers are used in the PV system. The proposed MPPT neural network controller is tested and validated using the Matlab/Simulink modeling and simulation tool under different conditions of climatic variation, which is directly equipped with an Artificial Neural Networks toolbox.

Modeling of a Photovoltaic Module under Matlab/Simulink
The basic structure of a PV cell can be modeled as basic electrical components [15]. Figure 2 shows the PN semiconductor junction and the different components that make up a PV cell. The photon-electron circulation process can be  The current source and the diode are an ideal model of a PV cell, but in reality, there are additional parasitic components. The PN junction is mounted in parallel with a parallel capacitance Cp and a parallel resistor Rsh (also called shunt resistor), whereas the wires of conduct connected to the PV cell are associated with a series resistor Rs, and inductance in series Ls. These parasitic components are often ignored when a simple representation of a PV cell or panel is necessary, but they must be taken into account when precise modeling is recommended.
The simple PV model can be implemented under Matlab/Simulink as illustrated in Figure 3, where the inputs are solar irradiation G, ambient temperature T and voltage of PV (Vin). The outputs are the current intensity of PV (I PV ) and the power (P PV ). We did a simulation under Matlab/Simulink. The curve of the intensity of the PV module depending on the voltage of the PV module as well as the curve of the power of the PV module as a function of the voltage of the PV module is shown in Figure 4 and Figure 5 respectively.
The star indicates the maximum power point, where the PV module will produce its maximum power. For a voltage lower than that of the MPP, the current is relatively constant when the voltage varies in the same way as a current source. For a voltage higher than that of the MPP, the voltage is relatively constant when the current varies as a voltage source. The open circuit voltage (V OC ) is the PV voltage when the current is zero (0 A) and the short-circuit current (I SC ) is the current which corresponds to a zero voltage.
The current-voltage and power-voltage curves in Figure 4 and Figure 5 are under a specific condition of solar irradiation and of ambient temperature.
During the day, the two curves can sometimes vary gradually (minutes to hours) and sometimes very quickly (seconds), due to the passages of clouds.
As the irradiation and the ambient temperature vary, the curve of I -V characteristic also varies as shown in Figure 6. The irradiation is directly proportional      [16].
to the currents of the characteristic. When the irradiation increases the short-circuit current and the current of the maximum power point also increases; the temperature is inversely proportional to the voltages of the characteristic. When the temperature increases, the open circuit voltage and the voltage at the maximum power point decrease. According to these trends, a PV cell will produce more energy when the light intensity is high and the temperature is low. However, these kinds of environmental conditions are not common, when a greater light intensity hits an object its temperature tends to increase at the same time.

Maximum Power Point Tracking (MPPT) Methods Operating under the Conditions of Varying Mission Profiles (Solar Irradiation and Ambient Temperature)
Due to short and long variations in solar irradiation and ambient temperature, the right part of the MPP as shown in Figure 7 [16].
The main advantages of these methods are that 1) they are generic, they are suitable for all PV modules, 2) they do not ask for PV information, 3) they work well under most conditions and 4) they are simple to perform in a controller digital with less computation required. However, these methods have some  These failures have inspired many publications that aim to overcome these problems. The advanced MPPT methods most widely used in the literature are based on fuzzy logic [17], neural networks [18], genetic algorithms and particle swarm optimization [19], etc.

MPPT Perturbation and Observation Technique (P&O)
The perturbation and observation method (P&O MPPT) is based on the property, that the derivative of the power-voltage characteristic of the PV module/array is positive to the left of the MPP, negative to the right and zero at the MPP point [18].
where k and k − 1 are the consecutive times, α > 0 is a constant determining the The output voltage of the PV module/array is regulated to the desired value  [21] is presented in Figure 8 below. The process is repeated until the gradient value pv pv P V ∂ ∂ is less than the preset threshold value, indicating that the convergence of the MPP is almost achieved with the desired precision.
A methodology for the design of the control unit such as the operating processes of P&O MPPT with the optimal values of the step of progression and the period of disturbance is proposed in [22]. An algorithm to dynamically adapt the number of perturbations according to the conditions of solar irradiation is proposed in [23] to increase the response step of the P&O algorithm and reduce

Techniques Based on MPPT Artificial Intelligence
Artificial intelligence techniques such as neural network and fuzzy logic are also well applied to perform the MPPT process. An artificial neural network is a computer model inspired by the biological neural network. In such a model, a neuron is a processing unit that first linearly weighs the inputs, then works out the sum with a non-linear function, called an activation function (AF), and finally sends the results to the following neurons Figure 9. The model of a common neuron is given by Equation (5), where Z is the argument of AF.   A large number of training processes are available, but it is the retro-propagation method that is the best known and the most used. The training of the algorithm consists in minimizing the total error E defined by the following equation [24]: where n O is the nth measurement read at the output of the network and n t is the nth target (the estimated output).
So, each input/output pair constitutes a sample. The back-propagation algorithm calculates the error E and distributes the return of the output to the input neurons through the hidden neurons using the equation [24]: where w is the weight between two neurons, training. This number is calculated by the following empirical formula [24]: where h N is the number of neurons, 1 N is the number of input neurons, 0 N is the number of output neurons, and E N is the number samples of training. In order to ensure network accuracy, the training sample is continuously adjusted after each training by passing all test data to the trained ANN model and the results recorded. Then it is compared to the measurements. In case of convergence, the performance of the network is reproduced by calculating the performance factor. Data validation is used as an additional check on model performance. If the performance of the network is quite correct on the sample and validation test, we can consider that the network is good enough to generate a fair periodic cycle.

Comparison of MPPT Techniques for Varying Conditions of Solar Irradiation
A comparison of the functional characteristics of the above MPPT methods is presented in The efficiency is further reduced with the precision of the knowledge of the functional parameters of the PV source, which is necessary for their implementation. In digital MPPT optimization algorithms, a scanning process is periodically repeated to detect possible changes in the position of the MPP, which results in a reduction in its efficiency due to the losses of energy generated until the convergence at MPP point, is performed. Numerical algorithms do not require specific knowledge of the system for their applications, but the complexity of their implementations is higher than for those of P&O and InC methods. The robustness of these numerical techniques is affected by external disturbances, so they are not able to consider the estimation errors, which arise from the decisions made during each iteration, until a new scanning process is carried out. The robustness of the RCC technique can easily be affected by the impact of external variations on the computational accuracy of the correlation function. In addition, a suitable consistent design of the power converter and MPPT controller is required for the implementation of our RCC MPPT method, thus requiring the availability of system knowledge. The complexity of the control circuit of

MPPT Technique Based on Artificial Neuron Network
The architecture of the adapted neural network consists of three layers. The input layers made up of two neurons like we have two inputs (solar irradiation and ambient temperature). The hidden layers, including n neurons; this number is selected following the execution of rules of thumb starting with a large number of neurons and eliminating unnecessary ones provided that a stable network and precise output are sought. The output layer contains a neuron that corresponds to the optimal periodic cycle. First, measurements of solar irradiation and ambient temperature are fed into an artificial neural network (ANN) and the corresponding optimum value of the operating cycle (periodic cycle) of the DC/DC converter is estimated, a structure is presented (see Figure 10) [22]. In order to obtain accurate results, the ANN should be trained using prior quantitative measurements in real-time operation in the MPPT tracker unit, which is a disadvantage.
The values of the connection weights and the ANN thresholds are selected randomly at the start of the training process and then during the training they are set in order to minimize the difference between the estimated and formed data.
An ANN is a massively distributed parallel processor that has a natural tendency to store experimental knowledge and make it available for use. The power of RNAs in the identification and development system of adaptive controllers makes them well suited for PV system applications such as PV module MPPT maximum power point tracking. A non-recurring multilayer network has been developed to calculate the optimal DC/DC periodic cycle considering variations in solar irradiation and ambient temperature.

Hybrid Model of Artificial Neuron Network
Based on the analysis of Table 1, we proposed to hybridize the different techniques in order to have a robust MPP tracking approach to external disturbances. We first use a set of solar irradiation and ambient temperature samples or data from the PV module datasheet to train the neural networks. We used data over the period of one year collected from renewable energy agency of Mali.
This database included the irradiation, temperature, voltage and current values of PV modules and we calculated the corresponding periodic cycles. The measurements were taken hourly for a year, a sample number of 8760 used for training our neural networks.
The formation of the networks follows the following steps: the first step consists of injecting the data into the networks, then calculating the objective functions (e.g., periodic cycle). If the best solution is reached, another technique will be used to control the conversion system in order to pursue the point of maximum power. This technique can be either, the perturbation and observation method, conduction by incrementation, fuzzy logic or artificial neural network.
In our study case we used the artificial neural network method. Figure 11 illustrates the structure of our proposed approach.

Training of Neural Networks
In this work, the backpropagation ANN composed of three hidden layers is used with logsig activation functions. This optimal number of the hidden layer is obtained on a heuristic basis so that the accuracy of the prediction is acceptable. As mentioned earlier, training neural networks requires two modes: offline mode and online mode. Figure 11. Structure of our proposed approach. The strength of ANNs in system identification and adaptive controller development makes them well suited for PV system applications such as maximum power point tracking. In engineering applications, a multi-layered perceptron network formed by the backpropagation method is the most widely used technique.
A non-recurring multilayer network has been developed in order to estimate the optimum voltage and current at the maximum power point (MPP) given the variation in irradiation and ambient temperature.
The architecture of the neural network adopted is made up of three layers.
Input layers contain two neurons because they have two inputs (solar radiation and ambient temperature). The hidden layer consists of ten neurons; this number is selected following the execution of rules of thumb starting with a high number of neurons and eliminating those which are unnecessary provided network stability and output precision are achieved.
The output layer contains two neurons which correspond to the optimum voltage and current corresponding to the MPP. Figure 12 illustrates the architecture of this network. The training is done offline using the Matlab Toolbox and the MPPT controller offered in SIMULINK is shown in Figure 13.
The 8760 data collected from Mali's renewable energy agency were used for the training of the artificial neural networks. These measurements include solar irradiation and ambient temperature, which are taken from sunrise to sunset.
The one-year database is used for the formation of two networks.
To ensure network accuracy, the network is continuously adjusted after each training by passing the test data set to the trained ANN model and recording the    G, T). The input variables of the second neural network are the optimum voltage and current estimated by the ANN model corresponding to a given solar radiation and to operating cell temperature conditions. The output variable is the corresponding duty cycle. Data for the inputs are collected from the same measurements as the first ANN model. The database is used to train the network and the others are used to verify the data. The database will be randomly divided up in three kings of samples: data of training, data of validation and data of testing. Data of training are presented to the network during training and the network adjusted according to its error. Data of validation are used to measure network generalization halt training when generalization stops improving. Data of testing have no effect on training and so provide an independent measure of network performance during and after training. Usually, we set aside samples for validation at 15%, 15% for testing and 70% for training. So, 6132 samples were used to train networks, 1314 samples to validation and 1314 to testing.
Then these networks formed in offline mode are used in line mode (see Figure 14) in order to continue the MPP. The proposed hybrid neural network MPPT controller is tested and validated using the Matlab/Simulink modeling and simulation tool under different conditions. The Simulink model consisting of an MSX-60 module, a DC/DC converter driven by our hybrid model of neural networks and a load is shown in Figure 14.

Simulation and Results
The MATLAB/Simulink simulation tool is used for the complete simulation of the model produced. The MSX-60 PV module with the characteristic shown in   The simulation is made on the conditions of variation of irradiation and at ambient temperature. Figure 15 and Figure 16 show the results obtained: We can clearly see in Figure 15 among the two algorithms, that the algorithm of the hybrid system of neural networks gives values closer to the theoretical values and more precise. We also observe that the response time of RNA-hybrid is shorter than that of the perturbation and P&O observation. In addition, the

Conclusions
In the first part, we presented a study on the different maximum power point tracking methods carried out in the literature. We then highlighted the different limits of these techniques through a comparative study. In this work, the approach of maximum power point tracking based on hybrid neural networks was presented, as our contribution. The simulation is made on the conditions of variation of irradiation and ambient temperature. Figure 15 and Figure 16 illustrate the different results, we can clearly see in Figure 16 that among the two algorithms, the hybrid neural network system algorithm gives values closer to the theoretical values and more precise. We also find that the response time of RNA-hybrid is shorter than the Perturbation and observation P&O. In addition, the proposed hybrid algorithm tracks the maximum power point more quickly during different conditions variations. The quality of the output power of the PV module for the ANN-hybrid approach exhibits very good performance in the event of a sudden change in solar irradiation in terms of: response time and overshoot ( Figure 16). In addition, the P&O technique is more dependent on temperature than the ANN-hybrid technique (Figure 16(a) (zone 1)).
The results of this hybrid approach of neural networks are better compared to the classical method of perturbation and observation P&O in terms of response time, overshoots and rapid stabilization around the MPP point during sudden changes in solar irradiation and ambient temperature.
Thanks to more efficient conversion systems which aim to maximize the production of PV modules, hybrid photovoltaic systems coupled to the electricity grid are becoming more and more interesting but the management of the pro-