A neuro-fuzzy approach for tracking maximum power point of photovoltaic solar system

This work presents a hybrid soft-computing methodology approach for intelligent maximum power point tracking (MPPT) techniques of a photovoltaic (PV) system under any expected operating conditions using artificial neural network-fuzzy (neuro-fuzzy). The proposed technique predicts the calculation of the duty cycle ensuring optimal power transfer between the PV generator and the load. The neuro-fuzzy hybrid method combines artificial neural network (ANN) to direct the controller to the region where the MPP is located with its reference voltage estimator and its block of neural order. After that, the fuzzy logic controller (FLC) with rule inference begins to establish the photovoltaic solar system at the MPP. The obtained simulation results using MATLAB/simulink software for the proposed approach compared to ANN and the perturb and observe (P&O), proved that neuro-fuzzy approach fulfilled to extract the optimum power with pertinence, efficiency and precision.


INTRODUCTION
Energy production is a challenge of great importance for the years to come. The energy needs of industrialized societies as well as developing countries are steadily increasing. This production has tripled since the 1960s to the present day. All global energy production comes from fossil sources. The consumption of these sources gives rise to greenhouse gas emissions and therefore an increase in pollution. In addition, the excessive consumption of natural resource stocks reduces the reserves of this type of energy in a dangerous way for future generations. Renewable energies such as wind power, solar energy, biomass energy and hydropower are promising solutions to compete with mass energy sources such as fossil and nuclear energy. Renewable energy means energy from the sun, wind, earth heat, water or biomass. Unlike fossil fuels, renewable energies are energies with unlimited resources. Solar radiation is distributed over the entire surface of the earth; its density is not great and causes no conflict between countries unlike oil. Among these resources, solar energy is considered today as one of the most reliable renewable energies, daily and respectful of the environment the source [1], [2]. Photovoltaic energy has nowadays an increased importance in electrical power applications, since it is considered as an essentially inexhaustible and broadly available energy resource [3].

Photovoltaic solar module
The PV solar module used in this study consists of polycrystalline silicon solar cells electrically. Its main electrical specifications are shown in Table 1.

Simulation model of a PV generator
The mathematical models of the PV generator are defined in the following equations. Figure 2 shows the equivalent circuit of a solar cell using a single diode model due to accuracy for photovoltaic (PV) studies. A solar panel is composed of several photovoltaic cells employing series or parallel or series-parallel external connections. The following equations describe the I-V characteristic of a solar cell [21]: After combination of the equations above, the generalize current voltage equation of a photovoltaic (PV) model is: Where: ∆T=T-T n : The deviation from standard temperature.

Influence of temperature and irradiation on PV operating
For various values of the irradiation G, and cells' temperature T, the I-V characteristics of the analysed PV panel are shown respectively in Figure 3 and   Depending on weather conditions, a PV generator connected to a load can operate in a large margin of current and voltage [22]. Figure 3 and Figure 4 show that the open circuit voltage Vco is increasing with the irradiation and decreasing slightly as the cell temperature increases. On the one hand, the short circuit current Isc is linearly depending on the ambient irradiation in direct proportion, while the open circuit voltage decrease slightly as the cell temperature increases. Therefore, the maximum power that could be generated by a PV system is slightly depending on the temperature and irradiation variations: the maximum power increases as the irradiation increases and vice versa, on the other hand a PV generator performs better for low temperature than raised one [12].

The changes on temperature and irradiation
It is known that temperature may be high despite the very little presence of any irradiation clouds. It is also known that the temperature change and the irradiation disposed relatively, the irradiation increases, more heat traditionally increased, and vice versa.

DC/DC boost converter
A DC/DC converter the transfer of maximum energy from photovoltaic panel PV to load. A DC/DC converter is the interface that regulates the adaptation between the photovoltaic PV panel and the load to ensure our load closer to the MPP. Figure 5 shows the electrical circuit of the DC-DC converter Boost type. The Boost type converter is a voltage booster. In this converter, the value of the output voltage is always greater than that of the input. The inductance currently stores energy. When the switch is off (the ideal switch is open), the load receives this energy in addition to the GPV energy. In this type of converter, if we consider that Vin is the voltage of the GPV, V out is the voltage of the load and D is the duty cycle, then the relationship between these voltages and the load results in the (7):

MPPT USING (P&O) METHOD
The principle of this type of control is based on the disturbance of the value of the voltage of the GPV and the observation of the behaviour of the resulting power [23]. Figure 6 shows the algorithm associated with a P&O command. We note that we need two sensors to measure the power of the GPV as a function of time. Today, the P&O algorithm is widely used because of its simplicity and ease of implementation. In another sense, it has some disadvantages. For example, according to the characteristic curve P-V of PV panel we can never reach ΔP = 0. Each time V increases or decreases the power will be changed which makes the implementation of the step Ppv k+1 =Ppv k in the algorithm without profit. This instability in the value of P will lead to instability around the optimal value of the power. However, this instability can be reduced by minimizing the increment value of the search algorithm.

NEURO-FUZZY MAXIMUM POWER POINT APPROACH
The Neuro-Fuzzy approach consists of two stages; the first one is composed of multi-layered feed forwarded artificial neural network. The architecture composed of three layers: inputs, hidden and output layers while the second one is a fuzzy-rule-based. Figure 7 show the proposed structure of the neuro-fuzzy approach. The hybrid model is composed of a neural model and a fuzzy logic controller.
The role of the neural model is to search for the region where MPP is located and the fuzzy controller helps to find and establish the MPP in that region. This approach consists the same MPPT Fuzzy logic controller, but we will decrease the pace of the duty cycle because we need a high degree of precision, on the one hand. On the other hand, the role of the neural network is to direct the controller to the region where the MPP is located. Therefore, we must first build the neural network that is preparing a learning base and learn the network, then implement this neural network in the control circuit, followed by fuzzy logic controller.

The MPPT controller with ANN controller
The new technique, which chooses the pursuit of the maximum power point, is the neural method. We will apply it to approximate the output, which is the voltage that corresponds to this power, as a function of irradiation changes, and temperature, is the tracking of the variation of the maximum power point. Where our system needs to evolve, quickly and efficiently.

Mathematical modelling of an artificial neuron
The mathematical model of an artificial neuron is illustrated in Figure 8. A neuron consists essentially of an integrator that performs the weighted sum of its inputs. The result n of this sum is then transformed by a transfer function f, which produces the output D of the neuron. The R inputs of the neurons correspond to the vector P = [ p 1 p 2 ……p R ] T , while W= [W 1,1 W 1,2 .... W 1,R ] T , represents the vector of the weights of the neuron. The output n of the integrator is given by the following equation [15], [24]: This can also be written in matrix form: This output corresponds to a weighted sum of weights and inputs minus what is called the bias b of the neuron. The result n of the weighted sum is called the activation level of the neuron. The bias b is also called the activation threshold of the neuron. When the activation level reaches or exceeds the threshold b, then the argument of becomes positive (or zero). Otherwise, it is negative [15], [24]. There is an obvious analogy with biological neurons as shown in Table 2.
Under MATLAB/simulink, the role of the neural network is to direct the controller to the region where the MPP is located. Thus, it is necessary to build the neural network, i.e. to prepare a learning base and to learn the network, and then implement this neural network in the control circuit. The activation function makes it possible to define the internal state of the neuron according to its total input. There are several types of activation functions [25]. The activation function used in our neural network, which is a neural network multilayer is the sigmoid function for the hidden layer and the linear function for the output layer.

Multilayer network (multilayer perceptron MLP)
An MLP is made up of several layers: an input layer, one or more hidden or intermediate layers, and an output layer. Two successive layers are fully connected, and all connections are unidirectional. In such a network, there are no connections between two neurons of the same layer. An MLP has therefore: 1) An input layer that receives the data to be processed; 2) One or more intermediate or hidden layers performing the specific processing of the network; 3) An output layer that presents the network responses. The purpose of learning is to estimate network parameters by minimizing an error function. Learning is supervised. The error function thus represents the distance that exists between the calculated response of the network and its desired response. The learning consists in applying to the network pairs of inputs and outputs (desired outputs), and then applying a learning algorithm to modify the various parameters of the network. The learning algorithm used for this type of network is the gradient back propagation (GBP) [23].
The structure of the neural network used in the control system. This network has an input layer containing two inputs (Irradiation and Temperature), a hidden layer of 9 neurons and an output layer containing a single neuron (the voltage V).
At the end of the learning phase, we obtain the final neural network implementation, which gives us a value very close to the exact value of the MPP. It admits as inputs the irradiation and temperature and as output, the voltage close to the MPP [26].

The MPPT Controller with Fuzzy Logic
A Fuzzy Logic Control (FLC) is used to work as an MPPT controller that tracks the optimal operating point of a PV panel. Fuzzy Logic Control is one of the most used techniques in different engineering challenges of its multi-rule-based characteristics [27]. Fuzzy logic control has a simple and clear procedure because exact mathematical modelling and technical quantities of a system are not required for this controller [28]. The fuzzy controller consists of three blocks: the first block fuzzification which numerical input variables (Vpv, Ppv) are converted into linguistic variable (E, DE) based on a membership function. The second block is devoted to inference rules, while the last block is the defuzzification for returning to the real domain (D). This last operation uses the centre of mass to determine the value of the output [29]. Figure  9 shows the basic structure of the used MPPT Fuzzy controller [29].
Where, Ppv(k) is the power delivered by PV panel and Vpv(k) is the terminal voltage of the module at sample k.
Fuzzification: The resulting linguistic variables have been used for the MPPT fuzzy controller: PB (positive big), PS (positive small), ZE (zero), NS (negative small) and NB (negative big) for expressing the reel inputs and output variables. Figure 10a, Figure 10b and Figure 11 illustrate the membership functions of five fuzzy subsets for the input's variables E and DE and the output variable D.  Table 3 shows the rules table of the fuzzy controller where all inputs in the matrix are [E, DE] [30]. Defuzzification: The process of defuzzification converts the inferred fuzzy control action into a numerical value at the output (D) by making the combination of the outputs resulting from each rule. In this paper the centre of gravity defuzzifier, which is the most common one, is adopted. In the Figure 12 is shown the surface output D= f (E, DE) of the MPPT controller.  Figure 1 represent the general diagram of the whole system, which composed of the PV array, block of DC/DC Boost converter, block of the novel neuro-fuzzy method and the resistive load. In the present study, a hybrid model, neuro-fuzzy, looking for to extract the maximum power for PV solar system in minimum time and a high degree of precision. The role of MPPT fuzzy logic controller is to choose the corresponding area region, which finds the MPP with decreasing the pace of the duty cycle. Then the neural network is to direct the controller to the region where the MPP is located. Several performance criteria are reported in the ANN literature as: the response time, learning base and learn the network. Thereby, the estimation performances of the neuro-fuzzy approach and the single ANN will be evaluated only in term of estimation time for extract the maximum power of PV solar system. The same thing was compared with the conventional algorithm (P&O) regarding to the maximum power extracted under MATLAB/simulink. The theoretical and simulation results acquired with Neuro-Fuzzy, artificial neural network Controller and P&O, in checking the MPP of the analysed PV module, for various values of solar irradiation G and cells' temperature T are given in Table 4. Therefore, this table confirms that the neuro-fuzzy gives a quick response with stability around MPP than the conventional ANN and the P&O. It also extracts the maximum power in short time with efficiency and pertinence. Nevertheless, this table expresses the most effort method between the conventional ANN and classical P&O methods, these methods are limited around a small value especially of the maximum power with long time to response the P&O but the proposed Neuro-Fuzzy method overcome these limitations through a better definition of the model complexity based on the fuzzy rules. There are several performance criteria in the literature of the ANN method as mentioned before. In this study, after evaluated methods only in term of estimation. We have based on the calculation of the error between the measured values and the theoretical values of each method treated in this article P&O, ANN and neuro-fuzzy approach. This calculation reveals the minimal error of the neuro-fuzzy approach compared to the other methods P&O and ANN, on the one hand. On the other hand, we will calculate the efficiency to have the performance, speed and ability to respond to the PV system in a relevant and effective way.  Figure 13 and Figure 14 respectively shows the PV output Power for different considered control at STC weather conditions and low weather conditions. At STC weather conditions mean under the solar irradiation G = 1000 W/m2 and PV cells' temperature TC = 25°C, we can see that the proposed hybrid model Neuro-Fuzzy approach achieved the most accurate estimation comparing to the ANN and P&O methods. At time 0.48s, the proposed hybrid model extracts the maximum power of the system equal Pout=108W, while the ANN method extract Pout=100,4W and P&O extract Pout=100,3W with oscillation around MPP. At low conditions, mean under the solar irradiation G = 600 W/m2 and PV cells' temperature TC = 15°C, the simulation results that the Neuro-Fuzzy hybrid model gives the best results of the maximum power at time 0.5s, although during evolution, the two MPPT methods are beginning before the hybrid model Neuro-Fuzzy. However, the last one contributes the best value of Power in short time with long steady regime without oscillation around the MPP. Figure 15 presents the simulation output of the PV system (extracted power) during variation weather conditions using the Neuro-Fuzzy approach and the single ANN compared to conventional MPPT method P&O. The Neuro-Fuzzy MPPT methodology accomplished better performances then the single ANN or the P&O algorithms that can fail to track the MPP or oscillates around it under rapidly changing climatic conditions. The performance of the MPPT can be detected according to the efficiency [31]- [34]. The efficiency calculated by the following (13): The efficiency of P&O, ANN and Neuro-Fuzzy controllers shows that the Neuro-Fuzzy controller can generate up to 99% of the actual maximum power compared to the ANN controller can generate up to 93% and P&O can generate up to 92% of it [14] as shown in Figure 16. In fact, the proposed Neuro-Fuzzy approach-based method attained the highest power efficiency with 6% of extra-generated power comparing to the single ANN and more than 3% to the P&O algorithm because of its oscillations around the MPP.

SIMULATION RESULTS AND DISCUSSION
To develop the new Neuro-Fuzzy controller approach, we relied on several articles in the literature among them [12], [30]. A kind of comparison in state of the art between our approach and two references [12], [30] in tabular format. In Table 5, a summary of the power efficiency between our approach and the reference [30], which is based on Toolbox ANFIS under MATLAB/simulink, in one hand. In the other hand, summarizes the error estimate between our approach and the reference [12]. This table shows that the power efficiency of the ANFIS method reaches 100% under the STC conditions and our approach reaches a value up to 99%. Under the variations of atmospheric conditions, the power efficiency of our approach always remains up to 99%, which shows the relevance of our neuro-fuzzy approach compared to the ANFIS method, which is already predefined in the MATLAB/simulink toolbox. After that, it illustrates that our new approach has higher percentages of errors for P&O or ANN methods, compared to the comparative method. In other words, the percentage of the error is large in our approach that the error is minimal compared to the other reference.  Figure 16. The efficiency of P&O, ANN and Neuro-Fuzzy controllers

CONCLUSION
In this paper, a new MPPT methodology was applied to photovoltaic system based on a proposed Neuro-Fuzzy hybrid model. The whole system was simulated under MATLAB/simulink environment. In this study, we started by modelling the nonlinear system, which is the photovoltaic solar module, was demonstrated using the single-diode electrical model and simulated in different weather conditions. After that, learning about DC/DC converter has for role adapting the duty cycle to extract the maximum power, and transfer this energy from the photovoltaic solar to the load. Then, the most important part is the hybrid model: Neuro-Fuzzy approach. The developed Neuro-Fuzzy approach consists of two stages; the first one is composed of Inputs, one hidden layer with 9 neurons and one output feed forwarded ANN and the second one is a fuzzy-rule-based simulating under MATLAB/simulink. The proposed neuro-fuzzy approach showed the ability to faithfully emulate the dynamic and nonlinear behaviour of a photovoltaic generator under a large wide of climatic conditions. The completely photovoltaic solar system performance was tested with constant and several rapid irradiation and temperature variations. The accuracy of our proposed model Neuro-fuzzy approach can generate up to 99% of the actual maximum power, which is more than the other algorithm such as P&O and ANN.
Therefore, the simulation results proved that the proposed Neuro-Fuzzy approach of the system performances, in terms of efficiency of power, precision and speed, was not degraded, as the MPPT dispositive was capable to track the maximum power point an optimal operating condition under any rapid changing meteoric conditions.