Maximum power point tracking of the solar power plants in shadow mode through artificial neural network
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Abstract
The use of solar cells despite being free of contamination and unlimited in terms of the amount of energy is considered as a costly way to generate energy. Two main factors may be enumerated as follows. First of all, the amount of sunlight and ambient temperature affected the amount of energy received from sunlight by solar panels, as long as the amount of sunlight changes overnight in line with changing weather conditions and the second one is the low efficiency of the energy conversion. The main reason for the low electrical efficiency is the nonlinear variation of the output voltage and current along with the change of the amount of radiation, the change of the temperature of the operating environment and the change of the electric charge, respectively. To address this concern, the maximum point of the photovoltaic system can be tracked through an appropriate algorithm and pushes the system point to the optimal point. In a word, the key goal of the investigation presented here is to provide an approach that in the high speed and precision of convergence to the maximum power point is well considered. So far, a large number of available methods have been used to increase the efficiency of solar cells. Some of these are associated with problems in the tracking process or they respond slowly. It should be noted that a set of them are depended on the types and structures of solar cells and also their implementation is very complex and costly. Therefore, this study has focused on intelligencebased techniques such as artificial neural networks to solve all the problems mentioned. The investigated outcomes verify the effectiveness of the approach performance proposed.
Keywords
Maximum Power point tracking Solar cells Photovoltaic system Artificial neural networksIntroduction

High cost and very low efficiency (about 9–16%);

Continuous changes in the amount of power produced by atmospheric conditions (the temperature and the radiation).
Many works have been done in the field of modeling and controlling PV cells. The study of maximum power point tracking techniques to use in the partial shadow conditions (PSC) is part of these works. The PSC conditions often occur in large PV power generation systems. It causes loss of system power output, the effects of hot spots, and safety and reliability problems. As long as the PSC occurs, the power–voltage characteristic curve shows several peak value, because this curve represents a general maximum power point and several local maximum power points. Regarding the materials presented in [5], it contains various information from the general maximum power point tracking (MPPT) algorithms and the appropriate hardware design for the PSC. Based on the electrical characteristics, the PV cell modeled in the study is equivalent to a diode. This model includes an current source \( I_{\text{S}} \), a diode current \( I_{\text{d}} \), a parallel equivalent resistance \( R_{\text{P}} \), and an equivalent series resistance \( R_{\text{S}} \). The output current of the PV module, \( I_{\text{PV}} \), is different between the current generated by the light \( I_{\text{S}} \) and the diode current \( I_{\text{d}} \). That research includes several algorithms and hardware architectures related to solving the PSC problems that collects, classifies and compares the new MPPT techniques from a variety of references. Finally, the MATLAB software has been widely used to simulate the five common MPPT algorithms and detect its tracking performance. According to the simulation results, agent systembased MPPT methods can still be improved in terms of accuracy of tracking.
In Ref. [6], analysis and enhancement of the photovoltaic cell efficiency by the MPPT incremental conductance method under nonlinear loading conditions has been investigated. This research presents experimental tests for types of energy efficiency obtained from a photovoltaic unit under nonlinear loading in combination with the MPPT incremental conductance algorithm. The focus of that study was to evaluate the photovoltaic panel under nonlinear load conditions using an experimental setup of a photovoltaic array connected to a DC–AC converter and KVA inverter that produced a nonlinear load. In nonlinear loading conditions, both the simulation and the experiment showed that the MPPT method does not reach the maximum power point due to the waves in the current and eventually leads to a reduction in productivity. In that study, the panel current is applied as a function of the load apparent resistance in the MPPT algorithm to eliminate the power change by varying the apparent resistance of the load and providing the voltage under the nonlinear conditions. This system was simulated using the Simulink MATLAB software for nonlinear loads. A TMDSSOLAREXPKIT was used to control the MPPT. In the second case, the inverter was connected to a singlephase network. When a voltage increase occurs in the network, photovoltaic power falls. This power reduction is reduced using the proposed MPPT method.
In Ref. [7], a review of different methods of tracing the maximum power point in photovoltaic systems has been made. The PV power in electrical power generation is constantly increasing. The MPPT tracking in the PV systems presents an important work and a challenge issue. In the MPPT method, the DC–DC converter is set to be the maximum power obtained from the PV system. In that study, the existing MPPT strategies such as classical one (including perturb and observe, incremental conductance, current sweep and constant voltage method) and the modern MPPT methods (including the MPPTbased artificial intelligence network ANN, the MPPTbased fuzzy controller FLC, the MPPTbased metaheuristic algorithms).
In Ref. [8], the methods of maximum power point tracking of the PV system for a uniform sunshine and partial shadowing conditions are investigated. For this purpose, it examines the most advanced MPPT methods in the PV power system. The main methods to be examined are: observation and tracking, incremental conductance and hill climbing. In addition, adaptive variation of these methods is considered. Furthermore, the most recent MPPT techniques using soft computing methods such as fuzzy logic control, artificial neural networks and evolutionary algorithms are included in that study. That research also provides a detailed operation for the MPPT in the uniform sunshine process and its focus is on the application of the above methods in partial shading conditions.
In Ref. [9], the MPPT control scheme is presented with the help of intelligent neural network algorithm based on a inverter controlled by hysteresis current for photovoltaic systems. These days, the photovoltaic panel is one of the most important sources of renewable energy. This panel can use DC power directly in the related applications. In the daily life, it generally works with AC loads. The proposed inverter in that study has a robust performance and easy operation capability. The controlled inverter with fixedbanded hysteresis has been determined and the load variations with the THD output current are set to be less than 5%. The inverter is developed by the threelevel technique. The MPPT is designed through the artificial neural network. In that study, the feeding of AC systems by solar power is analyzed in isolation mode and the results are obtained. The results indicate that the artificial neural network method has very satisfactory results with an efficiency of 99%.
In Ref. [10], the original and accurate simulation of the photovoltaic system is proposed based on the sevenparametric model. The output characteristics of the photovoltaic array are highly nonlinear. Therefore, the study and analysis of the performance of the PV system in the changing environmental conditions requires an efficient and accurate model for the PV. The proposed simulator can produce accurate specifications of the output of the PV system under different operating conditions. Also, this simulator is flexible enough and can simulate different combinations of the PV panels with parallel/serial connections. The power of the proposed simulator is shown under the conditions of a partial shadow. Moreover, the performance of the developed simulator has been confirmed by connecting it to the actual power electronic converter and the maximum power point controller. The proposed PV simulator should facilitate different aspects of the design of the PV systems and be very useful in assessing the behavior of newly developed controllers before their practical implementation.
In this study, first, the problem caused due to the presence of several local maximum points on the multidimensional array P–I characteristic curve is explained. The main problem investigated is designing a new method for the performance of two arrays with series connection at their maximum point. In this study, a new method provided to maximize power is presented in two steps, which, by ignoring local maxima, if any, the maximum location is determined. The first step includes a search algorithm that determines the location of approximate performance point near the general maximum power point and uses it as the starting point of the second stage. The first step is repeated if the temperature changes or radiation of the PV array is increased by 30%, which is obtained by trial and error. The second step can be any maximum tracking method. In this study, P and O and RCC methods are used. The tracking efficiency was about 95% using two methods and the convergence time under varying atmospheric conditions was 15 Ms. Innovation of the proposed method is to use a search algorithm that receives the power and current of the PV array, and general maximum is estimated in its output. This algorithm improves the capability of existing onestep methods and increases their efficiency [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22].
The rest of the paper is organized as follows: “The preliminary of components”, “The proposed control approach” is discussed. “The simulations” and “Conclusion” are finally addressed.
The preliminary of components
The orbital model of photovoltaic cell
The PV module
The resistance in the equivalent circuit defines the losses in the cell. The losses in the affected cell are the cases such as the reflection of sunlight at the cell surface, the absorption of photons without the creation of electrons and free holes, the redistribution of electrons and voids, and such related cases. According to Fig. 1, the solar cell’s characteristic equation is expressed by the following equation [11].
Variables of the PV cell
Variable  Explanation 

\( V_{\text{pv}} \)  The PV cell output voltage 
\( I_{\text{pv}} \)  The PV cell output current 
\( G \)  The intensity of the sun’s radiation 
\( T \)  Cell temperature 
\( T_{\text{r}} \)  Reference temperature 
\( I_{\text{ph}} \)  The luminous power produced in the PV cell 
\( I_{0} \)  The saturation current of the PV cell 
\( A , B \)  Correction coefficients 
\( K \)  Boltzmann’s constant 
\( q \)  Elementary charge 
\( R_{\text{S}} \)  Series resistance of the PV Cell 
\( N_{\text{s}} \)  Number of serial cells 
\( N_{\text{p}} \)  Number of parallel cells 
The characteristics curve of the PV module
Factors affecting the performance of the modules and their characteristic curves
 (A)Temperature: an increase in temperature decreases the voltage and the current that is almost constant as shown in Fig. 3.
 (B)The intensity of the sun radiation: the increase in the intensity of the radiation increases the current and the voltage that is almost constant as shown in Fig. 4.
 (C)
Array structure: the performance of the array depends on the type of cells used and the quality of manufacturing by the manufacturer. The values of \( R_{\text{SH}} \) and \( R_{\text{S}} \) can vary with respect to the structure. The value of \( R_{\text{SH}} \) approaches the infinite and the value of \( R_{\text{S}} \) approaches the zero in a highquality cell.
 (D)
Shadows: there are complete or incomplete shadows, which are often created by passing clouds, the adjacent buildings and the towers, the trees, the electricity and the telecommunication stands, and so on. In the penumbra conditions, several local maximum points—in addition to the general maximum—are created, and therefore, the characteristics of the PV array are complex. This makes it more difficult to track maximum point.
Description of the problem

Creating a shadow by the adjacent the buildings and the towers, the trees, the power towers, the telecommunications and etc. on the PV array in urban areas.

Change in the angle of the radiation during a day or a season or passing clouds.
It is observed that the above array has a local maximum point in addition to a general maximum under the penumbra conditions and since the goal is the maximum point tracking, this can make tracking more difficult [21]. The significant drop in the power received from the PV array due to shadow has caused designers to consider the smallest possible shadow to select the right place for creating the PV farm. It should also be noted that the penumbra is associated with the temperature drop. So, in short, we can say that the shadow creates one or more local maximums, in addition to general maximum, and this causes the maximum power point tracking problem to make mistakes sometimes. Since the goal is to determine the maximum general point, there are several algorithms for this purpose, which are discussed in the next section of the proposed control approach.
The proposed control approach
To discuss the proposed control approach, it is first essential to note that the shadow on the two modules having the series of connection creates a local maximum and a general maximum. The maximum local tracking instead of the general maximum leads to decrease the power, significantly. The method presented in this study provides a twostage maximum power tracking method that determines the maximum point for two modules having serial connection. In the first step, the radiation and the temperature of the array is measured and the final P–I curve is found. Then, a search algorithm is implemented to approximate the MPP location with two current and power parameters at the MPP point. When the weather conditions exceed beyond a certain level, the search is repeated. In the second step, the actual characteristic curve starts the search for MPP from the estimated point in the first stage or from its previous performance point, which depends on changes in the performance conditions. Each of the MPPT singlestep methods introduced in the previous section can be used in the second stage. As mentioned earlier, the second phase of this approach is performed using P and O and RCC methods, and this investigation uses the artificial neural network. In one such case, P and O and RCC methods are used to perform the second phase of this algorithm, and the neural network is realized, correspondingly.
The first step
As long as each module of the PV array has the certain change in ΔG and ΔT, the corresponding P–I curve is formed and the search algorithm is carried out to find both the local and general maximum. If there are both maximums, the general maximum is determined by the controller. The amount of changes in ΔG and ΔT throughout the day is not constant due to their different changes pattern. Therefore, the approximated value of these changes causes the controller to form a new P–I curve and begin a new search, which should be determined during the simulations of the system. The idea of providing the search algorithm can be useful when it does not call on a regular basis. This position may occur in an environment with rapid meteorological conditions (less than one second) to find the maximum point that should be difficult. Obviously, this search algorithm can be a solution to find the maximum of a function. But the search algorithm is provided as the starting point in the second stage, so it is not always online except in two modes: one at the start of the simulation that runs once and the other is the high variations of ΔG and ΔT from a given limit.
The second step
Therefore, if there is a maximum operating point or indirectly \( D_{\text{opt}} \) is known in any given temperature and the radiation conditions, by comparing \( D_{\text{opt}} \) and D, with a particular algorithm, the array operating point can be directed to the maximum operating point, which ultimately leads to maximum power. The input of the artificial neural network is the change of the power to the output voltage of the PV array and its output is the optimal duty cycle. The structure of the artificial neural network realized in this investigation is R–S1–S2, where R is the number of inputs of the network and is equal to 1, S1 is the number of neurons in the first layer (hidden layer) and is equal to 100, and finally S2 is the number of the neurons of the second layer (output layer) which is equal to 1, as well. Finally, the back propagation (BP) learning rule has been used for network training, while the estimated error is less than 0.0002.
The overall system
The simulations

First simulation entitled 2 StagesNeural Network Simulation 1 (2SNNSI): In this simulation, changes in the weather conditions are very fast and the first stage is run several times.

Second simulation entitled 2 StagesNeural Network Simulation 2 (2SNNS2): In this simulation, changes in the weather conditions are moderate and the first phase may be implemented.

Third simulation entitled 2 StagesNeural Network Simulation 3 (2SNNS3): In this simulation, weather conditions changes are very slow and similar to a place with temperate climate, and the first stage, is not implemented except at the beginning of the simulation.
Similar studies have been carried out in the previous years, which their second phase has been done using the RCC and the P and O methods. In fact, this study is a generalization of them. Therefore, the inputs and the first stage of this investigation are similar to the previous studies to show the capabilities of the neural network as a second step, and finally, the simulations of this section are compared with the simulations performed in the past. In the following, the main simulation is presented using the trained network matrices and biases, and its implementation and results are presented.
The first simulation
The values of the MPP point in the first simulation and comparison with the twostep RCC and P and O methods
Time  Voltage in MPP (V)  Current in MPP (A)  Power in MPP (W)  Tracked power (W) P and O(W)  Power tracked RCC(W)  Power tracked NN(W)  Percentage error 

\( 0 < t < 0.02 \)  16.7  2.98  49.78  ≈ 50  ≈ 49.5  49.73  0.1 
\( 0.02 < t < 0.04 \)  34.99  3  105  ≈ 105  ≈ 104.9  ≈ 105  
\( 0.04 < t < 0.06 \)  33.41  2.98  99.55  ≈ 100  ≈ 99.55  ≈ 99.55  
\( 0.06 < t < 0.06 \)  36.22  3.01  109  ≈ 109  ≈ 109  ≈ 109  
\( 0.08 < t < 0.1 \)  36.71  2.1  75.74  ≈ 76  ≈ 75.75  ≈ 75.51  0.31 
It is clearly observed that the system has reached the exact MPP point with great precision. The actual value of tracked power is the average value because it associated with a bit of ripple. It is clear that the tracking error in all cases is less than 1%. Also, the system converges to real values within 0.005 s.
The second simulation
The values of the MPP point in the second simulation and comparison with the twostep RCC and P and O methods
Time  Voltage in MPP (V)  Current in MPP (A)  Power in MPP (W)  Tracked power (W) P and O(W)  Power tracked RCC(W)  Power tracked NN(W)  Percentage error 

\( 0 < t < 0.02 \)  15.69  1.48  23.21  ≈ 23  ≈ 23.1  ≈ 23.14  0.301 
\( 0.02 < t < 0.04 \)  16.7  2.98  49.78  ≈ 50  ≈ 48  ≈ 49.7  0 
\( 0.04 < t < 0.06 \)  19.51  3.04  59.32  ≈ 60  ≈ 59.3  ≈ 59.32  0 
\( 0.06 < t < 0.08 \)  19.51  3.04  59.32  ≈ 60  ≈ 59.3  ≈ 59.32  0 
\( 0.08 < t < 0.1 \)  19.51  3.04  59.32  ≈ 60  ≈ 59.33  ≈ 59.32  0 
It is obvious that the system has reached the real MPP point. It is clear that the tracking error in all cases is less than 0.5%.
The third simulation
The values of the MPP point in the third simulation and comparison with the twostep RCC and P and O methods
Time  Voltage in MPP (V)  Current in MPP (A)  Power in MPP (W)  Tracked power (W) P and O(W)  Power tracked RCC(W)  Power tracked NN(W)  Percentage error 

\( 0 < t < 0.02 \)  17.33  2.7  46.79  ≈ 47  ≈ 46.79  ≈ 46.79  0 
\( 0.02 < t < 0.04 \)  17.5  3  52.49  ≈ 53  ≈ 52.4  ≈ 52.49  0 
\( 0.04 < t < 0.06 \)  17.1  2.99  51.13  ≈ 51  ≈ 51  ≈ 51.13  0 
\( 0.06 < t < 0.08 \)  17.1  2.99  51.13  ≈ 51  ≈ 51  ≈ 51.13  0 
\( 0.08 < t < 0.1 \)  17.1  2.99  51.13  ≈ 51  ≈ 51  ≈ 51.13  0 
Comparing the investigated outcomes with the previous research
The previous investigation, i.e., fuzzyPID controller  The proposed approach, i.e., artificial neural network  

ISE Index  3.348  1.703 
IAE Index  3.038  1.306 
ITSE Index  1.319  0.563 
ITAE Index  0.341  0.721 
Conclusion

Step 1: Estimating the maximum general point.

Step 2: Determining the maximum general point.
The neural networks are designed in the second stage. While the temperature or radiation changes on each module are greater than 25%, the first stage is implemented because the general maximum area changes. But if the changes are less than this value, the second step of the general maximum found, because the P–I curve has not changed significantly. The successful performance of the approach for tracking maximum power is confirmed by simulation software MATLAB/SIMULINK for 100 ms. Then, three simulations are carried out to illustrate the performance of the proposed twostage method, which are different in terms of degree of variations in the atmospheric conditions. Finally, the flexibility of the proposed approach is shown. The proposed one is able to accurately track the maximum power point with a precision and efficiency of over 98% and a convergence time of about 10 ms for large atmospheric variations. The convergence time of this method is faster than other twostep methods. Subsequently, the proposed approach can be argued in competition with other potential techniques.
Notes
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