The maximum power point tracking (MPPT) problem has attracted the attention of many researchers, because it is convenient to obtain the maximum power of a photovoltaic module regardless of the weather conditions and the load. In this paper, a novel control for a boost DC/DC converter has been introduced. It is based on a sliding mode controller (SMC) that takes a current signal as reference instead of a voltage, which is generated by a neuronal reference current generator. That reference current indicates the current (
In the recent Paris Conference [
Due to its simplicity of operation, robustness, and cheapness, photovoltaic solar energy is a very appropriate source of energy, especially for emerging countries, where the construction of large electrical infrastructures is infeasible in some areas. Moreover, in recent years, great progress in this area, better efficiency, and improved performance of photovoltaic modules have been achieved. These factors, along with the advancement of electronic technology, make this type of energy even more valued.
The optimal operation of a photovoltaic system depends on two types of variables; the first type is those that are imposed and depend on weather conditions, that is, irradiance and temperature. The second type of variables is those that can be modified to search for the desired performance of the system, given the weather conditions. This is the case that we are facing in this paper, that is, working at the maximum power point. In order to get it, it is mandatory to get an appropriate performance of the converter.
The search of control algorithms for improving converters performance in photovoltaic systems has a considerable significance for many researchers [
When a sliding mode controller is tuned by scientists or practitioners, it is desired to have a model of the photovoltaic module to control in order to carry out preliminary analytic or simulated tests instead of using the actual module. In the literature, there are a number of models of different complexities to explain the electrical behavior of photovoltaic modules. In order to clarify such variety, we can make a first division into theoretical and empirical models. Theoretical models use a characteristic equation [
The most complete model used in the literature is based on a double diode equivalent circuit which leads to a 7parameter model, that is,
In [
A number of researchers make some approximations of the characteristic parameters. The most usual of them is to assume that
RamosHernanz et al. use polynomial interpolation and describe a model which allows obtaining only the
Another approach to the empirical methods is modeling the behavior of the photovoltaic elements by means of artificial neuronal networks [
Researchers reported a relative MSE of 2% and 1%, respectively, but the test has been done with training data, so in fact they have reported the training accuracy. In this paper, a new sliding mode controller (SMC) for maximum power point tracking in a photovoltaic module is introduced, and its performance is demonstrated in a real installation. Its main characteristic is that as reference generator it uses an artificial neural network which will seek for a reference current
In order to design the SMC controller, we have carried out several tasks related to the three main elements of the autonomous photovoltaic system (photovoltaic module, converter, and load):
A model of the Mitsubishi Electric PVTD185MF5 185 W photovoltaic module has been developed based on neural networks, using actual measurements taken during 18 months, with an approximate average duration of ten minutes for each measure. A total of 62,912 samples (
These real data have been used to draw the characteristic curves of the module and calculate the MPP in each one of them. These points were learned by a second artificial neural network in order to obtain the reference current at which that the module operates at its optimum point, given the power supplied by the module and the temperature. That is, a neuronal reference current generator implementation has been obtained.
A SMC has been designed, so that, given a reference current, the photovoltaic module will work at its point of maximum power.
And finally, the joint behavior of all these components has been validated through simulated and real tests using the installation that is at the Faculty of Engineering VitoriaGasteiz (University of the Basque Country, Spain).
The document is structured as follows: in Section
A solar cell can be modeled as a PN semiconductor junction which when exposed to light converts light energy into electrical energy, generating a DC current which will mainly depend on the existing solar irradiance and temperature.
Electric generators are usually classified as current or voltage sources. A photovoltaic device shows a functional mixed behavior, which is a source of current or voltage depending on the operating point in which the device is working.
Most manufacturers provide few experimental data on the performance of solar cells working at ideal operating conditions. These data are typically provided in Standard Test Conditions (STC) (1,000 W/m^{2}, 25° (±2)°C, AM 1.5 according to EN 60904). There are manufacturers that also provide these data for other conditions (800 W/m^{2}, Nominal Operating Cell Temperature (NOCT), AM 1.5). Usually the provided data are short circuit current (
The basic model of a photovoltaic generator is a photovoltaic cell. The cell can be modeled as a diode, usually made of silicon and designed to maximize the absorption of photons and to minimize the reflection, converting a part of the received solar energy to electric energy. The ideal cell model is presented in the dotted area of Figure
Twodiode model of a photovoltaic cell.
However, there are some recombination phenomena in the material, specifically in the depletion layer of the semiconductor which can be modeled through a second diode, leading to a twodiode model. The typical twodiode equivalent circuit of a photovoltaic cell is shown in Figure
Analyzing the schema of Figure
Many researchers use some simplifications obtaining equations that define the model of a single diode [
Analyzing the schema of Figure
Onediode model of a photovoltaic cell.
There are a number of data which cannot be found in data sheets as series resistance (
Both (
We define the current produced between electrodes of a photocell as the photogenerated current or photocurrent according to
Moreover, the reverse saturation current of the diode (
In order to apply these concepts to the development of a solar cell model, we have chosen the PVMitsubishi TD1185MF5 PV module for its modeling. This module has 50 polycrystalline cells connected in series. Its main characteristics are specified in Table
Key specifications of the Mitsubishi PV module.
Manufacturer  Mitsubishi 

Model  PVTD185MF5 
Cell type  Polycrystalline 
Maximum power [W]  185 
Open circuit voltage 
30.60 
Short circuit current 
8.13 
Voltage at 
24.40 
Current at 
7.58 
Temperature coefficient of 
−0.346 
Temperature coefficient of 
0.057 
Nominal operating cell temperature (NOCT) [°C]  47.5 
One of the best tools to describe the operation of a photovoltaic module is the currentvoltage (
Conceptually, the
In order to evaluate the performance of solar cells and the photovoltaic systems design, we will rely on the electrical characteristics, that is, in the relations of voltagecurrent of the cells under different levels of radiation and temperatures. This requires understanding how solar radiation, the cell temperature, and electrical loads affect the behavior of the characteristic curves. The particular point of current and voltage of the curve at which the photovoltaic device works is determined by the load to which it is connected. If we have a high knowledge of these curves we can make a correct photovoltaic system design and an appropriate evaluation.
Figure
Characteristic curves of a photovoltaic module.
A DC converter must provide at its output a regulated DC voltage of a desired value. It must be done in the most efficient way and with as fewer losses as possible.
The most commonly used method to control the output voltage is the pulse width modulation (PWM), which consists in using a constant switching time (
The power given to the load is a function of the duty cycle (
In photovoltaic systems, the DC/DC converter is placed between the PV generator and load, being responsible for adapting the energy produced by the generator following a defined control strategy, which usually tries that the system works at the maximum power point to increase the efficiency of the installation.
A concrete type of converter that we have used in our installation due to its characteristics is the boost converter. It provides an average output voltage exceeding the input value. We can see the converter topology in Figure
BOOST converter.
These converters are nonlinear circuits, so in order to study them as linear circuits it is usual to decompose them into two subcircuits. Its linear operation mode depends on the state of the switch
When the switch
When the switch
In the case of a boost converter in continuous driving operating mode, the relations between the input (
Analyzing (
The dynamic model of a circuit of a boost converter is defined by
Artificial neural networks (ANNs) are based on the operation mode of biological neural networks, although they have different functions and structures. ANNs try to mimic the human brain which is a very complex, nonlinear, and parallel system. In other words, it can perform many simultaneous operations unlike traditional computers, which only can perform one sequential operation at the same time.
The basic component of calculation is usually called neuron, node, or unit. It receives one or more inputs (
Generic artificial neural network structure.
The sliding mode control (SMC) is defined as using a control signal, switching at high frequency in order to carry the system state to a scalar field. The structure of the controller varies so that a representative point of the system follows a defined trajectory in the state space. It is based on the fact that it is easier to control firstorder systems than those of order
The advantages of SMC are great accuracy, good stability, simplicity, and ruggedness, especially when the dynamics of the system in closed loop slides by the sliding surface, because it remains insensitive to variations in the model parameters and to external perturbations.
If in a system there is a sliding mode, the trajectories that intersect the sliding region remain on
Sliding surface.
In order to analyze this technique, we will consider a nonlinear dynamical system defined by the following equations:
The variable sliding surface in time domain is defined in the state space
The purpose of the control is to keep the surface to zero. This is a linear differential equation whose unique solution is
We define the following control signal:
We say that the converter is controlled in sliding mode when the law described by (
If the dynamics of the system are out of the sliding region and they are above it, the control will switch to the value
The execution of the control law to get the system to slide across the surface means that the switching frequency is infinite, which is physically impossible. Therefore, we will use a modified control law expressed in
The sliding surface is characterized by the following conditions of invariance or ideal sliding dynamics of (
These conditions guarantee that the trajectory of the system state is addressed to the sliding surface (
System stability can be analyzed using the method of Lyapunov stability. The Lyapunov function is a scalar positive function. The desired function is one that ensures monitoring of the variable to control the reference value. We define the positive function of the form
If the function is derived, (
The function decreases if the derivative is negative.
A system meets the slip condition when the scalar
This section will describe the steps taken for modeling the Mitsubishi PVTD185MF5 module. It is located on the roof of the Faculty of Engineering of VitoriaGasteiz (University of the Basque Country, Spain). The model is obtained from experimental data (32,916 samples), taken during 18 months. The measurements were made randomly with an approximate average duration of ten minutes, during which four magnitudes were measured (temperature, irradiance, current, and voltage) varying the load resistance.
Figure
Scheme of measurement elements for data logging.
Besides, there is a variable resistance to act as a variable load and obtain different pairs of voltage and current with the same irradiance and temperature. The variable resistance value is controlled according to our convenience, but the temperature and the irradiance depend on the climatological conditions.
The involved measurement elements for data logging are the following:
The data measured and recorded using the CBManager are saved in plain ASCII files. After some minor modifications as changing decimal sign (. by ,) and separator (, by ;) and eliminating unnecessary data, these files are imported into a Microsoft Excel file in order to obtain graphics which allow detecting outliers or corrupted data, so that a single file with 62,916 samples of measured data (current
We import these data into the MathWorks Matlab environment and generate four vectors, one for each measured magnitude. Since we will use an artificial neural network to generate the model, with these vectors we form the network input and output, in such a way that the generated neural network will have threedimensional input patterns (
During the structure design phase, we heuristically chose a onelayer feedforward artificial neural network composed of three inputs, one output, and 15 nodes in the hidden layer. Once the network architecture was designed, we proceed to train it to learn the desired behavior defined through the input and output correspondences. In this phase, the ANN calculates its predictions and compares them with the actual values of the variable that had tried to predict them, so that the network learns that there were erroneous predictions and modifies the synaptic weights in order to reduce that error. This process is driven by a training algorithm, which presents sequentially the training data at the input layer of the ANN. In this case, the LevenbergMarquardt algorithm has been used. We call “epoch” to a complete presentation of all training data during the learning process. Learning occurs epoch to epoch until the weights and thresholds are stabilized and the error criterion on the complete training set converges to a minimum value following a metric, in our case, the Mean Square Error (MSE).
After training phase, it is expected that the ANN shows a behavior similar to the actual photovoltaic module, even when new inputs are presented at its input layer.
Of the total number of 62,916 samples of experimental data obtained, we use 44,042 samples pairs for training (70%), 9,437 for validation (15%), and the remaining 9,437 for test (15%). The network was trained with backpropagation LevenbergMarquardt algorithm during 1000 epochs, obtaining a network with a Mean Squared Error (MSE) of 6.1553 × 10^{−2} A and with a training correlation coefficient
Training correlation coefficient.
In Figure
Model validation.
Moreover, using a test dataset of 9,437 samples a test correlation coefficient
Test correlation coefficient.
With these results, we can state that the model is accurate enough to be used in those studies where the Mitsubishi PVTD185MF module is implied.
Boost converter function is to take the output of the photovoltaic module and transform it to obtain the maximum power. The behavior of the converter depends on the sliding control which obtains the reference (
In order to obtain the reference current generator (
Knowing this line, for any power value, it is straight to know which current value, at the maximum power point, that should be used as reference current. Since the power generated by the module also depends on the temperature, it is necessary to obtain these straight lines at different temperature values.
In order to design the reference current generator, we will use the same experimental data used to obtain the model of the photovoltaic module in Section
In this case, the 62,192 samples will be divided into groups of temperature of 5°C, going from 5°C to 50°C. Each one of these groups is divided again into irradiance groups with values from 100 to 1,000 W/m^{2} and step 100 W/m^{2}. With the values of each group (combination of temperature and irradiance), the characteristic curves
Lines of MPP for different temperatures (°C).
With these values, we trained an ANN to learn the function
We obtained the maximum power points data to carry out the ANN training calculating them for power values ranging from 15 to 110 W with step of 5 W, while for temperature values range from from 15 to 50°C with step of 5°C. In this way, we got a set of 160 triplets (
An ANN of four hidden nodes was trained with backpropagation LevenbergMarquardt algorithm. After 489 iterations, a network with a Mean Squared Error (MSE) of 2.036 × 10^{−3} A and a training correlation coefficient
Train correlation coefficient.
Test correlation coefficient.
As we have seen in the previous section, the neural network will help us determine currents of reference required by the system at all times; then the converter will force the photovoltaic system to work with the reference value obtained and thus in the area of the maximum power
In order to limit the control signal of operating range for the duty cycle of our DC/DC converter, the integral of the control signal is limited between 0.1 and 0.9.
The demonstration of stability of the proposed controller is based on the theory of Lyapunov stability. For this purpose a Lyapunov function is defined by
Taking into account the expression of
Behavior of the
We check stability because if
For this reason and to make the tracking error be zero (
In this section, we present our results divided into two subsections attending to their nature:
The first test carried out in order to test the performance of the controller analyzes its response when there are sudden irradiance changes. As shown in Figure
Temperature (constant) and irradiance (step) input values.
As we can see in Figure
Power response when sudden irradiance changes.
The second test is devoted to study the behavior of the controller when there are sudden temperature changes. In this case, the irradiance is constant (800 W/m^{2}), while the temperature changes suddenly from 10 to 45°C, as shown in Figure
Temperature (step) and irradiance (constant) input values.
In this case, we also can see in Figure
Power response when sudden temperature changes.
In this section, we will analyze the behavior of the proposed controller under real conditions.
In order to carry out the experiments, we used a realtime digital sign processor (DSP) model dSPACE DSP1104 integrated with MathWorks Matlab/Simulink through its toolbox for realtime work and RealTime Interface (RTI). This is widely used in industry and research because it reduces the time gap between the simulation and the development of real implementation, profiting from its capability to simulate failures and to analyze the behavior of the real system.
The installation in which the experiments have been carried out consists of the Mitsubishi PVTD185MF5 photovoltaic module, a boost converter, a DSP model dSPACE DSP1104, a variable load, and a personal computer for data storage, as shown in the schematics of Figure
Boost converter parameters.
Boost converter  

Schottky  2x MURF1560GT  600 V, 15 A, 0.4 V to 10 A/150°C 
IGBT  1x HGT40N60B3  600 V, 40 A, 1.5 V to 150°C 

6x PCV256408  560 

2x TK Series  1500 
System block diagram.
Picture of the actual installation.
The communication between the DSP and the computer has been done using the ControlDesk Next Generation 5.1 software, which allows display on the screen and manipulating realtime system variables through a graphical user interface.
Once the experimental setup is fixed, the first step is to find out which is the maximum power point for the actual conditions in which the system is working. For this purpose, the variable load is connected directly to the photovoltaic module and its value is varied from its minimum to its maximum value (0–47 Ω) gathering pairs of
Now that the value that the converter should follow is known, the installation is prepared to make the measurements.
The experiment is to vary the load and check that the power supplied to the load by the converter follows the power given by the photovoltaic module, in such a way that although the load varies, the converter continues operating at the maximum power point under the existing irradiance and temperature conditions at each moment.
During the experiment the load was manually varied from 23 Ω to 39 Ω, so the change is not immediate as can be seen in Figure
Behavior of the load resistance
During the experiment, the temperature (blue line) and the irradiance (red line) are quite stable due to its short duration, remaining on approximate values of 33°C and 635 W/m^{2} as can be seen in Figure
Behavior of temperature
Figure
Finally, the voltage and current values in the load can be seen in Figure
Behavior of load voltage
After this real experiment, we can state that the designed converter has also a good performance when the load value is changed.
In this paper, we have addressed one of the more outstanding problems when dealing with photovoltaic modules, that is, the maximum power point tracking problem when a boost DC/DC converter is used.
In the first part of the paper, we have given a short background on some key topics regarding the paper, as the basic description of a photovoltaic generator and its characteristic curves, boost DC/DC converters, artificial neuronal networks, and sliding mode control.
Later, we have detailed all the components of a real photovoltaic installation placed at the Faculty of Engineering VitoriaGasteiz (Basque Country University, Spain). That installation has been used to acquire data about the real operation of the Mitsubishi Electric PVTD185MF5 185 W photovoltaic module. We have explained how the data have been gathered and the process used to train an artificial neural network to learn the behavior of the real module, obtaining a very accurate model with MSE = 0.062 A and
Once we have got a validated model of the photovoltaic module, which allows us to make simulations, we design the sliding mode controller. The controller generates a pulse signal to control the boost DC/DC converter, but in turn, it needs a reference signal. In this work, we have used as reference a current signal, more specifically, the current at which the module gives maximum power for a given temperature and irradiance conditions. That information was obtained from the real gathered data and since we are dealing with a sliding mode controller, it has represented as a sliding surface.
Finally, we have carried out several tests in order to validate the controller and its robustness when there are sudden changes in temperature, irradiance, and load. Simulated and real tests have shown that the controller that provides a good overall performance guaranteeing that the power in the output of the converter is very close to the power of the photovoltaic module output, this one being the second main contribution of the paper.
The authors declare that they have no competing interests.
The authors are very grateful to the UPV/EHU for its support through Projects GIU13/41 and UFI11/07.