Control and Energy Management Laboratory, National School of Engineering of Sfax, Sfax, Tunisia

Email: rihab.mahjoub@yahoo.fr

Copyright © 2014 by authors and Scientific Research Publishing Inc.

This work is licensed under the Creative Commons Attribution International License (CC BY).

http://creativecommons.org/licenses/by/4.0/

Received 18 May 2014; revised 25 June 2014; accepted 2 July 2014

ABSTRACT

The employment of maximum power point tracking techniques in the photovoltaic power systems is well known and even of immense importance. There are various techniques to track the maximum power point reported in several literatures. In such context, there is an increasing interest in developing a more appropriate and effective maximum power point tracking control methodology to ensure that the photovoltaic arrays guarantee as much of their available output power as possible to the load for any temperature and solar radiation levels. In this paper, theoretical details of the work, carried out to develop and implement a maximum power point tracking controller using neural networks for a stand-alone photovoltaic system, are presented. Attention has been also paid to the command of the power converter to achieve maximum power point tracking. Simulations results, using Matlab/Simulink software, presented for this approach under rapid variation of insolation and temperature conditions, confirm the effectiveness of the proposed method both in terms of efficiency and fast response time. Negligible oscillations around the maximum power point and easy implementation are the main advantages of the proposed maximum power point tracking (MPPT) control method.

Keywords:Maximum Power Point Tracking (MPPT), Photovoltaic (PV) System, Neural Network, Buck Converter

1. Introduction

In the last few decades, harnessing solar energy found its high usefulness as a way to solve the problems of the energy crisis, due to the continuously growth of the global energy demand, and the global warming from the wide spread utilization of fossil fuels [1] . Solar energy is directly convertible into electrical energy by means of photovoltaic arrays through semi-conductors [2] . However, solar photovoltaic energy, still presents a vast area of competition comparing to conventional energy resources due its high installation cost and the low energy conversion efficiency of PV cells [3] . Therefore, several studies are being developed in order to minimize these drawbacks by optimizing the performance of PV systems through the operation of conversion systems to increase the output efficiency of the overall system. This approach is commonly named as Maximum Power Point Tracking (MPPT) [4] . The MPPT is a controlled DC/DC converter inserted between the PV source and the load that monitors the photovoltaic array to operate at its maximum power point (MPP) depending on the load state, PV array generation, PV cell temperature and solar radiation variations [5] . In such a direction, previous researches have focused on different MPPT techniques and algorithms. They differ in many aspects such as complexity, sensors required, convergence speed, cost and range of effectiveness. The most encountered methods known as the hill-climbing techniques, examples include P&O method and incremental conductance method. Those methods are the most commonly applied in practice due to their simplicity and ease of implementation. However, the shortcomings are also well-known: oscillations around the MPP and they can get lost and track the MPP in the wrong direction under sudden atmospheric conditions changes [6] . More recently, intelligent methods as fuzzy logic and artificial neural networks are being adopted for photovoltaic applications, mainly because of their flexibility, symbolic reasoning and explanation capabilities that are useful to deal with strong nonlinearities and complex systems [6] . In all cases, the proposed MPPT techniques ensure MPP from PV array. However, since hill-climbing methods determine the MPP by moving the functioning along the P-V curve of the PV array, they cannot deliver fast decision face to climate disturbance or load fluctuation. Hence an overall system delay is consequently observed [5] . Many researches have estimated the MPPT by neural networks method and calculated the MPP of the PV array by the neural network controller. This work aims to simulate and control a stand-alone PV system in order to continuously harvest maximum power from the PV array. For that purpose, this paper proposes an effective MPPT technique for DC/DC converter connecting a PV array with a load stage. The structure of the proposed MPPT control method is based on the use of neural network controllers. This controller can track the MPP not only accurately but also its dynamic response is very fast in response to the change of climatic parameters in comparison with the conventional MPPT control methods. The benefits of using neural networks are that there is no requirement for knowledge on internal PV system parameters, less computational effort and they provide a compact solution for multivariable problems. The present paper will be organized as follows. Next section describes the photovoltaic system configuration. The photovoltaic array and the DC/DC converter modeling are exposed in Section 3. Section 4 presents the maximum power point tracking strategy, the validation of the proposed approach is provided in Section 5. In Section 6, conclusions end this paper.

2. Photovoltaic System Configuration

The model scheme of the studied stand-alone photovoltaic system and its control are as shown in Figure 1. It consists of a PV array, a DC bus capacitor, a DC/DC converter, a load stage and an MPPT control unit. When the sunlight strikes the photovoltaic array, this latter converts solar energy to electric energy. The electric energy is then fed to the DC power stage which is used to adjust the PV array output voltage to a value corresponding to the maximum power deliverable to the load. The MPPT control bloc, which is the key bloc of our system and necessary to obtain the maximum power from the PV array under any variation of irradiation and temperature, includes two main parts: first, the neural network controller which receives solar radiation and photovoltaic cell temperature as inputs and estimates the optimum PV array voltage corresponding to maximum power as output. Second, the power stage control which switches the power transistor ON and OFF to carry out the maximum power from the PV array, it is a dual-loop feedback control, the external loop is voltage loop, while the internal loop is output current loop, those loops are adjusted through PI control and then will be regarded as modulation wave to compare with high frequency triangular wave in PWM wave generator.

3. Photovoltaic System Modeling

For convenience and completeness of the paper, we will explain hereafter the plant modeling which is an essential step for the control analysis, so special care should be taken to ensure its accuracy. The modeling of the system can be divided into two parts: modeling of the PV array and the modeling of the buck type DC/DC converter.

3.1. PV Array Model

To design the model of the photovoltaic array, we should first focus on finding the electrical equivalent to that source. For that purpose, it is worthwhile to deduce the electrical model of a PV array from that of a single PV cell circuit. For accurate modeling, two diode circuits could have been used but our scope of work is limited to single diode model. This model is useful to simulate the PV array behavior with Matlab/Simulink software, it is a test bed of several works found in the literature [5] [7] [8] . A photovoltaic cell is basically a p-n junction semiconductor which converts solar light energy into electricity. Parameters of the solar cell are modeled as in Figure 2.

Conceptually, photovoltaic cells are grouped together in order to form photovoltaic modules [9] . A photovoltaic array is composed of parallel modules each one including photovoltaic cell serial connected [5] . The relationship between the PV array output current and voltage is given by:

(1)

where and are respectively the PV array output current and voltage, the generated photocurrent, and respectively the serial and the parallel resistances of the PV cell, is the electron charge, the Boltzman’s constant, A is the p-n junction ideality factor, is the cell temperature and is related to the temperature as follows:

(2)

where is the cell reference temperature, is the reverse saturation current at and is the

band-gap energy of the semiconductor used in the cell. Similarly, the photocurrent depends on the solar radiation and the cell temperature as follows:

(3)

where is the photovoltaic array short-circuit current at and reference radiation, is the solar radiation and the temperature coefficient for short circuit current. The PV array power is then calculated as,

(4)

3.2. Buck Converter Model

As previously mentioned, a step-down DC/DC converter is inserted between the PV array and the load stage in order to drive the operating point of the PV array to the maximum power point which is detected by the neural network controller. This is accomplished by varying the duty cycle of the DC/DC conveter and thus adjusting the PV array output voltage.

Referring to Figure 3, the buck converter transfer function is obtained by considering its steady state operation as follows:

(5)

where is the duty cycle given by the power stage control, is the output voltage and the output PV array voltage. In current terms, the latter transfer function can be rewritten as following:

(6)

where and are the DC/DC input and output currents respectively. From the above equations, we can deduce that; and are the input-output voltage and current couples respectively across the DC/DC converter.

The differential equations that describe the input and the output of the DC/DC buck converter respectively are obtained through the direct application of Kirchoff’s current and voltage laws. They are expressed as follows:

(7)

(8)

where and is the capacitance of the DC-bus capacitor and its leakage resistance, and represent respectively the inductance and the equivalent series resistance of the output filter, is the voltage of the load stage.

4. MPPT Control Strategy

As was previously explained, MPPT techniques are necessary in photovoltaic applications because the maximum

power point of photovoltaic arrays varies with irradiation and temperature so that, the use of MPPT techniques is highly required in order to obtain the maximum power from a solar array. Over the past decades, many methods to find MPP have been developed and published. Among these techniques, the Perturb & Observe, an improvement over perturb & observe algorithm, was suggested by using Incremental Conductance algorithm, after this, a method based on evaluation of Parasitic Capacitance was used, and so on [6] . In the present application, a different kind of MPPT approach using artificial neural network has been employed. In this technique two stages are achieved to track MPP of PV array. In the first stage, by the acquisition of the weather parameters “” (irradiation) and “” (temperature), which are the inputs of the neural network controller, we estimate the optimal voltage corresponding to the MPP. In the second stage, the error between the optimal voltage, which is the output of the neural network controller, and the measured output voltage of the PV array is fed to the power stage control in order to generate the optimal duty cycle for driving the DC/DC converter close to the MPP. The input and output data are from the model based simulations results. This proposed structure depends on the PV array characteristic curve.

4.1. Neural Network MPPT Controller

Recently, neural network (NN) controllers have been strongly developed not only in theory but also in application [10] , they have attracted widespread interest in electrical engineering and they have been introduced in various fields of electro-technical applications, such as, in the tracking of the MPP in the PV systems. Those controllers have the advantage to be robust and relatively simple to design as they don’t require the knowledge of physical definitions with exact model for PV array and have self adapting capabilities [11] .

NN can generally be thought of as black box device that accepts inputs and generates outputs [5] . In our application, it is used to estimate the optimum voltage which corresponds to the MPP at any given solar radiation and PV array temperature. For that purpose, we elaborated a linear network that, when presented with a set of given input vectors, produces output of corresponding target vectors. For each input vector we can calculate the network’s output vector. The difference between an output vector and its target vector is the error. Unlike most other network architectures, NNs can be designed directly if input/target vector pairs are known. The main goal of linear NN is to find values for the network weights and biases such that the sum of the squares of the errors is minimized or below a specific value by using the function “newlind”. The following formula expresses the average of the sum of these errors [11] :

(9)

where is the number of elements in the input vector read by the network, is the target vector and is the output vector.

As shown in Figure 4, the NN controller consists of three layers. The input layer is composed of two nodes in inputs that are, the PV array temperature and the solar radiation. The hidden layer composed of one hundred nodes whose function of activation is “purelin”. The output layer is composed of one node that the optimum voltage which corresponds to MPP.

4.2. Power Stage Control

Referring to Figure 1 and Figure 4, the output of the power stage control is used as a driver signal to turn ON and OFF the power transistor to carry out the maximum power from the PV source. When the transistor is switched ON, the current in the buck inductor increases linearly, so that the diode is turned OFF. However, when the transistor is switched OFF, the energy stored in the inductor is released through the diode to the load.

The power stage control is depicted in Figure 5. As it can be seen, it is designed with a cascade of two PI control loops, the first one is implemented at the DC link capacitor for the optimum output PV array voltage regulation, the second, is placed at the output filter to regulate the current injected to the load. The choice of proportional integral corrector provides the precision of the system and does not have any impact on stability and damping. Indeed, the presence of the integrator increase the degree of the system but the zero allows maintaining system stability.

The development of the PI controllers is as follows: by applying Laplace transformation for Equation (7), we get:

(10)

where,

(11)

A closed loop for Equation (10) gives us the following equation:

(12)

denotes the PI voltage controller which is developed by poles placement for stabilization of Equation (10). Then we can deduce the equation of the reference output current of the converter as following according to Equation (5):

(13)

This term will be incorporated in the current control loop of the inductance. Laplace transformation for Equation (8) gives us the following equation:

(14)

where,

(15)

A closed loop current control for Equation (14) gives us the following equation:

(16)

denotes the PI current controller. Substituting the term in Equation (5) yields the optimal duty cycle which is used to pilot the DC/DC converter.

5. Simulation Results

The proposed electrical power system was simulated with the software package Matlab/Simulink. In detail Sim Power Systems, toolbox was used to guarantee the electrical behaviors of the PV system. The parameters of the photovoltaic array and the electrical power system which were simulated are given in Table 1 and Table 2 respectively.

Based on the fact that the PV array outputs depend on solar radiation and ambient temperature as in Equations (1) and (3), Figure 6 give the power-voltage (P-V) and the current-voltage (I-V) characteristics for different values of solar radiation G and with constant ambient temperature T = 25˚C.

Figure 7 presents the same parameter curves for different ambient temperature T but with constant solar radiation W/m².

From these characteristics, it can be concluded that the increase in solar radiation leads to an increase of the operating point for maximum power generated. We can also observe that the current due the cut-off circuit is positively varying with solar radiation variations, whereas the voltage in the open circuit remains quasi constant. Figure 7 shows that the effect of temperature is slightly significant. The temperature has a negligible effect on the cut-off circuit current. However, the open circuit voltage decays as the temperature increases.

In a first step, in order to evaluate the proposed neural network controller, three statistical parameters have been calculated for the test sets, the average percentage absolute error APAE, the mean bias error MBE and the root mean square error RMSE. The APAE is defined as follows [12] :