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This article describes a technique that allows a photovoltaic (PV) production unit to obtain the maximum power at all times. Here, we use the MPPT control via fuzzy logic on a DC/DC boost-type converter. In order to achieve our goals, we first proceeded to model a PV panel. The resulting model offers the possibility to better account for the influence of different physical quantities such as temperature, irradiation, series resistance, shunt resistance and diode saturation current. Thus, the maximum power to be provided by the PV system is acquired by fuzzification and defuzzification of the input and output variables of the converter. Subsequently, a virtual model of an 800 Watt PV prototype is implemented in the Matlab environment. The simulation results obtained and presented, show the feasibility and efficiency of the proposed technology. Indeed, for a disturbance caused by a variation in brightness, our system guarantees the maximum stable power after 1.4 s. While for a load variation, the maximum power is continuous.

The incident of 04 November 2006 where Europe was plunged into darkness for an hour, the worst of the general Black-Out, pushed energy suppliers to opt for the integration of decentralized production into low-voltage electricity networks. However, the development of this decentralized production and the liberalization of the electricity market led to many new scientific and technical problems [

The aim of this work is to increase the reliability of the MPPT control over the PV parameters. In this paper, the fuzzy logic method will be used to control the inverter in order to always obtain the maximum power. The remaining sections of the article are organized as follows: In section 2, we describe the method and the materials used. Section 3 is devoted to the results, discussions and comments. Then follows the conclusion.

The structure of our photovoltaic system controlled by the MPPT controller is shown in

The photovoltaic module represented by its equivalent electrical diagram given in _{sh}, the series resistance R_{S}. In the end, appears in this diagram, the diode for the polarization of the cell and the phenomenon of recombination of minority carriers [

The mathematical expressions describing the current-voltage characteristics for different environmental conditions: temperature and irradiation are developed as follows [

I p v + I D + I s h = I p h (1)

Or V D = R s h I s h ⇒ I s h = V p v + R S I p v R s h with

V D = V p v + R S I p v (2)

and

I D = I 0 ( exp ( q n K T ( V p v + R S I p v ) ) − 1 ) (3)

I p v = I p h − I 0 ( exp ( q n K T ( V p v + R S I p v ) ) − 1 ) − V p v + R S I p v R s h (4)

By asking W ( x ) exp ( W ( x ) ) = x [

I p v = I p h + I 0 − V p v R s h 1 + R S R s h − n V T h R S W [ I 0 R S n V T h ( 1 + R S R s h ) exp ( V p v + ( I p h + I 0 ) R S n V T h ( 1 + R S R s h ) ) ] (5)

with V T h = K T q .

On the other hand, the expressions for the photon current, the energy supplied by a cell, and the cell resistances as a function of the temperatures and the effective and standard irradiation are developed by the following equations:

I p h = [ I s c + K i ( T − T 0 ) ] G G 0 (6)

I 0 = I p h exp ( V o c N − 1 ) = [ I s c + K i ( T − T 0 ) ] G G 0 exp ( q ( V o c + K v ( T − T 0 ) ) a K T N s ) − 1 (7)

I s = I 0 ( T T 0 ) 3 exp [ q E g n K ( 1 T − 1 T 0 ) ] (8)

To obtain the maximum power, the current and the voltage should have their maximum values.

P max , m = V m p I m p (9)

Using Equation (4) for the maximum value of the current, Equation (9) becomes:

P max , m = V m p [ I p h − I 0 ( exp ( q n K T ( V m p + R S I m p ) ) − 1 ) − V m p + R S I m p R s h ] (10)

Or

I_{pv}: Photovoltaic current (A);

I_{sc}: Short-circuit current (A);

I_{ph}: Light generated current (A);

K_{i}: I_{sc} coefficient of temperature (A/˚C);

K_{v}: V_{oc} coefficient of temperature (V/˚C);

E_{g}: Gap energy (1.2 eV for crystalline silicon);

G_{0}: Standard lighting (1000 W/m^{2});

I_{0}: Saturation current of the diode (A);

K: Boltzmann constant (1.381 × 10^{−23} J/K);

R_{S} : Series resistance (Ω);

R_{sh}: Parallel resistance (Ω);

T: Effective cell temperature in kelvin (K);

T_{0}: Standard temperature (1000 W/m^{2}).

Consequently, the physical behavior of the photovoltaic module is related to I p h , I 0 , R S and R s h on the one hand, and on the other hand with two other environmental parameters namely temperature and solar irradiation [

The Boost converter is the most suitable for the PV system, because it has a simple structure and a higher voltage gain than other converters for a given duty cycle [

This converter is governed by the following equations:

v 0 = 1 1 − D v p v (11)

i p v = 1 1 − D i 0 (12)

i L = i p v − c 1 d v p v d t (13)

i 0 = ( 1 − d ) i L − c 2 d v 0 d t (14)

where v 0 and i 0 represent respectively the duty cycle, the output voltage and the current of the Boost converter.

In addition, we will optimize the DC/DC converters used as the interface between the PV generator and the load. This converter allows us to extract the maximum power and to operate this generator at its maximum power point using an MPPT (Maxumun Power Point tracking) controller. As it increases power, the power changes as well as the voltage. These variations are translated by the following equations:

Δ P p v = P p v ( k ) − P p v ( k − 1 ) (15)

Δ V p v = V p v ( k ) − V p v ( k − 1 ) (16)

P p v ( k ) and V p v ( k ) are respectively the power and the voltage of the photovoltaic generator at an instant k.

1) Influence of illumination

Here we evaluate in Matlab Simulink, the influence of sunlight on the PV system. The model equivalent to a diode of the photovoltaic cell shown in

2) Influence of temperature

As the temperature varies according to time and period, we set the interval range [0˚C - 100˚C]. The model in

For standard illuminance (E = 1 kW/m^{2}). It can be seen from _{co} decreases while the short-circuit current I_{cc} is relatively constant and therefore the power decreases.

We notice that the no-load voltage of a module decreases with increasing module temperature while the short-circuit current increases slightly. Thus, the increase in temperature has a negative influence on the power as it decreases. At a constant temperature, the value of the short-circuit current is directly proportional to the radiation intensity. In contrast, the open-circuit voltage does not vary in the same proportion, but remains almost identical. This means that the power of the module is practically proportional to the illuminance. Thus, the power points are at approximately the same voltage.

Fuzzy logic provides a systematic approach to create the automatic control algorithm by exploiting linguistic variables. In contrast to binary logic, fuzzy variables can ensure a value between 0 and 1. This command has the advantage of being a robust and relatively simple to build [

The purpose of fuzzification is to transform input variables that are initially numerical variables into linguistic variables or scrambled (fuzzy) variables. So we have two input variables, namely the error E(k) and the error variation ∆E(k) defined by the following equations [

E ( k ) = Δ P p v Δ V p v (17)

Using Equations (15) and (16) we obtain:

E ( k ) = P p v ( k ) − P p v ( k − 1 ) V p v ( k ) − V p v ( k − 1 ) (18)

Δ E ( k ) = E ( k ) − E ( k − 1 ) (19)

Thus its variables will be denoted Negative Big(NB), Negative Small (NS), Null Error (ZE), Positive Small (PS), Positive Big (PB) [

Inference is a step that allows us to define a logical relationship between input E, ∆E and output D. The truth table described in

Defuzzification: This step consists in carrying out the inverse operation of fuzzification, i.e. obtaining a numerical value understandable by the external environment (output D) from a fuzzy definition.

Our fuzzy logic control is developed using the fuzzy toolbox from Matlab/Simulink. The inputs of the fuzzy logic controller are E which shows whether the operating point of the load is located to the left or right of the maximum power bridge and ∆E which shows the direction of the operating point. Their equations are given in (18) and (19). The output of the fuzzy controller D represents the change in the duty cycle of the DC-DC converter. The triangular adhesion functions are chosen for simplicity—they show the fuzzy rule basis created in the current work based on intuitive reasoning and experience. The block diagram for the fuzzy logic controller is shown in Figures 12-14.

E/∆E | NB | NS | ZE | PS | PB |
---|---|---|---|---|---|

NB | ZE | ZE | NB | NB | NB |

NS | ZE | ZE | NS | NS | NS |

ZE | NS | ZE | ZE | ZE | PS |

PS | PS | PS | PS | ZE | ZE |

PB | PB | PB | PB | ZE | ZE |

After the result in

After simulating our system with the fuzzy MPPT control, we find that in the case of a disturbance caused by the change in brightness, the system converges to the MPP and remains stable with a minimal ripple rate compared to other types of control. On the other hand, in the case of a disturbance due to the load, the system is insensitive to the disturbance, the power remains stable and does not fluctuate (

This paper proposed a solution to maintain the power at the maximum operating point regardless of irradiation weather and temperature conditions this, by the good of the MPPT control by fuzzy logic. The simulation results are satisfactory for the reliability of the MPPT control over the PV parameters. The support of the DC/DC converter played an important role regarding the stability of the energy. Furthermore, in anticipation of the integration of distributed generation from renewable sources into the power grid, the grid operator will have to impose special conditions for their connection to guarantee the stability and quality

of the grid. Thus, the development of PV in the LV grid may be the most appropriate solution to reduce peak consumption and participate in the grid service. Although these results are interesting, other perspectives can be considered, i.e. the reduction of the harmonic distortion rate by a DCM-controlled boost converter (duty cycle modulation).

The authors declare no conflicts of interest regarding the publication of this paper.

Jeannot, B.G., Jacques, M.J. and Jeannot, M.M. (2020) Reliability of the MPPT Control on the Energy Parameters of a Photovoltaic Generator. World Journal of Engineering and Technology, 8, 537-550. https://doi.org/10.4236/wjet.2020.83038