Fuuzzy logic controller Rules.

## 1. Introduction

Nowadays renewable energy techniques for power production are mature and reliable. The photovoltaic (PV) energy is the most promising source of energy since it is pollution free and abundantly available everywhere in the world. PV energy is especially beneficial in remote sites like deserts or rural zones where the difficulties to transport fuel and the lack of energy grid lines make the use of conventional resources impossble. Pumping water in these sites is a vital task that requires a feasible source of energy to supply power to the electrical elements of the pumping structure.

This work analyses the control of a stand-alone PV pumping system. The success of a PV application depends on the effectiveness of the power electronic devices to efficiently operate the photovoltaic generator (PVG) even under variable climatic conditions The big need is to extract the maximum of power from the PVG at any climatic input levels. Therefore, the reliability of the MPPT controller is of paramount importance in successful PV pumping applications.

The MPPT control is a challenge, because the PVG sunshine energy input flux may change at any time. In fact, the PV system is considered as a non-linear complex one. For these reasons, the design of an appropriate setup controller is difficult to build. In the literature, numerous MPPT methods have been developed, among them: The hill climbing, incremental conductance and the P&O [1]. These algorithms consist of introducing a crisp values positive or negative (decrease or increase) all around the actual PVG operating point. From the previous power point position, the trajectory of the new one helps the algorithm to decide on the command output value. This algorithm may fail to act as an accurate MPPT because of the used crisp value (step size) that is mainly fixed by trial and tests running.

The intelligent techniques have recently attracted the interest of engineers due to several facts: as Self-Optimization fast convergence and simplicity of combination with classical extremum seeking [2], [3]. In this work the interest was focus on applying these techniques on the photovoltaic fields. In this work, the control strategy is described and tested in the context of a highly dynamic input.

## 2. Modeling of photovoltaic system

One can substitute a PV cell to an equivalent electric circuit which includes a power supply, resistors and a diode as shown in figure 2.

The power source generate a current called an *I*_{ph} current, this last depends on the irradiation amount. [1], [4], [5].

Up on the node law;

The current

And the cell current is

With *I*_{rs} reverse saturation current is:

The modeling of a PV Array depending on Ns and Np is then deduced as [5]:

Finally the I_{p} panel current can be given by

The cartelistic I-V in various irradiation and temperature is shown in figure 3

It is clear to find the three specific operating points in figure 3(a) [5].

zone of voltage: characterized by an open circuit voltage V

_{OC}.,zone of current: characterized by a short – circuit current I

_{SC},Zone of maximum of power (P

_{max}.) It is necessary to operate the PV at the third zone to extract the maximum power from the PVG.

## 3. Boost converter

DC-DC converters are electronic devices used whenever is needed to change DC electrical power efficiently from one voltage level to another. A DC-DC converter is an adapter controlling the load power through a regulated duty cycle. In order to step up the voltage, the operation consists of switching an IGBT (Figure 4) at a high commutation frequency, with output voltage control by varying the switching duty cycle (D) [6] and [7].

Where D is the actual duty cycle.

## 4. P&O algorithm principle

Due to its simplicity, P&O algorithm is the most popular one [5]. The principle of this scheme is to generate a crisp value by acting (decrease /increase) on the duty cycle actual command (D) and then observe the output power reaction. If the actual power P(k) is lower than the previous one, then the acting direction is inversed otherwise it is maintained [8], [9].

When dP/ dV>0, the voltage is increased, this yields to

D (K)= D (K)+∆D, (∆D: crisp value)

When dP/ dV< 0, the voltage is decreased through

D (k) = D (k −1) −∆D.

The ∆D crisp value is chosen by trial and tests in simulation. The P&O diagram is shown in figure 5:

If the crisp value ∆D is very big or very small then we may lose information as shown in figure 6. Despite the P&O algorithm is easy to implement it has mainly the following problems [9]:

the PV system always operates in an oscillating mode.

the operation of PV system may fail to track the maximum power point.

The ΔD crisp value is chosen by trial and tests in simulation. The P&O diagram is illustrated in fig. 5.

## 5. Intelligent Artificial MPPT Control technics

In this section, the most investigated Intelligent Artificial control techniques are considered. In particular, The artificial neuronal networks (ANN), the Fuzzy Logic control (FLC), and the adaptive neuro-fuzzy inference system (ANFIS) as the best one that combines the FLC and ANN advantages.

### 5.1. ANN

Artificial Neural network (ANN) method have been employed successfully in solving problems with a high degree of complexness in various fields and applications including pattern recognition, identification vision, prediction,control systems and classification, [10]. Now the ANN can be used in order to solve a lot of problems that are difficult for conventional computers or even for human beings. ANNs, overcome the limitations of the conventional approaches, and present a solution by extracting the desired information directly from the experimental data. The fundamental element of a neural-network is neurons. The method is based on neurons receiving input from other neurons, after that the ANN combines them in a non-linear operation and then generate outputs as a final result. [11].

Artificial neural network was used as a controller to track the maximum power point by commanding the boost converter. Effectively the MPPT artificial neural controller is composed in general by a three layers, first; an input, then hidden and finally an output layer [12],[13], This connection is characterized respectively by weights, w^{I} and w^{o}, like presented in figure 7.

The mathematical expressions define the relation between the input and the output signals are given in equation 8, 9 and 10.

The output layer :

The output hidden layer:

The hidden layer:

qWhere ‘*nc’* represent the neurons number in the hidden and ‘*ne ‘* the output layer. The data vector *x*_{i} represents the input signals that are given in equation 11 [11].

in the ANN_MPPT Controller, an activation function defines each neuron. The sigmoid function has been chosen for this work.

To achieve the required input/output relationship, an adjustment of weights between the output layer and the hidden layer, and the input layer and the hidden layer is required. for the weights updating ;the back propagation algorithm is used, by minimized an error function defined in equation 12 [11].

Where D^{*}(k) is the desired output, E_{na}(k) is the accrued output, and e_{na}(k) represent the error between the desired and accrued output

The updating of weights is calculated by using the gradient method [11].

Where η_{na}^{o}, η_{na}^{I} are respectively the ANN learning rates for the hidden and the output layer.

The quantity

Figure 8 is the windows given by the Matlab at the starting of learning, where the neural model performance, the structure, the learning function, and the maximum training patterns, are given. It’s clear that the ANN performance is good as shown in figure 9 witch present an error of learning equal to 10E-8 the neural architecture used for this model is [11].:

2 neurons in the input layer,

2 neurons in the first next hidden layer, and 4 neurons in the second one

1 neuron in the output layer

the learning rates is 0.01

The training pattern is 100 epoch.

For simulation work, the Data Base has been created by using the *Ip*-and *Vp* then calculating the optimal duty cycle eq (21).

Utilizing equation (7)

The result obtained using the _{ideal with} *V*_{opt} and *I*_{opt} are respectively the voltage and current of the Maximum power point

### 5.2. Fuzzy-logic control (FLC)

FLC is a way that mimics the human capability of judgment and reasoning [12]. A typical FLC based approach is composed by three modules [13]. fuzzification, Inference, defuzzification to made a closed-loop system that uses the process of fuzzification to generate fuzzy inputs to an inference engine processes the fuzzy sets using a library of IF-THEN. The defuzzification is the inverse process, used in a FLC control system in order to generate the create step size real values.

To adjust the controller input/output, SE, SCE and Sd gains are introduced. The controller crisp value (∆D) is the output and the two variables E and CE represent respectively the error and it’s derivate as the controller inputs [14].

With

The input E (k) shows if the load operating point at the instant k is located on the left or on the right of the maximum power point on the PV characteristic, while the input CE (k) expresses the moving direction of this point.

The fuzzy inference is carried out by using Mamdani method, Table 1, and the defuzzification uses the center of gravity to compute the controller output [14]:

The control rules are indicated in Table 1 with E and CE as inputs and ∆D as output. The corresponding variables member ship functions are given in Figure11.

The membership functions of E, CE and ∆D are depicted in figure 11:

E | |||||

ZO | |||||

ZO | ZO | ||||

ZO | ZO | ||||

Z0 | ZO | ZO | ZO | ||

ZO | ZO | ||||

ZO | ZO |

### 5.3. An adaptive neuro-fuzzy inference contol

Neuro-fuzzy technique is combining the ANN learning methods and the fuzzy inference system (FIS) [15], [16], [17]. In general the FIS structure consists of three important components: and the rule base one, for rule fuzzy selection [18]; a database, which defines the fuzzy rules MF and a decision generator, that bring up the inference procedure to finally generate an output as shown in Figure 12. The FLC concepts are based on knowledge from expert and in the other hand the neural network models are using a data base. Moreover, neuro-fuzzy approach seems covenant and suitable if both advantages of the tow method are combined. The neuro-fuzzy controller is the called, in this work adaptive network (ANFIS). The structure of the system is an adaptive network running as a first-order Sugeno fuzzy inference system. The hybrid ANFIS learning rule, combine the back-propagation gradient-descent first and second a least-squares algorithm for identification and optimization of the the Sugeno first order system. The the ANFIS working process is simplified by an equivalent ANFIS architecture with two rules are given in Figure 13 [4], [16], [18].

The given architecture has five layers and every node in a layer has a similar function. The two fuzzy rules, in which outputs are dressed as linear combinations of their inputs, are [4]:

Layer 1: consists of adaptive nodes that generate membership grades of linguistic labels based upon premise signals, using any appropriate parameterized membership function such as the generalized bell function given by [4]:

Where output O1,i is the output of the ith node in the first layer, x is the input to node i, Ai is a linguistic label (“small,” “large,” etc.) from fuzzy set A =(A1, A2, B1, B2,) associated with he node, and {ai, bi, ci} is the premise parameter set used to adjust the shape of the membership function [4]:.

Layer 2: are fixed nodes designated Π, which represent the firing strength of each rule. The output of each node is the fuzzy AND (product or MIN) of all the input signals [4]::

Layer 3: The outputs are the normalized firing strengths. Each node is a fixed rule labeled N. The output of the ith node is the ratio of the ith rule’s firing strength to the sum of all the rules firing strengths [4]::

Layer 4: the equation gives the rule outputs is:

With

Layer 5: the ANFIS output is given by:

The ANFIS controller developed in this section includes ' Ip ' and ' P ' as inputs and 'D’ as output which represent respectively, the PV current, the PV-Power and the converter duty cycle ratio. The input variables allow the ANFIS to generate the converter command. This last is applied to the converter, in order to ensure the adaptation of the power provided by PVG. This controller yields to an automatic fuzzy rules generation based on the Sugeno inference model. The equivalent neural structure of the proposed ANFIS is given in figure 13, figure 14 show the MPPT-ANFIS validation and errors curves.

## 6. Simulation results

In this section the performance of MPPT controller; Fuzzy, Neuronal, ANFIS will be distingue by the comparison between them and MPPT_{ideal}, he signal corresponding to the ideal MPPT present the reference used to compare the performances of various MPPT controllers

### 6.1. FLC

The figure 15 shows that the Fuzzy flow th MPPT_{ideal}, the FLC controllers ensure a good maximum power tracking. Nevertheless, the fuzzy regulator is oscillating around the MPP zone and is not powerful especially on weak irradiation level.

### 6.2. Neuronal network

The acquired sizes I_{P} and P are the input. The output of the controller is the duty cyclic D commanding an MLI block of the controller. The figure 16 contains the data base adopted for the training. This base corresponds to the MPPT ideal.

The figure 16 show well that controller MPPT ANN presents a mediocre performances with respect to the request of the incidental system with precipice irradiation variation. The time and the training memory capacity as well as the heaviness of a significant data base form one huge flexibility handicaps. To overcome these problems, we propose in the following section the algorithm combining the FLC and RNA.

### 6.3. ANFIS

The acquired sizes I_{P} and P are the input. The duty cyclic D is the output ordering the MLI block of Boost converter. Figure 17 contains the data base adopted for the training of the ANFIS. This base corresponds to ideal MPPT (MPPT ideal).

### 6.4. Comparative study

The ANFIS-MPPT Controller ensured the compensation of a reliable tracking on the low values of irradiation as shown in figure 17. The figure 18 confirms this improvement of the tracking in term of speed, increasing the step response and decreasing of error. Comparing performance put in evidence that the ANFIS precedes the RNA and the Fuzzy logic on MPPT action.

Figure 19 allows compare the different methods (P&O, Neuron, Fuzzy, ANFIS and MPPT _{ideal}) and this for a PV system coupled to a resistive load under a constant temperature and an irradiation (G=1000W / m², T=25C°)

The figure 18 illustrates the dynamic responses of the duty cycle and of the power of the GPV for a step of incidental irradiation of 1000W/m² and a temperature of 25°C. It is to be announced that the fuzzy controller presents a great oscillation beyond and an assailant mode to 0.6 seconds and a static error. The ANFIS and the P&O have the same response time. The RNA and for its parallel structure, justifies well the response time relatively instantaneous. The P&O and the RNA present the same static error which is larger than the fuzzy logic controller. The ANFIS MPPT is presented relatively as the most powerful controller with a static error near to zero. The figure 19 gives the plan of phase of the duty cycle according to the tension of the GPV. It is it should be noted that controller ANFIS-MPPT converges exactly towards the ideal MPPT with good performances superiors to the others.

## 7. Application: Water pumping

### 7.1. Dc motor model

The mathematical relation that describes the dynamic model of a DC motor is given by [19]:

With, *La, Kt, Va* and *Ia* are armature resistance, armature inductance, back emf constant (also motor torque constant), armature voltage and current, f is constant viscous friction coefficient and J the inertia Moment. In the mechanical equation (32) *Tem* and *TL* are the motor and the load (pump) torque, respectively [20].

### 7.2. Modeling of DC Water Pump

Recently, photovoltaic pumps use attracts more and more attention. For a positive displacement pump, the water flow of this type is depending on the drive moto shaft speed.

The piston of the pump uses the volume variations caused by the piston displacement in a cavity. The displacements in a different produce an aspiration or repression phase’s dependence on the direction.

The pump piston moves in a first direction, the liquid is compressed: the induction valve is closing and the repression valve will be open. And then the operation will be reversed when the pump piston moves the second direction. This type of pump has the advantage of dry operation. However, the flow generated by this pump is limited. The model of the positive displacement pump load torque with is [21].

The mathematical model that connects the pump water flow rate to the water column ‘h’ and power P and is: [22].

Figure 19 shows the characteristics of the power according to the flow rate (P=f (Q)). They are dressed according to various heights of the water columns as given by equations 34 and 35, [4].

From figure 19 it is easily to deduce that for a water height of 20 m, eq. 12 yields to the pumped water flow rate [11].

The MPPT ANFIS controller improves the PVG performances as clearly seen in PVG outputs tracking curves. The obtained results confirm the benefit in water flow rate is improved.

## 8. Conclusion

In this work a modeling study of the PV pumping system components is presented. Moreover in order to improve PV system performance, different maximum power point controller was studied and investigated. The system behavior incorporating the P&O, Fuzzy, ANN and neuro fuzzy were investigated and compared based on an extensive simulation work. Finally the Maximum Power Point tracking of PV pumping system is ensured by using an ANFIS controller. Performed simulation tests for the complete system lead to two main conclusions. The proposed PV system performances are highly boosted and the pumping flow rate benefit is going up to three times more [4].

## Symbols

G: | Global insulation (W /m²) |

Gref : | Reference insulation (W /m2) |

I p: | Cell output current |

Vp: | Cell output voltage |

I : | Light-generated current source (A) |

Rs: | cell series resistance (Ω) |

Rp | Cell parallel resistance (Ω) |

n: | Solar ideal factor |

Irs : | Reverse diode saturation current(A) |

KSCT: | Short circuit current temperature coefficient (A/°K) |

Tc : | Cell junction temperature (°C) |

Tc_ref : | Reference cell temperature(°C) |

β : | Boltzmann constant ( 1.38e-23) |

Eg: | Band gap energy (ev) |

ns | Number of series cells. |

D | duty cycle |