Paper Title (use style: paper title) [301582]

[anonimizat]*, [anonimizat]**, Said Drid***, and M.E.H. Benbouzid****

*[anonimizat]-Hamma, 40000, Algeria

**Laboratory of Innovative Technology (LTI), [anonimizat] l'Aisne, 02880 Cuffies, France.

***[anonimizat]. [anonimizat] 2, [anonimizat], 05000, Algeria

****[anonimizat] 4325 [anonimizat] 93837, 29238 Brest, France

e-mails: [anonimizat], [anonimizat], [anonimizat], [anonimizat]

Abstract— This paper deals with maximum power point tracking of the photovoltaic system using hybrid Neural Network and Kalman filter Algorithm. The design of maximum power point tracking algorithms for Photovoltaic systems can be greatly enhanced by using advanced and accurate models. The analytic equation of the PV model cannot be easily expressed because the relationship between parameters is nonlinear. Using a neural network can improve the accuracy of the electrical equivalent circuit parameters where they depend on solar irradiation and temperature. The proposed neural network is trained once by using some measured I–V and P–V curves and to keep in account the change of all the parameters at different operating conditions. [anonimizat], and to maximize the power of photovoltaic system a Kalman filter method have been used. The proposed algorithm is tested under different operating conditions. All results confirm the effectiveness of our approach.

Keywords—Photovoltaic; Neural Network; Kalman filter ; [anonimizat]; MPPT.

Introduction

Today photovoltaic (PV) systems are becoming more and more popular with increase of energy demand and there is also a great environmental pollution around the world due to fossils and oxides. Solar energy which is free and abundant in most parts of world has proven to be economical source of energy in many applications [1]. The energy that the earth receives from the sun is so enormous and so lasting that the total energy consumed annually by the entire world is supplied in as short a time as half an hour. The sun is a [anonimizat]. [anonimizat]. [anonimizat]. It does not have any moving parts and no materials consumed or emitted. Unfortunately,[3] [anonimizat] (9 to 16%), especially under low irradiation conditions and the amount of electric power generated by solar array changes continuously with the weather conditions like irradiation and temperature.

The photovoltaic module converts solar energy by photovoltaic effect into direct current (DC) stored in batteries as energy banks. The inverter technology converts the stored energy into an alternating current (AC) for various applications. The booster converter (a step-up converter) is a DC-to-DC power converter with an output voltage greater than its input voltage [2–3].

Various authors have proposed and developed different modeling and simulation techniques for the static solar photovoltaic system based on analytical and numerical techniques. However, due to the peculiar nature of the solar photovoltaic module an efficient technique to solve this problem is crucially important. Contemporary literatures have employed the use of various application tools such as Labview, Pspice and Matlab Simulink to solve the complex non-linear characteristics of the solar photovoltaic array based on standard mathematical generalised equation [4-5]. The artificial neural network techniques have been employed in various research fields suitable in handling complex non-linearities, uncertainties and variations in the input parameters in a controlled system. The training set of the neural network was constructed starting from the curves generated by the mathematical model. Each curve is identified by a pair of climate parameters {G, T}, then for each pair of temperature and irradiance. The V-I characteristics is highly nonlinear and change with irradiation and temperature. In general, there is a unique point on the V-I curve called the maximum power point MPP at which the PV array operates at maximum efficiency. Using the maximum power point tracker MPPT to track the MPP increases the generated energy from PV system about 30%. MPPT must be fast to track the MPP effectively and smart to avoid divergence in fast changing irradiance or temperature.

When this system of tracking is designed, it must be able to maintain the values of the output signals within the desired ranges, before any disturbance control should be able to make decisions for necessary actions, and maintain system within certain parameters, default.

As conventional control systems often may be ineffective or inefficient to noise, it is necessary to implement new systems, whose response to the above problem, and approach the ideal response. The Kalman filter is an alternative, able to significantly improve system response to problems and noise.

The Neural network model and Kalman filter control. The tracking algorithm integrated with a solar PV system has been simulated with boost DC-DC converter in stand – alone PV system. The proposed PV system with boost DC-DC converter is shown in Fig.1. The given model operates very fast in comparison on with available methods and has proper accuracy in maximum power point tracking (MPPT).

Fig.1. Photovoltaic module with DC-DC boost converter.

GENERAL SOLAR CELL MODEL

Conventional one diode electrical Model

A PV cell can be represented by an equivalent circuit [5] as shown in Fig. 2. The characteristics of this PV cell can be obtained using standard equation (01).

Fig. 2 Equivalent circuit of PV cell

IPV = photovoltaic current

IO = saturation current

Vt = NS k T/q, thermal voltage of array

Ns = cell connected in series

T = is the temperature of the p-n junction

k = Boltzmann constant

q = electron charge

RS = equivalent series resistance of the array

RP = equivalent parallel resistance of the array

a = diode ideality constant

Fig. 2 shows the single diode model. A single solar cell will produce only a limited power. Therefore it is usual practice in order to get desired power rating the solar cells are connected in parallel and series circuits which form a module. Such modules are again connected in parallel and series to form a solar array or panel to get required voltage and current. The equivalent series and parallel resistance of the array are denoted by the symbol RS and RP respectively in the equivalent circuit.

From the general I-V characteristic of the practical photovoltaic device one can observe that the series resistance RS value will dominate in the voltage source region and the parallel resistance RP value will dominate in the current source region of operation.

The general equation of a PV cell describes the relationship between current and voltage of the cell.

Since the value of shunt resistance RP is high compared to value of series resistance RS the current through the parallel resistance can be neglected. The light generated current of the photovoltaic cell depends linearly on the solar irradiation and is also influenced by the temperature [6] given by the equation (02)

IPV= is the light generated current at nominal condition (250C and 1000 W/ m²)

ΔT = T – Tn

T = actual temperature [K]

Tn = nominal temperature [K]

KI = current coefficients

G = irradiation on the device surface [W/m2]

Gn = nominal irradiation

The current and voltage coefficients KV and KI are included as shown in equation (03) in order to take the saturation current IO which is strongly dependent on the temperature.

KV = voltage coefficients

KI = current coefficients

Fig.3 shows the simulated P-V characteristics for varying irradiation and temperature in MATLAB/SIMULINK environment. It can be observed from simulated results as shown in Fig. 3(a), the photo current is directly proportional to irradiation. It is noted from Fig. 3(b) that the terminal voltage increases with decreasing temperature

Fig. 3. Simulated waveforms showing the effect of

(a) Irradiation and (b) temperature on P-V characteristics.

The manufacturer’s data at standard conditions are given as Pmax = 80W, Imax = 4.515 A and Vmax = 21.6V. The simulation results obtained were: Pmax = 78.51W,

Imax = 4.35 A and Vmax = 18.2 V. [4-6].

Simulated I-V, P-V characteristics for the maximum power point tracking (MPPT) is shown in Fig.4.

At this Maximum Power Point (MPP), the solar array is matched to its load and when operated at this point the array will yield the maximum power output. From Fig. 4 (a) & (b), it is observed that the power output has an almost linear relationship with array voltage unit, hence the MPP is attained. Any further increase in voltage results in power reduction [7]

Fig.4. PV array simulated curves

(a) I-V curve (25°C) and (b) P-V curve (1000w/m2).

Neural network model

The usual mathematical model photovoltaic cell provided a satisfactory result but required detailed knowledge of physical parameters relating to the photovoltaic cell material, weather condition, illumination factor and temperature. For that reason, the derived mathematical model may be inexact [5]. Neural network modeling does not require any physical definitions for a photovoltaic array, that's why they have a potential to provide a superior method of deriving non-linear models than the already established conventional techniques. The photovoltaic array was modeled using techniques of ANN namely back propagation neural network.

Back Propagation is a multilayer feed forward network. It was created by generalizing the Widrow-Hoff learning rule to multiple-layer networks and nonlinear differentiable transfer functions [8]. Input vectors and the corresponding target vectors are used to train a network until it can approximate a function, associate input vectors with specific output vectors, or classify input vectors in an appropriate way as defined. Networks with biases, a sigmoid layer, and a linear output layer are capable of approximating any function with a finite number of discontinuities [8]. The back-propagation computation is derived using the chain rule of calculus. The term back-propagation refers to the manner in which the gradient is computed for nonlinear multilayer networks, it involves performing computations backwards through the network.

In the basic back-propagation training algorithm the weights are moved in the direction of the negative gradient. The training process requires a set of examples of proper network behavior – network inputs and target outputs. During training the weights and biases of the performance function for feed forward networks is mean square error MSE – the average squared error between the network outputs and the target outputs [9].

Fig. 5: Back-Propagation Neural Network for PV array modeling having 3 inputs 4 neurons in hidden layer and 1 output

Fig. 6: Matlab generated Back-Propagation Neural Network for PV array modeling having 3 inputs 4 neurons in hidden layer and 1 output

The proposed architecture of Artificial Neural Network (ANN) for modeling consists of three layer structure of 3-4-1. The input to the ANN is a linear layer consisting of three neurons whose inputs are radiation, temperature and array voltage. The hidden layer in Back Propagation consists of four neurons with tangent sigmoid function. Sigmoid transfer function is used here because it is differentiable. The output layer of the ANN consists of one linear neuron with purelin function which is a linear transfer function and it give the value of load current. Every neuron is provided with biasing which is not shown in the Fig. 6.

DC – DC BOOST CONVERTER

A dual stage power electronic system comprising a boost type dc-dc converter and an inverter is used to feed the power generated by the PV array to the load. To maintain the load voltage constant a DC-DC step up converter is introduced between the PV array and the inverter. The block schematic of the proposed scheme is shown in Fig. 1.

In this scheme a PV array feeds DC-DC converter used in step-up configuration.. For a dc-dc boost converter, by using the averaging concept, the input–output voltage relationship for continuous conduction mode is given by

Where, D = duty cycle. Since the duty ratio “D” is between 0 and 1 the output voltage must be higher than the input voltage in magnitude [9-10].

Kalman filter MPPT Controller

Kalman filter principle

The Kalman filter is a well-known recursive algorithm that takes the stochastic state space model of the system together with measured outputs to achieve the optimal estimation of states. Noise effect in the system is decreased due to recursive cycles which finally lead to the true value of measurement [6].

Fig. 7 shows the generic block diagram of Kalman Filter.

Fig. 7 show the input x[k] at iteration t, and the control process u[k] at iteration k, the added process noise w and the added measurement noise v. Then the Linear Kalman filter [6] equations are given as follows.

Time update (prediction state)

Here Q is the process noise covariance, be the state estimate at iteration given by the results from former iterations, be the state estimate at iteration k given by the measurement output y[k], be the priori error covariance and () be the posteriori error covariance. A & B are constants. And according to equation (05), is similar to.

Measurement updates (correction state)

Where R is the measurement noise covariance, is the Kalman gain & C is constant. The above equations [8] represent Kalman filter implementation for a generic linear discrete system. The time update predicts forward state estimate and error covariance. The estimates are then put into measurement update which acts as correction mechanism and correct the estimated values. As the above cycle takes place multiple times turn by turn the noises are reduced and the error covariance becomes closer and closer to zero.

MPPT using linear Kalman filter approach

The MPPT using by the Kalman filter is an alternative to expect an acceptable performance against both the noises and dynamic environmental condition changes. Due to the estimation ability of the Kalman filter in the dynamic system with the noisy environment, the accurate MPP can be predicted by the Kalman filter without any drop of system dynamics; other MPPT methods sometimes lose their system dynamics partially to eliminate the noise effects. High computing amount of the Kalman filter may be considered to a disadvantage.

According to the P – V curve of a solar photovoltaic cell, power increases with a gradual positive slope until reaches one optimal point and decreases after that steeply. Based on that feature the MPPT algorithm is governed by the given state equation (7) where is the value of voltage updated by the MPPT controller at iteration k+1.

M is the step size corrector and denotes the slope of the P – V curve at instant K of solar array. The slope is same as control unit u[K] and on adding process noise w into the system a similar one dimension linear state space equation can be formed. The measurement equation is dependent on and measurement noise v.

Considering as the reference voltage at given instant we get the updated measurement equation (08) as

Two known values, and are used for Kalman filter estimate.

Operating Summary in Proposed Method

Table 1 is the summary of the time and measurement updates in proposed method. From the computed Kalman gain, the estimated voltage and error covariance are corrected to and respectively in the measurement update. The time update estimates the forwarding voltage and error covariance based on the voltage and. Consequently, the estimation result is expected to be closer to a MPP than as a result of these cycles [12].

Table 1 : Measurement and time updates in general Kalman filter

Results and discussion

Response of MPPT Kalman algorithm in front of weather conditions change:

Solar irradiation change

By the applying different solar irradiation disturbances to the ANN model we obtain the output voltage transient response of boost converter. Fig 8 present the variation of the solar irradiation from [1000 to 100] W/m² with fixed temperature T= 25°c.

Figs 09 present the impact of the variation of solar irradiation on the photovoltaic system with the proposed algorithm.

Fig 10 and Fig 11 represents the I-V and P-V characteristic and shows as the impact of the variation solar irradiation represented by E1…..E10.Under this condition, the algorithm of maximization gives rise to spiral shaped which represent the different point of maximization of photovoltaic system. . .

Temperature change

We applied an abrupt temperature change from 25 °C to 75 °C. Fig 12 present the variation of the temperatures from [25 to 75] °c with fixed solar irradiation E= 25°c.

Fig 13 present the behavior of the power of the photovoltaic system when we applied a variation on temperature.

Fig 14 and Fig 15 represents the I-V and P-V characteristic and shows as the impact of the variation solar irradiation represented by T1…..T10.This change in temperatures will involve a fast change of the optimal panel voltage, and the MPPT algorithm reacts in a fast and consistent behavior. Although fast temperature changes are not usual, this simulation allows us to evaluate the robustness of the MPPT algorithm.

Simulation results show that Kalman MPPT algorithm can quickly and accurately find the maximum power of ANN model and achieved a accurate sense of the maximum power output.

Fig.8 Solar irradiation change

Fig.9.PV power according irradiation variations

Fig.10 I-V characteristic

Fig.11 P-V characteristic with solar irradiation change

Fig.12 Temperature change

Fig.13. PV power according temperature variations

Fig.14 I-V characteristic with Temperature change

Fig.15 P-V characteristic with Temperature change

Conclusion

In this paper a hybrid Neural Network-Kalman filter algorithm is presented in order that PV systems operate at maximum power point, even if there are temperature and irradiation changes.

This algorithm robustness was noticeable in the estimation of locate the maximum power point voltage range, the voltage range with a small step as a control voltage to the corresponding instantaneous power, accurate and Features simple nonlinear filtering power curve, after power is relatively select the maximum power point and the corresponding control voltage. Not only guarantees the tracking speed and improve the tracking accuracy; judging by the state of mutation status tracking in front of weather conditions change, avoiding MPPT algorithm "miscarriage of justice" issue. The system was analyzed and designed, and performance was studied by simulation with simulink matlab.

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