A photovoltaic maximum power tracking using neural networks

WM-5-3 A PHOTOVOLTAIC MAXIMUM POWER TRACKING USING NEURAL NETWORKS Hussein M. Mashaly Adel M. Sharaf Dept. of Electrical Engineering, UM3 Fredericton, N.B. Canada E3B 5A3

Mohamed Mansour Ahmed A. El-Sattar Dept. of Electrical Power and Machines Ain Shams University, Cairo Egypt 3rd IEEE-CCA

Keywords: Solar energy, neural networks, intelligent control, power systems.

Abstract

by on-line training for weight adaptation. 2. Modelling of PV line-commutated inverter scheme

The paper presents Iaboratory implementation of a photovoltaic artificial neural network (ANN) based maximum power tracking controller. The control objective is to track the maximum available solar power in a photovoltaic array interfaced to an elecmc utility gnd via a line-commutated inverter. The inverse dynamic characteristics of ths interface scheme is identified via offline training using a multi-layer perceptron type neural network. The ANN output is used as the comol signal to vary the line-commutated inverter firing control angle, hence track the available maximum solar power. The weights of the ANN is also updated by a novel on-line training algorithm which utilizes the on-line power mismatch error. This ensures on-line maximum solar power tracking. The proposed controller is compared with a well tuned conventional proportional plus integral PI controller to validate its effectiveness.

The PV scheme structure is shown in Figure 2. The solar array is emulated using the quasi-static solar cell model equation relating voltage and current as follows (1)

$y= IsNp ,

(2)

V,=

V,N,

where V, is the single cell voltage, I, is the cell current, q is the charge of an elecuon, K is Boltzman’s constant, A is completion factor and its value is in the range 1 to 3 [6], T is the absolute temperature, $h is the photo current, I, is the reverse saturation current, R, is the equivalent series resistance of the cell, J& is the solar array current, Vp is the array voltage, N, is the number of strings in parallel, N, is the number of solar cells in series for one string and B is a constant equal to (l+RJR&), where & is the equivalent shunt resistance of the cell. The photo-current $h is a function of the solar insolation level SIand cell temperature and its variation with SIis given as

1. Introduction

Renewable photovoltaic (PV)interface schemes with the electric utility grid are rapidly growing in recent years. The scheme comprises a Photovoltaic PV array, DC link and line-commutated inverter as the ekments of this energy converter. Figure 1 shows The power-current characteristics of the PV anay it is nonlinear and depend on the solar insolation level and operating cell temperature. Photovoltaic arrays cost is still high, so it is recommended to utilize the maxi” available solar power at all times. There are number of control schemes for regulating the output power of the PV m y , some use conventional PID controllers [6], others used rule based f i z z y logic tracking regulators [7,8]. Recently ANN technology has attracted new interest in electrical power engineering applications, refs. [2] to [5] gve examples of these new applications. This paper presents a novel ANN based controller for maximum solar power on-line m k m g and u m o n of a photovoltaic energy interface scheme. The proposed ANN controller is trained by off-line training using a bench mark model and

0-7803-1872-2/94/$4.00 0 1994 IEEE

V, = (A.KT/q) In ((I, - BI, - I,) /’ I,) - I$,

$,=kS,

(3)

where k is a constant of value 0.56 Amps/W/cm2and S, is the solar insolation level in W/cm’ [ 6 ] . The characteristic equation relating the PV cell’s voltage to current and the associated parameters such as N,, N, etc. are programmed into a PC AT digid computer and used to control the ourput of a dc power amplifier whose output volt-ampere characteristics are made to emulate the actual PV solar array characteristics. Using an A/D data translation card DT282 1, the solar insolation level S, and the array current $. are sampled at sampling interval 0.08 sec. and input to the digital computer PV emulator, then used to compute the corresponding b , V , , I,. Knowing the cell current I, and using the above characteristic equation, the full array output voltage Vp is computed on-line as a voltage reference signal which is fed to the power ampWier

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neuron in every layer receives its input from the previous layer, then activate it by the sigmoid activation function and send the output to the next layer. The output vector of the network is the output of all neurons in the output layer. It has been proved that a network with one hidden layer 1s sufficient to approximateany nonlinear conmuous function [3]. In t h s paper a two layer feed-forward perceptron network is utilized. It has an input vector with five variables, one hdden layer with ten hidden neurons, and one output layer with one neuron. Ths network is employed in the process inverse dynamic model identificationand in the neural nerwork controller mcture. The multi-layer perceptron is represented by a recovering and learning stages, Figure 3 shows a schemahc diagram of this multi-layer perceptron, the recovering stage is described as follows

through the D/A converter of the data translation card DT2821. By appropriately setting the gain of the power amplifier, the solar array’s voltage-current V-I nonlinear characteristic can be emulated at the power amplifieroutput. This PV array computer based simulator is used as a nonlinear quasi-statx dc source to experimentally verify the proposed ANN control scheme with the f i z q logic controller bench mark model in the laboratory testing. The photovoltaic array is interconnected to the electric utility via a dc link line-commutated inverter ( f ~ n delay g angle aI in the range (95” to 180). The dynamic equation introduced by the DC link smoothing reactor is

where & and L,,c are the DC lmk smoothng reactor resistance and rnductance respectwely, V, is the DC controlled voltage at the sx-pulse inverter dc side, and it IS related to the utrlity hne to neutral voltage V, (peak value) by the followmg equanon

where X,, is the commutamg reactance represenring AC transformer inductance. The inverter output voltage V, (peak value) is related to the uthty’s line to neutral voltage V, @e& value) by the rums ran0 (q:1) of the output transformer (that is V, = n,V,). The output power of the PV m y is

where: i = l , 2,-_-N j = 1 -. 7 ____ N J Wlj -weight between input i and neuron j in the hidden layer W, -weight between hdden layer neuron j and output layer neuron a, -input to the network Y -input to neuron j m the hdden layer a, -output of neuron J in the hidden layer U, -input to the neuron in the output layer 00 -output of the neuron in the output layer f,(.) -sigmoid activat~onfunction 1 / ( 1 + e-’ ) BJ -bias of the neuron j in the hidden layer Bo -bias of the output neuron 7

i6)

The optimal maximum power operating point of Fig 1 is determined for dfferent solar w l a t i o n levels S , using an off-line curve fitting model. The data obtained is least squares-curve fitted and used to relate P, to S, variations using a second order polynomial. assuming constant cell tempemure. pnf= -1 1.575 + 4785.7 S, + 4706.8 SI’

17)

The learning stage is performed by updatlng the weights and biases using Back-Propagation BP algorithm with the descent gradent method in order to minimize a mean squared error performance index E, and it is given as

The on-line reference power P,, is computed using equation (7) and the amy power P, is also calculated using equations (1-6). 3. Multi-layer feed-forward perceptron With error back-propagation

where V, is the he-commutated inverter control signal and it is the target o q u t for the network. The weights and biases are updated by BP algorithm as follows:

The multi-layer feed forward perceptron structure is one of the most popular neural networks architecture. It has an mput layer, an output layer and one or more hdden layers, each layer has a certain specified number of neurons. The network receives the outside mput. scale it by weights and biases passes it to the neurons in the next layer. Each

Wj(k+l) = WJ (k)+ p&a,(k)

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(13)

Wjj(k+l) = Wjj(k) + &(k)

(15)

Bj(k+l) = Bj(k) + pkj

(18)

model can lead to sluggish control performance, because it is difficult to have a global training data ensembles to describe all possible excursions and dynamic situations [4,5]. To over come this limitations the inverse process model weights and biases are also updated on-line using the same tuning steps described through equations 8 to 18 by BP algorithm, only equation 14 is modified to use the actual on-he process power error and it is given as

where p is the learning rate. Selecting the ANN structure, number of layers, number of neurons in each layer and the learning rate is done using a guided trial and error approach as given in many refs. [1,2,3]. The inverse dynamic characteristic of the process is identified by the above described multi-layer feed-forward perceptron. It is trained based on the network output error. The input-output data patterns are obtained from the bench mark model using the robust fuzzy logic FL controller over a wide range of operating conditions and excursions. The fuzzy controller performance is described by the authors in ref. [81. Any other conventional well tuned PID controller could have be utilized for the same training purpose. The training set has 600 input-output patterns, the network inputs are the power reference, actual process output power and the conirol voltage as well as their delayed or prior values, at which i' stands for the time delay operator. The delayed values represent the process time slice performance history, they allow the network which realize a static function map to learn the process dynamic performance. MATLAB sofhvare package (version 4) with the neural networks toolbook was used for the off-line training of the input-output ensembles using an (IBM 486/33 M H z ). The training parameters are listed as follows:

The on-line training and weight adaptation is done using the actual process output error (PJk) - P,(k)) instead of the ANN network output error used earlier in the off-line training phase, because the network is CoMected in series with process then its error (V,(k) - o,(k)) is usually unknown due to the absence of a target value for V, at a certain operating point. The on-line haining enhances the power tracking capabilityof thls energy conversion scheme. Figure 5 shows the neural network control structure with the on-line training procedure. 4. Experimental results The proposed photovoltaic interface scheme with the novel ANN controller is implemented using an AT PC lgital computer with a data translation card DT282 1. The scheme variables are updated at a sampling interval equal to 0.08 sec. Figure 6 depicts the scheme dynamic performance for both the A." and the bench mark fuzzy logic controller at (+-) step change in the solar insolation level S, from 0.059 to 0.078 (W/cm2).It is clear that the ANN based controller has a better response than the fuzzy logic controller. Figure 7 shows the scheme performance with the ANN controller for a (+-) step change in the solar insolation S,from 0.025 to 0.08 (Wkm'). A well tuned conventional proportional plus integral PI controller is compared with this scheme in order to vahdate the ANN controller effectiveness. Figure 8 depicts the scheme performance with the PI controller for the same dynarmc conditions as Figure 7. It is clear that the ANN gves better dynarmc tracking results than the PI controller under same operating condtions, for which the PI controller shows slightly steady state oscillations as indicated in Figure 8. Figures 6 and 7 validate the robustness of the proposed ANN tracking controller for maximum power m k i n g and efficient energy utilization.

9 inputs = 5 f: outputs = 1 f: hidden layer = 1 f: hidden layer neurons = 10 # output layer = 1 # output layer neurons = 1 training patterns = 600 learning rate = 0.00001 training time = 7 hours error goal = 0.0001 number of training iterations = 30000

The txaining program calculates the weight matrix W,j [5xlO] with the bias matrix Bj [lox11 for the input to hdden layer mapping, and a weight matk Wj [1x 1OJ with bias Bo for the hidden layer to output layer mapping. Figure 4 shows the neural network structure and the function approximation mapping for inverse dynamic model identification using the fuzzy logic controller. The weights and biases obtained only from off-line training are used to validate the ANN controller operation. The output of the ANN (0,)is used to adjust the line-commutated inverter firing angle a,.hence the power dram from the PV solar array is varied on-line in order to track and extract the maximum available solar power from the PV array at all times. (0,) is in the range (0 to 5 ) Volts and is corresponding to firing control angle a,range (180"to 90"). It is well known using this inverse "stationary" process

5. Conclusions An on-line successively tunable artificial neural networks

based controller is presented in this paper for on-line maximum solar power tracking of a photovoltaic electric utility interface scheme. The ANN network is an inverse dynamic process and an equivalent function mapping. Offline training is done first using a bench mark fuzzy logic

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Controller for a DC Motor”, IEEE Trans. on E. C.. Vol. 8, KO.1, March 1 9 9 3 , ~107-113. ~. [4] X. Cui and K. Shin, “Application of Neural Networks to Temperature Control in Thermal Power Plants”, Engg. Applic. Artif. Intell. Vol. 5, No. 6 , 1992, pp. 527-538. [5] D. S. Hofer, D. Neumerkel and K. Hunt, “Neural Control of a Steel Rolllng Mill”, IEEE Control System Magazine, June 1993, pp. 69-75. [6] O.Wasynczuk, “Modelling and Dynamic Performance of a Line-Commutated Photovoltaic Inverter System”. IEEE Trans. on E. C., Vol. 4, No. 3, Sept. 1989, pp. 3 7-343. [A Hilloowala R M. and Sharaf A. M., “A Rule-Based Fuzzy Logic Controller for a PWM Inverter in Photovoltaic Energy Conversion Scheme”, Proceedmg IEEE IAS Conference Houston, October 1992. [8] H. M. Mashaly, A. M. Sharaf, M. Mansour and A. A. El-Sattar, “Fuzzy Logic Controller for Maximum Power Trackmg in Line-Commutated Photovoltaic Inverter Scheme”, CCECE’ 93, Sept. 1993, pp. 12871290.

controller then the ANN network weights and biases are updated successively on-line using the actual process output power error. The proposed controller is compared with a well tuned PI controller. The experimental results validate the tracking robustness of the neural network based solar power traclung controller, also it gives a better results than the conventional PI controller in terms of over shoot, under shoot and steady state error pmcularly under parameter variations and dynamic excursions. 6. References [l] Paul J. Werbos, “Back propagation Through Time:

What It Does and How to Do It”, Proceehgs of the IEEE, Vol. 78, No. 10, October 1990, pp. 1550-1560. [2] Y. Zhang, G . P. Chen 0. P. Malic, and G. S . Hope, “An Artificial Neural Network Based Adaptive power system stabillzer”. IEEE Trans. on E.C., Vol. 8, No. 1, March 1993, pp. 71-77. [3] S.Weerasooriya and M. A. El-Sharkaw, “Laboratory lmplementadon of a Neural Network Trajectory

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Fig. 1 Power current characteristics of the PV array at T=28” and different solar insolation levels.

Fig. 2 Block diagram of experimental setup of the PV array and line-commutated inverter scheme.

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Fig. 3 Multi-layer perceptron network.

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Fig, 5 A N N controller with on-line training using the power error.

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Time in sec. Fig. 7 Power change for +- step change in SI from 0.025 to 0.08 W/cmZwith the A" controller.

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