The total of 200 patterns has been calculated for optimal couple sizing (CAop, CSop) as described above. From this set 180 patterns were used for the training of the network and 20 were used as for testing and validation for the model. These data have been randomly select. The architecture that gave the best results is shown in figure 4, which has two neurons in the input layer and two neurons in the output layer. However, the number of the neurons in the hidden layer must be adjusted during the learning phase, so that the network can be trained efficiently. Developed model can be generating the optimal sizing coefficients from only the geographical coordinate. These coefficients allow calculating the PV-array area (APV) and the useful accumulator capacity (Cu). The diagram block of developed model is provides in Fig.5. Note that the input/output data are the altitude, the longitude, optimal PV capacity (Caop) and optimal storage capacity (CSop) corresponding respectively ui(k), u2(k), yi(k) and y2(k).

Results

Fig.5. Diagram block of developed model

Once a satisfactory degree of input-output mapping has been reached, the MLP-IIR network training is frozen and the set of completely is an unknown test data that w. as applied for validation. After simulation of many different structures, we found that the best performance is obtained with a one hidden layer with 8 neurons. Table 2 displays the statistical features (mean, variance and correlation coefficient) between the measured coefficients and those estimated by our model, it is found that there is no significant difference between the estimated and the measured coefficient from the statistical features point of view. The correlation coefficient obtained for the validation data set is 97.9% for CAOP and 98.9% for CSOP. In this respect, the closer to unity these values are the better the prediction accuracy.

Table 2 Comparison between actual and estimated results Statistical tests Optimal sizing Calculated Estimated Variance Correlation couples Mean Mean coefficient (%) CAOP 1.076 1.051 0.270 97.9 CSOP 1.135 2.112 0.226 98.9

Table 3 lists an example of the results obtained after conducting several simulation comparisons in terms of performance among different neural network structures. The performance the model significantly as the number of hidden neurons is increased until 8 neurons. At this point, adding more hidden neurons to the networks results in a slight
improvement in performance. The MLP-IIR model present good results and take less iteration compared between other neural structures. Figure 6, shows clearly there is almost a complete agreement between the measured (numerical model) and estimated coefficients by our model MLP-IIR, also a contribution with the others neural networks.

Table 3. Training results from each network structures Network structure Mean Square Error (MSE) # of Iterations MSE for test set MLP 2x4x4x2 0.095 640 0.087 2x6x2 0.074 935 0.060 2x10x2 0.087 1054 0.092 RBF 2x2x2 0.051 368 0.074 2x6x2 0.043 436 0.065 2x8x2 0.035 525 0.045 MLP-IIR 2x4x2 0.021 163 0.032 2x8x2 0.013 250 0.022

In this part, we present an example in order to illustrate how one uses this model to determine the PV-array area and useful capacity. Firstly, you were to give in input of the model the geographical coordinate of the site, which you want install the PV system. Then, from the model we obtain the Caop, and Csop, for given consumption, Eq(1) allows to calculate the APV and the Cu, the number of solar modules and batteries are determining according to unit dimension of module and the storage capacity of the battery. Table 4 shows the results obtained for some sites from the north towards the south of Algeria.

Table 4. Example of sizing in isolated sites Sites LLP=1%, L=2KW/Day Latitude (Deg.) Longitude (Deg.) Caop PV-array Area Apv (m2) Csop Useful accumulator capacity CU (KW) 36 0 1.92 7.8049 1.74 2.87 35 8 2.59 8.0000 2.46 3.14 34 2 1.98 6.2051 1.85 2.48 33 -1 1.25 3.3333 1.52 2.10 32 9 0.96 2.1224 1.31 1.52 31 -4 0.95 1.9200 1.29 1.52 30 -3 0.90 1.4815 0.97 1.08 29 5 0.87 1.2857 0.86 0.70 28 -2 0.78 0.9655 0.83 0.70 27 10 0.78 0.9333 0.78 0.62 26 2 0.77 0.9180 0.78 0.56 25 -2 0.77 0.7742 0.76 0.56

Fig.6. Comparison between measured and others estimated models

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3tes

Conclusion

The objective of this work is to train the MLP-IIR model to learn the estimation and modeling of the optimal sizing coefficients of stand-alone PV system with a minimum of input data. Once trained, the MLP-IIR estimates these coefficients faster. The validation of the model was performed with unknown sizing coefficient, which the network has not seen before. The ability of the network to make acceptable estimations even in an unusual day is an advantage of the present method. It should be stressed that the training of the network required about 1 minute on a Pentium III 800MHz machine. The estimation with correlation coefficient of 98 % was obtained. This accuracy is well within the acceptable level used by design engineers. The traditional methods of sizing PV system (empirical, analytical, numerical and hybrid) allows to estimate the sizing of PV system for one given site, and requires the availability of several parameters such as the daily solar radiation data, altitude, longitude, the load, the characteristics of stand alone PV system, the inclination of the panels and to take very much computing time for estimation of optimal coefficients. On the other hand, the model that we developed allows estimating the PV-array area and the storage capacity from a minimum input data (altitude, longitude) based on the optimal sizing coefficients and does not take much time for simulation. The advantage of this model is to estimate of the PV-array area and the storage capacity in any site in Algeria particularly in isolated sites, where the global solar radiation data is not always available. Also, this presents a good result compared between other neural network architecture. The results have been obtained for Algerian meteorological data, but the methodology can be applied to any geographical area.

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