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• model + ANFIS model Figure 3. Proposed ANFIS models for predicting the equivalent electrical circuit parameters. A set of 400 data pairs is used for training the developed ANFIS model. Three different PV module manufacturing types, namely monocrystalline, multicrystalline, and thin film, are present in the dataset and the created model is particularly effective for these manufacturing types of PV modules. A set of 30 data samples that is not included in the training is used for the testing. The stopping criterion is completing 10 training epochs. As ANFIS converges very fast, there is no need to use more than 10 training epochs. The weights are batch-updated and a bell-shaped curve is used as a membership function (MF). Each MF takes 3 parameters stored in the weight vector of the bell fuzzy axon and the output of the fuzzy axon is computed by: M F (x, w) = 1 1 + x −w 2 w 2w 1 , (14) where x represents the input and w represents the weight of the bell fuzzy axon. The MFs of fuzzy axons can be modified through back propagation during training to accelerate convergence. Results and discussion Implementation of ANFIS models A total of 400 data pairs are used for training. In each ANFIS structure, the number of fuzzy rules is chosen as 5. The learning algorithm is a hybrid combining back propagation, gradient-descent, and a least-squares algorithm. After training, completely unknown data parameters are presented to the model and the performance is tested. Figure 4 shows the comparisons of the actual and simulated values for checking the data set. The accuracies of the obtained models for PV modules are analyzed through a comparison between checking the data provided from the manufacturer and the corresponding simulated data obtained from the ANFIS output. Figures 4a, 4b, and 4c show the analysis results for each ANFIS structure created to extract the ideality factor ( n) , series resistance ( R s ) , and shunt resistance ( R sh ) , respectively. The average testing error obtained for n is 0.0373, for R s is 0.004116, and for R sh is 911. 0.035 0.0 3 0.025 0.0 2 0.015 0.0 1 0.005 5 10 15 20 25 30 Checking data index # for R s s 800 c 700 600 500 400 300 200 100 5 10 15 20 25 30 Checking data index # for R sh O ut put O ut put
• Figure 4. Comparison of the actual data (checking data) and ANFIS extracted data (FIS output) for the equivalent parameters of the PV modules, namely a) n , b) R s , and c) R sh Table 1 shows the actual equivalent parameters provided from the manufacturer and the predicted parameters of n, R s , and R sh obtained by means of the ANFIS for 3 different types of PV modules, namely monocrystalline (Shell SP70 [26]), polycrystalline (Kyocera KC60 [27] and Shell S75 [28]), and thin film (Shell ST40 [29]). The electrical characteristic data for these PV modules at standard test conditions (STC) are given in Table 2. The predicted values are obtained from testing the proposed ANFIS models for each equivalent parameter. The I L and I values are determined from Eqs. (5) and (7), and consequently, the single-diode equivalent circuit can be built. In Table 1, the P max values are estimated at a solar irradiance of 600 W/m 2 and at 25 ◦ C. It can be seen from Table 1 that the proposed ANFIS-based model shows good correspondence to the actual data, and therefore this model can be considered sufficient for the purpose of further study. Figures 5a and 5b show the relative percentage errors for the V mp and I mp values at different irradiance levels and at a 25 ◦ C constant temperature for the utilized PV modules, namely Shell SP70 (monocrystalline), Kyocera KC60, Shell S75 (multicrystalline), and ST40 (thin-film). The practical data from the manufacturers of PV modules are used in the percentage relative error calculation as actual data. The temperature is kept constant at 25 ◦ C. The relative error is the difference of the actual and proposed method results of the V mp and I mp values divided by the actual values. Table Estimated equivalent parameters of 3 different kinds of PV modules. Shell SP70 Kyocera KC60 Shell S75 Shell ST40 monocrystalline multicrystalline multicrystalline thin film Actual Predicted Actual Predicted Actual Predicted Actual Predicted value value value value value value value value R s (Ω) 0.44 0.47 0.15 0.17 0.19 0.17 14 17 R sh (Ω) 180 204 450 413 200 173 300 318 N 3 28 35 37 35 36 5 48 P max 6 72 05 83 63 47 74 87 0.5 1 5 2 5 1000 800 600 400 200 Solar irradiance (W/m 2 ) values provided from the manufacturer and the simulation results for the equivalent parameters obtained by the ANFIS models proposed in this paper. The temperature was kept constant at 25 ◦ C. As can be seen in these tables, the proposed model generates satisfactory results for a wide range of operating conditions. Unlike the previous works suggested by other researchers, an iterative technique is not required, and the proposed method is more advantageous compared with the conventional nonlinear programming techniques [30,31]. Because the method does not depend on the initial conditions, trapping to local minima solutions can be avoided.
• Application to a stand-alone PV system with battery charging To evaluate further the performance of the proposed PV model in the MPPT operation, a PV system with a battery charging application has been simulated. The model-based MPPT algorithm is implemented in a DCDC converter to maximize the power generated by the PV module, independently of the temperature and solar irradiation. The schematic diagram of the PV system implemented in the power electronics simulator (PSIM) simulation software [32] is shown in Figure 6. Here, in order to simulate the PV modules and implement the MPPT algorithm, the codes are built in Visual C ++ software and linked to the simulation by dynamic link libraries. In the PVMODEL.dll module, a single-diode model of the PV modules has been built to simulate the different kinds of PV modules investigated in this paper. The MPPT.dll module is used as a controller to implement the MPPT algorithm, including the proportional-integral–type control. The inputs into the controller are the solar irradiance ( G) , temperature ( T ) , PV voltage ( V P V ) , and PV current ( I P V ) , and the single output is used to produce the reference signal for the DC-DC buck converter. The MPPT operation in the circuit is implemented based on the voltage. In the proposed method, the maximum power points for the corresponding solar irradiance and temperature values are searched by solving the obtained equations for the single-diode model of PV modules. The PV system is tested for 3 kinds of PV modules under changing insolation conditions. The results for the theoretical and proposed method are shown in Figures 7a–7d. The actual parameters and the parameters from the proposed method are used to model the PV modules in the PSIM schematic, at a constant temperature of 25 ◦ C, and for a step change of the solar irradiation between 800 and 1000 W/m 2 The results demonstrate that the acquired model is sufficiently accurate for real-time MPPT applications. Compared with the conventional P&O algorithm, the model-based algorithm provides a better transient response, as the MPP is obtained beforehand and a search is not required. The method also performs well for rapidly changing atmospheric conditions, as the calculations can be done very fast and the MPP is tracked using the obtained reference value. Because the obtained model is simple, the MPPT operation can be easily implemented using low-cost microcontrollers. The proposed ANFIS-based estimation method can be applied to the widely available manufacturing type of PV modules present on the market. This advantage is provided by the reason that the training data include 3 different types. For higher accuracy of the results and to increase the generalization ability, a larger amount of training data should be provided to the ANFIS. It should be noted that, for the newer technology of PV modules, the predictive performance can be satisfactory only if the training data are provided to characterize the new technology of PV modules. Otherwise, accurate results are not guaranteed for new samples outside of the available training set. T abl e
• Predict base d m o de l fo r th e S he ll SP7 Irradiation in tensi 1000 800 600 400 200 T abl e Predi fo r th e Ky o cer a K C6 m ulticr Irradiation in tensi 1000 800 600 400 200
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