ANFIS-based estimation of PV module equivalent parameters: application to a stand-alone PV system with MPPT controller

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1. 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