In this research an improved approach for sizing standalone PV system (SAPV) is presented. This work is an improved work developed previously by the authors. The previous work is based on the analytical method which faced some concerns regarding the difficulty of finding the model’s coefficients. Therefore, the proposed approach in this research is based on a combination of an analytical method and a machine learning approach for a generalized artificial neural network (GRNN). The GRNN assists to predict the optimal size of a PV system using the geographical coordinates of the targeted site instead of using mathematical formulas. Employing the GRNN facilitates the use of a previously developed method by the authors and avoids some of its drawbacks. The approach has been tested using data from five Malaysian sites. According to the results, the proposed method can be efficiently used for SAPV sizing whereas the proposed GRNN based model predicts the sizing curves of the PV system accurately with a prediction error of 0.6%. Moreover, hourly meteorological and load demand data are used in this research in order to consider the uncertainty of the solar energy and the load demand.

Photovoltaic systems are environment-friendly energy systems. Thus, PV system installation has been given a big concern in the last three decades. However, PV systems’ high capital cost is considered one of the most important challenges to this technology, especially when it is compared with conventional power systems. Therefore, many research works are being conducted in order to propose methods for optimization of PV systems so as to provide reliable systems with minimal capital cost. In this context, Sharma et al. in [

In the literature, works related to PV system sizing can be categorized into intuitive, numerical, and analytical methods. The intuitive method is defined according to [

Due to the difficulty in calculating the optimum PV size by the simulation and analytical methods, artificial neural networks (ANN) are employed to overcome these limitations. For optimizing PV systems in many regions in Algeria, a combined numerical and ANN method has been used [

To overcome the limitations of the abovementioned methods in determining optimal sizing of PV systems, we propose an improved approach using a general regression neural network (GRNN) to predict the PV array and battery capacities in terms of LLP, latitude, and longitude. By using the GRNN model, the calculation for the optimum PV size of a standalone PV (SAPV) system can be automated and improved without the need for extensive mathematical calculations or graphical analysis techniques.

The background theory and formulation used in the analytical method for sizing SAPV system as proposed in [

PV module efficiency depends on cell temperature and it can be given as function of reference efficiency (

The difference between the energy at the front end of a PV system

System availability (reliability) is an important issue to be considered in designing of PV system. 100% availability of a PV system means that the system is able to cover the load demand all the year time without shortages. Consequently, 99% availability means that the system is not able to cover the load demand in 88 hours during one year time. This means that high PV system availability leads to high reliability and vice versa. However, high reliable PV system results high initial cost and, thus, it is not feasible to consider very high availability rates in designing PV system. The availability of a PV system can be as a loss of load probability (LLP) index. LLP is defined as the ratio of annual energy deficit to annual load demand and it is given by

The optimization process presented in [

Artificial neural networks (ANNs) are nonalgorithmic information processing systems which are able to learn and generalize the relationship between input and output variables from the recorded data. In this work we apply a GRNN model to improve the method presented in [

Topology of the GRNN used to predict the optimum size of a SAPV.

A generalized regression neural network (GRNN) is a probabilistic neural network consisting of an input layer, a hidden layer, a pattern/summation layer, and a decision node. Each predictor variable has a corresponding input neuron. The input values standardize the input values by subtracting the median and scaling the value to the interquartile range. The input layer feeds the hidden neuron layers where each training pattern is represented by a hidden neuron. In the pattern layer, there are only two neurons, a denominator summation unit and a numerator summation unit. The denominator summation unit adds up the weights of the values coming from each of the hidden neurons. The numerator summation unit adds up the weights of the values multiplied by the actual target value for each hidden neuron. The decision node divides the values accumulated by the numerator summation unit by the value in the denominator summation unit and produces the predicted target value of the GRNN. The advantage of GRNNs is simplicity, fast training, good approximation also with smaller training sets, and, thus, high efficiency in comparison to other networks [

In general, there is no rule to determine the optimum number of hidden nodes in the hidden layer without training several networks and estimating the generalization error of each one. Large number of hidden nodes resulted in high generalization error due to the overfitting and high variance. In the meanwhile, low number of hidden units causes large training and generalization error due to underfitting and high statistical bias [

In this research, three variables are used as input parameters for the input nodes of the input layer, latitude, longitude, and LLP. Two nodes are at the output layer, namely,

As mentioned before, in [

PV array sizing curve.

Figure

Battery capacity at different LLP.

From these figures, it is concluded that the proposed model is able to predict system sizing curve using only the location coordinates as well as the loss of load probability which can be considered as an advantage when it is compared to other ANN based models such as the models presented in [

Simulated load demand.

Based on the developed ANN, the optimum sizing ratios for the considered site (Kuala Lumpur) are ^{2} area, and 16% conversion efficiency (as reference value) and the rated battery voltage operates on 12 volts with a charging efficiency of 80% and an inverter conversion efficiency of 90%. The required PV array and battery capacities are 2.5 kWp and 324 Ah/12 V, respectively. The power generated by the proposed photovoltaic system is calculated with respect to the load (see Figure

Generated power by the designed system.

Energy balance for designed PV system.

Dumped power for the designed PV system.

Figure

Battery storage SOC for the designed PV system.

Loss of load days for the designed PV system.

In [

An ANN model is used to facilitate the use of a developed method for sizing PV system for Malaysia. The proposed ANN model predicts the size of the PV system in terms of LLP, latitude, and longitude. The developed ANN model showed high accuracy in predicting the PV system size whereas the MAPE is 0.6%. However, to ensure the validity of the proposed method, a designed example for a specific load is conducted considering the uncertainty in the solar radiation and the variation of the load demand. To validate the designed system we used a simulation based on hourly solar radiation and load demand. As a result, the LLP of the designed system is found to be 0.5% which indicates a sufficiently high reliability of the designed system.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work is supported by Lakeside Labs, Klagenfurt, Austria, and funded by the European Regional Development Fund (ERDF) and the Carinthian Economic Promotion Fund (KWF) under Grants KWF 20214|23743|35470 (Project MONERGY) and 20214|22935|34445 (Project Smart Microgrid).