Battery State-of-Charge Estimation Using ANN and ANFIS for Photovoltaic System

Ⅰ. Introduction

The interest in renewable energy industries, such as solar power generation and wind power generation, is increasing worldwide. This is due to the increasing severity of global environmental problems, such as the depletion of petroleum resources and global warming. The number of facilities that charge batteries using solar energy is also increasing. Among them, solar streetlights using photovoltaic (PV) power generation are ubiquitous, and their demand is continuing to increase [1].

A solar streetlight system is a standalone system. A standalone system has advantages, such as not requiring electric wire construction and reducing CO2 because it is operated by PV power generation. However, the system operation time is dependent on the battery. A day with less than 0.1 h of sufficient sunlight for power generation is considered a sunless day, and solar streetlights are guaranteed to function for at least three sunless day [2]. In other words, it is possible to operate the system stably by calculating the battery state of charge (SOC) so that the light-emitting diode (LED) lamp can be lit for three days by the power stored in the battery even when power generation is not possible due to the weather. The equation for obtaining the number of sunless days is as follows:

where n is number of sunless day, SOC is the state of charge, V is the nominal voltage, W is the power consumption, a is the loss factor of battery.

The SOC is determined according to the amount of charge from the solar cell module and the amount of power consumed by the LED lamp. Therefore, (1) can be used to determine whether at least three sunless days can always be guaranteed to control the LED lamp power consumption. This can be achieved by accurately estimating the battery SOC to be can actively adjust the available day in sunless day. Therefore, it is necessary not only to depend on the initial battery design capacity, but also to predict the present battery SOC more accurately and control the power consumption of the LED lamp to guarantee with greater certainty the number of days of idle time.

Current methods of estimating SOC are as follows [3]. The first is the Kalman filter method, which can estimate SOC with high accuracy. However, this method has high computational complexity and is difficult to use [4]. The second method is the current integration (CI) method, in which SOC is determined by the previous capacity and the capacity charged or discharged. This method integrates the charge and discharge currents and subtracts the initial SOC to estimate the current SOC. However, this method increases the error over time due to the accumulation of sensor errors. Therefore, it must be regularly calibrated to estimate the accurate SOC [5]. Finally, the open circuit voltage (OCV) method estimates the battery SOC by measuring the OCV. However, this method cannot be easily applied to a system operating in real time because it performs measurement without connecting the load [6]. Lupi et al. studied SOC estimation using FUDS and US06 drive cycle for electric vehicles [7].

In recent years, neural network (NN) models have been used in various fields, such as pattern recognition and classification [8]. The advantages of using a NN model for fault diagnosis include the fact that the system can be efficiently identified and the system parameters can be adjusted by adaptive learning and parallel processing [9]-[13].

This paper proposes a lead–acid battery SOC estimation method using an artificial NN (ANN) and an adaptive neuro-fuzzy inference system (ANFIS). The ANN model uses three different training methods (gradient descent (GD), Levenberg–Marquardt (LM), and scaled conjugate gradient (SCG) under the same network configuration. In this study, the performance of each network is compared.

Ⅱ. Neural-network structure

2.1 Artificial neural network

The basic structure of an ANN is presented in Fig. 1. An ANN consists of an input layer, hidden layer, and output layer. Each layer is composed of nodes and weights between the nodes. An ANN computes the correct output values for given input values. It also predicts the best generalized output for new input values even if the input values are not used for learning.

Fig. 1.

Structure of ANN

2.2 Adaptive neuro-fuzzy inference system

In the ANFIS model [14], the Sugeno fuzzy model is a systematic method of generating fuzzy rules from the input data and output datasets. Furthermore, it uses a hybrid learning method that is a mixture of the least squares estimator and GD method. The hybrid learning method has the advantage of being able to converge quickly [15].

As illustrated in Fig. 2, ANFIS is divided into six layers: the input layer, fuzzification layer, rule layer, normalization layer, defuzzification layer, and summation neuron layer. x_n represents the input values, A_n represents the sets of fuzzy, f_n represents the output function, and y represents the output value as follows:

Fig. 2.

Structure of ANFIS

$\[ y=k_0+k_1{x}_1+k_2{x}_2+\cdots +k_m{x}_m \]$

(2)

where k₀, k₁, and k₂ are the sets of arguments of set in rule i.

Ⅲ. Optimization methods

3.2 Levenberg-Marquardt method

The LM approach is a modification of the Newton method [17][18]. Using this approach, the Hessian matrix does not need to be calculated; therefore, it has fewer iterations and a fast convergence speed for secondary orders. M is the set of thresholds and weights of each layer, as illustrated in (9), and P(M) is presented in (10).

$\[ M=\left[\begin{array}{ccc}{w}_{11}& w_{12}\dots w_{IH}& \theta J\left(1\right)\dots \theta J\left(H\right)\\ V_{11}& V_{12}\dots V_{HO}& \theta I\left(1\right)\dots \theta I\left(O\right)\end{array}\right] \]$

(9)

$\[ \begin{array}{c}P\left(M\right)=\sum _{i=1}^I{e}_i{\left(M\right)}^2\hfill \\ \nabla P\left(M\right)=J^T\left(M\right)E\left(M\right)\hfill \\ {\nabla }^{2}P\left(M\right)=J^T\left(M\right)E\left(M\right)+S\left(M\right)\hfill \end{array} \]$

(10)

where E(M) express e_i(M), I is the number of patterns, J(M) is the Jacobian matrix as in (11), and S(M) is the error function as in (12).

$\[ J\left(M\right)=\left[\begin{array}{ccc}\frac{\partial e_1\left(M\right)}{\partial N_1}& \frac{\partial e_1\left(M\right)}{\partial N_2}& \frac{\partial e_1\left(M\right)}{\partial N_i}\\ \frac{\partial e_2\left(M\right)}{\partial N_1}& \frac{\partial e_2\left(M\right)}{\partial N_2}& \frac{\partial e_2\left(M\right)}{\partial N_i}\\ \frac{\partial e_I\left(M\right)}{\partial N_1}& \frac{\partial e_I\left(M\right)}{\partial N_2}& \frac{\partial e_I\left(M\right)}{\partial N_i}\end{array}\right] \]$

(11)

$\[ S\left(M\right)=\sum _{i=1}^I{e}_i\left(M\right){\nabla }^2{e}_j\left(M\right) \]$

(12)

$\[ \begin{array}{c}TRIANGLEM=J^T\left(M\right)E\left(M\right)\left[J^T\left(M\right)J\left(M\right)\right.\\ {\left.+\mu diag\left(J^T\left(M\right)J\left(M\right)\right)\right]}^{-1}\end{array} \]$

(13)

where ΔM is the adjustment quantity of M, and adjusting M represents adjusting the weights and bias, μ > 0 as constant.

This algorithm increases μ if the training fails and decreases μ if the training is successful. The algorithm steps are as follows:

Ⅳ. Proposed SOC estimation methods

The battery SOC estimation methods using ANN or ANFIS are proposed in this work. The concept of the SOC estimation method proposed is shown in Fig. 3. When the power production of the PV system by the solar panel is performed, it stores the charge start voltage together with the charge mode and starts to integrate the current. However, when power production is not performed, SOC estimation is performed by the proposed method together with the discharge mode.

Fig. 3.

Flow chart of battery SOC estimation for PV system

To perform battery SOC estimation using the proposed methods, the charge start voltage (V_c) and the integrated charge current (I_c) are used as input parameters in these models. The reason for using these three parameters as training data of the NNs is that they have an important relation to lead–acid battery SOC. The reference SOC is obtained by (14) as follows:

where I_d is the integral discharge current until the full discharge voltage, and C_N is the nominal capacity of the battery.

In this study, there are four SOC estimation models using NNs for the PV system, and their performance is compared using the mean squared error (MSE) and root MSE (RMSE). The scheme of battery SOC estimation methods using ANN or ANFIS is illustrated in Fig. 4. Based on the collected data, SOC estimation models were constructed with an ANN using GD, LM, SCG, and ANFIS using Hybrid. Then, the performance of the SOC estimation models generated using untrained data was compared.

Fig. 4.

Scheme of proposed battery SOC estimation methods

Ⅴ. Experiment results

5.1 Data acquisition environment

The experimental environment was designed to obtain real data required for battery SOC estimation for PV systems, as displayed in Fig. 5. In the experiment, 28 datasets were used. The datasets were divided into 22 datasets and six datasets as training data and test data, respectively.

Fig. 5.

Block diagram of experimental setup

The experimental environment consisted of a lead–acid battery, an electronic load, a power supply, a battery controller, and a PC. The battery controller prevented overcharging and overdischarging of the battery. In addition, the battery controller connected in series to the PC, and the data acquired by the battery controller were sent to the PC in real time. The power supply and electronic load were used to charge and discharge the battery. Table 1 presents a detailed specification of the experimental equipment.

Table 1.

Specification of experimental equipment

5.3 Comparison of SOC estimation models

The experiment was conducted using MATLAB, and the computer specifications were as follows: the central processing unit was Intel Core i7-3770 and the random-access memory was 8 GB. Three ANN models and one ANFIS model were implemented for the SOC estimation experiment.

The accuracy of the ANN-GD model was 98.74%, which was the second-best result; however, the learning time to the desired target was 10,432 epochs, which was considerably longer than that of other models. The accuracy of the ANN-LM model was 97.83%, which was the lowest of the three models. The accuracy of the ANN-SCG model was 98.7%, which was the third-best accuracy. Finally, the accuracy of the ANFIS model was 98.8%, which was superior among the four models, and the learning speed had the best performance with 81 epochs. An SOC estimation graph for six untrained data among the 28 collected data is presented in Fig. 6, and performance comparison is summarized in Table 2.

Fig. 6.

Plot of battery SOC estimation

Table 2.

Experimental results of the training methods

The experimental results indicate that the ANFIS model had the best performance among the four SOC estimation models for the PV system. To test the ANFIS model in a real environment, a monitoring program implemented in MATLAB was applied to the environment in Fig. 5, as illustrated in Fig. 7.

Fig. 7.

Application of ANFIS model in SOC estimation

The experimental results demonstrated that it was possible to effectively estimate the SOC of a 100-Ah lead–acid battery for PV systems using the implemented program.

Ⅵ. Conclusions

Battery SOC estimation methods using ANNs and ANFISs were proposed for PV systems. Based on the collected data, four models (ANN-GD, ANN-LM, ANN-SCG, and ANFIS) were implemented and compared using MATLAB. The experimental results revealed that the ANFIS model had 98.8% accuracy and 81-epoch performance and demonstrated the best SOC estimation performance for a PV system among the four models. Furthermore, the possibility of commercialization was confirmed by applying the ANFIS model to an actual environment. Future work will focus on the application of the proposed method to lithium batteries and on the performance comparison between the proposed SOC estimation methods and conventional methods.

Acknowledgments

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. 2019R1I1A3A01058319).

This study was supported by the BK21 Plus project funded by the Ministry of Education, Korea (21A20131600011).

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