W-IFL: An Improved Maximum Power Point Control Model to Promote Renewable-Powered Vehicles

Abstract

Driven by economic development and environmental protection, vehicles are gradually renovating their power to renewable energy. As an essential part of renewable energy, photovoltaic (PV) energy is highly valued and studied worldwide. Future social development is inseparable from it when facing the current situation of exhausting fossil energy and highly polluting. To solve the problem of the low utilization of converting solar power to electrical energy, this paper proposes a wavelet-improved fuzzy logic (W-IFL) maximum power point (MPP) control model. The W-IFL designs a wavelet network for predicting the MPP and fuzzy rules for tracking the MPP, which achieves full online control on the basis of a neural-fuzzy structure. Comparative analysis indicates that W-IFL outperforms other widely used MPP tracking (MPPT) methods, which reduces oscillation at MPP, prediction error, and tracking time, and improves training efficiency and controlling ability, thus making it more rational to promote the development of the vehicle industry.

1. Introduction

The world has made great efforts to protect the environment [1,2]. Many countries have signed agreements, such as the Kyoto Protocol and the Paris Climate Agreement, to reduce carbon dioxide emissions, which account for 77% of greenhouse gases [3]. The Paris climate agreement aims to reduce carbon emissions by 37% by 2030 [4]. Transport currently accounts for nearly a quarter of global direct CO₂ emissions from fuel combustion, with nearly three-quarters of those emissions coming from road vehicles using the internal combustion engine (ICE) [5].

To reduce this share, the most promising way is to replace conventional cars with electric vehicles (EVs) [6]. However, greenhouse gas emissions are produced by EVs in the process of supplying electricity. This will effectively be transferred from where they are used to where the electricity is produced, namely power plants. This has the benefit that electric vehicles will not emit any harmful substances in crowded urban centers; thus, renewable energy-driven EVs are much more energy efficient and clean.

Therefore, solar and wind power have recently become the world’s most popular power sources [7,8]. To generate electricity from the wind, expensive and large-scale infrastructure in the form of wind turbines is required. As a result, charging electric vehicles to generate energy through specific solar photovoltaic (PV) systems is becoming a more general solution [9]. Specifically, PV panels can be installed on the roof of a vehicle [8], or PV carports can be used to charge electric vehicle batteries [6]. Moreover, the experimental results indicate that sufficient PV panels are able to meet the power demand of the complete battery charging process of EVs [10].

Based on this, the geometric optimization of the overall space, energy evaluation, and component lightweight of the prototype PV system suitable for EVs have been studied by some scholars [11,12]. Solar PV-powered electric vehicles are currently a technically feasible and increasingly economically attractive option in the transport sector in most countries [5]. Specifically, the use of dedicated solar PV charging systems will further reduce CO₂ emissions from road transport. For instance, PV roofs can save up to 14 g CO₂/km, and it has also been highlighted that the wide implementation of this technology could bring an annual reduction of 250,000 tons of CO₂ emissions in the EU-28 [13]. Furthermore, additional benefits may include reduced local grid overloads and increased grid flexibility [5].

However, everything has two sides. PV systems have significant advantages, such as abundant fuel, free selection of materials, independent process, environmental protection, quietness, long life, and low maintenance costs [14,15,16,17]. However, the widely used PV systems have a fatal shortcoming of low efficiency. The effective way to solve this problem is to track the maximum power point (MPPT) during the power generation process. Therefore, an MPP controller is needed to improve the efficiency of PV systems. [15,16,17].

To date, existing studies have, accordingly, explored the optimal artificial neural networks (ANNs) and fuzzy and heuristics controls, e.g., perturb and observe (P&O) [18], backpropagation (BP) [19], fuzzy logic (FL) [20], and genetic algorithms (GAs) [21], etc., methods. These studies, collectively, outline a critical role for MPPT, namely controlling the MPP online via training the model with an artificially designed structure. Nevertheless, since the control variables and model parameters are required to adjust frequently, three main challenges still exist in these experiments in terms of apparent oscillation at the MPP, insufficient accuracy, and slow convergence. In detail, these three challenges can hardly reach the maximum output power and commonly generate transient jumps during long-period control.

Hence, to address these issues, this paper proposes a wavelet-improved fuzzy logic MPP control model, namely W-IFL. The W-IFL adopts the neural-fuzzy structure to achieve adaptively online control of the MPP with high performance. In particular, the W-IFL has the following two contributions.

• Compared to existing ANN methods, the wavelet network avoids the subjective selection of hidden layer numbers when processing discrete-time data, which notably reduces the oscillation at the MPP by 50.0%, and efficiently improves the training efficiency and prediction accuracy by 85.7% and 67.7%, respectively;
• Improved fuzzy rules can, accordingly, outperform other control models in terms of tracking speed and accuracy, with average improvements of 55.3% and 62.3%, respectively.

In general, the proposed W-IFL model can efficiently and effectively optimize the current low utilization of converting solar power to electricity, thus providing a blueprint for endurance-limited vehicles powered by renewable energy, which can significantly promote their development.

The overall structure is divided into five sections. Section 2 introduces related solutions and emerging challenges. Section 3 and Section 4 elaborate on the methodology, application, and evaluation of the proposed W-IFL. Finally, Section 5 summarizes this study and sketches future research directions.

2. Related Works

Since tracking the MPP can effectively optimize PV power generation, a considerable amount of studies have been published on MPPT methods. For example, various MPPT methods can, in general, be divided into P&O [22,23,24], incremental conductance (IC) [25,26,27], mountain climbing [28,29,30], FL [31], GA [27], and ANN [32].

To illustrate, Md Hasan Anowar et al. [33] proposed an IC algorithm with an integral regulator to control the duty cycle of the boost converter. The method they offered successfully provided a stable MPP and could track changing atmospheric conditions more quickly. Zhanghong et al. [34] reduced the step size of the traditional FL method and increased the control rules to reduce search loss and MPP oscillation and improve control stability. These methods have many achievements, but their limitations are apparent, such as requiring a large number of sensors, thus leading to high complexity and cost.

Therefore, interest has been generated in ANN technology. The ability of ANNs to predict unknown parameters inspired its application in MPP tracking. NNs can be trained offline for nonlinear mapping and then can be used effectively in an online environment [35]. To overcome the inherent shortcomings of complex ANN operations, researchers have made many optimizations, e.g., F. Dkhichi et al. [36] introduced MPPT in the case of load changes, and the NN can still provide the correct duty cycle to optimize the PV system. Jyothy, L.P et al. [37] comparatively indicated that ANN methods have smaller steady-state errors but a higher training demand. S. Messalti et al. [38] proposed a new P&O-based NN method, which improves the tracking accuracy, response time and overshoot of MPP. A. Harrag et al. [39] proposed a single-sensor NN method that can effectively track the MPP, thereby reducing the cost and complexity of the PV MPP controller. However, the selection of network parameters in these methods is too subjective and unclear, making it fluctuate in training and challenging to converge.

In summary, whilst a considerable body of research has been carried out on MPPT, much less fits the discrete-time and rapid-response characteristics. In addition, it seems to be a common problem that existing studies focus on mathematical modeling but neglect the fully online process. When controlling according to the above methods, three challenges in terms of notable oscillation for MPP, insufficient accuracy for tracking, and slow convergence for controlling, are increasingly apparent.

Particularly driven by diverse and emerging energy demands, conventional fuels are being renovated to renewable energy for sustainability. Hence, it is an urgent need to study and improve the tracking and controlling strategies to achieve high utilization of solar power, thus effectively promoting and rationally guiding the development of the vehicle industry.

3. The W-IFL Methodology

This section uses 3 subsections to present the framework, predictor, and controller of the proposed W-IFL MPP Control Model.

3.1. Model Construction

As existing tracking methods, in general, require frequently and artificially adjusting monitoring parameters offline and increasing sensors to ensure the controlling accuracy online, which may inevitably increase MPP oscillation, resulting in high cost and complexity, the tracking model can be set up as a neural-fuzzy (NF) structure to optimize accuracy and efficiency, where the predictor trains the controller’s output, and the prediction from predictor is used as controller’s input.

However, since current ANN and FL methods have the subjective definition of their initializations, leading to the lack of systematicity and interpretability of the controlling process, e.g., the widely used BP network [40] or classic FL controller [34] use fixed transfer or membership functions. These methods, in general, have good accuracy but loss flexibility, and they may not meet the actual tracking requirements.

Therefore, the proposed W-IFL MPP Control Model, namely W-IFL MPPT Model in Figure 1A, can be used to better support effective and efficient tracking. For example, the wavelet function eases the calculation of orthogonal basis and weight independently, thus avoiding blindness when designing a NN structure. Moreover, the discrete training data collected from PV cells, as shown in

Table 1. Data example of PV Cell Output.

Temperature (°C)	Time	Irradiance $\left(\mathit{l}\mathit{x}\right)$	PV Cell Output Voltage (V)
34.0	9:24	767,000	38.53
34.0	9:45	785,000	37.33
35.1	11:20	810,000	30.05
36.0	13:39	214,000	28.19
34.8	14:40	1,000,000	28.15
35.0	14:43	974,000	28.01

, also indicate the feasibility of W-IFL to process non-timing signals.

The model structure, as described in Figure 1B, illustrates that the inputs to the wavelet predictor are temperature, time, and irradiance, which output the voltage at predicted MPP to the fuzzy controller. Therefore, the fuzzy controller also requires the actual voltage and current for fuzzing and the variables, namely ke, kec, and kdu, for controlling. In addition, feedback from the controller to the predictor transfers the offset voltage, thereby supporting online training, prediction, and control.

3.2. Wavelet Predictor

As designed in Figure 1B, the wavelet predictor is a 3-layer network. This is due to the fact that the output characteristic curve of a PV cell is nonlinear in time, which cannot be approximated by less than 3 layers, and more layers will increase the computation complexity exponentially [41].

Combing the discrete-time data illustrated in Table 1, hence, to obtain three kinds of information in terms of (a) smooth & continuous wavelet amplitude, (b) amplitude, and (c) phase of the temporal PV system, the non-orthogonal and complex-valued wavelet function, as described in Equation (1), is chosen as the transfer function $\phi \left(t\right)$, namely the Morlet function [42].

$$\phi \left(x\right)=C{e}^{\frac{x^2}{2}}\cos \left(5x\right);\left(C is a constant\right)$$

(1)

Temperature, irradiance, and time are represented in the input layer via $x_1$ to $x_3$, respectively. The number of neurons in the hidden layer is $n \left(n=1, 2, 3,\dots \right)$, and only one neuron exists in the output layer, namely the predicted voltage at MPP.

Notably, once set the following parameters: $w$ is the weight, $i \& j$ represent two neurons, $m$ expresses the layer number, $b$ indicates the output of the last neuron, $a$ means neuron’s input, and $j \& k$ state the $k^{th}$ output of neuron, $j$, and the interlayer relations can be mathematically summarized as Equation (2).

$$\begin{array}{l}{a}_{jk}^m={\displaystyle {\displaystyle \sum }_i}{w}_{jk}^m{b}_{ik}^{m-1}\hfill \\ b_{jk}^m=\phi \left(a_{jk}^m\right)\hfill \end{array}$$

(2)

In this 3-layer network, $b_{jk}^1=x_{k-j+1}$ and $b_{jk}^3={\widehat{x}}_{k+1}$, the predicted output, ${\widehat{x}}_{k,}$ can be obtained through the Morlet function, as described in Equation (3).

$$\begin{gathered} a_{jk}^2={\displaystyle \sum }_{i=1}{w}_{ij}^2{x}_{k-j+1} \\ {b}_{jk}^2={\phi }_2\left(\frac{a_{jk}^2-b_j}{a_j}\right) \\ {\widehat{x}}_{k+1}={\displaystyle \sum }_{j=1}{b}_{jk}^2{w}_j^3={\displaystyle \sum }_{j=1}{\phi }_2\left(\frac{a_{jk}^2-b_j}{a_j}\right)w_j^3 \end{gathered}$$

(3)

Equation (4) uses the mean square error, $\theta ,$ between the predicted and actual values as the objective function.

$$\theta =\frac{1}{2}{\left({\widehat{x}}_k-x_k\right)}^2$$

(4)

Furthermore, the wavelet predictor adopts conjugate gradient descent to minimize $\theta$ to achieve optimization.

3.3. IFL Controller

In this controller, as summarized in Equation (5), inputs need to be fuzzed to generate control variables, i.e., ke, kec, and kdu.

$$\begin{gathered} dP/dU=ke=\frac{P_k-P_{k-1}}{I_k-I_{k-1}} \\ \mathrm{∆}dP/dU=kec={\widehat{x}}_k-U_k \\ \mathrm{∆}U=kdu=e_k-e_{k-1} \end{gathered}$$

(5)

Precisely, $P_k$, $I_k$, $U_k$, and ${\widehat{x}}_k$, are the power, voltage, current, and predicted voltage of the PV cell at time k, respectively. The fuzzy domain factor, kdu, can, accordingly, reflect the offset voltage; thus, it is clear that $e_k=0$ means the PV cell works at MPP (time = k).

The fuzzy logic, in general, specifies some rules that each variable should correspond to a fuzzy subset and a membership function to control the unknown output [43]. In addition, As considering the influence of environmental factors such as temperature and irradiance, the PV cell’s output may change rapidly, and the controller should choose a triangular function to improve controlling resolution.

Therefore, the definition of fuzzy rules and corresponding membership functions in the proposed controller is described in

Table 2. Fuzzy Rules for IFL Controller.

	$\mathit{d}\mathit{P}/\mathit{d}\mathit{U}$	NB	NS	Z	PS	PB
$\mathbf{\Delta }\mathit{d}\mathit{P}/\mathit{d}\mathit{U}$
NB		PB	PS	NS	NB	NB
NS		PB	PS	NS	NS	NB
Z		PB	PS	Z	NS	NB
PS		PB	PS	Z	Z	NB
PB		PB	PS	PS	Z	NB

and Figure 2.

Notably, since there are 2 inputs to the fuzzy controller for calculation, and each input is divided into five fuzzy subsets, the fuzzy rules can, accordingly, be determined as 5 × 5 = 25 in Table 2. What is more, based on the predicted voltage from the wavelet predictor, the role of the variables defined above is to quickly adjust the duty cycle, d, of the filter, thereby controlling the system’s work at the MPP.

4. Results & Discuss

The highlights of W-IFL solving are illustrated in terms of the training process, prediction error, and control accuracy in this section.

4.1. Results

As described in the previous section, Figure 3 can indicate the training process of the wavelet predictor after normalizing the data.

Therefore, the experimental results can be summarized in that the X-axis means the training iteration, and the Y-axis describes the error between the predicted and actual voltage. Since the wavelet network adaptively configures the appropriate number of hidden layers, it reaches a satisfactory accuracy of prediction at the 470th iteration.

The overlap between the predicted and actual values also proves that the wavelet predictor has the ability to predict MPP as long as the network is trained. In addition, the repeated training can, in general, demonstrate that the average error is around −3 dB and the prediction success rate reaches 85–90%.

Furthermore, the results of the proposed W-IFL are described in Figure 4, including the error curve (black) of the predictor and the output power (red) of the controller. Precisely, the error of the wavelet predictor is around 1 dB, and the output power of the IFL controller stabilizes at 260.9 W.

4.2. Discuss

To better evaluate the performance of different methods, uniformly set the same initializations, e.g., voltage & current of the PV cell at MPP to $35.5 \mathrm{V}$ & $7.4 \mathrm{A}$, the same sampling period, etc., Figure 4 also shows the comparison for prediction error and control accuracy between the proposed W-IFL and some MPPT methods.

Specifically, based on the heuristic algorithms, Zhang Yan et al. [40] provided a new network structure of BP networks to optimize MPP oscillation. Zhanghong et al. [34] designed fuzzy rules to achieve good MPP control. Moreover, Jagtap et al. [44] and Owusu et al. [45] proposed new algorithms to optimize the traditional P&O and IC MPP control models, respectively.

As illustrated in Figure 4a, the error curve of the proposed wavelet predictor is smoother and faster and reaches the convergence at around the 54th iteration with oscillation reduction by 50%. Precisely, the subjective selection of training parameters for the existing BP network may lead to relatively poor predicted results, such as converged at the 167th iteration with an average error of −7 dB. Hence, the proposed predictor has about 85.7% and 67.7% improvements in terms of efficiency and error, respectively.

Figure 4b then demonstrates that the proposed IFL controller can catch the MPP at around 0.05 s, and the others are 0.11 s, 0.1 s, and 0.13 s, respectively. The disturbance of power output is also stable, which is quite approximate to the actual MPP, i.e., $35.5 \mathrm{V}\times 7.4 \mathrm{A}=262.7 \mathrm{W}$. This indicates that the improved controller has significantly optimized the tracking speed and accuracy, which is consistent with the trend of higher predicted accuracy. In addition, extracting the output power of other methods can get an average of 98.4 W. In other words, compared to other control models, the IFL controller has, on average, 55.3% and 62.3% improvements in controlling capture time and output power, respectively.

In general, this evaluation shows that the proposed MPP control model, namely W-IFL, has the advantages of shorter transition process time, faster response, no steady-state error, and no overshoot.

5. Conclusions & Future Works

The current low utilization rate of solar energy and the high cost of PV power generation systems that convert solar energy into electrical energy is still restricting the use of solar energy, thus limiting the development of vehicles with renewable energy, e.g., the endurance of cars powered by PV roofs, etc. In order to sufficiently improve the conversion efficiency of solar energy, it is always vital to maintain the maximum power point (MPP) output of PV cells.

Therefore, this paper proposes a wavelet-improved fuzzy logic (W-IFL) MPP control model to help ease the battery capacity constraints of electric vehicles, and the simulation results verify its high control performance between the widely used MPPT methods.

As compared to similar methods, W-IFL can, accordingly, obtain the following improvements. The wavelet predictor saves the trouble of artificially selecting the number of hidden layers and reduces error oscillation by 50.0%. The prediction success rate reaches 85%–90 %, and the training efficiency and prediction accuracy are improved by 85.7% and 67.7%, respectively. Moreover, the disturbance at the MPP in the IFL controller is eliminated. The MPP capture time is reduced to 0.05 s, with an optimization degree of 55.3%, and the controlling ability is improved by 62.3%, which is significantly better than the existing models.

This work was carried out preliminarily to obtain the present results. However, problems such as practical use or the lack of comprehensive constraints still exist. For example, the PV cell in this paper is simulated based on the mathematical model, which may lead to the different outputs of actual loads. Therefore, as the closure of this study, one recommendation for further research is to combine actual loads and other parts to achieve unified control. Another research direction is collecting sample data with more features, e.g., humidity, etc., to ensure the higher accuracy of the ANN training.