Energy Management Strategies of PV-Battery/Supercapacitor System for Electric Vehicles

A century later, the global automobile park has become gigantic, stabilizing in industrialized countries but exploding in emerging countries (China, India, etc.) This very significant growth in the automobile park has required governments to take action to reduce polluting emissions. At the beginning of the 1970s, the first anti-pollution standards appeared and forced car manufacturers and oil tankers to find technical solutions to reduce harmful emissions [1, 2]. Today, CO₂ emissions remain the major concern of international governments. However, this gas poses a real threat to humans and the environment. The rejection of CO₂ in the atmosphere increases each year by 2%, the road transport sector in 2020 represented 12% of the anthro pogenic greenhouse gas (GHG) emissions globally [3]. If nothing is done, we would see a doubling of these emissions by 2050. The consequences would be dramatic and irreversible for man and the environment: climate change, modifications of ecosystems, etc. [4].

Furthermore, transportation is essential to any community. Therefore, the development of a nation's social and economic systems in a balanced manner depends greatly on its transportation infrastructure. The heavy reliance of the global transportation system on fossil fuels, namely gas and oil, is one of its main issues. Transport, comprising freight and passenger travel, accounts for one-third of the total final energy consumption. This sector uses fossil fuels [5].

Hence, oil remains the most consumed primary energy in the world and the transport sector is clearly the main sector of activity for the use of petroleum products. In a context where primary energy resources are dwindling, it is essential to find ways to reduce this consumption. One of the solutions, other than using biofuels, is the introduction of photovoltaic solar energy, which allows for certain autonomy and reduces fuel consumption [1, 6]. For our country, Algeria has an excellent breeding ground, which places it in good position for the exploitation of clean and sustainable solar energy [7].

However, solar energy is a clean, limitless, free, and environmentally beneficial energy source that is also sustainable. It is therefore very crucial to use it to give energy to EVs because it is highly efficient and does not pollute the environment. The startling state of global warming forces the complete implementation of a transportation system powered by renewable energy. More application and a way to use green energy are made possible by the vehicle's utilization of solar energy. The quantity of carbon dioxide that cars produce would be drastically reduced if such a vehicle became commonplace, as would the need for oil [8, 9].

In recent years, as part of its energy transition and fight against climate change, Algeria has been moving towards electric vehicles. Solar vehicles have many advantages over conventional vehicles powered by fossil fuels. Firstly, they use a renewable and clean energy source, which is solar energy, which significantly reduces greenhouse gas emissions and helps fight climate change. In addition, solar energy is an inexhaustible resource, unlike limited fossil fuels. This means that solar vehicles are not dependent on oil price fluctuations and can offer greater economic stability [8].

This research presents a HESS utilizing batteries and supercapacitors. The integration of supercapacitors into HESS for EVs has garnered significant interest from researchers and is viewed as a viable solution, as indicated in the literature review [10-13]. Lithium-ion batteries have been shown in a number of published studies to have a lower power density despite having a higher energy density than other rechargeable batteries [14-16]. Many approaches existing in the literature developing hybrid supply for electric vehicle using solar energy. Raut et al. [17] have studied several batteries topologies with supercapacitor using Matlab/Simulink simulation. The results have shown that the passive topology was the most suitable for the simulated system. Salama and Vokony [18] have focused on hybrid storage using a battery and superconducting coil. A fuzzy logic controller (FLC) has been implemented to manage the charging and discharging of superconducting coils and the battery with the PV system. Zhu et al. [19] have presented the power management and sizing guidelines for an EV supplied by a battery-supercapacitor (HESS). The optimization strategy for the HESS is done to reduce the battery degradation and its costs.

Since the PV system requires a reliable power storage system, and the electric vehicle requires a power supply adaptable with transients of the motor, we have simulated our electric vehicle with using Li-ion battery storage (high energy density) or with supercapacitor storage (high power density with quick response to instantaneous transients) and this to evaluate the efficiency of each system. In our paper, the simulation of electric vehicle supplied by PV panel with Hybrid Energy Storage System (HESS) composed of Li-ion battery and supercapacitor. The novelty of our paper is the energy management strategies proposed to ensure efficient function of each component (Li-ion battery and supercapacitor) which permit an optimal operating for electric vehicle, prolong its lifespan, reduce the cost of components replacement and reduce damages caused by transients. We note that the used MPPT algorithm is the fuzzy logic. The remainder of this paper is organized as follows: Section 2 provides a description of an electric vehicle system. Section 3 describes the hybrid energy storage system and their modelling. In Section 4, the flowchart of the algorithm for the system management is elaborated. The discussion of the simulation results is illustrated in Section 5. Section 6 briefs about the conclusions and future scope.

The hybrid energy storage system that is suggested to be used in conjunction with a photovoltaic power system to power an electric vehicle is shown in Figure 2 [20]. The HESS topologies are categorized as passive, active, or semi-active based on how storage devices are connected to the DC Bus. A passive HESS occurs when storage devices are directly linked to the DC Bus. A semi-active HESS involves one storage device connected to the DC Bus via a bi-directional DC-DC converter. An active HESS is defined by the connection of two storage devices through bi-directional DC-DC converters to the DC Bus, as discussed in the literature [21-24].

This study employs a fully active parallel topology, utilizing two bi-directional buck-boost DC-DC converters to interface the onboard energy storage units with the DC Bus.

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Figure 2. Schematic proposed HESS structure

The system modelling covered in this section includes the averaged state-space model of the bi-directional buck-boost DC-DC converters, the supercapacitor, the Lithium-ion battery, and the photovoltaic (PV) modules that are regulated by the fuzzy logic MPPT method.

3.1 PV panel model

The PV panels, as depicted in Figure 3, consist of several cells, each of which can be modeled as a circuit with a current source, a diode, and several resistive elements [25].

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Figure 3. Equivalent circuit of PV cell [25]

The current produced by the cell is described by the following equation [26]:

$I_{p v}=I_{p h}-I_S \times\left[\exp \left(\frac{q \times\left(V_{p v}+R_{S} . I_{p v}\right)}{A \cdot K \cdot T c}\right)-1\right]-\left(\frac{V_{p v}+R_s+I_{p v}}{R_{s h}}\right)$              (1)

where, $I_{p v}$ and $V_{p v}$ are the cell output current and voltage; $I_{p h}$: The photon current; $I_s$: The saturation current of the diode; $R_s$ and $R_{s h}$ are series and parallel resistances respectively; q: The electron charge $\left(1.6 \times 10^{-19} \mathrm{C}\right)$; A: The ideality factor of the $\mathrm{P}-\mathrm{N}$ junction; K: Boltzmann constant $\left(1.380649 \times 10^{-23} \mathrm{J}.K^{-1}\right); T_c$: Absolute cell temperature in Kelvin $(K)$.

The photovoltaic array modeled in MATLAB/Simulink is the SPR-315E WHT-D. The different parameters of the PV module are detailed in Table 1.

Table 1. PV panel parameters

This panel, under Standard Test Conditions (STC: G=1 kW/m², T=25°C), can provide a power output Pm of 315.072 w, which corresponds to a terminal voltage Vmp of 54.7 V.

3.2 MPPT fuzzy logic control

The fuzzy logic controller is based on fuzzy strategy logic defined with sentences rather than equations. Fuzzy controller inputs are signal error ($e$) and error variation ($\Delta e$), so to get control ($u$) as controller output, the latter is considered a fuzzy linguistic variable.The operating principle of the fuzzy logic control is schematized in Figure 4 [27].

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Figure 4. Fuzzy logic controller structure [27]

The fuzzy logic controller consists of three parts: Fuzzification, the inference rules and defuzzification.

3.2.1 Fuzzification

The process involves transforming the physical input variables into fuzzy sets and splitting the error ($e$) and variation of the error ($\Delta e$) at the sampled time instances ($k$) into two inputs, which are specified as follows [27]:

$e(k)=\frac{P(k)-P(k-1)}{V(k)-V(k-1)}$ with : $P(k)=P(k) \cdot i(k)$                   (2)

$\Delta e(k)=e(k)-e(k-1)$                  (3)

where, P(k) and V(k) are respectively the instantaneous power and voltage delivered by the PV module.

3.2.2 Inference or rules base

In this step, we try to find the relationship between input and output variables (expressed as linguistic variables). The number of these variables is determined according to the designer's choice, then a table is drawn up to define the basic operating rules of our algorithm. The sequence of our algorithm is made according to a mechanism defined on the basis rules mentioned in Table 2 and the decision is made according to these rules [27].

Table 2. Fuzzy logic basis rules

where, NB: Negative Big, MN: Medium Negative, NS: Negative Small, ZE: Zero, PS: Positive Small, MP: Medium Positive, PB: Positive Big.

3.2.3 Defuzzification

After interference, fuzzy magnitudes are obtained, which need to be transformed into physical magnitudes, so a resulting membership function is defined for the output variable to perform this task. It should be noted that there are several defuzzification methods, referred to the study [27]: maxima, average of maxima and center of gravity. We should note that the latter offers the best results.

Figure 5 and Figure 6 illustrate the simulation results of MPPT using fuzzy logic for both constant and variable irradiance conditions.

The fuzzy logic control offers the ability to handle variations in inputs (Irradiance) and outputs (EV power), it can be used for solar systems of different sizes and configurations. The main thing is to establish behavioral rules in order to converge towards the optimal point of operation quickly than other algorithms.

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Figure 5. MPPT fuzzy logic with contant irradiance: (a) Voltage, (b) Power

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Figure 6. MPPT fuzzy logic with variable irradiance: (a) Voltage, (b) Power

3.3 Lithium-ion battery modelling

This study utilizes a general lithium-ion battery model, chosen for its simplicity and widespread availability in MATLAB/Simulink. The charge, discharge cycles and the state of charge (SOC) are modelled as follows [12]:

Charge mode $\left(i^*<0\right)$:

$V_{B_{-} c h}=E_0-K \cdot \frac{Q}{0.1 \cdot Q+i t} \cdot i^*-K \cdot \frac{Q}{Q-i t} \cdot i t+A e^{-B \cdot i t}$                   (4)

Discharge mode $\left(i^*>0\right)$:

$V_{B_{-} d i s c h}=E_0-K \cdot \frac{Q}{Q+i t} \cdot i^*-K \cdot \frac{Q}{Q-i t} \cdot i t+A e^{-B \cdot i t}$                   (5)

$\operatorname{SOC}(\%)=100 \cdot\left(1-\int \frac{i(t) d t}{Q}\right)$                      (6)

where, V_B is the battery voltage (V), E_o is the battery constant voltage (V), K is the polarization constant (V/Ah), Q is the maximum battery capacity (Ah), i is the battery current (A), A is the exponential voltage (V), B is the exponential capacity (Ah^-1), and $i^*$ is the filtered current representing the low frequency dynamics (A).

The battery block that is being used comes from MATLAB/Simulink. It's a generic dynamic model that has been parameterized to reflect the most often used rechargeable battery types. The equivalent circuit is depicted in Figure 7 [12, 28].

The battery simulated is of lithium nickel manganese cobalt oxide (NMC) type. The parameters values of the model can be obtained from the discharge characteristic depicted in Figure 8. Therefore, the parameters values implemented in the simulation of the Li-ion battery model are as follows: E₀=216.8718 V, R=0.14388 Ω, K=0.1078 V/Ah, A=16.7952 V, B=4.3929 Ah^-1 [12].

Figure 8 demonstrates that a discharge curve is generally segmented into three distinct sections. The initial section shows an exponential decline in voltage as the battery discharges. This area is variable in width, contingent upon the battery type. The second section denotes the charge that can be extracted from the battery until the voltage falls below the battery's nominal voltage. Lastly, the third section denotes the battery's complete discharge, which occurs when the voltage swiftly decreases.

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Figure 7. Dynamic battery model [12, 28]

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Figure 8. Battery discharge characteristic [12]

Using the accumulator data listed in Table 3, the simulations aim to charge and then discharge the battery at a constant current [20].

Table 3. Li-ion battery parameters

3.4 Supercapacitor modelling

An RC equivalent circuit is used to represent the supercapacitor. It comprises a capacitance C, an equivalent parallel resistance R_sh that denotes self-discharging losses, and an equivalent series resistance R_s that denotes charging and discharging resistance. It is crucial to acknowledge that self-discharging losses are disregarded. The MATLAB/Simulink library contains the model illustrated in Figure 9. The supercapacitor output voltage Vsc and SOC equations are as follows [12, 29]:

$V_{s c}=R_s \cdot i+\left[U_{C 0}-\int_0^t \frac{i}{C} \cdot e^{t /\left(R_{s h} \cdot C\right)} d t\right] \cdot e^{t /\left(R_{s h} \cdot C\right)}$                   (7)

$\operatorname{SOC}(\%)=100 \cdot\left(1-\int \frac{i(t) d t}{C}\right)$                     (8)

where, U_C0 is the initial voltage of the ideal capacitor (C).

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Figure 9. Supercapacitor model [12]

The parameters of supercapacitor are illustrated in Table 4 [20].

Table 4. Supercapacitor parameters

3.5 DC-DC converters modelling

As shown in Figure 2, two bi-directional buck-boost DC-DC converters connect the on-boarded sources to the DC bus. Every converter has a single source attached to it. These converters serve to control the on-board sources charging and discharging currents as well as to match the battery voltage to the DC bus. In charging mode, the bi-directional converter transfers energy from the higher voltage side (DC-bus) to the lower voltage side (ESS device) by acting as a buck converter. It performs the duties of a boost converter when discharging [30-32].

Buck mode: $\mathrm{V}_0=\alpha . \mathrm{V}_{\mathrm{i}}$                          (9)

Boost mode: $V_0=V_i /(1-\alpha)$                 (10)

Buck-Boost mode: $V_0=\left(\frac{\alpha}{1-\alpha}\right) \cdot V_i$                    (11)

where, V₀, V_i, and $\alpha$, respectively, are the output voltage, input voltage, and duty cycle of the DC-DC converter.

Figure 10 illustrates respectively the basic configuration of a DC-DC buck Figure 10 (a), DC-DC boost Figure 10 (b) and DC-DC bi-directional buck- boost converter Figure 10 (c) [24, 33, 34].

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Figure 10. DC-DC converters: (a) DC-DC buck, (b) DC-DC boost, (c) DC-DC bi-directional buck- boost [33]

The parameters of the DC-DC converters are listed in Table 5.

Table 5. DC-DC converters parameters

The simulation was conducted using MATLAB/Simulink software, based on a variable solar profile (Figure 12), a temperature of 25°C, keeping power consumption for the EV maintained constant at 500 W throughout the experiment. The characteristics of the PV panel, battery and supercapacitor used are as described above.

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Figure 12. Solar profile

The results of the curves obtained for the PV panels are presented in Figure 13.

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Figure 13. PV Panel output signals: (a) Current, (b) Voltage

According to the curves presented in Figure 13(a), the current generated by the photovoltaic solar panel is significantly influenced by the irradiation profile used in the simulation (Figure 12). At an irradiance of 1000 W/m², the current maintains a stable value of approximately 24 A. It is important to note that this observation does not account for the initial transient phase of the simulation. When the irradiance drops to 500 W/m² at time t=1s, the current experiences a sharp decline. Subsequently, once the irradiance stabilizes at 500 W/m², the current levels off at around 13 A. Conversely, the voltage remains constant regardless of the variations in irradiance, as shown in Figure 13(b).

In the present section we will study the energy management strategies in the electric vehicle. Three cases will be presented and discussed:

Cases 1: Battery storage

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Figure 14. Battery signals: (a) Voltage, (b) Current, (c) State of Charge "SOC"

At the beginning of the simulation, the battery starts charging, increasing its state of charge from 50 % to 50.027 %. During this period, the voltage experiences fluctuations that are quickly stabilized by the regulation, ultimately reaching a value of 26.4 V. However, the current initially decreases sharply before stabilizing at approximately -13 A. Then at t = 1s, the voltage drops suddenly while the current increases due to the transition from charging to discharging. In the second phase, the battery enters discharge mode, reducing its state of charge from 50.027 % to nearly 50.020 %. During this phase, the voltage stabilizes at around 25.7 V, while the current rises and stabilizes at approximately 3 A. All of these variations are illustrated in Figure 14.

Cases 2: Supercapacitor storage

The corresponding state of charge curve indicates that the supercapacitor experienced two discharges (Figure 15): the first occurred at the beginning due to its rapid response, while the second was at time t = 1s, when both voltage (Figure 15 (a)) and current (Figure 15 (b)) reached their peak. At the end of simulation, the supercapacitor SOC is 98.92% as shown in Figure 15 (c).

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Figure 15. Supercapacitor signals: (a) Voltage, (b) Current, (c) State of Charge "SOC"

Cases 3: Battery/ Supercapacitor hybrid storage system

Figure 16 illustrates the power profiles of the PV panel; the electric vehicle and the hybrid storage system respectively.

The first curve in this figure illustrates the variation of photovoltaic power P_pv in accordance with the solar profile, showing a sharp decline at time t=1s, dropping from 1000 W/m² to 400 W/m². This value is below the requirement of the electric vehicle (500 W). In contrast, the EV power curve P_EV remains constant throughout the simulation, with only slight fluctuations as irradiance decreases, indicating the involvement of the storage system during this phase. We note that the incorporation phase of the storage system haven’t evoke a significant disturbance in the EV power, where the transition have been made softly, since the energy management strategy have optimized the power injected between supercapacitor (during 0.1 s) while the battery ensuring the rest required power after that period. The power curves of the hybrid storage system support this observation, as the battery power is negative in the first phase [0; 1 s], indicating it is in charging mode. Subsequently, it shifts to discharge mode in the second phase to compensate for the long-term power deficit of P_pv. The supercapacitor engages first during the power peak due to its specific characteristics (high energy density and rapid response time), effectively addressing the power deficit over a short period. On the other hand, the speed of passing between supercapacitor and battery is related to the converter parameters, where the current injected by supercapacitor must do not exceed the switching element characteristics (transient current and transient voltage).

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Figure 16. Power curves for a HESS