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# Improved estimation of battery equivalent resistance in bidirectional EV chargers

Baghaei M Sadegh, Zohra Kader, Maurice Fadel, Jerome Lachaize

► To cite this version:

Baghaei M Sadegh, Zohra Kader, Maurice Fadel, Jerome Lachaize. Improved estimation of battery equivalent resistance in bidirectional EV chargers. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0341 . hal-05067940

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Submitted on 14 May 2025

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Distributed under a Creative Commons Attribution 4.0 International License
Improved estimation of battery equivalent
resistance in bidirectional EV chargers

M. Sadegh Baghaei
LAPLACE,
Université de
Toulouse, CNRS,
INPT, UPS,
Toulouse, France

Kader Zohra
LAPLACE,
Université de
Toulouse, CNRS,
INPT, UPS,
Toulouse, France

Fadel Maurice
LAPLACE,
Université de
Toulouse, CNRS,
INPT, UPS,
Toulouse, France

Lachaize Jerome
SCHAEFFLER
44 av Gén de
Croutte, 31100
Toulouse, France

baghaei@laplace.uni
v-tlse.fr

zohra.kader@laplace
.univ-tlse.fr

fadel@laplace.univ-
tlse.fr

jerome.lachaize@vit
esco.com

**Keywords**

« On-board charger », « CLLC resonant converter », « Harmonics », « Charging », « System Modelling ».

**Abstract**

This paper presents an analysis and modelling approach for bidirectional CLLC resonant converters, addressing limitations in conventional methods like the First Harmonic Approximation (FHA). The proposed methodology based on Extended Harmonic Analysis (EHA) allows a dynamical estimation of a battery equivalent resistance across varying frequency and voltage ranges. The precision of gain characterization and performance are improved using the proposed method. MATLAB Simulink simulations validate the proposed EHA method, demonstrating significant improvements in prediction accuracy and power transfer efficiency. Compared to FHA, the EHA method reduces modelling errors by up to 78%.

**Introduction**

With the emergence and rapid growth of electric vehicles in recent years, a paradigm shift in the automobile industry is evident. As the world pushes for sustainability, EVs have become a beacon of hope in reducing carbon footprints and enhancing energy efficiency [1, 2]. Central to the functioning of these vehicles, is the need for efficient charging mechanisms. The car charger not only ensures the effective transfer of energy but also plays a crucial role in ensuring the longevity of the vehicle's battery, thus emphasizing its integral position in the EVs ecosystem.

The rapid adoption of EVs places increasing demands on the underlying charging infrastructure. As the intermediary between the electrical grid and the vehicle's battery, the charger must ensure optimized energy transfer, cater to different battery specifications, and often provide options for bidirectional energy flow. Typical, battery chargers allow only uni-directional power flow from Grid to Vehicle (G2V), i.e. in forward mode [3]. However, a battery charger capable of bidirectional power flow can be utilized in Vehicle-to-Grid (V2G), i.e. reverse mode, introduced as smart grid, to perform grid support function such as peak load levelling [4, 5]. The bi-directional AC/DC converter stands out in this field, offering greater efficiency and flexibility, as well as the possibility of implementing V2G energy solutions. Therefore, understanding and improving the control mechanisms of such converters is not just a technical endeavor, but a pressing need. Fig. 1, for instance, presents the principal structure of bidirectional on-board charger stage that is one of the most practical charging architectures in EVs system. Fig. 1, also delineates the power flow directions within the converter, highlighting two distinct modes: the powering mode (forward power flow) and the generating mode (backward power flow). These modes illustrate the converter's capability to manage bidirectional power transfer efficiently.

<figure><img src="image_3.png" /><figcaption>Fig. 1: Structure of bidirectional on-board charger stage.</figcaption></figure>
Two-stage on-board chargers in vehicles include a Power Factor Correction (PFC) module, which is reversible (AC/DC). This module connects to the distribution network on one side and a DC/DC converter on the other, ultimately linking to the traction battery. The DC/DC converter is crucial, as extensive research literature highlights its contribution to the dynamic behavior of the global process. Numerous topologies have been reviewed in the literature for DC-DC converters in electric vehicle charging systems. Among these, resonant converters are favored. [6, 7]. These types of converters, exhibits high efficiency due to Zero-Voltage Switching (ZVS) in the primary side and Zero Current Switching (ZCS) in the secondary side, and hence, they are a promising candidate topology [8]. For battery charging applications requiring bidirectional V2G power flow capability, CLLC resonant converters are commonly used. The goals of using these types of converters include enhancing efficiency, reducing switching losses, and ensuring safe operation through isolation capabilities. Also, it gives wide range operation in both frequency and battery voltage term. Fig. 2 depicts the structure of the CLLC bidirectional resonant converter. This architecture includes two DC source in each side, one imposed by the internal DC link, and another imposed by the battery voltage, the commutating switching keys and the resonant circuit CLLC ($C_1, L_1, L_m, L_2$ and $C_2$).

<figure><img src="image_4.png" /><figcaption>Fig. 2: Structure of the CLLC bidirectional resonant converter.</figcaption></figure>

The topology of resonant CLLC converter can be symmetric or asymmetric. In a symmetric topology, the reflected secondary $L_2$ and $C_2$ are equal to the series-connected primary $L_1'$ and $C_1'$ by considering the turn ratio of transformer as:

$$L_1 = n^2 * L_2 \qquad (1).$$

$$C_1 = n^{-2} * C_2 \qquad (2).$$

This structure consists of a high-frequency inverter stage followed by a rectifier stage to recharge the battery. The transformer ensures galvanic isolation between the power distribution network and the vehicle. The choice of high-

frequency energy transfer is dictated by the need for low transformer volume and large range of application. In the realm of power electronics, the CLLC resonant converter has emerged as a significant topology due to its high efficiency and versatility in various applications. However, accurately dynamic analysis and characterizing the gain and time-domain behavior of this converter remain a challenge. Modelling the resonant CLLC converter is usually done in the literature using FHA around a single point of operational frequency [9, 10, 11]. This assumption implies that the system is operating at constant power. Thus, approximating the behavior of the battery by an equivalent resistance allows to obtain sample models that are valid around the considered frequency point. Beyond this point, the FHA, and thus constant power operation, do no longer hold true, leading to inaccuracies in the obtained models. Here, our objective is to develop a dynamical model of the resonant CLLC converters that captures its behavior in a large frequency interval. This is possible by computing a dynamic estimation of the equivalent resistance to better emulate the battery's behavior. The modelling method presented in this paper reduces modeling errors by relying on power transfer, which is validated by MATLAB Simulink simulations. Note that in the literature, the impacts of the harmonics produced by the charger has been often studied [12]. However, in this paper, we propose a methodology that uses the harmonics in the battery side in order to improve the estimation of the battery equivalent resistance. And thus, improve the dynamical modelling of the converter under study.

The paper is organized as follows: First, the structure of the studied CLLC converter is introduced, along with the power equality approach to determine the battery equivalent resistance. Next, the parameters used for this study and the conduction operation modes are defined. Furthermore, the investigation focuses on the battery equivalent resistance estimation and charging current computation, with validation of the results performed through MATLAB Simulink simulations. Finally, the paper concludes with key insights.

# Analysis of CLLC resonant circuit and methodology

## The presented conversion structure

The proposed bidirectional full-bridge CLLC resonant converter, depicted in Fig. 2, features a full-bridge structure in both the primary inverting
stage and the secondary rectifying stage,
incorporating a high-frequency transformer for
galvanic isolation. In the primary stage, power
switches convert DC power to AC, enabling its
transfer through the transformer. The transformer,
modeled with magnetizing inductance Lm and a
turn ratio of 1:1. The transformer's leakage
inductance is combined with the resonant
inductors L1 and L2 on the primary and secondary
windings, respectively. Resonant capacitors C1
and C2 facilitate energy balancing and achieve a
high resonant frequency in conjunction with L1
and L2. The study will carry out only in forward
power mode.

The hypotheses taking into consideration:

* Ideal transformer.

* The components are perfect.

* The secondary components Q5, Q6, Q7, Q8 are not commutating when in forward mode, only the diodes function.

Current Waveform as a Function of
Frequency

Fig. 3 illustrates the current waveforms
obtained for a given battery voltage at three
frequencies: f << f<sub>r</sub>, f >> f<sub>r</sub> et f = f<sub>r</sub>, where f<sub>r</sub>
is the resonant frequency (f<sub>r</sub>= 100 kHz) for the
converter used. It can be observed that the FHA
analysis is more effective around the resonance.
As close to this point , the form of the current is
more sinusoidal. However, outside this range, the
harmonics distort the current waveform.
Therefore, to better model the behavior of the
converter outside this frequency range, a dynamic
method of calculating the equivalent resistance is
necessary.

<figure><img src="image_5.png" /><figcaption>Figure 3: Current waveform as a Function of Frequency.</figcaption></figure>

Obtain the battery equivalent resistance
using power equality approach

Fig. 4 presents an equivalent circuit of the
CLLCC converter shown in Fig. 2, meeting the
following assumptions:

* The switching of the rectifier depends on the sign of the current $I_{L2}$, (sign($I_{L2}$)).

* The secondary components are transferring to the primary side via the transformer turn ratio n.

* The input and output voltage source assumed to be completely squared waveform.

* The magnetizing inductance is modeled in parallel.

<figure><img src="image_6.png" /><figcaption>Fig. 4: Equivalent resonant circuit CLLCC.</figcaption></figure>

The current $I_{L2}$ and voltage $V_{out}$ waveforms
for a given frequency and battery voltage are in
phased as indicated in Fig. 3. This phase
alignment is due to the operation of the diode’s
rectifier, which ensure that the current and
voltage waveforms remain synchronized. Then, the following equivalent model represent in Fig. 5, can be considered. In this model, the battery after rectifier, is considered as resistance $R_{DC}$, thus, by transferring this resistance to alternative part i.e. before rectifier, the resistance $R_{ac}$ can be stated. It's worth noting that this model can be considered during calculation using both FHA and EHA. As it mentioned in [9], the relation between $R_{DC}$ and $R_{ac}$, from the first component of current and voltage, before and after the rectification part, can be given as:

$$R_{ac} = \frac{8}{\pi^2} * R_{DC} \qquad (3).$$

From the same argument, this relation can be demonstrated for other harmonics as:

$$R_{ac} = \frac{8}{m^2 \pi^2} * R_{DC} \qquad (4).$$

while m is the harmonic order.

<figure><img src="image_7.png" /><figcaption>Fig. 5: Battery equivalent model resistance based on rectifier part.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 6: Battery equivalent model resistance based on resonant circuit.</figcaption></figure>

The objective is to characterize and analyze the converter with the presence of nonlinearity and harmonics. $R_{ac}$ and secondary current $I_{L2}$ are linked by an implicit relationship conveying the power transferred into the battery. For calculating the battery equivalent resistance $R_{ac}$ as illustrating in Fig. 6, the power equality equation can be used in both side input and output.

$$P_{in} = P_{bat} \qquad (5).$$

By using EHA, the power can be assumed as sum of the power correspond to each harmonic of input and output source (squared sources). Thus, it can be expressed as:

$$\sum_{m=1,3,...}^{\infty} P_{in m} = \sum_{m=1,3,...}^{\infty} P_{bat m} \qquad (6).$$

$$(I_{in-rms m} \cdot V_{in-rms m} \cdot \cos(\theta m)) + \dots = \left(\frac{V_{bat}^2}{R_{DC}}\right) + \dots \qquad (7).$$

where m is the harmonic order and $\theta$ is the phase shift between the input voltage $V_{in}$ and the input current $I_{in}$. The input voltage of the resonant network, E, is a square waveform which varies from -E to +E because of the full-bridge structure. It can be mathematically expressed using the Fourier series as follows:

$$V_{in} = \frac{4E}{\pi} * \sum_{k=1,3,5,...}^{\infty} \frac{1}{k} * \sin(2\pi k f_s t) \qquad (8).$$

where t is the time parameter, k is the integer parameter for the Fourier series expansion, and $f_s$ is the switching frequency of the power switch, respectively. The output voltage of the resonant network, $V_{out}$, is a square waveform which varies from -$V_{bat}$ to +$V_{bat}$ because of battery voltage constrain. Its Fourier series can be stated as:

$$V_{out} = \frac{4V_{bat}}{\pi} \sum_{k=1,3,5,...}^{\infty} \frac{1}{k} * \sin(2\pi k f_s t - \phi_k) \qquad (9).$$

where $\phi_k$ is the phase shift with respect to the input voltage. The following table introduces the power related to each harmonic for input and output source. It's worth noting that the Root-Mean-Squared (RMS) values of quantities are considered. The RMS voltage and current are taking into account and the power factor $\cos(\theta)$ that indicate the real power portion of total input power. The power associated with each harmonic is defined and presented in Table I, illustrating the contribution of individual harmonics to the overall power.
<table><caption>**Table I: Power definition according to each harmonic.**</caption><thead><tr><th rowspan="2">Harmoni<br>c order m</th><th>Input power:</th><th>Output<br>power:</th></tr><tr><th><i>I</i><sub>in rms m</sub> · <i>V</i><sub>in rms m</sub> ·<br>cos (θm)</th><th><i>V</i><sub>bat-rms m</sub><sup>2</sup>/<i>R</i><sub>ac</sub></th></tr></thead><tbody><tr><td>First<br>harmonic</td><td><sup>4<i>V</i><sub>in</sub></sup>/<sub>π√2</sub> · <sup>4<i>V</i><sub>in</sub></sup>/<sub>π√2</sub> · <sup>real(<i>Z</i><sub>ac</sub>)</sup>/<sub>|<i>Z</i><sub>ac</sub>|</sub></td><td><sup>n<sup>2</sup>8 <i>V</i><sub>bat</sub><sup>2</sup></sup>/<sub>π<sup>2</sup> <i>R</i><sub>ac</sub></sub></td></tr><tr><td>Order 3</td><td><sup>4<i>V</i><sub>in</sub></sup>/<sub>3π√2</sub> · <sup>4<i>V</i><sub>in</sub></sup>/<sub>3π√2</sub> · <sup>real(<i>Z</i><sub>ac3</sub>)</sup>/<sub>|<i>Z</i><sub>ac3</sub>|</sub></td><td><sup>n<sup>2</sup>8 <i>V</i><sub>bat</sub><sup>2</sup></sup>/<sub>9π<sup>2</sup> <i>R</i><sub>ac</sub></sub></td></tr><tr><td>Order <b>m</b></td><td><sup>4<i>V</i><sub>in</sub></sup>/<sub><b>m</b>π√2</sub> · <sup>4<i>V</i><sub>in</sub></sup>/<sub><b>m</b>π√2</sub> · <sup>real(<i>Z</i><sub>acn</sub>)</sup>/<sub>|<i>Z</i><sub>acn</sub>|</sub></td><td><sup>n<sup>2</sup>8 <i>V</i><sub>bat</sub><sup>2</sup></sup>/<sub><b>m</b><sup>2</sup>π<sup>2</sup> <i>R</i><sub>ac</sub></sub></td></tr></tbody></table>

It's worth to note that the equivalent impedance of circuit in Fig. 6 correspond to each harmonic, is a function of the following quantities at related frequency.

$$Z_{acm} = f(R_{ac}, L_{1}, L_{2}, L_{m}, C_{1}, C_{2}, \omega, m) \quad (10).$$

## Specifications of system and operation range area

The performance of the proposed methodology should be assessed by comparing the simulations over the wide operating range of the frequency with several battery voltage. the CLLLC resonant converter simulated completely in appropriate environment. The specification shown in Table II is used to this aim [3].

<table><caption>**Table II: Study case parameters.**</caption><thead><tr><th>Parameter</th><th>Value</th></tr></thead><tbody><tr><td><i>L</i><sub>1</sub> = <i>L</i><sub>2</sub></td><td>25e-6 (H)</td></tr><tr><td><i>C</i><sub>1</sub> = <i>C</i><sub>2</sub></td><td>99e-9 (F)</td></tr><tr><td><i>L</i><sub>m</sub></td><td>125e-6 (H)</td></tr><tr><td>Turn ratio (n)</td><td>1</td></tr><tr><td><i>V</i><sub>in</sub></td><td>400 (V)</td></tr><tr><td><i>V</i><sub>battery</sub></td><td>200-400 (V)</td></tr><tr><td>Power</td><td>50-2500 (W)</td></tr></tbody></table>

For verifying the results of obtained resistance $R_{ac}$ via the simulated results, first, the conduction area mode must be determined. For this purpose, the static current $I_{L2}$ over range of frequency for

different battery voltage shall be obtained via Simulink. To determine the operation mode of the converter with the given parameters, the whole schematic of CLLLC bidirectional resonant converter is evaluated via Simulink MATLAB and the characterization of the steady state charging current $I_{L2}$ is obtained for different frequencies rest in applicable range. This characterization is illustrated in Fig. 7 as follows:

<figure><img src="image_9.png" /><figcaption>**Fig. 7: Steady state charging current over battery voltage variation and frequency.**</figcaption></figure>

Depending on the parameters, it is clearly seen from the steady state current graph in Fig. 7, that the system preferably operates in Continuous Conduction Mode (CCM) rather than Discontinuous Conduction Mode (DCM). In the following section we will only focus on CCM operating mode for the $R_{ac}$ calculation due to the parameter's specifications.

## Obtaining the alternative resistance $R_{ac}$, its analysis and charging current $I_{L2}$

### Analysis of the resistance $R_{ac}$ according to the harmonic number

The resistance study over number of used harmonics is given as below:

<figure><img src="image_10.png" /><figcaption>**Fig. 8: Obtained resistance over number of used harmonics.**</figcaption></figure>
These results are obtained using the iterative methods to earn the equivalent resistance based on the number of used harmonics. The results showcase an improvement in each iteration as indicated in Fig. 8. These performances are gotten for the points 136, 140 and 150 KHz and different battery voltage such 200,250 and 300 V, as indicated in Fig. 7 with colored star-point. As it is clearly observed from the Fig. 8, the obtained equivalent resistance by the proposed methodology, improves by increasing the number of used harmonics in each iteration. The total harmonic number, used in Fig. 8, is equal to 101. The red curves indicate that over increasing number of harmonics, The error will decrease, and the resistance will closely approximate the real extracted value.

Charging current study $I_{L2}$ and resistance equivalent $R_{ac}$ comparison using FHA and EHA with Simulink

First, to validate the methodology, it would be interesting to illustrate the different between only using FHA in the methodology and then EHA. To do this, Fig. 9 below, showcases the analytical current $I_{L2}$ and Fig. 10 depicts the resistance equivalent $R_{ac}$ using methodology for FHA and EHA.

<figure><img src="image_11.png" /><figcaption>Fig. 9: Analytical current $I_{L2}$ comparison using FHA, EHA and Simulink.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>Fig. 10: Obtained resistance $R_{ac}$ using FHA, EHA and Simulink.</figcaption></figure>

As shown in Fig. 9 and 10, there is a significant discrepancy between the results obtained using the FHA and EHA methodologies. The average error between FHA and EHA varies across the studied cases. Specifically, for battery voltages of 200 V, 250 V, and 300 V, the average errors related to FHA analysis, are 43%, 64%, and 78%, respectively. Thus, it clearly indicates that taking a greater number of harmonics into account is essential. Also, it can showcase the effectiveness of the used efficient methodology EHA in comparing to previous literatures which only used FHA.

Analysis of $I_{L2}$ over number of harmonics

To compare the results of charging current $I_{L2}$ from Simulink and methodology, it requires to use the obtained resistance into following equations.

$$ 
\begin{aligned}
i_{L2-rms}^2 &= \left(\frac{1}{2}\right) \left[ \sum_{m=1,3,...}^{\infty} \left( \frac{4nV_{bat}}{m\pi} \left( \frac{1}{R_{ac}} \right) \right)^2 \right] \\
&= \frac{8n^2V_{bat}^2}{\pi^2 R_{ac}^2} \left[ \sum_{m=1,3,...}^{\infty} \left( \frac{1}{m^2} \right) \right] \quad (11).
\end{aligned}
$$

Which m is the harmonic order and $R_{ac}$ is the alternative obtained resistance. Fig. 11, indicates the RMS current $I_{L2}$ for the 3 cases battery voltages as 200, 250 and 300 V.

<figure><img src="image_13.png" /><figcaption>Fig. 11: RMS current $I_{L2}$ values for the 3 cases battery voltages as 200,250 and 300 V.</figcaption></figure>

The average relative errors for the battery voltages 200, 250 and 300 are 5.2%, 6.7% and 7.8% respectively, the number of used harmonics is 51. Surely, by increasing the number of harmonics, the error will be decreased. The results showcase the effectiveness of the methodology used in this paper.

Gain analysis of the proposed methodology EHA
To derive the gain expression for the proposed model, the power balance equation can be utilized. Given that the input can be considered as consists of a series-connected voltage source, the superposition theorem can be applied to determine the net input power contributed by each harmonic source. As it stated before by the rms values, it can be described as below.

$$P_{in,m} = \frac{1}{2} |v_{in,m}| \cdot |i_{in,m}| \cos(\theta_m) = \frac{|v_{in,m}|^2}{2 \cdot Z_{ac,m}} \cos(\theta_m) \quad (12)$$

where m is the harmonic order, $Z_{ac,m}$ is the input impedance of system correspond to harmonic m, and $\theta_m$ is the phase shift between input voltage and current. The sum of input power is given as :

$$P_{in, m} = \sum_{m=1,3,...}^{\infty} \left[ \frac{|v_{in, m}|^2}{2 \cdot Z_{ac, m}} \cos(\theta_m) \right] \quad (13)$$

By equating it to the output power across the alternative equivalent resistance, the normalized gain expression for the proposed model is derived as:

$$G_{EHA} = \frac{n v_{out}}{v_{in}} = \sqrt{\left(\sum_{m=1,3,...}^{\infty} \frac{m^2 \pi^2}{8} * R_{ac} * \left[\frac{1}{2 \cdot Z_{ac,m}} \cos(\theta_m)\right]\right)} \quad (14)$$

Using the parameters provided in Table II, Fig. 12 depicts the Dc gain function $G_{EHA}$, $G_{FHA}$ and the real gain extracted from Simulink according to the frequency for case $V_{bat}$ equals to 200.

<figure><img src="image_14.png" /><figcaption>Fig. 12: the real gain compared to EHA and FHA method.</figcaption></figure>

As illustrated in Fig. 12, the effectiveness of the proposed methodology is evident, as the EHA exhibits significantly lower error compared to FHA, with the gain obtained through this method closely aligning with the real gain achieved via

Simulink. The error is reduced to less than 5 % between EHA and real gain.

## CONCLUSION

An EHA methodology has been proposed in this paper, to improve the accuracy of the equivalent resistance estimation of the battery. Compared to the existing analysis that overlook the variations in power and voltage around the battery and the changes in battery equivalent resistance posed by the rectifier and battery, the developed method shows an improved estimation of the battery equivalent resistance for a range of operating frequencies. Furthermore, the gain analysis of the EHA method demonstrated an appropriate match with the real gain obtained from Simulink simulations, showcasing significantly lower errors compared to the FHA method. The simulated results indicate an appropriate efficiency of the methodology by considering the predefined assumptions of resonant CLLC converter. These preliminary results allow us to investigate new challenges such as designing performant control lows that can be experimentally validated on real test bench. These two goals will be the subjects of our future works.

## REFERENCES

[1] M. Kesler, M. Kisacikoglu, and L. Tolbert, "Vehicle-to-Grid Reactive Power Operation Using Plug-in Electric Vehicle Bidirectional Off-Board Charger, in IEEE Transactions on Industrial Electronics, vol. PP, pp. 1-1, 2014.

[2] DERMANI, Majid Khalili et TRAJIN, Baptiste. System Level Modeling of Electromagnetic Couplings for the Energy Efficiency of Static Converters. In: 2024 IEEE International Conference on Industrial Technology (ICIT). IEEE, 2024. p. 1-6.

[3] Liu, Chaohui. "Analysis, design and control of DC-DC resonant converter for on-board bidirectional battery charger in electric vehicles." PhD diss., University of Sheffield, 2017.

[4] M. C. Kisacikoglu, B. Ozpineci, and L. M. Tolbert, "EV/PHEV Bidirectional Charger Assessment for V2G Reactive Power Operation," In IEEE Transactions on Power Electronics, vol. 28, pp. 5717-5727,2013.

[5] DERMANI, M. Khalili, BAGHAEI, M. S., COLAS, Frédéric, et al. Non-linear stability analysis of the electrical vehicle chargers power stage connected to the weak grid. In: CIRED Porto Workshop 2022: E-mobility and power distribution systems. IET, 2022. p. 955-959.

[6] Park, Junsung, and Sewan Choi. "Design and
control of a bidirectional resonant dc–dc converter for
automotive engine/battery hybrid power
generators." In IEEE Transactions on power
electronics 29, no. 7 (2013): 3748-3757.

[7] J. Deng, S. Li, S. Hu, C. C. Mi, and R. Ma, "Design Methodology of LLC Resonant Converters for Electric Vehicle Battery Chargers," In IEEE Transactions on Vehicular Technology, vol. 63, pp. 1581-1592, 2014.

[8] Tian, D., Tang, Y., & Shi, Z. (2024). Design and optimization of 30 kW CLLLC resonant converter for vehicle-to-grid applications. *International Journal of Circuit Theory and Applications*.

[9] G. A. Mudiyanselage, N. Keshmiri and A. Emadi, "A Review of DC-DC Resonant Converter Topologies and Control Techniques for Electric Vehicle Applications," in IEEE Open Journal of Power Electronics, vol. 4, pp. 945-964, 2023, doi: 10.1109/OJPEL.2023.3331180.

[10] R. Takarli, M. Adib, A. Vahedi and R. Beiranvand, "A Bidirectional CLLC Resonant Converter for EV Battery Charger Applications," 2023 14th Power Electronics, Drive Systems, and Technologies Conference (PEDSTC), Babol, Iran, Islamic Republic of, 2023, pp. 1-6, doi: 10.1109/PEDSTC57673.2023.10087140.

[11] H. Mousavi Somarin, N. Messi, F. Sarrafin Ardebili and L. Braz, "Comparison of Two Bidirectional 11KW 400V CLLC and CLLLC Resonant Converters for EV Applications," PCIM Europe 2024; International Exhibition and Conference for Power Electronics, Intelligent Motion, Renewable Energy and Energy Management, Nürnberg, Germany, 2024, pp. 2489-2497, doi: 10.30420/566262350.

[12] J. P. Trovão, P. G. Pereirinha, L. Trovão and H. M. Jorge, "Electric vehicles chargers’ characterization: Load demand and harmonic distortion," 11th International Conference on Electrical Power Quality and Utilisation, Lisbon, Portugal, 2011, pp. 1-7, doi: 10.1109/EPQU.2011.6128871.