# Data-Driven RUL Estimation for DC-Link Capacitor in Ultra-Fast EV Charging Systems

Suwaiba Mateen, Ahteshamul Haque, Mohammed Ali Khan, Thomas Ebel, Shabana Mehfuz

► To cite this version:

Suwaiba Mateen, Ahteshamul Haque, Mohammed Ali Khan, Thomas Ebel, Shabana Mehfuz. Data-Driven RUL Estimation for DC-Link Capacitor in Ultra-Fast EV Charging Systems. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0083. hal-05082094

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# Data-Driven RUL Estimation for DC-Link Capacitor in Ultra-Fast EV Charging Systems

Suwaiba Mateen¹, Ahteshamul Haque², Mohammed Ali Khan³, Thomas Ebel⁴, Shabana Mehfuz⁵

¹,²,⁵Advance Power Electronics Research Lab, Department of Electrical Engineering, Jamia Millia Islamia, New Delhi, India

³,⁴Centre for Industrial Electronics, University of Southern Denmark, Sonderborg, Denmark
¹suwaibamateen@gmail.com, ²ahaque@jmi.ac.in, ³moak@sdu.dk, ⁴ebel@sdu.dk, ⁵smehfuz@jmi.ac.in

## Acknowledgements

In this little text, which is optional, you may write your acknowledgements.

## Keywords

«Data driven», «Electric vehicle», «Electrolytic capacitor», «Equivalent Series Resistance (ESR)», «RUL prediction»

## Abstract

The reliability of ultra-fast electric vehicle charging systems heavily depends on the performance of critical components, notably the DC-link capacitor. This paper introduces a data driven approach for estimating the remaining useful life of DC-link capacitors in such systems. A virtual model of the system, developed as a digital twin, integrates real-time operational data with machine learning algorithms trained on historical degradation patterns. Key health indicators, such as a 30% reduction in capacitance (from 20,000 μF) and a 100% increase in Equivalent Series Resistance (from 0.4 mΩ), define the failure thresholds. Simulation-based validation demonstrates the effectiveness of the proposed methodology in accurately predicting capacitor degradation trends. This approach enhances the reliability of high-power EV charging systems and highlights the role of digital twins in predictive maintenance.

## Introduction

Growing environmental concerns about the impact of emissions from road transport are becoming increasingly prominent on both regional and global scales. Major car manufacturers worldwide are now under pressure

not only to reduce fuel consumption in gasoline and diesel vehicles but also to advance the development of zero-emission vehicles (ZEVs) such as electric vehicles (EVs), hybrid cars, and fuel-cell vehicles [1]. Additionally, the development of ultra-fast charging (UFC) infrastructure for EVs is crucial to support their widespread adoption [2]. The schematic for a UFC system is shown in Fig. 1. It consists of a Distributed Energy Source (DES) and a battery energy storage system (BESS), both connected to a DC bus via a DC-link capacitor. The lifespan of the system heavily depends on the reliability and performance of the DC-link capacitor, making it a critical component in the overall design [3]. Capacitor degradation symptoms are subtle at first and difficult to identify. If left unchecked, the gradual deterioration of system may lead to faults or failures. Even worse, there could be deadly mishaps that result in injuries, and property damage. Therefore, in order to assess the dependability and safety of UFC stations it is essential to predict the remaining useful life (RUL) of capacitors beforehand [4]. Based on past and current deterioration data, the RUL prediction of capacitors aims to estimate how long the capacitors will maintain good quality and performance. Authors in [5], proposed a kernel regression approach for RUL prediction of capacitors by utilising the parameter residual produced by the discrepancy between the estimated and measured capacitance. The equivalent series resistance (ESR) deterioration model served as the basis for another RUL forecast, and the mechanistic models and empirical formulas in [6] were used to estimate these ESR values. Capacitors' RUL estimations are mostly based on steady-state operating circumstances. The constants in the model are constant, and the capacitance, and resistance are typically utilized as indicators of degradation [7].
The working environment is very dynamic, therefore maintaining prediction accuracy depends heavily on parameter flexibility. To create an empirical model with great flexibility and adaptability for the electrolytic capacitor degradation trend, an optimization method was used in [8] to determine the minimum number of effective particles by adaptively varying the sample size. Even though research on the RUL prediction of capacitors has advanced, challenges related to the prediction still exist. Previous

studies concerning the RUL prediction of capacitors often focus on the accelerated aging tests and the associated experimental configuration, with the goal of obtaining the degradation datasets needed for the RUL prediction of the capacitors, as in [9]. In addition, a lot of the techniques also rely on physical models for control and prediction. As engineering equipment becomes more complicated, it becomes increasingly difficult to precisely derive the physical models of the failure process [10].

<figure><img src="image_2.png" /><figcaption>Fig. 1: Schematic of an Ultra-fast Charging (UFC) of an Electric Vehicle (EV)</figcaption></figure>

The data-driven approach is more suited for RUL prediction since it can infer the degradation process without requiring knowledge of the physics behind the degradation. In this paper, design and implementation of RUL algorithm for a DC-link capacitor in a UFC system is proposed. The degradation data for training is generated in MATLAB Simulink. The major contribution of paper is summed up as:

* The physical structure is used to build the equivalent circuit model for the electrolytic DC-link capacitor. The failure criterion is established by discussing the performance deterioration mechanism.

* The UFC system for electric vehicles (EVs) is modelled and the model is fed with the deterioration profiles of the ESR and capacitance over a 24-month simulated lifetime.

* Using a MATLAB simulation ensemble, the deterioration data is processed and analyzed for feature extraction.

* The real-time prediction of RUL with the Simulink model acting as the digital twin of an entire UFC system for EVs and its visualization.

* To replicate real-life deterioration uncertainties, the digital twin simulation is performed once every seven simulated days utilizing the degraded capacitance and ESR values augmented with extra Gaussian noise of variance 0.1.

## Designing the UFC system

The first step is to design and simulate an ultra-fast charging system for EVs on MATLAB Simulink platform as shown in Fig 1. The simulated EV charger is of capacity 100 kW. The designed model analyses the performance and control strategies of a charger connected to an EV
battery. The model includes key components such as an isolated DC-DC converter, also known as Electric Vehicle Supply Equipment (EVSE), which regulates the voltage and current supplied to the battery, ensuring efficient and safe charging, Unity Power Factor (UPF) Front End Converter (FEC) to control output DC bus voltage at 800 V, solar PV system that acts as DES, EV battery pack and the utility grid. The model integrates a control system that manages the charging stages, monitors the state of charge (SOC), and adjusts the power flow from the grid or solar plant accordingly. Additionally, a DC-link capacitor is used to stabilize the DC bus voltage at 800 V, which is critical for the reliable operation of the charger.

## DC Link Capacitor

For the designed system, a standard electrolytic capacitor is considered as a DC-link capacitor. An equivalent circuit of an electrolytic capacitor is shown in Fig. 2. The ideal capacitance between the anode and cathode of capacitor is denoted by $C_{AK}$; the sum of the dielectric losses and leakage between the two electrodes is clubbed together to form $R_P$; $R_S$ is the equivalent series resistance between the electrodes and connection; and L is the equivalent series inductance between the connection and winding [7].

<figure><img src="image_3.png" /><figcaption>Fig. 2: Equivalent circuit of electrolytic capacitor</figcaption></figure>

From the circuit, the impedance is calculated as,

$$ 
\begin{aligned}
Z_T &= j\omega L + R_S + \frac{R_P}{R_P + 1/j\omega C_{AK}} \\
&= j\omega L + \left( R_S + \frac{R_P}{1 + R_P^2 C_{AK}^2 \omega^2} \right) \\
&\quad + \frac{1}{j\omega C_{AK} \left( 1 + 1/R_P^2 C_{AK}^2 \omega^2 \right)}
\end{aligned} 
\quad (1) 
$$

From equation (1), it can be deduced that the circuit consists of a series combination of Equivalent Series Inductance (ESL), ESR and capacitance i.e.,

$$ ESL = L \quad (2) $$

$$ ESR = R_S + \frac{R_P}{1 + R_P^2 C_{AK}^2 \omega^2} \quad (3) $$

$$ C = C_{AK} \left( 1 + \frac{1}{R_P^2 C_{AK}^2 \omega^2} \right) \quad (4) $$

Since the value of ESL is in nH, it can be ignored [11]. Because of aging, C decreases and ESR increases in the circuit due to the depletion of electrolyte and increase in thickness of anode. The validity of ESR and C variations reflecting the degradation trend for capacitor has been demonstrated by the literature [12]. These two observed parameters can be used for its maintenance, failure prediction, and reliability assessment. Generally, C degrades linearly and ESR exponentially, according to the equation (5) and (6), respectively.

$$ C(t) = C_0 + \alpha t \quad (5) $$

$$ ESR(t) = ESR_0 e^{\beta t} \quad (6) $$

The commonly acknowledged failure threshold for electrolytic DC-link capacitors is a 30% decrease in capacitance and a 100% rise in ESR. The value of C and ESR at the time of failure $t_f$ is,

$$ C(t_f) = 0.7C_0 \quad (7) $$

$$ ESR(t_f) = 2ESR_0 \quad (8) $$

<figure><img src="image_4.png" /><figcaption>Fig. 3: Degradation profile for C and ESR</figcaption></figure>

To generate sufficient deterioration data and build a robust training dataset for RUL estimation, the degradation of capacitance and ESR was simulated over a 2-year lifespan until failure. The degradation profile for C and ESR generated in
MATLAB is shown in Fig 3. The value of $C_0$ and $ESR_0$ is set at 20,000µF and 0.4mΩ respectively.

## Degradation data of the Capacitor

To illustrate the degradation of the capacitor over time, an array of values for the two variables, C and ESR, are selected and a number of simulation scenarios are defined.

<figure><img src="image_5.png" /><figcaption>Fig. 4: Voltage across DC-link capacitor</figcaption></figure>

A for-loop is used to record the degraded value of voltage across capacitor once every 30 days. For the system, a total of 25 simulation inputs were obtained from the degradation variable vectors that were kept in variables C and ESR. For the two years, these inputs correspond to a single set of measurements taken every thirty days. The voltage across the DC-link capacitor is taken into account for analysis. This signal has characteristics that show how the capacitor deteriorates over time. Fig. 4 shows the voltage across the DC-link capacitor for the first scenario. The initial transients of the signal are ignored and the steady-state portion of the signal is used for analyses.

A short segment of the voltage across capacitor for the different 25 simulation inputs is shown in Fig. 5. This voltage shows change in the DC-link voltage over the lifetime of the capacitor and therefore, will be a good candidate for feature extraction.

<figure><img src="image_6.png" /><figcaption>Fig. 5: DC-link Capacitor Voltages for 25 simulation inputs</figcaption></figure>

## Feature Extraction

For the data processing Signal Envelope is utilized. Signal enveloping aids in separating the low-frequency content of the signals—which contains more pertinent information regarding the deterioration behavior of the capacitor—from the high-frequency content of the signals.

The well-designed degradation features can accurately depict how systems or component degradation is progressing. Therefore, in the next step, potential features are initially developed from raw data using statistical indicators. Evaluation measures are then used to determine the deterioration aspects. Assuming that the

obtained raw data is $x(k)$ ($k$ = 1, 2, ..., $S$ = 25), where $S$ represents the size of data. Next, Table I lists the candidate traits that were used in this investigation along with the formulas used to calculate them.

<table><caption>Table I: Degradation Features</caption><thead><tr><td>Feature</td><td>Equation</td></tr></thead><tbody><tr><td>Mean (x̄)</td><td>$$ \sum_{i=1}^{S} \frac{x_i}{S} $$</td></tr></tbody></table>
<table><tr><td>Peak value</td><td>max|x<sub>i</sub>|</td></tr><tr><td>Root Mean Square (RMS)</td><td>√(1/S) ∑<sub>i=1</sub><sup>S</sup> x<sub>i</sub><sup>2</sup></td></tr><tr><td>Standard deviation</td><td>√(Σ<sub>i=1</sub><sup>S</sup> (x<sub>i</sub> - x̄)<sup>2</sup>) / (S - 1)</td></tr><tr><td>Skewness</td><td>(1/S) Σ<sub>i=1</sub><sup>S</sup> (x<sub>i</sub> - x̄)<sup>3</sup> / [∫<sub>1/S</sub><sup>S</sup> Σ<sub>i=1</sub><sup>S</sup> (x<sub>i</sub> - x̄)<sup>2</sup>]<sup>3/2</sup></td></tr><tr><td>Signal to Noise Ratio (SNR)</td><td>Signal Power / Noise Power</td></tr><tr><td>Kurtosis</td><td>(1/S) Σ<sub>i=1</sub><sup>S</sup> (x<sub>i</sub> - x̄)<sup>4</sup> / [∫<sub>1/S</sub><sup>S</sup> Σ<sub>i=1</sub><sup>S</sup> (x<sub>i</sub> - x̄)<sup>2</sup>]<sup>2</sup></td></tr><tr><td>Shape factor</td><td>√(1/S) Σ<sub>i=1</sub><sup>S</sup> x<sub>i</sub><sup>2</sup> / (1/S) Σ<sub>i=1</sub><sup>S</sup> |x<sub>i</sub>|</td></tr><tr><td>Clearance factor</td><td>max|x<sub>i</sub>| / (√(1/S) Σ<sub>i=1</sub><sup>S</sup> √|x<sub>i</sub>|))<sup>2</sup></td></tr><tr><td>Impulse factor</td><td>max|x<sub>i</sub>| / (1/S) Σ<sub>i=1</sub><sup>S</sup> |x<sub>i</sub>|</td></tr><tr><td>Crest factor</td><td>max|x<sub>i</sub>| / √(1/S) Σ<sub>i=1</sub><sup>S</sup> x<sub>i</sub><sup>2</sup></td></tr><tr><td>Total Harmonic Distortion (THD)</td><td>Harmonic Component Power / Fundamental Power</td></tr><tr><td>SINAD</td><td>Total Signal Power / Noise plus Distortion Power</td></tr></table>

The degradation features that are chosen should be resilient against outliers, minimize the correlation between features and time, and accurately describe the performance decline characteristic of the components. The linearity

between features and time is measured via correlation. Robustness indicates a feature's ability to withstand outliers, whereas monotonicity evaluates a feature's inclination to rise or decrease. To get the degradation data, the features are thus assessed using the correlation, monotonicity, and robustness metrics. The unsupervised ranking method of variance is used to rank the resultant signal features. As seen from the Fig. 6, the good candidate for predicting the degradation will be SNR, followed by RMS, skewness and mean. The values obtained of variance for different features are shown in Table II.

<figure><img src="image_7.png" /><figcaption>Fig. 6: Feature ranking</figcaption></figure>

<table><caption>Table II: Variance of different features</caption><thead><tr><td>Feature</td><td>Variance</td></tr></thead><tbody><tr><td>SNR</td><td>1.0000</td></tr><tr><td>RMS</td><td>0.8603</td></tr><tr><td>Skewness</td><td>0.7538</td></tr><tr><td>Mean</td><td>0.7295</td></tr><tr><td>Kurtosis</td><td>0.6958</td></tr><tr><td>Shape factor</td><td>0.6604</td></tr><tr><td>Peak value</td><td>0.6344</td></tr><tr><td>Clearance factor</td><td>0.6174</td></tr><tr><td>Impulse factor</td><td>0.6044</td></tr><tr><td>Crest factor</td><td>0.5939</td></tr><tr><td>Standard deviation</td><td>0.5841</td></tr></tbody></table>
<table><tr><td>THD</td><td>0.5768</td></tr><tr><td>SINAD</td><td>0.5706</td></tr></table>

## Training the Prediction Model

The next step is to combine these sets of features into a single health indicator (HI) that represents the state of health for the overall charging system. The HI values obtained for the system can be used to simplify condition monitoring and RUL prediction [13]. The scalar linear regression equation used is,

$$H(t) = w_0 + w_1 f_1(t) + w_2 f_2(t) + \dots + w_S f_S(t) \quad (9)$$

Here, $w_0, w_1, \dots, w_S$ represent the coefficients that weight the feature contributions. The intercept value is $w_0$, and the values of the individual features at time t are represented by the $f_0, f_1, \dots, f_S$ terms. Usually, H is normalized to fall between [0,1] and [1, 0]. The scatter plot of values of HI, shown in Fig. 7, follows a negative linear trend.

<figure><img src="image_8.png" /><figcaption>Fig. 7: Health Indicator values of DC-link Capacitor</figcaption></figure>

### Algorithm

The model is fitted to the target using the elastic net method, which is associated with the lasso algorithm. Elastic net regularization is a common method for model reduction which balances a compromise between uncertainty and mean squared error.

The regularization parameter $\lambda$, is a non-negative parameter which determines how many predictors or features to include in the model. It is a crucial lasso tuning parameter. For a specified value of $\lambda$, it solves the problem as,

$$\min_{\beta_0, \beta} \left( \frac{1}{2N} \sum_{i=1}^{N} (y_i - \beta_0 - x_i^T \beta)^2 + \lambda \sum_{j=1}^{p} |\beta_j| \right)$$

Where N is the number of observations, $y_i$ is the response at observation i and $x_i$ is data, a vector of p values at observation i. The parameters $\beta_0$ and $\beta$ are scalar and p-vector respectively. The number of non-zero components of $\beta$ reduces as $\lambda$ rises. In addition to $\lambda$, the elastic net algorithm also uses $\alpha$, a second parameter that has a range of 0 to 1. There are advantages to using $\alpha$, particularly when dealing with highly correlated predictors. The problem is resolved by elastic net as,

$$\min_{\beta_0, \beta} \left( \frac{1}{2N} \sum_{i=1}^{N} (y_i - \beta_0 - x_i^T \beta)^2 + \lambda P_{\alpha}(\beta) \right)$$

Where,

$$\begin{aligned} P_{\alpha}(\beta) &= \frac{(1 - \alpha)}{2} \|\beta\|_{2}^{2} + \alpha \|\beta\|_{1} \\ &= \sum_{j=1}^{p} \left( \frac{(1 - \alpha)}{2} \beta_{j}^{2} + \alpha |\beta_{j}| \right) \end{aligned}$$

## Real-Time Prediction of RUL

A small amount of Gaussian noise with variance of 0.1 is added to the data to obtain multiple run-to-failure data sets. These data sets are then used to train a linear degradation model. The model is initialized in MATALB with parameters such as slope parameter $\theta$, the variance of $\theta$, intercept value $\phi$, variance of additive noise $\varepsilon$ and other parameters.

For real-time prediction of RUL, the simulation models act as a digital twin of an actual UFC system for EVs and predicts the RUL of DC link capacitor. The digital twin simulation is performed once every seven simulated days, with the degraded values of C and ESR supplemented with additional Gaussian noise to replicate the uncertainties associated with real-life degradation. Fig. 8 shows the predicted RUL of the capacitor and the actual RUL. The estimated RUL falls within the confidence bound throughout the 730 days.

The voltage sensors on the UFC system for EVs would measure the signal data in a real deployment of the RUL estimation algorithm. Features would then be derived from those signals and provided to the RUL algorithm as the health indicator input.
<figure><img src="image_9.png" /><figcaption>Fig. 8: Predicted RUL for the DC-link capacitor</figcaption></figure>

The RUL forecasts are not valid until a considerable deterioration slope shift is detected by the RUL model. The RUL prediction rapidly converges to the theoretical (actual) RUL value following this first transition interval, or the slope detection instant, and eventually reaches a final lifetime value of two years, as shown in Fig. 8.

## Conclusion

This study presented a data-driven approach for estimating the RUL of DC-link capacitors in ultra-fast electric vehicle charging systems. By leveraging a digital twin framework that integrates real-time operational data with machine learning models, the proposed method accurately predicts capacitor degradation trends. Key health indicators, such as a 30% reduction in capacitance and a 100% increase in Equivalent Series Resistance (ESR), were used to define failure thresholds. Simulation-based validation showed that the predicted RUL closely matched the actual RUL, demonstrating the reliability and precision of the proposed approach. The results highlight the potential of digital twins in enhancing the operational efficiency and reliability of high-power EV charging systems. By accurately predicting the remaining life of critical components, this approach enables proactive maintenance, reducing system downtime and extending component lifespan.

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