# Laboratory Measurements for Machine Learning-based Modelling of LV Harmonic Sources

Meriem Zanoun, Éric Labouré, Mohamed Bensetti, Trung Dung Le, Xavier Yang, Sébastien Gouraud

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Meriem Zanoun, Éric Labouré, Mohamed Bensetti, Trung Dung Le, Xavier Yang, et al. Laboratory Measurements for Machine Learning-based Modelling of LV Harmonic Sources. The 26th European Conference on Power Electronics and Applications, GDR SEEDS France & EPE Association, Mar 2025, Paris, France. 10.34746/epe2025-0137. hal-05101385

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# Laboratory Measurements for Machine Learning-based Modelling of LV Harmonic Sources

Meriem Zanoun¹,², Éric Labouré¹, Mohamed Bensetti¹, Trung Dung Le¹, Xavier Yang²,
Sébastien Gouraud²

¹Université Paris-Saclay, CentraleSupélec, CNRS, Laboratoire de Génie Electrique et Electronique de Paris, 91192, Gif-sur-Yvette, France.
Sorbonne Université, CNRS, Laboratoire de Génie Electrique et Electronique de Paris, 75252, Paris, France

²EDF Lab Paris-Saclay, 91120, Palaiseau, France

meriem.zanoun@centralesupelec.fr

## Keywords

«Power Electronics Converters», «Frequency Simulation», «Machine Learning», «Harmonic Injection», «Electric Vehicle Charger», «Measurements». «Distribution Grids».

## Abstract

As renewable energy grows, power electronic converters increase harmonic disturbances, affecting power quality. This study introduces a novel modelling methodology based on machine learning and laboratory databases for harmonic current prediction. A model using electric vehicle charger data demonstrates promising performance. Integrating these models into low-voltage network improves frequency-domain simulation and enhances grid analysis.

## Introduction

Ensuring a high-quality and reliable power supply is essential for the optimal functioning of equipment in both public and private power grids. A major challenge in achieving this goal is the management of harmonics and supra-harmonics [1], [2], which have increasingly compromised grid stability, reliability, and equipment lifespan despite existing standards [3], [4], [5].

The rise in harmonic distortions is driven by several factors, notably the shift to renewable energy sources and increased electrification. Low voltage (LV) distribution grids are particularly affected by the proliferation of electric vehicle chargers, solar systems, heat pumps, and household appliances [6]. These devices use power electronic converters that exhibit nonlinear behavior, generating harmonic currents that propagate through the grid and degrade voltage quality. Furthermore, these converters not only produce harmonics but are also affected by harmonics from other devices, potentially leading to harmonic amplification and further destabilizing the grid [7]. To mitigate the impact of harmonic interactions on electrical systems, accurately estimating these interactions has become crucial. The literature categorizes the modeling of these phenomena into two main approaches:

### a) Time Domain Model (TM)

When the topology of power electronic (PE) converters and their control laws are known, creating a digital twin of these devices allows for high accuracy testing of their behavior under various grid conditions without taking risk of damage. This method, however, has two significant drawbacks. First, equipment manufacturers often withhold technical and software details of their products due to privacy constraints. Second, time domain simulation can be computationally expensive [8].
## b) Frequency Domain Model (FM)

This approach utilizes a constant multi-frequency current source for harmonic modeling, providing a faster alternative to the traditional TM method. This approach is suitable for conventional disturbance loads that can be modeled as current sources, largely unaffected by grid voltage and impedance. However, it fails to accurately capture harmonic interactions in modern power quality studies, where loads no longer behave as current sources but as voltage sources [9]. Indeed, in modern loads and renewable energy-based generators such as, Adjustable-Speed Drives (ASDs), electric vehicles (EVs) and photovoltaic systems (PVs), voltage source converters (VSCs) based on transistors have been increasingly used as switching power supplies. Some of these devices act as voltage sources and are significantly influenced by grid voltage and impedance at the point of connection (POC). Therefore, modeling methods must be updated to reflect the nature of contemporary nonlinear loads [10].

Various research efforts have focused on hybrid approaches combining the time and frequency domains, frequency coupling admittance matrices, and iterative algorithms for advanced power quality modeling [11], [12], [13]. However, none have specifically addressed the prediction of harmonic currents in power electronic (PE) converters based on grid conditions, such as voltage and impedance.

In our previous work, [14] explored the nonlinear behavior of different PE converters and showed that the harmonic currents generated by a specific converter at the POC are intrinsically linked to the harmonic voltage and frequency impedance of the grid. Also [15] introduced a novel method that constructs a machine learning model to predict current harmonics using a database (DB) generated from time-domain simulations and evaluated some Machine learning (ML) techniques based only on root mean square (RMS) voltage and peak voltage.

In this paper, we aim to build the ML models by treating the nonlinear load as a black box, without detailed knowledge of its internal architecture. The purpose of these models extends beyond predicting the current harmonics for an individual converter. In

practical scenarios, multiple converters within the low-voltage grid interact, as illustrated in Fig.1. The goal of these models is to address this complexity by integrating them into harmonic iterative frequency simulations. This approach overcomes the limitations of traditional static current source models, which fail to accurately predict current harmonics due to their inability to account for grid configurations.

The rest of the paper is organized as follows: first, the methodology for modelling PE converters is presented, including explanations on the process of laboratory measurements to build an efficient database that accurately describes the device's behavior. Next, we describe in detail the different steps of the flowchart, outlining the training and evaluation process of several robust machine learning models under different scenarios, using relevant metrics to ensure their capability in predicting harmonic currents under varying grid conditions.

The chosen case study for this work is an electric vehicle charger (EVC) [16]. Finally, the results are discussed, and some conclusions will be given.

<figure><img src="image_2.png" /><figcaption>Figure 1 - Diagram of the Grid Structure with Multiple Nonlinear Loads.</figcaption></figure>

## Methodology

The key steps in the study outlined in this paper are as follows: first, laboratory measurement on selected device; then, data preprocessing; followed by MLM training & validation; and finally, iterative frequency simulation. We will discuss each of these steps in separate sections in detail.

## PE converter model with ML

Traditional time-domain (TD) models for harmonic source modeling face inherent limitations, which can be effectively addressed using machine learning (ML) techniques. ML uses statistical algorithms to analyze datasets,
revealing complex nonlinear relationships between harmonic voltages (inputs) and harmonic currents (outputs). Unlike TD models, ML approaches do not require extensive prior knowledge of the equipment and can adapt to real-world grid conditions.

Recent literature surveys highlight the increasing use of ML in solving various network-related challenges [16], such as fault detection and electrical consumption prediction. In this work, we aim to predict harmonic currents, including their magnitude and phase angle, based on key network parameters such as voltage, power, and impedance (Fig. 2). Proper problem formulation is essential to identify the suitable type of ML approach, such as supervised learning (regression/classification), unsupervised learning, or reinforcement learning. Since our goal is to predict continuous numerical values, this task is best addressed as a supervised regression problem [18].

<figure><img src="image_3.png" /><figcaption>Figure 2 - Inputs/outputs of the machine learning models.</figcaption></figure>

It is well known that training an ML model requires data. In this first section, we outline the process of constructing a suitable dataset for our specific case. In the second section, we investigate three state-of-the-art ML methods suitable for modeling harmonic sources. These methods are trained on a significant portion of laboratory datasets containing measurements under various harmonic voltage and impedance conditions. The models are then tested on unseen data scenarios to evaluate their robustness and accuracy. Performance is assessed using several metrics, which will be detailed in the third section.

## DB construction and preprocessing

The process of building the database through laboratory measurements (Fig.3, Fig.4) involves supplying the specified load with multiple different voltage scenarios. This is achieved by using:

- A harmonic voltage source generator generates signals within a range of 0-10V.

These signals are then amplified using a power amplifier to supply the equipment under test.

- The signals to be injected are specified using a .txt file with each row corresponding to a specific scenario to be injected. The columns represent the harmonic order, magnitudes (%), and phase angle (°) of the corresponding harmonic order.

- For each scenario, the magnitude of the harmonic voltage $U_h$ is a random value between 0 and the limit of emission $U_{hmax}$, as defined by the EN50160 standard, and the phase $\varphi_h$ is a random value between 0° and 360°.

We make sure that limits are not exceeded for each harmonic individually as well as for the total harmonic distortion (THDv) overall.

<figure><img src="image_4.png" /><figcaption>Figure 3 - Test bench diagram.</figcaption></figure>

This process can be repeated for various upstream impedances, with the upstream inductance being adjustable. In our case, we tested three inductance values: 100 µH, 400µH, and 800 µH and a low line resistance. Depending on the available equipment in the lab, measurements were conducted for each of these inductance configurations.

<figure><img src="image_5.png" /><figcaption>Figure 4 - Database construction process.</figcaption></figure>
Each scenario is run for 2 seconds, and between scenarios, a sinusoidal signal is applied to avoid significant transients. The time-domain waveforms of current and voltage at the POC are recorded for each scenario during the last 200 ms equivalent to 10 periods as defined in IEC 61000-4-7 to ensure steady-state conditions. A Fast Fourier Transform (FFT) is then applied, and the voltage and current harmonics are saved in tabular form as complex data.

# Machine Learning Techniques

## a) Regression Neural Network

A regression neural network (RNN) is a type of artificial neural network (ANN) designed to predict continuous output values. It consists of layers of interconnected neurons $a_j$, where each neuron processes input data using weights $w_{ij}$ and biases $b_j$, and applies an activation function $f$ to produce an output. The network is trained by adjusting the weights based on the error between the predicted and actual values.

This allows the network to learn complex relationships and detect more complex patterns in the data, making it well-suited for tasks where traditional linear regression might fail to capture non-linear dependencies as it's the case of harmonic behaviors.

$a_j = f(\sum_{i=1}^{n} w_{ij} \cdot x_i + b_j)$, $\hat{y} = \sum_{j=1}^{k} v_j a_j + c$

In our scenario, each output variable $\hat{y}$ to be predicted is managed by its own neural network. We aim to predict odd harmonic currents up to the 25th order [1, 3, 5...25], resulting in 13 orders. Since each order includes both magnitude and phase angle, we have two models per order, leading to a total of 26 variables to be predicted. Thus, we will have as many models as there are variables.

<figure><img src="image_6.png" /><figcaption>Figure 5 - Regression neural network diagram with one hidden layer.</figcaption></figure>

## b) Regression Tree

A regression tree (TREE) is a non-parametric supervised learning method that can be used for regression problems. It works by recursively partitioning the input data into subsets based on the value of one attribute at a time, similar to asking a series of questions. Each node in the tree represents a test on an attribute, each branch represents an outcome of the test, and each leaf node represents a predicted value. The tree aims to minimize uncertainty, measured by mean square error (MSE) or mean absolute error (MAE) error, and maximize information gain with each split.

Despite their simplicity and interpretability, regression trees can be unstable and prone to overfitting, but with proper management, they are powerful tools for making predictions in various fields.

Fig. 6 shows the hierarchical structure typical of decision trees, starting from a root node that splits into interior nodes and finally into leaf nodes.

<figure><img src="image_7.png" /><figcaption>Figure 6 - Decision Tree typical structure.</figcaption></figure>

## c) Random Forest

A Random Forest (RF) is an ensemble learning technique that combines multiple regression trees to improve predictive accuracy and control overfitting. By training each tree on different bootstrap samples of the data and using a random subset of features for splitting at each node, RF reduces the variance of the model. The final prediction is obtained by averaging the predictions from all individual trees, making the model more robust to overfitting and providing better generalization on unseen data.

While increasing the number of trees improves performance, it also increases computation time. RF is highly effective for complex
regression tasks, offering a balance between interpretability and predictive power.

<figure><img src="image_8.png" /><figcaption>Figure 7 - Random forest architecture.</figcaption></figure>

## Performance Evaluation Criteria of Models

After selecting the converter, building the database (DB), and training the ML models with the chosen methods, we proceed to analyze the results using error calculations on the magnitudes and phases of the predicted harmonic currents. To ensure an effective interpretation of the results, three evaluation metrics were employed to assess the performance of our models.

### a) MAPE (Mean Absolute Percentage Error)

This metric expresses the relative percentage error between the actual and predicted values of harmonic current magnitudes of the order h.

$$MAPE_h = \frac{100\%}{n} \sum_{i=1}^{n} \frac{|I_{h_i} - \hat{I}_{h_i}|}{|I_{h_i}|} \quad (1)$$

With n: total number of samples; h: harmonic order; I_h: target current magnitude of order h; I_h: predicted current magnitude of order h

### b) MAE (Mean Absolute Error)

This metric expresses the absolute error between the phase angles of the actual and predicted currents of the order h, measured in degrees.

$$MAE_h = \frac{1}{n} \sum_{i=1}^{n} |\varphi_{h_i} - \hat{\varphi}_{h_i}| \quad (2)$$

With φ_h: target current phase angle of order h; I_h: predicted current phase angle of order h

### c) RRMSE (Relative Root Mean Square Error)

Unlike the other two metrics, which reflect errors in the frequency domain, this one

measures the error on the reconstructed time-domain waveforms.

$$RRMSE = 100\% \frac{\sqrt{\frac{1}{n} \sum_{i=1}^{n} (I(t)_i - \hat{I}(t)_i)^2}}{\sqrt{\frac{1}{n} \sum_{i=1}^{n} I(t)_i^2}} \quad (3)$$

With I(t): Target temporal current; I(t): predicted temporal current

## ML Model integration to LV Grid

The objective is to conduct a harmonic power flow (HPF) analysis of electrical power systems, considering harmonics generated by a nonlinear load modeled using ML, to determine whether the proposed method is suitable in system and converge or not [19]. The primary goals of HPF analysis are to quantify harmonic levels, such as Total Harmonic Distortion (THD), assess the impact at various points in the grid, and design effective mitigation measures, like adding filters, to reduce harmonic effects. This harmonic analysis can be conducted using industrial tools such as PowerFactory and OpenDSS, employing different solver algorithms like Newton-Raphson, Fast Decoupled Power Flow, and Backward/Forward Sweep (BFS).

## Grid Component Modeling

To simplify the validation of our black-box machine learning models (MLMs) developed using the Matlab toolbox and integrated into a power grid through iterative frequency simulation, we initially chose to model the grid using Simulink, as both tools are Matlab-based. However, it is feasible to integrate them into an industrial tool in the future.

Although Simulink is primarily designed for time-domain simulation, we modeled the grid components in the frequency domain and conducted frequency simulations to validate the accuracy of the MLMs.

This process works similarly to a BFS where voltage is propagated, the load modeled by the MLM technique is supplied, and the corresponding current is returned. This current then goes upstream through the network via the line impedance, distorting the voltage, which becomes the new input for the MLM. This cycle continues until the MLM returns the same current across several successive iterations.
<figure><img src="image_9.png" /><figcaption>Figure 8 – Machine learning model of PE converters integrated into Matlab/Simulink for frequency simulation.</figcaption></figure>

This is indeed an iterative calculation based on frequency analysis because:

- The voltage waveform is measured and decomposed into a Fourier series (FFT) which requires a minimum time window of 20ms.

- Using the harmonic decomposition of the voltage, the harmonic current is predicted by the MLM model. Once done, an inverse Fourier transformation (IFFT) is applied to obtain the temporal current waveform.

- This current is injected into the grid.

- The network voltage is distorted.

- The process is repeated in the next period until the solution stabilizes.

# Results

## MLMs validation with laboratory measurement

We present the results from applying ML techniques to model an EV charger, which converts AC current from the electrical grid into DC current to recharge the vehicle's battery using a specific rectifier, a non-linear load.

The study involved training the three ML techniques: RNN, TREE and RF. These models were tested on the same test dataset comprising 20% of the total dataset, which includes approximately 3000 samples. These samples represent 3000 different scenarios of supply voltage and can be summarized in Fig. 9 using boxplots to illustrate the variations in magnitudes and phases injected, as well as the current provided by the EV charger. Our analysis shows significant correlation between EVC harmonic currents and the supply voltage.

<figure><img src="image_10.png" /><figcaption>Figure 9 – (a) Variations of magnitudes and phases of supply voltage and (b) measured current.</figcaption></figure>

The models were evaluated using several metrics. Among the three models, the RNN demonstrated the lowest error rates across all metrics, followed by the RF, and then the TREE model, as shown in Fig. 10.

The superior performance of the RF compared to the TREE model was expected, as RF represents an ensemble approach that enhances the performance of individual decision trees. Comparing the RF and RNN models, the RNN outperformed RF, likely due to its superior ability to capture non-linear patterns in the data. The RNN achieved a MAPE of less than 8% for magnitude predictions and a MAE of under 10° for phase predictions. When assessing the RRMSE, all three models performed similarly, though the RNN still exhibited the best performance, with errors less than a maximum of 3% as depicted in Fig. 11.

<figure><img src="image_11.png" /><figcaption>Figure 10 – MAPE and MAE errors for magnitudes and phases predicted by ML model.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>Figure 11 – RRMSE error on the current waveforms for the three techniques.</figcaption></figure>

Based on these results, the RNN model was selected for further analysis due to its superior accuracy in capturing the non-linear characteristics of the EV charger data. We plotted in Fig. 12 the best and worst samples in terms of RRMSE, and we also analyzed the frequency spectrum and waveform of both the target and predicted currents.

<figure><img src="image_13.png" /><figcaption>Figure 12 - Temporal and frequency representation of the best (a, b) and worst (c, d) current predicted by the RNN model</figcaption></figure>

## Integration of MLMs on LV Grid

We validate the approach using a simple LV grid ($U_n$ = 400V) connected to a medium voltage 20kV substation. In this setup shown in Figure 13, we can control the supply voltage, whether it is polluted with harmonics or perfectly sinusoidal. The medium-voltage grid is connected to a transformer that steps down the voltage to LV, which is then linked to the MLM of the EVC through a LV line. Equivalent network impedance is close to the one used in laboratory measurements. The MLM model is

imported into Simulink using the Regression Neural Network Predict block.

<figure><img src="image_14.png" /><figcaption>Figure 13 - Simulink diagram of the studied LV network</figcaption></figure>

The current evolution throughout the iterations is depicted in Fig.14. Note that each period represents an iteration. In the initial iteration, the waveforms exhibit fluctuations. However, after approximately five iterations, the signals converge.

Given that we do not have the actual current waveform generated by the nonlinear load, we compared the converged result to the most similar signal in the database to ensure accuracy. The Fig.15 below demonstrates that, although the signals are not identical, they are very close to each other, providing a qualitative indication of the waveform's accuracy.

<figure><img src="image_15.png" /><figcaption>Figure 14 - Evolution of the current at the POC over iterations</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Figure 15 - Comparison of Current and voltage waveforms from the simulation with reference waveforms.</figcaption></figure>
Conclusion

This study introduced a novel methodology for modeling PE converters. This approach leverages machine learning techniques and integrates laboratory measurement data to represent nonlinear loads as a black-box model. We compared three different ML models and evaluated them using various metrics. Our results demonstrated that the RNN meta-model accurately captures the nonlinear relationships in the current generated by the PE converter, as tested on an EVC. The integration of the validated MLM into a simple LV grid, using a hybrid temporal/frequency iterative simulation, confirmed the suitability of our approach for harmonic power flow studies.

Future work will involve enhancing the complexity of the LV grid by adding capacitors and by incorporating multiple MLM models, alongside other nonlinear and linear loads, to evaluate system convergence using the same tool. Additionally, we aim to integrate the MLM model into industrial tools designed for harmonic load flow (HLF) analysis, assessing system convergence in real-grids applications. Furthermore, we plan to model other types of nonlinear loads, such as heat pumps and LED lamps and TVs, to enrich the study and explore the feasibility of our approach across various types of loads. This future work may also involve classifying loads based on their feasibility and error tolerance within this modeling framework.

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