[Paper Review] Data Set Description: Identifying the Physics Behind an Electric Motor -- Data-Driven Learning of the Electrical Behavior (Part II)

Sören Hanke, Oliver Wallscheid+1 more|arXiv (Cornell University)|Mar 13, 2020

Model Reduction and Neural Networks2 references4 citations

TL;DR

This paper presents a large-scale, high-fidelity data set of 40 million multidimensional samples from a three-phase PMSM and two-level IGBT inverter, collected across a defined operating range to enable data-driven modeling of electrical behavior. It proposes methods—using ordinary differential equations, least squares, and machine learning—to extract accurate models for model predictive control, demonstrating that balanced data distribution across operating points significantly improves model generalization and control performance.

ABSTRACT

A data set was recorded to evaluate different methods for extracting mathematical models for a three-phase permanent magnet synchronous motor (PMSM) and a two-level IGBT inverter from measurement data. It consists of approximately 40 million multidimensional samples from a defined operating range of the drive. This document describes how to use the published data set \cite{Dataset} and how to extract models using introductory examples. The examples are based on known ordinary differential equations, the least squares method or on (deep) machine learning methods. The extracted models are used for the prediction of system states in a model predictive control (MPC) environment of the drive. In case of model deviations, the performance utilizing MPC remains below its potential. This is the case for state-of-the-art white-box models that are based only on nominal drive parameters and are valid in only limited operation regions. Moreover, many parasitic effects (e.g. from the feeding inverter) are normally not covered in white-box models. In order to achieve a high control performance, it is necessary to use models that cover the motor behavior in all operating points sufficiently well.

Motivation & Objective

• To develop a comprehensive data-driven approach for modeling the electrical behavior of a PMSM and IGBT inverter under real-world operating conditions.
• To address the limitations of white-box models that fail to capture parasitic effects like magnetic saturation, capacitive coupling, and temperature dependencies.
• To enable high-performance model predictive control (MPC) by creating accurate, physics-informed models covering the entire operating range.
• To propose a method for balancing training data across operating points to improve generalization in machine learning and least-squares modeling.
• To provide a publicly available, well-documented data set for benchmarking and advancing data-driven system identification in electric drives.

Proposed method

• The data set consists of 40 million samples from a PMSM and IGBT inverter, recorded across a defined current, voltage, and speed range with a fixed DC link voltage.
• Samples include dq-currents, rotor position, and active voltage space vector at consecutive time steps, enabling dynamic system modeling.
• The operating range is partitioned into a grid (10 A steps for id, iq; π/18 rad for ε_el) to define classes for data balancing.
• A subset-based approach assigns each sample to a specific voltage vector (elementary vector), enabling per-vector model learning.
• Data balancing is achieved by limiting each class to a target number of samples (e.g., 48), ensuring homogeneity across operating points.
• Models are trained using least squares and machine learning (e.g., neural networks), with performance validated on non-homogeneous test subsets.

Experimental results

Research questions

• RQ1 How can data-driven modeling improve the accuracy of PMSM and inverter models compared to traditional white-box approaches?
• RQ2 What is the impact of uneven data distribution on the performance of least squares and machine learning models in electric drive systems?
• RQ3 Can a balanced data set be systematically constructed from real measurement data to enhance model generalization across the entire operating range?
• RQ4 How does the inclusion of parasitic effects (e.g., magnetic saturation, capacitive coupling) in data-driven models affect MPC performance?
• RQ5 To what extent can data-driven models trained on a subset of voltage vectors be generalized to the full operating range?

Key findings

• The data set contains approximately 40 million multidimensional samples from a PMSM and IGBT inverter across a defined operating range.
• Using a grid-based class assignment with 10 A steps for id and iq, and π/18 rad for ε_el, 16,956 valid classes were identified per voltage vector subset.
• With a target of 48 samples per class, 99% of the valid classes achieved the desired balance, enabling high-quality training for least squares and neural network models.
• The zero voltage vector (v₁) was selected frequently due to the DC link voltage and operating range, resulting in a higher sample count per class.
• The proposed data balancing method ensures that models trained on the balanced subset generalize well, reducing performance loss in MPC due to model-plant mismatch.
• The data set is publicly available on Kaggle, enabling reproducible benchmarking of data-driven modeling techniques for electric drives.