⚡ electrical engineering

Experimental Electrical Parameter Identification and Model Validation of an Induction Motor for Digital Twin Applications

This paper presents an experimental methodology for identifying and validating the electrical parameters of an induction motor within a digital twin framework, utilizing synchronized measurements and steady-state tests to achieve a highly accurate time-domain model with minimal simulation error across various operating conditions.

Original authors: Darjon Dhamo, Denis Panxhi, Aida Spahiu

Published 2026-09-23

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CC BY 4.0

Original authors: Darjon Dhamo, Denis Panxhi, Aida Spahiu

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the modern industrial world, heavy machinery relies on electric motors to turn wheels, pump fluids, and drive conveyor belts. Among these, the induction motor is a workhorse, a rugged device that converts electricity into motion without the need for direct electrical contact with its spinning parts. To keep these machines running efficiently and to predict when they might fail, engineers often create a "digital twin." This is a virtual copy of the physical motor that lives inside a computer. For this virtual copy to be useful, it must behave exactly like the real machine. If the computer model thinks the motor is stronger or weaker than it actually is, the predictions it makes about maintenance or performance will be wrong. The challenge lies in figuring out the precise internal electrical values of a specific motor, as these values can shift slightly depending on how the motor is built and how it is used. Without these accurate numbers, the digital twin is just a rough sketch rather than a reliable replica.

Researchers at the Polytechnic University of Tirana set out to build a more trustworthy digital twin for an induction motor by carefully measuring its real-world behavior and translating those measurements into a computer model. They began by constructing a test bench where a small electric motor was connected to a generator, which acted as a load to simulate the resistance the motor would face in a factory. To understand the motor's true nature, they did not rely on the manufacturer's general specifications. Instead, they performed a series of hands-on experiments. They measured the voltage and current flowing into the motor while it was running, while it was stopped with its shaft locked in place, and while it was spinning freely without any load. Because the power supply used in these tests creates a choppy, high-frequency signal that can obscure the true electrical flow, the researchers used a mathematical technique to filter out the noise. This allowed them to isolate the smooth, fundamental wave of electricity that actually drives the motor, stripping away the electrical static caused by the power converter.

With these clean measurements in hand, the team calculated the specific electrical properties of the motor, such as the resistance of its internal wires and the inductance, which is a measure of how the motor stores magnetic energy. They determined these values using standard tests: a direct current test to find the resistance of the stationary windings, a locked-rotor test to understand how the motor behaves when it cannot spin, and a no-load test to see how it handles magnetic fields when running freely. Once they had these numbers, they built a time-based computer model in a simulation environment. This model was designed to mimic the motor's electrical reactions second by second. To ensure the model was truly accurate and not just lucky, they tested it against data from time periods they had not used to calculate the numbers. This separation was crucial; it meant that if the model matched the real motor, it was because the model was fundamentally correct, not because the researchers had simply tweaked the numbers to fit that specific moment in time.

The results showed that the calibrated model was remarkably precise. When the researchers simulated the motor with its shaft locked, the computer's prediction of the electrical current matched the real measurement almost perfectly, with a difference so small it was barely measurable. In the tests where the motor was spinning freely at various speeds, the model continued to track the real motor's behavior with high fidelity, capturing the nuances of the current flow across a range of frequencies. The researchers noted that while their model did not include a specific component for energy lost as heat in the motor's core, the agreement between the simulation and reality remained strong, with the simulated current following the measured current closely. This success demonstrates that the method they developed can produce a digital twin that is physically consistent and reliable. By proving that a model built from offline measurements can accurately predict real-world performance, the study provides a solid foundation for future systems that will monitor motors in real-time, adjusting their internal calculations as conditions change to prevent failures before they happen.

Technical Summary: Experimental Electrical Parameter Identification and Model Validation of an Induction Motor for Digital Twin Applications

Problem Statement
The development of high-fidelity Digital Twins (DT) for electric drives requires parameter values that are both physically consistent and predictive across various operating regimes. While numerous optimization and observer methods exist for parameter estimation, there is a need for robust offline experimental workflows that can decouple parameter tuning from model validation. Specifically, distinguishing whether discrepancies between simulation and measurement arise from model structural mismatches or from parameters varying with the operating point remains a critical challenge in creating reliable DT baselines for induction motors (IM).

Methodology
The authors propose an offline experimental workflow to estimate electrical parameters and validate a time-domain synchronous direct-quadrature (dq) model within a MATLAB/Simulink environment. The methodology proceeds through four distinct stages:

Experimental Setup and Data Acquisition:
A 130 W squirrel-cage induction motor, connected in a delta configuration and driven by a Mitsubishi FR-AC VFD, serves as the test subject. The motor is mechanically coupled to an alternator acting as an adjustable electrical load. Synchronized measurements of terminal voltage and stator current are acquired using a National Instruments USB-6009 DAQ at a sampling rate of 20 kS/s. To ensure signal integrity, line currents are measured via shunt resistors (avoiding transformer/Hall sensor errors), and voltages are scaled via resistive dividers, with both signals isolated using AMC1300 amplifiers.
Signal Processing:
To mitigate the influence of Pulse Width Modulation (PWM) harmonics and noise, the acquired voltage and current waveforms undergo a least-squares sinusoidal fit. This process extracts the fundamental phasor components at the commanded operating frequency, providing clean complex phasors and reconstructed waveforms for subsequent analysis.
Parameter Estimation:
Electrical parameters are derived using standard laboratory tests, with all quantities evaluated at the fundamental frequency:
- DC Test: A low DC voltage is applied immediately after a loaded regime to estimate stator resistance ( $R_s$ ) while minimizing inductive transients.
- Locked-Rotor Test: Performed at reduced voltages (30–50 V) and low frequencies (10–15 Hz) to estimate the referred rotor resistance ( $R'_r$ ) and leakage inductance ( $L_\sigma$ ).
- No-Load Test: Conducted at frequencies ranging from 30 to 50 Hz to estimate the magnetizing inductance ( $L_m$ ).
Model Validation:
The identified parameters are implemented in a time-domain dq model. Crucially, validation is performed on time intervals distinct from those used for estimation. This separation ensures that any residual error is attributed to model mismatch rather than parameter tuning at the same operating point. The model is tested under locked-rotor and no-load conditions, comparing simulated current against measured current using residual analysis and performance metrics (RMSE, NRMSE, $R^2$ ).

Key Contributions
The paper outlines four primary contributions:

An experimental workflow for extracting fundamental voltage and current components from variable speed IM drive measurements using least-squares fitting.
The estimation of electrical parameters ( $R_s$ , $R'_r$ , $L_\sigma$ , $L_m$ ) derived from DC, locked-rotor, and no-load tests.
The integration of these identified parameters into a time-domain induction motor model specifically for Digital Twin applications.
The validation of the calibrated model under locked-rotor and no-load regimes using residual-based performance indicators, demonstrating the efficacy of the separation between estimation and validation timeframes.

Results
The validation results demonstrate a high degree of agreement between the simulated and measured data:

Locked-Rotor Regime: The model reproduces the short-circuit dynamics with extreme precision. The normalized root mean square error (NRMSE) is approximately 0.05%, with an $R^2$ value of 1.0.
No-Load Regime: The model maintains high tracking accuracy across the 40–50 Hz range. The NRMSE ranges from approximately 3.93% to 4.19%, with $R^2$ values around 0.998.
Parameter Selection: The study selected specific parameter values (e.g., $R_s = 60.5 \, \Omega$ , $R'_r = 42.205 \, \Omega$ , $L_\sigma = 0.6679 \, \text{H}$ , $L_m = 1.729 \, \text{H}$ ) based on stable low-frequency estimates (10 Hz for locked-rotor) and the intended V/f operating region (30–50 Hz for no-load).
Modeling Note: The validation intentionally excluded core-loss resistance ( $R_c$ ) as the standard dq model used in Simulink neglects the iron-loss resistor, a choice made to align with future online estimation goals.

Significance and Claims
The authors claim that this work provides a physically consistent baseline for the induction motor's electrical subsystem within a Digital Twin framework. By decoupling parameter estimation from model validation, the study establishes a reliable foundation for subsequent applications. The paper explicitly states that these results support the use of the calibrated model for future online adaptation and condition monitoring. The authors do not claim immediate deployment of predictive maintenance but rather position this calibrated offline model as the necessary precursor for developing online parameter estimators (such as an Extended Kalman Filter) that can handle thermal effects and load variations in real-time.

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