Analysis of Low-Signal Behavior in Electric Motors for Auto-Motive Applications: Measurement, Impedance Evaluation, and Dummy Load Definition

Abstract

This study investigates the low-signal behavior of electric motors in automotive applications, emphasizing impedance measurement, evaluation, and the definition of a simplified dummy load. A comprehensive experimental analysis was conducted on two induction motors with different power ratings (300 W and 45 kW), exploring the influence of winding topology, rotor position, and excitation amplitude on the impedance response. A simplified equivalent circuit model (ECM), derived solely from terminal impedance measurements, was developed and validated to construct a practical dummy load. This model facilitates realistic simulations without requiring detailed internal motor specifications. Experimental results confirm that the dummy load accurately replicates the measured impedance characteristics in the low-to-mid frequency range, demonstrating its effectiveness for electromagnetic interference (EMI) prediction and system-level simulations in automotive electric drive system.

1. Introduction

Electric motors play a fundamental role in modern automotive applications, particularly in electric and hybrid vehicles, where efficiency, reliability, and precise control are critical. Three-phase induction motors, first invented by Tesla in 1887, have gained widespread use due to their cost-effectiveness, robustness, and operation without permanent magnets [1].

Accurate impedance modeling of electric motors is necessary for improving control algorithms, fault diagnostics, and mitigation of electrical resonances. Various methods, including equivalent circuit models (ECMs) [2,3], finite element models (FEM) [4], and equivalent magnetic circuit models, have been explored in the literature. ECMs are most commonly used due to their intuitive lumped-parameter structure [5]. However, many existing ECMs exhibit complex, high-order behaviors across broad frequency bands, limiting their practical applicability.

Recent motor impedance modeling efforts have primarily concentrated on the high-frequency domain, targeting EMI suppression and conducted-emission modeling. For example, Ahola et al. developed a measurement-based model for low-voltage motors in the 10 kHz–30 MHz range [6]. Zare [7] and Benecke et al. [8] expanded these modeling approaches up to 1 GHz for EMI predictions. Grassi et al. [9] also presented a high-frequency SPICE simulation framework that incorporates powertrain parasitic parameters above 150 kHz. Additionally, impedance-based health monitoring at standstill has been explored to diagnose motor faults effectively [10]. However, these studies do not sufficiently address the mid- and low-frequency impedance domains, critical for controller design, inverter interactions, and hardware-in-the-loop (HIL) testing with dummy loads.

Mirafzal et al. [11] demonstrated that key motor parameters could be reliably estimated from low-frequency impedance data, with limited impact on high-frequency characteristics. Simplified broadband modeling approaches, based on terminal impedance measurements, have proven practical and do not require internal motor specifications [12].

Analyzing low-signal impedance behavior is challenging due to variations in motor wiring configurations (open, star, and delta), each uniquely influencing phase-to-phase interactions and modal-specific behavior. This analysis is particularly important for automotive applications since motors frequently operate under varying load conditions, ranging from near-zero to full-load operation. Under low-power conditions, winding impedance, stray capacitances, and resonance phenomena significantly affect motor performance.

Stray capacitances, appearing between windings, windings and the motor frame, and within the laminated core, also significantly influence motor impedance. At low frequencies, impedance is primarily inductive and resistive, but at higher frequencies, stray capacitances dominate, significantly affecting leakage currents and shaft voltages [13]. Additionally, temperature variations complicate impedance modeling since winding resistance, capacitance, and inductance change with thermal conditions, necessitating consideration in accurate ECM development [5].

Motor impedance is fundamentally determined by resistance, inductance, and capacitance. Resistance governs power dissipation through copper losses, eddy currents, and proximity effects [7]; inductance represents energy storage and affects the low-frequency voltage response; capacitance introduces resonance effects at higher frequencies, significantly influencing impedance through capacitive coupling between windings and the motor casing [14]. Accurate modeling of these elements is essential for comprehensive impedance characterization.

As illustrated in Figure 1 for three-phase asynchronous motors, the impedance model includes main winding inductances (L1, L2, L3), DC resistances (R1, R2, R3), winding capacitances (C1, C2, C3), winding-to-frame capacitances (C4–C9), and inter-phase winding capacitances (C10–C15). These parameters collectively refine motor impedance characteristics, directly influencing interactions with power electronic circuits.

This study proposes a simplified, reduced-order ECM derived solely from measured impedance characteristics, consisting of one inductor, one capacitor, and two resistors. Compared to higher-order models, this configuration optimizes the trade-off between modeling accuracy and implementation simplicity, making it particularly suitable for practical applications like dummy-load design, controller development, and EMC testing.

The primary goal of this study is to provide a standardized, experimentally validated simple RLC model representing the frequency-dependent impedance behavior of three-phase asynchronous motors under low-signal conditions. Experimental impedance measurements were conducted using a Bode 100 impedance analyzer over the frequency range of 10 Hz–40 MHz. These data were then utilized to develop and validate the simplified ECM. A practical dummy load configuration was also defined, enabling standardized motor impedance testing to enhance repeatability and reliability in automotive applications.

To validate the proposed ECM, impedance measurements across a wide frequency range were conducted on two electric motors: a 45 kW industrial motor and a 300 W laboratory motor. In both cases, the simplified model showed good agreement with measured impedance data from 10 Hz to the first resonance frequency. Frequency-dependent parameters were directly extracted from experimental data, enabling resonance tracking and control-oriented analysis without needing detailed motor geometry or extensive parameter identification.

2. Experimental Setup

A systematic approach was employed to measure the impedance characteristics of electric motors, ensuring consistency and accuracy across different frequency ranges. The experimental setup included precise measurement tools, standardized motor configurations, and controlled test conditions to analyze the behavior of low signal impedance effectively.

2.1. Measurement System

The impedance of the motors was measured across a broad frequency spectrum using a Bode 100 Impedance Analyzer, which enables high-precision frequency response analysis. This instrument was selected due to its capability to capture the impedance behavior from low frequencies, where inductive characteristics dominate, to higher frequencies, where capacitive effects become more prominent. The measurement procedure involved recording impedance data over a frequency range from 10 Hz to 40 MHz, allowing a comprehensive assessment of the motor’s electrical response.

To improve the accuracy of the collected data, the measurement resolution was adjusted over two stages. In the initial stage, 201 measurement points were used to obtain an overview of the impedance behavior, while in the final stage, the resolution was increased to 1601 measurement points to provide a more refined impedance spectrum. A logarithmic sweep method was employed to ensure higher measurement density at lower frequencies, where impedance variations are more significant. Additionally, the source power level of the impedance analyzer was initially set at 0 dBm and later increased to 13 dBm to improve signal-to-noise ratio and measurement reliability.

2.2. Testbench Configurations

The experimental setup included two testbenches to compare the impedance behavior of motors with different power ratings. The first motor tested was a Siemens 300 W asynchronous motor, Figure 2b, selected due to its widespread use in industrial applications. The second motor was a Siemens 45 kW asynchronous motor, Figure 2a, chosen to investigate the scaling effects of motor power on impedance characteristics. By comparing these two motors, it was possible to analyze the influence of power rating on impedance behavior, including resonance frequencies, phase impedance variations, and frequency-dependent losses.

3. Measurement Procedure

3.1. Initial Test Configurations

Each motor was configured in different impedance setups to assess the impact of circuit topology on impedance characteristics. To ensure measurement accuracy, the impedance analyzer and test cables were calibrated before test. Zero calibration was performed to compensate for the impedance of test leads and connectors, minimizing measurement distortions.

As shown in

Table 1. The list of test step configurations and measurements.

Configuration
Measurement	Open (O)	Star (Y)	Triangle (Δ)
1	U1–U2	U1–Y	U1–W1
2	V1–V2	V1–Y	V1–U1
3	W1–W2	W1–Y	W1–V1
4	U1–REL	U1–REL	U1–REL
5	V1–REL	V1–REL	V1–REL
6	W1–REL	W1–REL	W1–REL
7	U2–REL
8	V2–REL
9	W2–REL

, three fundamental phase configurations were examined: open, star, and triangle. In the open configuration, phase terminals were left unconnected to analyze their independent impedance response. In the star configuration, all three phases were connected to a common neutral point, which provided insights into symmetrical phase interactions. In the triangle configuration, the phase windings were interconnected in a closed-loop arrangement, allowing an evaluation of how circulating currents and phase coupling influenced impedance behavior. Additionally, impedance measurements were conducted with reference to the motor casing (ground potential).

This study included variations in rotor position to analyze dynamic impedance behavior and assess how rotor displacement influences phase interactions. To achieve this, as shown in Figure 3, rotor positions were incrementally adjusted from 0 mm to 20 mm, in 2.5 mm steps, allowing for a detailed examination of how mechanical positioning affects electrical impedance characteristics across different phase configurations.

3.2. Final Measurement Adjustments

To improve the precision of impedance measurements, several refinements were introduced in the final testing phase. The number of data points collected was increased from 201 to 1601, allowing for finer resolution of impedance variations. The source power level of the impedance analyzer also increased from 0 dBm to 16 dBm to enhance the stability of measured values.

The potential influence of test wiring on measurement results, as shown in Figure 4, was also evaluated by testing different cable lengths and configurations. The final setup was optimized by shortening measurement which leads to reduce unintended capacitance and inductance, ensuring that the recorded impedance values accurately reflected the motor’s electrical properties rather than extraneous parasitic effects.

The final tests were conducted and optimized based on the evaluation of the initial results to ensure more accurate and reliable measurements. As shown in Figure 5, the test included two phase configurations: open U1_U2 and star U1_Y, to analyze their impact on motor impedance characteristics.

4. Results and Discussion

This section presents a detailed evaluation of impedance measurements obtained from two motors (300 W and 45 kW). The impact of motor scale, winding topology, excitation amplitude, and rotor position on the resonance frequency and impedance peak magnitude is thoroughly examined. These measurements provide the foundation for the subsequent identification of parameters for the ECM.

The analysis encompasses six distinct test scenarios: (i) comparison of the 300 W and 45 kW motors, (ii) comparison of open-ended and star configurations for the 300 W motor, (iii) a similar comparison for the 45 kW motor, (iv) source-level variation on the 45 kW motor, (v) source-level variation on the 300 W motor, and (vi) rotor-position variation on the 45 kW motor. Each scenario is analyzed through the measured |Z| and ∠Z data, and the derived characteristics are compared to guide the dummy-load design.

Figure 6 illustrates a comparative impedance sweep of the 300 W and 45 kW motors, clearly showing the three canonical impedance regions: inductive rise, LC resonance, and capacitive decay. The 300 W motor resonates at approximately 19.6 kHz with a peak impedance magnitude of around 95 kΩ, whereas the 45 kW motor exhibits resonance at a significantly higher frequency of approximately 178 kHz with a notably lower peak magnitude of about 1.3 kΩ. These results confirm that, as motor power rating increases, the resonance frequency shifts upward, and the associated impedance peak is reduced.

Both motors display similar qualitative behaviors, characterized by a single dominant resonance, comparable phase transitions, and consistent high-frequency slopes. This similarity suggests that the fundamental electromagnetic interactions governing impedance are preserved across different motor scales. However, quantitatively, the resonance frequency of the 45 kW motor is approximately 4.5 times higher, and its impedance magnitude is roughly 80 times lower than that of the 300 W motor. This clearly highlights the influence of power rating on the impedance profile.

Figure 7 compares the open-ended and star connection configurations for the 300 W motor. Both configurations exhibit nearly identical impedance behavior in the low-frequency region, demonstrating that the series inductance remains largely unaffected by the terminal connection. Significant differences, however, become evident near resonance: the open-ended configuration resonates at 19.6 kHz, while the star configuration resonates at 17.6 kHz. Correspondingly, the peak impedance drops from 95 kΩ in the open configuration to 75 kΩ in the star configuration. Moreover, the impedance in the star configuration decays more rapidly beyond resonance, indicating an earlier capacitive dominance due to increased effective capacitance from inter-phase coupling.

The analysis of the 45 kW motor configurations (Figure 8) similarly reveals minimal differences at low and high frequencies, where impedance profiles overlap closely. In the resonance region, however, significant variations emerge. The open configuration exhibits resonance at 178 kHz with a peak impedance of 1295 Ω, whereas the star configuration shifts the resonance downward to 98.4 kHz and reduces the peak impedance to 708 Ω. This shift is consistent with an increase in effective inter-phase capacitance, modifying the resonance condition and causing earlier and more damped LC behavior. As observed with the 300 W motor, these configuration-induced differences are localized to mid-frequency bands and must be considered in ECM parameter estimation.

In Figure 9, impedance spectra of the 45 kW motor were measured at three source levels: 0 dBm, 8 dBm, and 16 dBm. The broadband impedance response remains highly consistent across these levels, with only minor deviations observed at very low frequencies. These slight increases in impedance at higher excitation levels suggest subtle magnetization effects. Nevertheless, impedance curves in the resonance and high-frequency regions are virtually identical, confirming the linear, level-independent behavior of the 45 kW motor across the tested amplitude range. This characteristic simplifies both measurement and ECM modeling tasks.

Figure 10 contrasts this with the behavior of the 300 W motor under varying source levels. While stable in low- and high-frequency regions, the main resonance at approximately 19.6 kHz broadens and lowers in peak impedance magnitude at higher excitation levels. Additionally, the slope of the phase slightly flattens, indicating mild nonlinear effects or increased dielectric losses with elevated input power.

Overall, both motors demonstrate predominantly linear impedance characteristics. However, the 300 W motor displays greater sensitivity to source-level variations in the resonance region, likely due to its inherently higher impedance and reduced energy dissipation capacity. Conversely, the 45 kW motor maintains consistent impedance characteristics across varying excitation levels, enhancing repeatability and reliability.

Finally, rotor-position influence on the impedance was evaluated by conducting measurements at angular positions from 0° to 20° in increments of 2.5° (Figure 11). Across the entire frequency range, |Z| and ∠Z spectra remain indistinguishable, exhibiting no meaningful variations in resonance frequency, peak magnitude, or high-frequency slopes. These findings indicate that under standstill and no-load conditions, the motor impedance is primarily governed by stator construction and winding parasitic properties, rendering rotor position variability negligible. Thus, explicit rotor position modeling in the equivalent circuit framework is unnecessary.

5. Dummy Load Definition

As shown in Figure 12, a simplified dummy load was defined to replicate the impedance behavior observed in the tested motors. The model consists of lumped R, L, and C elements and is intended to reproduce the main resonance peak and asymptotic behavior in low- and mid-frequency regions in an approximate but meaningful way.

To determine the parameters of this model, key values were extracted from the measured impedance data discussed in Section 4. The DC resistance was determined by applying a current source and measuring the DC gain across the motor terminals. The high-frequency resistance (R_ω) was defined as the maximum value of the impedance magnitude observed in the frequency response. As shown in Figure 13, measurements at 100 Hz and 1 kHz were used to estimate inductance, and their average value was used for the model.

Based on the assumption of a second-order structure, the capacitance was then calculated using Formula (1), the dominant resonance frequency:

$$\mathrm{C}={\displaystyle \frac{1}{\mathrm{L}{\omega }_0^2+{\mathrm{R}}^2/\mathrm{L}}}$$

(1)

The parasitic capacitances were lumped into a single effective C in the dummy load model to include the effects of parasitic capacitive coupling, multiple contributions, such as inter-winding, winding-to-frame, and inter-phase capacitances (e.g., C₁, C₄, C₇, C₁₀ to C₁₄). This simplification enables a compact second-order model while retaining the key resonance features observed in the measurements.

Table 2. Extracted R, L, and C values for 300 W and 45 kW motors.

Configuration	${\mathit{R}}_{\mathit{\omega }}\left[\mathsf{\Omega }\right]$	C [pF]	L [mH]	${\mathit{R}}_{\mathit{DC}}\left[\mathsf{\Omega }\right]$	${\mathit{f}}_0\left[\mathbf{kHz}\right]$
300 W—U1U2	95.3 k	233	286	240	19.60
45 kW—U1U2	1295	258	3.10	0.080	178
300 W—U1–Y	74.7 k	284	286	240	17.65
45 kW—U1–Y	708	830	3.14	0.080	98.40

summarizes the resulting R, L, and C values for both the 300 W and 45 kW motors.

To validate the defined dummy load model, frequency–domain simulations were conducted using the extracted RLC parameters from Table 2. The simulated impedance magnitude and phase were compared to the corresponding measured responses. As shown in Figure 14, the 300 W motor in the U1–U2 configuration exhibits the first resonance around 19.6 kHz. The simulation closely reproduces both the magnitude and phase profiles, including the steep resonance peak and the transition into capacitive behavior at higher frequencies.

Similarly, Figure 15 presents the comparison for the same motor in the U1–Y configuration. Here too, the second-order model captures the main impedance characteristics, with in the low-to-mid frequency range.

The results for the 45 kW motor are presented in Figure 16 and Figure 17. In the U1–U2 case (Figure 16), the simulated resonance at approximately 178 kHz matches the measured peak position and amplitude.

The overall trend in both |Z| and ∠Z is followed well up to around 200 kHz. For the U1–Y configuration (Figure 17), the model tracks the impedance behavior over a wide frequency range, with small deviations at very low and bigger deviations at high frequencies are attributed to higher-order dynamics not included in the simplified RLC structure.

These results confirm that the defined dummy load model offers a valid approximation of the measured impedance response in both motor sizes and wiring configurations. The second-order representation captures the essential frequency-dependent behavior of the system and can be confidently used in simulation-based evaluations where real motor behavior needs to be emulated by an analyzable and compact circuit equivalent.

6. Conclusions and Future Aspects

This study focused on analyzing the low-signal impedance behavior of electric motors used in automotive applications. This research aimed to address modeling to a detailed evaluation in the low-to-mid frequency range, which is more representative of many operational scenarios in electric vehicles. By doing so, it provides a foundation for more modeling of motor behavior under low-excitation conditions, which is essential for improving EMI prediction, fault diagnosis, and system-level simulation in automotive drive systems.

In this work, a comprehensive experimental analysis was carried out on two asynchronous induction motors with different power ratings (300 W and 45 kW). Measurements were conducted across multiple configurations, including open and star-connected windings, varying source amplitudes, and rotor positions. The impedance responses were analyzed to identify resonance behavior, low-frequency trends, and configuration-specific patterns. These datasets were then used to parameterize a simplified second-order ECM based on measured RLC characteristics, as a dummy load, enabling a practical and repeatable method for simulating motor behavior without needing internal motor details.

The results demonstrated clear differences between motor sizes in terms of impedance amplitude, resonance frequency, and capacitive transition behavior. The 300 W motor showed a resonance at approximately 19.6 kHz, while the 45 kW machine exhibited a higher resonance frequency around 178 kHz due to lower inductance and capacitance values. Furthermore, winding topology had a significant impact, with open-ended configurations exhibiting stronger resonance peaks compared to star connections. Rotor position and source-level variation, although less dominant, were also found to subtly affect the impedance curves, particularly in the vicinity of resonance frequencies.

At the core of this research was the development of a simplified dummy load model. The dummy load was simulated based on extracted RLC parameters from impedance measurements. The measurement-to-simulation comparison confirmed the ECM’s validity within the mid- and low-frequency range.

It serves as a practical surrogate for real motors in system-level simulations or EMI testing setups. This approach enables engineers to replicate the key electrical behavior of motors without needing access to internal specifications or conducting costly and repetitive experiments. The simplicity of the dummy load allows integration into SPICE simulations or controller design workflows, accelerating development cycles in automotive applications.

While this study establishes a foundation for low-signal impedance analysis, several areas warrant further investigation. An essential next step is the experimental validation of the dummy load model through physical implementation and testing under dynamic conditions. By constructing a state–space circuit that reflects frequency-dependent RLC parameters, future studies can benchmark simulation results against real-time measurements more precisely. Additionally, extending the impedance analysis to synchronous machines—particularly permanent magnet synchronous motors (PMSMs)—would be valuable, as their distinct magnetic structures lead to different EMI behavior. A comparative study between asynchronous and synchronous machines could guide model refinement and control optimization.

Another promising direction lies in temperature-dependent impedance analysis. By incorporating thermal sensors into the measurement setup, future work could analyze how impedance varies with heat, leading to thermally robust design strategies. Overall, the combination of dynamic simulation, high-frequency extension, thermal modeling, and experimental hardware realization will significantly enhance the accuracy and applicability of dummy load models in the evolving field of electromobility.