Synchronous Machine Stator Impedance Characterization

Accurate modeling of electrical machine impedances is crucial for designing control systems, fault diagnosis, and performance optimization in power generation and industrial drives. Our Frequency Domain Identification Toolbox enables precise impedance characterization across wide frequency ranges with minimal experimental effort.

The Challenge

In this case study, we needed to identify the stator impedance transfer function of a synchronous electrical machine by:

Capturing dynamics across an extremely wide frequency range (10 mHz to 240 Hz)
Determining an appropriate model structure with physical interpretability
Maintaining high accuracy with minimal model complexity
Converting identified parameters to physically meaningful circuit elements

Measurement Setup

The experimental setup utilized a standstill frequency response measurement approach, with the rotor mechanically fixed in position. Current excitation was applied to the stator windings (input), and voltage was measured across the same windings (output). The setup specifically measured the d-axis characteristics of the machine.

Solution Approach

Using our Frequency Domain Identification Toolbox, we implemented a strategic multi-band excitation approach:

1.) Multi-band Excitation Strategy: We applied three different multisine signals:

- - - - Low-frequency band: 10 mHz to 990 mHz
        Medium-frequency band: 1 Hz to 99 Hz
        High-frequency band: 20 Hz to 240 Hz

This approach covered more than 4 decades of frequency range without requiring extremely long time records.

2.) Model Structure Selection: Because of the basically inductive nature of the impedance, it is reasonable to choose the numerator order higher than that of the denominator. E.g. models of orders 1/0, 2/1 and 3/2 can be tried in ELiS. A 1/0 system would correspond to a physically reasonable serial R-L model, the 2/1 one includes a further serial R-L branch, in parallel with the inductance, while the 3/2 model includes a second R-L branch, in parallel with the main inductance again. The physical parameters can be directly calculated from the parameters of the identified system.

3.) Model Refinement: Starting with a 2/1 model that showed good overall fit, we incrementally increased the order to 3/2 to improve low-frequency accuracy.

Results

The final 3/2 model provided excellent fitting across the entire frequency range:

- - Significantly better cost function (6676) compared to the 2/1 model (29010)
  - Lower mean model error (0.1467 vs 0.3222)
  - Improved Akaike criterion (7207 vs 30660)
  - Better visual match across all frequency bands, particularly at low frequencies

Conclusion

This case study demonstrates how our Frequency Domain Identification Toolbox efficiently handles challenging identification problems spanning multiple frequency decades. The combination of strategic excitation design and flexible model selection enables users to obtain physically interpretable models that accurately represent complex electrical machine dynamics. The identified parameters can be directly converted to physically meaningful circuit elements, making this approach invaluable for electric machine analysis and control system design.