Z-tool is a Python-based implementation for the frequendy-domain stability analysis of modern power systems.
The core functionalities are measurement/characterization of EMT models in the frequency domain and small-signal stability assessment.
The analysis relies on an existing system model in the EMT simulation software PSCAD and/or input frequency response data.
The following features are currently implemented and validated:
- Voltage perturbation-based admittance scan at several nodes, including converter-based systems and black-box components, via frequency_sweep
- Stability assessment via Generalized Nyquist Criteria applicable to standalone-stable MIMO systems
- Oscillation mode identification via closed-loop eigenvalue decomposition and bus participation factors, EVD
- Passivity assessment and small gain theorem application
- Sensitivity of the Nyquist loci with respect to the components’ admittance via loci_sensitivity
- Automated stability analysis building the system matrices and computing previous and more metrics via stability_analysis
- Frame conversion functions, e.g. from dq-frame to alpha/beta-frame and to positive/negative sequence
The flowchart below summarizes a common usage of the tool for stability studies, including frequency-domain system identification (frequency_sweep) and several stability analysis functions (stability):
Installation
To use the toolbox, the following pre-requisites are needed.
- Python 3.7 or higher together with
- PSCAD v5 or higher is recommended.
- Install the Z-tool via cmd
py -m pip install ztoolacdc or using the repository files. Similarly, cmd py -m pip install ztoolacdc --upgrade updates the package.
Usage
A generic usage of the package can be summarized in the following steps:
- Add the Z-tool PSCAD library to your PSCAD project
- Place the tool’s scan blocks at the target buses and name them uniquely
- Define the resulting connectivity of the scan blocks (only for multi-infeed analyses)
- Specify the basic simulation settings and frequency range for the study
- Run the frequency scan and small-signal stability analysis functions
Follow the example(s) described here for more guidance. More details on the approach and implemented functions can be found in the papers below and/or this webinar with the complementary slides. The GUI is currently under development.
Other features
- Transfer function scan via the frequency_sweep_TF function, see the example here
- Change of PSCAD component values for parametric studies, see the example here
- Rational fitting via least-squares optimization with the mode_estimation function, see the example here
- Alternative computation of participation factors, e.g. extended PFs via EVD
- Singular value (sigmas) computation for the sensitivity and complementary sensitivity functions with small_gain
- Exploit the symmetric properties of the system to reduce the scan time (optional)
- Base conversion for the analysis of systems with different voltage levels in stability_analysis
- Linear interpolation of the node and edge matrices for increased frequency resolution in stability_analysis
- PSCAD control arguments: disabling unnecessary outputs, clear temporary files, keep PSCAD open, retain certificate, etc.
- Previous snapshots can be re-used to speed-up simulations
- Snapshot simulation plots for a quick look into the initialization run
If you find the Z-tool useful in your work, we kindly request that you cite the following publications, which you can freely access here and here.
@INPROCEEDINGS{Cifuentes2024,
author={{Cifuentes Garcia}, Francisco Javier and Roose, Thomas and Sakinci, Özgür Can and Lee, Dongyeong and Dewangan, Lokesh and Avdiaj, Eros and Beerten, Jef},
booktitle={2024 IEEE PES Innovative Smart Grid Technologies Europe (ISGT EUROPE)},
title={Automated Frequency-Domain Small-Signal Stability Analysis of Electrical Energy Hubs},
year={2024},
pages={1-6},
doi={10.1109/ISGTEUROPE62998.2024.10863484}}
@article{Cifuentes2025,
author = {Francisco Javier {Cifuentes Garcia} and Jef Beerten},
title = {Z-Tool: Frequency-domain characterization of EMT models for small-signal stability analysis},
journal = {Electric Power Systems Research},
volume = {252},
pages = {112405},
year = {2026},
doi = {https://doi.org/10.1016/j.epsr.2025.112405}}
For queries about the package or related work please feel free to reach out to Fransciso Javier Cifuentes Garcia. You can find more open-source tools for power systems analysis in the etch website.
License
This is a free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. Z-tool is distributed in the hope that it will be useful, but without any warranty; without even the implied warranty of merchantability or fitness for a particular purpose. See the GNU General Public License for more details.
Contributors
- Francisco Javier Cifuentes Garcia: Main developer
- Thomas Roose: Initial stability analysis functions
- Jeroen Tant, Jan Kircheis, Eros Avdiaj and Özgür Can Sakinci: Validation and support
Future work
- Scans in split projects
- Switch between current and voltage perturbation
- Computation of stability margin
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