State-Space Extraction

Discrete-time state-space model is extracted from the EMT MNA simulation model. The extracted model is assembled in the form:

where:

• $\mathbf{x}$ is the extraction-state vector,
• $\mathbf{x}_{\mathrm{MNA}}$ is the full MNA unknown vector,
• $\mathbf{Y}$ is the active MNA system matrix,
• $\mathbf{A}_{d,\mathrm{local}}$ contains local component state-transition contributions,
• $\mathbf{B}_{d,\mathrm{MNA}}$ maps MNA unknowns to the state update,
• $\mathbf{C}_{d,\mathrm{MNA}}$ maps extraction states to MNA current injections.

Eliminating the MNA unknown vector gives the global discrete-time state matrix

The resulting matrix $\mathbf{A}_{d}$ describes the homogeneous discrete-time dynamics of the EMT MNA simulation model at the current operating point and system-matrix configuration.

References

• J. A. Hollman and J. R. Marti, Step-by-step eigenvalue analysis with EMTP discrete-time solutions, IEEE Transactions on Power Systems, 2010. https://doi.org/10.1109/TPWRS.2009.2039810
• Y. Han, H. Sun, B. Huang, S. Qin, M. Mu, and Y. Yu, “Discrete-Time State-Space Construction Method for SSO Analysis of Renewable Power Generation Integrated AC/DC Hybrid System,” IEEE Transactions on Power Systems, 2022. https://doi.org/10.1109/TPWRS.2021.3115248