Power system examples

1 Description

These first order systems are given in generalized state space form

$E\dot{x}(t)=A x(t)+B u(t), \quad y(t)=Cx(t)+Du(t).\qquad (1)$

and originated at CEPEL for simulating large power systems.

They come in different sizes and variants, including both SISO and MIMO systems having regular or singular $E$ matrices. In the latter case the DAEs are of index 1 and using simple row and column permutations, $E,A$ can be brought into the form

$E=\left[ \begin{array}{cc}I_{n_f}&0\\0&0\end{array}\right],\quad A=\left[ \begin{array}{cc}A_{11}&A_{12}\\A_{21}&A_{22}\end{array}\right],$

where $n_f$ denotes the number of finite eigenvalues in $\Lambda(A,E)$ and $A_{22}\in\mathbb{R}^{n-n_f\times n-n_f}$ is regular. A complete overview over these systems can be found in table below. The power system served as benchmark examples for Dominant Pole based Modal Truncation and for a special adaption of Balanced Truncation for the DAE systems.

3 References

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4 Contact

Joost Rommes User:kuerschner