Power system examples

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Description

These first order systems are given in generalized state space form

$E\dot{x}(t)=Ax(t)+Bu(t),y(t)=Cx(t)+Du(t).(1)$

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

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

where $n_f$ denotes the number of finite eigenvalues in $\mathrm{\Lambda }(A,E)$ 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.

References

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