Power system examples

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Description

These first order systems are given in generalized state space form

$E\dot{x}(t)=Ax(t)+Bu(t),y(t)=Cx(t)+Du(t),E,A\in {\mathbb{ℝ}}^{n\times n},B\in {\mathbb{ℝ}}^{n\times m},C\in {\mathbb{ℝ}}^{p\times n},D\in {\mathbb{ℝ}}^{p\times m}$

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 systems served as benchmark examples for Dominant Pole based Modal Truncation and for a special adaption of Balanced Truncation for the index-1 DAE systems.

Data

The table below lists the charateristics of all power systems. The files can be downloadet at https://sites.google.com/site/rommes/software.

Name	$n$	$m$	$p$	Type
New England	66	1	1	ODE
BIPS/97	13251	1	1	DAE
BIPS/1997	13250	1	1	DAE
BIPS/2007	21476	1	1	DAE
BIPS/97,MIMO8	13309	8	8	DAE
BIPS/97,MIMO28	13251	28	28	DAE
BIPS/97,MIMO46	13250	46	46	DAE
Juba5723	40337	2	1	DAE
Bauru5727	40366	2	2	DAE
zeros_nopss	13296	46	46	DAE
xingo6u	20738	1	6	DAE
nopss	11685	1	1	DAE
bips98_606	7135	4	4	DAE
bips98_1142	9735	4	4	DAE
bips98_1450	11305	4	4	DAE
bips07_1693	13275	4	4	DAE
bips07_1998	15066	4	4	DAE
bips07_2476	16861	4	4	DAE
bips07_3078	21128	4	4	DAE
PI Sections 20-80				ODE

References

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