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Document EMT line parameter models#459

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Document EMT line parameter models#459
lukelowry wants to merge 1 commit into
lukel/fd-line-devfrom
lukel/line-params-docs

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@lukelowry lukelowry commented Jun 21, 2026

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Description

The line parameters of transmission lines can also be modeled as a model in our framework, using $\omega$ instead of $t$ as the independent variable:

$$ 0=F(\omega, y, y') $$

Details to come.

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Further comments

Diagram of the models and how they compound and depend on each other

image

The Gamma model ($\gamma$) is the one that took the most design effort, allowing us to obtain the frequency-dependent modal domain values of $\alpha$ and $\beta$ using an eigenvalue-tracking DAE! We will need a small-matrix eigensolver since the matrix version of $\gamma$ is $\mathbf{\Gamma}\in\mathbb{C}^N\times N$ and in general $\mathbf{\Gamma}\neq\mathbf{\Gamma}^\dagger$. The eigenvalues and eigenvectors only need to be computed once at some initial $\omega_0$, and then the model tracks them as $\omega$ advances.

@lukelowry lukelowry added the documentation Improvements or additions to documentation label Jun 21, 2026
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