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Update eigenvalues documentation
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Signed-off-by: Georgii Tishenin <georgii.tishenin@eonerc.rwth-aachen.de>
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georgii-tishenin committed May 14, 2024
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14 changes: 12 additions & 2 deletions docs/hugo/content/en/docs/Overview/eigenvalues.md
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Expand Up @@ -20,7 +20,7 @@ where $\mathbf{S}$ is a sign matrix, $\mathbf{G}_{b}$ is a discretization matrix
The MNA power system conductance matrix $\mathbf{G}$ is available from power system MNA model. To prepare the rest of the matrices, each power system component needs to be stamped into $\mathbf{A}_{bn}$ and $\mathbf{A}_{nb}$, while dynamic components also need to be stamped into $\mathbf{S}$ and $\mathbf{G}_{b}$ matrices.


``eigenvalues`` $\mathbf{\lambda}$ of the time-continuous state-space model matrix $A$ can then be recovered from ``discreteEigenvalues`` $\mathbf{z}$. Assuming the Trapezoidal rule of discretization in EMT domain, the equation is:
``eigenvalues`` $\mathbf{\lambda}$ of the time-continuous state-space model matrix $A$ can then be calculated from ``discreteEigenvalues`` $\mathbf{z}$. Assuming the Trapezoidal rule of discretization in EMT domain, the equation is:

$$
\mathbf{\lambda}=\frac{2}{\Delta t} \frac{\mathbf{z} - 1}{\mathbf{z} + 1}
Expand All @@ -30,4 +30,14 @@ $$
## Implementation

The ``MNAEigenvalueExtractor`` class is a template class responsible for extracting eigenvalues.
The ``EigenvalueCompInterface`` and ``EigenvalueDynamicCompInterface`` are interfaces to be implemented by all components participating in eigenvalue extraction. These interfaces provide the signatures of the functions that are used to stamp a component into the matrices $\mathbf{A}_{bn}$, $\mathbf{A}_{nb}$, $\mathbf{S}$ and $\mathbf{G}_{b}$.
The ``EigenvalueCompInterface`` is interface to be implemented by all components participating in eigenvalue extraction. The ``EigenvalueDynamicCompInterface`` is interface to be implemented by all _dynamic_ components participating in eigenvalue extraction. These interfaces provide the signatures of the functions that are used to stamp a component into the matrices $\mathbf{A}_{bn}$, $\mathbf{A}_{nb}$, $\mathbf{S}$ and $\mathbf{G}_{b}$.

The table below provides an overview of the components, that support eigenvalue extraction in EMT and in DP domains:

| Component |Is dynamic?| EMT domain, Ph1 | DP domain, Ph1 |
| -------- |-------- | -------- | -------- |
| ``Resistor`` |&mdash;| &#x2714; | &#x2714; |
| ``Inductor`` |&#x2714;| &#x2714; | &#x2714; |
| ``Capacitor`` |&#x2714;| &#x2714; | &#x2714; |
| ``Switch`` |&mdash;| &mdash; | &#x2714; |
| ``VoltageSource`` |&mdash;| &#x2714; | &#x2714; |

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