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Add branch power calculation explanation in docs #815

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17 changes: 17 additions & 0 deletions docs/user_manual/calculations.md
Original file line number Diff line number Diff line change
Expand Up @@ -125,6 +125,23 @@ Output:
- Node voltage magnitude and angle
- Current flowing through branches and fault.

#### Common calculations

Power flowing through a branch is calculated by voltage and current for any type of calculations in the following way:

$$
\begin{eqnarray}
\underline{S_{branch-side}} = \sqrt{3} \cdot \underline{U_{LL-side-node}} \cdot \underline{I_{branch-side}}
\end{eqnarray}
$$

These quantities are in complex form. Hence, they can be constructed by PGM output attributes in the following way:

* For $\underline{U}$ of nodes, `u` is the magnitude and `u_angle` is the angle. Also the line to neutral voltage can be converted into line to line voltage by $ U_{LN} = U_{LL} / \sqrt{3}$. Check [Node Steady State Output](components.md#steady-state-output) to find out which quantity is relevant in your calculation.

* For $\underline{I}$ of branches, `i_side` is the magnitude. Its angle can be found from `p_side` and `q_side` by: $\arctan(\frac{P_{side} + j \cdot Q_{side}}{\underline{U}})^{*}$.
The `side` here can be `from`, `to` for {hoverxreftooltip}`user_manual/components:Branch`es, `1`, `2`, `3` for {hoverxreftooltip}`user_manual/components:Branch3`s.

### Power flow algorithms

Two types of power flow algorithms are implemented in power-grid-model; iterative algorithms (Newton-Raphson / Iterative current) and linear algorithms (Linear / Linear current).
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