Merge branch 'main' into feature/links-part-3

Author: figueroa1395

.github/workflows/build-test-release.yml

@@ -322,7 +322,7 @@ jobs:
         run: echo "${{ steps.tag.outputs.tag }}"
 
       - name: Create GitHub release
-        uses: softprops/action-gh-release@v2
+        uses: softprops/action-gh-release@v3
         if: (inputs.create_release)
         with:
           files: |

docs/algorithms/pf-algorithms.md

@@ -15,18 +15,14 @@ For a summary and guidance on choosing the right algorithm, see
 The nodal equations of a power system network can be written as:
 
 $$
-    \begin{eqnarray}
-        I_N    & = Y_{bus}U_N
-    \end{eqnarray}
+I_N = Y_{bus}U_N
 $$
 
 Where $I_N$ is the $N$ vector of source currents injected into each bus and $U_N$ is the $N$ vector of bus voltages.
 The complex power delivered to bus $k$ is:
 
 $$
-    \begin{eqnarray}
-        S_{k}    & =  P_k + jQ_k & = U_{k} I_{k}^{*}
-    \end{eqnarray}
+S_{k} = P_k + jQ_k = U_{k} I_{k}^{*}
 $$
 
 Power flow equations are based on solving the nodal equations above to obtain the voltage magnitude and voltage angle at
@@ -47,9 +43,7 @@ This is the traditional method for power flow calculations.
 This method uses a Taylor series, ignoring the higher order terms, to solve the nonlinear set of equations iteratively:
 
 $$
-    \begin{eqnarray}
-        f(x)    & =  y
-    \end{eqnarray}
+f(x) =  y
 $$
 
 Where:
@@ -101,19 +95,17 @@ As can be seen in the equations above $\delta_1$ and $V_1$ are omitted, because
 In each iteration $i$ the following equation is solved:
 
 $$
-    \begin{eqnarray}
-        J(i) \Delta x(i)    & =  \Delta y(i)
-    \end{eqnarray}
+J(i) \Delta x(i) =  \Delta y(i)
 $$
 
 Where
 
 $$
-    \begin{eqnarray}
-        \Delta x(i)    & =  x(i+1) - x(i)
-        \quad\text{and}\quad
-        \Delta y(i)    & =  y - f(x(i))
-    \end{eqnarray}
+\begin{aligned}
+    \Delta x(i)    & =  x(i+1) - x(i)
+    \quad\text{and}\quad
+    \Delta y(i)    & =  y - f(x(i))
+\end{aligned}
 $$
 
 $J$ is the [Jacobian](https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant), a matrix with all partial

docs/algorithms/sc-algorithms.md

@@ -14,7 +14,9 @@ For a summary and guidance, see [Calculations](../user_manual/calculations.md#sh
 In the short circuit calculation, the following equations are solved with border conditions of faults added as
 constraints.
 
-$$ \begin{eqnarray} I_N & = Y_{bus}U_N \end{eqnarray} $$
+$$
+I_N = Y_{bus}U_N
+$$
 
 This gives the initial symmetrical short circuit current ($I_k^{\prime\prime}$) for a fault.
 This quantity is then used to derive almost all further calculations of short circuit studies applications.

docs/algorithms/se-algorithms.md

@@ -32,9 +32,7 @@ The goal of WLS state estimation is to evaluate the state variable with the high
 measurement input, by solving:
 
 $$
-  \begin{eqnarray}
-    \min r(\underline{U}) = \dfrac{1}{2} (f(\underline{U}) - \underline{z})^H W (f(\underline{U}) - \underline{z})
-  \end{eqnarray}
+\min r(\underline{U}) = \dfrac{1}{2} (f(\underline{U}) - \underline{z})^H W (f(\underline{U}) - \underline{z})
 $$
 
 Where:
@@ -82,23 +80,21 @@ For example, there can be multiple voltage sensors on the same bus.
 The measurement data can be merged into one virtual measurement using a Kalman filter:
 
 $$
-    \begin{eqnarray}
-            z = \dfrac{\sum_{k=1}^{N_{sensor}} z_k \sigma_k^{-2}}{\sum_{k=1}^{N_{sensor}} \sigma_k^{-2}}
-    \end{eqnarray}
+z = \dfrac{\sum_{k=1}^{N_{sensor}} z_k \sigma_k^{-2}}{\sum_{k=1}^{N_{sensor}} \sigma_k^{-2}}
 $$
 
 Where $z_k$ and $\sigma_k$ are the measured value and standard deviation of individual measurements.
 
 Multiple appliance measurements (power measurements) on one bus are aggregated as the total injection at the bus:
 
 $$
-    \begin{eqnarray}
-            \underline{S} = \sum_{k=1}^{N_{appliance}} \underline{S}_k
-            \quad\text{and}\quad
-            \sigma_P^2 = \sum_{k=1}^{N_{appliance}} \sigma_{P,k}^2
-            \quad\text{and}\quad
-            \sigma_Q^2 = \sum_{k=1}^{N_{appliance}} \sigma_{Q,k}^2
-    \end{eqnarray}
+\begin{aligned}
+    \underline{S} = \sum_{k=1}^{N_{appliance}} \underline{S}_k
+    \quad\text{and}\quad
+    \sigma_P^2 = \sum_{k=1}^{N_{appliance}} \sigma_{P,k}^2
+    \quad\text{and}\quad
+    \sigma_Q^2 = \sum_{k=1}^{N_{appliance}} \sigma_{Q,k}^2
+\end{aligned}
 $$
 
 Where $S_k$ and $\sigma_{P,k}$ and $\sigma_{Q,k}$ are the measured value and the standard deviation of the individual
@@ -150,26 +146,14 @@ The following illustrates how this works for `sym_current_sensor`s in symmetric
 See also [the full mathematical workout](https://github.com/PowerGridModel/power-grid-model/issues/547).
 
 $$
-   \begin{eqnarray}
-        & \mathrm{Re}\left\{I\right\} = I \cos\theta
-   \end{eqnarray}
-$$
-$$
-   \begin{eqnarray}
-        & \mathrm{Im}\left\{I\right\} = I \sin\theta
-   \end{eqnarray}
-$$
-$$
-   \begin{eqnarray}
-        & \text{Var}\left(\mathrm{Re}\left\{I\right\}\right) =
-            \sigma_i^2 \cos^2\theta + I^2 \sigma_{\theta}^2\sin^2\theta
-   \end{eqnarray}
-$$
-$$
-   \begin{eqnarray}
-        & \text{Var}\left(\mathrm{Im}\left\{I\right\}\right) =
-            \sigma_i^2 \sin^2\theta + I^2 \sigma_{\theta}^2\cos^2\theta
-   \end{eqnarray}
+\begin{aligned}
+    & \mathrm{Re}\left\{I\right\} = I \cos\theta \\
+    & \mathrm{Im}\left\{I\right\} = I \sin\theta \\
+    & \text{Var}\left(\mathrm{Re}\left\{I\right\}\right) =
+        \sigma_i^2 \cos^2\theta + I^2 \sigma_{\theta}^2\sin^2\theta \\
+    & \text{Var}\left(\mathrm{Im}\left\{I\right\}\right) =
+        \sigma_i^2 \sin^2\theta + I^2 \sigma_{\theta}^2\cos^2\theta
+\end{aligned}
 $$
 
 ## Iterative linear state estimation
@@ -188,9 +172,7 @@ Therefore, traditional measurements are linearized prior to running the algorith
   $\theta_i$ is the intrinsic transformer phase shift:
 
 $$
-    \begin{eqnarray}
-            \underline{U}_i = U_i \cdot e^{j \theta_i}
-    \end{eqnarray}
+\underline{U}_i = U_i \cdot e^{j \theta_i}
 $$
 
 - Branch current with global angle: The global angle current measurement captures the phase offset relative to the same
@@ -201,9 +183,7 @@ $$
   angle).
 
 $$
-    \begin{eqnarray}
-            \underline{I} = I_i \cdot e^{j \theta_i}
-    \end{eqnarray}
+\underline{I} = I_i \cdot e^{j \theta_i}
 $$
 
 - Branch current with local angle: Sometimes, (accurate) voltage measurements are not available for a branch, which
@@ -217,10 +197,8 @@ $$
   Given the measured (linearized) voltage phasor, the current phasor is calculated as follows:
 
 $$
-    \begin{equation}
-        \underline{I} = \underline{I}_{\text{local}}^{*} \frac{\underline{U}}{|\underline{U}|}
-        = \underline{I}_{\text{local}}^{*} \cdot e^{j \theta}
-    \end{equation}
+\underline{I} = \underline{I}_{\text{local}}^{*} \frac{\underline{U}}{|\underline{U}|}
+    = \underline{I}_{\text{local}}^{*} \cdot e^{j \theta}
 $$
 
 where $\underline{U}$ is either measured voltage magnitude at the bus or assumed unity magnitude, with the intrinsic
@@ -232,19 +210,15 @@ $\theta$ is the phase angle of the voltage.
   Given the measured (linearized) voltage phasor, the current phasor is calculated as follows:
 
 $$
-    \begin{eqnarray}
-            \underline{I} = (\underline{S}/\underline{U})^*
-    \end{eqnarray}
+\underline{I} = (\underline{S}/\underline{U})^*
 $$
 
 - Bus power injection: Similar as above, to translate the power flow to a complex current phasor, if the bus voltage is
   not measured, the nominal voltage with zero angle will be used as an estimation.
   The current phasor is calculated as follows:
 
 $$
-    \begin{eqnarray}
-            \underline{I} = (\underline{S}/\underline{U})^*
-    \end{eqnarray}
+\underline{I} = (\underline{S}/\underline{U})^*
 $$
 
 The aggregated apparent power flow is considered as a single measurement, with variance

docs/user_manual/calculations.md

@@ -85,17 +85,13 @@ Due to the relative nature of `u_angle` (relevant only in systems with at least
 conditions should be met:
 
 $$
-    \begin{eqnarray}
-        n_{measurements}    & >= & n_{unknowns}
-    \end{eqnarray}
+n_{measurements} >= n_{unknowns}
 $$
 
 Where
 
 $$
-    \begin{eqnarray}
-        n_{unknowns}    & = & 2 & \cdot & n_{nodes} - 1
-    \end{eqnarray}
+n_{unknowns} = 2 \cdot n_{nodes} - 1
 $$
 
 The number of measurements can be found by taking the sum of the following:
@@ -201,9 +197,7 @@ Output:
 Power flowing through a branch is calculated by voltage and current for any type of calculations in the following way:
 
 $$
-    \begin{eqnarray}
-        \underline{S_{branch-side}} = \sqrt{3} \cdot \underline{U_{LL-side-node}} \cdot \underline{I_{branch-side}}
-    \end{eqnarray}
+\underline{S_{branch-side}} = \sqrt{3} \cdot \underline{U_{LL-side-node}} \cdot \underline{I_{branch-side}}^*
 $$
 
 These quantities are in complex form.