Add figure for spatial clustering methods

openego · Mar 15, 2024 · 667be36 · 667be36
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diff --git a/doc/images/complexity_spatial.png b/doc/images/complexity_spatial.png
diff --git a/doc/theoretical_background.rst b/doc/theoretical_background.rst
@@ -53,12 +53,18 @@ The data model is characterised by a high spatial (about 8,000 electrical and 60
 Reduction in Spatial Dimension:
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-The **ehv clustering** maps all electrical nodes with a voltage level below the extra-high voltage level to their nearest neighboring node in the extra-high voltage level with the Dijkstra’s algorithm (110 kV —> 220 / 380 kV).
+The **ehv clustering** maps all electrical nodes with a voltage level below the extra-high voltage level to their nearest neighboring node in the extra-high voltage level with the Dijkstra’s algorithm (110 kV —> 220 kV / 380 kV).
 
 The **k-means Clustering** reduces the electrical or gas network to an adjustable number of nodes by considering the geographical position of the respective nodes. This method has been implemented within PyPSA by [Hoersch]_.
 
 The **k-medoids Dijkstra Clustering** aggregates nodes considering the network topology. First, a k-medoids Clustering is used dividing the original nodes of the network into groups by their geographical positions while identifiying the geographical medoid nodes per cluster. Afterwards, the original nodes in the original network are assigned to the former identified medoids considering the original network’s topology applying a Dijkstra’s algorithm considering the line lengths. Afterall, the original nodes are represented by one aggregated node per cluster at the position of the former identified medoid node.
 
+The procedures of the two methods are depicted in the following figure [Esterl2024]_:
+
+.. figure:: images/complexity_spatial.png
+   :align: center
+   :width: 800
+
 In general, the clustering of the **sector-coupled system** is divided into two steps:
 First, the electrical and gas grid are clustered independently using one of the methods described above. Afterwards, nodes of the other sectors (hydrogen, heat, e-mobility and DSM nodes) are mapped according to their connection to electricity or gas buses and aggregated to one node per carrier.