Urban Power Grid Topology and Hierarchy Identification from Open Data
Shiliang Zhang, Sabita Maharjan, Alexey Vinel, Shui Yu
cs.LG
2026-06-19
UiO, KIT, and UTS use OSM and NVE data to link all 7,330 Alna buildings by road-constrained clustering and spanning trees, with pole ties of 475.9 km past a 464 km grid.
High-voltage lines usually show up on public maps. The last mile usually does not. It is the low-voltage run from transformers and poles to each building, and utilities keep it private for security and commercial reasons. Rooftop solar, EV charging, and cascading faults in microgrids all sit on that segment. Without the links, those studies use a made-up network.
Smart meters are the standard input for topology identification. KNN, Gaussian mixtures, LSTMs, and Lasso all need one reading per customer, and collection at district or city scale hits privacy limits. Open geospatial work already rebuilds the European high-voltage grid, traces distribution lines from roads and street-view imagery, and synthesizes national low-voltage networks. Those maps mostly stop at the primary grid or a single representative feeder. Poles and service drops are not placed in one voltage hierarchy.
Two public sources are fused. OpenStreetMap supplies building footprints, land use, the road graph, and some line geometry. Norway's NVE supplies substations, transformers, poles, and transmission and distribution geometries. The learning step is HDBSCAN, density clustering that does not ask for a cluster count in advance and that marks sparse points as outliers. Shortest paths and spanning trees do the rest. No neural net is trained on labeled topology.
High- and medium-voltage lines are grouped from low voltage to high. Candidate joints are road crossings and intersections. Dijkstra's algorithm, shortest paths on a weighted graph, picks the road-constrained link between neighboring voltage levels, and power is allowed to flow only downward. A transformer is attached only when its voltage matches. Meshes already in the source geometry stay. Every new edge is a shortest path along roads.
Poles often have no recorded conductor. Land use first separates residential areas from commercial and industrial ones, so a feeder is not drawn across unrelated neighborhoods. HDBSCAN then clusters poles inside each zone. The preferred link is the nearest pole on the same side of the road, tested by projecting both poles onto the nearest segment. If the test fails, the pole joins its nearest neighbor in the cluster. Outliers join the nearest pole anywhere. Overhead lines rarely cross a street without a reason, so same-side rank comes first.
Buildings are split and clustered the same way. Road distance is the weight for a minimum spanning tree inside each cluster: every building is linked, cycles are absent, and total length is minimal. Low-voltage feeders are usually operated radially, so a tree is closer to practice than an arbitrary set of edges. Buildings outside every cluster follow the road to the nearest clustered building in the zone. Each cluster makes one attachment, to the nearer of the nearest pole and the nearest low-voltage line, again along the road.
Alna, Oslo, covers about 13.68 million square meters, with 7,330 buildings, 2,787 poles, and 8 substations.
| Link | Voltage | Count | Length |
| Existing lines | 11–420 kV | 127 | about 464 km |
| Pole to pole | 11 kV | 187 | 161.6 km |
| Pole to primary grid | 11 kV | 170 | 475.9 km |
| Building to grid | 400 V | 704 | 248.2 km |
| Building to building | 230 V | 704 | 260.1 km |
Those 127 existing lines are 34 at 11 kV (121.6 km), 59 at 47 kV (63.5 km), 3 at 132 kV (20.4 km), 30 at 300 kV (166.9 km), and 1 at 420 kV (91.7 km). Pole-to-grid links alone total 475.9 km, longer than that whole skeleton.
Waiheke Island, New Zealand, covers about 93 million square meters, with 11,795 buildings, 2,512 poles, and one substation. Its poles are already tied to lines in OSM, so pole-to-pole inference is skipped. Existing lines are 28.3 km at 400 V (124 lines), 99.6 km at 11 kV (118), and 23.8 km at 33 kV (4). The new geometry is mostly 774 building-to-building lines at 230 V (297.9 km) and 537 building-to-grid lines at 400 V (56.2 km), plus one 54 m line at 11 kV into the only substation.
Building counts are the same order of magnitude, and so are the service-drop counts. The paper reads that as evidence the pipeline runs across different grid shapes. There is no hit rate against a real distribution map, and no error comparison with street-view mapping or synthetic low-voltage generators.
Without the utility's internal map, public poles can fix the skeleton and roads plus land use can draw the last mile, with each step inspectable in a GIS. A service edge points at an OSM building, so type and floor count are already attached, and rooftop PV or weather can be joined later. Power flow, cascading faults, and hosting capacity need that per-building node.
Demand is not estimated, and no power flow is solved. The digital twin stays future work. Alna already exceeds 7,000 load points, and the whole of Oslo would pass 80,000 buildings. The paper notes that real-time power flow at that size runs into computation first. Aggregation can shrink the model. The error aggregation adds is not measured.
The last mile has no ground truth. The paper states that a perfect reconstruction is impossible. The two cases show that the pipeline finishes and that the lines follow roads. They do not show that the links are correct. Labels of 230 V and 400 V are assigned by level in the hierarchy. On Waiheke, a crossing between voltage levels is treated as a transformer.
In Alna, 170 pole-to-grid links total 475.9 km, about 2.8 km each. That is long for an urban tap, and typical feeder length is not used as a filter. The building layer lists 704 links and, at the same time, says all 7,330 buildings are connected. If 704 counts tree edges, it cannot cover that many nodes. Merged line features are the more plausible reading. Node counts, connected components, HDBSCAN size settings, and parameter sensitivity are unreported, so the claim that every building is attached cannot be audited.
New edges are shortest paths. Meshes and normally open switches are mostly inherited from the input geometry. Cables that leave the road, and dedicated lines that cross a neighborhood, are systematically misplaced. A city that does not publish pole coordinates loses an entire layer. Waiheke is almost OSM alone. Alna also has NVE. The two cases are not the same data regime.