Electrical Partitioning#

Clusters nodes based on electrical distance computed from Power Transfer Distribution Factors (PTDF).

Required Attributes#

  • Nodes: ac_island (AC island identifier)

  • Edges: x (reactance)

Mathematical Background#

Electrical distance is based on how power flows through the network:

  1. Incidence Matrix (K): Describes network topology

  2. Susceptance Matrix (B): \(\mathbf{B} = \mathbf{K}_\mathrm{sba}^\top \cdot \text{diag}(\mathbf{b}) \cdot \mathbf{K}_\mathrm{sba}\)

  3. PTDF Matrix: \(\mathbf{PTDF} = \text{diag}(\mathrm{b}) \cdot \mathbf{K}_\mathrm{sba} \cdot \mathbf{B}^{-1}\)

  4. Electrical Distance: \(d_{ij} = ||\mathrm{PTDF}_{:,i} - \mathrm{PTDF}_{:,j}||_2\)

Nodes with similar PTDF columns have similar impact on power flows of lines.

Available Strategies#

Strategy

Algorithm

Description

electrical_kmeans

K-Means

Electrical clustering with arbitrary node as centroid

electrical_kmedoids

K-Medoids

Electrical clustering with existing node as centroid (e.g. Kron-Reduction)

Basic Usage#

partition = manager.partition(
    "electrical_kmeans",
    n_clusters=10
)

AC-Island Handling#

Electrical partitioning is always AC-island aware:

  • PTDF is computed independently for each AC island

  • Nodes in different islands have infinite distance

  • Each island is clustered separately

        flowchart TB
    subgraph Island0[AC Island 0]
        A[Cluster 0] --- B[Cluster 1]
    end

    subgraph Island1[AC Island 1]
        C[Cluster 2] --- D[Cluster 3]
    end

    Island0 -.->|DC Link| Island1

    style A fill:#2993B5,stroke:#1d6f8a,color:#fff
    style B fill:#2993B5,stroke:#1d6f8a,color:#fff
    style C fill:#0fad6b,stroke:#076b3f,color:#fff
    style D fill:#0fad6b,stroke:#076b3f,color:#fff

Configuration#

from npap.partitioning import ElectricalDistanceConfig

# Custom configuration
config = ElectricalDistanceConfig(
    zero_reactance_replacement=1e-5,  # Replace zero reactance
    regularization_factor=1e-10,       # Matrix regularization
    infinite_distance=1e4              # Inter-island distance
)

partition = manager.partition(
    "electrical_kmeans",
    n_clusters=10,
    config=config
)
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