Private Functions

haversine{T<:Real}(c1::Tuple{T,T}, c2::Tuple{T,T})

Compute distance between two pairs of latitude and longitude using the haversine formula.

haversine(b1::Bus, b2::Bus)

Compute distance between two buses from their latitude and longitude using the haversine formula.

subs_dist(inds1, inds2, buses, b_dist)

Compute distance between two substations using equation 1 from the REFERENCE.

REFERENCE: Birchfield, Adam B., et al. "Grid Structural Characteristics as Validation Criteria for Synthetic Networks." IEEE Transactions on Power Systems (2016).

twst!(grid, k)

Execute Tunable Weight Spannning Tree algorithm for the grid using weight 'k'.

REFERENCE: Soltan, Saleh, and Gil Zussman. "Generation of synthetic spatially embedded power grid networks." arXiv:1508.04447 [cs.SY], Aug. 2015.

reinforce!(grid, m, a, b, g, t, N)

Execute the Reinforcement procedure to increase robustness of a grid.

Arguments:

• m: total number of connections

• a, b, g, t: paramaters of the model (see REFERENCE)

• N: number of nearest neighbors in the average distance computation

REFERENCE: Soltan, Saleh, and Gil Zussman. "Generation of synthetic spatially embedded power grid networks." arXiv:1508.04447 [cs.SY], Aug. 2015.

connect_buses!(grid)

Create reference links between buses that are connected according to the connectivity matrix of the grid.

connect_subs!(grid)

Determine which substations are connected to each other through their buses.

cluster_loads!(grid,nload)

Execute aglomerative clustering of all load buses into 'nload' substations using geographic distances as metric.

fill_gen!(sub, gens, MW)

Group generators ('gens') into substations ('subs') by geographic proximity until generation threshold 'MW' is reached.

cluster_load_gen!(grid, nboth)

Create 'nboth' substations with both load and generation, chosen randomly.

cluster_gens!(grid, ngen)

Execute aglomerative clustering of generators into 'ngen' substations.

laplacian(con_mat::AbstractMatrix{<:Real})

Return the Laplacian matrix for a graph defined by adjacency matrix con_mat.

dijkstra(con_mat::AbstractMatrix{<:Real}, v1)

Compute minimum distances to each node in the network with connectivity matrix con_mat, starting from node v1, using Dijkstra's algorithm.

floyd_warshall(weights::AbstractMatrix{<:Real})

Compute minimum distances to each node in the network using Floyd-Warshall's algorithm. Here we assume that the weigths matrix is symmetric.

linear_imped(a::Bus, b::Bus)

Return an impedance value for a transmission line connecting buses a and b, using a simple linear approximation. This value is loosely based on the two references below. Values based on resistances for dc currents at 50C and 350kV lines.

REF 1: Electric Power Research Institute (EPRI). Transmission Line Reference Book, 345 kV and Above. Palo Alto, CA: The Institute, 1975. REF 2: J. Glover, M. Sarma and T. Overbye, Power System Analysis and Design. Stamford, CT: Cengage Learning, 2012.

rand_imped(a::Bus, b::Bus)

Return an impedance value for a transmission line connecting buses a and b, using a simple linear approximation with a randomly chosen coefficient. The range we adopted is based on the values for ACSR cables from the ref: J. Glover, M. Sarma and T. Overbye, Power System Analysis and Design. Stanford, CT: Cengage Learning, 2012.

volt_cap(a::Bus, b::Bus)

Return a current carrying capacity value for a transmission line connecting buses a and b based on their operating voltages. This value is loosely based on the reference: Electric Power Research Institute (EPRI). Transmission Line Reference Book, 345 kV and Above. Palo Alto, CA: The Institute, 1975.