This is a page for short code blocks that I personally think are nice.

More code is on my Github.

Work in progress! Check back in the future.

Check if an electric power system is radial

A power system is "radial" if there are no loops in the circuit.

If we call \(L\) and \(U\) the lower and upper off-diagonal components the network admittance matrix \(Y \in \mathbb{C}^{n \times n}\), then the network is not radial if

\[ \sum_{i} \sum_j L_{ij} \geq n,\\ \text{where} \ (i,j) \in \{(i,j): L_{ij} \neq 0 \}, \]

or alternatively,

\[ \sum_i \sum_j U_{ij} \geq n,\\ \text{where} \ (i,j) \in \{(i,j): U_{ij} \neq 0 \}. \]

This function tells you if a PowerModels.jl network model is radial or not.

using LinearAlgebra

Given a network's admittance matrix Y, determine if that network is radial.
In other words, determine if there are no electrical loops.
    Y: NxN Network admittance matrix
function is_radial(Y::AbstractMatrix)
    n = size(Y)[1]

    #Upper and lower off-diagonal elements
    U(A::AbstractMatrix) = [A[i] for i in CartesianIndices(A) if i[1]>i[2]]
    L(A::AbstractMatrix) = [A[i] for i in CartesianIndices(A) if i[1]<i[2]]
    #Get the nonzero upper and lower off diagonal elements
    nz_upper = [1 for y_ij in U(Y) if y_ij != 0]
    nz_lower = [1 for y_ij in L(Y) if y_ij != 0]
    return !(sum(nz_upper)>n-1 || sum(nz_lower) >n-1)

#EXAMPLE: case4_dist admittance matrix
Y = [133.333-266.667im -66.6667+133.333im 0.0+0.0im -65.0407+130.081im;
    -66.6667+133.333im 133.333-266.667im -66.6667+133.333im 0.0+0.0im;
    0.0+0.0im -66.6667+133.333im  66.6667-133.333im  0.0+0.0im;
    -65.0407+130.081im 0.0+0.0im 0.0+0.0im 63.4543-126.909im]


Thanks Prof. Grijalva for explaining this concept to me.

CC BY-SA 4.0 Samuel Talkington. Last modified: May 05, 2022. Website built with Franklin.jl and the Julia programming language.