Injection shift factors for DC power flow. Accommodates both single slack and distributed slack (droop response).

isf.jl

"""
Calculate injection shift factor matrix.
Each row corresponds to a line in the network.
Each column corresponds to a node.
Credit to Jonathon Martin for derivation.

Inputs:
* `Y`: full admittance matrix
* `lines`: vector of tuples; each tuple encodes a line as (i,j)
* `ref`: index of angle reference bus
* `k`: vector of generator participation factors
"""
function isf(
    Y::AbstractArray,
    lines::Vector{Tuple{Int64,Int64}},
    ref::Int64,
    k=[NaN]::Vector{Float64}
    )

    Y = full(Y)
    n,l = (size(Y,1),length(lines))

    Bflow = zeros(l,n)
    for idx in 1:l
        i,j = lines[idx]
        Bflow[idx,i] =  Y[i,j]
        Bflow[idx,j] = -Y[i,j]
    end
    
    if length(k) != 1
        Y[:,ref] = k
        B = Y
        Bflow[:,ref] = zeros(l)
    else
        nonref = setdiff(1:n,ref)
        B = Y[nonref,nonref]
        Bflow = Bflow[:,nonref]
    end
    return Bflow/B
end