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43c68a3 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 | # UnitCommitment.jl: Optimization Package for Security-Constrained Unit Commitment
# Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
# Released under the modified BSD license. See COPYING.md for more details.
using SparseArrays, Base.Threads, LinearAlgebra, JuMP
"""
_injection_shift_factors(; buses, lines)
Returns a (B-1)xL matrix M, where B is the number of buses and L is the number
of transmission lines. For a given bus b and transmission line l, the entry
M[l.offset, b.offset] indicates the amount of power (in MW) that flows through
transmission line l when 1 MW of power is injected at b and withdrawn from the
slack bus (the bus that has offset zero).
"""
function _injection_shift_factors(;
buses::Array{Bus},
lines::Array{TransmissionLine},
)
susceptance = _susceptance_matrix(lines)
incidence = _reduced_incidence_matrix(buses = buses, lines = lines)
laplacian = transpose(incidence) * susceptance * incidence
isf = susceptance * incidence * inv(Array(laplacian))
return isf
end
"""
_reduced_incidence_matrix(; buses::Array{Bus}, lines::Array{TransmissionLine})
Returns the incidence matrix for the network, with the column corresponding to
the slack bus is removed. More precisely, returns a (B-1) x L matrix, where B
is the number of buses and L is the number of lines. For each row, there is a 1
element and a -1 element, indicating the source and target buses, respectively,
for that line.
"""
function _reduced_incidence_matrix(;
buses::Array{Bus},
lines::Array{TransmissionLine},
)
matrix = spzeros(Float64, length(lines), length(buses) - 1)
for line in lines
if line.source.offset > 0
matrix[line.offset, line.source.offset] = 1
end
if line.target.offset > 0
matrix[line.offset, line.target.offset] = -1
end
end
return matrix
end
"""
_susceptance_matrix(lines::Array{TransmissionLine})
Returns a LxL diagonal matrix, where each diagonal entry is the susceptance of
the corresponding transmission line.
"""
function _susceptance_matrix(lines::Array{TransmissionLine})
return Diagonal([l.susceptance for l in lines])
end
"""
_line_outage_factors(; buses, lines, isf)
Returns a LxL matrix containing the Line Outage Distribution Factors (LODFs)
for the given network. This matrix how does the pre-contingency flow change
when each individual transmission line is removed.
"""
function _line_outage_factors(;
buses::Array{Bus,1},
lines::Array{TransmissionLine,1},
isf::Array{Float64,2},
)::Array{Float64,2}
incidence = Array(_reduced_incidence_matrix(lines = lines, buses = buses))
lodf::Array{Float64,2} = isf * transpose(incidence)
_, n = size(lodf)
for i in 1:n
lodf[:, i] *= 1.0 / (1.0 - lodf[i, i])
lodf[i, i] = -1
end
return lodf
end
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