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dcp.jl
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dcp.jl
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export
DCPPowerModel, StandardDCPForm,
DCPLLPowerModel, StandardDCPLLForm
""
@compat abstract type AbstractDCPForm <: AbstractPowerFormulation end
""
@compat abstract type StandardDCPForm <: AbstractDCPForm end
""
const DCPPowerModel = GenericPowerModel{StandardDCPForm}
"default DC constructor"
DCPPowerModel(data::Dict{String,Any}; kwargs...) =
GenericPowerModel(data, StandardDCPForm; kwargs...)
""
variable_voltage{T <: AbstractDCPForm}(pm::GenericPowerModel{T}; kwargs...) =
variable_phase_angle(pm; kwargs...)
""
variable_voltage_ne{T <: AbstractDCPForm}(pm::GenericPowerModel{T}; kwargs...) = nothing
""
function variable_generation{T <: AbstractDCPForm}(pm::GenericPowerModel{T}; kwargs...)
variable_active_generation(pm; kwargs...)
# omit reactive variables
end
""
function variable_line_flow{T <: AbstractDCPForm}(pm::GenericPowerModel{T}; kwargs...)
variable_active_line_flow(pm; kwargs...)
# omit reactive variables
end
""
function variable_line_flow_ne{T <: AbstractDCPForm}(pm::GenericPowerModel{T}; kwargs...)
# do nothing, this model does not have reactive variables
variable_active_line_flow_ne(pm; kwargs...)
end
""
function variable_active_line_flow{T <: StandardDCPForm}(pm::GenericPowerModel{T}; bounded = true)
if bounded
@variable(pm.model, -pm.ref[:branch][l]["rate_a"] <= p[(l,i,j) in pm.ref[:arcs_from]] <= pm.ref[:branch][l]["rate_a"], start = getstart(pm.ref[:branch], l, "p_start"))
else
@variable(pm.model, p[(l,i,j) in pm.ref[:arcs_from]], start = getstart(pm.ref[:branch], l, "p_start"))
end
p_expr = Dict([((l,i,j), 1.0*p[(l,i,j)]) for (l,i,j) in pm.ref[:arcs_from]])
p_expr = merge(p_expr, Dict([((l,j,i), -1.0*p[(l,i,j)]) for (l,i,j) in pm.ref[:arcs_from]]))
pm.model.ext[:p_expr] = p_expr
end
""
function variable_active_line_flow_ne{T <: StandardDCPForm}(pm::GenericPowerModel{T})
@variable(pm.model, -pm.ref[:ne_branch][l]["rate_a"] <= p_ne[(l,i,j) in pm.ref[:ne_arcs_from]] <= pm.ref[:ne_branch][l]["rate_a"], start = getstart(pm.ref[:ne_branch], l, "p_start"))
p_ne_expr = Dict([((l,i,j), 1.0*p_ne[(l,i,j)]) for (l,i,j) in pm.ref[:ne_arcs_from]])
p_ne_expr = merge(p_ne_expr, Dict([((l,j,i), -1.0*p_ne[(l,i,j)]) for (l,i,j) in pm.ref[:ne_arcs_from]]))
pm.model.ext[:p_ne_expr] = p_ne_expr
end
"do nothing, this model does not have complex voltage variables"
constraint_voltage{T <: AbstractDCPForm}(pm::GenericPowerModel{T}) = nothing
"do nothing, this model does not have complex voltage variables"
constraint_voltage_ne{T <: AbstractDCPForm}(pm::GenericPowerModel{T}) = nothing
""
constraint_theta_ref{T <: AbstractDCPForm}(pm::GenericPowerModel{T}, ref_bus) =
Set([@constraint(pm.model, getvariable(pm.model, :t)[ref_bus] == 0)])
"do nothing, this model does not have voltage variables"
constraint_voltage_magnitude_setpoint{T <: AbstractDCPForm}(pm::GenericPowerModel{T}, i, vm, epsilon) = Set()
"do nothing, this model does not have reactive variables"
constraint_reactive_gen_setpoint{T <: AbstractDCPForm}(pm::GenericPowerModel{T}, i, qg) = Set()
""
function constraint_kcl_shunt{T <: AbstractDCPForm}(pm::GenericPowerModel{T}, i, bus_arcs, bus_gens, pd, qd, gs, bs)
pg = getvariable(pm.model, :pg)
p_expr = pm.model.ext[:p_expr]
c = @constraint(pm.model, sum(p_expr[a] for a in bus_arcs) == sum(pg[g] for g in bus_gens) - pd - gs*1.0^2)
# omit reactive constraint
return Set([c])
end
""
function constraint_kcl_shunt_ne{T <: AbstractDCPForm}(pm::GenericPowerModel{T}, i, bus_arcs, bus_arcs_ne, bus_gens, pd, qd, gs, bs)
pg = getvariable(pm.model, :pg)
p_expr = pm.model.ext[:p_expr]
p_ne_expr = pm.model.ext[:p_ne_expr]
c = @constraint(pm.model, sum(p_expr[a] for a in bus_arcs) + sum(p_ne_expr[a] for a in bus_arcs_ne) == sum(pg[g] for g in bus_gens) - pd - gs*1.0^2)
return Set([c])
end
"""
Creates Ohms constraints (yt post fix indicates that Y and T values are in rectangular form)
```
p[f_idx] == -b*(t[f_bus] - t[t_bus])
```
"""
function constraint_ohms_yt_from{T <: AbstractDCPForm}(pm::GenericPowerModel{T}, f_bus, t_bus, f_idx, t_idx, g, b, c, tr, ti, tm)
p_fr = getvariable(pm.model, :p)[f_idx]
t_fr = getvariable(pm.model, :t)[f_bus]
t_to = getvariable(pm.model, :t)[t_bus]
c = @constraint(pm.model, p_fr == -b*(t_fr - t_to))
# omit reactive constraint
return Set([c])
end
"Do nothing, this model is symmetric"
constraint_ohms_yt_to{T <: AbstractDCPForm}(pm::GenericPowerModel{T}, f_bus, t_bus, f_idx, t_idx, g, b, c, tr, ti, tm) = Set()
function constraint_ohms_yt_from_ne{T <: AbstractDCPForm}(pm::GenericPowerModel{T}, i, f_bus, t_bus, f_idx, t_idx, g, b, c, tr, ti, tm, t_min, t_max)
p_fr = getvariable(pm.model, :p_ne)[f_idx]
t_fr = getvariable(pm.model, :t)[f_bus]
t_to = getvariable(pm.model, :t)[t_bus]
z = getvariable(pm.model, :line_ne)[i]
c1 = @constraint(pm.model, p_fr <= -b*(t_fr - t_to + t_max*(1-z)) )
c2 = @constraint(pm.model, p_fr >= -b*(t_fr - t_to + t_min*(1-z)) )
return Set([c1, c2])
end
"Do nothing, this model is symmetric"
constraint_ohms_yt_to_ne{T <: AbstractDCPForm}(pm::GenericPowerModel{T}, i, f_bus, t_bus, f_idx, t_idx, g, b, c, tr, ti, tm, t_min, t_max) = Set()
"`angmin <= t[f_bus] - t[t_bus] <= angmax`"
function constraint_phase_angle_difference{T <: AbstractDCPForm}(pm::GenericPowerModel{T}, f_bus, t_bus, angmin, angmax)
t_fr = getvariable(pm.model, :t)[f_bus]
t_to = getvariable(pm.model, :t)[t_bus]
c1 = @constraint(pm.model, t_fr - t_to <= angmax)
c2 = @constraint(pm.model, t_fr - t_to >= angmin)
return Set([c1, c2])
end
"`-rate_a <= p[f_idx] <= rate_a`"
function constraint_thermal_limit_from{T <: AbstractDCPForm}(pm::GenericPowerModel{T}, f_idx, rate_a)
p_fr = getvariable(pm.model, :p)[f_idx]
if getlowerbound(p_fr) < -rate_a
setlowerbound(p_fr, -rate_a)
end
if getupperbound(p_fr) > rate_a
setupperbound(p_fr, rate_a)
end
return Set()
end
"Do nothing, this model is symmetric"
constraint_thermal_limit_to{T <: AbstractDCPForm}(pm::GenericPowerModel{T}, t_idx, rate_a) = Set()
""
function add_bus_voltage_setpoint{T <: AbstractDCPForm}(sol, pm::GenericPowerModel{T})
add_setpoint(sol, pm, "bus", "bus_i", "vm", :v; default_value = (item) -> 1)
add_setpoint(sol, pm, "bus", "bus_i", "va", :t)
end
""
function add_branch_flow_setpoint{T <: AbstractDCPForm}(sol, pm::GenericPowerModel{T})
# check the line flows were requested
if haskey(pm.setting, "output") && haskey(pm.setting["output"], "line_flows") && pm.setting["output"]["line_flows"] == true
mva_base = pm.data["baseMVA"]
add_setpoint(sol, pm, "branch", "index", "p_from", :p; scale = (x,item) -> x*mva_base, extract_var = (var,idx,item) -> var[(idx, item["f_bus"], item["t_bus"])])
add_setpoint(sol, pm, "branch", "index", "q_from", :q; scale = (x,item) -> x*mva_base, extract_var = (var,idx,item) -> var[(idx, item["f_bus"], item["t_bus"])])
add_setpoint(sol, pm, "branch", "index", "p_to", :p; scale = (x,item) -> -x*mva_base, extract_var = (var,idx,item) -> var[(idx, item["f_bus"], item["t_bus"])])
add_setpoint(sol, pm, "branch", "index", "q_to", :q; scale = (x,item) -> -x*mva_base, extract_var = (var,idx,item) -> var[(idx, item["f_bus"], item["t_bus"])])
end
end
""
variable_voltage_on_off{T <: AbstractDCPForm}(pm::GenericPowerModel{T}; kwargs...) = variable_phase_angle(pm; kwargs...)
"do nothing, this model does not have complex voltage variables"
constraint_voltage_on_off{T <: AbstractDCPForm}(pm::GenericPowerModel{T}) = nothing
"`-b*(t[f_bus] - t[t_bus] + t_min*(1-line_z[i])) <= p[f_idx] <= -b*(t[f_bus] - t[t_bus] + t_max*(1-line_z[i]))`"
function constraint_ohms_yt_from_on_off{T <: AbstractDCPForm}(pm::GenericPowerModel{T}, i, f_bus, t_bus, f_idx, t_idx, g, b, c, tr, ti, tm, t_min, t_max)
p_fr = getvariable(pm.model, :p)[f_idx]
t_fr = getvariable(pm.model, :t)[f_bus]
t_to = getvariable(pm.model, :t)[t_bus]
z = getvariable(pm.model, :line_z)[i]
c1 = @constraint(pm.model, p_fr <= -b*(t_fr - t_to + t_max*(1-z)) )
c2 = @constraint(pm.model, p_fr >= -b*(t_fr - t_to + t_min*(1-z)) )
return Set([c1, c2])
end
"Do nothing, this model is symmetric"
constraint_ohms_yt_to_on_off{T <: AbstractDCPForm}(pm::GenericPowerModel{T}, i, f_bus, t_bus, f_idx, t_idx, g, b, c, tr, ti, tm, t_min, t_max) = Set()
"""
Generic on/off thermal limit constraint
```
-rate_a*line_z[i] <= p[f_idx] <= rate_a*line_z[i]
```
"""
function constraint_thermal_limit_from_on_off{T <: AbstractDCPForm}(pm::GenericPowerModel{T}, i, f_idx, rate_a)
p_fr = getvariable(pm.model, :p)[f_idx]
z = getvariable(pm.model, :line_z)[i]
c1 = @constraint(pm.model, p_fr <= rate_a*z)
c2 = @constraint(pm.model, p_fr >= -rate_a*z)
return Set([c1, c2])
end
"""
Generic on/off thermal limit constraint
```
-rate_a*line_ne[i] <= p_ne[f_idx] <= rate_a*line_ne[i]
```
"""
function constraint_thermal_limit_from_ne{T <: AbstractDCPForm}(pm::GenericPowerModel{T}, i, f_idx, rate_a)
p_fr = getvariable(pm.model, :p_ne)[f_idx]
z = getvariable(pm.model, :line_ne)[i]
c1 = @constraint(pm.model, p_fr <= rate_a*z)
c2 = @constraint(pm.model, p_fr >= -rate_a*z)
return Set([c1, c2])
end
"nothing to do, from handles both sides"
constraint_thermal_limit_to_on_off{T <: AbstractDCPForm}(pm::GenericPowerModel{T}, i, t_idx, rate_a) = Set()
"nothing to do, from handles both sides"
constraint_thermal_limit_to_ne{T <: AbstractDCPForm}(pm::GenericPowerModel{T}, i, t_idx, rate_a) = Set()
"`angmin*line_z[i] + t_min*(1-line_z[i]) <= t[f_bus] - t[t_bus] <= angmax*line_z[i] + t_max*(1-line_z[i])`"
function constraint_phase_angle_difference_on_off{T <: AbstractDCPForm}(pm::GenericPowerModel{T}, i, f_bus, t_bus, angmin, angmax, t_min, t_max)
t_fr = getvariable(pm.model, :t)[f_bus]
t_to = getvariable(pm.model, :t)[t_bus]
z = getvariable(pm.model, :line_z)[i]
c1 = @constraint(pm.model, t_fr - t_to <= angmax*z + t_max*(1-z))
c2 = @constraint(pm.model, t_fr - t_to >= angmin*z + t_min*(1-z))
return Set([c1, c2])
end
"`angmin*line_ne[i] + t_min*(1-line_ne[i]) <= t[f_bus] - t[t_bus] <= angmax*line_ne[i] + t_max*(1-line_ne[i])`"
function constraint_phase_angle_difference_ne{T <: AbstractDCPForm}(pm::GenericPowerModel{T}, i, f_bus, t_bus, angmin, angmax, t_min, t_max)
t_fr = getvariable(pm.model, :t)[f_bus]
t_to = getvariable(pm.model, :t)[t_bus]
z = getvariable(pm.model, :line_ne)[i]
c1 = @constraint(pm.model, t_fr - t_to <= angmax*z + t_max*(1-z))
c2 = @constraint(pm.model, t_fr - t_to >= angmin*z + t_min*(1-z))
return Set([c1, c2])
end
""
@compat abstract type AbstractDCPLLForm <: AbstractDCPForm end
""
@compat abstract type StandardDCPLLForm <: AbstractDCPLLForm end
""
const DCPLLPowerModel = GenericPowerModel{StandardDCPLLForm}
"default DC constructor"
DCPLLPowerModel(data::Dict{String,Any}; kwargs...) = GenericPowerModel(data, StandardDCPLLForm; kwargs...)
"`sum(p[a] for a in bus_arcs) == sum(pg[g] for g in bus_gens) - pd - gs*1.0^2`"
function constraint_kcl_shunt{T <: AbstractDCPLLForm}(pm::GenericPowerModel{T}, i, bus_arcs, bus_gens, pd, qd, gs, bs)
pg = getvariable(pm.model, :pg)
p = getvariable(pm.model, :p)
c = @constraint(pm.model, sum(p[a] for a in bus_arcs) == sum(pg[g] for g in bus_gens) - pd - gs*1.0^2)
return Set([c])
end
"`sum(p[a] for a in bus_arcs) + sum(p_ne[a] for a in bus_arcs_ne) == sum(pg[g] for g in bus_gens) - pd - gs*1.0^2`"
function constraint_kcl_shunt_ne{T <: AbstractDCPLLForm}(pm::GenericPowerModel{T}, i, bus_arcs, bus_arcs_ne, bus_gens, pd, qd, gs, bs)
p = getvariable(pm.model, :p)
p_ne = getvariable(pm.model, :p_ne)
pg = getvariable(pm.model, :pg)
c = @constraint(pm.model, sum(p[a] for a in bus_arcs) + sum(p_ne[a] for a in bus_arcs_ne) == sum(pg[g] for g in bus_gens) - pd - gs*1.0^2)
return Set([c])
end
"""
Creates Ohms constraints (yt post fix indicates that Y and T values are in rectangular form)
```
-b*(t[f_bus] - t[t_bus] + t_min*(1-line_z[i])) <= p[f_idx] <= -b*(t[f_bus] - t[t_bus] + t_max*(1-line_z[i]))
```
"""
function constraint_ohms_yt_from_on_off{T <: AbstractDCPLLForm}(pm::GenericPowerModel{T}, i, f_bus, t_bus, f_idx, t_idx, g, b, c, tr, ti, tm, t_min, t_max)
p_fr = getvariable(pm.model, :p)[f_idx]
p_to = getvariable(pm.model, :p)[t_idx]
t_fr = getvariable(pm.model, :t)[f_bus]
t_to = getvariable(pm.model, :t)[t_bus]
z = getvariable(pm.model, :line_z)[i]
c1 = @constraint(pm.model, p_fr <= -b*(t_fr - t_to + t_max*(1-z)) )
c2 = @constraint(pm.model, p_fr >= -b*(t_fr - t_to + t_min*(1-z)) )
return Set([c1, c2])
end
"""
Creates Ohms constraints (yt post fix indicates that Y and T values are in rectangular form)
```
p[f_idx] + p[t_idx] >= r*( (-b*(t[f_bus] - t[t_bus]))^2 - (-b*(t_m))^2*(1-line_z[i]) )
```
where `r = g/(g^2 + b^2)` and `t_m = max(|t_min|, |t_max|)`
"""
function constraint_ohms_yt_to_on_off{T <: AbstractDCPLLForm}(pm::GenericPowerModel{T}, i, f_bus, t_bus, f_idx, t_idx, g, b, c, tr, ti, tm, t_min, t_max)
p_fr = getvariable(pm.model, :p)[f_idx]
p_to = getvariable(pm.model, :p)[t_idx]
t_fr = getvariable(pm.model, :t)[f_bus]
t_to = getvariable(pm.model, :t)[t_bus]
z = getvariable(pm.model, :line_z)[i]
r = g/(g^2 + b^2)
t_m = max(abs(t_min),abs(t_max))
c = @constraint(pm.model, p_fr + p_to >= r*( (-b*(t_fr - t_to))^2 - (-b*(t_m))^2*(1-z) ) )
return Set([c])
end
"""
Creates Ohms constraints (yt post fix indicates that Y and T values are in rectangular form)
```
-b*(t[f_bus] - t[t_bus] + t_min*(1-line_ne[i])) <= p_ne[f_idx] <= -b*(t[f_bus] - t[t_bus] + t_max*(1-line_ne[i]))
```
"""
function constraint_ohms_yt_from_ne{T <: AbstractDCPLLForm}(pm::GenericPowerModel{T}, i, f_bus, t_bus, f_idx, t_idx, g, b, c, tr, ti, tm, t_min, t_max)
p_fr = getvariable(pm.model, :p_ne)[f_idx]
p_to = getvariable(pm.model, :p_ne)[t_idx]
t_fr = getvariable(pm.model, :t)[f_bus]
t_to = getvariable(pm.model, :t)[t_bus]
z = getvariable(pm.model, :line_ne)[i]
c1 = @constraint(pm.model, p_fr <= -b*(t_fr - t_to + t_max*(1-z)) )
c2 = @constraint(pm.model, p_fr >= -b*(t_fr - t_to + t_min*(1-z)) )
return Set([c1, c2])
end
"""
Creates Ohms constraints (yt post fix indicates that Y and T values are in rectangular form)
```
p_ne[f_idx] + p_ne[t_idx] >= r*( (-b*(t[f_bus] - t[t_bus]))^2 - (-b*(t_m))^2*(1-line_ne[i]) )
```
where `r = g/(g^2 + b^2)` and `t_m = max(|t_min|, |t_max|)`
"""
function constraint_ohms_yt_to_ne{T <: AbstractDCPLLForm}(pm::GenericPowerModel{T}, i, f_bus, t_bus, f_idx, t_idx, g, b, c, tr, ti, tm, t_min, t_max)
p_fr = getvariable(pm.model, :p_ne)[f_idx]
p_to = getvariable(pm.model, :p_ne)[t_idx]
t_fr = getvariable(pm.model, :t)[f_bus]
t_to = getvariable(pm.model, :t)[t_bus]
z = getvariable(pm.model, :line_ne)[i]
r = g/(g^2 + b^2)
t_m = max(abs(t_min),abs(t_max))
c = @constraint(pm.model, p_fr + p_to >= r*( (-b*(t_fr - t_to))^2 - (-b*(t_m))^2*(1-z) ) )
return Set([c])
end
"`-rate_a*line_z[i] <= p[t_idx] <= rate_a*line_z[i]`"
function constraint_thermal_limit_to_on_off{T <: AbstractDCPLLForm}(pm::GenericPowerModel{T}, i, t_idx, rate_a)
p_to = getvariable(pm.model, :p)[t_idx]
z = getvariable(pm.model, :line_z)[i]
c1 = @constraint(pm.model, p_to <= rate_a*z)
c2 = @constraint(pm.model, p_to >= -rate_a*z)
return Set([c1, c2])
end
"`-rate_a*line_ne[i] <= p_ne[t_idx] <= rate_a*line_ne[i]`"
function constraint_thermal_limit_to_ne{T <: AbstractDCPLLForm}(pm::GenericPowerModel{T}, i, t_idx, rate_a)
p_to = getvariable(pm.model, :p_ne)[t_idx]
z = getvariable(pm.model, :line_ne)[i]
c1 = @constraint(pm.model, p_to <= rate_a*z)
c2 = @constraint(pm.model, p_to >= -rate_a*z)
return Set([c1, c2])
end