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acp.jl
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acp.jl
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### polar form of the non-convex AC equations
""
function variable_bus_voltage(pm::AbstractACPModel; kwargs...)
variable_bus_voltage_angle(pm; kwargs...)
variable_bus_voltage_magnitude(pm; kwargs...)
end
""
function sol_data_model!(pm::AbstractACPModel, solution::Dict)
# nothing to do, this is in the data model space by default
end
""
function variable_ne_branch_voltage(pm::AbstractACPModel; kwargs...)
end
"do nothing, this model does not have complex voltage constraints"
function constraint_ne_model_voltage(pm::AbstractACPModel; kwargs...)
end
"`v[i] == vm`"
function constraint_voltage_magnitude_setpoint(pm::AbstractACPModel, n::Int, i::Int, vm)
v = var(pm, n, :vm, i)
JuMP.@constraint(pm.model, v == vm)
end
function constraint_current_limit_from(pm::AbstractACPModel, n::Int, f_idx, c_rating_a)
l,i,j = f_idx
vm_fr = var(pm, n, :vm, i)
p_fr = var(pm, n, :p, f_idx)
q_fr = var(pm, n, :q, f_idx)
JuMP.@constraint(pm.model, p_fr^2 + q_fr^2 <= vm_fr^2*c_rating_a^2)
end
function constraint_current_limit_to(pm::AbstractACPModel, n::Int, t_idx, c_rating_a)
l,j,i = t_idx
vm_to = var(pm, n, :vm, j)
p_to = var(pm, n, :p, t_idx)
q_to = var(pm, n, :q, t_idx)
JuMP.@constraint(pm.model, p_to^2 + q_to^2 <= vm_to^2*c_rating_a^2)
end
""
function constraint_power_balance(pm::AbstractACPModel, n::Int, i::Int, bus_arcs, bus_arcs_dc, bus_arcs_sw, bus_gens, bus_storage, bus_pd, bus_qd, bus_gs, bus_bs)
vm = var(pm, n, :vm, i)
p = get(var(pm, n), :p, Dict()); _check_var_keys(p, bus_arcs, "active power", "branch")
q = get(var(pm, n), :q, Dict()); _check_var_keys(q, bus_arcs, "reactive power", "branch")
pg = get(var(pm, n), :pg, Dict()); _check_var_keys(pg, bus_gens, "active power", "generator")
qg = get(var(pm, n), :qg, Dict()); _check_var_keys(qg, bus_gens, "reactive power", "generator")
ps = get(var(pm, n), :ps, Dict()); _check_var_keys(ps, bus_storage, "active power", "storage")
qs = get(var(pm, n), :qs, Dict()); _check_var_keys(qs, bus_storage, "reactive power", "storage")
psw = get(var(pm, n), :psw, Dict()); _check_var_keys(psw, bus_arcs_sw, "active power", "switch")
qsw = get(var(pm, n), :qsw, Dict()); _check_var_keys(qsw, bus_arcs_sw, "reactive power", "switch")
p_dc = get(var(pm, n), :p_dc, Dict()); _check_var_keys(p_dc, bus_arcs_dc, "active power", "dcline")
q_dc = get(var(pm, n), :q_dc, Dict()); _check_var_keys(q_dc, bus_arcs_dc, "reactive power", "dcline")
cstr_p = JuMP.@constraint(pm.model,
sum(p[a] for a in bus_arcs)
+ sum(p_dc[a_dc] for a_dc in bus_arcs_dc)
+ sum(psw[a_sw] for a_sw in bus_arcs_sw)
==
sum(pg[g] for g in bus_gens)
- sum(ps[s] for s in bus_storage)
- sum(pd for (i,pd) in bus_pd)
- sum(gs for (i,gs) in bus_gs)*vm^2
)
cstr_q = JuMP.@constraint(pm.model,
sum(q[a] for a in bus_arcs)
+ sum(q_dc[a_dc] for a_dc in bus_arcs_dc)
+ sum(qsw[a_sw] for a_sw in bus_arcs_sw)
==
sum(qg[g] for g in bus_gens)
- sum(qs[s] for s in bus_storage)
- sum(qd for (i,qd) in bus_qd)
+ sum(bs for (i,bs) in bus_bs)*vm^2
)
if _IM.report_duals(pm)
sol(pm, n, :bus, i)[:lam_kcl_r] = cstr_p
sol(pm, n, :bus, i)[:lam_kcl_i] = cstr_q
end
end
""
function constraint_power_balance_ls(pm::AbstractACPModel, n::Int, i::Int, bus_arcs, bus_arcs_dc, bus_arcs_sw, bus_gens, bus_storage, bus_pd, bus_qd, bus_gs, bus_bs)
vm = var(pm, n, :vm, i)
p = get(var(pm, n), :p, Dict()); _check_var_keys(p, bus_arcs, "active power", "branch")
q = get(var(pm, n), :q, Dict()); _check_var_keys(q, bus_arcs, "reactive power", "branch")
pg = get(var(pm, n), :pg, Dict()); _check_var_keys(pg, bus_gens, "active power", "generator")
qg = get(var(pm, n), :qg, Dict()); _check_var_keys(qg, bus_gens, "reactive power", "generator")
ps = get(var(pm, n), :ps, Dict()); _check_var_keys(ps, bus_storage, "active power", "storage")
qs = get(var(pm, n), :qs, Dict()); _check_var_keys(qs, bus_storage, "reactive power", "storage")
psw = get(var(pm, n), :psw, Dict()); _check_var_keys(psw, bus_arcs_sw, "active power", "switch")
qsw = get(var(pm, n), :qsw, Dict()); _check_var_keys(qsw, bus_arcs_sw, "reactive power", "switch")
p_dc = get(var(pm, n), :p_dc, Dict()); _check_var_keys(p_dc, bus_arcs_dc, "active power", "dcline")
q_dc = get(var(pm, n), :q_dc, Dict()); _check_var_keys(q_dc, bus_arcs_dc, "reactive power", "dcline")
z_demand = get(var(pm, n), :z_demand, Dict()); _check_var_keys(z_demand, keys(bus_pd), "power factor", "load")
z_shunt = get(var(pm, n), :z_shunt, Dict()); _check_var_keys(z_shunt, keys(bus_gs), "power factor", "shunt")
cstr_p = JuMP.@constraint(pm.model,
sum(p[a] for a in bus_arcs)
+ sum(p_dc[a_dc] for a_dc in bus_arcs_dc)
+ sum(psw[a_sw] for a_sw in bus_arcs_sw)
==
sum(pg[g] for g in bus_gens)
- sum(ps[s] for s in bus_storage)
- sum(pd*z_demand[i] for (i,pd) in bus_pd)
- sum(gs*z_shunt[i] for (i,gs) in bus_gs)*vm^2
)
cstr_q = JuMP.@constraint(pm.model,
sum(q[a] for a in bus_arcs)
+ sum(q_dc[a_dc] for a_dc in bus_arcs_dc)
+ sum(qsw[a_sw] for a_sw in bus_arcs_sw)
==
sum(qg[g] for g in bus_gens)
- sum(qs[s] for s in bus_storage)
- sum(qd*z_demand[i] for (i,qd) in bus_qd)
+ sum(bs*z_shunt[i] for (i,bs) in bus_bs)*vm^2
)
if _IM.report_duals(pm)
sol(pm, n, :bus, i)[:lam_kcl_r] = cstr_p
sol(pm, n, :bus, i)[:lam_kcl_i] = cstr_q
end
end
""
function constraint_ne_power_balance(pm::AbstractACPModel, n::Int, i::Int, bus_arcs, bus_arcs_dc, bus_arcs_sw, bus_arcs_ne, bus_gens, bus_storage, bus_pd, bus_qd, bus_gs, bus_bs)
vm = var(pm, n, :vm, i)
p = get(var(pm, n), :p, Dict()); _check_var_keys(p, bus_arcs, "active power", "branch")
q = get(var(pm, n), :q, Dict()); _check_var_keys(q, bus_arcs, "reactive power", "branch")
pg = get(var(pm, n), :pg, Dict()); _check_var_keys(pg, bus_gens, "active power", "generator")
qg = get(var(pm, n), :qg, Dict()); _check_var_keys(qg, bus_gens, "reactive power", "generator")
ps = get(var(pm, n), :ps, Dict()); _check_var_keys(ps, bus_storage, "active power", "storage")
qs = get(var(pm, n), :qs, Dict()); _check_var_keys(qs, bus_storage, "reactive power", "storage")
psw = get(var(pm, n), :psw, Dict()); _check_var_keys(psw, bus_arcs_sw, "active power", "switch")
qsw = get(var(pm, n), :qsw, Dict()); _check_var_keys(qsw, bus_arcs_sw, "reactive power", "switch")
p_dc = get(var(pm, n), :p_dc, Dict()); _check_var_keys(p_dc, bus_arcs_dc, "active power", "dcline")
q_dc = get(var(pm, n), :q_dc, Dict()); _check_var_keys(q_dc, bus_arcs_dc, "reactive power", "dcline")
p_ne = get(var(pm, n), :p_ne, Dict()); _check_var_keys(p_ne, bus_arcs_ne, "active power", "ne_branch")
q_ne = get(var(pm, n), :q_ne, Dict()); _check_var_keys(q_ne, bus_arcs_ne, "reactive power", "ne_branch")
JuMP.@constraint(pm.model,
sum(p[a] for a in bus_arcs)
+ sum(p_dc[a_dc] for a_dc in bus_arcs_dc)
+ sum(psw[a_sw] for a_sw in bus_arcs_sw)
+ sum(p_ne[a] for a in bus_arcs_ne)
==
sum(pg[g] for g in bus_gens)
- sum(ps[s] for s in bus_storage)
- sum(pd for pd in values(bus_pd))
- sum(gs for gs in values(bus_gs))*vm^2
)
JuMP.@constraint(pm.model,
sum(q[a] for a in bus_arcs)
+ sum(q_dc[a_dc] for a_dc in bus_arcs_dc)
+ sum(qsw[a_sw] for a_sw in bus_arcs_sw)
+ sum(q_ne[a] for a in bus_arcs_ne)
==
sum(qg[g] for g in bus_gens)
- sum(qs[s] for s in bus_storage)
- sum(qd for qd in values(bus_qd))
+ sum(bs for bs in values(bus_bs))*vm^2
)
end
""
function expression_branch_power_ohms_yt_from(pm::AbstractACPModel, n::Int, f_bus, t_bus, f_idx, t_idx, g, b, g_fr, b_fr, tr, ti, tm)
vm_fr = var(pm, n, :vm, f_bus)
vm_to = var(pm, n, :vm, t_bus)
va_fr = var(pm, n, :va, f_bus)
va_to = var(pm, n, :va, t_bus)
var(pm, n, :p)[f_idx] = JuMP.@expression(pm.model, (g+g_fr)/tm^2*vm_fr^2 + (-g*tr+b*ti)/tm^2*(vm_fr*vm_to*cos(va_fr-va_to)) + (-b*tr-g*ti)/tm^2*(vm_fr*vm_to*sin(va_fr-va_to)) )
var(pm, n, :q)[f_idx] = JuMP.@expression(pm.model, -(b+b_fr)/tm^2*vm_fr^2 - (-b*tr-g*ti)/tm^2*(vm_fr*vm_to*cos(va_fr-va_to)) + (-g*tr+b*ti)/tm^2*(vm_fr*vm_to*sin(va_fr-va_to)) )
end
""
function expression_branch_power_ohms_yt_to(pm::AbstractACPModel, n::Int, f_bus, t_bus, f_idx, t_idx, g, b, g_to, b_to, tr, ti, tm)
vm_fr = var(pm, n, :vm, f_bus)
vm_to = var(pm, n, :vm, t_bus)
va_fr = var(pm, n, :va, f_bus)
va_to = var(pm, n, :va, t_bus)
var(pm, n, :p)[t_idx] = JuMP.@expression(pm.model, (g+g_to)*vm_to^2 + (-g*tr-b*ti)/tm^2*(vm_to*vm_fr*cos(va_to-va_fr)) + (-b*tr+g*ti)/tm^2*(vm_to*vm_fr*sin(va_to-va_fr)) )
var(pm, n, :q)[t_idx] = JuMP.@expression(pm.model, -(b+b_to)*vm_to^2 - (-b*tr+g*ti)/tm^2*(vm_to*vm_fr*cos(va_to-va_fr)) + (-g*tr-b*ti)/tm^2*(vm_to*vm_fr*sin(va_to-va_fr)) )
end
"""
Creates Ohms constraints (yt post fix indicates that Y and T values are in rectangular form)
```
p[f_idx] == (g+g_fr)/tm*v[f_bus]^2 + (-g*tr+b*ti)/tm^2*(v[f_bus]*v[t_bus]*cos(t[f_bus]-t[t_bus])) + (-b*tr-g*ti)/tm^2*(v[f_bus]*v[t_bus]*sin(t[f_bus]-t[t_bus]))
q[f_idx] == -(b+b_fr)/tm*v[f_bus]^2 - (-b*tr-g*ti)/tm^2*(v[f_bus]*v[t_bus]*cos(t[f_bus]-t[t_bus])) + (-g*tr+b*ti)/tm^2*(v[f_bus]*v[t_bus]*sin(t[f_bus]-t[t_bus]))
```
"""
function constraint_ohms_yt_from(pm::AbstractACPModel, n::Int, f_bus, t_bus, f_idx, t_idx, g, b, g_fr, b_fr, tr, ti, tm)
p_fr = var(pm, n, :p, f_idx)
q_fr = var(pm, n, :q, f_idx)
vm_fr = var(pm, n, :vm, f_bus)
vm_to = var(pm, n, :vm, t_bus)
va_fr = var(pm, n, :va, f_bus)
va_to = var(pm, n, :va, t_bus)
JuMP.@constraint(pm.model, p_fr == (g+g_fr)/tm^2*vm_fr^2 + (-g*tr+b*ti)/tm^2*(vm_fr*vm_to*cos(va_fr-va_to)) + (-b*tr-g*ti)/tm^2*(vm_fr*vm_to*sin(va_fr-va_to)) )
JuMP.@constraint(pm.model, q_fr == -(b+b_fr)/tm^2*vm_fr^2 - (-b*tr-g*ti)/tm^2*(vm_fr*vm_to*cos(va_fr-va_to)) + (-g*tr+b*ti)/tm^2*(vm_fr*vm_to*sin(va_fr-va_to)) )
end
"""
Creates Ohms constraints (yt post fix indicates that Y and T values are in rectangular form)
```
p[t_idx] == (g+g_to)*v[t_bus]^2 + (-g*tr-b*ti)/tm^2*(v[t_bus]*v[f_bus]*cos(t[t_bus]-t[f_bus])) + (-b*tr+g*ti)/tm^2*(v[t_bus]*v[f_bus]*sin(t[t_bus]-t[f_bus]))
q[t_idx] == -(b+b_to)*v[t_bus]^2 - (-b*tr+g*ti)/tm^2*(v[t_bus]*v[f_bus]*cos(t[f_bus]-t[t_bus])) + (-g*tr-b*ti)/tm^2*(v[t_bus]*v[f_bus]*sin(t[t_bus]-t[f_bus]))
```
"""
function constraint_ohms_yt_to(pm::AbstractACPModel, n::Int, f_bus, t_bus, f_idx, t_idx, g, b, g_to, b_to, tr, ti, tm)
p_to = var(pm, n, :p, t_idx)
q_to = var(pm, n, :q, t_idx)
vm_fr = var(pm, n, :vm, f_bus)
vm_to = var(pm, n, :vm, t_bus)
va_fr = var(pm, n, :va, f_bus)
va_to = var(pm, n, :va, t_bus)
JuMP.@constraint(pm.model, p_to == (g+g_to)*vm_to^2 + (-g*tr-b*ti)/tm^2*(vm_to*vm_fr*cos(va_to-va_fr)) + (-b*tr+g*ti)/tm^2*(vm_to*vm_fr*sin(va_to-va_fr)) )
JuMP.@constraint(pm.model, q_to == -(b+b_to)*vm_to^2 - (-b*tr+g*ti)/tm^2*(vm_to*vm_fr*cos(va_to-va_fr)) + (-g*tr-b*ti)/tm^2*(vm_to*vm_fr*sin(va_to-va_fr)) )
end
"""
Creates Ohms constraints for AC models (y post fix indicates that Y values are in rectangular form)
```
p[f_idx] == (g+g_fr)*(v[f_bus]/tr)^2 + -g*v[f_bus]/tr*v[t_bus]*cos(t[f_bus]-t[t_bus]-as) + -b*v[f_bus]/tr*v[t_bus]*sin(t[f_bus]-t[t_bus]-as)
q[f_idx] == -(b+b_fr)*(v[f_bus]/tr)^2 + b*v[f_bus]/tr*v[t_bus]*cos(t[f_bus]-t[t_bus]-as) + -g*v[f_bus]/tr*v[t_bus]*sin(t[f_bus]-t[t_bus]-as)
```
"""
function constraint_ohms_y_from(pm::AbstractACPModel, n::Int, f_bus, t_bus, f_idx, t_idx, g, b, g_fr, b_fr, tm, ta)
p_fr = var(pm, n, :p, f_idx)
q_fr = var(pm, n, :q, f_idx)
vm_fr = var(pm, n, :vm, f_bus)
vm_to = var(pm, n, :vm, t_bus)
va_fr = var(pm, n, :va, f_bus)
va_to = var(pm, n, :va, t_bus)
JuMP.@constraint(pm.model, p_fr == (g+g_fr)*(vm_fr/tm)^2 - g*vm_fr/tm*vm_to*cos(va_fr-va_to-ta) + -b*vm_fr/tm*vm_to*sin(va_fr-va_to-ta) )
JuMP.@constraint(pm.model, q_fr == -(b+b_fr)*(vm_fr/tm)^2 + b*vm_fr/tm*vm_to*cos(va_fr-va_to-ta) + -g*vm_fr/tm*vm_to*sin(va_fr-va_to-ta) )
end
"""
Creates Ohms constraints for AC models (y post fix indicates that Y values are in rectangular form)
```
p[t_idx] == (g+g_to)*v[t_bus]^2 + -g*v[t_bus]*v[f_bus]/tr*cos(t[t_bus]-t[f_bus]+as) + -b*v[t_bus]*v[f_bus]/tr*sin(t[t_bus]-t[f_bus]+as)
q[t_idx] == -(b+b_to)*v[t_bus]^2 + b*v[t_bus]*v[f_bus]/tr*cos(t[f_bus]-t[t_bus]+as) + -g*v[t_bus]*v[f_bus]/tr*sin(t[t_bus]-t[f_bus]+as)
```
"""
function constraint_ohms_y_to(pm::AbstractACPModel, n::Int, f_bus, t_bus, f_idx, t_idx, g, b, g_to, b_to, tm, ta)
p_to = var(pm, n, :p, t_idx)
q_to = var(pm, n, :q, t_idx)
vm_fr = var(pm, n, :vm, f_bus)
vm_to = var(pm, n, :vm, t_bus)
va_fr = var(pm, n, :va, f_bus)
va_to = var(pm, n, :va, t_bus)
JuMP.@constraint(pm.model, p_to == (g+g_to)*vm_to^2 - g*vm_to*vm_fr/tm*cos(va_to-va_fr+ta) + -b*vm_to*vm_fr/tm*sin(va_to-va_fr+ta) )
JuMP.@constraint(pm.model, q_to == -(b+b_to)*vm_to^2 + b*vm_to*vm_fr/tm*cos(va_to-va_fr+ta) + -g*vm_to*vm_fr/tm*sin(va_to-va_fr+ta) )
end
""
function constraint_switch_state_closed(pm::AbstractACPModel, n::Int, f_bus, t_bus)
vm_fr = var(pm, n, :vm, f_bus)
vm_to = var(pm, n, :vm, t_bus)
va_fr = var(pm, n, :va, f_bus)
va_to = var(pm, n, :va, t_bus)
JuMP.@constraint(pm.model, vm_fr == vm_to)
JuMP.@constraint(pm.model, va_fr == va_to)
end
""
function constraint_switch_voltage_on_off(pm::AbstractACPModel, n::Int, i, f_bus, t_bus, vad_min, vad_max)
vm_fr = var(pm, n, :vm, f_bus)
vm_to = var(pm, n, :vm, t_bus)
va_fr = var(pm, n, :va, f_bus)
va_to = var(pm, n, :va, t_bus)
z = var(pm, n, :z_switch, i)
JuMP.@constraint(pm.model, z*vm_fr == z*vm_to)
JuMP.@constraint(pm.model, z*va_fr == z*va_to)
end
""
function variable_bus_voltage_on_off(pm::AbstractACPModel; kwargs...)
variable_bus_voltage_angle(pm; kwargs...)
variable_bus_voltage_magnitude(pm; kwargs...)
end
"do nothing, this model does not have complex voltage constraints"
function constraint_model_voltage_on_off(pm::AbstractACPModel; kwargs...)
end
"""
```
p[f_idx] == z*(g/tm*v[f_bus]^2 + (-g*tr+b*ti)/tm^2*(v[f_bus]*v[t_bus]*cos(t[f_bus]-t[t_bus])) + (-b*tr-g*ti)/tm^2*(v[f_bus]*v[t_bus]*sin(t[f_bus]-t[t_bus])))
q[f_idx] == z*(-(b+c/2)/tm*v[f_bus]^2 - (-b*tr-g*ti)/tm^2*(v[f_bus]*v[t_bus]*cos(t[f_bus]-t[t_bus])) + (-g*tr+b*ti)/tm^2*(v[f_bus]*v[t_bus]*sin(t[f_bus]-t[t_bus])))
```
"""
function constraint_ohms_yt_from_on_off(pm::AbstractACPModel, n::Int, i, f_bus, t_bus, f_idx, t_idx, g, b, g_fr, b_fr, tr, ti, tm, vad_min, vad_max)
p_fr = var(pm, n, :p, f_idx)
q_fr = var(pm, n, :q, f_idx)
vm_fr = var(pm, n, :vm, f_bus)
vm_to = var(pm, n, :vm, t_bus)
va_fr = var(pm, n, :va, f_bus)
va_to = var(pm, n, :va, t_bus)
z = var(pm, n, :z_branch, i)
JuMP.@constraint(pm.model, p_fr == z*( (g+g_fr)/tm^2*vm_fr^2 + (-g*tr+b*ti)/tm^2*(vm_fr*vm_to*cos(va_fr-va_to)) + (-b*tr-g*ti)/tm^2*(vm_fr*vm_to*sin(va_fr-va_to))) )
JuMP.@constraint(pm.model, q_fr == z*(-(b+b_fr)/tm^2*vm_fr^2 - (-b*tr-g*ti)/tm^2*(vm_fr*vm_to*cos(va_fr-va_to)) + (-g*tr+b*ti)/tm^2*(vm_fr*vm_to*sin(va_fr-va_to))) )
end
"""
```
p[t_idx] == z*(g*v[t_bus]^2 + (-g*tr-b*ti)/tm^2*(v[t_bus]*v[f_bus]*cos(t[t_bus]-t[f_bus])) + (-b*tr+g*ti)/tm^2*(v[t_bus]*v[f_bus]*sin(t[t_bus]-t[f_bus])))
q[t_idx] == z*(-(b+c/2)*v[t_bus]^2 - (-b*tr+g*ti)/tm^2*(v[t_bus]*v[f_bus]*cos(t[f_bus]-t[t_bus])) + (-g*tr-b*ti)/tm^2*(v[t_bus]*v[f_bus]*sin(t[t_bus]-t[f_bus])))
```
"""
function constraint_ohms_yt_to_on_off(pm::AbstractACPModel, n::Int, i, f_bus, t_bus, f_idx, t_idx, g, b, g_to, b_to, tr, ti, tm, vad_min, vad_max)
p_to = var(pm, n, :p, t_idx)
q_to = var(pm, n, :q, t_idx)
vm_fr = var(pm, n, :vm, f_bus)
vm_to = var(pm, n, :vm, t_bus)
va_fr = var(pm, n, :va, f_bus)
va_to = var(pm, n, :va, t_bus)
z = var(pm, n, :z_branch, i)
JuMP.@constraint(pm.model, p_to == z*( (g+g_to)*vm_to^2 + (-g*tr-b*ti)/tm^2*(vm_to*vm_fr*cos(va_to-va_fr)) + (-b*tr+g*ti)/tm^2*(vm_to*vm_fr*sin(va_to-va_fr))) )
JuMP.@constraint(pm.model, q_to == z*(-(b+b_to)*vm_to^2 - (-b*tr+g*ti)/tm^2*(vm_to*vm_fr*cos(va_to-va_fr)) + (-g*tr-b*ti)/tm^2*(vm_to*vm_fr*sin(va_to-va_fr))) )
end
"""
```
p_ne[f_idx] == z*(g/tm*v[f_bus]^2 + (-g*tr+b*ti)/tm^2*(v[f_bus]*v[t_bus]*cos(t[f_bus]-t[t_bus])) + (-b*tr-g*ti)/tm^2*(v[f_bus]*v[t_bus]*sin(t[f_bus]-t[t_bus])))
q_ne[f_idx] == z*(-(b+c/2)/tm*v[f_bus]^2 - (-b*tr-g*ti)/tm^2*(v[f_bus]*v[t_bus]*cos(t[f_bus]-t[t_bus])) + (-g*tr+b*ti)/tm^2*(v[f_bus]*v[t_bus]*sin(t[f_bus]-t[t_bus])))
```
"""
function constraint_ne_ohms_yt_from(pm::AbstractACPModel, n::Int, i, f_bus, t_bus, f_idx, t_idx, g, b, g_fr, b_fr, tr, ti, tm, vad_min, vad_max)
p_fr = var(pm, n, :p_ne, f_idx)
q_fr = var(pm, n, :q_ne, f_idx)
vm_fr = var(pm, n, :vm, f_bus)
vm_to = var(pm, n, :vm, t_bus)
va_fr = var(pm, n, :va, f_bus)
va_to = var(pm, n, :va, t_bus)
z = var(pm, n, :branch_ne, i)
JuMP.@constraint(pm.model, p_fr == z*( (g+g_fr)/tm^2*vm_fr^2 + (-g*tr+b*ti)/tm^2*(vm_fr*vm_to*cos(va_fr-va_to)) + (-b*tr-g*ti)/tm^2*(vm_fr*vm_to*sin(va_fr-va_to))) )
JuMP.@constraint(pm.model, q_fr == z*(-(b+b_fr)/tm^2*vm_fr^2 - (-b*tr-g*ti)/tm^2*(vm_fr*vm_to*cos(va_fr-va_to)) + (-g*tr+b*ti)/tm^2*(vm_fr*vm_to*sin(va_fr-va_to))) )
end
"""
```
p_ne[t_idx] == z*(g*v[t_bus]^2 + (-g*tr-b*ti)/tm^2*(v[t_bus]*v[f_bus]*cos(t[t_bus]-t[f_bus])) + (-b*tr+g*ti)/tm^2*(v[t_bus]*v[f_bus]*sin(t[t_bus]-t[f_bus])))
q_ne[t_idx] == z*(-(b+c/2)*v[t_bus]^2 - (-b*tr+g*ti)/tm^2*(v[t_bus]*v[f_bus]*cos(t[f_bus]-t[t_bus])) + (-g*tr-b*ti)/tm^2*(v[t_bus]*v[f_bus]*sin(t[t_bus]-t[f_bus])))
```
"""
function constraint_ne_ohms_yt_to(pm::AbstractACPModel, n::Int, i, f_bus, t_bus, f_idx, t_idx, g, b, g_to, b_to, tr, ti, tm, vad_min, vad_max)
p_to = var(pm, n, :p_ne, t_idx)
q_to = var(pm, n, :q_ne, t_idx)
vm_fr = var(pm, n, :vm, f_bus)
vm_to = var(pm, n, :vm, t_bus)
va_fr = var(pm, n, :va, f_bus)
va_to = var(pm, n, :va, t_bus)
z = var(pm, n, :branch_ne, i)
JuMP.@constraint(pm.model, p_to == z*( (g+g_to)*vm_to^2 + (-g*tr-b*ti)/tm^2*(vm_to*vm_fr*cos(va_to-va_fr)) + (-b*tr+g*ti)/tm^2*(vm_to*vm_fr*sin(va_to-va_fr))) )
JuMP.@constraint(pm.model, q_to == z*(-(b+b_to)*vm_to^2 - (-b*tr+g*ti)/tm^2*(vm_to*vm_fr*cos(va_to-va_fr)) + (-g*tr-b*ti)/tm^2*(vm_to*vm_fr*sin(va_to-va_fr))) )
end
"""
Creates Ohms constraints with variables for complex transformation ratio (y post fix indicates Y is in rectangular form)
```
p[f_idx] == (g+g_fr)/tm*v[f_bus]^2 + (-g)/tm*(v[f_bus]*v[t_bus]*cos(t[f_bus]-t[t_bus]-ta)) + (-b)/tm*(v[f_bus]*v[t_bus]*sin(t[f_bus]-t[t_bus]-ta))
q[f_idx] == -(b+b_fr)/tm*v[f_bus]^2 - (-b)/tm*(v[f_bus]*v[t_bus]*cos(t[f_bus]-t[t_bus]-ta)) + (-g)/tm*(v[f_bus]*v[t_bus]*sin(t[f_bus]-t[t_bus]-ta))
```
"""
function constraint_ohms_y_oltc_pst_from(pm::AbstractACPModel, n::Int, f_bus, t_bus, f_idx, t_idx, g, b, g_fr, b_fr)
p_fr = var(pm, n, :p, f_idx)
q_fr = var(pm, n, :q, f_idx)
vm_fr = var(pm, n, :vm, f_bus)
vm_to = var(pm, n, :vm, t_bus)
va_fr = var(pm, n, :va, f_bus)
va_to = var(pm, n, :va, t_bus)
tm = var(pm, n, :tm, f_idx[1])
ta = var(pm, n, :ta, f_idx[1])
JuMP.@constraint(pm.model, p_fr == (g+g_fr)/tm^2*vm_fr^2 + (-g)/tm*(vm_fr*vm_to*cos(va_fr-va_to-ta)) + (-b)/tm*(vm_fr*vm_to*sin(va_fr-va_to-ta)) )
JuMP.@constraint(pm.model, q_fr == -(b+b_fr)/tm^2*vm_fr^2 - (-b)/tm*(vm_fr*vm_to*cos(va_fr-va_to-ta)) + (-g)/tm*(vm_fr*vm_to*sin(va_fr-va_to-ta)) )
end
"""
Creates Ohms constraints with variables for complex transformation ratio (y post fix indicates Y is in rectangular form)
```
p[t_idx] == (g+g_to)*v[t_bus]^2 + (-g)/tm*(v[t_bus]*v[f_bus]*cos(t[t_bus]-t[f_bus]+ta)) + (-b)/tm*(v[t_bus]*v[f_bus]*sin(t[t_bus]-t[f_bus]+ta))
q[t_idx] == -(b+b_to)*v[t_bus]^2 - (-b)/tm*(v[t_bus]*v[f_bus]*cos(t[f_bus]-t[t_bus]+ta)) + (-g)/tm*(v[t_bus]*v[f_bus]*sin(t[t_bus]-t[f_bus]+ta))
```
"""
function constraint_ohms_y_oltc_pst_to(pm::AbstractACPModel, n::Int, f_bus, t_bus, f_idx, t_idx, g, b, g_to, b_to)
p_to = var(pm, n, :p, t_idx)
q_to = var(pm, n, :q, t_idx)
vm_fr = var(pm, n, :vm, f_bus)
vm_to = var(pm, n, :vm, t_bus)
va_fr = var(pm, n, :va, f_bus)
va_to = var(pm, n, :va, t_bus)
tm = var(pm, n, :tm, f_idx[1])
ta = var(pm, n, :ta, f_idx[1])
JuMP.@constraint(pm.model, p_to == (g+g_to)*vm_to^2 + -g/tm*(vm_to*vm_fr*cos(va_to-va_fr+ta)) + -b/tm*(vm_to*vm_fr*sin(va_to-va_fr+ta)) )
JuMP.@constraint(pm.model, q_to == -(b+b_to)*vm_to^2 - -b/tm*(vm_to*vm_fr*cos(va_to-va_fr+ta)) + -g/tm*(vm_to*vm_fr*sin(va_to-va_fr+ta)) )
end
""
function constraint_ohms_y_pst_from(pm::AbstractACPModel, n::Int, f_bus, t_bus, f_idx, t_idx, g, b, g_fr, b_fr, tm)
p_fr = var(pm, n, :p, f_idx)
q_fr = var(pm, n, :q, f_idx)
vm_fr = var(pm, n, :vm, f_bus)
vm_to = var(pm, n, :vm, t_bus)
va_fr = var(pm, n, :va, f_bus)
va_to = var(pm, n, :va, t_bus)
ta = var(pm, n, :ta, f_idx[1])
JuMP.@constraint(pm.model, p_fr == (g+g_fr)/tm^2*vm_fr^2 + (-g)/tm*(vm_fr*vm_to*cos(va_fr-va_to-ta)) + (-b)/tm*(vm_fr*vm_to*sin(va_fr-va_to-ta)) )
JuMP.@constraint(pm.model, q_fr == -(b+b_fr)/tm^2*vm_fr^2 - (-b)/tm*(vm_fr*vm_to*cos(va_fr-va_to-ta)) + (-g)/tm*(vm_fr*vm_to*sin(va_fr-va_to-ta)) )
end
""
function constraint_ohms_y_pst_to(pm::AbstractACPModel, n::Int, f_bus, t_bus, f_idx, t_idx, g, b, g_to, b_to, tm)
p_to = var(pm, n, :p, t_idx)
q_to = var(pm, n, :q, t_idx)
vm_fr = var(pm, n, :vm, f_bus)
vm_to = var(pm, n, :vm, t_bus)
va_fr = var(pm, n, :va, f_bus)
va_to = var(pm, n, :va, t_bus)
ta = var(pm, n, :ta, f_idx[1])
JuMP.@constraint(pm.model, p_to == (g+g_to)*vm_to^2 + -g/tm*(vm_to*vm_fr*cos(va_to-va_fr+ta)) + -b/tm*(vm_to*vm_fr*sin(va_to-va_fr+ta)) )
JuMP.@constraint(pm.model, q_to == -(b+b_to)*vm_to^2 - -b/tm*(vm_to*vm_fr*cos(va_to-va_fr+ta)) + -g/tm*(vm_to*vm_fr*sin(va_to-va_fr+ta)) )
end
"`angmin <= z_branch[i]*(t[f_bus] - t[t_bus]) <= angmax`"
function constraint_voltage_angle_difference_on_off(pm::AbstractACPModel, n::Int, f_idx, angmin, angmax, vad_min, vad_max)
i, f_bus, t_bus = f_idx
va_fr = var(pm, n, :va, f_bus)
va_to = var(pm, n, :va, t_bus)
z = var(pm, n, :z_branch, i)
JuMP.@constraint(pm.model, z*(va_fr - va_to) <= z*angmax)
JuMP.@constraint(pm.model, z*(va_fr - va_to) >= z*angmin)
end
"`angmin <= branch_ne[i]*(t[f_bus] - t[t_bus]) <= angmax`"
function constraint_ne_voltage_angle_difference(pm::AbstractACPModel, n::Int, f_idx, angmin, angmax, vad_min, vad_max)
i, f_bus, t_bus = f_idx
va_fr = var(pm, n, :va, f_bus)
va_to = var(pm, n, :va, t_bus)
z = var(pm, n, :branch_ne, i)
JuMP.@constraint(pm.model, angmin <= z*(va_fr - va_to) <= angmax)
end
"""
```
p[f_idx] + p[t_idx] >= 0
q[f_idx] + q[t_idx] >= -c/2*(v[f_bus]^2/tr^2 + v[t_bus]^2)
```
"""
function constraint_power_losses_lb(pm::AbstractACPModel, n::Int, f_bus, t_bus, f_idx, t_idx, g_fr, b_fr, g_to, b_to, tr)
vm_fr = var(pm, n, :vm, f_bus)
vm_to = var(pm, n, :vm, t_bus)
p_fr = var(pm, n, :p, f_idx)
q_fr = var(pm, n, :q, f_idx)
p_to = var(pm, n, :p, t_idx)
q_to = var(pm, n, :q, t_idx)
@assert(g_fr == 0 && g_to == 0)
c = b_fr + b_to
# TODO: Derive updated constraint from first principles
JuMP.@constraint(m, p_fr + p_to >= 0)
JuMP.@constraint(m, q_fr + q_to >= -c/2*(vm_fr^2/tr^2 + vm_to^2))
end
""
function constraint_storage_current_limit(pm::AbstractACPModel, n::Int, i, bus, rating)
vm = var(pm, n, :vm, bus)
ps = var(pm, n, :ps, i)
qs = var(pm, n, :qs, i)
JuMP.@constraint(pm.model, ps^2 + qs^2 <= rating^2*vm^2)
end
""
function constraint_storage_losses(pm::AbstractACPModel, n::Int, i, bus, r, x, p_loss, q_loss)
vm = var(pm, n, :vm, bus)
ps = var(pm, n, :ps, i)
qs = var(pm, n, :qs, i)
sc = var(pm, n, :sc, i)
sd = var(pm, n, :sd, i)
qsc = var(pm, n, :qsc, i)
JuMP.@constraint(pm.model, ps + (sd - sc) == p_loss + r*(ps^2 + qs^2)/vm^2)
JuMP.@constraint(pm.model, qs == qsc + q_loss + x*(ps^2 + qs^2)/vm^2)
end