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jump_models.jl
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using JuMP
using DelimitedFiles
function get_mpcmodel(circuit, demand, T; has_ramping=true,
phase1=false, piecewise=false,
prev_val=nothing, u_on=nothing, u_su=nothing, u_sd=nothing, con=nothing, coff=nothing)
#=
Args:
circuit - Circuit instance
demand - Load instance
=#
m = Model()
# Shortcuts
baseMVA = circuit.baseMVA
busref = circuit.busref
bus = circuit.bus
line = circuit.line
gen = circuit.gen
yline = circuit.yline
ybus = circuit.ybus
busdict = circuit.busdict
frombus = circuit.frombus
tobus = circuit.tobus
bus2gen = circuit.bus2gen
Pd = demand.pd
Qd = demand.qd
# T = size(Pd,2)
num_buses = length(bus)
num_gens = length(gen)
num_lines = length(line)
if isnothing(u_on)
u_on = ones(Int, num_gens, T)
u_su = zeros(Int, num_gens, T)
u_sd = zeros(Int, num_gens, T)
end
#=
Pg[t, g]: real power at (time, generator) p_{t,g}
Qg[t, g]: reactive power at (time, generator) q_{t,g}
Vm[t, b]: voltage magnitude at (time, bus) v_{t,i}
Va[t, b]: voltage angle at (time, bus) \theta_{t, i}
=#
# @variable(m, gen[g].Pmin <= Pg[t=1:T,g=1:num_gens] <= gen[g].Pmax)
# @variable(m, gen[g].Qmin <= Qg[t=1:T,g=1:num_gens] <= gen[g].Qmax)
@variable(m, gen[g].Pmin * u_on[g,t] <= Pg[t=1:T,g=1:num_gens] <= gen[g].Pmax * u_on[g,t])
@variable(m, gen[g].Qmin * u_on[g,t] <= Qg[t=1:T,g=1:num_gens] <= gen[g].Qmax * u_on[g,t])
@variable(m, bus[b].Vmin <= Vm[t=1:T,b=1:num_buses] <= bus[b].Vmax)
@variable(m, Va[t=1:T,b=1:num_buses])
# Voltage angle has fixed value at reference bus (lower = upper)
# But no lower or upper bound on other Va[t, b]. Why? because it is sin, cos so doesn't matter.
for t in 1:T
set_lower_bound(Va[t,busref], bus[busref].Va)
set_upper_bound(Va[t,busref], bus[busref].Va)
end
#= Objective function
If not piecewise, then it is a quadratic sum of the real power at (t,g)
\sum_t\sum_g gencost1[g] * (baseMVA * Pg[t,g])^2
+ gencost2[g] * (baseMVA * Pg[t,g])
+ gencost3[g]
=#
uc_cost = sum(con[g] * sum(u_su[g,t] for t=1:T) + coff[g] * sum(u_sd[g,t] for t=1:T) for g=1:num_gens)
if piecewise
@variable(m, Cg[t=1:T,g=1:num_gens])
@NLobjective(m, Min, sum(Cg[t,g] for t=1:T,g=1:num_gens) + uc_cost)
@constraint(m, plcurve[t=1:T,g=1:num_gens,p=1:gen[g].n-1],
Cg[t,g] - (((gen[g].coeff[2*p+2] - gen[g].coeff[2*p])/(gen[g].coeff[2*p+1] - gen[g].coeff[2*p-1]))*(baseMVA*Pg[t,g] - gen[g].coeff[2*p-1]) + gen[g].coeff[2*p]) >= 0
)
else
@NLobjective(m, Min, sum(gen[g].coeff[gen[g].n-2]*(baseMVA*Pg[t,g])^2
+ gen[g].coeff[gen[g].n-1]*(baseMVA*Pg[t,g])
+ gen[g].coeff[gen[g].n] for t=1:T,g=1:num_gens) + uc_cost)
end
# Ramping up/down constraints
if has_ramping
if phase1 == false
# @constraint(m, ramping[t=1:T-1,g=1:num_gens],
# -gen[g].ramp_agc <= Pg[t+1,g] - Pg[t,g] <= gen[g].ramp_agc)
@constraint(m, ramping[t=1:T-1,g=1:num_gens],
-gen[g].ramp_agc * u_on[g,t+1] - gen[g].Pmax * u_sd[g,t+1] <= Pg[t+1,g] - Pg[t,g] <= gen[g].ramp_agc * u_on[g,t] + gen[g].Pmax * u_su[g,t+1])
else
@constraint(m, ramping[t=1:T,g=1:num_gens],
-gen[g].ramp_agc <= Pg[t,g] - prev_val[g] <= gen[g].ramp_agc)
end
end
# Power flow constraints: real part
@NLconstraint(m, pfreal[t=1:T,b=1:num_buses],
(sum(yline[l].YffR for l in frombus[b])
+ sum(yline[l].YttR for l in tobus[b])
+ ybus[b].YshR)*Vm[t,b]^2
+ sum(Vm[t,b]*Vm[t,busdict[line[l].to]]*
(yline[l].YftR*cos(Va[t,b]-Va[t,busdict[line[l].to]])
+ yline[l].YftI*sin(Va[t,b]-Va[t,busdict[line[l].to]]))
for l in frombus[b])
+ sum(Vm[t,b]*Vm[t,busdict[line[l].from]]*
(yline[l].YtfR*cos(Va[t,b]-Va[t,busdict[line[l].from]])
+ yline[l].YtfI*sin(Va[t,b]-Va[t,busdict[line[l].from]]))
for l in tobus[b])
- (sum(baseMVA*Pg[t,g] for g in bus2gen[b]) - Pd[b,t]) / baseMVA
== 0)
# Power flow constraints: imaginary part
@NLconstraint(m, pfimag[t=1:T,b=1:num_buses],
(sum(-yline[l].YffI for l in frombus[b])
+ sum(-yline[l].YttI for l in tobus[b])
- ybus[b].YshI)*Vm[t,b]^2
+ sum(Vm[t,b]*Vm[t,busdict[line[l].to]]*
(-yline[l].YftI*cos(Va[t,b]-Va[t,busdict[line[l].to]])
+ yline[l].YftR*sin(Va[t,b]-Va[t,busdict[line[l].to]]))
for l in frombus[b])
+ sum(Vm[t,b]*Vm[t,busdict[line[l].from]]*
(-yline[l].YtfI*cos(Va[t,b]-Va[t,busdict[line[l].from]])
+ yline[l].YtfR*sin(Va[t,b]-Va[t,busdict[line[l].from]]))
for l in tobus[b])
- (sum(baseMVA*Qg[t,g] for g in bus2gen[b]) - Qd[b,t]) / baseMVA
== 0)
# Line limits
# rateA - admittance rate?
rateA = getfield.(line, :rateA) # equiv to getattr for struct
limind = findall((rateA .!= 0) .& (rateA .< 1.0e10))
num_linelimits = length(limind)
Yff_abs2 = zeros(num_linelimits)
Yft_abs2 = zeros(num_linelimits)
Yre = zeros(num_linelimits)
Yim = zeros(num_linelimits)
flowmax = zeros(num_linelimits)
for i in 1:num_linelimits
# Apparent power limits (from bus)
l = limind[i]
flowmax[i] = (line[l].rateA / baseMVA)^2
Yff_abs2[i] = yline[l].YffR^2 + yline[l].YffI^2
Yft_abs2[i] = yline[l].YftR^2 + yline[l].YftI^2
Yre[i] = yline[l].YffR*yline[l].YftR + yline[l].YffI*yline[l].YftI
Yim[i] = -yline[l].YffR*yline[l].YftI + yline[l].YffI*yline[l].YftR
end
@NLconstraint(m, flowmaxfrom[t=1:T,i=1:num_linelimits],
Vm[t,busdict[line[limind[i]].from]]^2 *
(Yff_abs2[i]*Vm[t,busdict[line[limind[i]].from]]^2
+ Yft_abs2[i]*Vm[t,busdict[line[limind[i]].to]]^2
+ 2*Vm[t,busdict[line[limind[i]].from]]*Vm[t,busdict[line[limind[i]].to]]*
(Yre[i]*cos(Va[t,busdict[line[limind[i]].from]] - Va[t,busdict[line[limind[i]].to]])
- Yim[i]*sin(Va[t,busdict[line[limind[i]].from]] - Va[t,busdict[line[limind[i]].to]]))
) - flowmax[i] <= 0)
Ytf_abs2 = zeros(num_linelimits)
Ytt_abs2 = zeros(num_linelimits)
for i in 1:num_linelimits
# Apparent power limits (to bus)
l = limind[i]
Ytf_abs2[i] = yline[l].YtfR^2 + yline[l].YtfI^2
Ytt_abs2[i] = yline[l].YttR^2 + yline[l].YttI^2
Yre[i] = yline[l].YtfR*yline[l].YttR + yline[l].YtfI*yline[l].YttI
Yim[i] = -yline[l].YtfR*yline[l].YttI + yline[l].YtfI*yline[l].YttR
end
@NLconstraint(m, flowmaxto[t=1:T,i=1:num_linelimits],
Vm[t,busdict[line[limind[i]].to]]^2 *
(Ytf_abs2[i]*Vm[t,busdict[line[limind[i]].from]]^2
+ Ytt_abs2[i]*Vm[t,busdict[line[limind[i]].to]]^2
+ 2*Vm[t,busdict[line[limind[i]].from]]*Vm[t,busdict[line[limind[i]].to]]*
(Yre[i]*cos(Va[t,busdict[line[limind[i]].from]] - Va[t,busdict[line[limind[i]].to]])
-Yim[i]*sin(Va[t,busdict[line[limind[i]].from]] - Va[t,busdict[line[limind[i]].to]]))
) - flowmax[i] <=0)
return m
end
function get_ucmodel(circuit, demand, T,
v0, tu, td, hu, hd, con, coff;
has_ramping=true,
phase1=false, piecewise=false,
prev_val=nothing, cont_relax=false)
#=
Args:
circuit - Circuit instance
demand - Load instance
=#
m = Model()
# Shortcuts
baseMVA = circuit.baseMVA
busref = circuit.busref
bus = circuit.bus
line = circuit.line
gen = circuit.gen
yline = circuit.yline
ybus = circuit.ybus
busdict = circuit.busdict
frombus = circuit.frombus
tobus = circuit.tobus
bus2gen = circuit.bus2gen
Pd = demand.pd
Qd = demand.qd
# T = size(Pd,2)
num_buses = length(bus)
num_gens = length(gen)
num_lines = length(line)
#=
u_on[g,t]: generator g is on or off at time t
u_su[g,t]: generator g is started up at time t
u_sd[g,t]: generator g is shut down at time t
=#
if cont_relax
@variable(m, u_on[g=1:num_gens,t=1:T], lower_bound=0, upper_bound=1)
@variable(m, u_su[g=1:num_gens,t=1:T], lower_bound=0, upper_bound=1)
@variable(m, u_sd[g=1:num_gens,t=1:T], lower_bound=0, upper_bound=1)
else
@variable(m, u_on[g=1:num_gens,t=1:T], Bin)
@variable(m, u_su[g=1:num_gens,t=1:T], Bin)
@variable(m, u_sd[g=1:num_gens,t=1:T], Bin)
end
@constraint(m, uc_state_init[g=1:num_gens], v0[g] - u_on[g,1] + u_su[g,1] - u_sd[g,1] == 0)
@constraint(m, uc_state[g=1:num_gens,t=1:T-1], u_on[g,t] - u_on[g,t+1] + u_su[g,t+1] - u_sd[g,t+1] == 0)
@constraint(m, initial_on[g=1:num_gens], sum(1-u_on[g,t] for t in 1:hu[g]) == 0)
@constraint(m, initial_off[g=1:num_gens], sum(u_on[g,t] for t in 1:hd[g]) == 0)
# @constraint(m, min_ontime[g=1:num_gens,t=tu[g]:T], sum(u_su[g,t] for i in t-tu[g]+1:t) <= u_on[g,t])
# @constraint(m, min_offtime[g=1:num_gens,t=td[g]:T], sum(u_sd[g,t] for i in t-td[g]+1:t) <= 1 - u_on[g,t])
for g=1:num_gens
if tu[g] > 0
@constraint(m, [t=tu[g]:T], sum(u_su[g,t] for i in t-tu[g]+1:t) <= u_on[g,t])
end
if td[g] > 0
@constraint(m, [t=td[g]:T], sum(u_sd[g,t] for i in t-td[g]+1:t) <= 1 - u_on[g,t])
end
end
@expression(m, uc_cost, sum(con[g] * sum(u_su[g,t] for t=1:T) + coff[g] * sum(u_sd[g,t] for t=1:T) for g=1:num_gens) )
#=
Pg[t, g]: real power at (time, generator) p_{t,g}
Qg[t, g]: reactive power at (time, generator) q_{t,g}
Vm[t, b]: voltage magnitude at (time, bus) v_{t,i}
Va[t, b]: voltage angle at (time, bus) \theta_{t, i}
=#
@variable(m, Pg[t=1:T,g=1:num_gens])
@variable(m, Qg[t=1:T,g=1:num_gens])
@variable(m, bus[b].Vmin <= Vm[t=1:T,b=1:num_buses] <= bus[b].Vmax)
@variable(m, Va[t=1:T,b=1:num_buses])
@constraint(m, pg_lower_bound[t=1:T,g=1:num_gens], Pg[t,g] >= gen[g].Pmin * u_on[g,t])
@constraint(m, pg_upper_bound[t=1:T,g=1:num_gens], Pg[t,g] <= gen[g].Pmax * u_on[g,t])
@constraint(m, qg_lower_bound[t=1:T,g=1:num_gens], Qg[t,g] >= gen[g].Qmin * u_on[g,t])
@constraint(m, qg_upper_bound[t=1:T,g=1:num_gens], Qg[t,g] <= gen[g].Qmax * u_on[g,t])
# Voltage angle has fixed value at reference bus (lower = upper)
# But no lower or upper bound on other Va[t, b]. Why? because it is sin, cos so doesn't matter.
for t in 1:T
set_lower_bound(Va[t,busref], bus[busref].Va)
set_upper_bound(Va[t,busref], bus[busref].Va)
end
#= Objective function
If not piecewise, then it is a quadratic sum of the real power at (t,g)
\sum_t\sum_g gencost1[g] * (baseMVA * Pg[t,g])^2
+ gencost2[g] * (baseMVA * Pg[t,g])
+ gencost3[g]
=#
if piecewise
@variable(m, Cg[t=1:T,g=1:num_gens])
@NLobjective(m, Min, sum(Cg[t,g] for t=1:T,g=1:num_gens) + uc_cost)
@constraint(m, plcurve[t=1:T,g=1:num_gens,p=1:gen[g].n-1],
Cg[t,g] - (((gen[g].coeff[2*p+2] - gen[g].coeff[2*p])/(gen[g].coeff[2*p+1] - gen[g].coeff[2*p-1]))*(baseMVA*Pg[t,g] - gen[g].coeff[2*p-1]) + gen[g].coeff[2*p]) >= 0
)
else
@NLobjective(m, Min, sum(gen[g].coeff[gen[g].n-2]*(baseMVA*Pg[t,g])^2
+ gen[g].coeff[gen[g].n-1]*(baseMVA*Pg[t,g])
+ gen[g].coeff[gen[g].n] for t=1:T,g=1:num_gens) + uc_cost)
end
# Ramping up/down constraints
if has_ramping
if phase1 == false
@constraint(m, ramping_up[t=1:T-1,g=1:num_gens],
Pg[t+1,g] - Pg[t,g] <= gen[g].ramp_agc * u_on[g,t] + gen[g].Pmax * u_su[g,t+1])
@constraint(m, ramping_down[t=1:T-1,g=1:num_gens],
Pg[t+1,g] - Pg[t,g] >= -gen[g].ramp_agc * u_on[g,t+1] - gen[g].Pmax * u_sd[g,t+1])
else
@constraint(m, ramping[t=1:T,g=1:num_gens],
-gen[g].ramp_agc <= Pg[t,g] - prev_val[g] <= gen[g].ramp_agc)
end
end
# Power flow constraints: real part
@NLconstraint(m, pfreal[t=1:T,b=1:num_buses],
(sum(yline[l].YffR for l in frombus[b])
+ sum(yline[l].YttR for l in tobus[b])
+ ybus[b].YshR)*Vm[t,b]^2
+ sum(Vm[t,b]*Vm[t,busdict[line[l].to]]*
(yline[l].YftR*cos(Va[t,b]-Va[t,busdict[line[l].to]])
+ yline[l].YftI*sin(Va[t,b]-Va[t,busdict[line[l].to]]))
for l in frombus[b])
+ sum(Vm[t,b]*Vm[t,busdict[line[l].from]]*
(yline[l].YtfR*cos(Va[t,b]-Va[t,busdict[line[l].from]])
+ yline[l].YtfI*sin(Va[t,b]-Va[t,busdict[line[l].from]]))
for l in tobus[b])
- (sum(baseMVA*Pg[t,g] for g in bus2gen[b]) - Pd[b,t]) / baseMVA
== 0)
# Power flow constraints: imaginary part
@NLconstraint(m, pfimag[t=1:T,b=1:num_buses],
(sum(-yline[l].YffI for l in frombus[b])
+ sum(-yline[l].YttI for l in tobus[b])
- ybus[b].YshI)*Vm[t,b]^2
+ sum(Vm[t,b]*Vm[t,busdict[line[l].to]]*
(-yline[l].YftI*cos(Va[t,b]-Va[t,busdict[line[l].to]])
+ yline[l].YftR*sin(Va[t,b]-Va[t,busdict[line[l].to]]))
for l in frombus[b])
+ sum(Vm[t,b]*Vm[t,busdict[line[l].from]]*
(-yline[l].YtfI*cos(Va[t,b]-Va[t,busdict[line[l].from]])
+ yline[l].YtfR*sin(Va[t,b]-Va[t,busdict[line[l].from]]))
for l in tobus[b])
- (sum(baseMVA*Qg[t,g] for g in bus2gen[b]) - Qd[b,t]) / baseMVA
== 0)
# Line limits
# rateA - admittance rate?
rateA = getfield.(line, :rateA) # equiv to getattr for struct
limind = findall((rateA .!= 0) .& (rateA .< 1.0e10))
num_linelimits = length(limind)
Yff_abs2 = zeros(num_linelimits)
Yft_abs2 = zeros(num_linelimits)
Yre = zeros(num_linelimits)
Yim = zeros(num_linelimits)
flowmax = zeros(num_linelimits)
for i in 1:num_linelimits
# Apparent power limits (from bus)
l = limind[i]
flowmax[i] = (line[l].rateA / baseMVA)^2
Yff_abs2[i] = yline[l].YffR^2 + yline[l].YffI^2
Yft_abs2[i] = yline[l].YftR^2 + yline[l].YftI^2
Yre[i] = yline[l].YffR*yline[l].YftR + yline[l].YffI*yline[l].YftI
Yim[i] = -yline[l].YffR*yline[l].YftI + yline[l].YffI*yline[l].YftR
end
@NLconstraint(m, flowmaxfrom[t=1:T,i=1:num_linelimits],
Vm[t,busdict[line[limind[i]].from]]^2 *
(Yff_abs2[i]*Vm[t,busdict[line[limind[i]].from]]^2
+ Yft_abs2[i]*Vm[t,busdict[line[limind[i]].to]]^2
+ 2*Vm[t,busdict[line[limind[i]].from]]*Vm[t,busdict[line[limind[i]].to]]*
(Yre[i]*cos(Va[t,busdict[line[limind[i]].from]] - Va[t,busdict[line[limind[i]].to]])
- Yim[i]*sin(Va[t,busdict[line[limind[i]].from]] - Va[t,busdict[line[limind[i]].to]]))
) - flowmax[i] <= 0)
Ytf_abs2 = zeros(num_linelimits)
Ytt_abs2 = zeros(num_linelimits)
for i in 1:num_linelimits
# Apparent power limits (to bus)
l = limind[i]
Ytf_abs2[i] = yline[l].YtfR^2 + yline[l].YtfI^2
Ytt_abs2[i] = yline[l].YttR^2 + yline[l].YttI^2
Yre[i] = yline[l].YtfR*yline[l].YttR + yline[l].YtfI*yline[l].YttI
Yim[i] = -yline[l].YtfR*yline[l].YttI + yline[l].YtfI*yline[l].YttR
end
@NLconstraint(m, flowmaxto[t=1:T,i=1:num_linelimits],
Vm[t,busdict[line[limind[i]].to]]^2 *
(Ytf_abs2[i]*Vm[t,busdict[line[limind[i]].from]]^2
+ Ytt_abs2[i]*Vm[t,busdict[line[limind[i]].to]]^2
+ 2*Vm[t,busdict[line[limind[i]].from]]*Vm[t,busdict[line[limind[i]].to]]*
(Yre[i]*cos(Va[t,busdict[line[limind[i]].from]] - Va[t,busdict[line[limind[i]].to]])
-Yim[i]*sin(Va[t,busdict[line[limind[i]].from]] - Va[t,busdict[line[limind[i]].to]]))
) - flowmax[i] <=0)
return m
end
function solve_multiperiod(circuit, load, T)
model = get_mpcmodel(circuit, load, T)
set_optimizer(model, Ipopt.Optimizer)
optimize!(model)
return model
end
function solve_multiperiod_with_uc(circuit, load, T, u_on, u_su, u_sd, con, coff)
model = get_mpcmodel(circuit, load, T, u_on=u_on, u_su=u_su, u_sd=u_sd, con=con, coff=coff)
set_optimizer(model, Ipopt.Optimizer)
optimize!(model)
return model
end
#=
function feasibility_check(v0, tu, td, hu, hd, u_on)
T = length(u_on)
u_su = zeros(Int, T)
u_sd = zeros(Int, T)
u_su[1] = max(u_on[1] - v0, 0)
u_sd[1] = max(v0 - u_on[1], 0)
for t in 2:T
u_su[t] = max(u_on[t] - u_on[t-1], 0)
u_sd[t] = max(u_on[t-1] - u_on[t], 0)
end
# This check is not necessary, only for debugging purposes
@assert v0 - u_on[1] + u_su[1] - u_sd[1] == 0
for t in 2:T
@assert u_on[t-1] - u_on[t] + u_su[t] - u_sd[t] == 0
end
if sum(1 .- u_on[1:hu]) != 0
return 0
end
if sum(u_on[1:hd]) != 0
return 0
end
for t in tu:T
if sum(u_su[t-tu+1:t]) > u_on[t]
return 0
end
end
for t in td:T
if sum(u_sd[t-td+1:t]) > 1 - u_on[t]
return 0
end
end
return 1
end
function generate_uc_feasible_solutions(v0, tu, td, hu, hd, T)
s = Set()
for i in 0:2^T-1
u_on = reverse(digits(i, base=2, pad=T))
if feasibility_check(v0, tu, td, hu, hd, u_on) == 1
push!(s, i)
end
end
return s
end
=#