parent
f69d378d47
commit
fc8995eff1
@ -0,0 +1,102 @@
|
||||
# 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.
|
||||
|
||||
function _add_production_piecewise_linear_eqs!(
|
||||
model::JuMP.Model,
|
||||
g::Unit,
|
||||
formulation::KnuOstWat18,
|
||||
)::Nothing
|
||||
eq_prod_above_def = _init(model, :eq_prod_above_def)
|
||||
eq_segprod_limit_a = _init(model, :eq_segprod_limit_a)
|
||||
eq_segprod_limit_b = _init(model, :eq_segprod_limit_b)
|
||||
eq_segprod_limit_c = _init(model, :eq_segprod_limit_c)
|
||||
prod_above = model[:prod_above]
|
||||
segprod = model[:segprod]
|
||||
is_on = model[:is_on]
|
||||
switch_on = model[:switch_on]
|
||||
switch_off = model[:switch_off]
|
||||
gn = g.name
|
||||
K = length(g.cost_segments)
|
||||
T = model[:instance].time
|
||||
|
||||
for t in 1:T
|
||||
for k in 1:K
|
||||
# Pbar^{k-1)
|
||||
Pbar0 =
|
||||
g.min_power[t] +
|
||||
(k > 1 ? sum(g.cost_segments[ell].mw[t] for ell in 1:k-1) : 0.0)
|
||||
# Pbar^k
|
||||
Pbar1 = g.cost_segments[k].mw[t] + Pbar0
|
||||
|
||||
Cv = 0.0
|
||||
SU = g.startup_limit # startup rate
|
||||
if Pbar1 <= SU
|
||||
Cv = 0.0
|
||||
elseif Pbar0 < SU # && Pbar1 > SU
|
||||
Cv = Pbar1 - SU
|
||||
else # Pbar0 >= SU
|
||||
# this will imply that we cannot produce along this segment if
|
||||
# switch_on = 1
|
||||
Cv = g.cost_segments[k].mw[t]
|
||||
end
|
||||
Cw = 0.0
|
||||
SD = g.shutdown_limit # shutdown rate
|
||||
if Pbar1 <= SD
|
||||
Cw = 0.0
|
||||
elseif Pbar0 < SD # && Pbar1 > SD
|
||||
Cw = Pbar1 - SD
|
||||
else # Pbar0 >= SD
|
||||
Cw = g.cost_segments[k].mw[t]
|
||||
end
|
||||
|
||||
if g.min_uptime > 1
|
||||
# Equation (46) in Kneuven et al. (2020)
|
||||
eq_segprod_limit_a[gn, t, k] = @constraint(
|
||||
model,
|
||||
segprod[gn, t, k] <=
|
||||
g.cost_segments[k].mw[t] * is_on[gn, t] -
|
||||
Cv * switch_on[gn, t] -
|
||||
(t < T ? Cw * switch_off[gn, t+1] : 0.0)
|
||||
)
|
||||
else
|
||||
# Equation (47a)/(48a) in Kneuven et al. (2020)
|
||||
eq_segprod_limit_b[gn, t, k] = @constraint(
|
||||
model,
|
||||
segprod[gn, t, k] <=
|
||||
g.cost_segments[k].mw[t] * is_on[gn, t] -
|
||||
Cv * switch_on[gn, t] -
|
||||
(t < T ? max(0, Cv - Cw) * switch_off[gn, t+1] : 0.0)
|
||||
)
|
||||
|
||||
# Equation (47b)/(48b) in Kneuven et al. (2020)
|
||||
eq_segprod_limit_c[gn, t, k] = @constraint(
|
||||
model,
|
||||
segprod[gn, t, k] <=
|
||||
g.cost_segments[k].mw[t] * is_on[gn, t] -
|
||||
max(0, Cw - Cv) * switch_on[gn, t] -
|
||||
(t < T ? Cw * switch_off[gn, t+1] : 0.0)
|
||||
)
|
||||
end
|
||||
|
||||
# Definition of production
|
||||
# Equation (43) in Kneuven et al. (2020)
|
||||
eq_prod_above_def[gn, t] = @constraint(
|
||||
model,
|
||||
prod_above[gn, t] == sum(segprod[gn, t, k] for k in 1:K)
|
||||
)
|
||||
|
||||
# Objective function
|
||||
# Equation (44) in Kneuven et al. (2020)
|
||||
add_to_expression!(
|
||||
model[:obj],
|
||||
segprod[gn, t, k],
|
||||
g.cost_segments[k].cost[t],
|
||||
)
|
||||
|
||||
# Also add an explicit upper bound on segprod to make the solver's
|
||||
# work a bit easier
|
||||
set_upper_bound(segprod[gn, t, k], g.cost_segments[k].mw[t])
|
||||
end
|
||||
end
|
||||
end
|
||||
@ -0,0 +1,12 @@
|
||||
# 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.
|
||||
|
||||
"""
|
||||
Formulation described in:
|
||||
|
||||
Knueven, B., Ostrowski, J., & Watson, J. P. (2018). Exploiting identical
|
||||
generators in unit commitment. IEEE Transactions on Power Systems, 33(4),
|
||||
4496-4507.
|
||||
"""
|
||||
struct KnuOstWat18 <: PiecewiseLinearCostsFormulation end
|
||||
Loading…
Reference in new issue