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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 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 | # 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::ThermalUnit,
formulation_prod_vars::Gar1962.ProdVars,
formulation_pwl_costs::KnuOstWat2018.PwlCosts,
formulation_status_vars::Gar1962.StatusVars,
sc::UnitCommitmentScenario,
)::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)
segprod = model[:segprod]
gn = g.name
K = length(g.cost_segments)
T = model[:instance].time
# Gar1962.ProdVars
prod_above = model[:prod_above]
# Gar1962.StatusVars
is_on = model[:is_on]
switch_on = model[:switch_on]
switch_off = model[:switch_off]
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[sc.name, gn, t, k] = @constraint(
model,
segprod[sc.name, 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[sc.name, gn, t, k] = @constraint(
model,
segprod[sc.name, 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[sc.name, gn, t, k] = @constraint(
model,
segprod[sc.name, 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[sc.name, gn, t] = @constraint(
model,
prod_above[sc.name, gn, t] ==
sum(segprod[sc.name, gn, t, k] for k in 1:K)
)
# Objective function
# Equation (44) in Kneuven et al. (2020)
add_to_expression!(
model[:obj],
segprod[sc.name, gn, t, k],
sc.probability * 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[sc.name, gn, t, k],
g.cost_segments[k].mw[t],
)
end
end
end
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