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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 | # UnitCommitmentFL.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_ramp_eqs!(
model::JuMP.Model,
g::ThermalUnit,
::Gar1962.ProdVars,
::WanHob2016.Ramping,
::Gar1962.StatusVars,
sc::UnitCommitmentScenario,
)::Nothing
is_initially_on = (g.initial_status > 0)
SU = g.startup_limit
SD = g.shutdown_limit
RU = g.ramp_up_limit
RD = g.ramp_down_limit
gn = g.name
minp = g.min_power
maxp = g.max_power
initial_power = g.initial_power
is_on = model[:is_on]
prod_above = model[:prod_above]
upflexiramp = model[:upflexiramp]
dwflexiramp = model[:dwflexiramp]
mfg = model[:mfg]
if length(g.reserves) > 1
error("Each generator may only provide one flexiramp reserve")
end
for r in g.reserves
if r.type !== "flexiramp"
error(
"This formulation only supports flexiramp reserves, not $(r.type)",
)
end
rn = r.name
for t in 1:model[:instance].time
@constraint(
model,
prod_above[sc.name, gn, t] + (is_on[gn, t] * minp[t]) <=
mfg[sc.name, gn, t]
) # Eq. (19) in Wang & Hobbs (2016)
@constraint(model, mfg[sc.name, gn, t] <= is_on[gn, t] * maxp[t]) # Eq. (22) in Wang & Hobbs (2016)
if t != model[:instance].time
@constraint(
model,
minp[t] * (is_on[gn, t+1] + is_on[gn, t] - 1) <=
prod_above[sc.name, gn, t] -
dwflexiramp[sc.name, rn, gn, t] + (is_on[gn, t] * minp[t])
) # first inequality of Eq. (20) in Wang & Hobbs (2016)
@constraint(
model,
prod_above[sc.name, gn, t] -
dwflexiramp[sc.name, rn, gn, t] +
(is_on[gn, t] * minp[t]) <=
mfg[sc.name, gn, t+1] + (maxp[t] * (1 - is_on[gn, t+1]))
) # second inequality of Eq. (20) in Wang & Hobbs (2016)
@constraint(
model,
minp[t] * (is_on[gn, t+1] + is_on[gn, t] - 1) <=
prod_above[sc.name, gn, t] +
upflexiramp[sc.name, rn, gn, t] +
(is_on[gn, t] * minp[t])
) # first inequality of Eq. (21) in Wang & Hobbs (2016)
@constraint(
model,
prod_above[sc.name, gn, t] +
upflexiramp[sc.name, rn, gn, t] +
(is_on[gn, t] * minp[t]) <=
mfg[sc.name, gn, t+1] + (maxp[t] * (1 - is_on[gn, t+1]))
) # second inequality of Eq. (21) in Wang & Hobbs (2016)
if t != 1
@constraint(
model,
mfg[sc.name, gn, t] <=
prod_above[sc.name, gn, t-1] +
(is_on[gn, t-1] * minp[t]) +
(RU * is_on[gn, t-1]) +
(SU * (is_on[gn, t] - is_on[gn, t-1])) +
maxp[t] * (1 - is_on[gn, t])
) # Eq. (23) in Wang & Hobbs (2016)
@constraint(
model,
(
prod_above[sc.name, gn, t-1] +
(is_on[gn, t-1] * minp[t])
) - (
prod_above[sc.name, gn, t] +
(is_on[gn, t] * minp[t])
) <=
RD * is_on[gn, t] +
SD * (is_on[gn, t-1] - is_on[gn, t]) +
maxp[t] * (1 - is_on[gn, t-1])
) # Eq. (25) in Wang & Hobbs (2016)
else
@constraint(
model,
mfg[sc.name, gn, t] <=
initial_power +
(RU * is_initially_on) +
(SU * (is_on[gn, t] - is_initially_on)) +
maxp[t] * (1 - is_on[gn, t])
) # Eq. (23) in Wang & Hobbs (2016) for the first time period
@constraint(
model,
initial_power - (
prod_above[sc.name, gn, t] +
(is_on[gn, t] * minp[t])
) <=
RD * is_on[gn, t] +
SD * (is_initially_on - is_on[gn, t]) +
maxp[t] * (1 - is_initially_on)
) # Eq. (25) in Wang & Hobbs (2016) for the first time period
end
@constraint(
model,
mfg[sc.name, gn, t] <=
(SD * (is_on[gn, t] - is_on[gn, t+1])) +
(maxp[t] * is_on[gn, t+1])
) # Eq. (24) in Wang & Hobbs (2016)
@constraint(
model,
-RD * is_on[gn, t+1] -
SD * (is_on[gn, t] - is_on[gn, t+1]) -
maxp[t] * (1 - is_on[gn, t]) <=
upflexiramp[sc.name, rn, gn, t]
) # first inequality of Eq. (26) in Wang & Hobbs (2016)
@constraint(
model,
upflexiramp[sc.name, rn, gn, t] <=
RU * is_on[gn, t] +
SU * (is_on[gn, t+1] - is_on[gn, t]) +
maxp[t] * (1 - is_on[gn, t+1])
) # second inequality of Eq. (26) in Wang & Hobbs (2016)
@constraint(
model,
-RU * is_on[gn, t] - SU * (is_on[gn, t+1] - is_on[gn, t]) -
maxp[t] * (1 - is_on[gn, t+1]) <=
dwflexiramp[sc.name, rn, gn, t]
) # first inequality of Eq. (27) in Wang & Hobbs (2016)
@constraint(
model,
dwflexiramp[sc.name, rn, gn, t] <=
RD * is_on[gn, t+1] +
SD * (is_on[gn, t] - is_on[gn, t+1]) +
maxp[t] * (1 - is_on[gn, t])
) # second inequality of Eq. (27) in Wang & Hobbs (2016)
@constraint(
model,
-maxp[t] * is_on[gn, t] + minp[t] * is_on[gn, t+1] <=
upflexiramp[sc.name, rn, gn, t]
) # first inequality of Eq. (28) in Wang & Hobbs (2016)
@constraint(
model,
upflexiramp[sc.name, rn, gn, t] <= maxp[t] * is_on[gn, t+1]
) # second inequality of Eq. (28) in Wang & Hobbs (2016)
@constraint(
model,
-maxp[t] * is_on[gn, t+1] <=
dwflexiramp[sc.name, rn, gn, t]
) # first inequality of Eq. (29) in Wang & Hobbs (2016)
@constraint(
model,
dwflexiramp[sc.name, rn, gn, t] <=
(maxp[t] * is_on[gn, t]) - (minp[t] * is_on[gn, t+1])
) # second inequality of Eq. (29) in Wang & Hobbs (2016)
else
@constraint(
model,
mfg[sc.name, gn, t] <=
prod_above[sc.name, gn, t-1] +
(is_on[gn, t-1] * minp[t]) +
(RU * is_on[gn, t-1]) +
(SU * (is_on[gn, t] - is_on[gn, t-1])) +
maxp[t] * (1 - is_on[gn, t])
) # Eq. (23) in Wang & Hobbs (2016) for the last time period
@constraint(
model,
(
prod_above[sc.name, gn, t-1] +
(is_on[gn, t-1] * minp[t])
) -
(prod_above[sc.name, gn, t] + (is_on[gn, t] * minp[t])) <=
RD * is_on[gn, t] +
SD * (is_on[gn, t-1] - is_on[gn, t]) +
maxp[t] * (1 - is_on[gn, t-1])
) # Eq. (25) in Wang & Hobbs (2016) for the last time period
end
end
end
end
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