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UnitCommitment.jl
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pull/13/head
Aleksandr Kazachkov 4 years ago
parent 8ddb062401
commit b53902d559
11 changed files with 158 additions and 123 deletions
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2
src/instance/read.jl
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@ -100,7 +100,7 @@ function _from_json(json; repair = true)
) )
shortfall_penalty = timeseries( shortfall_penalty = timeseries(
json["Parameters"]["Reserve shortfall penalty (\$/MW)"], json["Parameters"]["Reserve shortfall penalty (\$/MW)"],
default=[0. for t in 1:T] default = [0.0 for t in 1:T],
) )
# Read buses # Read buses

2
src/model/formulations/DamKucRajAta2016/ramp.jl
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@ -35,7 +35,7 @@ function _add_ramp_eqs!(
RESERVES_WHEN_RAMP_DOWN = true RESERVES_WHEN_RAMP_DOWN = true
RESERVES_WHEN_SHUT_DOWN = true RESERVES_WHEN_SHUT_DOWN = true
is_initially_on = _is_initially_on(g) is_initially_on = _is_initially_on(g)
# The following are the same for generator g across all time periods # The following are the same for generator g across all time periods
SU = g.startup_limit # startup rate SU = g.startup_limit # startup rate
SD = g.shutdown_limit # shutdown rate SD = g.shutdown_limit # shutdown rate

13
src/model/formulations/Gar1962/status.jl
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@ -12,7 +12,7 @@ function _add_status_vars!(
model::JuMP.Model, model::JuMP.Model,
g::Unit, g::Unit,
formulation_status_vars::Gar1962.StatusVars, formulation_status_vars::Gar1962.StatusVars,
ALWAYS_CREATE_VARS = false ALWAYS_CREATE_VARS = false,
)::Nothing )::Nothing
is_on = _init(model, :is_on) is_on = _init(model, :is_on)
switch_on = _init(model, :switch_on) switch_on = _init(model, :switch_on)
@ -38,12 +38,16 @@ function _add_status_vars!(
end end
end end
if g.must_run[t] if g.must_run[t]
# If the generator _must_ run, then it is obviously on and cannot be switched off # If the generator _must_ run, then it is obviously on and cannot be switched off
# In the first time period, force unit to switch on if was off before # In the first time period, force unit to switch on if was off before
# Otherwise, unit is on, and will never turn off, so will never need to turn on # Otherwise, unit is on, and will never turn off, so will never need to turn on
fix(is_on[g.name, t], 1.0; force = true) fix(is_on[g.name, t], 1.0; force = true)
fix(switch_on[g.name, t], (t == 1 ? 1.0 - _is_initially_on(g) : 0.0); force = true) fix(
switch_on[g.name, t],
(t == 1 ? 1.0 - _is_initially_on(g) : 0.0);
force = true,
)
fix(switch_off[g.name, t], 0.0; force = true) fix(switch_off[g.name, t], 0.0; force = true)
end end
else else
@ -57,7 +61,8 @@ function _add_status_vars!(
end end
if g.must_run[t] if g.must_run[t]
is_on[g.name, t] = 1.0 is_on[g.name, t] = 1.0
switch_on[g.name, t] = (t == 1 ? 1.0 - _is_initially_on(g) : 0.0) switch_on[g.name, t] =
(t == 1 ? 1.0 - _is_initially_on(g) : 0.0)
switch_off[g.name, t] = 0.0 switch_off[g.name, t] = 0.0
end end
end # check if ALWAYS_CREATE_VARS end # check if ALWAYS_CREATE_VARS

58
src/model/formulations/GenMorRam2017/startstop.jl
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@ -2,7 +2,6 @@
# Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved. # Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
# Released under the modified BSD license. See COPYING.md for more details. # Released under the modified BSD license. See COPYING.md for more details.
""" """
_add_startup_shutdown_limit_eqs!(model::JuMP.Model, g::Unit)::Nothing _add_startup_shutdown_limit_eqs!(model::JuMP.Model, g::Unit)::Nothing
@ -45,41 +44,52 @@ function _add_startup_shutdown_limit_eqs!(model::JuMP.Model, g::Unit)::Nothing
if g.initial_power > g.shutdown_limit if g.initial_power > g.shutdown_limit
#eqs.shutdown_limit[gi, 0] = @constraint(mip, vars.switch_off[gi, 1] <= 0) #eqs.shutdown_limit[gi, 0] = @constraint(mip, vars.switch_off[gi, 1] <= 0)
fix(switch_off[gi, 1], 0.; force = true) fix(switch_off[gi, 1], 0.0; force = true)
end end
for t = 1:T for t in 1:T
## 2020-10-09 amk: added eqn (20) and check of g.min_uptime ## 2020-10-09 amk: added eqn (20) and check of g.min_uptime
# Not present in (23) in Kneueven et al. # Not present in (23) in Kneueven et al.
if g.min_uptime > 1 if g.min_uptime > 1
# Equation (20) in Kneuven et al. (2020) # Equation (20) in Kneuven et al. (2020)
eqs.startstop_limit[gi,t] = eqs.startstop_limit[gi, t] = @constraint(
@constraint(model, model,
prod_above[gi, t] + reserve[gi, t] prod_above[gi, t] + reserve[gi, t] <=
<= (g.max_power[t] - g.min_power[t]) * is_on[gi, t] (g.max_power[t] - g.min_power[t]) * is_on[gi, t] -
- max(0, g.max_power[t] - g.startup_limit) * switch_on[gi, t] max(0, g.max_power[t] - g.startup_limit) * switch_on[gi, t] - (
- (t < T ? max(0, g.max_power[t] - g.shutdown_limit) * switch_off[gi, t+1] : 0.) t < T ?
) max(0, g.max_power[t] - g.shutdown_limit) *
switch_off[gi, t+1] : 0.0
)
)
else else
## Startup limits ## Startup limits
# Equation (23a) in Kneuven et al. (2020) # Equation (23a) in Kneuven et al. (2020)
eqs.startup_limit[gi, t] = eqs.startup_limit[gi, t] = @constraint(
@constraint(model, model,
prod_above[gi, t] + reserve[gi, t] prod_above[gi, t] + reserve[gi, t] <=
<= (g.max_power[t] - g.min_power[t]) * is_on[gi, t] (g.max_power[t] - g.min_power[t]) * is_on[gi, t] -
- max(0, g.max_power[t] - g.startup_limit) * switch_on[gi, t] max(0, g.max_power[t] - g.startup_limit) * switch_on[gi, t] - (
- (t < T ? max(0, g.startup_limit - g.shutdown_limit) * switch_off[gi, t+1] : 0.) t < T ?
) max(0, g.startup_limit - g.shutdown_limit) *
switch_off[gi, t+1] : 0.0
)
)
## Shutdown limits ## Shutdown limits
if t < T if t < T
# Equation (23b) in Kneuven et al. (2020) # Equation (23b) in Kneuven et al. (2020)
eqs.shutdown_limit[gi, t] = eqs.shutdown_limit[gi, t] = @constraint(
@constraint(model, model,
prod_above[gi, t] + reserve[gi, t] prod_above[gi, t] + reserve[gi, t] <=
<= (g.max_power[t] - g.min_power[t]) * xis_on[gi, t] (g.max_power[t] - g.min_power[t]) * xis_on[gi, t] - (
- (t < T ? max(0, g.max_power[t] - g.shutdown_limit) * switch_off[gi, t+1] : 0.) t < T ?
- max(0, g.shutdown_limit - g.startup_limit) * switch_on[gi, t]) max(0, g.max_power[t] - g.shutdown_limit) *
switch_off[gi, t+1] : 0.0
) -
max(0, g.shutdown_limit - g.startup_limit) *
switch_on[gi, t]
)
end end
end # check if g.min_uptime > 1 end # check if g.min_uptime > 1
end # loop over time end # loop over time

73
src/model/formulations/KnuOstWat2018/scosts.jl
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@ -61,56 +61,63 @@ function _add_startup_cost_eqs!(
# Equation (59) in Kneuven et al. (2020) # Equation (59) in Kneuven et al. (2020)
# Relate downtime_arc with switch_on # Relate downtime_arc with switch_on
# "switch_on[g,t] >= x_g(t',t) for all t' \in [t-TC+1, t-DT]" # "switch_on[g,t] >= x_g(t',t) for all t' \in [t-TC+1, t-DT]"
eq_startup_at_t[gn, t] = eq_startup_at_t[gn, t] = @constraint(
@constraint(model, model,
switch_on[gn, t] switch_on[gn, t] >= sum(
>= sum(downtime_arc[gn,tmp_t,t] downtime_arc[gn, tmp_t, t] for
for tmp_t in t-TC+1:t-DT if tmp_t >= 1) tmp_t in t-TC+1:t-DT if tmp_t >= 1
) )
)
# Equation (60) in Kneuven et al. (2020) # Equation (60) in Kneuven et al. (2020)
# "switch_off[g,t] >= x_g(t,t') for all t' \in [t+DT, t+TC-1]" # "switch_off[g,t] >= x_g(t,t') for all t' \in [t+DT, t+TC-1]"
eqs.shutdown_at_t[gn, t] = eqs.shutdown_at_t[gn, t] = @constraint(
@constraint(model, model,
switch_off[gn, t] switch_off[gn, t] >= sum(
>= sum(downtime_arc[gn,t,tmp_t] downtime_arc[gn, t, tmp_t] for
for tmp_t in t+DT:t+TC-1 if tmp_t <= T) tmp_t in t+DT:t+TC-1 if tmp_t <= T
) )
)
# Objective function terms for start-up costs # Objective function terms for start-up costs
# Equation (61) in Kneuven et al. (2020) # Equation (61) in Kneuven et al. (2020)
default_category = S default_category = S
if initial_time_shutdown > 0 && t + initial_time_shutdown - 1 < TC if initial_time_shutdown > 0 && t + initial_time_shutdown - 1 < TC
for s in 1:S-1 for s in 1:S-1
# If off for x periods before, then belongs to category s # If off for x periods before, then belongs to category s
# if -x+1 in [t-delay[s+1]+1,t-delay[s]] # if -x+1 in [t-delay[s+1]+1,t-delay[s]]
# or, equivalently, if total time off in [delay[s], delay[s+1]-1] # or, equivalently, if total time off in [delay[s], delay[s+1]-1]
# where total time off = t - 1 + initial_time_shutdown # where total time off = t - 1 + initial_time_shutdown
# (the -1 because not off for current time period) # (the -1 because not off for current time period)
if t + initial_time_shutdown - 1 < g.startup_categories[s+1].delay if t + initial_time_shutdown - 1 <
default_category = s g.startup_categories[s+1].delay
break # does not go into next category default_category = s
end break # does not go into next category
end
end end
end end
add_to_expression!(model[:obj], add_to_expression!(
switch_on[gn, t], model[:obj],
g.startup_categories[default_category].cost) switch_on[gn, t],
g.startup_categories[default_category].cost,
)
for s in 1:S-1 for s in 1:S-1
# Objective function terms for start-up costs # Objective function terms for start-up costs
# Equation (61) in Kneuven et al. (2020) # Equation (61) in Kneuven et al. (2020)
# Says to replace the cost of last category with cost of category s # Says to replace the cost of last category with cost of category s
start_range = max((t - g.startup_categories[s + 1].delay + 1),1) start_range = max((t - g.startup_categories[s+1].delay + 1), 1)
end_range = min((t - g.startup_categories[s].delay),T-1) end_range = min((t - g.startup_categories[s].delay), T - 1)
for tmp_t in start_range:end_range for tmp_t in start_range:end_range
if (t < tmp_t + DT) || (t >= tmp_t + TC) # the second clause should never be true for s < S if (t < tmp_t + DT) || (t >= tmp_t + TC) # the second clause should never be true for s < S
continue continue
end end
add_to_expression!(model[:obj], add_to_expression!(
downtime_arc[gn,tmp_t,t], model[:obj],
g.startup_categories[s].cost - g.startup_categories[S].cost) downtime_arc[gn, tmp_t, t],
g.startup_categories[s].cost - g.startup_categories[S].cost,
)
end end
end # iterate over startup categories end # iterate over startup categories
end # iterate over time end # iterate over time
end # add_startup_costs_KneOstWat20 end # add_startup_costs_KneOstWat20

6
src/model/formulations/MorLatRam2013/scosts.jl
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@ -51,8 +51,7 @@ function _add_startup_cost_eqs!(
# Equation (55) in Kneuven et al. (2020) # Equation (55) in Kneuven et al. (2020)
eq_startup_choose[gn, t] = @constraint( eq_startup_choose[gn, t] = @constraint(
model, model,
switch_on[gn, t] == switch_on[gn, t] == sum(startup[gn, t, s] for s in 1:S)
sum(startup[gn, t, s] for s in 1:S)
) )
for s in 1:S for s in 1:S
@ -71,7 +70,8 @@ function _add_startup_cost_eqs!(
eq_startup_restrict[gn, t, s] = @constraint( eq_startup_restrict[gn, t, s] = @constraint(
model, model,
startup[gn, t, s] <= startup[gn, t, s] <=
initial_sum + sum(switch_off[gn, i] for i in range if i >= 1) initial_sum +
sum(switch_off[gn, i] for i in range if i >= 1)
) )
end # if s < S (not the last category) end # if s < S (not the last category)

41
src/model/formulations/MorLatRam2013/startstop.jl
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@ -2,7 +2,6 @@
# Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved. # Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
# Released under the modified BSD license. See COPYING.md for more details. # Released under the modified BSD license. See COPYING.md for more details.
""" """
_add_startup_shutdown_limit_eqs!(model::JuMP.Model, g::Unit)::Nothing _add_startup_shutdown_limit_eqs!(model::JuMP.Model, g::Unit)::Nothing
@ -42,26 +41,28 @@ function _add_startup_shutdown_limit_eqs!(model::JuMP.Model, g::Unit)::Nothing
T = model[:instance].time T = model[:instance].time
gi = g.name gi = g.name
for t = 1:T for t in 1:T
## 2020-10-09 amk: added eqn (20) and check of g.min_uptime ## 2020-10-09 amk: added eqn (20) and check of g.min_uptime
if g.min_uptime > 1 && t < T if g.min_uptime > 1 && t < T
# Equation (20) in Kneuven et al. (2020) # Equation (20) in Kneuven et al. (2020)
# UT > 1 required, to guarantee that vars.switch_on[gi, t] and vars.switch_off[gi, t+1] are not both = 1 at the same time # UT > 1 required, to guarantee that vars.switch_on[gi, t] and vars.switch_off[gi, t+1] are not both = 1 at the same time
eq_startstop_limit[gi,t] = eq_startstop_limit[gi, t] = @constraint(
@constraint(model, model,
prod_above[gi, t] + reserve[gi, t] prod_above[gi, t] + reserve[gi, t] <=
<= (g.max_power[t] - g.min_power[t]) * is_on[gi, t] (g.max_power[t] - g.min_power[t]) * is_on[gi, t] -
- max(0, g.max_power[t] - g.startup_limit) * switch_on[gi, t] max(0, g.max_power[t] - g.startup_limit) * switch_on[gi, t] -
- max(0, g.max_power[t] - g.shutdown_limit) * switch_off[gi, t+1]) max(0, g.max_power[t] - g.shutdown_limit) * switch_off[gi, t+1]
)
else else
## Startup limits ## Startup limits
# Equation (21a) in Kneuven et al. (2020) # Equation (21a) in Kneuven et al. (2020)
# Proposed by Morales-España et al. (2013a) # Proposed by Morales-España et al. (2013a)
eqs_startup_limit[gi, t] = eqs_startup_limit[gi, t] = @constraint(
@constraint(model, model,
prod_above[gi, t] + reserve[gi, t] prod_above[gi, t] + reserve[gi, t] <=
<= (g.max_power[t] - g.min_power[t]) * is_on[gi, t] (g.max_power[t] - g.min_power[t]) * is_on[gi, t] -
- max(0, g.max_power[t] - g.startup_limit) * switch_on[gi, t]) max(0, g.max_power[t] - g.startup_limit) * switch_on[gi, t]
)
## Shutdown limits ## Shutdown limits
if t < T if t < T
@ -74,12 +75,14 @@ function _add_startup_shutdown_limit_eqs!(model::JuMP.Model, g::Unit)::Nothing
# amk: if shutdown_limit is the max prod of generator in time period before shutting down, # amk: if shutdown_limit is the max prod of generator in time period before shutting down,
# then it makes sense to count reserves, because otherwise, if reserves ≠ 0, # then it makes sense to count reserves, because otherwise, if reserves ≠ 0,
# then the generator will actually produce more than the limit # then the generator will actually produce more than the limit
eqs.shutdown_limit[gi, t] = eqs.shutdown_limit[gi, t] = @constraint(
@constraint(model, model,
prod_above[gi, t] prod_above[gi, t] +
+ (RESERVES_WHEN_SHUT_DOWN ? reserve[gi, t] : 0.) # amk added (RESERVES_WHEN_SHUT_DOWN ? reserve[gi, t] : 0.0) <=
<= (g.max_power[t] - g.min_power[t]) * is_on[gi, t] (g.max_power[t] - g.min_power[t]) * is_on[gi, t] -
- max(0, g.max_power[t] - g.shutdown_limit) * switch_off[gi, t+1]) max(0, g.max_power[t] - g.shutdown_limit) *
switch_off[gi, t+1]
)
end end
end # check if g.min_uptime > 1 end # check if g.min_uptime > 1
end # loop over time end # loop over time

2
src/model/formulations/NowRom2000/scosts.jl
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@ -16,5 +16,5 @@ function _add_startup_cost_eqs!(
g::Unit, g::Unit,
formulation::MorLatRam2013.StartupCosts, formulation::MorLatRam2013.StartupCosts,
)::Nothing )::Nothing
error("Not implemented.") return error("Not implemented.")
end end

28
src/model/formulations/OstAnjVan2012/ramp.jl
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@ -53,31 +53,33 @@ function _add_ramp_eqs!(
SD = g.shutdown_limit # shutdown rate SD = g.shutdown_limit # shutdown rate
RU = g.ramp_up_limit # ramp up rate RU = g.ramp_up_limit # ramp up rate
RD = g.ramp_down_limit # ramp down rate RD = g.ramp_down_limit # ramp down rate
# TODO check initial conditions, but maybe okay as long as (35) and (36) are also used # TODO check initial conditions, but maybe okay as long as (35) and (36) are also used
for t in 1:model[:instance].time for t in 1:model[:instance].time
Pbar = g.max_power[t] Pbar = g.max_power[t]
#TRD = floor((Pbar - SU)/RD) #TRD = floor((Pbar - SU)/RD)
# TODO check amk changed TRD wrt Kneuven et al. # TODO check amk changed TRD wrt Kneuven et al.
TRD = ceil((Pbar - SD) / RD) # ramp down time TRD = ceil((Pbar - SD) / RD) # ramp down time
if Pbar < 1e-7 if Pbar < 1e-7
# Skip this time period if max power = 0 # Skip this time period if max power = 0
continue continue
end end
if UT >= 1 if UT >= 1
# Equation (37) in Kneuven et al. (2020) # Equation (37) in Kneuven et al. (2020)
KSD = min( TRD, UT-1, T-t-1 ) KSD = min(TRD, UT - 1, T - t - 1)
eq_str_prod_limit[gn, t] = eq_str_prod_limit[gn, t] = @constraint(
@constraint(model, model,
prod_above[gn, t] + g.min_power[t] * is_on[gn, t] prod_above[gn, t] +
+ (RESERVES_WHEN_RAMP_DOWN ? reserve[gn, t] : 0.) # amk added; TODO: should this be RESERVES_WHEN_RAMP_DOWN or RESERVES_WHEN_SHUT_DOWN? g.min_power[t] * is_on[gn, t] +
<= Pbar * is_on[gi, t] (RESERVES_WHEN_RAMP_DOWN ? reserve[gn, t] : 0.0) <=
- sum((Pbar - (SD + i * RD)) * switch_off[gi, t+1+i] Pbar * is_on[gi, t] - sum(
for i in 0:KSD) (Pbar - (SD + i * RD)) * switch_off[gi, t+1+i] for
) i in 0:KSD
)
)
end # check UT >= 1 end # check UT >= 1
end # loop over time end # loop over time
end end

18
src/model/formulations/base/system.jl
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@ -76,19 +76,21 @@ function _add_reserve_eqs!(model::JuMP.Model)::Nothing
shortfall_penalty = instance.shortfall_penalty[t] shortfall_penalty = instance.shortfall_penalty[t]
eq_min_reserve[t] = @constraint( eq_min_reserve[t] = @constraint(
model, model,
sum(model[:reserve][g.name, t] for g in instance.units) sum(model[:reserve][g.name, t] for g in instance.units) + (
+ (shortfall_penalty > 1e-7 ? model[:reserve_shortfall][t] : 0.) shortfall_penalty > 1e-7 ? model[:reserve_shortfall][t] : 0.0
>= instance.reserves.spinning[t] ) >= instance.reserves.spinning[t]
) )
# Account for shortfall contribution to objective # Account for shortfall contribution to objective
if shortfall_penalty > 1e-7 if shortfall_penalty > 1e-7
add_to_expression!(model.obj, add_to_expression!(
shortfall_penalty, model.obj,
model[:reserve_shortfall][t]) shortfall_penalty,
model[:reserve_shortfall][t],
)
else else
# Not added to the model at all # Not added to the model at all
#fix(model.vars.reserve_shortfall[t], 0.; force=true) #fix(model.vars.reserve_shortfall[t], 0.; force=true)
end end
end # loop over time end # loop over time
return return

38
src/model/formulations/base/unit.jl
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@ -57,7 +57,11 @@ _is_initially_on(g::Unit)::Float64 = (g.initial_status > 0 ? 1.0 : 0.0)
Add `:reserve` variable to `model`, fixed to zero if no spinning reserves specified. Add `:reserve` variable to `model`, fixed to zero if no spinning reserves specified.
""" """
function _add_reserve_vars!(model::JuMP.Model, g::Unit, ALWAYS_CREATE_VARS = false)::Nothing function _add_reserve_vars!(
model::JuMP.Model,
g::Unit,
ALWAYS_CREATE_VARS = false,
)::Nothing
reserve = _init(model, :reserve) reserve = _init(model, :reserve)
reserve_shortfall = _init(model, :reserve_shortfall) # for accounting for shortfall penalty in the objective reserve_shortfall = _init(model, :reserve_shortfall) # for accounting for shortfall penalty in the objective
for t in 1:model[:instance].time for t in 1:model[:instance].time
@ -137,9 +141,9 @@ function _add_startup_shutdown_limit_eqs!(model::JuMP.Model, g::Unit)::Nothing
# Generator producing too much to be turned off in the first time period # Generator producing too much to be turned off in the first time period
# (can a binary variable have bounds x = 0?) # (can a binary variable have bounds x = 0?)
#eqs.shutdown_limit[gi, 0] = @constraint(mip, vars.switch_off[gi, 1] <= 0) #eqs.shutdown_limit[gi, 0] = @constraint(mip, vars.switch_off[gi, 1] <= 0)
fix(model.vars.switch_off[gi, 1], 0.; force = true) fix(model.vars.switch_off[gi, 1], 0.0; force = true)
#eq_shutdown_limit[g.name, 0] = #eq_shutdown_limit[g.name, 0] =
#@constraint(model, switch_off[g.name, 1] <= 0) #@constraint(model, switch_off[g.name, 1] <= 0)
end end
if t < T if t < T
eq_shutdown_limit[g.name, t] = @constraint( eq_shutdown_limit[g.name, t] = @constraint(
@ -164,14 +168,16 @@ Variables
function _add_shutdown_cost_eqs!(model::JuMP.Modle, g::Unit)::Nothing function _add_shutdown_cost_eqs!(model::JuMP.Modle, g::Unit)::Nothing
T = model[:instance].time T = model[:instance].time
gi = g.name gi = g.name
for t = 1:T for t in 1:T
shutdown_cost = 0. shutdown_cost = 0.0
if shutdown_cost > 1e-7 if shutdown_cost > 1e-7
# Equation (62) in Kneuven et al. (2020) # Equation (62) in Kneuven et al. (2020)
add_to_expression!(model[:obj], add_to_expression!(
model[:switch_off][gi, t], model[:obj],
shutdown_cost) model[:switch_off][gi, t],
end shutdown_cost,
)
end
end # loop over time end # loop over time
end # _add_shutdown_cost_eqs! end # _add_shutdown_cost_eqs!
@ -256,18 +262,18 @@ function _add_min_uptime_downtime_eqs!(model::JuMP.Model, g::Unit)::Nothing
# Equation (4) in Kneuven et al. (2020) # Equation (4) in Kneuven et al. (2020)
eq_min_uptime[g.name, t] = @constraint( eq_min_uptime[g.name, t] = @constraint(
model, model,
sum(switch_on[g.name, i] for i in (t-g.min_uptime+1):t if i >= 1) sum(switch_on[g.name, i] for i in (t-g.min_uptime+1):t if i >= 1) <= is_on[g.name, t]
<= is_on[g.name, t]
) )
# Minimum down-time # Minimum down-time
# Equation (5) in Kneuven et al. (2020) # Equation (5) in Kneuven et al. (2020)
eq_min_downtime[g.name, t] = @constraint( eq_min_downtime[g.name, t] = @constraint(
model, model,
sum(switch_off[g.name, i] for i in (t-g.min_downtime+1):t if i >= 1) sum(
<= 1 - is_on[g.name, t] switch_off[g.name, i] for i in (t-g.min_downtime+1):t if i >= 1
) <= 1 - is_on[g.name, t]
) )
# Minimum up/down-time for initial periods # Minimum up/down-time for initial periods
# Equations (3a) and (3b) in Kneuven et al. (2020) # Equations (3a) and (3b) in Kneuven et al. (2020)
# (using :switch_on and :switch_off instead of :is_on) # (using :switch_on and :switch_off instead of :is_on)

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