oyurdakul
4 years ago
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# UnitCommitmentFL.jl: Optimization Package for Security-Constrained Unit Commitment
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# Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
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# Released under the modified BSD license. See COPYING.md for more details.
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function _add_flexiramp_vars!(model::JuMP.Model, g::Unit)::Nothing
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upflexiramp = _init(model, :upflexiramp)
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upflexiramp_shortfall = _init(model, :upflexiramp_shortfall)
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mfg=_init(model,:mfg)
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dwflexiramp = _init(model, :dwflexiramp)
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dwflexiramp_shortfall = _init(model, :dwflexiramp_shortfall)
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for t in 1:model[:instance].time
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# maximum feasible generation, \bar{g_{its}} in Wang & Hobbs (2016)
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mfg[g.name,t]=@variable(model, lower_bound = 0)
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if g.provides_flexiramp_reserves[t]
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upflexiramp[g.name, t] = @variable(model) # up-flexiramp, ur_{it} in Wang & Hobbs (2016)
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dwflexiramp[g.name, t] = @variable(model) # down-flexiramp, dr_{it} in Wang & Hobbs (2016)
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else
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upflexiramp[g.name, t] = 0.0
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dwflexiramp[g.name, t] = 0.0
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end
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upflexiramp_shortfall[t] =
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(model[:instance].flexiramp_shortfall_penalty[t] >= 0) ?
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@variable(model, lower_bound = 0) : 0.0
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dwflexiramp_shortfall[t] =
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(model[:instance].flexiramp_shortfall_penalty[t] >= 0) ?
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@variable(model, lower_bound = 0) : 0.0
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end
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return
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end
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function _add_ramp_eqs!(
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model::JuMP.Model,
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g::Unit,
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formulation_prod_vars::Gar1962.ProdVars,
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formulation_ramping::WanHob2016.Ramping,
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formulation_status_vars::Gar1962.StatusVars,
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)::Nothing
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is_initially_on = (g.initial_status > 0)
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SU = g.startup_limit
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SD = g.shutdown_limit
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RU = g.ramp_up_limit
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RD = g.ramp_down_limit
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gn = g.name
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minp=g.min_power
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maxp=g.max_power
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initial_power=g.initial_power
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is_on = model[:is_on]
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prod_above = model[:prod_above]
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upflexiramp=model[:upflexiramp]
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dwflexiramp=model[:dwflexiramp]
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mfg=model[:mfg]
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for t in 1:model[:instance].time
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@constraint(model, prod_above[gn, t] + (is_on[gn,t]*minp[t])
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<=mfg[gn,t]) # Eq. (19) in Wang & Hobbs (2016)
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@constraint(model, mfg[gn,t]<= is_on[gn,t]* maxp[t]) # Eq. (22) in Wang & Hobbs (2016)
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if t!=model[:instance].time
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@constraint(model, minp[t] * (is_on[gn,t+1]+is_on[gn,t]-1) <=
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prod_above[gn, t] - dwflexiramp[gn,t] +(is_on[gn,t]*minp[t])
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) # first inequality of Eq. (20) in Wang & Hobbs (2016)
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@constraint(model, prod_above[gn, t] - dwflexiramp[gn,t] + (is_on[gn,t]*minp[t]) <=
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mfg[gn,t+1]
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+ (maxp[t] * (1-is_on[gn,t+1]))
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) # second inequality of Eq. (20) in Wang & Hobbs (2016)
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@constraint(model, minp[t] * (is_on[gn,t+1]+is_on[gn,t]-1) <=
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prod_above[gn, t] + upflexiramp[gn,t] + (is_on[gn,t]*minp[t])
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) # first inequality of Eq. (21) in Wang & Hobbs (2016)
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@constraint(model, prod_above[gn, t] + upflexiramp[gn,t] +(is_on[gn,t]*minp[t]) <=
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mfg[gn,t+1] + (maxp[t] * (1-is_on[gn,t+1]))
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) # second inequality of Eq. (21) in Wang & Hobbs (2016)
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if t!=1
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@constraint(model, mfg[gn,t]<=prod_above[gn,t-1] + (is_on[gn,t-1]*minp[t])
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+ (RU * is_on[gn,t-1])
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+ (SU*(is_on[gn,t] - is_on[gn,t-1]))
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+ maxp[t] * (1-is_on[gn,t])
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) # Eq. (23) in Wang & Hobbs (2016)
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@constraint(model, (prod_above[gn,t-1] + (is_on[gn,t-1]*minp[t]))
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- (prod_above[gn,t] + (is_on[gn,t]*minp[t]))
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<= RD * is_on[gn,t]
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+ SD * (is_on[gn,t-1] - is_on[gn,t])
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+ maxp[t] * (1-is_on[gn,t-1])
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) # Eq. (25) in Wang & Hobbs (2016)
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else
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@constraint(model, mfg[gn,t]<=initial_power
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+ (RU * is_initially_on)
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+ (SU*(is_on[gn,t] - is_initially_on))
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+ maxp[t] * (1-is_on[gn,t])
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) # Eq. (23) in Wang & Hobbs (2016) for the first time period
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@constraint(model, initial_power
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- (prod_above[gn,t] + (is_on[gn,t]*minp[t]))
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<= RD * is_on[gn,t]
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+ SD * (is_initially_on - is_on[gn,t])
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+ maxp[t] * (1-is_initially_on)
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) # Eq. (25) in Wang & Hobbs (2016) for the first time period
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end
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@constraint(model, mfg[gn,t]<=
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(SD*(is_on[gn,t] - is_on[gn,t+1]))
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+ (maxp[t] * is_on[gn,t+1])
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) # Eq. (24) in Wang & Hobbs (2016)
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@constraint(model, -RD * is_on[gn,t+1]
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-SD * (is_on[gn,t]-is_on[gn,t+1])
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-maxp[t] * (1-is_on[gn,t])
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<= upflexiramp[gn,t]
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) # first inequality of Eq. (26) in Wang & Hobbs (2016)
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@constraint(model, upflexiramp[gn,t] <=
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RU * is_on[gn,t]
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+ SU * (is_on[gn,t+1]-is_on[gn,t])
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+ maxp[t] * (1-is_on[gn,t+1])
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) # second inequality of Eq. (26) in Wang & Hobbs (2016)
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@constraint(model, -RU * is_on[gn,t]
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-SU * (is_on[gn,t+1]-is_on[gn,t])
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-maxp[t] * (1-is_on[gn,t+1])
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<= dwflexiramp[gn,t]
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) # first inequality of Eq. (27) in Wang & Hobbs (2016)
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@constraint(model, dwflexiramp[gn,t] <=
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RD * is_on[gn,t+1]
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+ SD * (is_on[gn,t]-is_on[gn,t+1])
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+ maxp[t] * (1-is_on[gn,t])
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) # second inequality of Eq. (27) in Wang & Hobbs (2016)
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@constraint(model, -maxp[t] * is_on[gn,t]
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+minp[t] * is_on[gn,t+1]
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<= upflexiramp[gn,t]
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) # first inequality of Eq. (28) in Wang & Hobbs (2016)
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@constraint(model, upflexiramp[gn,t] <=
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maxp[t] * is_on[gn,t+1]
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) # second inequality of Eq. (28) in Wang & Hobbs (2016)
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@constraint(model, -maxp[t] * is_on[gn,t+1]
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<= dwflexiramp[gn,t]
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) # first inequality of Eq. (29) in Wang & Hobbs (2016)
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@constraint(model, dwflexiramp[gn,t] <=
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(maxp[t] * is_on[gn,t])
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-(minp[t] * is_on[gn,t+1])
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) # second inequality of Eq. (29) in Wang & Hobbs (2016)
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else
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@constraint(model, mfg[gn,t]<=prod_above[gn,t-1] + (is_on[gn,t-1]*minp[t])
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+ (RU * is_on[gn,t-1])
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+ (SU*(is_on[gn,t] - is_on[gn,t-1]))
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+ maxp[t] * (1-is_on[gn,t])
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) # Eq. (23) in Wang & Hobbs (2016) for the last time period
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@constraint(model, (prod_above[gn,t-1] + (is_on[gn,t-1]*minp[t]))
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- (prod_above[gn,t] + (is_on[gn,t]*minp[t]))
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<= RD * is_on[gn,t]
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+ SD * (is_on[gn,t-1] - is_on[gn,t])
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+ maxp[t] * (1-is_on[gn,t-1])
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) # Eq. (25) in Wang & Hobbs (2016) for the last time period
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end
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end
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end
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@ -0,0 +1,18 @@
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# UnitCommitmentFL.jl: Optimization Package for Security-Constrained Unit Commitment
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# Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
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# Released under the modified BSD license. See COPYING.md for more details.
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"""
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Formulation described in:
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B. Wang and B. F. Hobbs, "Real-Time Markets for Flexiramp: A Stochastic
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Unit Commitment-Based Analysis," in IEEE Transactions on Power Systems,
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vol. 31, no. 2, pp. 846-860, March 2016, doi: 10.1109/TPWRS.2015.2411268.
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"""
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module WanHob2016
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import ..RampingFormulation
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struct Ramping <: RampingFormulation end
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end
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