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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::PanGua16,
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)::Nothing
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# TODO: Move upper case constants to model[:instance]
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RESERVES_WHEN_SHUT_DOWN = true
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gn = g.name
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is_on = model[:is_on]
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prod_above = model[:prod_above]
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reserve = model[:reserve]
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switch_off = model[:switch_off]
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switch_on = model[:switch_on]
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eq_str_prod_limit = _init(model, :eq_str_prod_limit)
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eq_prod_limit_ramp_up_extra_period =
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_init(model, :eq_prod_limit_ramp_up_extra_period)
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eq_prod_limit_shutdown_trajectory =
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_init(model, :eq_prod_limit_shutdown_trajectory)
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UT = g.min_uptime
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SU = g.startup_limit # startup rate, i.e., max production right after startup
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SD = g.shutdown_limit # shutdown rate, i.e., max production right before shutdown
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RU = g.ramp_up_limit # ramp up rate
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RD = g.ramp_down_limit # ramp down rate
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T = model[:instance].time
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for t in 1:T
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Pbar = g.max_power[t]
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if Pbar < 1e-7
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# Skip this time period if max power = 0
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continue
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end
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#TRD = floor((Pbar - SU) / RD) # ramp down time
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# TODO check amk changed TRD wrt Kneuven et al.
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TRD = ceil((Pbar - SD) / RD) # ramp down time
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TRU = floor((Pbar - SU) / RU) # ramp up time, can be negative if Pbar < SU
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# TODO check initial time periods: what if generator has been running for x periods?
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# But maybe ok as long as (35) and (36) are also used...
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if UT > 1
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# Equation (38) in Kneuven et al. (2020)
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# Generalization of (20)
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# Necessary that if any of the switch_on = 1 in the sum,
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# then switch_off[gn, t+1] = 0
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eq_str_prod_limit[gn, t] = @constraint(
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model,
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prod_above[gn, t] +
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g.min_power[t] * is_on[gn, t] +
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reserve[gn, t] <=
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Pbar * is_on[gn, t] -
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(t < T ? (Pbar - SD) * switch_off[gn, t+1] : 0.0) - sum(
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(Pbar - (SU + i * RU)) * switch_on[gn, t-i] for
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i in 0:min(UT - 2, TRU, t - 1)
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)
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)
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if UT - 2 < TRU
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# Equation (40) in Kneuven et al. (2020)
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# Covers an additional time period of the ramp-up trajectory, compared to (38)
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eq_prod_limit_ramp_up_extra_period[gn, t] = @constraint(
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model,
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prod_above[gn, t] +
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g.min_power[t] * is_on[gn, t] +
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reserve[gn, t] <=
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Pbar * is_on[gn, t] - sum(
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(Pbar - (SU + i * RU)) * switch_on[gn, t-i] for
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i in 0:min(UT - 1, TRU, t - 1)
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)
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)
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end
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# Add in shutdown trajectory if KSD >= 0 (else this is dominated by (38))
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KSD = min(TRD, UT - 1, T - t - 1)
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if KSD > 0
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KSU = min(TRU, UT - 2 - KSD, t - 1)
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# Equation (41) in Kneuven et al. (2020)
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eq_prod_limit_shutdown_trajectory[gn, t] = @constraint(
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model,
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prod_above[gn, t] +
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g.min_power[t] * is_on[gn, t] +
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(RESERVES_WHEN_SHUT_DOWN ? reserve[gn, t] : 0.0) <=
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Pbar * is_on[gn, t] - sum(
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(Pbar - (SD + i * RD)) * switch_off[gn, t+1+i] for
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i in 0:KSD
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) - sum(
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(Pbar - (SU + i * RU)) * switch_on[gn, t-i] for
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i in 0:KSU
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) - (
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(KSU >= TRU || KSU > t - 2) ? 0.0 :
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max(0, (SU + (KSU + 1) * RU) - (SD + TRD * RD)) *
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switch_on[gn, t-(KSU+1)]
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)
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)
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end
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end
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end
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end
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@ -0,0 +1,11 @@
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# UnitCommitment.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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Pan, K., & Guan, Y. (2016). Strong formulations for multistage stochastic
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self-scheduling unit commitment. Operations Research, 64(6), 1482-1498.
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"""
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struct PanGua16 <: RampingFormulation end
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Reference in new issue