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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_ramp_eqs!(
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model::JuMP.Model,
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g::Unit,
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::Gar1962.ProdVars,
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::WanHob2016.Ramping,
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::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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if length(g.reserves) > 1
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error("Each generator may only provide one flexiramp reserve")
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end
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for r in g.reserves
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if r.type !== "flexiramp"
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error("This formulation only supports flexiramp reserves, not $(r.type)")
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end
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rn = r.name
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for t in 1:model[:instance].time
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@constraint(
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model,
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prod_above[gn, t] + (is_on[gn, t] * minp[t]) <= mfg[rn, gn, t]
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) # Eq. (19) in Wang & Hobbs (2016)
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@constraint(model, mfg[rn, 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(
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model,
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minp[t] * (is_on[gn, t+1] + is_on[gn, t] - 1) <=
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prod_above[gn, t] - dwflexiramp[rn, gn, t] +
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(is_on[gn, t] * minp[t])
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) # first inequality of Eq. (20) in Wang & Hobbs (2016)
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@constraint(
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model,
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prod_above[gn, t] - dwflexiramp[rn, gn, t] +
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(is_on[gn, t] * minp[t]) <=
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mfg[rn, gn, t+1] + (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(
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model,
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minp[t] * (is_on[gn, t+1] + is_on[gn, t] - 1) <=
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prod_above[gn, t] +
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upflexiramp[rn, gn, t] +
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(is_on[gn, t] * minp[t])
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) # first inequality of Eq. (21) in Wang & Hobbs (2016)
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@constraint(
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model,
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prod_above[gn, t] +
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upflexiramp[rn, gn, t] +
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(is_on[gn, t] * minp[t]) <=
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mfg[rn, 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(
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model,
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mfg[rn, gn, t] <=
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prod_above[gn, t-1] +
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(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(
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model,
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(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(
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model,
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mfg[rn, gn, t] <=
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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(
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model,
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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(
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model,
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mfg[rn, 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(
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model,
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-RD * is_on[gn, t+1] - SD * (is_on[gn, t] - is_on[gn, t+1]) -
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maxp[t] * (1 - is_on[gn, t]) <= upflexiramp[rn, gn, t]
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) # first inequality of Eq. (26) in Wang & Hobbs (2016)
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@constraint(
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model,
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upflexiramp[rn, 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(
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model,
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-RU * is_on[gn, t] - SU * (is_on[gn, t+1] - is_on[gn, t]) -
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maxp[t] * (1 - is_on[gn, t+1]) <= dwflexiramp[rn, gn, t]
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) # first inequality of Eq. (27) in Wang & Hobbs (2016)
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@constraint(
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model,
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dwflexiramp[rn, 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(
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model,
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-maxp[t] * is_on[gn, t] + minp[t] * is_on[gn, t+1] <=
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upflexiramp[rn, gn, t]
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) # first inequality of Eq. (28) in Wang & Hobbs (2016)
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@constraint(model, upflexiramp[rn, gn, t] <= maxp[t] * is_on[gn, t+1]) # second inequality of Eq. (28) in Wang & Hobbs (2016)
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@constraint(model, -maxp[t] * is_on[gn, t+1] <= dwflexiramp[rn, gn, t]) # first inequality of Eq. (29) in Wang & Hobbs (2016)
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@constraint(
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model,
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dwflexiramp[rn, gn, t] <=
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(maxp[t] * is_on[gn, t]) - (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(
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model,
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mfg[rn, gn, t] <=
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prod_above[gn, t-1] +
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(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(
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model,
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(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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end
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@ -0,0 +1,17 @@
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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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