Aleksandr Kazachkov
4 years ago
parent
5afb2363af
commit
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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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_add_startup_shutdown_limit_eqs!(model::JuMP.Model, g::Unit)::Nothing
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Startup and shutdown limits from Gentile et al. (2017).
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Eqns. (20), (23a), and (23b) in Knueven et al. (2020).
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Creates constraints `eq_startstop_limit`, `eq_startup_limit`, and `eq_shutdown_limit`
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using variables `Gar1962.StatusVars`, `prod_above` from `Gar1962.ProdVars`, and `reserve`.
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Constraints
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---
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* `eq_startstop_limit`
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* `eq_startup_limit`
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* `eq_shutdown_limit`
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"""
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function _add_startup_shutdown_limit_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_status_vars::Gar1962.StatusVars,
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)::Nothing
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# TODO: Move upper case constants to model[:instance]
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RESERVES_WHEN_START_UP = true
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RESERVES_WHEN_RAMP_UP = true
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RESERVES_WHEN_RAMP_DOWN = true
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RESERVES_WHEN_SHUT_DOWN = true
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eq_startstop_limit = _init(model, :eq_startstop_limit)
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eq_shutdown_limit = _init(model, :eq_shutdown_limit)
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eq_startup_limit = _init(model, :eq_startup_limit)
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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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T = model[:instance].time
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gi = g.name
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if g.initial_power > g.shutdown_limit
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#eqs.shutdown_limit[gi, 0] = @constraint(mip, vars.switch_off[gi, 1] <= 0)
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if formulation_status_vars.always_create_vars
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fix(switch_off[gi, 1], 0.0; force = true)
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@constraint(mip, vars.switch_off[gi, 1] <= 0)
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else
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switch_off[gi, 1] = 0.0
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end
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end
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for t in 1:T
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## 2020-10-09 amk: added eqn (20) and check of g.min_uptime
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# Not present in (23) in Kneueven et al.
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if g.min_uptime > 1
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# Equation (20) in Knueven et al. (2020)
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eqs.startstop_limit[gi, t] = @constraint(
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model,
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prod_above[gi, t] + reserve[gi, t] <=
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(g.max_power[t] - g.min_power[t]) * is_on[gi, t] -
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max(0, g.max_power[t] - g.startup_limit) * switch_on[gi, t] - (
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t < T ?
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max(0, g.max_power[t] - g.shutdown_limit) *
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switch_off[gi, t+1] : 0.0
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)
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)
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else
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## Startup limits
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# Equation (23a) in Knueven et al. (2020)
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eqs.startup_limit[gi, t] = @constraint(
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model,
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prod_above[gi, t] + reserve[gi, t] <=
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(g.max_power[t] - g.min_power[t]) * is_on[gi, t] -
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max(0, g.max_power[t] - g.startup_limit) * switch_on[gi, t] - (
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t < T ?
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max(0, g.startup_limit - g.shutdown_limit) *
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switch_off[gi, t+1] : 0.0
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)
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)
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## Shutdown limits
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if t < T
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# Equation (23b) in Knueven et al. (2020)
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eqs.shutdown_limit[gi, t] = @constraint(
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model,
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prod_above[gi, t] + reserve[gi, t] <=
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(g.max_power[t] - g.min_power[t]) * xis_on[gi, t] - (
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t < T ?
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max(0, g.max_power[t] - g.shutdown_limit) *
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switch_off[gi, t+1] : 0.0
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) -
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max(0, g.shutdown_limit - g.startup_limit) *
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switch_on[gi, t]
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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 +1,89 @@
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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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_add_startup_shutdown_limit_eqs!(model::JuMP.Model, g::Unit)::Nothing
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Startup and shutdown limits from Morales-España et al. (2013a).
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Eqns. (20), (21a), and (21b) in Knueven et al. (2020).
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Uses variable `prod_above` from `Gar1962.ProdVars`, the variables in `Gar1962.StatusVars`, and `reserve`
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to generate constraints below.
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Constraints
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---
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* :eq_startstop_limit
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* :eq_startup_limit
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* :eq_shutdown_limit
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"""
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function _add_startup_shutdown_limit_eqs!(
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model::JuMP.Model,
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g::Unit,
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formulation_status_vars::Gar1962.StatusVars,
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formulation_prod_vars::Gar1962.ProdVars,
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)::Nothing
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# TODO: Move upper case constants to model[:instance]
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RESERVES_WHEN_START_UP = true
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RESERVES_WHEN_RAMP_UP = true
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RESERVES_WHEN_RAMP_DOWN = true
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RESERVES_WHEN_SHUT_DOWN = true
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eq_startstop_limit = _init(model, :eq_startstop_limit)
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eq_shutdown_limit = _init(model, :eq_shutdown_limit)
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eq_startup_limit = _init(model, :eq_startup_limit)
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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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T = model[:instance].time
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gi = g.name
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for t in 1:T
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## 2020-10-09 amk: added eqn (20) and check of g.min_uptime
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if g.min_uptime > 1 && t < T
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# Equation (20) in Knueven et al. (2020)
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# 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
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eq_startstop_limit[gi, t] = @constraint(
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model,
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prod_above[gi, t] + reserve[gi, t] <=
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(g.max_power[t] - g.min_power[t]) * is_on[gi, t] -
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max(0, g.max_power[t] - g.startup_limit) * switch_on[gi, t] -
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max(0, g.max_power[t] - g.shutdown_limit) * switch_off[gi, t+1]
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)
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else
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## Startup limits
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# Equation (21a) in Knueven et al. (2020)
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# Proposed by Morales-España et al. (2013a)
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eqs_startup_limit[gi, t] = @constraint(
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model,
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prod_above[gi, t] + reserve[gi, t] <=
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(g.max_power[t] - g.min_power[t]) * is_on[gi, t] -
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max(0, g.max_power[t] - g.startup_limit) * switch_on[gi, t]
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)
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## Shutdown limits
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if t < T
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# Equation (21b) in Knueven et al. (2020)
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# TODO different from what was in previous model, due to reserve variable
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# ax: ideally should have reserve_up and reserve_down variables
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# i.e., the generator should be able to increase/decrease production as specified
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# (this is a heuristic for a "robust" solution,
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# in case there is an outage or a surge, and flow has to be redirected)
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# amk: if shutdown_limit is the max prod of generator in time period before shutting down,
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# then it makes sense to count reserves, because otherwise, if reserves ≠ 0,
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# then the generator will actually produce more than the limit
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eqs.shutdown_limit[gi, t] = @constraint(
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model,
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prod_above[gi, t] +
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(RESERVES_WHEN_SHUT_DOWN ? reserve[gi, t] : 0.0) <=
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(g.max_power[t] - g.min_power[t]) * is_on[gi, t] -
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max(0, g.max_power[t] - g.shutdown_limit) *
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switch_off[gi, t+1]
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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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