Added comments on formulations, added start/stop constraints into MorLatRam and GenMorRam, added ability to add shortfall penalty.
Aleksandr Kazachkov
4 years ago
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7a1b6f0f55
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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 Kneuven et al. (2020).
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Variables
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---
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* :is_on
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* :prod_above
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* :reserve
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* :switch_on
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* :switch_off
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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!(model::JuMP.Model, g::Unit)::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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fix(switch_off[gi, 1], 0.; force = true)
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end
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for t = 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 Kneuven et al. (2020)
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eqs.startstop_limit[gi,t] =
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@constraint(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 ? max(0, g.max_power[t] - g.shutdown_limit) * switch_off[gi, t+1] : 0.)
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)
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else
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## Startup limits
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# Equation (23a) in Kneuven et al. (2020)
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eqs.startup_limit[gi, t] =
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@constraint(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 ? max(0, g.startup_limit - g.shutdown_limit) * switch_off[gi, t+1] : 0.)
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)
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## Shutdown limits
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if t < T
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# Equation (23b) in Kneuven et al. (2020)
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eqs.shutdown_limit[gi, t] =
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@constraint(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 ? max(0, g.max_power[t] - g.shutdown_limit) * switch_off[gi, t+1] : 0.)
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- max(0, g.shutdown_limit - g.startup_limit) * switch_on[gi, t])
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end
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end # check if g.min_uptime > 1
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end # loop over time
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end # _add_startup_shutdown_limit_eqs!
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@ -0,0 +1,86 @@
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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 Kneuven et al. (2020).
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Variables
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---
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* :is_on
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* :prod_above
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* :reserve
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* :switch_on
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* :switch_off
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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!(model::JuMP.Model, g::Unit)::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 = 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 Kneuven 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] =
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@constraint(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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else
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## Startup limits
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# Equation (21a) in Kneuven et al. (2020)
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# Proposed by Morales-España et al. (2013a)
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eqs_startup_limit[gi, t] =
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@constraint(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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## Shutdown limits
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if t < T
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# Equation (21b) in Kneuven 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] =
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@constraint(model,
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prod_above[gi, t]
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+ (RESERVES_WHEN_SHUT_DOWN ? reserve[gi, t] : 0.) # amk added
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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) * switch_off[gi, t+1])
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end
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end # check if g.min_uptime > 1
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end # loop over time
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end # _add_startup_shutdown_limit_eqs!
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@ -0,0 +1,20 @@
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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_cost_eqs!
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Based on Nowak and Römisch, 2000.
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Introduces auxiliary startup cost variable, c_g^SU(t) for each time period,
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and uses startup status variable, u_g(t);
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there are exponentially many facets in this space,
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but there is a linear-time separation algorithm (Brandenburg et al., 2017).
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"""
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function _add_startup_cost_eqs!(
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model::JuMP.Model,
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g::Unit,
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formulation::MorLatRam2013.StartupCosts,
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)::Nothing
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error("Not implemented.")
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end
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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_ramp_eqs!
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Ensure constraints on ramping are met.
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Based on Ostrowski, Anjos, Vannelli (2012).
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Eqn (37) in Kneuven et al. (2020).
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Variables
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---
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* :is_on
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* :prod_above
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* :reserve
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Constraints
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---
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* :eq_str_prod_limit
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"""
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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::MorLatRam2013.Ramping,
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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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is_initially_on = _is_initially_on(g)
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gn = g.name
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eq_str_prod_limit = _init(model, :eq_str_prod_limit)
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# Variables that we need
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reserve = model[:reserve]
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# Gar1962.ProdVars
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prod_above = model[:prod_above]
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# Gar1962.StatusVars
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is_on = model[:is_on]
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switch_off = model[:switch_off]
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# The following are the same for generator g across all time periods
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UT = g.min_uptime
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SU = g.startup_limit # startup rate
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SD = g.shutdown_limit # shutdown rate
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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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# TODO check initial conditions, but maybe okay as long as (35) and (36) are also used
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for t in 1:model[:instance].time
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Pbar = g.max_power[t]
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#TRD = floor((Pbar - SU)/RD)
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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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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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if UT >= 1
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# Equation (37) in Kneuven et al. (2020)
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KSD = min( TRD, UT-1, T-t-1 )
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eq_str_prod_limit[gn, t] =
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@constraint(model,
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prod_above[gn, t] + g.min_power[t] * is_on[gn, t]
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+ (RESERVES_WHEN_RAMP_DOWN ? reserve[gn, t] : 0.) # amk added; TODO: should this be RESERVES_WHEN_RAMP_DOWN or RESERVES_WHEN_SHUT_DOWN?
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<= Pbar * is_on[gi, t]
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- sum((Pbar - (SD + i * RD)) * switch_off[gi, t+1+i]
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for i in 0:KSD)
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)
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end # check UT >= 1
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end # loop over time
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end
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