src/model/formulations/Gar1962/prod.jl

# UnitCommitment.jl: Optimization Package for Security-Constrained Unit Commitment
# Copyright (C) 2020, UChicago Argonne, LLC. All rights reserved.
# Released under the modified BSD license. See COPYING.md for more details.

function _add_production_vars!(
    model::JuMP.Model,
    g::ThermalUnit,
    formulation_prod_vars::Gar1962.ProdVars,
    sc::UnitCommitmentScenario,
)::Nothing
    prod_above = _init(model, :prod_above)
    segprod = _init(model, :segprod)
    for t in 1:model[:instance].time
        for k in 1:length(g.cost_segments)
            segprod[sc.name, g.name, t, k] = @variable(model, lower_bound = 0, base_name =  "segprod_$(sc.name)_$(g.name)_$(t)_$(k)")
        end
        prod_above[sc.name, g.name, t] = @variable(model, lower_bound = 0, base_name =  "prod_above_$(sc.name)_$(g.name)_$(t)")
    end
    return
end

function _add_production_limit_eqs!(
    model::JuMP.Model,
    g::ThermalUnit,
    formulation_prod_vars::Gar1962.ProdVars,
    # [1]
    formulation_power_trajectories::Nothing,
    sc::UnitCommitmentScenario,
)::Nothing
    eq_prod_limit = _init(model, :eq_prod_limit)
    is_on = model[:is_on]
    prod_above = model[:prod_above]
    reserve = _total_reserves(model, g, sc)
    gn = g.name
    for t in 1:model[:instance].time
        # Objective function terms for production costs
        # Part of (69) of Kneuven et al. (2020) as C^R_g * u_g(t) term

        # Production limit
        # Equation (18) in Kneuven et al. (2020)
        #   as \bar{p}_g(t) \le \bar{P}_g u_g(t)
        # amk: this is a weaker version of (20) and (21) in Kneuven et al. (2020)
        #      but keeping it here in case those are not present
        power_diff = max(g.max_power[t], 0.0) - max(g.min_power[t], 0.0)
        if power_diff < 1e-7
            power_diff = 0.0
        end
        eq_prod_limit[sc.name, gn, t] = @constraint(
            model,
            prod_above[sc.name, gn, t] + reserve[t] <=
            power_diff * is_on[gn, t]
        )
    end
    return
end

# [2]
function _add_production_limit_eqs!(
    model::JuMP.Model,
    g::ThermalUnit,
    formulation_prod_vars::Gar1962.ProdVars,
    formulation_power_trajectories::ArrCon2004.PowerTrajectories,
    sc::UnitCommitmentScenario
)::Nothing
    if isempty(g.startup_curve) || isempty(g.shutdown_curve)
        eq_prod_limit = _init(model, :eq_prod_limit)
        is_on         = model[:is_on]
        prod_above    = model[:prod_above]
        reserve       = _total_reserves(model, g, sc)
        gn            = g.name
        for t in 1:model[:instance].time
            power_diff = max(g.max_power[t], 0.0) - max(g.min_power[t], 0.0)
            power_diff < 1e-7 && (power_diff = 0.0)
            eq_prod_limit[sc.name, gn, t] = @constraint(
                model,
                prod_above[sc.name, gn, t] + reserve[t] <=
                power_diff * is_on[gn, t]
            )
        end
        return
    end
    prod_above = model[:prod_above]
    for t in 1:model[:instance].time
        set_lower_bound(prod_above[sc.name, g.name, t], -g.min_power[t])
    end

    eq_prod_limit = _init(model, :eq_prod_limit)
    is_on         = model[:is_on]
    switch_on     = model[:switch_on]
    switch_off    = model[:switch_off]
    reserve       = _total_reserves(model, g, sc)
    gn            = g.name
    T             = model[:instance].time

    UD = length(g.startup_curve)
    DD = length(g.shutdown_curve)
    P_U = g.startup_curve
    P_D = g.shutdown_curve

    for t in 1:T
        Pmin = g.min_power[t]
        Pmax = g.max_power[t]
        power_diff = max(Pmax, 0.0) - max(Pmin, 0.0)
        power_diff < 1e-7 && (power_diff = 0.0)

        # Σ y(t-i+1)
        sum_y = @expression(model,
            sum(switch_on[gn, t-i+1] for i in 1:UD if t-i+1 >= 1; init=0))

        # Σ z(t+i)
        sum_z = @expression(model,
            sum(switch_off[gn, t+i] for i in 1:DD if t+i <= T; init=0))

        # Σ (P_U[i]-Pmin)·y(t-i+1)
        su_above = @expression(model,
            sum((P_U[i] - Pmin) * switch_on[gn, t-i+1]
                for i in 1:UD if t-i+1 >= 1; init=0.0))

        # Σ (P_D[i]-Pmin)·z(t+DD-i+1)
        sd_above = @expression(model,
            sum((P_D[i] - Pmin) * switch_off[gn, t+DD-i+1]
                for i in 1:DD if t+DD-i+1 >= 1 && t+DD-i+1 <= T; init=0.0))

        # [3]约束(3)(4)
        eq_prod_limit[sc.name, gn, t] = @constraint(
            model,
            prod_above[sc.name, gn, t] + reserve[t] <=
                su_above +
                sd_above +
                power_diff * (is_on[gn, t] - sum_y - sum_z)
        )
    end
    return
end