UnitCommitment.jl/src/model/formulations/WanHob2016/ramp.jl

# UnitCommitmentFL.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_flexiramp_vars!(model::JuMP.Model, g::Unit)::Nothing
    upflexiramp = _init(model, :upflexiramp)
    upflexiramp_shortfall = _init(model, :upflexiramp_shortfall)
    mfg = _init(model, :mfg)
    dwflexiramp = _init(model, :dwflexiramp)
    dwflexiramp_shortfall = _init(model, :dwflexiramp_shortfall)
    for t in 1:model[:instance].time
        # maximum feasible generation, \bar{g_{its}} in Wang & Hobbs (2016)
        mfg[g.name, t] = @variable(model, lower_bound = 0)
        if g.provides_flexiramp_reserves[t]
            upflexiramp[g.name, t] = @variable(model) # up-flexiramp, ur_{it} in Wang & Hobbs (2016)
            dwflexiramp[g.name, t] = @variable(model) # down-flexiramp, dr_{it} in Wang & Hobbs (2016)
        else
            upflexiramp[g.name, t] = 0.0
            dwflexiramp[g.name, t] = 0.0
        end
        upflexiramp_shortfall[t] =
            (model[:instance].flexiramp_shortfall_penalty[t] >= 0) ?
            @variable(model, lower_bound = 0) : 0.0
        dwflexiramp_shortfall[t] =
            (model[:instance].flexiramp_shortfall_penalty[t] >= 0) ?
            @variable(model, lower_bound = 0) : 0.0
    end
    return
end

function _add_ramp_eqs!(
    model::JuMP.Model,
    g::Unit,
    formulation_prod_vars::Gar1962.ProdVars,
    formulation_ramping::WanHob2016.Ramping,
    formulation_status_vars::Gar1962.StatusVars,
)::Nothing
    is_initially_on = (g.initial_status > 0)
    SU = g.startup_limit
    SD = g.shutdown_limit
    RU = g.ramp_up_limit
    RD = g.ramp_down_limit
    gn = g.name
    minp = g.min_power
    maxp = g.max_power
    initial_power = g.initial_power

    is_on = model[:is_on]
    prod_above = model[:prod_above]
    upflexiramp = model[:upflexiramp]
    dwflexiramp = model[:dwflexiramp]
    mfg = model[:mfg]

    for t in 1:model[:instance].time
        @constraint(
            model,
            prod_above[gn, t] + (is_on[gn, t] * minp[t]) <= mfg[gn, t]
        ) # Eq. (19) in Wang & Hobbs (2016)
        @constraint(model, mfg[gn, t] <= is_on[gn, t] * maxp[t]) # Eq. (22) in Wang & Hobbs (2016)
        if t != model[:instance].time
            @constraint(
                model,
                minp[t] * (is_on[gn, t+1] + is_on[gn, t] - 1) <=
                prod_above[gn, t] - dwflexiramp[gn, t] +
                (is_on[gn, t] * minp[t])
            ) # first inequality of Eq. (20) in Wang & Hobbs (2016)
            @constraint(
                model,
                prod_above[gn, t] - dwflexiramp[gn, t] +
                (is_on[gn, t] * minp[t]) <=
                mfg[gn, t+1] + (maxp[t] * (1 - is_on[gn, t+1]))
            ) # second inequality of Eq. (20) in Wang & Hobbs (2016)
            @constraint(
                model,
                minp[t] * (is_on[gn, t+1] + is_on[gn, t] - 1) <=
                prod_above[gn, t] +
                upflexiramp[gn, t] +
                (is_on[gn, t] * minp[t])
            ) # first inequality of Eq. (21) in Wang & Hobbs (2016)
            @constraint(
                model,
                prod_above[gn, t] +
                upflexiramp[gn, t] +
                (is_on[gn, t] * minp[t]) <=
                mfg[gn, t+1] + (maxp[t] * (1 - is_on[gn, t+1]))
            ) # second inequality of Eq. (21) in Wang & Hobbs (2016)
            if t != 1
                @constraint(
                    model,
                    mfg[gn, t] <=
                    prod_above[gn, t-1] +
                    (is_on[gn, t-1] * minp[t]) +
                    (RU * is_on[gn, t-1]) +
                    (SU * (is_on[gn, t] - is_on[gn, t-1])) +
                    maxp[t] * (1 - is_on[gn, t])
                ) # Eq. (23) in Wang & Hobbs (2016)
                @constraint(
                    model,
                    (prod_above[gn, t-1] + (is_on[gn, t-1] * minp[t])) -
                    (prod_above[gn, t] + (is_on[gn, t] * minp[t])) <=
                    RD * is_on[gn, t] +
                    SD * (is_on[gn, t-1] - is_on[gn, t]) +
                    maxp[t] * (1 - is_on[gn, t-1])
                ) # Eq. (25) in Wang & Hobbs (2016)
            else
                @constraint(
                    model,
                    mfg[gn, t] <=
                    initial_power +
                    (RU * is_initially_on) +
                    (SU * (is_on[gn, t] - is_initially_on)) +
                    maxp[t] * (1 - is_on[gn, t])
                ) # Eq. (23) in Wang & Hobbs (2016) for the first time period
                @constraint(
                    model,
                    initial_power -
                    (prod_above[gn, t] + (is_on[gn, t] * minp[t])) <=
                    RD * is_on[gn, t] +
                    SD * (is_initially_on - is_on[gn, t]) +
                    maxp[t] * (1 - is_initially_on)
                ) # Eq. (25) in Wang & Hobbs (2016) for the first time period
            end
            @constraint(
                model,
                mfg[gn, t] <=
                (SD * (is_on[gn, t] - is_on[gn, t+1])) +
                (maxp[t] * is_on[gn, t+1])
            ) # Eq. (24) in Wang & Hobbs (2016)
            @constraint(
                model,
                -RD * is_on[gn, t+1] - SD * (is_on[gn, t] - is_on[gn, t+1]) -
                maxp[t] * (1 - is_on[gn, t]) <= upflexiramp[gn, t]
            ) # first inequality of Eq. (26) in Wang & Hobbs (2016)
            @constraint(
                model,
                upflexiramp[gn, t] <=
                RU * is_on[gn, t] +
                SU * (is_on[gn, t+1] - is_on[gn, t]) +
                maxp[t] * (1 - is_on[gn, t+1])
            ) # second inequality of Eq. (26) in Wang & Hobbs (2016)
            @constraint(
                model,
                -RU * is_on[gn, t] - SU * (is_on[gn, t+1] - is_on[gn, t]) -
                maxp[t] * (1 - is_on[gn, t+1]) <= dwflexiramp[gn, t]
            ) # first inequality of Eq. (27) in Wang & Hobbs (2016)
            @constraint(
                model,
                dwflexiramp[gn, t] <=
                RD * is_on[gn, t+1] +
                SD * (is_on[gn, t] - is_on[gn, t+1]) +
                maxp[t] * (1 - is_on[gn, t])
            ) # second inequality of Eq. (27) in Wang & Hobbs (2016)
            @constraint(
                model,
                -maxp[t] * is_on[gn, t] + minp[t] * is_on[gn, t+1] <=
                upflexiramp[gn, t]
            ) # first inequality of Eq. (28) in Wang & Hobbs (2016)
            @constraint(model, upflexiramp[gn, t] <= maxp[t] * is_on[gn, t+1]) # second inequality of Eq. (28) in Wang & Hobbs (2016)
            @constraint(model, -maxp[t] * is_on[gn, t+1] <= dwflexiramp[gn, t]) # first inequality of Eq. (29) in Wang & Hobbs (2016)
            @constraint(
                model,
                dwflexiramp[gn, t] <=
                (maxp[t] * is_on[gn, t]) - (minp[t] * is_on[gn, t+1])
            ) # second inequality of Eq. (29) in Wang & Hobbs (2016)
        else
            @constraint(
                model,
                mfg[gn, t] <=
                prod_above[gn, t-1] +
                (is_on[gn, t-1] * minp[t]) +
                (RU * is_on[gn, t-1]) +
                (SU * (is_on[gn, t] - is_on[gn, t-1])) +
                maxp[t] * (1 - is_on[gn, t])
            ) # Eq. (23) in Wang & Hobbs (2016) for the last time period
            @constraint(
                model,
                (prod_above[gn, t-1] + (is_on[gn, t-1] * minp[t])) -
                (prod_above[gn, t] + (is_on[gn, t] * minp[t])) <=
                RD * is_on[gn, t] +
                SD * (is_on[gn, t-1] - is_on[gn, t]) +
                maxp[t] * (1 - is_on[gn, t-1])
            ) # Eq. (25) in Wang & Hobbs (2016) for the last time period
        end
    end
end