add flexiramp

src/model/formulations/WanHob2016/ramp.jl

@@ -0,0 +1,152 @@
+# 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

src/model/formulations/WanHob2016/structs.jl

@@ -0,0 +1,18 @@
+# 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.
+
+"""
+Formulation described in:
+    B. Wang and B. F. Hobbs, "Real-Time Markets for Flexiramp: A Stochastic 
+    Unit Commitment-Based Analysis," in IEEE Transactions on Power Systems, 
+    vol. 31, no. 2, pp. 846-860, March 2016, doi: 10.1109/TPWRS.2015.2411268.
+"""
+module WanHob2016
+
+import ..RampingFormulation
+
+
+struct Ramping <: RampingFormulation end
+
+end

src/model/formulations/base/system.jl

@@ -5,6 +5,7 @@
 function _add_system_wide_eqs!(model::JuMP.Model)::Nothing
     _add_net_injection_eqs!(model)
     _add_reserve_eqs!(model)
+    _add_flexiramp_eqs!(model) # Add system-wide flexiramp requirements
     return
 end
 
@@ -54,3 +55,41 @@ function _add_reserve_eqs!(model::JuMP.Model)::Nothing
     end
     return
 end
+
+function _add_flexiramp_eqs!(model::JuMP.Model)::Nothing
+     # Note: The flexpramp requirements in Wang & Hobbs (2016) are imposed as hard constraints 
+    #       through Eq. (17) and Eq. (18). The constraints eq_min_upflexiramp[t] and eq_min_dwflexiramp[t] 
+    #       provided below are modified versions of Eq. (17) and Eq. (18), respectively, in that   
+    #       they include slack variables for flexiramp shortfall, which are penalized in the
+    #       objective function.
+    eq_min_upflexiramp = _init(model, :eq_min_upflexiramp)
+    eq_min_dwflexiramp = _init(model, :eq_min_dwflexiramp)
+    instance = model[:instance]
+    for t in 1:instance.time
+        flexiramp_shortfall_penalty = instance.flexiramp_shortfall_penalty[t]
+        # Eq. (17) in Wang & Hobbs (2016)
+        eq_min_upflexiramp[t] = @constraint(
+            model,
+            sum(model[:upflexiramp][g.name, t] for g in instance.units) +
+            (flexiramp_shortfall_penalty >= 0 ? model[:upflexiramp_shortfall][t] : 0.0) >=
+            instance.reserves.upflexiramp[t]
+        )
+        # Eq. (18) in Wang & Hobbs (2016)
+        eq_min_dwflexiramp[t] = @constraint(
+            model,
+            sum(model[:dwflexiramp][g.name, t] for g in instance.units) +
+            (flexiramp_shortfall_penalty >= 0 ? model[:dwflexiramp_shortfall][t] : 0.0) >=
+            instance.reserves.dwflexiramp[t]
+        )
+
+        # Account for flexiramp shortfall contribution to objective
+        if flexiramp_shortfall_penalty >= 0
+            add_to_expression!(
+                model[:obj],
+                flexiramp_shortfall_penalty,
+                (model[:upflexiramp_shortfall][t]+model[:dwflexiramp_shortfall][t]),
+            )
+        end
+    end
+    return
+end

src/model/formulations/base/unit.jl

@@ -13,6 +13,7 @@ function _add_unit!(model::JuMP.Model, g::Unit, formulation::Formulation)
     # Variables
     _add_production_vars!(model, g, formulation.prod_vars)
     _add_reserve_vars!(model, g)
+    _add_flexiramp_vars!(model, g) # Add variables for flexiramp
     _add_startup_shutdown_vars!(model, g)
     _add_status_vars!(model, g, formulation.status_vars)