Segmented cycle degradation

src/constraints/battery_degradation.jl

@@ -1,20 +1,23 @@
 # REopt®, Copyright (c) Alliance for Sustainable Energy, LLC. See also https://github.com/NREL/REopt.jl/blob/master/LICENSE.
 
 
-function add_degradation_variables(m, p)
+function add_degradation_variables(m, p, segments)
     days = 1:365*p.s.financial.analysis_years
     @variable(m, Eavg[days] >= 0)
-    @variable(m, Eplus_sum[days] >= 0)
-    @variable(m, Eminus_sum[days] >= 0)
+    @variable(m, Eplus_sum[days, 1:segments] >= 0) # energy charged for each day for each segment level
+    @variable(m, Eminus_sum[days, 1:segments] >= 0) # energy discharged for each day for each segment level
     @variable(m, EFC[days] >= 0)
     @variable(m, SOH[days])
+    @variable(m, dvSegmentChargePower[p.time_steps, 1:segments] >= 0) # charge power for each ts for each segment 
+    @variable(m, dvSegmentDischargePower[p.time_steps, 1:segments] >= 0); # discharge power for each ts for each segment
 end
 
 
 function constrain_degradation_variables(m, p; b="ElectricStorage")
     days = 1:365*p.s.financial.analysis_years
     ts_per_day = 24 / p.hours_per_time_step
     ts_per_year = ts_per_day * 365
+    J = length(p.s.storage.attr[b].degradation.cycle_fade_coefficient); # Number of segments
     ts0 = Dict()
     tsF = Dict()
     for d in days
@@ -24,21 +27,54 @@ function constrain_degradation_variables(m, p; b="ElectricStorage")
             tsF[d] = Int(ts_per_day * 365)
         end
     end
+
     @constraint(m, [d in days],
         m[:Eavg][d] == 1/ts_per_day * sum(m[:dvStoredEnergy][b, ts] for ts in ts0[d]:tsF[d])
     )
+
     @constraint(m, [d in days],
-        m[:Eplus_sum][d] == 
+        sum(m[:Eplus_sum][d, j] for j in 1:J) == 
             p.hours_per_time_step * (
                 sum(m[:dvProductionToStorage][b, t, ts] for t in p.techs.elec, ts in ts0[d]:tsF[d]) 
                 + sum(m[:dvGridToStorage][b, ts] for ts in ts0[d]:tsF[d])
             )
     )
+
     @constraint(m, [d in days],
-        m[:Eminus_sum][d] == p.hours_per_time_step * sum(m[:dvDischargeFromStorage][b, ts] for ts in ts0[d]:tsF[d])
+        sum(m[:Eminus_sum][d, j] for j in 1:J) == 
+            p.hours_per_time_step * sum(m[:dvDischargeFromStorage][b, ts] for ts in ts0[d]:tsF[d])
     )
+
     @constraint(m, [d in days],
-        m[:EFC][d] == (m[:Eplus_sum][d] + m[:Eminus_sum][d]) / 2
+        m[:EFC][d] == sum(m[:Eplus_sum][d, j] + m[:Eminus_sum][d, j] for j in 1:J) / 2
+    )
+
+    # Power in equals power into storage from grid or local production
+    @constraint(m, [ts in p.time_steps],
+    sum(m[:dvSegmentChargePower][ts, j] for j in 1:J) == sum(
+        m[:dvProductionToStorage][b, t, ts] for t in p.techs.elec) + m[:dvGridToStorage][b, ts]
+    )
+
+    # Power out equals power discharged from storage to any destination
+    @constraint(m, [ts in p.time_steps],
+    sum(m[:dvSegmentDischargePower][ts, j] for j in 1:J) == m[:dvDischargeFromStorage][b, ts]);
+
+    # Balance charging with daily e_plus, here is only collect all power across the day, so don't need to times efficiency
+    @constraint(m, [d in days, j in 1:J], m[:Eplus_sum][d, j] == sum(m[:dvSegmentChargePower][ts0[d]:tsF[d], j])*p.hours_per_time_step)
+    @constraint(m, [d in days, j in 1:J], m[:Eminus_sum][d, j] == sum(m[:dvSegmentDischargePower][ts0[d]:tsF[d], j])*p.hours_per_time_step);
+    #[az] we may want to adjust the notation to "ts, j for ts in ts0[d]:tsF[d] so it reads the same as the other constraints in REopt
+
+    # energy limit, replace SOC limitation
+    @constraint(
+        m,
+        [ts in p.time_steps, j in 1:J],
+        m[:dvSegmentChargePower][ts, j]*p.hours_per_time_step <= p.s.storage.attr[b].degradation.cycle_fade_coefficient[j]*m[:dvStorageEnergy][b]
+    )
+
+    @constraint(
+        m,
+        [ts in p.time_steps, j in 1:J],
+        m[:dvSegmentDischargePower][ts, j]*p.hours_per_time_step <= p.s.storage.attr[b].degradation.cycle_fade_coefficient[j]*m[:dvStorageEnergy][b]
     )
 end
 
@@ -54,7 +90,7 @@ function add_degradation(m, p; b="ElectricStorage")
     # Indices
     days = 1:365*p.s.financial.analysis_years
     months = 1:p.s.financial.analysis_years*12
-
+    J = length(p.s.storage.attr[b].degradation.cycle_fade_coefficient); # Number of segments
     strategy = p.s.storage.attr[b].degradation.maintenance_strategy
 
     if isempty(p.s.storage.attr[b].degradation.maintenance_cost_per_kwh)
@@ -74,15 +110,15 @@ function add_degradation(m, p; b="ElectricStorage")
         throw(@error("The degradation maintenance_cost_per_kwh must have a length of $(length(days)-1)."))
     end
 
-    add_degradation_variables(m, p)
+    add_degradation_variables(m, p, J)
     constrain_degradation_variables(m, p, b=b)
 
     @constraint(m, [d in 2:days[end]],
         m[:SOH][d] == m[:SOH][d-1] - p.hours_per_time_step * (
             p.s.storage.attr[b].degradation.calendar_fade_coefficient * 
             p.s.storage.attr[b].degradation.time_exponent * 
             m[:Eavg][d-1] * d^(p.s.storage.attr[b].degradation.time_exponent-1) + 
-            p.s.storage.attr[b].degradation.cycle_fade_coefficient * m[:EFC][d-1]
+            sum(p.s.storage.attr[b].degradation.cycle_fade_coefficient[j] * m[:Eminus_sum][d-1, j] for j in 1:J)
         )
     )
     # NOTE SOH can be negative
@@ -182,7 +218,7 @@ function add_degradation(m, p; b="ElectricStorage")
         @expression(m, residual_value, sum(residual_values[mth] * m[:dvSOHChangeTimesEnergy][mth] for mth in months))
 
     elseif strategy == "augmentation"
-
+        @info "Augmentation BESS degradation costs."
         @expression(m, degr_cost,
             sum(
                 p.s.storage.attr[b].degradation.maintenance_cost_per_kwh[d-1] * (m[:SOH][d-1] - m[:SOH][d])

src/core/energy_storage/electric_storage.jl

@@ -146,7 +146,7 @@ Note that not all of the above inputs are necessary. When not providing `calenda
 """
 Base.@kwdef mutable struct Degradation
     calendar_fade_coefficient::Real = 2.55E-03
-    cycle_fade_coefficient::Real = 9.83E-05
+    cycle_fade_coefficient::Vector{<:Real} = [9.83E-05]
     time_exponent::Real = 0.42
     installed_cost_per_kwh_declination_rate::Real = 0.05
     maintenance_strategy::String = "augmentation"  # one of ["augmentation", "replacement"]
@@ -325,6 +325,10 @@ struct ElectricStorage <: AbstractElectricStorage
 
         if haskey(d, :degradation)
             degr = Degradation(;dictkeys_tosymbols(d[:degradation])...)
+
+            if length(degr.cycle_fade_coefficient) > 1
+                @info "Modeling segmented cycle fade battery degradation costing"
+            end
         else
             degr = Degradation()
         end