Custom Example for using piecewise linear conversion

assets/examples/61_piecewise_linear_addon.iesopt.yaml

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+config:
+  general:
+    version:
+      core: 2.6.4
+  optimization:
+    problem_type: MILP
+    snapshots:
+      count: 9
+    solver:
+      name: highs
+  paths:
+    addons: files/61
+
+addons:
+  CustomMath: {}
+
+carriers:
+  electricity: {}
+  gas: {}
+
+components:
+  grid_electricity:
+    type: Node
+    carrier: electricity
+
+  grid_gas:
+    type: Node
+    carrier: gas
+
+  demand_elec:
+    type: Profile
+    carrier: electricity
+    node_from: grid_electricity
+    value: [2.75,  5.50,  7.00,  8.00,  9.00, 10.00, 5.00, 5.00, 15.00]
+
+  create_gas:
+    type: Profile
+    carrier: gas
+    node_to: grid_gas
+    mode: create
+    cost: 50.0

assets/examples/61_piecewise_linear_addon.yaml

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+config:
+  general:
+    version:
+      core: 2.6.3
+  optimization:
+    problem_type: MILP
+    snapshots:
+      count: 9
+    solver:
+      name: highs
+  paths:
+    addons: files/61
+
+addons:
+  CustomMath: {}
+
+carriers:
+  electricity: {}
+  gas: {}
+
+components:
+  grid_electricity:
+    type: Node
+    carrier: electricity
+
+  grid_gas:
+    type: Node
+    carrier: gas
+
+  demand_elec:
+    type: Profile
+    carrier: electricity
+    node_from: grid_electricity
+    value: [2.75,  5.50,  7.00,  8.00,  9.00, 10.00, 5.00, 5.00, 15.00]
+
+  create_gas:
+    type: Profile
+    carrier: gas
+    node_to: grid_gas
+    mode: create
+    cost: 50.0

assets/examples/files/61/CustomMath.jl

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+module IESoptAddon_CustomMath
+
+using IESopt
+import JuMP
+
+function initialize!(model::JuMP.Model, config::Dict)
+    # All functions are expected to return `true` if everything went well.
+    return true
+end
+
+# The following functions are called after they were called for all core components:
+# - setup!
+# - construct_expressions!
+# - construct_variables!
+# - construct_constraints!
+# - construct_objective!
+#
+# If you do not need to modify the model during a specific step, you can just not implement the function.
+
+function construct_variables!(model::JuMP.Model, config::Dict)
+    T = get_T(model)
+
+    node_input = get_component(model, "grid_gas")
+    node_output = get_component(model, "grid_electricity")
+
+    # we create here the breakpoints of the inputs let's take 20  BPs
+    Pmax = 20.
+    a,b,c = [0.7012, 0.0662, 0.3671 ] # coeffs for efficiency
+
+    function eta(P::Float64)
+        prel = P/Pmax
+        return 0.1 + c *( prel^a / (prel^a + b^a)  )
+    end
+    function power_input(P::Float64)
+        return P/eta(P)
+    end
+
+    output_bp = collect(range(0.0, Pmax, length=10))   # electricity out
+    input_bp  = power_input.(output_bp)               # gas in
+    N = length(input_bp)
+    ## ======================
+
+    @assert N == length(output_bp)
+
+    JuMP.@variable(model, var_input[t in T], lower_bound=0.0)
+    JuMP.@variable(model, var_output[t in T] >= 0.0, container=Array)
+
+    node_output.exp.generation = [1.0 * var_output[t] for t in T] ## IESopt exp fields want AffExpr / Vector{AffExpr}, so make it explicitly affine
+
+    JuMP.@variable(model, 0<= λ[t in T, i in 1:N] <= 1.0) # SOS2 weights PER snapshot
+
+    JuMP.@constraints( model, begin
+        [t in T], var_input[t]  == sum(λ[t,i] * input_bp[i]   for i in 1:N)
+        [t in T], var_output[t] == sum(λ[t,i] * output_bp[i]  for i in 1:N)
+        [t in T], sum(λ[t,i] for i in 1:N) == 1
+    end)
+    JuMP.@constraint( model,[t in T], λ[t, 1:N] in JuMP.SOS2() )
+
+    for t in T
+        JuMP.add_to_expression!(node_input.exp.injection[t], model[:var_input][t], -1.0)
+        JuMP.add_to_expression!(node_output.exp.injection[t], node_output.exp.generation[t], 1.0)
+    end
+
+    return true
+end
+
+end

assets/examples/files/61/efficiency_plot.jl

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+using Plots
+import JuMP
+Pmax = 100.
+a,b,c = [0.7012, 0.0662, 0.3671 ] # coeffs for efficiency
+
+function eta(P::Float64)
+    prel = P/Pmax
+    return 0.1 + c *( prel^a / (prel^a + b^a)  )
+end
+
+function eta_const(P::Float64)
+    return 0.35
+end
+P = collect( range(0, Pmax, 110) )
+eta_P = eta.(P)
+
+p1 = plot(P, eta_P, label="True efficiency")
+
+input_bp = collect( range(0, Pmax, 20) ) #20 breakpoints
+ouptput_bp = eta.(input_bp)
+
+
+plot!(p1, input_bp, ouptput_bp, label="piecewise linear, 20 BPs")
+plot!(p1, input_bp, eta_const.(input_bp), label="constant efficiency")
+
+input_bp = collect( range(0, Pmax, 10) ) #20 breakpoints
+ouptput_bp = eta.(input_bp)
+
+plot!(p1, input_bp, ouptput_bp, label="piecewise linear, 10 BPs")
+
+input_bp = [0, 5, 10, 15.0, 20, 25, 45, 60, 80, 100]
+ouptput_bp = eta.(input_bp)
+
+plot!(p1, input_bp, ouptput_bp, label="piecewise linear, 10 BPs - not equally spaced")