Piecewise linear costs - economies of scale

Description

Add a piecewise cost function that reduces the incremental increase in investment costs with increasing technology rated capacity. This emulates "economies of scale", where the more of a technology there is deployed, the less expensive each additional investment in deployment.

A more detailing example can be found in our [dedicated tutorial][defining-piecewise-linear-constraints].

New indexed parameters:

• piecewise_cost_investment_x (defining the new set breakpoints)
• piecewise_cost_investment_y (defining the new set breakpoints)

YAML definition

Download the YAML example

dimensions:
  breakpoints:
    dtype: integer
    description: SOS2 piecewise breakpoints
    iterator: breakpoint

parameters:
  piecewise_cost_investment_x:
    description: Flow capacity values at each breakpoint
  piecewise_cost_investment_y:
    description: Investment cost values at each breakpoint

variables:
  piecewise_cost_investment:
    description: Investment cost that increases monotonically
    foreach: [nodes, techs, carriers, costs]
    where: any(piecewise_cost_investment_x, over=breakpoints) AND any(piecewise_cost_investment_y, over=breakpoints)
    unit: cost
    default: 0
    bounds:
      min: 0
      max: .inf

piecewise_constraints:
  sos2_piecewise_costs:
    description: >
      Set investment cost values along a piecewise curve using special ordered sets of type 2 (SOS2).
    foreach: [nodes, techs, carriers, costs]
    where: any(piecewise_cost_investment_x, over=breakpoints) AND any(piecewise_cost_investment_y, over=breakpoints)
    x_expression: flow_cap
    x_values: piecewise_cost_investment_x
    y_expression: piecewise_cost_investment
    y_values: piecewise_cost_investment_y

global_expressions:
  # Update this global expression from the base math to include piecewise costs
  cost_investment:
    where: >
      (cost_investment_flow_cap OR cost_investment_storage_cap
      OR cost_investment_source_cap OR cost_investment_area_use
      OR piecewise_cost_investment)
    equations:
      - expression: >
          sum(cost_investment_flow_cap, over=carriers) +
          cost_investment_storage_cap +
          cost_investment_source_cap +
          cost_investment_area_use +
          sum(piecewise_cost_investment, over=carriers)