Demand share per timestep as decision variable

Description

Allows the model to decide on how a fraction of demand for a carrier is met by the given group of technologies, which will each have the same share in each timestep. Variables and constraints defined here could be extended to iterate over nodes and over carriers if desired. If summing over nodes, remove the summation over nodes in the constraints and add it into the list in demand_share_per_timestep_decision_sum (if using). If summing over carriers, the slicing of sink_use_equals will need to change per carrier by using a where statement in slices: ....

The share is relative to the flow sink from a specified demand technology (or group thereof) only.

Specifying relaxation inside the constraint to a non-zero value allows the constraint some flexibility around a given value, making a model easier to solve.

New indexed parameters:

• relaxation (defined here directly)
• demand_share_limit (defined here directly)

Helper functions used:

• sum (expression)
• select_from_lookup_arrays (expression)

YAML definition

Download the YAML example

variables:
  demand_share_per_timestep_decision:
    description: >
      Relative share of demand that a given technology must meet per node.
    unit: fraction
    foreach: [nodes, techs]
    where: NOT config.mode=operate AND decide_demand_share
    bounds:
      min: 0
      max: .inf

# The two main constraints enforce that the shares are the same in each timestep,
# with an optional relaxation.

constraints:
  demand_share_per_timestep_decision_main_min:
    description: >-
      Limit the lower bound of a technology's outflow to the share of demand
      that the model has decided it will meet.
    foreach: [nodes, techs, timesteps]
    where: demand_share_per_timestep_decision
    equations:
      - expression: >
          flow_out[carriers=$carrier] >=
          (1 - $relaxation)
          * select_from_lookup_arrays(sink_use_equals, techs=decide_demand_share)
          * demand_share_per_timestep_decision
    sub_expressions:
      # 0 == no relaxation
      # 0.01 == 1% relaxation
      # (lhs == rhs -> lhs >= 0.99 * rhs & lhs <= 1.01 * rhs)
      relaxation: &relaxation_component
        - where: demand_share_relaxation
          expression: demand_share_relaxation
        - where: NOT demand_share_relaxation
          expression: "0"
    slices: &slice
      carrier:
        - expression: demand_share_carrier  # assigned as an indexed parameter

  demand_share_per_timestep_decision_main_max:
    description: >-
      Limit the upper bound of a technology's outflow to
      the share of demand that the model has decided it will meet.
    foreach: [nodes, techs, timesteps]
    where: demand_share_per_timestep_decision
    equations:
      - expression: >
          flow_out[carriers=$carrier] <=
          (1 + $relaxation)
          * select_from_lookup_arrays(sink_use_equals, techs=decide_demand_share)
          * demand_share_per_timestep_decision
    sub_expressions:
      relaxation: *relaxation_component
    slices: *slice

# The optional additional sum constraint ensures that all decision shares add up
# to a specified share of carrier demand (here, 50% = 0.5 of electricity demand).

  demand_share_per_timestep_decision_sum:
    description: >-
      Limit the total share of demand that can be met by technologies controlled
      by the `demand_share_per_timestep_decision` variable.
    foreach: [nodes, timesteps]
    where: demand_share_per_timestep_decision AND demand_share_limit
    equations:
      - expression: >
          sum(demand_share_per_timestep_decision, over=[techs])
          == demand_share_limit