Multi-stage modeling overview

This section describes the available features, inputs and model components related to formulating and solving multi-stage investment planning problems. Two different types of multi-stage problems can be setup:

  • Perfect foresight: A single multi-stage investment planning problem that simultaneously optimizes capacity and operations across all specified investment stages
  • Myopic: Sequential solution of single-stage investment planning for each investment stage, where capacity additions and retirements from the previous stages are used to determine initial (or existing) capacity at the beginning of the current stage.

The table below summarizes the key differences in the two model setups.

Perfect foresightMyopic
No. of optimization problems solved1Equal to number of investment stages
Objective function cost basisNet present valueAnnualized costs
Price/dual variable information available?NoYes

Additional inputs needed for multi-stage modeling (need to convert to tables)

Input data files

Instead of one set of input files, there is one directory of input files that needs to be provided for each planning period or stage (e.g., “Inputs/Inputsp1/” for the first period “Inputs/Inputsp2/” for the second period, etc.). Below we list the additional parameters that must be provided in the corresponding stage-specific input files to instantiate a multi-stage planning problem.

Min_Retired_Cap_MWMinimum capacity in MW that must retire in this planning stage.
Min_Retired_Energy_Cap_MWMinimum energy capacity in MW that must retire in this planning stage.
Min_Retired_Charge_Cap_MWMinimum charge capacity in MW that must retire in this planning stage.
LifetimeThe operational lifespan in years of this technology after which it must be retired.
Capital_Recovery_PeriodThe technology-specific period in years over which initial capital costs must be recovered.
WACCThe technology-specific weighted average cost of capital.
Line_Max_Flow_Possible_MWThe maximum transmission capacity of the line, as opposed to Line_Max_Reinforcement_MW which now specifies the maximum expansion to the line in one stage.
Capital_Recovery_PeriodThe line-specific period in years over which initial capital costs must be recovered.
WACCThe line-specific weighted average cost of capital.

Settings Files

A separate settings.yml file includes a list of parameters to be specified to formulate the multi-stage planning model.

NumStagesThe number of model investment planning stages.
StageLengthsA list of lengths of each model stage in years (e.g., [10, 10, 10] for three stages each of length 10). Note that stages could be defined to be of varying length.
Myopic0 = perfect foresight, 1 = myopic model (see above table)
ConvergenceToleranceThe relative optimality gap used for convergence of the dual dynamic programming algorithm. Only required when Myopic = 0
WACCRate used to discount non-technology-specific costs from stage to stage (i.e., the “social discount rate”).
MultiStageConcatenateDesignates whether to use time domain reduction for the full set of input data together (1) or to reduce only the first stage data and apply the returned representative periods to the rest of the input data (0).