LT Plan - Timing and Staging Constraints
Contents
1. Introduction
The earliest possible start date of a project is set using the Generator or Line Project Start Date property. The number of units that can be built is set by the property Max Units Built, and this can vary across time to vary the total number of units built in aggregate. The property Max Units Built in Year limits the number of units built in any particular year. For example, in the following data an increasing total number of units can be built over the course of the horizon, but never more than one any in year:
| Property | Value | Unit | Date Form |
|---|---|---|---|
| Max Units Built | 0 | - | |
| Max Units Built | 1 | - | 1/01/2012 |
| Max Units Built | 2 | - | 1/01/2015 |
| Max Units Built | 4 | - | 1/01/2020 |
| Max Units Built in Year | 1 | - |
Any number of units up to the Max Units Built can be forced into service using the Min Units Built. You can also force a minimum number of units to be built in a particular year using the Min Units Built in Year property.
More complex timing constraints are possible, including linking the build/retire decisions of different generators/lines by using generic Constraint class.
2. Multi-Stage Plant and Project Dependencies
Often a 'project' consists of multiple stages and there is a defined staging order and unique performance parameters for each stage. This is modelled in LT Plan using one Generator object per stage, and with the setting of appropriate build and retire inputs, and finally with generic constraints to link the stages.
Consider the following example.
A combined cycle plant can be built in one of two ways:
- First as a open-cycle plant of low efficiency with a later upgrade to higher-efficiency combined cycle; or
- as a combined cycle plant in one 'stage'.
Assume also that the open-cycle stage can be built 'immediately' whereas the combined-cycle can only be in service at or after 1/01/2012.
Firstly we create Generator objects to represent the two stages (GT and CCGT), and a generator to represent the option to build the CCGT in one step.
| Generator | Property | Value | Unit | Date From |
|---|---|---|---|---|
| CCGT_stage1 | Units | 0 | - | |
| CCGT_stage1 | Max Capacity | 75 | MW | |
| CCGT_stage1 | Heat Rate | 11 | GJ/MWh | |
| CCGT_stage1 | Max Units Built | 1 | - | 1/01/2009 |
| CCGT_stage1 | Max Units Retired | 1 | - | |
| CCGT_stage1 | Build Cost | 110 | $/kW | |
| CCGT_stage1 | Economic Life | 30 | years | |
| CCGT_stage1 | WACC | 30 | % |
| Generator | Property | Value | Unit | Date From |
|---|---|---|---|---|
| CCGT_stage2 | Units | 0 | - | |
| CCGT_stage2 | Max Capacity | 325 | MW | |
| CCGT_stage2 | Heat Rate | 7.5 | GJ/MWh | |
| CCGT_stage2 | Max Units Built | 1 | - | 1/01/2012 |
| CCGT_stage2 | Build Cost | 120 | $/kW | |
| CCGT_stage2 | Economic Life | 30 | years | |
| CCGT_stage2 | WACC | 12 | % |
| Generator | Property | Value | Unit | Date From |
|---|---|---|---|---|
| CCGT | Units | 0 | - | |
| CCGT | Max Capacity | 325 | MW | |
| CCGT | Heat Rate | 7.5 | GJ/MWh | |
| CCGT | Max Units Built | 1 | - | 1/01/2011 |
| CCGT | Build Cost | 210 | $/kW | |
| CCGT | Economic Life | 30 | years | |
| CCGT | WACC | 12 | % |
The Build Cost is allowed to change over time however for this example we assume a static value. Note also that the "CCGT_stage1" generator must allow 'retirement' by setting the Max Units Retired property. This is so that it can be superseded by the stage 2 plant.
We now link the stages with Constraints to ensure that:
- "CCGT_stage2" is built only if "CCGT_stage1" is built first
- "CCGT_stage1" 'retires' when "CCGT_stage2" is built
- "CCGT_stage1" and "CCGT" are mutually exclusive
3. Mutually Exclusive Projects
To make two projects, i and j, mutually exclusive we need to create a constraint in the formulation like this:
∑ ( y ) ( GenBuild(i,y) ) + ∑ ( y ) ( GenBuild(j,y) ) ≤ 1Note that in this equation y indexes the time periods (years in LT Plan).
Here we create the Constraint object "CCGT_mutually_exclusive", then add in to it the Generators "CCGT_stage1" and "CCGT". We then define the following data:
| Membership | Property | Value |
|---|---|---|
| CCGT_mutually_exclusive | Sense | <= |
| CCGT_mutually_exclusive | RHS | 1 |
| CCGT_mutually_exclusive.Generators.CCGT_stage1 | Units Built Coefficient | 1.0 |
| CCGT_mutually_exclusive.Generators.CCGT | Units Built Coefficient | 1.0 |
4. Project Staging
To make sure that the "stage 1" and "stage 2" projects follow each other in sequence we need to create an equation like this:
GenBuild(i,y) - GenRetire(j,y) ≤ 0 ∀ yHere we create the Constraint object "CCGT_staging", then add the Generators "CCGT_stage1" and "CCGT_stage2" to the Constraint Generators collection. We then define the following data:
| Membership | Property | Value |
|---|---|---|
| CCGT_staging | Sense | <= |
| CCGT_staging | RHS | 0 |
| CCGT_staging.Generators.CCGT_stage1 | Units Retired in Year Coefficient | -1.0 |
| CCGT_staging.Generators.CCGT_stage2 | Units Built in Year Coefficient | 1.0 |
Note the use of Units Built in Year Coefficient and Units Retired in Year Coefficient, which creates constraints for each year, rather than summing across all years as in the mutually exclusive projects case above.