NOTE: The values of Max Units Built must logically be monotonically non-decreasing over time.

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 This is so that it can be superseded by the stage 2 plant.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) ) ≤ 1

Note 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 ∀ y

Here 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.

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