Decision Variable Time Lag

Units:	-
Default Value:	0
Validation Rule:	Any Value
Description:	Time lag for terms in the generic decision variable definition.

Decision Variable Time Lag allows you to define a decision variable that corresponds to variables in the simulation in a previous/next time period. For example you might want to define a variable that represents the Generation of a Generator in the simulation period immediate preceding the current period. In this case the Time Lag would be set to one.

When the Time Lag is negative, the definition constraints in the last few periods are freed as they involve variables in the next simulation step. Accordingly, the decision variables corresponding to these periods are not constrained but their values can be set via the lower/upper bound properties.

Another way to realize the negative Time Lag constraints is by introducing some positive Time Lag decision variables and moving the constraints involving future variables to the next optimization step. However, we should not break the links between steps and the first few constraints in the first simulation step involving these decision variables might cause infeasibility which, however, can be solved by freeing these constraints by setting both the constraint sense and RHS.

It is important to understand that Time Lag only works when you use a Definition Constraint and does not apply when you refer to the Decision Variable via the Constraint Decision Variables Value Coefficient.

Thus the method for defining a Time Lag is:

Create a Constraint object to act as the definition for the Decision Variable (and will apply the Time Lag)
Add that Constraint to the Decision Variable Definition collection
Now any coefficient you set in this Constraint will be time lagged appropriately.

You may then refer to this time-lagged Decision Variable in other Constraint objects with the Constraint Decision Variables Value Coefficient.

Note

Decision Variable's with Time Lag defined will be excluded from any non-chronological simulation phases.
When different interval resolution is applied to look ahead periods, the time-lagged variable definition would be incorrect.

Time Lag can be applied to the following coefficients:

Constraint Generators

Constraint Storages

Constraint Waterways

Flow Coefficient

Constraint Fuels

Offtake Coefficient

Constraint Reserves

Provision Coefficient

Constraint Decision Variables

Value Coefficient

Constraint Gas Plants

Gas Plant Production Coefficient

Constraint Water Plants

Example

In the following example we define a ramp constraint across two generators "Baseload" and "Intermediate" of 10 MW in any period. The objects defined are:

Class	Name	Category	Description
Constraint	Generation(t) Definition	-	Definition for Decision Variable "Generation(t)"
Constraint	Generation(t-1) Definition	-	Definition for Decision Variable "Generation(t-1)"
Constraint	Max Ramp Up	-	Constraint on ramp up rate
Constraint	Max Ramp Down	-	Constraint on ramp down rate
Decision Variable	Generation(t)	-	Generation in current period
Decision Variable	Generation(t-1)	-	Generation in previous period

The memberships are:

Collection	Parent Name	Child Name
Generator.Constraints	Generation(t) Definition	Baseload
Generator.Constraints	Generation(t) Definition	Intermediate
Generator.Constraints	Generation(t-1) Definition	Baseload
Generator.Constraints	Generation(t-1) Definition	Intermediate
Constraint.Decision Variables	Max Ramp Up	Generation(t)
Constraint.Decision Variables	Max Ramp Up	Generation(t-1)
Constraint.Decision Variables	Max Ramp Down	Generation(t)
Constraint.Decision Variables	Max Ramp Down	Generation(t-1)
Decision Variable.Definition	Generation(t)	Generation(t) Definition
Decision Variable.Definition	Generation(t-1)	Generation(t-1) Definition

The attributes are:

Membership	Attribute	Value
Decision Variable ( Generation(t) )	Time Lag	0
Decision Variable ( Generation(t-1) )	Time Lag	1

The properties are:

Membership	Property	Value	Units	Band
Constraint ( Generation(t) Definition )	RHS	0	-	1
Constraint ( Generation(t-1) Definition )	RHS	0	-	1
Constraint ( Max Ramp Down )	Sense	1	-	1
Constraint ( Max Ramp Down )	RHS	-10	-	1
Constraint ( Max Ramp Up )	Sense	-1	-	1
Constraint ( Max Ramp Up )	RHS	10	-	1
Constraint ( Generation(t) Definition ).Generators ( Baseload )	Generation Coefficient	-1	-	1
Constraint ( Generation(t) Definition ).Generators ( Intermediate )	Generation Coefficient	-1	-	1
Constraint ( Generation(t-1) Definition ).Generators ( Baseload )	Generation Coefficient	-1	-	1
Constraint ( Generation(t-1) Definition ).Generators ( Intermediate )	Generation Coefficient	-1	-	1
Constraint ( Max Ramp Down ).Decision Variables ( Generation(t) )	Value Coefficient	1	-	1
Constraint ( Max Ramp Down ).Decision Variables ( Generation(t-1) )	Value Coefficient	-1	-	1
Constraint ( Max Ramp Up ).Decision Variables ( Generation(t) )	Value Coefficient	1	-	1
Constraint ( Max Ramp Up ).Decision Variables ( Generation(t-1) )	Value Coefficient	-1	-	1

This produces equations like the following:

 Con_Generation(t) Definition{1}: - GenLoad_Baseload{1} - GenLoad_Intermediate{1} + Var_Generation(t){1} = 0 
 Con_Generation(t) Definition{2}: - GenLoad_Baseload{2} - GenLoad_Intermediate{2} + Var_Generation(t){2} = 0 
 ...
 Con_Generation(t-1) Definition{1}: Var_Generation(t-1){1} = 40 
 Con_Generation(t-1) Definition{2}: - GenLoad_Baseload{1} - GenLoad_Intermediate{1} + Var_Generation(t-1){2} = 0 
 ...
 Con_Max_Ramp_Down{1}:  Var_Generation_(t){1} - Var_Generation_(t_1){1} >= -10
 Con_Max_Ramp_Down{2}:  Var_Generation_(t){2} - Var_Generation_(t_1){2} >= -10
 ...
 Con_Max Ramp Up{1}: Var_Generation(t){1} - Var_Generation(t-1){1} <= 10 
 Con_Max Ramp Up{2}: Var_Generation(t){2} - Var_Generation(t-1){2} <= 10 
 ...

Note that we have also set Generator Initial Generation for "Baseload" of 40 and "Intermediate" of zero, which is necessary when using time-lagged coefficients.