Constraint Penalty Price
| Units: | $ |
| Mode: | Input Only |
| Multi-band: | True |
| Default Value: | 0 |
| Validation Rule: | Any Value |
| Key Property: | No |
| Description: | Price for violating the constraint where the special value of -1 indicates that no violation is allowed. |
| Detail: |
Constraint Penalty Price is used with or without Penalty Quantity to create soft constraints.
If only one level of penalty is required then setting the Penalty Price property alone will ensure that any violations are priced at that level. Setting the Penalty Quantity property will limit the amount of constraint violation allowed at the given price. Any number of violation tranches (or bands) may be specified using pairs of Penalty Quantity and Penalty Price with increasing band numbers as shown in the example below.
The Penalty Price property has the same units as the RHS, e.g. for an interval type constraint on generation, the right-hand side will be entered in megawatts so the penalty price should be entered in $/MWh is assumed, but for the annual emission limit shown below $/tonne is assumed because the right-hand side is in tonnes (thousands of the base unit).
Convexity of penalty price/quantities is assumed, meaning that bands order is not forced. It is not required to introduce monotonically increasing penalty prices in consecutive bands (as in example below), although bands can be reordered by the solver.
Example:
| Property | Value | Units | Band |
|---|---|---|---|
| RHS Year | 150000000 | - | 1 |
| Penalty Quantity | 30000000 | - | 1 |
| Penalty Quantity | 2000000 | - | 2 |
| Penalty Price | 1 | $ | 1 |
| Penalty Price | 0.3333 | $ | 2 |
In example above, penalty in band 2 would have a 'higher' priority
than band 1.
Negative Penalty Price is allowed and creates incentive to violate the constraint 'e.g.' to create a water value function on a Storage though you should be careful not to create an unbounded (dual infeasible) problem. Additionally, there is a special case of a single-band of Penalty Price equal to -1 and this indicates that the Constraint is hard. This is useful for enforcing the Constraint strictly in selected periods.
Example:
| Property | Value | Units | Band | Date From | Date To | Timeslice |
|---|---|---|---|---|---|---|
| RHS | 100 | - | 1 | |||
| Penalty Price | -1 | $ | 1 | PEAK | ||
| Penalty Price | 100 | $ | 1 | OFF-PEAK |
In this example the Constraint is strictly binding during "PEAK"
periods, and a soft constraint with penalty price 100 during
"OFF-PEAK". These periods of time are defined using Timeslice
objects.
NOTE: Very large or very small values for Penalty Price, e.g. greater than 1E+06 or less than 1E-6, can cause numerical instability in the solver and should be avoided.
See also: