Model Soft Constraints using Penalty Prices

Once the network and scenario files are loaded into the SAInt project environment, a constraint of a network object can be relaxed using a penalty price event. A PRC suffix in a scenario event extension identifies the penalty price events. Similar to other properties, this event overwrites the default penalty price value.

The prioritization of the soft constraint is based on the value of the penalty price. If the penalty price is lower than the marginal production cost, the constraint will be violated since paying the penalty is cheaper than producing. Additionally, constraints with a higher penalty have priority over constraints with a lower penalty. In this example, the PSET and PSETPRC events are created for the electric demand object, as shown in Figure 1. The PSET event has an assigned profile (PRF_DEMAND), while the PSETPRC event has a value of 200 [$/MWh], the penalty for not serving the demand’s set point.

After executing the scenario optimization, the results can be analyzed using the table functions in the Command Window. Figure 2 compares the demand penalty price and the marginal cost of the "COAL" generator. During the optimization, since the generator’s marginal cost is lower than the penalty price for not serving the demand, the generator is dispatched to meet the PSET of the demand.

Based on the results shown in Figure 2, the PSET constraint can be relaxed by lowering the penalty price. Edit the value of the PSETPRC event to 72 [$/MWh]. As a result, the PSET is changed to a soft constraint and is violated if the marginal cost of the generator is higher than the new penalty price, as shown in Figure 3.