Interesting question, but I have myself no deeper insights into the curtailment issues.

As far as I can see, in TIMES curtailment basically occurs only when the price of electricity falls to zero. The marginal of the commodity balance is zero when consumption + storage charge (=the energy sold) is falling below production + storage discharge (=supply). Thus, the value of the lost generation due to curtailment would in general be zero. Negative prices can only occur in TIMES if you have modelled the electricity balances with a fixed equation type (FX), and if the curtailment of variable generation is being limited (for example, by using fixed or lower-bounded AFs). However, I think that most variable generation is already today being implemented with active control systems allowing optimized curtailments, and so I would think negative prices should probably no longer occur in the future, unless I am missing something?

Currently, apart from the residual load facility (see

https://iea-etsap.org/docs/TIMES-RLDC-Documentation.pdf), there are no other features in TIMES dedicated specifically to the modelling of curtailments. Therefore, the modeller is mostly left with the generic features of TIMES (including the dispatching features), with respect to curtailment modeling.

For taking into account the operational constraints of thermal plants, you can use the TIMES dispatching features (minimum stable operation levels, start-up / shut-down costs, minimum on-line / off-line times, ramping constraints, and partial load efficiencies), for better modelling of the system under potential curtailment situations.

If you can formulate what you want in mathematical terms, I see no reason why it could not be modelled in TIMES. If you have your (linearized) mathematical formulation ready, but don't know how to implement it in TIMES, I am sure I can try to help with it.