Calculating marginal emission in Unit commitment problem

[leewing159]

Hello, I am working on solving a unit commitment problem,

and I'd like to calculate the increase in greenhouse gas emissions (marginal carbon intensity) when electricity load increases by one unit.
--> delta(emission)/delta(load) where load is a paramter.

Post-calculating the emission factor of the marginal generator (most expensive) can be done to calculate,
However, it would be preferable if I could identify this during the optimization process.

For example, using a method similar to EQ_Emission.m(h).

I understand that since the objective function in Unit commitment problem is the minimizing generation cost,
the marginal value of the Equation_DemandBalance is the marginal price. (-> delta(cost)/delta(load))

However, I am unsure about the best way to calculate the marginal value of greenhouse gas emissions. [delta(emission)/delta(load)]

Could you please suggest an approach for calculating the marginal emissions from marginal electricity production in the context of the unit commitment problem?

Thank you.