Interpretation of a marginal value

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Interpretation of a marginal value

Post by clem_c » 2 months ago

Dear all,

I'm running into an issue with my GAMS modeling, and I'm hoping that you can give me some insight. It's about the interpretation of a shadow price, and I'm sure your expertise can give me some clue.

Context: It's a linear program allowing to perform a economic dispatch in the electricity sector (with investment in new capacities allowed but constrained). I've got a lot of storage, performing the study on a year.
All my technologies that are not constraint in term of installed capacity are at the equilibrium after the optimization (which means revenue = fixed cost)

Interest : I'm interested in the price formation in this context.
Indeed, in an energy market model with storage, we are coupling our primal equations across many time steps. Thus, an increase in demand may be served either via:
- An increase in production for the current time step (these are what I have interpreted easily, equal to marginal cost of production)
- An increase in production across other time steps (these are production prices multiplied by efficiency rate of my storage)
- The apparition of lost load
- And, where I'm struggling, an increase in the installed capacity when everything is at full output and if it cost less than loss load.

Issue : However, where I'm struggling is that for I've got prices that I think are link to 4) but I can't link it to a specific production unit (neither to the value of lost load or other possibilities)

The objective function would be modified by the cost of the investment, the cost of production of the one unit more, but also by all the savings that would have been performed thanks to this new capacity [All investment are made at the beginning and for the whole year]. This latest points, I don't know how to assess it that's why I'm struggling to understand the resulting shadow price.

Do you have any clue ?
Thanks a lot,

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