I have spent some time reading VFI in InfHorz: Howards, PFI, and relation to implicit finite differences, which gives some background to the question(s) I pose here.
I’m modeling an energy provider (InfHorz) navigating an energy transition from fossil to renewable energy over a period of years (lots of transport runs on fossil fuel today, if you must know). Ignoring for the moment how the users of this energy are modeled (and how they transition), the naive solution that my model gives is that it should just do the whole transition in year 1 because that’s “best”. It’s also unrealistic.
I’d like to add to the model the constraint that the energy provider can install some small finite number of renewable units per period based on solving the GE for that period. Then we compute the optimum for the next period, and so forth, through the transition. This seems to call for an InfHorz experience asset, but I’m having trouble wrapping my head around what that means, because I’m having trouble relating in my own mind the concepts of InfHorz equilibrium time (a and aprime) with transition time (discrete periods). Strangely, I feel comfortable with FHorz equilibrium time (where ages flesh out a time-like distribution that is nevertheless a snapshot of actual time).
I also note that the experience asset implementation seems to be designed to move at most one grid point per period, not “some small finite number”. The posting I referenced at the top explains how experience assets increase efficiency of the solver by dramatically lowering the choice space within the state space. And perhaps I could leverage that by scaling my “small finite number” to 1 and taking advantage of the fact that I can extract intra-grid values from that, giving me the ability to recover my small finite number by multiplying and rounding.
Perahps I am overthinking things, and should just implement an aprimeFn that maps a decision variable to the range of increments reasonable within the model, and low, the right thing will happen. I.e., the decision variable gives me the “small finite number” which the aprime function digests into a maximum per-period investment value, creating a more incremental transition.
However, I don’t see (yet) how to communicate from one period in the transition to the next the new baseline of installed renewable capacity.
And there’s a lot of InfHorz_ExpAsset cases not yet implemented, so I want to make sure I’m understanding things before I push forward into that. If I’m misunderstanding which tools I should be using for my model, I’d rather pick the right tools from the Toolkit than to try to adapt the wrong tools to my purpose.