Counting non negative instances of a variable for use in constraint - efficient formulation?

I have a constraint in my model which limits the number of non-negative instances of a variable. Specifically, I have a power balance where there is a slack (load shedding) variable, and I limit the number of times that it can be non-zero:

\sum_{g \in G} gen_{g,t} = D_t + ls_t \quad t \in T \\ lsi_t + eps \geq ls_t / D_t \\ \sum_{t \in T} lsi_t \leq LOLE

where lsi_t is a binary variable and eps is a small number to avoid computational issues.

My question is whether there is literature on efficient formulations of the above, similarly to how, say, in unit commitment the formulation with 3 binary variables tends to be more efficient than with only 1. I imagine there must be some operations research literature on the subject, but searching for key words similar to the ones used in the title haven’t proved useful.

Thanks in advance.

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