Multi TS skeleton

[Godelaine]

Describe the current behavior

No response

Describe the expected behavior

1st iteration: only preventive
1)N (number of timestamps) CASTOR with only preventive network actions
2) Output : N Rao Results
3) 1 Computation with N RaoInputs with only linear actions.

Describe the motivation

No response

Extra Information

No response

[bqth29]

For topological optimization, the strategy we wanted to use was to optimize all 24 timestamps in parallel to save as must computation time as possible and then to merge everything in a single linear problem to optimize range actions.

This can be done without too much work. However, even if it will may not be part of the first POC, we have to keep in mind that there will possibly be constraints in terms of remedial action changes between two consecutive timestamps.

In that case, if we want to keep the parallel topological optimization while respecting constraints, will have to constraint the number of applicable remedial actions at each time stamps.

Let $t$ be a timestamp and $t - 1$ and $t + 1$ be respectively its previous and next timestamps. Let $\Delta RA_{\max} (t - 1, t)$ and $\Delta RA_{\max} (t, t + 1)$ be respectively the maximum number of remedial action changes between timestamps $t - 1$ and $t$, and $t$ and $t + 1$.

Then, we shall constraint the maximum number of topological actions applicable at $t$ to $\min \left ( \lfloor \frac{\Delta RA_{\max} (t - 1, t)}{2} \rfloor, \lfloor \frac{\Delta RA_{\max} (t, t + 1)}{2} \rfloor \right )$.

Indeed, the worst case is that $\frac{\Delta RA_{\max} (t - 1, t)}{2} \rfloor$ topological actions are applied at $t - 1$ and deactivated at $t$. Similarly, $\lfloor \frac{\Delta RA_{\max} (t, t + 1)}{2} \rfloor$ that were not applied at $t$ are applied at $t + 1$. Finally, $\min \left ( \lfloor \frac{\Delta RA_{\max} (t - 1, t)}{2} \rfloor, \lfloor \frac{\Delta RA_{\max} (t, t + 1)}{2} \rfloor \right )$ remedial actions are applied at $t$. The total number of changes are:

• $\min \left ( \lfloor \frac{\Delta RA_{\max} (t - 1, t)}{2} \rfloor, \lfloor \frac{\Delta RA_{\max} (t, t + 1)}{2} \rfloor \right ) + \lfloor \frac{\Delta RA_{\max} (t - 1, t)}{2} \rfloor\leq 2 \times \lfloor \frac{\Delta RA_{\max} (t - 1, t)}{2} \rfloor \leq \Delta RA_{\max} (t - 1, t)$ between $t - 1$ and $t$
• $\min \left ( \lfloor \frac{\Delta RA_{\max} (t - 1, t)}{2} \rfloor, \lfloor \frac{\Delta RA_{\max} (t, t + 1)}{2} \rfloor \right ) + \lfloor \frac{\Delta RA_{\max} (t, t + 1)}{2} \rfloor \leq 2 \times \lfloor \frac{\Delta RA_{\max} (t, t + 1)}{2} \rfloor \leq \Delta RA_{\max} (t, t + 1)$ between $t$ and $t + 1$

That way, both constraints are respected, even though it might be highly sub-optimal.

[bqth29]

How to consider that a RA was activated between 2 consecutive TS in MIP ?

Maybe use XOR-like variables to compute the number of changes: $\sum_{r} | \delta(r, t + 1) - \delta(r, t) |$