## Overview

To be able to face the combinatorial complexity of the problem, without having to simplify / linearize the impact of the available remedial actions available, the problem is divided into preventive and curative perimeters.
The definition of CNEC and associated usage rules allows to distinguish four temporal situations or instants in the problem:

• “Before outage situation”: immediately before the occurrence of a fault.
• “After outage situation”: immediately after the occurrence of a fault and prior to the potential application of post-fault actions (if applicable).
• “After automatons”: grid situations which follow the application of automatic remedial actions (automatons) (if applicable) in the case of a particular contingency. Note that this perimeter is simulated, not optimised
• “After curative situations”: grid situations which follow the application of curative actions (if applicable) in the case of a particular contingency.

This leads to the consideration of different optimisation perimeters. Each perimeter calls for the application of one set of remedial actions. The preventive perimeter is the first computed. Optimisation will try to maximise the objective function value on this first perimeter. Then, each contingency in curative defines one perimeter of curative optimisation. Optimisation will try to maximize the objective function value of each of these perimeters.

## Preventive perimeter

The preventive perimeter is made up of:

• CNECs of the “before outage situation” defined with a limit of type PATL (Permanent limit). This corresponds to the so-called “N state” situation.
• CNECs of the “after outage situation” defined with a limit of type TATL (Temporary limit).

Overloads potentially reached on this perimeter are to be solved with preventive actions.

## Automaton perimeters

An automaton perimeter is defined for each defined contingency. Each automaton perimeter is formed by:

• CNECs of the “after automatons” defined with a limit of type PATL. All CNECs are defined upon the same contingency.

Overloads potentially reached on this perimeter can possibly be solved with automatons. Preventive actions already applied in the “after outage situation” have to be considered in this situation (from the starting point of the automaton perimeter).

## Curative perimeters

Finally, a curative perimeter is defined for each defined contingency. Each curative perimeter is formed by:

• CNECs of the “after curative situation” defined with a limit of type PATL. All CNECs defined upon the same contingency.

Overloads potentially reached on this perimeter are to be solved with curative actions. Preventive and automatic actions already applied in the “after automatons” situation have to be considered in this situation (from the starting point of the curative perimeter).

This separation between the perimeters is justified by the fact that curative remedial actions are sufficient to solve the constraints which may appear in the curative situation (but were not already treated at preventive stage due to higher admissible limit).

Only TSOs owning curative actions allow CNECs to have a TATL which exceeds the PATL value. Operating the system with curative actions allows to overload a line temporarily, thus allowing more flexibility in grid operations.

Operationally, curative actions are sized in order to overcome the difference between these two limits (TATL-PATL).
While during preventive actions, only the TATL has to be respected (active flow should remain below this value), curative actions (if properly sized), should be able to reduce the active flow in order to respect the PATL value.
Where curative actions are not sized properly and are not sufficient to respect the two limits, CASTOR will then investigate additional preventive remedial actions, by running a second preventive optimisation.

Therefore, preventive optimisation is more permissive with CNECs defined with a TATL larger than the PATL: this allows preventive optimisation to focus preferably on CNECs with a low TATL (in particular where TSOs do not define curative actions).
When switching to the curative problem, the PATL applies, and the potential negative impact of previously found preventive actions (limited by the consideration of TATL) should be overcome by the available curative actions.

In the example below, preventive actions applied might have a negative impact on a particular CNEC (if the objective function value can be increased through the application of this action) when compared with the initial situation:

• The flow in “1- initial situation” is lower than in “2- after outage”, the margin is positive in both situations (PATL for 1, TATL for 2). But flow in situation 2 is higher than in situation 1 on this particular CNEC.
• When studying the flow in curative (“3- After curative”), PATL applies, and the CNEC is initially seen in overload against this limit due to applied preventive actions. Curative actions should then normally make the flow go below the PATL value.

## Extension of the preventive perimeter to the curative situation when no curative actions are available

The availability of curative actions is first assessed prior to the preventive optimisation:
In the case where no curative action is available for a given CNEC which is to be described in the curative problem, the curative CNEC will be treated directly within the preventive optimisation perimeter (outage 2 in figure below).
As a result, the current limit considered in the preventive optimisation of this particular CNEC will be the PATL and not the TATL.

This ensures that the optimisation avoids finding a preventive solution where the flow of this CNEC would lie between the PATL and TATL value. If such preventive solution were selected, due to the unavailability of curative actions, the flow in curative would remain higher than the PATL value, which would correspond to an overload on the grid element (situation for Outage 2 in the figure below).