Modelling the maximum minimum margin objective¶
Used input data¶
Name |
Symbol |
Details |
|---|---|---|
OptimisedFlowCnecs |
\(c \in \mathcal{C} ^{o}\) |
Set of FlowCnecs[1] which are ‘optimised’. OptimisedFlowCnecs is a subset of FlowCnecs: \(\mathcal{C} ^{o} \subset \mathcal{C}\) |
upper threshold |
\(f^{+}_{threshold} (c)\) |
Upper threshold of FlowCnec \(c\), in flow unit, as defined in the CRAC |
lower threshold |
\(f^{-}_{threshold} (c)\) |
Lower threshold of FlowCnec \(c\), in flow unit, defined in the CRAC |
nominal voltage |
\(U_{nom}(c)\) |
Nominal voltage of OptimizedFlowCnec \(c\) |
Defined optimization variables¶
Name |
Symbol |
Details |
Type |
Index |
Unit |
Lower bound |
Upper bound |
|---|---|---|---|---|---|---|---|
Minimum margin |
\(MM\) |
the minimum margin over all OptimizedFlowCnecs |
Real value |
one scalar variable for the whole problem |
MW or AMPERE (depending on flow unit |
\(-\infty\) |
\(+\infty\) |
Used optimization variables¶
Name |
Symbol |
Defined in |
|---|---|---|
Flow |
\(F(c)\) |
Defined constraints¶
💡 Max Min Margin constraints are considered in the flow unit in the MIP.
Define the minimum margin variable¶
Note that OptimizedFlowCnec might have only one threshold (upper or lower), in that case, only one of the two above constraints is defined.
Contribution to the objective function¶
The minimum margin should be maximised: