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

\(F(c)\)

CoreProblemFiller

Defined constraints

💡 Max Min Margin constraints are considered in the flow unit in the MIP.

Define the minimum margin variable

\[ \begin{equation} MM \leq f^{+}_{threshold} (c) - F(c), \forall c \in \mathcal{C} ^{o} \end{equation} \]
\[ \begin{equation} MM \leq F(c) - f^{-}_{threshold} (c), \forall c \in \mathcal{C} ^{o} \end{equation} \]

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:

\[ \begin{equation} \min (-MM) \end{equation} \]