Modelling loopflows and their virtual cost#
Used input data#
Name 
Symbol 
Details 

LoopFlowCnecs 
\(c \in \mathcal{C} ^{lf}\) 
Set of FlowCnecs[1] with a loopflow threshold. (for example, in CORE CC, loopflows are monitored on crossborder CNECs). LoopFlowCnecs is a subset of FlowCnecs: \(\mathcal{C} ^{lf} \subset \mathcal{C}\) 
Reference commercial flow 
\(f^{commercial} (c)\) 
Commercial flow[2], of LoopFlowCnec \(c\), at the beginning of the optimization, in MW. 
initial loopflow 
\(f^{loop} _ {0} (c)\) 
loopflow before RAO of LoopFlowCnec \(c\), in MW 
loopflow threshold 
\(lf^{threshold} (c)\) 
loopflow threshold of the LoopFlowCnec \(c\), in MW, as defined in the CRAC. 
Used parameters#
Name 
Symbol 
Details 

This filler is only used if this extension is added. 

\(c^{accincrease}_{lf}\) 
The increase of the initial loopflow that is allowed by the optimisation, see loopflowacceptableincrease. 

\(c^{adjcoeff}_{lf}\) 
This parameter acts as a margin that tightens the loopflow constraints bounds in the linear problem. It conceptually behaves as the coefficient \(c^{adjustment}\) from the constraint below: 

\(c^{penalty}_{lf}\) 
penalisation, in the objective function, of the excess of 1 MW of loopflow 
Defined optimization variables#
Name 
Symbol 
Details 
Type 
Index 
Unit 
Lower bound 
Upper bound 

loopflow excess 
\(S^{lf} (c)\) 
Slack variable for loopflow constraint of FlowCnec c. 
Real value 
One variable for every element of \(\mathcal{C} ^{lf}\) 
MW 
0 
\(+\infty\) 
Used optimization variables#
Name 
Symbol 
Defined in 

Flow 
\(F(c)\) 
Defined constraints#
Keeping the loopflows within their bounds#
With \(\overline{f^{loop} (c)}\) the loopflow threshold, constant defined as:
The two first terms of the max define the actual loopflow upper bound:
either as the threshold defined in the CRAC,
or as the initial loopflow value of the FlowCnec, on which the acceptable increase coefficient is added
The last term ensures that the initial situation is always feasible, whatever the configuration parameters.
Contribution to the objective function#
Penalisation of the loopflow excess in the objective function:
This penalisation is part of the virtual cost.