Modelling un-optimised CNECs (PSTs)#

⚠️ NOTE
These constraints are not compatible with Modelling un-optimised CNECs (CRAs).
Only one of both features can be activated through RAO parameters.

Used input data#

Name	Symbol	Details
FlowCnecs	\(c \in \mathcal{C}\)	Set of optimised FlowCnecs
Upper threshold	\(f^{+}_{threshold} (c)\)	Upper threshold of FlowCnec \(c\), in MW, defined in the CRAC
Lower threshold	\(f^{-}_{threshold} (c)\)	Lower threshold of FlowCnec \(c\), in MW, defined in the CRAC
RA upper bound	\(A^{+}(r,s)\)	Upper bound of allowed range for range action \(r\) at state \(s\)[1]
RA lower bound	\(A^{-}(r,s)\)	Lower bound of allowed range for range action \(r\) at state \(s\)[1]
Sensitivities	\(\sigma _{n}(r,c,s)\)	sensitivity of RangeAction \(r\) on FlowCnec \(c\) for state \(s\)
cnecPstPairs	\((c, r)\in \mathcal{CP}\)	These are CNEC-PST combinations defined by the user in the do-not-optimize-cnec-secured-by-its-pst parameter.

Used parameters#

Name	Details
do-not-optimize-cnec-secured-by-its-pst	This filler is only used if this parameter contains CNEC-PST combinations.

Defined optimization variables#

Name	Symbol	Details	Type	Index	Unit	Lower bound	Upper bound
DoOptimize	\(DoOptimize(c)\)	FlowCnec \(c\) should be optimized. Equal to 0 if its associated PST has enough taps left to secure it, 1 otherwise.	Binary	One variable for every CNEC element \(c\) in \(\mathcal{CP}\)	no unit	0	1

Used optimization variables#

Name	Symbol	Defined in
Flow	\(F(c)\)	CoreProblemFiller
RA setpoint	\(A(r)\)	CoreProblemFiller

Defined constraints#

Defining the “don’t optimize CNEC” binary variable#

It should be equal to 1 if the PST has enough taps left to secure the associated CNEC.
This is estimated using sensitivity values.

\(\forall (c, r)\in \mathcal{CP}\) let \(s\) be the state on which \(c\) is evaluated and \(bigM(r, s) = A^{+}(r, s) - A^{-}(r, s)\)

if \(\sigma _{n}(r,c,s) \gt 0\)

\[ \begin{equation} A(r, s) \geq A^{-}(r, s) - \frac{f^{+}_{threshold} (c) - F(c)}{\sigma _{n}(r,c,s)} - bigM(r, s) \times DoOptimize(c) \end{equation} \]

\[ \begin{equation} A(r, s) \leq A^{+}(r, s) + \frac{F(c) - f^{-}_{threshold} (c)}{\sigma _{n}(r,c,s)} + bigM(r, s) \times DoOptimize(c) \end{equation} \]

if \(\sigma _{n}(r,c,s) \lt 0\)

\[ \begin{equation} A(r, s) \geq A^{-}(r, s) - \frac{f^{-}_{threshold} (c) - F(c)}{\sigma _{n}(r,c,s)} - bigM(r, s) \times DoOptimize(c) \end{equation} \]

\[ \begin{equation} A(r, s) \leq A^{+}(r, s) + \frac{F(c) - f^{+}_{threshold} (c)}{\sigma _{n}(r,c,s)} + bigM(r, s) \times DoOptimize(c) \end{equation} \]

Note that a FlowCnec might have only one threshold (upper or lower), in that case, only one of the two above constraints is defined.

Updating the minimum margin constraints#

(These are originally defined in MaxMinMarginFiller and MaxMinRelativeMarginFiller)

For CNECs which should not be optimized, their RAM should not be taken into account in the minimum margin variable unless their margin is decreased.

So we can release the minimum margin constraints if DoOptimize is equal to 0. In order to do this, we just need to add the following term to these constraints’ right side:

\[ \begin{equation} (1 - DoOptimize(c)) \times 2 \times MaxRAM, \forall (c, r) \in \mathcal{CP} \end{equation} \]

Note that this term should be divided by the absolute PTDF sum for relative margins, but it is not done explicitly in the code because this coefficient is brought to the left-side of the constraint.

Contribution to the objective function#

Given the updated constraints above, the “un-optimised CNECs” will no longer count in the minimum margin (thus in the objective function) unless they are overloaded and their associated PST cannot relieve the overload.