The tie lines connecting the multiple areas can be considered.
Power can be flexibly transferred between connected areas. Transmission losses cannot be taken into account. Instead, a penalty is incurred in proportion to the amount of electricity transmitted, which is added to the objective function (cost).
GF and LFC reserve and tertiary reserve can also be flexible.
By changing the setting, the reserve can be limited.
• You can choose to specify total transfer capability (TTC) and margin of tie line as a fixed value for the entire period, by month or time period, or by optimization time granularity. The default is fixed for the entire period.
The margin secured in day-ahead scheduling is zero for intra-day scheduling. This allows more inter-regional flexible capacity to be available than in intra-day scheduling. This tool can choose to retain the same amount of margin as day-ahead scheduling for intra-day scheduling. By default, the margin for intra-day scheduling is set to 0.
See the following pages for definitions of each set, index, constant, and variable.
Interchange power constraint for tie lines $$
\begin{align}
p_{t,tie}^{\text{forward}}
& \leq \left( P_{t,tie}^{\text{TTC, forward}} -
P_{t,tie}^{\text{Margin, forward}} \right) d_{t,tie}
& \forall t \in T, \forall tie \in \textit{TIE}
& \qquad (1)
\\
p_{t,tie}^{\text{counter}}
& \leq \left( P_{t,tie}^{\text{TTC, counter}} -
P_{t,tie}^{\text{Margin, counter}} \right) ( 1- d_{t,tie} )
& \forall t \in T, \forall tie \in \textit{TIE}
& \qquad (2)
\end{align}
$$
Power flow direction of GF&LFC reserve constraints for tie lines $$
\begin{align}
p_{t,tie}^{\text{GF\&LFC},\text{UP, forward}}
& \leq \left( P_{t,tie}^{\text{TTC, forward}} +
P_{t,tie}^{\text{TTC, counter}} \right) d_{t,tie}^{\text{GF\&LFC},\text{UP}}
& \forall t \in T, \forall tie \in \textit{TIE}
& \qquad (1)
\\
p_{t,tie}^{\text{GF\&LFC},\text{UP, counter}}
& \leq \left( P_{t,tie}^{\text{TTC, forward}} +
P_{t,tie}^{\text{TTC, counter}} \right) \left( 1 - d_{t,tie}^{\text{GF\&LFC},\text{UP}} \right)
& \forall t \in T, \forall tie \in \textit{TIE}
& \qquad (2)
\\
p_{t,tie}^{\text{GF\&LFC},\text{DOWN, forward}}
& \leq \left( P_{t,tie}^{\text{TTC, forward}} +
P_{t,tie}^{\text{TTC, counter}} \right) d_{t,tie}^{\text{GF\&LFC},\text{DOWN}}
& \forall t \in T, \forall tie \in \textit{TIE}
& \qquad (3)
\\
p_{t,tie}^{\text{GF\&LFC},\text{DOWN, counter}}
& \leq \left( P_{t,tie}^{\text{TTC, forward}} +
P_{t,tie}^{\text{TTC, counter}} \right) \left( 1 - d_{t,tie}^{\text{GF\&LFC},\text{DOWN}} \right)
& \forall t \in T, \forall tie \in \textit{TIE}
& \qquad (4)
\end{align}
$$
Power flow direction of tertiary reserve constraints for tie lines $$
\begin{align}
p_{t,tie}^{\text{Tert},\text{UP, forward}}
& \leq \left( P_{t,tie}^{\text{TTC, forward}} +
P_{t,tie}^{\text{TTC, counter}} \right) d_{t,tie}^{\text{Tert},\text{UP}}
& \forall t \in T, \forall tie \in \textit{TIE}
& \qquad (1)
\\
p_{t,tie}^{\text{Tert},\text{UP, counter}}
& \leq \left( P_{t,tie}^{\text{TTC, forward}} +
P_{t,tie}^{\text{TTC, counter}} \right) \left( 1 - d_{t,tie}^{\text{Tert},\text{UP}} \right)
& \forall t \in T, \forall tie \in \textit{TIE}
& \qquad (2)
\\
p_{t,tie}^{\text{Tert},\text{DOWN, forward}}
& \leq \left( P_{t,tie}^{\text{TTC, forward}} +
P_{t,tie}^{\text{TTC, counter}} \right) d_{t,tie}^{\text{Tert},\text{DOWN}}
& \forall t \in T, \forall tie \in \textit{TIE}
& \qquad (3)
\\
p_{t,tie}^{\text{Tert},\text{DOWN, counter}}
& \leq \left( P_{t,tie}^{\text{TTC, forward}} +
P_{t,tie}^{\text{TTC, counter}} \right) \left( 1 - d_{t,tie}^{\text{Tert},\text{DOWN}} \right)
& \forall t \in T, \forall tie \in \textit{TIE}
& \qquad (4)
\end{align}
$$
Maximum interchange flexibility constraints for tie lines $$
\begin{align}
p_{t,tie}^{\text{GF\&LFC},\text{UP, forward}} + p_{t,tie}^{\text{Tert},\text{UP, forward}}
& \leq P_{t,tie}^{\text{TTC, forward}} - p_{t,tie}^{\text{forward}} + p_{t,tie}^{\text{counter}}
& \forall t \in T, \forall tie \in \textit{TIE}
& \qquad (1)
\\
p_{t,tie}^{\text{GF\&LFC},\text{UP, counter}} + p_{t,tie}^{\text{Tert},\text{UP, counter}}
& \leq P_{t,tie}^{\text{TTC, counter}} - p_{t,tie}^{\text{counter}} + p_{t,tie}^{\text{forward}}
& \forall t \in T, \forall tie \in \textit{TIE}
& \qquad (2)
\\
p_{t,tie}^{\text{GF\&LFC},\text{DOWN, forward}} + p_{t,tie}^{\text{Tert},\text{DOWN, forward}}
& \leq P_{t,tie}^{\text{TTC, counter}} - p_{t,tie}^{\text{counter}} + p_{t,tie}^{\text{forward}}
& \forall t \in T, \forall tie \in \textit{TIE}
& \qquad (3)
\\
p_{t,tie}^{\text{GF\&LFC},\text{DOWN, counter}} + p_{t,tie}^{\text{Tert},\text{DOWN, counter}}
& \leq P_{t,tie}^{\text{TTC, forward}} - p_{t,tie}^{\text{forward}} + p_{t,tie}^{\text{counter}}
& \forall t \in T, \forall tie \in \textit{TIE}
& \qquad (4)
\end{align}
$$
$$
\begin{align}
p_{t,tie}^{\text{GF\&LFC},\text{UP, forward}}
& \leq P_{t,tie}^{\text{GF\&LFC},\text{UP, forwardMAX}}
& \forall t \in T, \forall tie \in \textit{TIE}
& \qquad (5)
\\
p_{t,tie}^{\text{GF\&LFC},\text{UP, counter}}
& \leq P_{t,tie}^{\text{GF\&LFC},\text{UP, counterMAX}}
& \forall t \in T, \forall tie \in \textit{TIE}
& \qquad (6)
\\
p_{t,tie}^{\text{GF\&LFC},\text{DOWN, forward}}
& \leq P_{t,tie}^{\text{GF\&LFC},\text{DOWN, forwardMAX}}
& \forall t \in T, \forall tie \in \textit{TIE}
& \qquad (7)
\\
p_{t,tie}^{\text{GF\&LFC},\text{DOWN, counter}}
& \leq P_{t,tie}^{\text{GF\&LFC},\text{DOWN, counterMAX}}
& \forall t \in T, \forall tie \in \textit{TIE}
& \qquad (8)
\end{align}
$$
$$
\begin{align}
p_{t,tie}^{\text{Tert},\text{UP, forward}}
& \leq P_{t,tie}^{\text{Tert},\text{UP, forwardMAX}}
& \forall t \in T, \forall tie \in \textit{TIE}
& \qquad (9)
\\
p_{t,tie}^{\text{Tert},\text{UP, counter}}
& \leq P_{t,tie}^{\text{Tert},\text{UP, counterMAX}}
& \forall t \in T, \forall tie \in \textit{TIE}
& \qquad (10)
\\
p_{t,tie}^{\text{Tert},\text{DOWN, forward}}
& \leq P_{t,tie}^{\text{Tert},\text{DOWN, forwardMAX}}
& \forall t \in T, \forall tie \in \textit{TIE}
& \qquad (11)
\\
p_{t,tie}^{\text{Tert},\text{DOWN, counter}}
& \leq P_{t,tie}^{\text{Tert},\text{DOWN, counterMAX}}
& \forall t \in T, \forall tie \in \textit{TIE}
& \qquad (12)
\end{align}
$$
Condition name
Default value
Setting name on the configuration file
Change from the above formula when set to False
Availability of power supply through tie lines
True
flexible_p_tie
interchange power $p_{t,tie}^{\text{forward}}$ , $p_{t,tie}^{\text{counter}}$ are fixed at 0
Depends on the tie line GF&LFC Up-reserve flexible or not
True
flexible_p_tie_gf_lfc_up
interchange GF&LFC up-reserve $p_{t,tie}^{\text{GF\&LFC},\text{UP, forward}}$ , $p_{t,tie}^{\text{GF\&LFC},\text{UP, counter}}$ are fixed at 0
Depends on the tie line GF&LFC Down-reserve flexible or not
False
flexible_p_tie_gf_lfc_down
interchange GF&LFC down-reserve $p_{t,tie}^{\text{GF\&LFC},\text{DOWN, forward}}$ , $p_{t,tie}^{\text{GF\&LFC},\text{DOWN, counter}}$ is fixed at 0
Depends on the tie line tertiary Up-reserve Flexibility
True
flexible_p_tie_tert_up
Fused tertiary up-reserve $p_{t,tie}^{\text{Tert},\text{UP, forward}}$ , $p_{t,tie}^{\text{Tert},\text{UP, counter}}$ is fixed at 0
Depends on the tie line tertiary down-reserve flexible or not
False
flexible_p_tie_tert_down
Fused tertiary down-reserve $p_{t,tie}^{\text{Tert},\text{DOWN, forward}}$ , $p_{t,tie}^{\text{Tert},\text{DOWN, counter}}$ is fixed at 0
Consideration of operational capacity constraints of tie lines
True
consider_TTC
operating capacity $P_{t,tie}^{\text{TTC, forward}}$ , $P_{t,tie}^{\text{TTC, counter}}$ to 100 times
Consideration of maximum flexibility reserve constraints for tie lines
False
consider_maximum_ reserve_constraint_for_tie
Equations (5) through (12) of the maximum flexibility reserve constraint of the tie line are not considered
Consideration of operating margins for tie lines in day-ahead planning
False
consider_tie_margin_in_intra-day
intra-day planning only, operational margin of tie lines $P_{t,tie}^{\text{Margin, forward}}$ , $P_{t,tie}^{\text{Margin, counter}}$ to 0.
