Transmission

Transmission lines allow energy transport between price areas. The transmission system is represented as in a transportation model, with a topology and capacities. There is no separation between AC and DC lines/cables.

A flow connection between two areas is defined with a direction. Flow in a connection is then represented by a pair of nonnegative variables, where \( tran\_to \) represents flow in the positive direction, and \( tran\_from\) in the negative direction.

\[ 0 \leq tran\_to(c,k) \leq \textrm{TranMax}(c,k) \qquad , \forall \enspace c \in Connections,\ k \in Timesteps \]

\[ 0 \leq tran\_from(c,k) \leq \textrm{TranMax}(c,k) \qquad , \forall \enspace c \in Connections,\ k \in Timesteps \]

Ramping

Changes in flow in a line between two consecutive time steps can be constrained by ramping limits \( \textrm{RampMax}(l,k) \). These limits are assumed symmetric for upwards and downwards ramping.

\[ \textrm{RAMP}(c,k): -\textrm{RampMax}(c,k) \leq \Bigr(tran\_to(c,k) - tran\_from(c,k)\Bigr)\ - \]

\[ \Bigr(tran\_to(c,k-1) - tran\_from(c,k-1)\Bigr) \leq \textrm{RampMax}(c,k) \qquad, \forall c,k\]

In the special case of k=1, \( tran\_to(c,0) \) and \( tran\_from(c,0) \) are obtained from the solution of the previous decision stage.