# 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.