Slack bus and main connex component

The slack bus \(s\) is determined by identifying the bus with the highest number of AC branches connected, within the main component (cc set to \(0\) in ampl_network_buses.txt). If multiple buses have such cardinality, the one with the highest identifier (num parameter) is chosen. In the event that no bus satisfies these conditions, the first bus defined in ampl_network_buses.txt is selected.

The OPFs are executed on the main connex component (i.e. buses connected to slack bus by AC branches) of the network. Consequently, buses connected to the slack only by HVDC lines are excluded.

This component is determined by solving the following optimization problem (the variables are bolded):

\[\text{maximize} \left(\sum\limits_{i} \boldsymbol{\theta_i^{cc}}\right)\]

where \(\boldsymbol{\theta_i^{cc}}\) is the voltage angle of bus \(i\), and with the following constraints:

\[\boldsymbol{\theta_s^{cc}} = 0 \quad (1)\]

\[\boldsymbol{\theta_i^{cc}} - \boldsymbol{\theta_j^{cc}} = 0, \quad ij \in BRANCH \quad (2)\]

\[0 \leq \boldsymbol{\theta_i^{cc}} \leq 1, \quad i \in BUS \quad (3)\]

If the solving is unsuccessful, the script reactiveopfexit.run is executed (see In case of inconsistency) and the execution is stopped. The sets of buses and branches belonging to the main connex component are now denoted \(BUSCC\) and \(BRANCHCC\), respectively.