Notations

Input parameters

Sets:

• $\mathcal{N} = \{1, ..., N\}$: Set of buses
• $\mathcal{E} = \{1, ..., E\}$: Set of branches
• $\mathcal{E}^{+}_{i}$: Set of branches leaving bus $i \in \mathcal{N}$
• $\mathcal{E}^{-}_{i}$: Set of branches entering bus $i \in \mathcal{N}$
• $\mathcal{G} = \{1, ..., G\}$: Set of generators
• $\mathcal{G}_{i} = \{1, ..., G_{i}\}$: Set of generators at bus $i \in \mathcal{N}$
• $\mathcal{L} = \{1, ..., L\}$: Set of loads at bus $i \in \mathcal{N}$
• $\mathcal{S} = \{1, ..., S\}$: Set of shunts
• $\mathcal{S} = \{1, ..., S_{i}\}$: Set of shunts at bus $i \in \mathcal{N}$.

Network data:

• $g^{s}_{s} + \mathbf{j} \, b^{s}_{s}$: complex admittance of shunt $s \in \mathcal{S}$
• $g_{e} + \mathbf{j} \, b_{e}$: complex admittance of branch $e \in \mathcal{E}$