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Also, constraint \eqref{28} functions analogous to constraint \eqref{12} in Section \ref{section2}. The lower bound of decomposition algorithm at iteration k can be obtained by solving the \textrm{MILP} optimization problem of \eqref{16}-\eqref{28} (i.e., $\textrm{LB}=\Psi_{\textrm{MP}}$).
\subsection{Sub-Problem}\label{subsection2}
Given the optimal switching maneuver obtained by solving \textrm{MP} at iteration k (i.e., $Z_\ell^k ~\forall \ell$), \textrm{SP} determines the worst-case realization of uncertain net nodal electricity demands by solving the following minimax cost optimization problem: