  Large horsepower induction motors play a critical role as industrial drives
in production facilities. The operational safety of distribution networks
during the starting transients of these motor loads is a critical concern for
the operators. In this paper, an analytical and convex optimization model is
derived representing the starting transients of the induction motor in a
semi-static fashion. This model is used to find the optimal energization
sequence of different loads (static and motor loads) following an outage in a
distribution network. The optimization problem includes the optimal control of
the converter-based DGs and autotransformers that are used for the induction
motor starting. These models together with the semi-static model of the
induction motor are integrated into a relaxed power flow formulation resulting
in a Mixed-Integer Second Order Cone Programming (SOCP) problem. This
formulation represents the transient operational limits that are imposed by
different protection devices both in the motor side and network side. The
functionality of the proposed optimization problem is evaluated in the case of
a large-scale test study and under different simulation scenarios. The
feasibility and accuracy of the optimization results are validated using I)
off-line time-domain simulations, and II) a Power Hardware-In-the-Loop
experiment.
