  The proliferation of distributed energy resources (DERs) im-poses new
challenges to distribution system operation, e.g., power quality issues. To
overcome these challenges and enhance system operation, it is critical to
effectively utilize all available resources and accurately characterize
unbalanced distribution networks in operational tools. This paper proposes a
convex second-order-cone programming (SOCP)-based AC optimal power flow (ACOPF)
model for three-phase unbalanced distribution net-works, including smart
inverters and Volt-VAr controller (VVC) devices. Reactive power-voltage (Q-V)
characteristics of smart inverters of solar photovoltaic (PV) units are also
modeled. More-over, the settings of Q-V characteristics of VVC are co-optimized
within the proposed ACOPF, considering the allowable range of the IEEE
1547-2018 standard. Furthermore, dynamic analyses are conducted to verify the
stability of optimal settings of VVC. The proposed models are tested on an
actual 1747-node primary distribution feeder in Arizona. The results illustrate
the effective-ness of the proposed ACOPF for unbalanced systems in provid-ing a
global optimal solution while capturing the non-linearity and non-convexity of
ACOPF. By co-optimizing settings, system operation is improved due to the
flexibility of adjusting reactive power output from PV units with VVC. The
time-domain simu-lations show that the optimal settings result in a stable
system
