  In recent years, microgrids, i.e., disconnected distribution systems, have
received increasing interest from power system utilities to support the
economic and resiliency posture of their systems. The economics of long
distance transmission lines prevent many remote communities from connecting to
bulk transmission systems and these communities rely on off-grid microgrid
technology. Furthermore, communities that are connected to the bulk
transmission system are investigating microgrid technologies that will support
their ability to disconnect and operate independently during extreme events. In
each of these cases, it is important to develop methodologies that support the
capability to design and operate microgrids in the absence of transmission over
long periods of time. Unfortunately, such planning problems tend to be
computationally difficult to solve and those that are straightforward to solve
often lack the modeling fidelity that inspires confidence in the results. To
address these issues, we first develop a high fidelity model for design and
operations of a microgrid that include component efficiencies, component
operating limits, battery modeling, unit commitment, capacity expansion, and
power flow physics; the resulting model is a mixed-integer
quadratically-constrained quadratic program (MIQCQP). We then develop an
iterative algorithm, referred to as the Model Predictive Control (MPC)
algorithm, that allows us to solve the resulting MIQCQP. We show, through
extensive computational experiments, that the MPC-based method can scale to
problems that have a very long planning horizon and provide high quality
solutions that lie within 5\% of optimal.
