Over the past century the electric power industry has evolved to support the delivery of power over long distances with highly interconnected transmission systems. Despite this evolution, some remote communities are not connected to these systems. These communities rely on small, disconnected distribution systems, i.e., microgrids to deliver power. However, as microgrids often are not held to the same reliability standards as transmission grids, remote communities can be at risk for extended blackouts. To address this issue, we develop an optimization model and an algorithm for capacity planning and operations of microgrids that include N -1 security and other practical modeling features like ac power flow physics, component efficiencies, and thermal limits. We demonstrate the computational effectiveness of our approach on two test systems; a modified version of the IEEE 13 node test feeder and a model of a distribution system in a remote community in Alaska.

Fundamental shifts in the structure and generation profile of electrical grids are occurring amidst increased demand for resilience. These two simultaneous trends create the need for new planning and operational practices for modern grids that account for the compounding uncertainties inherent in both resilience assessment and increasing contribution of variable inverter-based renewable energy sources. This work reviews the research work addressing the changing generation profile, state-of-the-art practices to address resilience, and research works at the intersection of these two topics in regards to electrical grids. The contribution of this work is to highlight the ongoing research in power system resilience and integration of variable inverter-based renewable energy sources in electrical grids, and to identify areas of current and further study at this intersection. Areas of research identified at this intersection include cyber-physical analysis of solar, wind, and distributed energy resources, microgrids, network evolution and observability, substation automation and self-healing, and probabilistic planning and operation methods.

Protecting inverter-interfaced microgrids is challenging as conventional time-overcurrent protection becomes unusable due to the lack of fault current. There is a great need for novel protective relaying methods that enable the application of protection coordination on microgrids, thereby allowing for microgrids with larger areas and numbers of loads while not compromising reliable power delivery. Tools for modeling and analyzing such microgrids under fault conditions are necessary in order to help design such protective relaying and operate microgrids in a configuration that can be protected, though there is currently a lack of tools applicable to inverter-interfaced microgrids. This paper introduces the concept of applying an optimization problem formulation to the topic of inverter-interfaced microgrid fault modeling, and discusses how it can be employed both for simulating short-circuits and as a set of constraints for optimal microgrid operation to ensure protective device coordination.

A major risk of geomagnetic disturbances (GMDs) is cascading failure of electrical grids. The modeling of GMD events and cascading outages in power systems is difficult, both independently and jointly, because of the many different mechanisms and physics involved. This paper introduces a relaxation based modeling of GMD-induced cascading failures: the dc approximation-based DCSIMSEP solver was adapted to simulate cascading as a result of GMDs, the full set of ac power flow equations were relaxed to guarantee optimality, and the reactive power losses were modeled while keeping the problem convex. The developed algorithm was implemented in PowerModelsGMD.jl - an open-source software specifically designed to model and analyze geomagnetic hazards - and demonstrated to work on the RTS-GMLC-GIC-EAST synthetic test network.

This study investigates the minimization of power losses in active distribution systems through the integration of Distributed Energy Resources (DERs) into a modified 20-node section of the IEEE 123-node test feeder. Using the Distribution Optimal Power Flow (D-OPF) framework, implemented in Julia using the PowerModelsDistribution (PMD) package and the IPOPT solver, the analysis incorporates 5 photovoltaic distributed generators (DGs), spanning both single-phase and three-phase systems. The framework optimizes active and reac-tive power flows while ensuring voltage stability. Comparative results demonstrated that the proposed framework effectively reduces power losses, balances PV generation, and maintains voltage profiles within permissible limits. The approach was validated through a strong alignment with results from a previous study, with minor deviations attributed to differences in tool methodologies. This study underscores the potential of advanced optimization frameworks to enhance the efficiency and per-formance of power distribution networks, paving the way for the future integration of larger-scale DERs and more complex systems.

A major risk of geomagnetic disturbances (GMDs) is cascading failure of electrical grids. The modeling of GMD events and cascading outages in power systems is difficult, both independently and jointly, because of the many different mechanisms and physics involved. This paper introduces a relaxation based modeling of GMD-induced cascading failures:~the dc approximation-based DCSIMSEP solver was adapted to simulate cascading as a result of GMDs, the full set of ac power flow equations were relaxed to guarantee optimality, and the reactive power losses were modeled while keeping the problem convex. The developed algorithm was implemented in PowerModelsGMD.jl - an open-source software specifically designed to model and analyze geomagnetic hazards - and demonstrated to work on the RTS-GMLC-GIC-EAST synthetic test network.