The developed suite of packages include PowerModelsDistribution.jl ([[https://github.com/lanl-ansi/PowerModelsDistribution.jl](https://github.com/lanl-ansi/PowerModelsDistribution.jl)]([https://github.com/lanl-ansi/PowerModelsDistribution.jl](https://github.com/lanl-ansi/PowerModelsDistribution.jl)) accessed on 9 April 2021) [59], PowerModels Restoration.jl ([[https://github.com/lanl-ansi/PowerModelsRestoration.jl](https://github.com/lanl-ansi/PowerModelsRestoration.jl)]([https://github.com/lanl-ansi/PowerModelsRestoration.jl](https://github.com/lanl-ansi/PowerModelsRestoration.jl)) accessed on 9 April 2021) [60], PowerModelsGMD.jl. ([[https://github.com/lanl-ansi/PowerModelsGMD.jl](https://github.com/lanl-ansi/PowerModelsGMD.jl)]([https://github.com/lanl-ansi/PowerModelsGMD.jl](https://github.com/lanl-ansi/PowerModelsGMD.jl)) accessed on 9 April 2021) [61]. Together they allow for solving a variety of power systems optimization problems, such as power flow, optimal power flow, minimum load shed, and optimal transmission switching. PMsP was developed in Julia [62], a high-level, just-in-time compiled programming language designed for scientific computing. Its current main application is for microgrids and distribution networks with distributed energy resources, including both synchronous and inverter-interfaced generation. PMsP is able to model balanced networks by using a positive sequence formulation, as well as unbalanced networks by using a three-wire Kron-reduced representation. Only three-phase faults are supported for balanced networks while for unbalanced networks, arbitrary fault configurations are supported via specifying them with an OpenDSS-style admittance matrix [63]. Both balanced and unbalanced formulations were validated against existing software. In the unbalanced formulation protective relaying that requires neutral current measurements can be supported by applying a linear transformation to represent the neutral current. The key contributions of this paper include the following: (1) formulated short-circuit current flow on unbalanced distribution networks or islanded microgrids in terms of an optimization problem, (2) developed optimization constraints for the short-circuit contribution of inverter-interfaced generation or storage, and (3) formulated constraints for protection coordination applicable to networked microgrids. These developments enable the implementation of planning and operational formulations for microgrids with inverter-interfaced generation, which allows for protection coordination to be maintained, thereby facilitating the reliable operation of large-scale networked microgrids. The remainder of this paper is organized as follows: Section 2 describes the optimization problem formulation for performing short-circuit studies with inverter-interfaced generation. Section 3 describes how the short-circuit constraints can be embedded into an operation or design problem to ensure protective device coordination. Sections 4 and 5 describe how the short-circuit constraints are applied to the IEEE 123-bus system to perform short-circuit analysis with grid-forming inverters in islanded mode. Finally, Section 6 summarizes the conclusions of this paper about the suitability of optimization-based frameworks for short-circuit analysis.