[PERSON] et al. [12] investigated admittance relaying and [13] dynamic state estimation for the protection of microgrids. Methods and techniques, however, must be evaluated in appropriate simulation tools to verify their effectiveness. A suitable tool for performing short-circuit studies in microgrids and modeling contribution from distributed generation, particularly from inverter-interfaced generation, is currently unavailable. Even though software solutions for modeling transient environments--such as MATLAB(r) Simscape [14], PSIM [15], PLECS(r) [16] for power electronics and PSCAD [17], EMTP-RV(r) [18], ATP [19] for power systems-do exist, their high computational costs and data requirements make them unsuitable for distribution network modeling, where the total number of nodes often exceed the \(10^{4}\) range. Modeling inverter-interfaced generation in a conventional phasor-based short-circuit analysis presents difficulties on account of the current-limiting behavior of inverters which introduces nonlinear behavior into the problem. The addition of outer iteration-loops to the short-circuit solver for setting inverter current setpoints becomes necessary [20; 21; 22; 23; 24; 25]. This paper discusses how an optimization-based formulation can be employed to perform short-circuit analysis. Such an approach allows for the potential to express protection coordination constraints directly within a design or operation problem (including line switching or generator commitment). These constraints ensure that a given switch state is feasible in terms of protective coordination, so protective devices can isolate a fault without causing an unacceptable number of loads to lose power. The feasibilities of switch states in smaller microgrids, or in larger microgrids where the number of switch-configurations is limited by operational restrictions, can be determined automatically. An automated approach can be executed sequentially by applying an optimal protection coordination (OPC) problem to each state [26; 27; 28; 29; 30]. As relay settings are explicitly calculated, the infeasible states for protection, which otherwise might not be detected by constraints on fault current, can be caught. These approaches are based on performing an offline fault study in advance, where the results provide an input to the OPC [31]. Both the fault study and the OPC must be performed for each switch-configuration individually. Performing a fault study to enumerate allowable states becomes infeasible in larger microgrids because the number of possible configurations grows exponentially with the number of switches. In these cases, eliminating the need for protection settings or using novel protection technologies with settings simple enough so that coordination becomes unnecessary are potential solutions to the problem becoming intractable [32; 33]. However, for traditional protection, a scalable approach is required. Directly encoding protection feasibility constraints into an optimal operation or planning problem is such an approach. This has been demonstrated for certain use cases, for example, transmission generation capacity expansion [34; 35; 36; 37] and fault current limiter placement [38; 39; 40]. In these studies, the short-circuit current constraints are encoded using \(Z_{bus}\), the inverse of the admittance matrix. This approach avoids the need to add additional variables for the fault currents. However, it is only valid for conventional synchronous generation where the generator sub-transient reactances can be included in \(Z_{bus}\) and \(Z_{bus}\) is relatively constant. This precludes its use in problem formulations that include line switching. Subsequent work has adapted this \(Z_{bus}\) approach to address the transmission network expansion planning problem that can cause significant changes in \(Z_{bus}\). One approach includes the application of meta-optimization algorithms, such as genetic algorithms [40]. Another applies [PERSON]'s decompositions across expansion scenarios [41].