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This article introduces a Robust Mixed-Integer Second Order Cone Programming (R-MISOCP) model for the resilience-oriented optimal scheduling of microgrids (MGs). This is developed for MGs that are islanded due to a scheduled interruption from the main grid, where minimizing both operational costs and load shedding is critical. The model introduced presents two main benefits. Firstly, an accurate second order cone power flow model (SOC-PF) is used, which ensures global optimality. Through a comparison with a piecewise linear power flow model on a modified IEEE 33 bus network, it is demonstrated that failure to accurately model power flow equations, can result in a significant underestimation of the operational cost of almost 12%. Secondly, uncertainty is modelled using a robust approach which allows trade-offs between the uncertainty that a MG operator is willing to tolerate, and performance. In this article, performance criteria considered are operational cost and load shedding. Market price, demand, renewable generation and islanding duration are considered as uncertain variables. Results show that by controlling the budget of uncertainty, the MG operator can achieve an almost 20% reduction in the operating cost, compared to a fully robust schedule, while achieving 0% probability of shedding more demand than expected.

MicroGrid Resilience-Oriented Scheduling: A Robust MISOCP Model