This paper 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 paper, 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.

Soft open points (SOPs) are power electronic devices which can replace conventional normally open points in distribution networks. SOPs enable full control of active power flow between the interconnected feeders and can inject reactive power at each node to which they are connected. SOPs integrated with energy storage (ES) have been recently proposed to realize both spatial and temporal flexibility in active distribution networks. The flexibility provided by integrated ES-SOP devices will allow network operators to run their networks closer to their limits, but only if there is appropriate management of the uncertainty arising from demand and renewable generation. The only existing model of an ES-SOP uses nonconvex nonlinear equations, neglects uncertainty, and represents converter losses in an oversimplistic manner. This paper presents a robust mixedinteger convex model for the optimal scheduling of integrated ES-SOPs to ensure a zero probability of constraint violation. Losses of the subsystems comprising the ES-SOP are modelled using a proposed binary-polynomial model, enabling efficient scheduling of the energization state of subsystems to reduce no-load losses. The ES-SOP is considered in this paper to be owned by the network operator to: 1) manage power flow constraints, 2) minimize cost of losses, and 3) maximize arbitrage profit.

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