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In this paper, we propose a data-driven preventive security-constrained AC optimal power flow (SC-OPF), which ensures small-signal stability and N-1 security. Our approach can be used by both system and market operators for optimizing redispatch or AC based market-clearing auctions. We derive decision trees from large datasets of operating points, which capture all security requirements and allow to define tractable decision rules that are implemented in the SC-OPF using mixedinteger nonlinear programming (MINLP). We propose a secondorder cone relaxation for the non-convex MINLP, which allows us to translate the non-convex and possibly disjoint feasible space of secure system operation to a convex mixed-integer OPF formulation. Our case study shows that the proposed approach increases the feasible space represented in the SC-OPF compared to conventional methods, can identify the global optimum as opposed to tested MINLP solvers and significantly reduces computation time due to a decreased problem size.

This paper deals with the impact of linear approximations for the unknown nonconvex confidence region of chanceconstrained AC optimal power flow problems. Such approximations are required for the formulation of tractable chance constraints. In this context, we introduce the first formulation of a chance-constrained second-order cone (SOC) OPF. The proposed formulation provides convergence guarantees due to its convexity, while it demonstrates high computational efficiency. Combined with an AC feasibility recovery, it is able to identify better solutions than chance-constrained nonconvex AC-OPF formulations. To the best of our knowledge, this paper is the first to perform a rigorous analysis of the AC feasibility recovery procedures for robust SOC-OPF problems. We identify the issues that arise from the linear approximations, and by using a reformulation of the quadratic chance constraints, we introduce new parameters able to reshape the approximation of the confidence region. We demonstrate our method on the IEEE 118-bus system.

The integration of large-scale renewable generation has major implications on the operation of power systems, two of which we address in this work. First, system operators have to deal with higher degrees of uncertainty due to forecast errors and variability in renewable energy production. Second, with abundant potential of renewable generation in remote locations, there is an increasing interest in the use of High Voltage Direct Current lines (HVDC) to increase transmission capacity. These HVDC transmission lines and the flexibility and controllability they offer must be incorporated effectively and safely into the system. In this work, we introduce an optimization tool that addresses both challenges by incorporating the full AC power flow equations, chance constraints to address the uncertainty of renewable infeed, modelling of point-to-point HVDC lines, and optimized corrective control policies to model the generator and HVDC response to uncertainty. The main contributions are twofold. First, we introduce a HVDC line model and the corresponding HVDC participation factors in a chance-constrained AC-OPF framework. Second, we modify an existing algorithm for solving the chance-constrained AC-OPF to allow for optimization of the generation and HVDC participation factors. Using realistic wind forecast data, for 10 and IEEE 39 bus systems with HVDC lines and wind farms, we show that our proposed OPF formulation achieves good in-and out-of-sample performance whereas not considering uncertainty leads to high constraint violation probabilities. In addition, we find that optimizing the participation factors reduces the cost of uncertainty significantly.