A Robust Second-Order Conic Programming Model with Effective Budget of Uncertainty in the Optimal Power Flow Problem

Integrating large-scale wind energy in modern power systems necessitates high-efficiency mathematical models to address classical assumptions in power systems. In particular, two main assumptions for wind energy integration in power systems have not been adequately studied. First, nonlinear AC power flow equations have been linearized in most of the literature. Such simplifications can lead to inaccurate power flow calculations and result in technical issues. Second, wind power uncertainties are inevitable and have been mostly modeled using traditional uncertainty modeling techniques, which may not be suitable for large-scale wind power integration. In this study, we addressed both challenges: we developed a tight second-order conic relaxation model for the optimal power flow problem and implemented the novel effective budget of uncertainty approach for uncertainty modeling to determine the maximum wind power admissibility and address the uncertainty in the model. To the best of our knowledge, this is the first study that proposes an effective, robust second-order conic programming model that simultaneously addresses the issues of power flow linearization and wind power uncertainty with the new paradigm on the budget of uncertainty approach. The numerical results revealed the advantages of the proposed model over traditional linearized power flow equations and traditional uncertainty modeling techniques.