Conic optimization has recently emerged as a powerful tool for designing tractable and
guaranteed algorithms for power system operation. On the one hand, tractability is crucial …

The power flow equations relate the power injections and voltages in an electric power
system and are therefore key to many power system optimization and control problems …

We propose general notions to deal with large scale polynomial optimization problems and
demonstrate their efficiency on a key industrial problem of the 21st century, namely the …

We propose a homogeneous primal-dual interior-point method to solve sum-of-squares
optimization problems by combining nonsymmetric conic optimization techniques and …

Power flow refers to the injection of power on the lines of an electrical grid, so that all the
injections at the nodes form a consistent flow within the network. Optimality, in this setting, is …

This paper presents a quadratically constrained programming (QCP) model to tackle the
optimal power flow (OPF) problem in distribution networks. The proposed model is fast …

Circuit polynomials are polynomials with properties that make it easy to compute sharp and
certifiable global lower bounds for them. Consequently, one may use them to find certifiable …

The planning of distributed energy resources has been challenged by the significant
uncertainties and complexities of distribution systems. To ensure system reliability, one often …

Power flow refers to the injection of power on the lines of an electrical grid, so that all the
injections at the nodes form a consistent flow within the network. Optimality, in this setting, is …

We propose the application of occupation measure theory to the classical problem of
transient stability analysis for power systems. This enables the computation of certified inner …