Smart Grid Seminar

Polynomial optimization where variables and data are complex numbers is used to model oscillatory phenomena in various applications such as electric power systems, imaging science, signal processing, and quantum mechanics.  Firstly, we propose a hierarchy of complex semidefinite programs as well as a semidefinite programming solver in complex numbers to find global solutions with reduced computational burden.  We'll apply these to large-scale sections of the European HV electricity transmission grid.  Secondly, we propose an algorithm for extracting global solutions once optimality has been reached, using the operator theoretic notion of hyponormality.  Finally, we show that this algorithm provides a variant to Prony's method, which is used for instance to determine inter-area oscillations from phasor measurement units (PMU).