Seminar Details
2021-10-19 (14h) : Multi-Stage Stochastic Programming for AC Optimal Power Flow Problems
At Euler building (room a.002)
Organized by Mathematical Engineering
Speaker :
David Wozabal (Technical University of Munich)
Abstract :
We propose the first computationally tractable framework to solve multi-stage stochastic optimal power flow (OPF) problems in alternating current (AC) power systems. To this end, we use recent results on convex semi-definite programming (SDP) relaxations of OPF problems in order to adapt the SDDP algorithm for problems with a Markovian structure employing scenario lattices to discretize the underlying randomness. We show that the usual SDDP lower bound remains valid and that the algorithm converges to a globally optimal solution of the stochastic AC-OPF problem as long as the SDP relaxations are tight. In the last part of the paper, we set up an extensive case study demonstrating the practical viability of our approach. In particular, we use the IEEE RTS-GMLC network to set up a storage sitting, sizing, and operation problem under uncertainty about demand and renewable generation. We show that the convex SDP relaxation of the stochastic problem is tight except in very rare cases. Furthermore, we demonstrate that after a reasonable number of iterations the algorithm finds a policy with a relatively small SDDP optimality gap that yields a significant added value over rolling deterministic planning.