Stochastic Optimization for Grid Planning Problems
P.E. Labeau (pelabeau [at] ulb [dot] ac [dot] be), J.C. Maun (jcmaun [at] ulb [dot] ac [dot] be), P. Henneaux (pierre [dot] henneaux [at] tractebel [dot] engie [dot] com)
With the growing share of renewable and distributed energy sources in the energy mix, the variability of the electricity generation has to be taken into account in all aspects of the electrical grid from operation to planning. The intrinsically stochastic behavior of the electricity demand has now to be combined with the stochastic nature of part of the electricity generation (wind farms, photovoltaic panels...). Power flows in the grid are subject to these uncertain injections and consumptions and become stochastic power flows. Grid planning problems are then stochastic optimization problems. Such problems can be solved through an AC Optimal Power Flow (OPF) whose objective is the minimization of the investment/operation costs of grid solution. The problem is formulated as a Mixed Integer Non Linear Problem (MINLP) which can be intractable for large grids with multiple uncertainties. Moreover, due to the uncertain context, this stochastic OPF (SOPF) is subject to stochastic constraints instead of classical deterministic one.
Following a preliminary project between Tractebel Power System Consulting and ULB on this topic, an approximate discrete solution of the problem could be searched for, by resorting to techniques like genetic algorithms. Linearizing the problem could lead to another approximation of the exact solution.
These approximate solutions of the full MINLP on specific test cases will be the objective of this master thesis.