  Transmission system operators need to adapt their decision-making tools to
the technological evolutions of the twenty first century. A computation
inherent to most tools seeks to find alternating-current power flows that
minimize power loss or generation cost. Mathematically, it consists in an
optimization problem that can be described using only addition and
multiplication of complex numbers (i.e. complex polynomial optimization). The
objective of this thesis is to find feasible points that are globally optimal.
One of the outcomes of this collaborative doctoral project is to transpose the
Lasserre hierarchy to complex numbers. We use it to compute globally optimal
power flows in the European high-voltage transmission network. It consist in a
sparse non-convex quadratically-constrained quadratic program with several
thousand variables and constraints. The complex hierarchy is generally more
tractable than the Lasserre hierarchy when applied to the optimal power flow
problem.
