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Application of Polynomial Optimization to Electricity Transmission Networks

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.