The so-called optimal power flow (OPF) problem is a cornerstone problem for the operational planning of
electric power systems. The solution of this nonlinear program provides an ensemble of generator set points
such that the network flow constraints and the power demand are satisfied whilst respecting engineering
constraints, e.g. line limits and generator limits. The formulation and reliable solution of OPF problems
is becoming increasingly challenging due to the influx of renewables—it is non longer certain how much
electricity is being produced where and by whom. Modeling uncertainties via random variables, this leads to
the so-called stochastic OPF problem. Its solution provides an ensemble of generator set points such that
the network flow constraints and the power demand are satisfied despite uncertain generation/production.
The stochastic OPF problem can be formulated as a nonlinear optimization problem with random variables
as decision variables. The solution of this problem can be obtained using Polynomial Chaos Expansion—
a Hilbert space method for random variables that is mathematically equivalent to Fourier expansion of
The objective of the project is to design and implement fast and reliable algorithms to solve stochastic
OPF via polynomial chaos expansion. This may involve automatic re-scaling of the problem or sparse grid
techniques, to name a few. The problem may be solved either via intrusive or non-intrusive techniques.
Other methods from the field of uncertainty quantification may be equally applicable.
We wish to emphasize that it is not required to have a strong background in electrical engineering. On
the contrary, a solid understanding of numerical optimization and/or uncertainty quantification is much
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