We provide a method to obtain stationary points for mathematical and equilibrium problems with equilibrium constraints (MPECs and EPECs). The MPECs and EPECs considered have linear complementarity constraints at the lower level. Our approach is to express the MPEC and EPEC as a complementarity problem by decomposing the dual variables associated with the bilinear constraints, and using a nonlinear optimization over a polytope to find stationary points. We apply this method to the generic setting of energy markets that have operational and infrastructure decisions among many players.
We introduce a multi-regional dynamic Computable General Equilibrium model representing the Norwegian Economy with a particular focus on the energy system. The model is used to study the effects of macroeconomic policies aimed at decarbonizing the Norwegian economy, such as the reduction of the size of the oil industry, the introduction of carbon capture and storage in the gas industry as well as the introduction of a hydrogen industry and the transition of the transport sector to the usage of hydrogen and electricity to substitute conventional fossil fuels.
joint work with Christoph Helmberg
Producing accurate and secure solutions to the Optimal Power Flow problem (OPF) becomes increasingly important due to rising demand and share of renewable energy sources. To this end, we consider an OPF model with additional decision variables associated with FACTS devices, such as phase-shifting transformers (PSTs) or thyristor-controlled series capacitors (TCSCs). We show, how a Lasserre hierarchy can be applied to this model. Finally, we provide results of numerical experiments on the resulting semidefinite programming (SDP) relaxation.