Franklin Djeumou Fomeni, PhD

Binary equilibrium in energy markets and transportation networks

In a competitive energy market, the independent system operator a.k.a ISO has to decide on the production level of each producer as well as the market price of the energy with the aim of achieving the equilibrium of the market. This decision often needs to take into account the physical constraints of each producer and the market-clearing constraints. However, most of the producers’ physical constraints involve binary variables, which may represent the ON/OFF statuses of power generators. These equilibrium problems are usually formulated as binary constrained mixed complementarity problems. Developing an efficient method for solving this family of problem for large power networks is still a challenge. Mainly because it presents a double layer of complexity, namely the complementarity and the integrality conditions that have to be satisfied.

One of my first research attempt in this area was to develop an efficient algorithm using mixed integer optimization approaches. More precisely, the algorithm uses the Reformulation and Linearization Technique (RLT) to re-write the complementarity conditions as linear constraints. Then, it solves a series of linear programs to replace some of the complementarity constraints with much simpler linear equations, and finally uses branch-and-bound (if needed) to solve the reduced problem.

Another focus of my research in this area is concerned with a study of equilibria in traffic networks and power systems with storage in the presence of logic constraints. The logic requirements here are modelled as binary variables that are added to standard complementarity-based equilibrium models. The resulting formulations are binary-constrained linear complementarity problems. Indeed, the traffic equilibrium problem consists of predicting steady state flows of vehicles in a transportation networks. My research shows how logic constraints can introduce some equity in the assignment of traffic flows when more than one equilibrium exists. For power systems with storage, the research shows how the presence of a storage operator in a power market may be beneficial in terms of stabilizing the price of electricity during peak demand periods. A particular novelty in this approach is that the storage operator operates as a service provider rather than a competitor to the power producers.