In analogy to extremal principles in physics, we introduce the Principle of Least Revenue for treating market equilibria. It postulates that equilibrium prices minimize the total excessive revenue of market’s participants. As a consequence, the necessary optimality conditions describe the clearance of markets, i.e. at equilibrium prices supply meets demand. It is crucial for our approach that the potential function of total excessive revenue be convex. This facilitates structural and algorithmic analysis of market equilibria by using convex optimization techniques. In particular, results on existence, uniqueness, and efficiency of market equilibria follow easily. The market decentralization fits into our approach by the introduction of trades or auctions. For that, Duality Theory of convex optimization applies. The computability of market equilibria is ensured by applying quasi-monotone subgradient methods for minimizing nonsmooth convex objective—total excessive revenue of the market’s participants. We give an explicit implementable algorithm for finding market equilibria which corresponds to real-life activities of market’s participants.

The work is done in collaboration with Yurii Nesterov.

Experience shows that large problems are most efficiently solved by simple methods. Stochastic programming problems typically involve expectations, probabilities and risk measures. This means large amounts of data to be organized, and inaccuracy in function evaluations. In this talk we deal with simple solution methods that only use function values and gradients. we discuss computational issues of decomposing risk-averse two-stage problems, and of handling probabilistic constraints in static problems. We adapted cutting-plane methods to such problems. Primal forms proved efficient for the former problem class, and dual forms for the latter class. To compare methods, we present several computational studies that were carried through in collaboration with different research teams. The importance of efficiency will be demonstrated in a case study.

The material of this talk is based on joint projects with the collaboration of Edit Csizmas, Rajmund Drenyovszki, Eldon F.D. Ellison, Achim Koberstein, Gautam Mitra, Olga Papp, Diana Roman, Leena Suhl, Tamas Szantai, Zoltan Szoke, Win van Ackooij, Tibor Vajnai, Christian Wolf, Victor Zverovich

Due to technological developments and political goals related to renewable energy and energy efficiency, the electricity system is undergoing significant changes. One of the main consequences, is an active demand side where consumers take a more active role. We model several classes of shiftable and curtailable loads in residential, commercial and industrial sectors. The benefits of demand response consist of a reduction in peak load consumption, which leads to reduction in capacity investments, production and consumption savings, reduced congestion phases, reliable integration of intermittent renewable resources and supply and demand flexibility.

We first present a model for the scheduling of energy flexibility in buildings. Next, we propose short-term decision-support models for aggregators that sell electricity to prosumers and buy back surplus electricity. The key element is that the aggregator can control flexible energy units at the prosumers. We demonstrate the approach in a generalized market design that is flexible enough to capture today’s market structure and still relevant in the next generation market design, both at wholesale and local level: an options market where flexibility is reserved for later use, a spot market for energy day-ahead or shorter, and a flexibility market where flexibility units are dispatched near real-time.

Finally, we look at the European level and analyse to what extent the demand response potential can facilitate an optimal transition to an European low emission power system. The results show that demand response decreases system operational costs and increases the capacity factors of IRES (Intermittent Renewable Sources). Results show that demand response capacity reduces investments in peak load plants and their capacity factors, from which follows lower CO2 emissions.