Abstract-A variety of energy resources has been identified as being flexible in their electric energy consumption or generation. This energetic flexibility can be used for various purposes such as minimizing energy procurement costs or providing ancillary services to power grids. To fully leverage the flexibility available from distributed small-scale resources, their flexibility must be quantified and aggregated. This paper introduces a generic and scalable approach for flexible energy systems to quantitatively describe and price their flexibility based on zonotopic sets. The description proposed allows aggregators to efficiently pool the flexibility of large numbers of systems and to make control and market decisions on the aggregate level. In addition, an algorithm is presented that distributes aggregate-level control decisions among the individual systems of the pool in an economically fair and computationally efficient way. Finally, it is shown how the zonotopic description of flexibility enables an efficient computation of aggregate regulation power bid-curves.

Abstract:A k-piece of a graph G is a connected subgraph of G all of whose nodes have degree at most k and at least one node has degree equal to k. We consider the problem of covering the maximum number of nodes of a graph by node disjoint k-pieces. When k = 1 this is the maximum matching problem, and when k = 2 this is the problem, recently studied by Kaneko [19], of covering the maximum number of nodes by disjoint paths of length greater than 1. We present a polynomial time algorithm for the problem as well as a Tutte-type existence theorem and a Berge-type min-max formula. We also solve the problem in the more general situation where the "pieces" are defined in terms of lower and upper bounds on the degrees.

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Traditionally in Hungary the soil cover under agricultural and forestry management is typically characterized independently and just approximately identically. Soil data collection is carried out and the databases of soil features are managed irrespectively. As a consequence, nationwide soil maps cannot be considered homogeneously predictive for soils of croplands and forests, plains and hilly/mountainous regions. In order to compile a national soil type map with harmonized legend as well as with spatially relatively homogeneous predictive power and accuracy, the authors unified their resources. Soil profile data originating from the two sources (agriculture and forestry) were cleaned up and harmonized according to a common soil type classification. Various methods were tested for the compilation of the target map: segmentation of a synthesized image consisting of the predictor variables, multi stage classification by Classification and Regression Trees, Random Forests and Artificial Neural Networks. Evaluation of the results showed that the object based, multi-level mapping approach performs significantly better than the simple classification techniques. A combination of best performing classifiers, when each classifier's vote on the same object is weighted according to its confidence in the voted class, led to the final product: a unified, national, soil type map with spatially consistent predictive capabilities.