Optimization of multidimensional cross-section tables for few-group core calculations

Multigroup diffusion codes for three dimensional LWR core analysis use as input data pre-generated homogenized few group cross sections and discontinuity factors for certain combinations of state variables, such as temperatures or densities. The simplest way of compiling those data are tabulated libraries, where a grid covering the domain of state variables is defined and the homogenized cross sections are computed at the grid points. Then, during the core calculation, an interpolation algorithm is used to compute the cross sections from the table values. Since interpolation errors depend on the distance between the grid points, a determined refinement of the mesh is required to reach a target accuracy, which could lead to large data storage volume and a large number of lattice transport calculations. In this paper, a simple and effective procedure to optimize the distribution of grid points for tabulated libraries is presented. Optimality is considered in the sense of building a non-uniform point distribution with the minimum number of grid points for each state variable satisfying a given target accuracy in k-effective. The procedure consists of determining the sensitivity coefficients of k-effective to cross sections using perturbation theory; and estimating the interpolation errors committed with different mesh steps for each state variable. These results allow evaluating the influence of interpolation errors of each cross section on k-effective for any combination of state variables, and estimating the optimal distance between grid points.

State of the Art and Future Trends in Grid Codes Applicable to Isolated Electrical Systems

Electrical power systems are changing their traditional structure, which was based on a little number of large generating power plants placed at great distances from loads by new models that tend to split the big production nodes in many smaller ones. The set of small groups which are located close to consumers and provide safe and quality energy is called distributed generation (DG). The proximity of the sources to the loads reduces losses associated with transportation and increases overall system efficiency. DG also favors the inclusion of renewable energy sources in isolated electrical systems or remote microgrids, because they can be installed where the natural resource is located. In both cases, as weak grids unable to get help from other nearby networks, it is essential to ensure appropriate behavior of DG sources to guarantee power system safety and stability. The grid codes sets out the technical requirements to be fulfilled for the sources connected in these electrical networks. In technical literature it is rather easy to find and compare grid codes for interconnected electrical systems. However, the existing literature is incomplete and sparse regarding isolated electrical systems and this happens due to the difficulties inherent in the pursuit of codes. Some countries have developed their own legislation only for their island territory (as Spain or France), others apply the same set of rules as in mainland, another group of island countries have elaborated a complete grid code for all generating sources and some others lack specific regulation. This paper aims to make a complete review of the state of the art in grid codes applicable to isolated systems, setting the comparison between them and defining the guidelines predictably followed by the upcoming regulations in these particular systems.