Grid Segment Research Articles

Improving Grid Transmission Capacity and Voltage Quality in Low-Voltage Grids with a High Proportion of Distributed Power Plants

The proportion of renewable energies in power generation is increasing according to the political aims in recent years. In low-voltage grids, these are mostly decentralized renewable energy systems such as photovoltaic power plants (PV) connected through inverters to the grid. The temporary reversal of the power flow causes overvoltage problems. Consequently, regenerative sources need to be turned off temporarily or on the long term the grid infrastructure has to be extended by the network operator. This paper describes two concepts to increase power capability and voltage quality of the grid. On the one hand reactive power generated by solar inverters is used to influence the grid voltage locally. On the other hand a controllable tap changer in a low-voltage transformer is able to influence the voltage in the whole low-voltage grid. Thus grid extension can be avoided in many cases or at least can be delayed. Voltage fluctuations due to varying power input, e.g. caused by passing clouds, can be reduced. Distributed data collection and central control is required to control a distributed system of multiple solar inverters installed in a grid segment. The concept can be applied not only to PV systems; it is rather a basic technology which can be used in future grids with distributed generation and storage.

A method of grid element cloning

A simple, reliable, and fast method of putting a new computational facilities into operation in a grid environment is described. This method was successfully tested as part of the grid segment at Dzhelepov Laboratory of Nuclear Problems, Joint Institute for Nuclear Research (JINR), for work at the ATLAS collaboration.

A coupling interface method for elliptic interface problems

We propose a coupling interface method (CIM) under Cartesian grid for solving elliptic complex interface problems in arbitrary dimensions, where the coefficients, the source terms, and the solutions may be discontinuous or singular across the interfaces. It consists of a first-order version (CIM1) and a second-order version (CIM2). In one dimension, the CIM1 is derived from a linear approximation on both sides of the interface. The method is extended to high dimensions through a dimension-by-dimension approach. To connect information from each dimension, a coupled equation for the first-order derivatives is derived through the jump conditions in each coordinate direction. The resulting stencil uses the standard 5 grid points in two dimensions and 7 grid points in three dimensions. Similarly, the CIM2 is derived from a quadratic approximation in each dimension. In high dimensions, a coupled equation for the principal second-order derivatives u x k x k is derived through the jump conditions in each coordinate direction. The cross derivatives are approximated by one-side interpolation. This approach reduces the number of grid points needed for one-side interpolation. The resulting stencil involves 8 grid points in two dimensions and 12–14 grid points in three dimensions. A numerical study for the condition number of the resulting linear system of the CIM2 in one dimension has been performed. It is shown that the condition number has the same behavior as that of the discrete Laplacian, independent of the relative location of the interface in a grid cell. Further, we also give a proof of the solvability of the coupling equations, provided the curvature κ of the interface satisfies κh ⩽ Const, where h is the mesh size. The CIM1 requires that the interface intersects each grid segment (the segment connecting two adjacent grid points) at most once. This is a very mild restriction and is always achievable by refining meshes. The CIM2 requires basically that the interface does not intersect two adjacent grid segments simultaneously. In practice, we classify the underlying Cartesian grid points into interiors, normal on-fronts, and exceptionals, where a standard central finite difference method, the CIM2, and the CIM1 are adopted, respectively. This hybrid CIM maintains second-order accuracy in most applications due to the fact that usually in d dimensions, the number of normal on-front grid points is O( h 1− d ) and the number of the exceptional points is O(1). Numerical convergence tests for the CIM1 and CIM2 are performed. A comparison study with other interface methods is also reported. Algebraic multigrid method is employed to solve the resulting linear system. Numerical tests demonstrate that CIM1 and CIM2 are respectively first order and second order in the maximal norm with less error as compared with other methods. In addition, this hybrid CIM passes many tests of complex interface problems in two and three dimensions. Therefore, we believe that it is a competitive method for complex interface problems.

Cooperative mobile guards in grids

A grid P is a connected union of vertical and horizontal segments. A mobile guard is a guard which is allowed to move along a grid segment, thus a point x is seen by a mobile guard g if either x is on the same segment as g or x is on a grid segment crossing g. A set of mobile guards is weakly cooperative if at any point on its patrol, every guard can be seen by at least one other guard. In this paper we discuss the classes of polygon-bounded grids and simple grids for which we propose a quadratic time algorithm for solving the problem of finding the minimum weakly cooperative guard set (MinWCMG). We also provide an O ( n log n ) time algorithm for the MinWCMG problem in horizontally or vertically unobstructed grids. Next, we investigate complete rectangular grids with obstacles. We show that as long as both dimensions of a grid are larger than the number of obstacles k, k + 2 weakly cooperative mobile guards always suffice to cover the grid. Finally, we prove that the MinWCMG problem is NP-hard even for grids in which every segment crosses at most three other segments. Consequently, the minimum k-periscope guard problem for 2D grids is NP-hard as well, and this answers the question posed by Gewali and Ntafos [L.P. Gewali, S. Ntafos, Covering grids and orthogonal polygons with periscope guards, Computational Geometry: Theory and Applications 2 (1993) 309–334].

Improvement of beam performance in the negative-ion based NBI system for JT-60U

The injection performance of the negative-ion based NBI (N-NBI) system for JT-60U has been improved by correcting beamlet deflection and improving spatial uniformity of negative ion production. Beamlet deflection at the peripheral region of the grid segment due to the distorted electric field at the bottom of the extractor has been observed. This was corrected by modifying the surface geometry at the extractor to form a flat electric field. Moreover, beamlet deflection due to beamlet–beamlet repulsion caused by space charge was also compensated for by extruding the edge of the bottom extractor. This resulted in a reduction of the heat loading on the NBI port limiter. As a result of the improvement above, continuous injection of a 2.6 MW H0 beam at 355 keV has been achieved for 10 s. Thus, long pulse injection up to the nominal pulse duration of JT-60U was demonstrated. This has opened up the prospect of long pulse operation of the negative-ion based NBI system for a steady-state tokamak reactor. So far, a maximum injection power of 5.8 MW at 400 keV, with a deuterium beam, and 6.2 MW at 381 keV, with a hydrogen beam, have been achieved in the JT-60U N-NBI. Uniformity of negative ion production was improved by tuning the filament emission current so as to direct more arc power into the region where less negative ion current was extracted.