A novel two-stage approach for energy-efficient timetabling for an urban rail transit network

Urban rail transit (URT) is the backbone transport mode in metropolitan areas to accommodate large travel demands. The high energy consumption of URT becomes a hotspot problem due to the ever-increasing operation mileages and pressing agendas of carbon neutralization. The high model complexity and inconsistency in the objectives of minimizing passenger travel time and operational energy consumption are the main challenges for energy-efficient timetabling for a URT network with multiple interlinked lines. This study proposes a general model framework of timetabling and passenger path choice in a URT network to minimize energy consumption under passenger travel time constraints. To obtain satisfactory energy-efficient nonuniform timetables, we suggest a novel model reformulation as a tree knapsack problem to determine train running times by a pseudo-polynomial dynamic programming algorithm in the first stage. Furthermore, a heuristic sequencing method is developed to determine nonuniform headways and dwell times in the second stage. The suggested model framework and solution algorithm are tested using a real-world URT network, and the results show that energy consumption can be considerably reduced given certain travel time increments

Determination of Stray Inductance of Low-Inductive Laminated Planar Multiport Busbars Using Vector Synthesis Method

Laminated busbars connect capacitors with switching power modules, and they are designed to have low stray inductance to minimize electromagnetic interference. Attempts to accurately measure the stray inductance of these busbars have not been successful. The challenge lies with the capacitors, as they excite the busbar producing their individual stray inductances. These individual stray inductances cannot be arithmetically averaged to establish the total stray inductance that applies when all the capacitors excite the busbar at the same time. It is also not possible to measure the stray inductance by simultaneous excitation of each capacitor port using impedance analyzers. This paper presents a solution to the above dilemma. A vector synthesis method is proposed, whereby the individual stray inductance from each capacitor port is measured using an impedance analyzer. Each stray inductance is then mapped into an xyz frame with a distinct direction. This mapping exercise allows the data to be vectored. The total stray inductance is then the sum of all the vectors. The effectiveness of the proposed method is demonstrated on a busbar designed for H-bridge inverters by comparing the simulation and practical results. The absolute error of the total stray inductance between the simulation and the proposed method is 0.48 nH. The proposed method improves the accuracy by 14.9% compared to the conventional technique in measuring stray inductances

The diagonal dimension of sub-C*-algebras

We introduce diagonal dimension, a version of nuclear dimension for diagonal sub-C*-algebras (sometimes also referred to as diagonal C*-pairs). Our concept has good permanence properties and detects more refined information than nuclear dimension. In many situations it is precisely how dynamical information is encoded in an associated C*-pair. For free actions on compact Hausdorff spaces, diagonal dimension of the crossed product with its canonical diagonal is bounded above by a product involving Kerr's tower dimension of the action and covering dimension of the space. It is bounded below by the dimension of the space, by the asymptotic dimension of the group, and by the fine tower dimension of the action. For a locally compact, Hausdorff, \'etale groupoid, diagonal dimension of the groupoid C*-algebra is bounded below by the dynamic asymptotic dimension of the groupoid. For free Cantor dynamical systems, diagonal dimension (defined at the level of the crossed product C*-algebra) and tower dimension (an entirely dynamical notion) agree on the nose. Similarly, for a finitely generated group diagonal dimension of its uniform Roe algebra with the canonical diagonal agrees precisely with asymptotic dimension of the group. This statement also holds for uniformly bounded metric spaces. We apply the lower bounds above to a number of further examples which show how diagonal dimension keeps track of information not seen by nuclear dimension.Comment: 70 page