An Algebraic Approach to DC Railway Electrification Verification

Gröbner bases have been applied to a number of problems related to the verification of Knowledge-Based Systems (KBS) and other problems within graph theory. In particular, the authors have developed in previous papers algebraic approaches to decide whether a situation in a railway interlocking system is safe or not. These algebraic approaches stand out because of the briefness of the code (as they use implementations of well-known algorithms for solving linear or algebraic systems provided by computer algebra systems). The authors have also developed a matrix-based computer tool that helps an expert to check whether a proposed railway electrification scenario (given through the topology of the railway station and the position of the isolation devices and the position and state of the “electrical bypasses” and feeders) fulfills the mandatory requirements of the Spanish railway infrastructure administrator (ADIF) for 3000 V railway electrifications or not. The second author works in the field of railway electrifications and he compares the present-day methods for verification of railway electrifications with the way KBS were verified in the past (manually by experts). In this article we approach this latter problem using algebraic techniques. The new computer tool is based on an algebraic translation of the problem (instead of based on the use of matrices) and is really simple and fast. Determining which electrification sections are under electric tension is computed solving linear systems (because in this case the graph is undirected and no polynomials of degree \(>\,1\) arise in the algebraic translation, so it is not necessary to use Gröbner bases, unlike in the two problems mentioned in the beginning of the Abstract). Therefore far bigger railway facilities can be addressed than if non-linear systems were involved.