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Top1. Introduction
Numerical models are widely used in all fields of physics and engineering, when experiments on the real system under study (s.u.s.) are expensive or even impossible, when the influence of some parameters is of interest and is not under operator’s control, when extreme conditions or worst cases are to be tested, but are not physically feasible, perfectly repeatable, or are even beyond s.u.s. capability. A working example of a large complex electrical system is a railway traction system (Ogunsola & Mariscotti, 2012; Mariscotti, 2003), that features also strict requirements for safety and its demonstration through simulation.
A railway is a very large network with an “unpractical” system for power distribution, with trains lying on the running rails below overhead conductors, from which they collect power through the pantographs. The return current flows back to the Electric Substations (ESS) through the so called return circuit. The power distribution scheme is single phase at industrial frequency or dc.
The specific arrangement and the peculiarities of an electrified railway require that the electrical parameters are calculated for conductors of very different shapes and materials, with different distance from the boundaries of the electromagnetic problem and subject to several factors, that lead to a significant uncertainty on their value (temperature, dirt, ageing of surfaces, moisture, type of sleepers, ballast and track, etc.) (Mariscotti, 2011; Mariscotti & Pozzobon, 2004a; Mariscotti & Pozzobon, 2004b; Mariscotti & Pozzobon, 2004c; Mariscotti & Pozzobon, 2005; Paul, 1994; Mariscotti, Ruscelli & Vanti, 2010).
The verification of a model is the evaluation of the correspondence to the requirements, even for single modules during their development. The validation of a simulation model aims at verifying that it meets its intended use, in terms of overall requirements and user’s expectations. The verification phase reviews intermediate elements, by means of static analysis techniques (inspections and reviews) and possibly dynamic techniques (execution of test runs of the simulator modules, maybe assisted by synthetic data). The validation is performed on the complete product (the simulator) and uses dynamic techniques, by executing test runs on reference cases (Naik & Tripathy, 2008). A very comprehensive analysis and an interesting theoretical framework for complex systems of different nature is presented in Min, Yan and Wang (2010). Testing of a software tool for scientific purposes is accompanied by the evaluation of the accuracy of its results with respect to reference experimental data, both characterized by their uncertainty (Min, Yan & Wang, 2010). Since a model is an abstraction of a system, perfect representation is not expected nor really required (Balci, 1997). Shannon (1975) indicates that “it is not at all certain that it is even theoretically possible to establish if we have an absolutely valid model”, so that the outcome of VV&T (Verification, Validation and Testing) applied to a model should be a degree of credibility.