The aim, and main contribution, of this paper is to propose a fine-tuned fast approximator, based on neural networks, that uses aggregated traction system information as inputs and outputs. This approximator can be used as an investment planning constraint in the optimization. It considers that there is a limit on the intensity of the train traffic, depending on the strength of the power system.
In the numerical examples of this paper, the approximator inputs are the power system configuration, the distance between a connection from contact line to the public grid to another connection, and the average number of trains for that distance. The output is the maximal attainable average velocity of trains of a specific kind for the by the inputs described railway power system section. An alternative output – the traveling time is also presented.
The main emphasis of this paper is on the example section, since the contribution of this paper is mainly to show on the improved simplicity and reality compliance. The applicative contribution is twofold, an improved TPSA as a planning/decision making program constraint, whereas it also can be used as a scientifically developed rule of thumb for a planner active in the field. The aim is not primarily to show that the idea works, or to motivate the principal idea, since that is done earlier.
The approximator facilitates studies of many railway power system loading scenarios, combined with different power system configurations, for investment planning analysis. The approximator is based on neural networks. An additional value of the approximator is that it provides an understanding of the relations between power system configuration and train traffic performance.
THE APPROXIMATOR MODEL
The remaining approximator inputs are inputs to a neural network. One individual neural network is used for each RPSS technology, as illustrated in Figure 1. Why this separation is done is well explained. In this paper, however, the number of inputs is reduced to two, the most needed ones, i.e. the power section length and the number of trains in the power section.
The power section lengths are numbers that the investment planner actively and directly can influence by choosing where to locate the CE. The longer a power section, the higher the impedance – regarding that everything else remains the same. A 100 km power section with AT catenaries have, on the other hand, for example, normally a higher impedance than a 110 km power section with AT technology and a supporting transmission line connected in parallel to it. The greater the number of trains, the higher the strain.
NUMERICAL EXAMPLE PREREQUISITES
The training data used for TPSA in this example are extracted out of TPSS simulations. The same models as in with the exception that the filter in the motor is disregarded. The simulations represent variations in traffic, length, and the power system technology of a typical Swedish RPSS section. However, the training data could as well have been created from measurements and be representing different types of railway power systems than the one used here. As a consequence of the Swedish-like model, the CEs, c.f. Figure 2, are here converter stations, and the high voltage line is of the in Sweden most common 132 kV type. Contact lines and transmission lines are in Figure 2 represented by impedances.
NUMERICAL RESULTS VISUALIZED
Two different outputs have been evaluated for TPSA, with more emphasis on the average velocity, Type A. Type A have been studied earlier. The traveling time as output has however some potential and is worth being evaluated in real investment analysis programs before rejected. For both of the outputs, TPSA is evaluated for input values far away from the training data, and from what is realistic in reality. If, however, TPSA is supposed to be used as an optimization constraint, it is important to know how it behaves also for values far away. For the rare occasions, where e.g., TPSA gives velocity estimates less than zero those can be handled by simply assigning zero velocity then.
CONCLUSION, SUMMARY, AND FUTURE WORK
A suggestion to an improved TPSA method, of estimating the power system impact on traffic performance, has been presented in Sections III and IV. The function approximator uses aggregated parametric values for inputs as well as for output. The proposed method is general in many ways. There are no indications that TPSA should not be possible to apply to other kinds of doubly fed RPSS:s (including doubly fed DC RPSS:s), than those used in the numeric example. TPSA has been applied to a small specific railway power supply system in order to confirm its usability.
TPSA was evaluated in Section V, for both output Type A and B, but with emphasis put on Type A. In most Type A configurations one hidden neuron was enough, and in most Type B configurations linear neural networks performed well.
In order to visualize the behavior of an RPSS, and how TPSA manages to adapt, a number of graphs in Figures 3–7 were presented and their content was discussed in detail in Section V.
It is obvious that TPSA manages to give reliable results in a fast way for given power system setups and traffic intensities. The results presented in this paper, show that by making many simulations (or detailed measurements) and studying the results – a feeling can be acquired for what is important regarding the railway power supply system and its interaction with the train traffic. Owing to that, the here presented approximator could be made. Improvements in TPSA can be made in the sense that for more all-embracing data sets, different inputs would be possible, see the discussions in Section III-E. Future work are naturally to apply TPSA in invest- ment decision programs, like in but improved. TPSA can also be applied in traffic planning programs.
Author: Lars Abrahamsson | Lennart Söder