Distribution of currents in 2 × 25 kV electric railway systems under normal conditions considering independently the catenaries in the same path
摘要
This article shows the distribution of currents in 2 × 25 kV electric railway systems under normal conditions considering independently the catenaries of different railways in the same path, in contrast with the most common previous methods that group those catenaries as a single equivalent element. In order to compute the distribution of currents, the circuit equations are formulated in a way which is useful to offer a simplified analytical solution as well as to numerically solve them. The simplified analytical solution is obtained considering ideal transformers and, under these conditions: (a) distributions of currents are deduced for cases with only one train, and the effect of train location can be easily understood and (b) cases with multiple trains are solved by superposition method. Cases considering autotransformer impedances are numerically solved, and it is shown that the effect of these impedances is very low, especially because they usually are small; consequently, the simplified analytical method is a good tool to obtain an approximate solution. The numerical results are compared with those from a previous model that considers both catenaries grouped as a single element. In these cases, catenaries and feeders are modeled using 3 × 3 or 2 × 2 impedance matrices to consider independently each catenary, or both as a single element, respectively. Although the use of 3 × 3 impedance matrices is indispensable to properly obtain the distribution of currents in the catenaries of the same path, it is herein shown that the other currents of the system can be accurately computed using 2 × 2 impedance matrices. On the other hand, the simplified analytical solution was also successfully verified by comparison with measured results for an example taken from the literature as well as with the results from ATP for this example.