Approximate method to compute the maximum rms current in a distribution feeder due to simultaneous inrush currents in downstream transformers

This article shows an approximate method to compute the maximum rms current in a distribution feeder due to simultaneous inrush currents in downstream transformers. In the first part of the article, a method for the exact calculation of inrush currents in distribution transformers (by solving the differential equations) is tested. This exact model was verified with experimental measurements. Subsequently, the exact model was applied in order to develop the proposed method. The approximate method requires two approximations, which only use simple algebraic functions. The first approximation is required to build an equivalent system for the simultaneous inrush currents of transformers in a distribution feeder. This equivalent system is composed by a single transformer, which is fed by an ideal voltage source connected in series with an impedance. The second approximation is required to compute the maximum inrush current of a transformer by assuming that the source impedance is not negligible. These novel approximations were tested for diverse integration time intervals. The results show that the accuracy of the developed method can be considered suitable because the average percentage error, in comparison with the exact model, is in the order of 4% for the first approximation and 5% for the second approximation. The developed method allows a straightforward calculation of the maximum rms current in a feeder due to inrush currents in downstream transformers, and the knowledge of this magnitude is useful for the proper coordination of overcurrent devices in electric power distribution systems.