Calculation of the Voltage Unbalance Factor for High-Speed Railway Substations with V-Connection Scheme

Abstract

In France, high-speed railway lines are powered by a 2 × 25 kV/50 Hz electrification system. The substations include two single-phase transformers connected to the high-voltage electrical transmission network on different pairs of phases according to a so-called “V-connection scheme”. In practice, due to the large variations in the power absorbed by the trains, this connection does not make it possible to satisfactorily limit the unbalance in the three-phase voltages. In order to correctly size a balancing system to be associated with the substation, it is necessary to calculate, with precision, the voltage unbalance factor as a function of the power drawn by the trains. In its first part, this paper presents modelling of the substation and proposes an algorithm which allows for the calculation of the upstream line voltage as a function of the power consumption at the secondary of the transformers. The voltage unbalance factor can then be determined over a long period of operation. In the second part of this paper, the same approach is applied with an unbalance-compensator based on Steinmetz circuits controlled by AC choppers. Finally, in both cases, the results of the calculations are validated by simulations performed with PLECS simulation software.

Improved Method for Determining Voltage Unbalance Factor Using Induction Motors

“…For an unbalanced three-phase voltage system, the VUF can be calculated with the mathematical expression (1), where V 2 is the module of the inverse component of the voltage, V 1 is the module of the direct component of the voltage, a = 0.5 • (−1 + j• √ 3), and V AB , V BC , and V CA are the line voltages of the system.…”

“…In practice, the correct measurement of the voltage unbalance factor (VUF) is necessary in measurement and control systems such as [1], where, due to the large variations in the power absorbed by trains, it is not possible to adequately limit the unbalance in the threephase voltages with which, in order to correctly determine the unbalance of the system, it is necessary to accurately calculate the voltage unbalance factor based on the power consumed by the trains, or [2] where the inaccuracy of the formulas that make them unusable when an unbalanced system is connected has been taken into account because they do not consider the active and reactive powers separately. In [3], how to quantify voltage unbalances according to the standards is discussed, and a new methodology is proposed to quantify the voltage unbalance factor (VUF) by measuring the voltage unbalance in three-phase installations by means of a new intelligent sensor based on a unique voltage sensor, which measures the voltage in direct current (DC).…”