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Auxiliary power system is an indispensable part of the train; the auxiliary systems of both electric locomotives and EMUs mainly are powered by one of the two ways, which are either from auxiliary windings of traction transformers or from DC-link voltage of traction converters. Powered by DC-link voltage of traction converters, the auxiliary systems were maintained of uninterruptable power supply with energy from electric braking. Meanwhile, powered by traction transformers, the auxiliary systems were always out of power while passing the neutral section of power supply grid and control system is powered by battery at this time.

Uninterrupted power supply of auxiliary power system powered by auxiliary winding of traction transformer was studied. Failure reasons why previous solutions cannot be realized are analyzed. An uninterruptable power supply scheme for the auxiliary systems powered by auxiliary windings of traction transformers is proposed in this paper. The validity of the proposed scheme is verified by simulation and experimental results and on-site operation of an upgraded HXD3C type locomotive. This scheme is attractive for upgrading practical locomotives with the auxiliary systems powered by auxiliary windings of traction transformers.

This scheme regenerates braking power supplied to auxiliary windings of traction transformers while a locomotive runs in the neutral section of the power supply grid. Control objectives of uninterrupted power supply technology are proposed, which are no overvoltage, no overcurrent and uninterrupted power supply.

The control strategies of the scheme ensure both overvoltage free and inrush current free when a locomotive enters or leaves the neutral section. Furthermore, this scheme is cost low by employing updated control strategy of software and add both the two current sensors and two connection wires of hardware.

The purpose of this paper is to evaluate the worst-case behavior of a given electronic circuit by varying the values of the components in a meaningful way in order not to exceed pre-defined currents or voltages limits during a transient operation.

An analytic formulation is used to identify the time-dependent solution of voltages or currents using proper state equations in closed form. Circuits with linear elements can be described by a system of differential equations, while circuits composing nonlinear elements are described by piecewise-linear models. A sequential quadratic program (SQP) is used to find the worst-case scenario.

It is found that the worst-case scenario can be obtained with as few solutions to the forward problem as possible by applying an SQP method.

The SQP method in combination with the analytic forward solver approach shows that the worst-case limit converges in a few steps even if the worst-case limit is not on the boundary of the parameters.