Nonlinear Modeling of Locomotive Propulsion System and Control

Abstract: In this report the motor side of a converter driven AC-locomotive is studied and modeled. The motor side consists of an asynchronous electrical engine, an indirect self controller, a voltage converter, a Pulse Width Modulator(PWM) and the train mechanics. The converter is supplied with voltage from a DC-link. The link is connected to a line converter which transfers energy from the railway net to the link. The modeling is made in frequency domain with a method allowing frequency interaction. The technique is based on the use of truncated Fourier series. The signals are described with vectors containing the Fourier coefficients. Matrices called Harmonic Transfer Matrices(HTM) are constructed to describe the relation between two such vectors. In Linear Time Invariant(LTI) systems the HTM:s are diagonal. Linear Time Periodic(LTP) systems on the other hand gives HTM:s with off-diagonal elements. That means an input frequency can generate other frequencies. Nonlinear systems also have this charasteristic, although they cannot be exactly described with HTM:s. For small perturbations around a periodic solution they are often well approximated with a HTM. In the report HTM:s are developed for each of the motor side components mentioned above. The engine and the controller are nonlinear but are approximated as LTP systems. A HTM is then easy to get. The converter and the PWM are nonlinear and are modeled together. The HTM is obtained analytically by considering changes of switch time points. A simple LTI mechanical model is used. The engine-controller-mechanics loop is closed and a HTM for the entire system is obtained. With it it is possible to see the spectral changes of motor variables such as stator current and mechanical frequency when the set point of the torque is changed. It is also possible to see the effects of spectral changes of the DC-link voltage on the motor and on the current in the DC-link. The results are compared to Simulink-simulations of the system. The agreement is good. An iterative procedure is also presented to make it possible to connect the motor side HTM with an analog model of the line side. Together they would model the entire locomotive. Such tests are not performed in this report.