1 Improved Stability of DC Catenary Fed Traction Drives using Two Stage Predictive Control Václav Šmídl, Member, IEEE, Štěpán Janouš, Zdeněk Peroutka, Member, IEEE, Abstract —Control of the main propulsion drive of a traction vehicle must secure excellent drive dynamics, but it also has to consider properties of the dc catenary. Specifically, the catenary voltage is subject to short cir- cuits, fast changes, harmonics and other disturbances which can vary in very wide range. Therefore, the drive is equipped by the catenary input LC filter. The filter is almost undamped by design in order to achieve maximum efficiency and the control strategy needs to secure active damping of the filter to guarantee the drive stability. Existing solutions for active damping usually introduce some drawback in dynamic proper- ties of the drive. In this paper, we study the use of two stage predictive control. Damping of the filter will be solved on a long horizon using linear controller. Dynamic properties of the drive will be guaranteed by optimization on a short horizon using the finite set model predictive control. These two approaches can be elegantly combined approximate dynamic pro- gramming. The resulting algorithm can be interpreted as a standard FS-MPC with a model-based designed loss function. Performance of the resulting controller was verified on a laboratory prototype of the main propulsion drive a light traction vehicle (tram) with PMSM drive of 10.7 kW. I. Introduction One of the main constraints of design of traction vehicles control fed from a dc catenary are the oscillations of an input catenary LC filter and the resulting instability of a traction drive. This problem is even more complicated in multi-motor propulsion units which operate many drives with their naturally almost undamped dc-link LC filters in parallel. The problems with the input LC filter are closely linked with frequency characteristics of the whole drive and so-called “drive resonant frequency”, e.g. [1]. A. Physical background of the phenomenon The problem of oscillations of catenary LC filter in dc catenary supplied traction drives is known for many years, e.g. [2], [3]. Traction drives use an input LC filter and not only a C-filter for the following reasons: (i) an effective limitation of the catenary current (due to fast changes of the catenary voltage and short-circuit of the catenary), and (ii) EMC issues. Thus, the LC filter is necessary for proper operation of the drive. On the other hand, the dc- link LC filter has negative impact on the traction drive stability. All authors are with the Regional Innovation Centre for Electrical Engineering University of West Bohemia, Pilsen, Czech Republic, email: vsmidl@rice.zcu.cz,peroutka@ieee.org Figure 1. Equivalent circuit of the dc catenary supplied traction drive with input LC filter The specifics of the traction drive are: i) excellent dynamic properties of its control which is an important objectives of the drive control design, hence this condition should be fulfilled, ii) the drive has a very high moment of inertia, i.e. the change of the vehicle speed is slow in comparison with electrical time constants, and iii) the input to the drive controller is a often the maximum achievable torque command, which will be considered as a constant for the stability purpose. Under the above stated conditions, the drive consumes constant active power from the dc-link filter under steady- state conditions. The equivalent circuit of the drive used for the description of the LC filter resonance is shown in Fig. 1. Voltage-source converter and ac motor can be replaced by an equivalent current source which models the filter load. The LC filter resonance can be excited by many events – by the drive itself (e.g. unsuitable control commands or drive harmonics) or from the outside. One of the most common effects from outside which can excite the filter oscillations is the change of the catenary voltage which can vary very fast due to different reasons. If the catenary voltage increases then the drive still takes the constant power from the dc-link filter (constant torque command and negligible speed change within the time interval of investigated transient phenomenon). Under some conditions, this may act as a positive feedback (or negative-resistance effect) which results in dangerous oscillations of the dc-link filter. This phenomenon can be also explained using frequency characteristics of the drive. The resonant frequency of the drive is clearly changing with the change of the position of the vehicle within the feeding section (change of the catenary parameters with