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Low-frequency instability in AC electric traction power systems has come to be a concern in recent years. Power oscillations in the range of 10-30 % of the system’s fundamental frequency are reported from all over the world after the introduction of large numbers of rail vehicles being equipped with modern power electronic traction chain solutions. The disturbance of rail traffic has been especially noticeable in Norway, where the railway power supply contains rotary frequency converters which show a poorly damped electromechanical eigenfrequency of approximately 1.6 Hz. The overall goal of the present thesis is to acquire knowledge concerning stability in the traction power system, focusing mainly on the low-frequency oscillations and interaction between electric rail vehicles and this particular rotary converter. An important part of this work is to establish a connection between the fields of both power electronics and power system analysis. The problem is approached by the development and study of basic differential equations and characteristics for the two main dynamical components in the system – the synchronous-synchronous rotary frequency converter and the advanced electric rail vehicle. These simplified models are used to obtain a better understanding of the dynamical behaviour of a full converter-vehicle simulation model which is studied by the use of both time simulations and linear analysis (eigenvalues and frequency responses). The developed vehicle model is open and independent of any specific vehicle manufacturer. The model’s basic validity however is investigated by comparison with measurements performed on a real-life electric rail vehicle. This thesis focuses on the small-signal behaviour of the power system in the mentioned low-frequency range. Detailed analytical investigations of the complex single-phase AC power system is difficult, thus most of the analytical studies in present thesis focusing on the active power oscillations are carried out by several simplifications. The largest simplification is the assumption of the AC voltage and current in phase and only considering their amplitude values. This is useful for initial understanding, but is insufficient when phase angles are to be taken into account. Therefore the simplified analytical considerations by principle are compared with the complete AC power system model in a rotating reference frame as commonly utilised for large power systems. However, for this full simulation model it has been found that traditional power system simplifications by use of standard RMS-values are insufficient in correctly representing the instability phenomenon compared with a more realistic instantaneous value model. Fast network dynamics and vehicle current controller which are commonly neglected, have to be included as well and consequently an enhanced RMS model is proposed. Two characteristics of the state-of-the-art electric rail vehicle are found to be of importantance. First, a control objective of the vehicle is to keep the power consumption constant and independent of the power supply conditions. This constant power load characteristic is shown to result in a positive feedback loop and basically violate a stability criterion derived for the rotary converter. Second, the time variance of a single-phase system results in several filter time constants giving dynamics in the low-frequency range. Of particular importance is the DC-link voltage control loop. These dynamics might additionally reduce the stability margins. This study’s main contribution is as a foundation for further investigation into low-frequency traction power system stability, especially in regard to the open vehicle model that is developed and discussed. A further focus should be on an understanding of more of the aspects of the AC system interaction and how to include this in a feasible method for power system study, in which the inner and commonly hidden details of the complex components are included, although not specifically disclosed. PhD i elektronteknikk PhD in Electrical Engineering

This master thesis presents a method for stability analysis. The dynamics of an electric system are described through frequency dependent impedances and admittances. This is presented with the basis of an electric traction vehicle. The frequency responses of the vehicle are revealed and verified through tests, compensations and analyzes of test measurements. After the introduction of advance electric traction vehicles, the electric traction system has experienced problems related to low frequency power oscillations. To solve these problems the dynamics of the vehicle is modeled. This is conducted from an input-output approach at the interface of the vehicle seen from the rest of the system. The input and output are small changes in voltage and current from a linearized operation point. The vehicle is presented as a set of four admittances. These admittances are functions of the oscillation frequency, further referred to as frequency responses. A description of an electric oscillating system can be done by using modulated signals. In this thesis, current and voltage are described as amplitude- and phase modulated components. Calculations with modulated components requires an extension of the phasor system. This extension, and relevant calculation rules and examples, are presented in this thesis. Further, tests to reveal the frequency responses of the vehicle is presented. Measurements from the tests show deviations from the specified excitation voltage. Analysis of the test measurements explains some of these deviations. Since the frequency responses do not depend on the excitation voltage, the tests are verified as sufficient for their purpose. After compensating for the test topology, a set of frequency responses for the vehicle are found. They are considered as correct, but have limitations. The numeric frequency responses are extracted to transfer functions. At last, usage of the transfer functions in stability analysis with several vehicles is presented.

Reducing grid harmonics and increasing grid stability are both major issues for the operation of rail vehicles. For stability investigation of complex power systems, simplified system models are in need in order to reduce the model complexity and the simulation time. In this thesis work the effect of modelling a voltage source converter (VSC) for traction power system with and without the detailed pulse width modulated (PWM)-switch model is modeled. Effect of different operating conditions for the switching model on the harmonic content of the system is also analyzed. The same disturbance is imposed for the two models and the low frequency oscillation of the DC- link voltage response is compared and analyzed. The effect of semiconductor switching on the stability limit of the system is also investigated. Furthermore, the performance of a PWM time delay compensation technique during transient is analyzed. The result shows that in the model including the switching the DC- link voltage oscillation is damped and has a better stability margin compared to the average model. In the detailed switching model a converter loss is included while in the average model a no loss ideal case scenario is considered. As far as the switching harmonic is considered, the switching model with an operational condition of a high switching frequency and a switching frequency with an integer multiple of the fundamental frequency has a low harmonic content on the system compared to the operating condition of a low switching frequency which is not integer multiple of the fundamental frequency. A unipolar voltage switching technique has also a tremendous advantage over the bipolar voltage switching technique as far as this harmonic content in the system is concerned. Using a unipolar voltage switching technique reduces the harmonic content in the overall railway system. For triangular carrier modulators, an average time delay from the reference voltage to the actuated PWM terminal voltage of half the switching frequency is assumed .The delay in DC- link voltage control loop caused by the switching dead-time effect was improved by compensation of dead-time in the inverse-park transformation block of the control loop. The comparison of the compensated and non-compensated model proves that the compensated model is better in terms of the overshoot of amplitude of transient.