Railway power systems operating at a nominal frequency below the frequency of the public grid (50 or 60 Hz) are special in many senses. One is that they exist in a just few countries around the world. However, for these countries such low frequency railways are a critical part of their infrastructure.

The number of published dynamic models as well as stability studies regarding low frequency railways is small, compared to corresponding publications regarding 50 Hz/60 Hz public grids. Since there are two main type of low frequency railways; synchronous and asynchronous, it makes the number of available useful publications even smaller. One important reason for this is the small share of such grids on a global scale, resulting in less research and development man hours spent on low frequency grids.

This work presents an open model of a (synchronous-synchronous) rotary frequency converter for electromechanical stability studies in the phasor domain, based on established synchronous machine models. The proposed model is designed such that it can be used with the available data for a rotary frequency converter.

The behaviour of the model is shown through numerical electromechanical transient stability simulations of two example cases, where a fault is cleared, and the subsequent oscillations are shown. The first example is a single-fed catenary section and the second is doubly-fed catenary section.

This paper continues the pursuit of getting a deeper understanding regarding the transient stability of low-frequency AC railway power systems operated at 16 2/3 Hz synchronously to the public grid. The focus is set on the impact of different load models. A simple constant-current load model is proposed and compared to a previously proposed and studied load model in which the train’s active power is regulated.

The study and comparison is made on exactly the same cases as and grid as with the already proposed and more advanced load model. The railway grid is equipped with a low-frequency AC high-voltage transmission line which is subjected to a fault. The study is limited to railways being fed by different distributions of RFC (Rotary Frequency Converter) types. Both AT (auto transformer) and BT (booster transformer) catenaries are considered.

The RFC dynamic models are essentially Anderson-Fouad models of two synchronous machines coupled mechanically by their rotors being connected to the same shaft.

The differences in load behaviour between the proposed constant-current load model and the previously proposed and studied voltage-dependent active power load model are analyzed and described in the paper.

Most low-frequency AC single-phase railway grids have both power-electronic based Static Frequency Converters (SFCs) and electrical-machine based Rotary Frequency Converters (RFCs) connecting them to the three-phase public grid.

Already today, in some such grids, a majority of the power conversion is from SFCs. As railway traffic (and thus power demand) increases, more SFCs are installed for capacity increase, while the number of RFCs remains (almost) constant. Thus, the share of SFCs is expected to increase, and the ratio of installed rotational inertia over installed power to decrease.

This paper investigates how different shares of SFCs affect the transient stability of low-frequency AC railway grids when having a mix of RFCs and SFCs converting three-phase AC power to single-phase AC power. Results from numerical simulations of the interactions that occur between converters when and after the grid is subject to a fault are presented.

The numerical studies show that with an increased share of SFCs there is an increased oscillatory behavior, for example in the voltage magnitude and active power after fault clearance.

Low-frequency AC railway grids are unique in the sense that a only few countries around the world uses them, still however, they are an important parts of their countries infrastructures. Due to the usage of a dierent frequency than the public grid of the country, conversion of frequency is needed for the interconnection. The frequency conversion is done by machine based rotary frequency converters or power electronic based static frequency converters.

When reinforcing with new power conversion capacity, mostly static frequency converters are installed since rotary frequency converters for railways have not been manufactured for some time. As more static frequency converterare introduced, the share of rotary frequency converters is reduced. It is not well explored how the stability of low-frequency AC railways is affected with a large share of static frequency converters.

In this thesis, the main goal has been to obtain knowledge of the stability of low-frequency AC railway grids, with focus on synchronous ones. The electromechanical stability of a synchronous low-frequency AC railway is explored through numerical simulations, where the transient stability is the main focus.

The main contributions of this thesis is proposing a model of a rotary frequency converter, proposing a model of a static frequency converter, and transient stability simulations. The model of the rotary frequency converter uses established machine models, whereas the static frequency converter model has been developed with help of measurements. It can be concluded that the proposed static frequency converter model captures the main behaviour of the measurements of a static frequency converter.

The transient stability of synchronous AC railway grids is studied, through numerical simulations. The studied cases are for instance dierent railway grid congurations with dierent types rotary frequency converters and railway grids with mixes of static frequency converters and static frequency converter.

The main conclusion is that the rotary frequency converter fed synchronous railway grids studied are transiently stable, and the studied railway grids where rotary frequency converters are gradually replaced with static frequency converter are also transiently stable. However, it was found that the studied railway grids obtain a heavier oscillatory behaviour when there is a mix of rotary frequency converters and static frequency converters.

This paper continues the pursuit of getting a deeper understanding regarding the transient stability of low-frequency AC railway power systems operated at 16 2/3 Hz that are synchronously connected to the public grid. Here, the focus is set on such grids with a low-frequency AC high-voltage transmission line subject to a fault. The study here is limited to railways being fed by different distributions of Rotary Frequency Converter (RFC) types. Both auto transformer (AT) and booster transformer (BT) catenaries are considered. No mixed model configurations in the converter stations (CSs) are considered in this study. Therefore, only interactions between RFCs in different CSs and between RFCs, the fault, and the load can take place in this study. The RFC dynamic models are essentially two Anderson-Fouad models of synchronous machines coupled mechanically by their rotors being connected to the same mechani- cal shaft. Besides the new cases studied, also a new voltage-dependent active power load model is presented and used in this study.

Using low frequency High Voltage Transmission systems (HV-T) in parallel with the catenary systemstrengthens the railway system by reducing the total impedance of the railway grid. A consequence ofthe reduced impedance is that converter stations are electrically closer to each other.Inside a converter station, different types of Rotary Frequency Converters (RFCs) are used. It is not wellexplored how different RFCs behaves and interacts with each other during and after a large disturbance,like a short circuit.The dynamics of an RFC are modelled by using the Andersson-Fouad model of a synchronous machine.The study presented in this paper investigates interactions inside and between converter stations, withdifferent types of RFC, for an HV-T system in parallel with a Booster Transformer catenary system.The numerical simulation results show, for instance, that the main power oscillation take place inside aconverter station with mixed configuration of RFC type after fault clearance.

One method of strengthening low frequency AC railway grids is to upgrade Booster Transformer (BT) catenary systems, to Auto Transformer (AT) catenary systems. An AT catenary system has lower equivalent impedance compared to a BT system. Thus, an upgrade makes the existing converter stations electrically closer.

Converter stations may have different types of Rotary Frequency Converters (RFCs) installed in them, and it is not well explored how different RFCs behaves and interact during and after a large disturbance.

Using the Anderson-Fouad model of synchronous machines to describe the dynamics of RFCs, several case studies have been performed through numerical simulations. The studies investigate the interactions within and between converter stations constituted with different RFC types, for BT as well AT catenary systems.

The numerical studies reveal that replacing BT with AT catenary systems, results in a more oscillatory system behaviour. This is seen for example in the power oscillations between and inside converter stations, after fault clearance.

In present-day railway power supply systems using an AC frequency lower than the one in the public power system of 50/60 Hz, high voltage overhead transmission lines are used as one measure of strengthening the railway power supply system grids. This option may be economically beneficial, compared to strengthening the grid purely by increasing the density of converter stations or increasing the cross section areas of the overhead catenary wires. High voltage AC transmission lines in the railway power supply system allow larger distances between converter stations than would otherwise be possible for a given amount of train traffic. Moreover, the introduction of AC transmission lines implies reduced line losses and reduced voltage level fluctuations at the catenary for a given amount of train traffic. However, due to the increased public and government resistance for additional overhead high voltage AC transmission lines in general, different alternatives will be needed for the future improvements and strengthening of railway power systems. For a more sustainable transport sector, the share and amount of railway traffic needs to increase, in which case such a strengthening becomes inevitable. Earlier, usage of VSC-HVDC transmission cables has been proposed as one alternative to overhead AC transmission lines. One of the main benefits with VSC-HVDC transmission is that control of power flows in the railway power systems is easier and that less converter capacity may be needed. Technically, VSC-HVDC transmission for railway power systems is a competitive solution as it offers a large variety of control options. However, there might be other more economical alternatives reducing the overall impedance in the railway power system. In public power systems with the frequency of 50/60 Hz, an excess of reactive power production in lowly utilized cables imposes an obstacle in replacing overhead transmission lines with cables. In low frequency AC railway power system, the capacitive properties are less significant allowing longer cables compared to 50/60 Hz power systems. Moreover, in converter-fed railways, some kind of reactive compensation will automatically be applied during low-load. At each converter station, voltage control is already present following the railway operation tradition. Therefore, in this paper, we propose AC cables as a measure of strengthening low-frequency AC railway power systems. The paper compares the electrical performances of two alternative reinforcement cable solutions with the base case of no reinforcement. The options of disconnecting or toggling the cables at low load as well as the automatic reactive compensation by converter voltage control are considered. Losses and voltage levels are compared for the different solutions. Investment costs and other relevant issues are discussed.

In today's Swedish and Norwegian low frequency railway power system the voltage at a converter is controlled such that its voltage will drop with increased reactive power output. However, for low frequency railways the influence of active power on voltage is larger compared to public power systems and alternative methods are interesting to investigate. This paper presents a modified voltage control law for increased load sharing between converter stations and reduce the risk for converter overload in low frequency railways power systems. The modified voltage control law is derived mathematically and tested with different droops for two case studies. The results confirms the increased load sharing between the converter stations. The results are analysed and discussed; ideas are presented to counteract some of the negative impacts of the modified voltage control law

This paper investigates the replacement of Rotary Frequency Converters(RFCs) with Static Frequency Converters (SFCs) in the Swedish synchronous-synchronous Railway Power Supply System (RPSS) operating at1623Hz. Thereis a need to investigate how such a system behaves when RFCs are partly replacedwith SFCs, as the SFCs do not have any physical inertia.Most of the transient stability studies published for synchronous-synchronousRPSS address the behaviour of a single RFC or SFC against an infinite bus.However, there are very few studies investigating a system with several RFCs,SFCs or a mix of both in the same converter station. This paper presents the resultsof a transient stability study with both RFCs and SFCs. The investigated casesconsist of faults at different locations, and present the results when an RFC isreplaced with an SFC in a converter station.