Mathematical modelling of a metro line with multistation and multiple train set and comparison of operational scenarios

According to the physical, geographical characteristics of the city, the country, or the continent, the rail systems used for passenger transportation vary according to the voltage, current and frequency preferences used in the national network's technology infrastructure, and the human population. While in certain locations in a city, inward systems, such as trams and light rails, are preferred for passenger transport, in other places transport systems separated from the city traffic by overpass and underground structures, such as metro and monorail systems, are preferred. Due to the geographical feature of Karaköy and Beyoğlu districts in Istanbul, a funicular system is used that connects these two districts. In Istanbul, Taksim district a tram system is used due to the historical characteristics, human population and physical conditions of Taksim. Each rail is a system with different characteristics. It is essential to perform engineering calculations carefully in new construction projects and old system revisions. For example, it is important to perform all calculations carefully, when high-speed trains are expected to run on railways built for older trains, or trains constructed for subways are expected to run on railways built for tramways. Social and technical aspects of new and revised systems should be analysed. Electrically operated rail system trains obtain their power from traction power supply systems, to be able to move and feed their auxiliary units. The traction power supply can be grouped into three types according to the power system provided by the transformer centre, the current collection system of the trains and the motors and drives used in the trains. Transformer centres provide direct current or alternating current for rail systems, while trains collect this current to move with either the overhead centenary system or the third rail system. Trains provide this movement with alternating current motors or direct current motors located on the train tracks bogies and direct current drive units or alternating current drive units which controls them. Computational success must be achieved to examine the operating scenarios of the rail systems in the design phase. A separate and integrated mathematical model of all system components should be formed which causes the mechanical motion starting from the electrical power input until it reaches the output power. It is possible to reach the final model by modelling the substation supply line, inverters, motors, especially the transformer model and combining it with the mechanical model. It is possible to simplify the model within certain assumptions. The topological and physical characteristics of the subway line can also be modelled. In this way, design calculations and design components can be made foreseeable in the design phase. Using the model installed, different braking, starting, failure and similar operating scenarios can be examined. Beginning from the energy transmission system, adverse effects, such as harmonics and losses, can be calculated. It is also possible to select the most suitable one when there is more than one option for a design component. In this thesis, the traction power supply system of a metro system with multiple stations and lines are modelled with MATLAB® Simulink program and analysed for many different situations. While the model is being constructed, the phase-to-phase voltage for the network is modelled as 154 kV, 3-phase and 50 Hz and for the traction transformer centres, the transformers are modelled as 25 MVA, 154 kV / 34.5 kV, 50 Hz. The output voltage of the transformers located in the traction transformer centres are modelled as 580V, rectifier 6, 12, 18 or 24 pulses through the LC filter to convey the 3rd current. The third rail is constructed to feed with 750V DC voltage and has equivalent 3rd rail, transit and turn resistances for each 1 km and equivalent lug resistors for each train. Train sets are modelled as consisting of four vehicles, but one of the vehicles is only a carrier vehicle, and there are no engines on it. A total of 12 squirrel cage asynchronous motors for each train set were used in three vehicles including four in each vehicle. Every two of these motors are driven by a single IGBT module. The motors are loaded with varying rotor speed and with 25%, 50%, 75% and 100% constant nominal load. The constant value function added to the model is connected to each motor in the trains and the amount of load can be changed by changing the fixed value. By changing the values of the model, equivalent rail, transition and rotation resistances, changing the inter-station distances, changing the train number and number of vehicles easily, changing the delay function values for the step function and PWM signal, changing the departure times of the trains, enabling the removal of one of the traction transformer centres at the desired time, the creation of similar faults and the alteration and analysis of many operating conditions such as these, by means of the cutter added to the output line of the transformer substations. One train-one station model, two trains-two stations model, two trains-four stations model and four trains-four stations model were created. Scenarios were run and traction characteristics of the trains and harmonic effects on the network were analysed. When different LC filters, rectifier transformers with different number of pulses in different loads, starting times, the number of the traction transformer centres and feeding points are used and one or more traction transformer centres are disconnected after a certain period. The data from the simulations show that the peak values of the rail currents are above 5000 A, even in the one train-one station model. This instantaneous high current should not be confused with short-circuit fault currents. As the distance between the feeding points of the traction transformer centres increases, some trains do not receive required currents. Therefore, in 750 V DC systems, the distance between traction transformer centres should be between one and three kilometres. This solves problems arising from voltage drop, and it allows transformer centres to be used as backups of each other, thus trains can continue to run uninterrupted. It should also be noted that as the number of pulses of the rectifiers increases, the total harmonic distortion affecting the network decreases. In models using 6 pulse rectifiers, the total harmonic distortion values have never fallen below 2.5%. The total harmonic distortion caused by current values are over 19% in each model used. For this reason, the use of 6 pulse rectifiers does not seem to be suitable for use in rail systems since it does not provide much energy quality for energy transmission systems. In the one train-one station model, voltage-caused THD created by 12-pulse rectifier systems, is beyond acceptable levels. Therefore, additional equipment such as active filters and passive filters, are recommended when 12-pulse rectifier are used. For models with 18 pulsed and 24 pulsed rectifiers, the total harmonic distortions values are in the acceptable range. Also, an increase in load increases the total harmonic distortion caused by the current and reduces the total harmonic distortion caused by the voltage.