Integrated simulator for AC traction power supply

1Tetsuo Uzuka, 1Masataka Akagi, 1Yasuji Hisamizu Railway Technical Research Institute, Kokubunji, Tokyo, Japan1

Abstract

We have developed a new integrated simulator for AC traction power supply for railway vehicles such as . It provides essential information for rating substations, catenaries and protective equipment. This software consists of three parts; energy consumption calculation of an individual during running, solving load voltages and currents in any branch of the ac traction feeding circuit (e.g. catenaries, feeders and transformers) with the 30 years old technique, and an integrated human interface skin.

Introduction

AC tractions are now widely used worldwide. To design locations or scale of substations for new lines, to investigate an induced voltage on communication lines, or to examine various phenomena in feeding circuits, such like voltage fluctuations and harmonics resonant; a correct calculate technique about ac feeding circuits is so important beyond doubt. The first experimental ac feeding circuit electrified in 1954 by former JNR (Japan National Railway). From that age, JR (Japan Railway) group handles this problem as a one of the most important technique. JNR developed an own program to calculate such a problem. This program, we call it “MUL”, can handle multiple conductors’ self induction effect and mutual induction effect appropriately. The MUL helped to revaluate AT (Autotransformer, 2x25kV) system, that invented in USA in 1911, to apply commercial frequency for Sanyo Shinkansen for revenue service in 1972. But to rating the substations, MUL is too difficult to use for ordinary engineers. Also MUL itself does not calculate train running data. Then we developed a human interface skin to envelope the MUL as a solver kernel, and added capability of evaluating train running, at last we formed a sophisticated integrated ac feeding simulator as follows.

AC feeding circuits

Figure 1 shows a typical installation of an AC feeding circuit with commercial frequency. Substations feed the circuit until sectioning posts. Receiving power from 3 phase power grid and paired single phase feeding circuit, known as a center feed system is popular in Japan. Intervals of substations are 40 – 50 km in normal Japanese case. Figure 2 shows major feeding systems from substation to the end of AC feeding circuit. AC feeding circuit begins from a basic feeding circuit (sometimes written as 1x25kV); BT (Booster transformer) system covers an induced voltage problem, and AT system produces a powerful and less-induced voltage system. Now AT system drives most of high speed with commercial frequency, such as Shinkansen (Japan), TGV (), (France and UK), KTX (Korea), (Italy), AVE (), THSR (Taiwan), and China. We should treat all these feeding system to investigate. Substation Trolley 22kV Simple Car Feeding Circuit Rail CNF Return Conductor Substation Section Trolley BT 22kV Booster Feeding Transformer Car (BT) Substation(SS) Substation Circuit Rail 3-phase to 2 phase CNF Capacitor Negative conversion Feeder Sectioning Substation (NF) +25kV Post(SP) Trolley up down up down Auto AT (25X2) 50kV Car Transformer Feeding Rail 0kV (AT) Circuit -25kV 40～60km Feeder Figure1: Typical installation of AC feeding circuit Figure 2: Basic, BT and AT feeding circuits Method of solving multiple conductors for AC feeding circuit

We use a well-proven multiple conductors solving engine for analyzing voltage and current distribution to guarantee a numerical accuracy. The engine has over 30 year’s history internal RTRI that calculate all the basic parameters of Shinkansen with autotransformer (AT, 2x25kV) and booster transformer (BT). The engine uses a common mathematical technique that handles AC feeding circuit (e.g. catenaries, feeders, rails, protective wires, and earth conductor) as parallel conductors with self induction and mutual inductions. Feeding circuits consist of m conductors such as trolleys, feeders, rails, protective wires, and soil. For example, in common Shinkansen, m should be 9 (trolley x2, feeder x2, rail x2, protective wire x2, and soil). There are several approaches to handle such a multi conductor circuit. Lee et.al. [2] successed to draw 8-port distributed circuit model to simulate harmonic distortion for double track high-speed line. On the contrary, Mariscotti et.al. [3] showed most simple case that m can be reduced to be 3 (trolley, feeder and rail). In the other hand, Varju et.al. [6] solved a feeding circuit as a kind of general power sending problem with their own solving technique. RTRI’s approach is that conductors should be 8 or more, because we have to study about rail potential problem and draw a various way of switch closing and opening in the long feeding circuit. But the circuit model can neglect capacitance to discuss about power simulation. In a power frequency (50/60Hz, Japan has both power frequencies) this approach has a sufficient accuracy. For harmonic analysis, capacitance becomes a main player. Automatically, the engine divides feeding circuit into n nodes and branches along a rail route from a substation to the end. Each node is a changing point of circumstances (e.g. substation or AT, geometry of conductors, tunnels, changing resistively of earth and existing of train) that has a parallel conductor which has potential (vector V(V) in equations below) and input current (vector G(A)) and admittance (matrix Y(S=1/ohm)). Every branch is a set of homogenous circumstance conductors those have passing current (vector I (A)) and own impedance (matrix Z (ohm)). Z matrix consists of self impedances and mutual impedances between each conductor which is derived from conductor’s geometry position, radius of conductor, resistance of direct current, feeding frequency and earth resistively with the equations of Carson-Pollaczek[1][4]. Node Node Node Node Node Y matrix might be singular in some case, and then 1 k-1 k k+1 n the engine determines voltages and current of every Branch Branch node with inverted impedance matrix Z-1 with k k+1 1 1 1 equation below using Schechter’s L-U algorithm [5]. G k-1 G k G k+1 1 1 1 1 1 This algorithm was born in about 40 years ago, but Conductor V k-1 I k V k I k+1V k 1 2 2 2 speed and accuracy is still sufficient in this case. G k-1 G k G k+1 2 2 2 Figure 3 and equations below show this concept. V2 2 V I k+1 V Conductor k-1 I k k k 2 Gm Gm Gm V – V + Z ・I = 0 (1) k-1 k k+1 k k-1 k k Vm Im Vm Im Vm Conductor k-1 k k k+1 k I2 + Y1・V1= G1 m Ik+1 - Ik + Yk・Vk = Gk -In + Yn・Vn = Gn Figure 3: Nodes and branches

Each train is located on specified node (position) as a constant current source between trolley and rail. Practically, every train is expressed as a serial resistance and reactance to realize specified current value and power factor. If the case when several trains in a calculating feeding circuit, the engine would adjust parameters of each trains with linear programming technique inside. In Japan, some traction substations have FACTS devices such as SVC or STATCOM for balancing power or suppressing voltage fluctuation. This program has an additional function to describe such FACTS devices emulating functions.

Calculate energy consumption of an individual train during running.

Diagram of trains, specifications of respective types of rolling stock, positions of gradients, curves, stations and tunnels in the line enable to determine every second’s position, velocity, and traction current of each individual train with a well-known equation of motion implemented in the program. Especially, high speed trains running at speeds exceeding 200km/h required correct approximation of running resistance. Then we switch running resistance quadratic velocity equation for both tunnel section and open section. Every second, program checks the position of a calculating train and positions of tunnels to determine resistance parameters. In addition, recent Shinkansen trains have a capability of constant velocity running. We developed a simplified adjusting notch algorithm and the reverse velocity curve fitting algorithm for these purposes. Also recent signal system in Shinkansen allows braking control with continuous curve to stop at stations. Then train has a back-track fitting curve algorithm for stopping at stations. To rating a feeding circuit, we don’t need too detailed accuracy for running trains. Then we neglect influences from signal systems to prevent train collision. All the trains would run along input diagram data, but each trains does not know other trains’ move. This abbreviation may lose accuracy of calculation for urban lines, which has a traffic jam in rush-hour. But for high speed lines we regard this method as appropriate. One train by one train, the program will calculate every second’s position, velocity, current, power factor along a diagram. Next, the program makes a file that express every second’s all trains’ data. Then the MUL solve whole voltage and current of feeding circuit of every second. This way, we should evaluate energy consumption.

Human interface skin

To solve feeding circuits with correctness, we should prepare so many parameters. All the input/output data in this simulator use a text (CSV) format that can assure coherence check by users if needed. On the other hand, implemented human interface skin helps users to prepare enormous data easily. Positions and parameters of fixed installations such as ATs, BTs, wire connections and gradients, curves, tunnels and additional velocity limits have their own matrix-like GUI prefaces with a simple drawing. Parameters of rolling stocks and train diagram have their own GUIs also. Figure 4 to 7 shows examples of GUI prefaces. Then integrated simulator software runs throughout the whole step from input data, train running consumption, feeding circuit calculation and output result on common personal computers. This simulator does not draw graphs of calculated result itself. But we can use any tools to make graphs with personal computer.

Figure 4: GUI for input route gradients Figure 5: GUI for input speed restrictions

Figure 6: GUI for input positions of substations Figure 7: GUI for input train diagram

Evaluating accuracy

We compared measured field data of Shinkansen and conservative lines and calculated data with this simulator. Figure 8 shows a favorable result of comparison. In this case, shape of energy consumption is very similar. Figure 9 shows a remarkable result of suppressing voltage fluctuations with FACTS device calculated.

25 0.6 Calculated 20 Measured 0.5 No care With compensation 15 0.4 10 0.3 5 0.2 0 Active power(MW) Active

-5 Voltage fluctuation(%) 0.1 -10 0.0 15:25 15:30 15:35 15:40 7:00 7:30 8:00 8:30 9:00 Time Time Figure 8: Comparison of field and calculated data Figure 9: Suppressing voltage fluctuation

Conclusions

We have developed an integrated simulation tool for AC traction. The evaluated data proved the reliability of this tool. We are using this simulator as a standard analyzing tool for various objects. For example, for construction of Taiwan High-speed Rail, in revenue service in 2007, additional works with this tool enabled EMC calculation of induced voltage on telephone lines along the railway route. References

[1] J. R. Carson, “Wave propagation in overhead wires with ground return,” Bell System Technical Journal, 5, 539-554, 1926 [2] H. Lee, C. Lee, G. Jang, S. Kwon, “Harmonic Analysis of the Korean High-speed Railway Using the Eight-Port Representation Model”, IEEE Trans. Power Delivery, Vol.21, No.2, 979-986, 2006 [3] A. Mariscotti, P. Pozzobon, M. Vanti, “Simplified Modeling of 2x25-kV AT Railway System for the Solution of Low Frequency and Large-Scale Problems,” IEEE Trans. Power Delivery, Vol.22, No.1, 296-301, 2007 [4] F. Pollaczek, “Ueber das Feld einer unendlicj langen wechselstromdurchflossenen Einfachleitung,” ENT 3, 339-359,1926 [5] S. Schechter, “Quasi-Tridiagonal Matrices and Type-Insensitive Difference Equations,” Quart. Appl. Math. 18, 285-295, 1960 [6] G. Varju, “Resonance phenomena in normal and auto-transformer railway feeding systems,” COST261 Budapest, 2002