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A NOVEL ON TRANSFORMATION FROM THREE VARIABLES TO TWO PHASE VARIABLES IN HIGH SPEED ELECTRIC RAILWAY 1 .Sravani.p, 2. Kiran kumar.p 1 M.Tech Student of JNTUA,EEE Dept,Kuppam Engineering college,Chittor,A.P, India 2 Asst.prof, EEE Dept, JNTU,Anantapur,Kuppam Engineering College,Chittor, AP-India, Abstract- In order to transform the three phase winding to two phase winding in high speed electric railway, park’s transformation is used. A symmetrical 2-pole,3-phase winding on the rotor is represented by three coils A,B,C each of N effective turns and mutually displaced by 120 o as shown in fig a. Maximum values of mmfs Fa,Fb,Fc are shown along their respective phase axes. The combined effect of these three mmfs results in a constant angular velocity depending on the poles and frequency. The mmfs of three phase and two phase systems can be rendered equal in magnitude by making any one of the following changes 1) by changing magnitude of the two phase currents 2) by changing number of turns of the two phase windings 3) by changing both the magnitude of currents and number of turns The disadvantage of the first two changes are the transformation of current and voltage differ. Hence the third one is discussed here. In this the transformation of voltage and current will not differ . Keywords- two phase winding, three phase winding, park’s transformation, two winding transformer, changing magnitude of currents and changing number of turns. I. INTRODUCTION In recent years, China's railway construction has entered a fast developing stage. Power quality becomes a major problem for railway power supply system[1]. In this paper discuss about the transformation from three phase variables to two phase variables. The equations expressing old variables in terms of new variables or vice versa are called transformation equations.The process of replacing one set of variables by another related set of variables is called winding transformation or merely transformation. The term “linear transformation” means that the transformation from old to new set of variables or vice versa is governed by linear equations. For example the Laplace transform is also a linear transformation. It transforms the time-domain (old variables) equation to s-domain(new variables) equation and another time have the needed time-domain solution, after manipulations. The transformation matrix may therefore be defined as a matrix containing the coefficients relating the old and new variables. Linear transformations in electrical machines are usually carried out for the purpose of obtaining new equations which are fewer in number or are more easily solved. For example, a 3-phase machine requires three voltage equations whereas its generalized model requires only two voltage equations which can be solved more easily as compared to three voltage equations. Due to the magnetic coupling amongst the three-phase windings, the circuit equations for a 3-phase machine are complicated, but this is not the state of affairs in the indefinite(or two axis) model, in which mmf acting along one axis has no mutual coupling with the mmf acting along the other axis. II INVARIANCE OF POWER: The transformations are made from old variables to new variables, and then produce solution with ease of the problem. Generally two transformations, one for voltage and the other for the current, have to be considered. The voltage transformations may be different from the current transformations since the rules of matrix algebra, do not put any restriction on the choice of the two transformations .But the two transformations should be so related that the variables, the whole system taking in both state of affairs. This principle of keeping up the power same under transformation from old to new set of variables is known as invariance of power. However if the transformations correspond to the power invariance, power and torques, calculated either from the new set of variables or from the original system of variables will yield identical results. III TRANSFORMATION FROM A DISPLACED BRUSH-AXIS: If a commutator machine has brushes displaced from d or q axes, a transformation is necessary from the displaced brush axis to d-q axes. Suppose one set of brushes, denoted by AA, makes an angle α with the d-axis as shown in fig a. The armature establishes an mmf Fa along its brush axis. This mmf Fa can be resolved along d-axis as Fd and along q-axis as Fq where Fd = Fa sin α and Fq = Fa cos α Fig.3.2.1 (a) one set of displaced brushes (b) its d-q equivalent (c) brush-shifting transformation. Thus two coils D and Q in fig b, with the currents given above are required to establish the equivalence of mmfs. In addition to brush pair AA, consider another set of brushes BB making an angle β with q-axis as shown in fig a .The mmfs set up by the brush pairs AA and BB are Fa and Fb respectively. The d-q axes coils, D and Q ,set up mmfs Fd and Fq along their respective axis . IV SYSTEM STRUCTURE symmetrical 2-pole,3-phase winding on the rotor is represented by three coils A,B,C each of N effective turns and mutually displaced by 120o as shown in fig a. Maximum values of mmfs Fa,Fb,Fc are shown along their respective phase axes. The combined effect of these three mmfs results in a constant angular velocity depending on the poles and frequency. The structure of phase conversion shown in above, (a) shows the three phase winding and (b) shows two phase winding. the transformed equations are i 2 1 1 ia ib ic 3 2 2 i 2 3 3 0 ib ic 3 2 2 Since the transformations for voltage and current are identical, impedance per phase of the two and three phase systems is the same. The above transformations can be expressed in matrix form as: i i 2 1 3 0 1 2 3 2 1 i a 2 i 3 b i 2 c The transformation matrix, containing the coefficients is a singular one and the inverse of matrix does not exist.To make it a non-singular or a square matrix , a zero sequence current io is chosen as the third equation and is defined as 1 ia ib ic i0 3 And in matrix form is i i i0 2 3 1 1 2 3 2 1 2 0 1 2 1 2 i a 3 ib 2 1 ic 2 The inverse of the above matrix ia ib ic 1 2 1 3 2 1 2 0 3 2 3 2 1 2 i 1 i 2 i 1 0 2 Three-Phase to Two-Phase Modulation Three-phase and two-phase Space Vector PWM modulation options are provided for the IRMCx203. The Volt-sec generated by the two PWM strategies are identical; however with 2-phase modulation the switching losses can be reduced significantly, especially when high switching frequency (>10Khz) is employed. Figure: three-phase and two phase modulation shows the switching pattern for one PWM cycle when the voltage vector is inside sector 1 Fig.Three Phase and Two Phase Modulation The field Two Phase PWM of the PWM Config write register group provides selection of three-phase or two-phase modulation. The default setting is three-phase modulation. Successful operation of two-phase modulation in the entire speed operating range will depend on hardware configuration. If the gate driver employs a bootstrap power supply strategy, misoperation will occur at low motor fundamental frequencies (< 2Hz) under two-phase modulation con trol. The above diagrams represents clark’s transformation. The SVM aim is to produce a settlement vector (m ) in the same plane for each modulation cycle. As the settlement vector may not be the same as any vector produced by the converter, its average value can be produced using more than one vector per modulation cycle by PWM-averaged near to the real value. Selecting proper vectors and applying them in a appropriate order helps the devices go to low switching frequencies. V SIMULATION RESULTS The software to detailed examination of the elements and calculate the characteristic of harmonic current is generated by the stimuli link module of Mat lab. First of all, the operating conditions are examined by the data given by traction calculation software. Then keep up the parameters of simulation and click on the run button and run the simulation program. The coming results used for harmonic flow calculation of electric railway traction power supply system and transmission system. Then the grid voltage and current have the similar phase under the traction condition, but the reverse under the braking condition. For the input currents of converter 1 and 2, it is mainly middle at 2 times of the carrier frequency, which is 500Hz.But due to cancelling of the odd harmonics for 500Hz, it is mainly middle at 4 times of the carrier frequency, that is 1000Hz. Fig(1). sinusoidal waveform Fig(2). transformer secondary side voltage Fig(3). Voltage and current waveforms at load side VI CONCLUSION This article studies the mathematical model and simulation of four-quadrant converter of CRH5 EMUs, specially studies the current distribution under the steady condition. Compared with the original “Shaoshan” series locomotives, EMUs use PWM rectifier, thus the power factor is close to 1 and the low harmonic content is obviously decreased, but the high-order harmonic content is slightly increased. In this paper, the preparation of the electric locomotives and EMUs simulation software, data interface can be called for other software to further analyze the spread law of the harmonic grid current in traction and the probability distribution of harmonic currents and so on. The effectiveness of the converter operation is verified for the harmonic supervision and cancellation when transient or time varying harmonics exhibit in power systems. The unique features of converter analysis, such as frequency identification without prior knowledge of frequency and the ability to identify damping factors, are useful to power system quality study. Further studies can be carried out for power quality study. Just as converter analysis was used with harmonic selective active filters, converter analysis may be applied to other measures to improve power quality. BIBILOGRAPHY The bibliography used for the project “POWER QUALITY ANALYSIS OF TRACTION SUPPLY SYSTEMS WITH HIGH SPEED TRAIN” is as follows. ARTICLES Cai-fei SHENG Yu-jie LIU FEi LIN Xiao-jie YOU Trillion Q ZHeng shccol of electrical engineering Beejing jiatong University Beijing,china [email protected] 978-1-424442800-7/09/$25.00 @ 2009 IEEE. BOOKS 1. Utilization of Electric power and Electric traction J.B GUPTA. 2. Power Electronics P.S.BIMBRA. 3. Circuit, Devices, and Applications of power electronics MUHAMMAD H.RASHID REFERENCES [1] Lu Fang, An Luo, Senior Member, IEEE, Xianyong Xu, Houhui Fang, “A Novel Power Quality Compensator for Negative sequence and Harmonic Currents in High-speed Electric Railway”, pp. 596-600, Nov. 2011 [2] Xiangzheng Xu, Baichao Chen, “Study on Control State and Development of Power Quality for Railway Traction Power Supply System,” Circuits, Communications and Systems, 2009. PACCS '09. Pacific-Asia Conference on 16-17, pp. 310-313, May 2009. [3] An Luo, Shuai Z.,Wenji Zhu, et al. “Development of Hybrid Active Power Filter Based on the Adaptive Fuzzy Dividing Frequency-Control Method,” IEEE Trans. Power Delivery, Vol.24, pp.424-432, Jan. 2009. Zhang Chen, Huang Jidong, “Conversion between the method of measurement of electrified railway radio disturbance in our country and the method stipulated by EN standard,” Environmental Electromagnetic, 2003. CEEM 2003. Proceedings. Asia-Pacific Conference on 4-7, pp. 596-600, Nov. 2003. [4] Zhao Wei, Tu Chun-ming, Luo An, et al. “A Novel Single-phase Hybrid Active Power Filter Applied to Electrical Railway System,” Proceedings of the CSEE, Vol 28, pp.51-56, July, 2008. [5] Zhuo Sun, Xinjian Jiang, Dongqi Zhu, et al. “A novel active power quality compensator topology for electrified railway,” IEEE Trans. On Power Electronics, vol.19, pp. 1036-1042, July, 2004. J.Cben, W.Lee, M.Chen, “Using a Static Var Compensator to Balance a Distribution System,” IEEE Transactions on Industry Applications, Vol l35, pp.298-304, April, 1999. [6] Zhang Chen, Huang Jidong, “Conversion between the method of measurement of electrified railway radio disturbance in our country and the method stipulated by EN standard,” Environmental Electromagnetic, 2003. CEEM 2003. Proceedings. Asia-Pacific Conference on 4-7, pp. 596-600, Nov. 2003. [7] Mochinaga, Y., Hisamizu, Y., Takeda, M., et al. “Static power conditioner using GTO converters for AC electric railway,” Power Conversion Conference, pp. 641-646, 2002. [8] G.F.Reed, M.Takeda, and I.Iyoda, “Improved power quality solutions using advanced solid-state switching and static compensation technologies,” in proc. IEEE Power Engineering Society Winter Meeting,1999, vol.2, pp.1132-1137. [9] O.Anaya-Lara and E.Acha,” Modelling and analysis of custom power systems by PSCAD/EMTDC”, IEEE Trans. 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