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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
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