group 24 train drive system (1)

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Assignment for power electronics

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  • 2014

    Si Thu Ko 11260318

    Alexander Kumbley 11256714

    YeMon Aung 11461732

    Power Electronics Design Project Train Drive System

  • Alexander Kumbley 11256714 , YeMon Aung 11461732, Si Thu KO 11260318

    1 | P a g e

    Table of Contents 1. Introduction ........................................................................................................................................ 2

    2. Project Overview ................................................................................................................................. 2

    3. Feeding system ................................................................................................................................... 3

    4. Traction Transformer and Line Converter .......................................................................................... 7

    4.1 Transformer Model ....................................................................................................................... 7

    4.2 DC Link........................................................................................................................................... 8

    4.3 Line Converter ............................................................................................................................... 9

    4.3.1 Single phase controlled bridge rectifier ............................................................................... 10

    4.3.2 Buck-Boost ........................................................................................................................... 11

    4.4 Full Simulation and Results ......................................................................................................... 12

    5. Regenerative Breaking ...................................................................................................................... 14

    5.1 Equations of the Braking Process ................................................................................................ 16

    6. Auxiliary inverter ............................................................................................................................... 18

    7. Battery Charger ................................................................................................................................. 21

    8. AC Induction Motor........................................................................................................................... 23

    8.2 AC drive system with Induction motors ...................................................................................... 24

    9. DC/AC inverter .............................................................................................................................. 30

    10. Conclusion ....................................................................................................................................... 31

    11.Reference ......................................................................................................................................... 31

  • Alexander Kumbley 11256714 , YeMon Aung 11461732, Si Thu KO 11260318

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    1. Introduction The aim of this assignment is to design the main components that an electrical multiple unit train

    requires to meet the specification assigned to us. The main structure for an electric train is:

    Feeding System: This is researched and designed by Alexander Kumbley (11256714)

    Traction Transformer and Line converter: This is researched and designed by Alexander Kumbley (11256714)

    Regenerative Breaking: This is researched and designed by Si Thu KO (11260318)

    Auxiliary Inverter (DC/DC converter, Battery Charger): This is researched and designed by Si Thu KO (11260318)

    DC/AC Inverter: This is researched and designed by Ye Mon Aung (11461732)

    AC induction Motor: This is researched and designed by Ye Mon Aung (11461732)

    The introduction was completed by Si Thu KO (11260318)

    The project overview was completed by Alexander Kumbley (11256714)

    The conclusion was completed by Ye Mon Aung (11461732)

    2. Project Overview The power electronic design project aims towards designing a power electronic system for a specific system which in our groups case is a train drive system. The project will include analysis of different theoretical and methodological techniques in the analysis of different train drive systems and the design of our power electronic system. When analysing the train drive system, research will be conducted on different topics related to train drive systems, which are:

    Voltages used with the train systems ( AC or DC)

    Regenerative breaking

    The type of drive motor

    Voltage stepping

    Power ratings

    Traction power network Gaining information in these specific areas allows our group to progress onto the design stage of the power system. In the design of our system, criteria which will be taken into consideration include:

  • Alexander Kumbley 11256714 , YeMon Aung 11461732, Si Thu KO 11260318

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    Understanding the operation of different semi-conductor switch mode devices which are used in high powered circuits

    How these semiconductor devices will be used in the control of the power system

    How other passive and active componentry will be Incorporated into the system

    Awareness of electromagnetic interference which may affect the system

    AC to DC conversion

    DC to DC conversion

    Topology used for the conversion

    Compensating for losses with the componentry used in the circuits

    The topology which all components will be used

    3. Feeding system The electrification system serves as the contact interface for current collection distribution of power.

    The delivery of current and power between overhead catenary wire/wires and trains uses a device

    such as bow collector, pantograph or trolley pole. Most Morden day EMUs use a pantograph, which

    is mounted on the roof of EMUs which use an overhead system. The pantograph is spring loaded

    which pushing up against the overhead catenary wire/wires, making contact with the wire to draw

    electricity.

    In our train drive system we have chosen to use an overhead catenary contact system which supplies

    a single phase 25Kvac voltage at 50 Hz using a single catenary. In our design we had a choice

    between four feeding system configurations:

    Type Characteristics / Advantages Conceptual Drawings Simple

    Feeding system

    Most simplistic feeding system in the overhead catenary line configuration

    Little interference with communication

    Higher rail potential than other feeding systems

    Booster Transformer

    feeding system

    A feeding system that uses a booster transformer

    Effective in reducing induction to communication lines

    Need a BT section

    Complicated contact wiring in the BT section

    Considerable impedance in the feeding system

    Auto Transformer

    feeding system

    Suitable for supplying high electricity volume because it can carry feeding voltage (power sent out from a substation) higher than that carried by an overhead contact line

    Can have a longer interval between substations than the other sections

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    Approximately a 10-km interval between two auto-transformers

    Coaxial cable feeding system

    High inverse barometer effect is effective in reducing induction to communication lines

    Do not need BT or other sections, simple conductor arrangement, suitable for narrow and small sections

    Expensive cables

    Reciprocating impedance is about 1/7 of the overhead contact line

    Need to pay attention to resonance with the harmonic current

    The reasoning behind choosing simple feeding 25Kvac system is that it is widely is various parts

    countries such as Australia, France and the United Kingdom. Although this system has its advantages

    there are also disadvantages of this system.

    Disadvantages of simple feeding 25Kvac system:

    Uses only one phase of the nominal 3-phase, inducing an imbalance on the three phase

    supply.

    Causes an unbalanced load, creating a huge power imbalance.

    For the calculation of the current delivered by the overhead line, we used the IEC 60850 - "Railway

    Applications. Supply voltages of traction systems" standardisation for the permissible range of

    voltages allowed.

    Electrification system

    Lowest non-permanent voltage

    Lowest permanent voltage

    Nominal voltage

    Highest permanent voltage

    Highest non-permanent voltage

    25,000 V, AC, 50 Hz

    17,500 V 19,000 V 25,000 V 27,500 V 29,000 V

    From research it was found that the EMUs have a general power classification of 3-4 MW. For our

    calculations we have used 3.5MW of power. Therefore the current delivered via the overhead

    catenary wire to the train is:

    =

    =

    Electrification system

    Lowest non-permanent current

    Lowest permanent current

    Nominal current

    Highest permanent current

    Highest non-permanent current

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    25,000 V, AC, 50 Hz

    200 A 184.2 A 140A 127.27 A 120.7 A

    The simple feeder system uses the overhead catenary wires to supply power to train at 3.5MW. As

    the rail is grounded, this is used as the return path allowing for the completion of the circuit.

    Figure.. Simple feeding model circuit

    The feeding simple has been modelled and simulated in PSIM under the normal parameters to

    simulate the path current path (The power factor is assumed to be 0.8 leading due to inductive

    load).

    = 3.5

    = 250

    = 14036.87

    =

    =25000

    14036.87

    = 120.63 + 131.67

    = +

    = 120.63

    = 2

    =

    2

    =131.67

    2 50

    = 491.11 mH

  • Alexander Kumbley 11256714 , YeMon Aung 11461732, Si Thu KO 11260318

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    Figure Simple Feeder Circuit

    Figure . Simple feeder circuit load voltage

    Figure. Simple Feeder circuit current

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    4. Traction Transformer and Line Converter The electric power for railway traction delivered from the catenary wire is stepped down through a

    traction transformer. The conventional power conversion process which is found in most modern

    trains consists of a low frequency transformer allowing the current from the AC overhead catenary

    wire to flow through the primary windings of the transformer to the rail creating a return path. The

    stepped down voltage at the secondary winding/windings are fed into a four-quadrant line chopper

    circuit, rectifying the AC voltage to DC voltage into a DC link voltage. The Low frequency transformer

    provides galvanic isolation, changes voltage levels and operates with AC quantities.

    Figure. Traction Transformer and Line Converter

    4.1 Transformer Model

    Figure.Traction Transformer

    For our model we are assuming an ideal transformer.

  • Alexander Kumbley 11256714 , YeMon Aung 11461732, Si Thu KO 11260318

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    The transformer parameters are as follows:

    Primary Voltage 25KV

    Secondary Voltage 5KV

    Primary winding turns 25

    Secondary winding turns 3

    Turns Ratio 25:3

    The current and voltage from the catenary wire is supplied to the primary winding of the ideal

    transformer. Therefore:

    = 25

    = 14036.87

    Calculating the secondary voltage Vs and current Ip:

    = 2

    1

    = 25000 3

    25

    = 3000

    = 1

    2

    = 14025

    3

    = 1166.67

    The secondary voltage and current are then feed into a Line converter where it is rectified to the

    desired DC Link Voltage.

    4.2 DC Link The DC Link term refers to a decoupling capacitor in the DC link. The DC link is an intermediate

    capacitor circuit used intermediately between converter circuits where it couples different electrical

    grids to one DC voltage. As both the converters that is used in our design are controlled, the

    switching network on the motor side generates large transients at switching frequencies.

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    The DC link help to reduce the transients in radiating back into the other converter circuits. In our

    design we require a DC Link voltage of 3KV DC which is used to supply the Inverter circuit for the

    motor along with a common point for the auxiliary power circuit. For the design of the DC link

    capacitor is it important needed to consider the high frequency ripple current from the output. We

    chose a Metallized Polypropylene (PP) Capacitor for our design. The WIMA DC LINK MKP 6 DC link

    is sufficient for our use.

    Special features which are incorporated with the DC Link:

    Very high volume/capacitance ratio

    Self-healing properties

    With cylindrical aluminium case for bus bar mounting

    Dry construction without electrolyte or oil

    No internal fuse required

    Negative capacitance change versus temperature

    Very low dielectric absorption according to RoHS 2011/65/EU

    Customer-specific capacitances or voltages on request

    Table DC Link data sheet

    The DC link will be in the line converter simulation.

    4.3 Line Converter Below is the following flow diagram of the supply of power to the conversion of AC to DC to provide

    a steady state 3KV DC voltage to the DC-Link. The line converter includes a single phase full

    controlled bridge rectifier to convert the 3KV AC voltage to 3KV DC voltage and a Buck-Boost DC to

    DC converter incorporating IGBTs (Insulated Gate Bipolar Transistor) for high voltage switching.

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    4.3.1 Single phase controlled bridge rectifier A single-phase full converter bridge consists of four SCRs. Thyristor pair T1 and T2 is simultaneously

    triggered and pair T3 and T4 is gated together. Voltage at the output terminals can be controlled by

    adjusting the firing angle delay of the thyristor. There is a wider control over the level of dc output

    voltage.

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    The full bridge inverter consists of 4 SCRS T1, T2, T3 and T4. There are four different switch states

    which apply to this circuit:

    State Transistor Load voltage

    1 T1 and T2 on + VDC, charging capacitor

    2 T3 and T4 on + Vdc, charging capacitor

    3 T1 and T3 on 0, control circuit should be designed to avoid this state

    4 T2 and T4 on 0, control circuit should be designed to avoid this state

    As stated above, the control circuit should be designed to avoid state 3 and 4 as this will cause short

    circuit across the ac voltage source.

    The graph below illustrates the switching periods of the transistors and the load voltage with respect

    to the states of T1, T2, T3 and T4.

    4.3.2 Buck-Boost A Buck-Boost converter is a type of switched mode power supply that combines the principles of the

    Buck Converter and the Boost converter in a single circuit. The buckboost converter is a type of DC-

    to-DC converter that has an output voltage magnitude that is either greater than or less than the

    input voltage magnitude. The output voltage is of the same polarity of the input, and can be lower or

    higher than the input. Such a non-inverting buck-boost converter may use a single inductor which is

    used for both the buck inductor and the boost inductor.

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    4.4 Full Simulation and Results

  • Alexander Kumbley 11256714 , YeMon Aung 11461732, Si Thu KO 11260318

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    5. Regenerative Breaking By using regenerative breaking, we can convert the energy of the train into usable power by

    diverting the braking current into current rail or the overhead line. Then the power can be received

    by another train which are connected to the line or sent it back to the grid. However, bank of

    resistor is needed to be installed to absorb excess energy which is created if no other trains are

    drawing power from the line.

    The locomotive equipment is built on the main step-down transformer with more secondary

    windings the four quadrant line side AC/DC converter, a DC link circuit and more DC/AC three phase

    inverters which supply the induction traction motor. In motoring mode of operation, the train

    receives the electric power through the overhead lines, through step-down transformer to the

    AC/DC converter which is operated as controlled rectifier and the DC/AC converters which typically

    operate as inverters. By regenerative, the induction motor operates as generator and DC/AC

    converter (the motor side converter) becomes rectifier using the voltage from DC links. Also the

    AC/DC converter (the line-side converter) becomes inverter and transfers the electrical power to the

    grid.

    Moreover, by using regenerative breaking, the overall energy efficiency of a vehicle can increase that

    is increases vehicle range and cuts down on pollution related to electricity generation. It can also

    increase the lifespan of friction braking systems, for instance, less use of traditional mechanical

    breaks leads to less wear over time.

    Figure 1 Regenerative Breaking Circuit

    The above is the circuit diagram of AC/AC conventional electric locomotive dynamic braking system.

    The main components are UCR-uncontrolled rectifier, AI-autonomous inverter, Rb-braking resistor,

    M1, M2, M3 as asynchronous traction motors and WS1, WS2, WS3 as wheel-sets.

  • Alexander Kumbley 11256714 , YeMon Aung 11461732, Si Thu KO 11260318

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    Figure 2 Torque-speed characteristic of induction traction motors regenerative braking

    The conditions for the motor being idle to exceed point n0 of torque-speed characteristic n=f(M),

    which is required in regenerative breaking, cannot be satisfied (see Fig 2). However, AC traction

    motors speed will be above no load speed n0 when the locomotive traction motor regenerative

    braking is returned to energy supply system.

    Figure 3 A circuit diagram of AC/AC current system electric locomotive regenerative braking energy

    computer control system

  • Alexander Kumbley 11256714 , YeMon Aung 11461732, Si Thu KO 11260318

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    5.1 Equations of the Braking Process Initially the train runs on the horizontal path with the speed (vi), then the speed must decrease in

    the range (vi Vf, Vf < vi) during a given time-interval (t*), with constant deceleration when the

    train runs on a down-hill path.

    The mechanical evolution during the braking interval (force, torque, speed, etc.) such as evolution of

    the braking force Fbr(t), braking mechanical power Pmbr(t), train speed v(t), induction traction motor

    torque Tm(t), motor rotor speed m(t).

    For the electrical traction machine are imposed the evolutions of the braking torque (Tbr(t)=Tm(t))

    and of the speed profile (mN(t)). Based on the fundamental equations of the induction traction

    machine: nominal stator phase voltage in star connection (UsN) and stator angular frequency (sN),

    nominal power (PN), nominal rotor speed (mN) and slip (SN), rotor angular frequency (rN), rated

    motor torque (TmN), etc. and main parameters: stator and (reduced) rotor resistances (Rs, Rr), stator

    and (reduced) rotor leakage inductances (Ls, Lr), magnetization inductance (Lm); the active loses are

    neglected, the paper simulates the evolutions of the main induction machine variables during the

    braking process (100 sec).

    In order to generate the stator voltage (UsN), the motor side converter has to be supplied with the

    nominal DC voltage (UDCN). The UDCN / UsN ratio will be kept constant therefore the value of the DC-

    link can be determined.

    The equation: U1 UDC / (1.41* ) will be used to estimate the input voltage (U1) of the line side

    converter which is given by the secondary winding of the step-down transformer from the traction

    power substation.

    Breaking Process Simulation

    For the equivalent induction traction motor:

    PN = 250kW;

    nN = 2900 rot/min; mN = 303.53 rad/sec;

    UsN = 750 V;

    fsN = 50Hz; sN = 314 rad/sec;

    ku = UsN / sN = 750/314 = 2.388;

    cos N = 0.85;

    Rs = 0.289 ;

    Rr = 0.217 ;

    Ls = 1.90*10-3;

    Lr = 2.39*10-3;

    Ls = 5.59*10-2;

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    Mechanical data for the braking process:

    Fbr(t) = 11375.25+9t-0.0225t2 [N] for t = (0-100sec)

    v(t) = 25-0.15t [m/s]

    Pbr(t) = Pmec(t) = (Fbr(t)*v(t)) [W]

    Equivalent radius R*=0.0747

    Tm(t) = * R** Fbr(t) = 0.89*0.0747* Fbr(t)

    m(t) = v(t)/ R*

    r(t) = Tm(t)/C; C=78.87

    s(t) = m(t)-r(t)

    Us(t) = (UsN/IsN)*s(t) = 2.388*s(t)

    Regenerated power for the national grid Pg

    Pg(t) = g*3Us(t)*Is(t)*coss(t); g0.75

    S(t) = r(t)/s(t) (

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    6. Auxiliary inverter The concept of battery storage technology is to expand regenerative brake energy into high-speed

    region and to stably supply DC power to the auxiliary power converter. Therefore, regenerative

    braking becomes possible by using hybrid traction system electric train inverter control technology

    and regenerated energy, temporarily stored in the batteries, can be used as auxiliary power for

    acceleration.

    Figure 4 Principal circuit diagram of Hybrid Traction System auxiliary power inverter

    DC/DC converter

    Figure 5 DC/DC converter design

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    Figure 6 DC/DC converter simulation

    We decided to choose BORDLINE M30 DC_750V Auxiliary converter as the design specification

    meets our requirement as M30 DC static converter is built with modern IGBT technology to provide

    a three-phase sinusoidal AC voltage output and DC voltage output for charging the battery.

    The BORDLINE M30 DC auxiliary converter consists of:

    1. Input and EMC filter with input fuses

    2. Pre-charging unit

    3. DC/DC converter with galvanic insulation to generate the DV voltage for the regulated

    intermediate DC link.

    4. Three phase inverter with sine filter

    5. DC/DC converter for battery charging

    6. AC 800PEC main control module

    7. Electronics power supply

    Figure 7 BORDLINE M30 DC_750V Auxiliary converter

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    Specification:

    DC line voltage 600/750 V

    DC

    Three-Phase AC output

    3 x 400 V / 50 Hz, 19 kVA

    DC output

    24 V

    DC

    , 12 kW

    DC output options

    36 / 48 / 72 / 110 V

    DC

    BUS interface

    CAN, MVB

    Product options

    Flat battery start device

    Dimensions (L x W x H)

    1400 x 850 x 450 mm

    Weight < 230 kg

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    Figure 8 BORDLINE M30 DC_750V Auxiliary converter

    7. Battery Charger We decided to use ZB24DC300 series battery charger as the design specification meets our

    requirement as ZB24DC300 is designed to charge the batteries and supply DC loads of the related

    voltage of 24 VDC which is also in co-operation with the buffer battery. The charger can also operate

    without the battery or with any type of battery.

    Specification:

    Input voltage 3400 VAC 50 Hz

    -15%+15%

    Rated voltage (Un) 24 VDC

    Rated voltage stability 1%

    Rated voltage ripples 0.5%

    Rated current (In) 300 A

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    Battery current reduction regulation (0.11) In

    Protection ratio IP55

    Housing dimensions -40 C+45 C

    MTBF (measured) 200,000 h

    Dimensions 483490222 mm (5U)

    Figure 9 ZB24DC300 series battery charger

    The system will ensure:

    1. Constant monitoring of the supply voltage

    2. Monitoring of output currents and voltages

    3. Generation of alarm signals

    4. Independent stabilisation of output current and battery current

    5. Thermal compensation of the battery voltage

    6. Diagnostics of the battery (circuit continuity)

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    The charger also includes 3 alarm contacts to signal when there is the lack of battery charging,

    overloading and having low output voltage.

    8. AC Induction Motor In recent decades, the use of AC motors in railway has grown rapidly. The three phase induction

    motor is the most commonly used type of traction motor in the railway industry. Some classical DC

    traction motors are still using but they are decreasing in number.

    The AC induction motor is a rotating electric machine designed to operate from a 3-phase source,

    alternating voltage. The variable speed drives, the source is normally an inverter to uses power

    switches to produce approximately sinusoidal voltages and currents of controllable magnitude and

    frequency. The turns in each winding are distributed for a current in a stator winding to produces an

    approximate sinusoidally-distributed flex density around the periphery of the air gap. Even three

    currents that are sinusoidal varying in time, they displaced in phase by 120 from each other.

    Torque-speed characteristic of induction traction motors traction modes by changing main

    frequency f1fi parameters

    Figure 10 Block diagram of battery charger system

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    The most effective way of controlling the three-phase inductions is by changing frequency so that a

    wide range speed control can be ensured and would only cause little additional losses.

    Relative slip formula:

    s = n1 (n2*n1)

    where:

    n1 the speed of the rotary field

    n2 speed of rotor (rotor speed on load)

    f1 main frequency; f1 = p*n*160 (p is the number of pole pairs)

    f2 frequency of the rotor voltage; f2 = p*n*260 (p is the number of pole pairs). Then;

    s = f1 f2*f1

    Asynchronous motors rotor speed:

    n2 = n1(1 - s) = 60*f1*p*(1-s)

    Advantages of AC induction motors over DC motors

    Compared to DC brush-type motor, it is more advantageous to use a three-phase induction

    motor with standby AC power systems. While DC brush-type motor is simpler to supply with power

    for operation but it construction has drawbacks. The DC motor has a mechanical commutator and

    brushes which contact while moving relative to one another. Thus, these components are subject to

    wear and needed to give periodic maintenances.

    The drawbacks from DC motors are eliminated in the construction of a three-phase motor. It

    has a simpler, brushless construction and therefore is highly reliable and requires relatively low

    maintenance. For these reasons it can be operated at higher speeds than a brush-type motor and

    has increased power to volume and weight ratio.

    These advantages make the three-phase brushless motor more attractive than the brush-

    type motor even though the brushless motor requires a more complex device/circuit to supply

    power to it from a DC battery. The brush-type motor requires a relatively simple DC to DC converter

    to power it, the three phase brushless motor requires a relatively more complex three-phase bridge

    inverter to generate the rotating magnetic field which operates the motor.

    8.2 AC drive system with Induction motors The Locomotive equipment is based on the main step-down transformer with more

    secondary windings the four quadrant line side AC/DC converter, A DC link circuit and after that

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    DC/AC three phase inverters which supply the induction traction motors. In motoring mode of

    operation, the electrical power is transferred from the national grid, through step-down transformer

    to the AC/DC converter which is operated as controlled rectifier and the DC/AC converters. Typically

    operated as inverters.

    This figure shows the simple circuit for Motor Drive system

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    This figure shows the stimulation of the Motor drive system

    We decided to choose NEMA motors TEFC as design specification as the design specification meets

    our requirements as induction motor.

    Specification

    Output power 950HP

    Number of poles 6

    Voltages 4kV

    Frequency 50Hz

    The models of the Induction traction motor and the motor-side converter

    Variable voltage and variable frequency ( VVVF ) are apply to modern AC drive electric motor

    by using proper power converters. Even the train system has more traction motors, it is considered

    an equivalent induction motor with one pole pair (p=1) and use following parameters:

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    The Power: P [kW]

    Stator voltage: Us [V]

    Supply angular frequency: s [rad/sec]

    Motor torque Tm [Nm]

    (cos)N

    Stator resistance Rs []

    Rotor resistance Rr []

    Stator leakage Los [H]

    Rotor leakage Lor [H]

    Lm [H]

    To calculate the air gap flux at constant level , we use this equation :

    Kv=

    = Constant

    Simplified motor torque equation is :

    Tm=3

    (

    )2. r

    Where (r) is the rotor angular frequency the actual slip is :

    S=

    =

    In generator mode m > s and result in S0) and figure for

    generator mode of operation (S

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    The desired evolution of the braking force and of the train is given in :

    For the induction traction motor in accord to the energy conservation law, with the efficiency= 1,

    result in:

    An equivalent radius ( R*) is introduced so that:

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    The model of the equivalent induction traction motor is based on the following equtions :

    The electrical power generated by braking is:

    The difference ( PBr(t) Pel(t) ) is given by the various loses : stator and rotor losses.

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    9. DC/AC inverter We decided to choose PSM-95 VDC to VAC inverter as design specification as the design

    specification meets our requirements as vehicle traction system.

    Specification:

    Input Voltage 3000 VDC

    Output Voltage 4x400 VAC

    Total output power 95 kVA

    Total efficiency >85%

    Protection ratio IP56

    Weight ca.700kg

    Dimensions Converter (501x2316x984)mm

    Input choke ( 480x698x524)mm

    Block Diagram

  • Alexander Kumbley 11256714 , YeMon Aung 11461732, Si Thu KO 11260318

    31 | P a g e

    10. Conclusion To conclude that our group spent a lot of time on doing researches and weekly meeting to discuss on

    project needed. We referenced Lecture notes, Power electronic Text Books and online researches in

    other to finish this project. After doing this researches and calculation we got brief ideas how to

    design the converter, inverter, induction motors and train drive system. Our group believed that this

    report will help further study.

    11.Reference Franquelo, L. G., Rodriguez, J., J. I. Leon, J. I., Kouro, S., Portillo, R. & Prats, M. A.M. 2008,

    The age of multilevel converters arrives, IEEE Industrial Electronics Magazine, vol. 2, No. 2,

    pp. 28-29.

    Boldea, I. & Nasar, S. 2001, The Induction Machine Handbook, CRC Press, pp. 198-206. Rech, C. & Pinheiro, J.R. 2007, Impact of hybrid multilevel modulation strategies on input and output harmonic performances, IEEE Trans. Power Electron, vol. 22, No. 3, pp. 967-977.