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Chapter 2 Chapter 2

Fundamental of Electric Traction Drives Fundamental of Electric Traction Drives DesignDesign

Wensheng Song PH.D

Email:[email protected]

Train Control & Traction Drive Lab,

Southwest Jiaotong University

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创新、自主研发

Outline

Mathematical Description of Mathematical Description of Train OperationTrain OperationProcessProcess

Train Forces DescriptionTrain Forces Description

Traction Characteristic Design of TrainTraction Characteristic Design of Train

Capability Calculation and Design of ACCapability Calculation and Design of AC--DCDC--AC AC Traction Drive SystemTraction Drive System

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Train operation process is a very complex control process, which is related to traction power supply, train signal, rail line section, all kinds of speed limit, train formation, train traction/braking performance, the operation experiences of driver and so on.The train operation objects are not only safety, arriving on schedule, reliability, high speed, high operation density, but also includes passengers’ comfortableness, train energy consumption saving, and exactness of train stop. Therefore,Train operation control system is a typical time-delaying, nonlinear, and multi-object system.The core problem is how to control the the traction/braking force of train running in various operation conditions in real-time.

Mathematical Description of Train Operation ProcessMathematical Description of Mathematical Description of Train OperationTrain Operation ProcessProcess

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Mathematical description of train operation process is the fundamental of studying and analyzing train traction control. Asthe time is used to the variable, the movement equations of train

are shown as follows:

Where c—The joint force of train (N/kN).—Acceleration coefficient;

r —Gyrating mass coefficient (usually 0.06 );J—Train energy consumption (J); p(t)—Train energy consumption per unit time (kW);

T—The whole trip operation time (s);v—The operation speed of train (m/s);s—The operation distance of train (m);t—The operation time of train (s);

dv cdt

ξ= ⋅ds vdt

=0

( )T

J p t dt= ∫

0.00981=1+

ξγ

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As the distance is used to the variable, The movement equations of train are derived as follows:

Where —Train energy consumption per unit distance (kW);S —The total operating distance of train (m);

The nonlinear movement equation of train is generally described as:

Where f(v) —The traction/braking force of train (N);w0(v) —The basic operating resistance force of train (N);g(s) —The additional operating resistance force of train (N);

( )sρ

0

( ) ( )S sJ d s

vρ

= ∫ dv cds v

ξ ⋅=

1dtds v

=

0( ( ) ( ) ( )) dvv f v w v g sds

ξ= − −

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Train Forces DescriptionTrain Forces DescriptionTrain Forces Description

The concept of adhesionAt the contact point of the driving wheelset and rail, the relative rest and non-sliding phenomenon of the driving wheelset and rail are named adhesion phenomenon, which is caused by the normal pressure of the wheelset.Traction force

(1)The axle traction force of the driving wheelset(fi)

which is also called the adhesion traction force. Actually, it is the static frictional force of the driving wheelset and rail.

(2)The axle traction force of the train (Fi)

which is to produce the torque Ti to drive the wheel rolling with the speed v.

i if G Mgμ μ= =

'i i i iF F T R= =

i if F=The Adhesion balancing situation:

---The Adhesion coefficientμ

Ri---Radius of circle

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The adhesion balancing situation will be damaged in the following conditions.

(1)If traction force Fi is larger than adhesion force fi, the idling phenomenon happens.

(2)If traction force Fi is lower than adhesion force fi, the sliding phenomenon happens.

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The train operation resistance force(1) The basic resistance force

It is produced by the friction and impact between components and parts, the train surface and air, the wheel and rail.

(2) The additional resistance forceIt is dependent on the steep gradient, the curve radius, andBridge & Tunnel situation of the rail line.

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The basic resistance force

The unit resistance is generally adopted to represent the train resistance

20 ( )W a b v c v M g= + ⋅ + ⋅ ⋅ ⋅

Where W0—The basic operation resistance force of train (N)M—The traciton quality (t)v—The operation speed of train(km/h)g—The acceleration of gravity (m/s2)

a,b,c—The coefficient being relative with mechanical resistance.

00 ( ) N/t

Wv

Mω = （）

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Traction demandsTraction demandsTraction demands

P=F×V

(1). The heavy load characteristic of the freight train results in the demand of the greater traction force

(2). The high speed characteristic of the passenger train results in the demand of the higher speed

F-(N)

V-(m/s)

Therefore, whether the head load freight locomotive or high speed passenger train, both of them require a greater traction power to satisfy with the demand of transportation.

The power:

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Traction Characteristic Design of TrainTractionTraction Characteristic Design of TrainCharacteristic Design of Train

The�relationship�curve�of�train�flange�traction/braking�force�and�speed�is�represented�as�

Traction�characteristic�of�train，which�is�the�most�important�and�original�datasheet�to�

calculate�the�performance�of�train�traction�and�braking.

Constant�Traction�Force�for�Start-up，Constant�Power�for�running

The�relationship�of�traction�force�and�power�is�shown�as�follows

3.6 kNkk

k

PFV⋅

= （）Accurate Constant Traction ForceConstant Traction Force

Constant PowerConstant Power

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Traction Characteristic Curve Design of TrainTraction Characteristic Curve Design ofTraction Characteristic Curve Design of TrainTrain

Traction Force

Power

resistance

Vmax

1.The starting traction force is dependent on the maximum starting acceleration and the average of the acceleration.

3.The traction force at the maximum speed point is satisfied with maxmax

3.6( ) kk

k

PF vv

=

2.The traction force at the turning point of pre-constant traction force region and constant power traction region is satisfied with m

3.6( ) kk

m

PF vv

=

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Traction Characteristic design of TrainTractionTraction Characteristic design of TrainCharacteristic design of Train

五种动车组特性曲线

0

100

200

300

400

500

600

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340

列车速度

列车牵引力、阻力（KN)

CRH5阻力

CRH3阻力

CRH2阻力

CRH1阻力

CRH1牵引力

CRH3牵引力

CRH380AL牵引力

CRH380BL牵引力

Train Traction Force and Resistance Force

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Capability Calculation and Design of AC-DC-AC Traction Drive System


Case 1: CRH2-300km/h, EMU

24Motors number300km/hThe operating speed

6M2TMarshalling350km/hThe max speed

6 Motor cars,4 Trailer

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The Structure Configurations of AC Traction Drive SystemThe Structure Configurations of AC Traction Drive SystemThe Structure Configurations of AC Traction Drive System

Gear box

AC motor

InverterPulseRectifier

Transformer

25000V

AC-DC-AC traction system for AC motor drive

Capacitor

Power line

Wheel

Traction Converter

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The Structure Configurations of CRH2 Traction Drive System

The Structure Configurations of CRH2 Traction The Structure Configurations of CRH2 Traction Drive SystemDrive System

M

M

M

M

abU

NI

dU

dI

MU

MIConverter InverterTransformerPantograph Motor

Auxiliary Winding:490kVA

AuAB

S1a

S2a

S3a

S4a

S1b

S2b

S3b

S4b

B

C1

C2

o

p

n

u1

u2

io

T1a

T2a

T3a

T4a

T1b

T2b

T3b

T4b

b

T1c

T2c

T3c

T4c

c

a iaibic

M3~

ɷ

25kV 50Hz

is

in

4 motors

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Capability Calculation and Design of AC-DC-AC Traction Drive SystemCapability Calculation and Design of ACCapability Calculation and Design of AC--DCDC--AC Traction AC Traction Drive SystemDrive System

?cP = ?TrS =

?TS =

?SIP =

?IP =

?MIP = ?MOP =

?kP =

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Capability Calculation and Design of AC-DC-AC Traction Drive SystemCapability Calculation and Design of ACCapability Calculation and Design of AC--DCDC--AC Traction AC Traction Drive SystemDrive System

Parameters Symbol (values or

calculation formulas) The output power of wheel-sets

Pk Power factor of Transformer

PfTr=1.0 The second winding voltage of transformer with no-load Es=1500

The efficiency of converter 0.975CONVη = The efficiency of inverter 0.985INNη = The efficiency of gear box 0.95Gearη = Power factor of traction motor 0.87MMPf = The efficiency of traction motor 0.94MMη = The output power of traction motor

MO MI MMP P η= × The input power of traction motor

PMI The voltage of traction motor ( 6 )M cE Eπ≤ × The current of traction motor

1 ( 3 )M I MI P E= The total output power of inverter

PI =PMI × Motor numbers The total output power of converter

c I INNP P η= The total output power of transformer /Tr c CONVP P η= The second winding current of transformer ( )s Tr s TrI P E Pf= ⋅

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Constant power point

135km/h

195.8kN

CRH2 300km/h Traction characteristics

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kP

1

342.7 / 0.87393.9(kVA)

I MI MMP P Pf===

144 393.91575.6(kVA)

I IP P== ×=

1575.6 / 0.9851599.6(kW)

c I INNP P η===

1599.6 / 0.9751640.6(kVA)

Tr c CONVP P η=

==

22 1640.6 /1 4903771.2(kVA)

T Tr Tr APUP P Pf P= +

= × +=

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