politecnico di milano · figure 1.01 representation of a pair of asynchronous motor fed by single...

POLITECNICO DI MILANO

Facoltà di Ingegneria Industriale

Corso di Laurea Magistrale in INGEGNERIA MECCANICA

Pair Synchronous Machines Fed by Single Inverter

Relatore:

Prof. Luigi Ferdinando Mapelli

Tesi di Laurea di:

Hamidreza TADAYONFARD

Matricola: 780864

ANNO ACCADEMICO 2014-2015

2

ACKNOWLEGEMENTS

The researcher acknowledges extreme gratitude and appreciation to

those who have given their respective assistance in this research.

Without their inspiring, challenging and encouraging support, this

Thesis would not have materialized. To them, the researcher gives

his sincerest thanks.

I would like to sincerely thank my research advisor, Dear Prof. Luigi

Ferdinando Mapelli who had given me the opportunity of doing this

thesis. He has never hesitated his help and was a real kind and

strong support for me. Special thanks to Prof. Federico Cheli who

has explained me some complexities very kindly.

I must thank Davide Barlini and other engineers in Alstom as well.

They made me a more practical engineer and I learned much useful

stuff there.

HAMIDREZA TADAYONFARD

3

TABLE OF CONTENTS

ACKNOWLEDGEMENTS

TABLE OF CONTENTS

LIST OF FIGURES

ABSTRACT

INTRODUCTION

CHAPTER 1. MECHANICAL EVALUATION

1.01. General Machine Properties

1.02. Different axle’s torque

1.03. Different initial angular position

1.04. Different axle’s angular velocity

CHAPTER 2. MECHANICAL STRATEGIES

2.01. Clutch

2.02. Viscous coupling

2.03. Mechanical differential

2.04. Bevel belt transmission

CHAPTER 3. ELECTRICAL STRATEGIES

3.01. A synchronous motor with an asynchronous mate

3.02. Control the inverter angle

CHAPTER 4. MODELING OF MACHINES

4.01. Motor’s equations

4.02. Torques’ Analysis

4.03. Currents’ Analysis

4.04. Efficiencies’’ Analysis

4.05. Acceptable interval

4.06. Motor’s properties…

4

4.07. Modeling on Simulink

4.08. Inverter

4.09. Mechanical inertia

4.10. Control strategy n.1

4.11. Control strategy n.2

4.12. Dynamics of the bogie

4.13. Involved perimeter

5

LIST OF FIGURES

Figure 1.01 representation of a pair of asynchronous motor fed by single inverter

Figure 1.02 representation of a pair of synchronous motor fed by two inverters

Figure 1.03 representation of a pair of synchronous motor fed by single inverter

Figure 1.04 two synchronous motors with different angle fed by one inverter

Figure 1.05 perimeters of wheels on a curve

Figure 1.06 different perimeters because of conical wheels

Figure 1.07 Phase difference definition = θ1 – θ2

Figure 1.08 representation of contacts’ points on the wheel.

Figure 2.01 illustration of clutch

Figure 2.02 illustration of viscous coupling

Figure 2.03 illustration of modified viscous coupling with one gearbox

Figure 2.04 illustration of bevel belt transmission

Figure 2.03 illustration of modified bevel belt with double gearbox

Figure 3.01 synchronous motor’s current direntions

Figure 4.01 synchronous motor’s voltage diagram

Figure 4.02 torques’ difference diagram

Figure 4.03 currents’ difference diagram

Figure 4.04 efficiencies’ difference diagram

Figure 4.05 current’s difference diagram [330A, 155Hz]



Figure 4.08 gamma angle by varying motor’s frequency

Figure 4.09 voltages Vsf and Usf by varying motor’s frequency

Figure 4.10 motor’s currents Isd, Isq and Isf by varying motor’s frequency

Figure 4.11 motor’s torque by varying motor’s frequency

Figure 4.12 primary simulink model of a synchronous motor

Figure 4.13 motor’s torque reaction

6

Figure 4.14 real inverter element

Figure 4.15 the voltage waves of the real inverter

Figure 4.16 representation of the ideal inverter

Figure 4.17 the voltage waves of the ideal inverter

Figure 4.18 constant mechanical resistance

Figure 4.19 variable mechanical resistance by inertia

Figure 4.20 motor’s position and speed with a constant resistance which is applied after one

second

Figure 4.21 representation of first synchronous motor of two motors

Figure 4.22 representation of second synchronous motor of two motors

Figure 4.23 representation of the inverter which makes run the motor in back

Figure 4.24 motor’s position and speed when inverter makes run the motor in back

Figure 4.25 representation of both motors and inverter which makes run motors by media angle

Figure 4.26 the strategy of inverter’s function

Figure 4.27 motors’ positions and speeds when the inverter makes run by media angle

Figure 4.28 illustrations of two degrees of freedoms of a shaft

Figure 4.29 illustrations of the effect of alpha on involved perimeter



7

ABSTRACT

This study tries to find a way to make run two parallel synchronous motors with

a single inverter. The research has been done on train’s motors. At the beginning

we thought only on mechanical solutions which might be useful as well, but

they are some limitation like space and they are quite expensive. Then by

finding electrical solutions, advantages of mechanical solutions are not any more

brilliant. an electrical solution does not need to space and it does not need to

material, so it is economic and on the other hand can satisfy the targets. on the

classical ways, inverter inputs the angle of the motor and outputs a vector

voltage by the same rotor’s position considering a phase-difference. But this law

is broken in this thesis and inverter does not apply a voltage respect to one

motor and it has under control both of motors. to control them there could be

many strategies, but in this study I tried two possibilities. The first one the

angular position of the motor in back and the second one the average angular

positions of both motors. The second try was effective; however there might be

other strategies which have a higher stability. As s suggestion the fraction ratio

of deference of two motors’ angular positions as inverter’s reference could be

efficacious.

8

INTRODUCTION

These years trains are a noticeable part of transportation and every new

generation possesses a higher technology to reach a more confortable trip and at

the same time to make a more efficient function. Years ago the fossils were the

main state of energy which for many reasons was convenient to use: but after

some years consuming energy in electric form became common and easy. One

of important areas which changed the design’s strategies is transportation sector.

Electric motors have a high power and a high controllability, and at the same

time they are less noisy and less pollutant. Now a very common type of trains’

motors is synchronous motor. One of its properties is complexity of making it

function. It is done by an inverter which respect to rotor’s angle applies a three-

phase voltage. Since the inverter costs a considerable number like three times

more than a train’s synchronous motor, and every motor needs one of them, it is

a clever idea if it could be possible to make run two motors with just one

inverter. In continue they are mentioned the hardships for realizing this think.

9

CHAPTER 1

MECHANICAL EVALUATION

General Machine Properties

This thesis tries to find the solution for an economic problem. Today train-

producers exploit tow Asynchronous machines fed by single inverter.

Figure 1.01 representation of a pair of asynchronous motor fed by single inverter

If we want to use two synchronous machines like some trains, we have to

utilize tow autonomous inverters as well.

Inverter

DC

AC

Asynch A

Asynch

B

10

Figure 1.02 representation of a pair of synchronous motor fed by two inverters

What are the benefits of synchronous machines? In fact the main difference

between synchronous motors and asynchronous motors is the efficiency.

The synchronous machines have a higher efficiency; it is 2 or 3 % higher

but in a long period it would be a considerable energy-saving. Another

synchronous machine’s advantage is the minor volume. By the same power,

a synchronous motor occupies smaller volume respect to asynchronous

motor; in another words with the same size, a synchronous motor can

produce a higher power than an asynchronous motor. By the way

synchronous machines have a higher programmability. It makes use for

example for a smooth start of the train’s movement; here it needs an open

loop programing.

For the purpose of money-saving utilizing two inverters is less advisable

and less convenient because one inverter costs three times more than a

motor. So if it would be possible to make rotate two synchronous motors

only by one inverter, we can call it a good idea. Now we want to make

another step forward. it seems really impossible but I try to find the

conditions which make it possible.

Inverter A

Inverter B

DC

AC

Synch B

DC

AC

Synch A

11

Figure 1.03 representation of a pair of synchronous motor fed by single inverter

What does happen if they would be connected like this? Obviously the

second motor does not function well and in a train it even neutralizes the

first motor’s force.

So should find the source of problems. In this case the problems can be

categorized in 3 sections.

Figure 1.04 two synchronous motors with different angle fed by one inverter

DC

AC

inverter

Synch A

Synch

B

12

There are 3 kinds of Problem Different axle’s torque Different initial angular position Different axle’s angulare velocity

And they will be evaluated one by one.

Different axle’s torque

During transitory step (from straight railway to curvy path) occurs an

alternative angular velocity because the perimeters which is passed by the

wheels are ellipse instead of circle

Figure 1.05 perimeters of wheels on a curve

Even if the train always moves on straight rails, the perimeter of any wheel

is not absolutely equal to other axle. Therefore they have different torques

and velocities.

13

Figure 1.06 different perimeters because of conical wheels

If one more applies a higher torque obviously it accelerates that axel and

it's undesirable. To avoid it i have found some articles which have some

solutions for this problem if the only problem would be this one. I verify

these solutions and also if they could be useful for all 3 problems.

Different initial angular position

Figure 1.07 Phase difference definition = θ1 – θ2

14

Phase difference equals (θ1 – θ2) as the figure’s representation.

Considering the left wheel’s angular position as θ1 and the right one θ2,

practically it is quite impossible to put them on the railway without any

phase difference. Even if at the beginning they would be completely

synchronized, they find a phase difference after a trip because of wheel’s

geometries’ imperfection and in the transitory part of movements

Different axle’s angular velocity

The last and more complicated problem is different axles’ velocities. In fact

velocities’ difference has many reasons like different wheels’ diameter or

when two axles rotate on a curvy path and in transitory part, the axles

rotate with different instant involved diameters.

15

Figure 1.08 representation of contacts’ points on the wheel.

Here the calculation of motors’ behavior is needed. Synchronous motor

dissimilar to continuous current motors needs a precise 3phase current

alimentation which it produce through a voltage transformer called

Inverter. The inverter inputs DC voltage and outputs 3 phase AC voltage.

The output 3phase voltage does not have a fix frequency like city power

(50Hz). Three phases are with 120° permanent phase shift. Inverter applies

voltage respect to the angular position of the motor with a bit different.

Because there is a uniform torque just if inverter follows the motor’s

angular position.

16

CHAPTER 2

MECHANICAL STRATEGIES

The solutions can be introduced in two sections; Mechanical solutions and

electrical solutions. Every solution can be useful for only for one of the

problems or more than one of them. Here I introduce these solutions and I

evaluate them one by one.

Mechanical solutions

o Clutch

Figure 2.01 illustration of clutch

A mechanical clutch works with 2 discs for engaging and disengaging the

power transmission, from driving shaft to driven shaft. The clutch can

control torque, velocity and phase difference; it means all three problems

http://en.wikipedia.org/wiki/Transmission_(mechanics)

http://en.wikipedia.org/wiki/Driving_shaft

17

would be solved. So through a feedback control it’s possible to control the

second motor’s angular position. However there are also some

disadvantages like energy wasting.

Advantages

Possibility to solve all three problems

Disadvantages

Energy wasting

Disk consuming

Less economic (clutch + mechanical actuator system)

Short maintenance period

Space occupying

o Viscous coupling

Figure 2.02 illustration of viscous coupling

18

Viscous coupling works through friction effect between two plates and oil.

It can control output torque in a range, but there is a problem that output

velocity is always a bit less that input shaft’s velocity and in this case the

shafts must rotate often with the same velocity. For resolving this problem,

it is needed a fix transmission ratio whereby it can have the equal velocity

or less.

Figure 2.03 illustration of modified viscous coupling with one gearbox

Advantages

Possibility to solve velocity and initial angle problems

Disadvantages

Energy wasting

by passing time, the oil’s properties will be changed and it affects on

transmission ratio

control’s complexity

short maintenance period

not economic

19

o Mechanical differential

In this way single synchronous motor will distribute force between 2 shafts

through mechanical differential

This solution will function most likely because years ago this system has

been used with a diesel motor and here a synchronous motor could be

substituted instead of diesel machine.

Advantages

have function without electrical control

the problems there are not any more

Disadvantages

Occupying a large space

Not economic

o Bevel belt transmission

This transmission system has a smooth variable transmission ratio and it

would be a way to synchronize 2 motors with a feedback system

Figure 2.04 illustration of bevel belt transmission

20

In this transmission system, the fundamental problem is that the belt

cannot support this amount of torque and the force breaks the belt. So the

modified version of that is shown here down when before and after the

bevels there are 2 gearboxes. The first gearbox has a transmission ratio

more than 1 so it increases the velocity and decreases the torque and it

becomes tolerable for the belt. The next gearbox neutralizes the first

gearbox’s effect. So it has a transmission ratio less than 1 and it is equal to

1/first gearbox’s ratio. Thus second gearbox increases torque and

decreases velocity. The bevels rotate faster but belt can support the

transmission torque.

Figure 2.03 illustration of modified bevel belt with double gearbox

Advantages

The range of transmission ratio is wide and very accurate

Disadvantages

It can solve only speed problem

Occupying a big space

short maintenance period

Less economic

It also needs an electrical feedback control

Slow reaction respect to other solutions

21

CHAPTER 3

ELECTRICAL STRATEGIES

o A synchronous motor with an asynchronous mate

It seems a good idea. Because inverter can produce 3phase voltage respect

to synchronous motor and the asynchronous motor just follow it because

asynchronous motor is not sensible like synchronous one. So till here

everything is OK. The problem is that if inverter applies the 3phase voltage

for synchronous motor, the asynchronous one rotates a bit slower and it

functions with a capacity less than synchronous one. There is another way

to compensate this property with a gearbox after asynchronous motor

which has a transmission ratio more than 1, so it increases the

asynchronous motor’s velocity. That is acceptable for now; But over here

there is a new hardship; the brake. Motors in this state do not have the

maximum brake capacity. If I decide to do the same strategy for braking as

well, I should put another gearbox with a transmission ratio smaller than 1

to have an appropriate brake. So if I do like this, I need 2 gearboxes, one for

acceleration, another one for deceleration and another state-changer which

changes the gear between these 2 gearboxes and all of this is too

complicated and it is not advisable. By the way all these stuffs occupy a

huge amount of space that in a bogie there is not. Another small problem

about this solution is that even if we decide to use 2 gearboxes, the

transmission ratio which can synchronize two motors’ torque, is not a fix

number and on the other hand the strategy for having the maximum

capacity of asynchronous motor is different by synchronous motor. The

result is that some money are saved by losing the capacity of train. It might

be more advisable if tow motors would be asynchronous. even from

commercial point of view, train companies who buy the train prefer and

require trains with the same motors. Hence there is strong evidence to

reject this solution.

22

o Control the inverter angle

to make rotate a synchronous motor, inverter produces a three-phase

current. Respect to these three phases there are another three phases

parallel on motor which have 120° distance among them. It is also defined

the term of Phase-Difference as an angle which between stator’s position

and rotor’s position. The phase-difference shows how much rotor tend to

rotate and produce torque. Until a known value which is 90° (electrical

degrees), by increasing phase-difference, rotor tends more to rotate and

rotor has a higher acceleration value. It means if this angle would be zero,

so the rotor does not rotate anymore. Hence to make function a

synchronous motor, it needs to control inverter’s phase as the phase-

difference remains an acceptable value. Like this inverter must follows

rotor’s position and applies its position plus difference. It is noticeable that

negative phase-difference makes rotor decelerate. Like this it is possible to

control the motor as it is required.

Figure 3.01 synchronous motor’s current directions

23

in this solution a control system plays with the inverter’s angle for two

motors so as to accelerate the motor in back and at the same time

decelerate the motor in advanced. Like this it can make two motor nearer. It

is obvious that motors in this phase does not function with maximum

capacity, but it is temporary and just when they arrive to the same point,

inverter can apply the correct angle to utilize the maximum motor’s

capacity and torque. After all of previous ways which answered negative for

some technical or economic reasons, this way possesses many advantages

at least to satisfy the primary conditions.

It needs no mechanical object for adding to bogie’s space, so it occupy no

space and has no cost for materials. It is a purely electrical solution which

functions just by a control system. Now after finding the way that could be

the final solution, it needs to evaluate all the details to ensure well-

functioning.

24

CHAPTER 4

MODELING OF MACHINES

Motor’s equations

Firstly it needs to know if inverter knows one motor as reference and has

not any control on another motor, what does happen. How much current do

they consume? And how much torque will produce by any motor?

To do that, it is necessary to study the synchronous motor’s behavior. These

verifications are in maximum voltage state. By using these formulas, they

are calculated the first and second motors’ torques, currents and

efficiencies

Figure 4.01 synchronous motor’s voltage diagram

25

Torques’ Analysis

These diagrams are plotted respect to phase difference which is defined the

angular difference between two motors. It is noticeable to mention that

these angles are electrical angle and often they are not coincident with

mechanical angle. it depends just to number of pair-poles. Since the motors

here under study possess 6 pair-poles, the mechanical angles are 1/6 times

of electrical angle. Here it is shown the torques’ diagram.

Figure 4.02 torques’ difference diagram

26

In this figure the blue line is 1st motor’s torque which is completely constant

and the green curve is 2nd motor’s torque and finally the red diagram is the

sum of them. There are some points to pay attention. The green diagram

intersects zero line in two points which are indicated with red rings. So the

summation is equal to just first motor’s torque, like if second motor would

be turned off. However the below part of red rings which second motor’s

torque is negative; so in a train, it even neutralizes another motor’s force

until a value which makes total torque zero (indicated with a red ball).

However there is an interesting part to mention that is an interval. In this

interval that I call it the acceptable interval, torques have a similar values

and for temporary conditions like transitory part is acceptable. The

acceptable interval in torque diagram and in 155Hz frequency is [-38.5°, 0°]

Currents’ Analysis

The next diagram is current diagram that has a considerable importance,

because it shows the electric consumption and on the other hand it defines

the electric equipment’s limitations. As a definition for the acceptable

interval on electric current diagram, I assumed a criterion like this: second

motor’s current does not exceed more than 10% of first motor’s current.

Figure 4.03 currents’ difference diagram

27

Here again the first motor’s current is linear because the inverter knows

first motor as reference so in these evaluations first motor functions

perfectly right. But second motor has a sinusoidal behavior respect to phase

difference (green diagram). And again red diagram is summation of current

consumption which obviously should be sinusoidal like second motor’s

curve. As it was said the criterion defines a band which has a upper value as

1.1 times first motor’s current and a downer value as 0.9 times first motor’s

current. in the zero point that means there is no phase difference, two

currents are coincident and by varying phase difference, second motor’s

current increases till near 460A. This value is not acceptable because it

consumes current very higher than nominal current and it can be

hazardous for power generator system. Hence the acceptable interval in

155Hz with maximum voltage is [-16.5°, 16.5°]

Efficiencies’ Analysis

Another verification is on the motors’ efficiencies.

28

Figure 4.04 efficiencies’ difference diagram

The first motor’s efficiency is a constant number near 1 and the second

motor’s efficiency varies from 0 to 1. As it is figured the second motor’s

efficiency has two drops till zero, coincident with zero values of torque.

Fortunately there is a large acceptable interval around 0° . The interval is

quite [-75°, 50°]. After these three evaluations of acceptable interval, they

are found three different intervals. Thus the smallest interval does limit the

final interval which could be acceptable. Therefore final acceptable interval

is [-16.5°, 0°]. This interval satisfies all three variables.

Then it is needed to repeat these calculations for other frequencies (omega)

and currents as well.

However I neglect to bring all diagrams here. So in every frequency the

minimum acceptable interval is different.

29

The variable which is easy to change, in order to control the machine is the

current. There is another natural variable that is the motor's velocity

(Omega).

Acceptable interval

Here there are several situations by different current and omega to observe

and verify the results which are motor's currents, torques and efficiencies.

The most significant result within this verification would be current's

behavior. The interval of acceptable slave motor's current (that is minus-

plus 10% of master motor's current) by decreasing the master motor's

current, decreases.

But there is a considerable point. The curve's slope in all cases is the same

because the changing motor’s current depends only on phase's difference. It

30

means the master current does not affect defined interval and the interval

decrees just because 10% of master current has changed. therefor if it is

considered ampere change instead of percentage of master current, it is

seen that for example in -20° the slave current rises 40 ampere and it does

not depend on omega and master current .



31


Here we can see the diagram of the voltages, currents and torques respect

to the revolutions per minutes

32

Motor’s properties


33

Figure 4.09 voltages Vsf and Usf by varying motor’s frequency

34

Figure 4.10 motor’s currents Isd, Isq and Isf by varying motor’s frequency

35

Figure 4.11 motor’s torque by varying motor’s frequency

Then it is modeled the synchronous motor fed by an ideal inverter. For

doing this there were two ways which are:

- Through the same equations that were used for calculating currents and

torques

- exploit the elements of Simulink

I have chosen the second one because it's visual and more intuitive. By the

way it is a helpful comparison the results of equations and Simulink in the

same situation which should be exactly equal

36

Modeling on Simulink

Here are shown the Simulink's map and the plots of 3phase voltage and

Torque. The resistant's torque is applied after 1 second.

Figure 4.12 primary Simulink model of a synchronous motor

Figure 4.13 motor’s torque reaction

37

Inverter

After that, it is time to discuss about simulation of the inverter; but there

are two possibilities:

1) Using a real inverter wave

2) For having the more precise results on other parts; because a non-ideal

sinusoidal wave disturbs other calculations. So it is required an ideal

inverter.

Figure 4.14 real inverter element

38

Figure 4.15 the voltage waves of the real inverter

On the other hand since the equations of motor are based on ideal inverter,

we could have the same results on Simulink if we apply voltage through an

ideal inverter. Therefore the inverter on Simulink doesn't have benefit

having undesirable signal shape. in an ideal inverter waves are completely

sinusoidal

Figure 4.16 representation of the ideal inverter

39

Figure 4.17 the voltage waves of the ideal inverter

with this elements we could simulate an ideal inverter which there is not in

reality, but it is compatible with equation's results.

Mechanical inertia

The mechanical modeling is one of detailed parts of the project. Firstly it

would be done only for one motor and finally it will expand for two parallel

motors. one of these details is the resistance torque which applies to motor.

This resistance torque would be a constant value or respected to motor’s

angular inertia or both of them. In this verifications since the motor is

heavy, and the bearings’ friction respect to the produced force is negligible

for now, the resistant torque consists just angular inertia multiplied by

motor’s acceleration. Here is the first step of substitute a close-loop

mechanical input instead of open-loop one.

40

Figure 4.18 constant mechanical resistance

The motor which is used in this model doesn't consist a real mechanical

simulation; because the resistant torque that impose to motor is constant,

but in this case for a realistic modeling of mechanical part, the input should

be velocity which is obtained through an integrator after torque value of

motor.

41

Figure 4.19 variable mechanical resistance by inertia

In this model there is the angular velocity as motor’s input that is a

feedback from motor.

Here it is represented system's behavior against a command. Motor can

reach the steady state quickly through a minimum oscillation. The gray line

shows position and the yellow line plots the motor’s angular velocity.

Figure 4.20 motor’s position and speed with a constant resistance which is applied after

one second

42

Control strategy n.1

Now it is the time to put two motors and one inverter to try some strategies

to make it function well.

As the first tentative, I put two motors and the inverter that knows the

motor in back as reference. So when two motors are not at the same

position, inverter accelerates the motor in back and at the same time

decelerates the motor in advanced. So after some moments the motor in

back should arrive to another motor and then they should have the same

angle. hence they should work right. I tried this strategy and here there are

the results.

Figure 4.21 representation of first synchronous motor of two motors

Figure 4.22 representation of second synchronous motor of two motors

Second synchronous motor

First synchronous motor

43

Figure 4.23 representation of the inverter which makes run the motor in back

Till here one inverter can make function two motors but there are still some

problems which are about mechanical linkage. it means in these motors

rotates like there was not another motor. so i try to find the mechanical

relationship between two shafts ; here there is the scheme of Simulink of

two independent motors. with this control system the inverter knows as

reference the motor which keeps back. however the results are not

satisfying.

In diagram is shown the position and velocity of one motor

Inverter

44

Figure 4.24 motor’s position and speed when inverter makes run the motor in back

The motors’ behaviors were quite equal and unfortunately when the motor

in back will arrive to the motor in advanced, it continues to go more and

now the other motor is in back. So inverter accelerates the motor in back

more than the other one. This story slowly slowly makes the system

instable. It is clear that system's readiness is too much and its reaction is

too quick.

Control strategy n.2

Then I repeat the calculation with another strategy; Using the media angle

of motors’ angular positions instead of the position of the motor in back.

Like this I reduce the readiness of the system so as to avoid instability and

diverging motors’ velocities.

45

Figure 4.25 representation of both motors and inverter which makes run motors by

media angle

Here, I try another time to synchronize the motors by applying the simple

average angle as inverter reference. If the system does not diverge and it

becomes stable, it is the acceptable way.

Figure 4.26 the strategy of inverter’s function

46

Figure 4.27 motors’ positions and speeds when the inverter makes run by media angle

As it is shown in the diagram, the motors function much better than before,

Because the velocities do not diverge. But there is still oscillation even if

does not diverge and does not make the system instable. So if the motors

were separately like two fan on the air, with this strategy it is not possible

to make them function like when there are two inverters; however this

oscillation on the train makes a huge disturb and vibration in the wagons

and it is absolutely unacceptable. Since my case is the train, there is another

last chance; another solution to compensate the oscillation. This solution is

mechanical stabilizer bogie system.

Dynamics of the bogie

To know the help that bogie system can offer, it is needed to study

dynamics of the bogie more deeply. One bogie is composed by two shafts

and the suspension system and every shaft has two wheels. Since the

wheels are conical, they do not have constant radii and by moving the shaft,

Time [s]

F θ1 θ2

. .

47

the radius will be changed. As it is indicated in the figure below, a shaft can

have three movements which two of them are dependent. Therefore every

single shaft possesses 2 degrees of freedom.

ΔΧ is the axial movement of the shaft to left and right. By this movement

radius of a wheel is increases and the opposite wheel’s radius is decreases

surely. This relation would be linear in a limited range. In fact the wheel’s

profile has two linear zones; but since one zone has a greater range, in these

calculations it is considered that the only zone is that one.

The next movement is Θ that is the rotation around the axis which in

direction of the train. While this movement seems completely different from

ΔΧ, but they are dependent and they have the same effect. By moving shaft

in this degree of freedom (ΔΧ or Θ) the involved perimeter is changed from

a circle to a bigger circle or smaller one. Hence this degree of freedom does

not reform the involved perimeter. There is a noticeable point to mention

that this degree of freedom does not change the shaft’s speed. By moving in

this degree of freedom the summation of two wheels’ perimeters is

constant. This degree of freedom is specially for the wagon’s compatibility

in a curvy path. Therefore this degree of freedom does not help the system

to synchronize two motors with a little velocity’s difference.

Figure 4.28 illustrations of two degrees of freedoms of a shaft

Θ and ΔΧ are dependent

48

The other degree of freedom is α, which is the rotation movement around

the axis perpendicular to the ground (Z axis). This degree of freedom makes

shaft to take an angle respect to the train’s motion. The main effect of this

movement is changing the involved perimeter in other way. This rotation

actually reshapes the involved perimeter from a circle to an ellipse. Thus

when shaft rotates in this degree of freedom, both of wheels of the shaft is

running a longer perimeter per cycle. In other words when two shafts

should traverse the same distance and one of them tends to rotate faster,

this ability let it to get an α angle and rotate faster while the path which

they both run is the same.

Figure 4.29 illustrations of the effect of alpha on involved perimeter

Involved perimeter

Here there are the plots which show the effect of any degree of freedom on

the involved perimeter. As it is expected the effect of ΔΧ or Θ on the

perimeter is linear and the effect of α on perimeter is non-linear and there

is a parabolic relation between them.

49



50

Different involved perimeters between 2 shafts theoretically can amortize

the shafts’ inertia to arrive to stable velocity. in order to do that it exploits

the effect of friction between wheels and railway. also for making

synchronous two shaft at the beginning of motion, since one motor is

accelerated towards ahead unlikely another motor which works in opposite

direction, they rotate through slippage and will find the same angular

position. this result is impossible if the motors were not on a railway.

51

CONCLUSIONS

The purpose of this Thesis is to make run two synchronous machines

through a single inverter. It could be done through some different

ways and therefore different qualities. Since the case of study for this

thesis, is about train’s motors, it should be found a solution

appropriated on special conditions. Reaching to the target of thesis

depend to the conditions of motors. In other words if the motors

were not on a railway, the solution would be different. This solution

considers two motors on a railway so as to have possibility to rotate

with different involved perimeter and also to have the slippage.

These two elements play key roles to synchronize two wheels.

Otherwise the inverter with the evaluated strategies could not

synchronize motors and stabilize them. If the motors were like two

fans on the air, they do not have action and reaction between them.

So in this case the only controller would be the inverter. But in train

case, there is opportunity to exploit mechanical contact to loose

inertia in order to reach the same velocity. The next step for this

study would be a more complex method to control a pair of motors

only and only through programing the inverter. That method should

work without the condition of mechanical contact.

52

REFERENCES

[1] Method Controlling Four Sets of Permanent Magnet Synchronous Motor

by One Inverter on a Railway Vehicl Hangzhou - China. 2014.

[2] A New Approach to Predictive Torque Control with Dual Parallel PMSM System

Ngoc Linh NGUYEN, Maurice FADEL, Ana LLOR - Université de Toulouse

[3] Direct Torque Control – A Solution for Mono Inverter-Dual Parallel PMSM System

Ngoc Linh NGUYEN, Maurice FADEL, Ana LLOR - 2013 21st Mediterranean

Conference on Control & Automation

[4] Predictive Torque Control – A Solution for Mono Inverter-Dual Parallel PMSM

System . Ngoc Linh NGUYEN, Maurice FADEL, Ana LLOR - Université de

Toulouse

[5] Synchronous Machines - U.A.Bakshi, M.V.Bakshi

Technical Publications, Jan 1, 2009

[6] D.c. Machines and Synchronous Machines - U.A.Bakshi, M.V.Bakshi

Technical Publications, Jan 1, 2009

[7] Railway Track Engineering - J. S. Mundrey

Tata McGraw-Hill Education, 2010

politecnico di milano · figure 1.01 representation of a pair of asynchronous motor fed by single...

Documents