LOAD SHARING SCHEMES IN MULTIPLE INDUCTION MOTOR DRIVE

APPLICATIONS USING VOLTS-PER-HERTZ CONTROL

by

Jaishankar Iyer

B.E., The University of Mumbai, India, 2006

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF

THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF APPLIED SCIENCES

in

THE FACULTY OF GRADUATE STUDIES

(Electrical and Computer Engineering)

THE UNIVERSITY OF BRITISH COLUMBIA

(Vancouver)

December 2011

© Jaishankar Iyer, 2011

ii

Abstract

Multi induction-motor (IM) drives are commonly used to share a mechanical load in a wide

range of industrial applications. In many existing auxiliary applications, the traditional low-

cost Volts-per-Hertz (V/F) drives are typically used in speed control mode to simultaneously

operate several IMs.

In multi-machine load-sharing applications, it is preferred to have number of identical IMs to

share the load equally. Under ideal conditions, the identical IMs would operate with equal

loading. However, in practice deviations of the load sharing among the IMs is possible due

to many factors including variations in internal or external parameters and operating

conditions of each individual IM. Such deviations may result in disproportionate sharing of

the mechanical load and even overloading one or several machines while some machines

may be under-loaded. The basic low-cost variable frequency drives (VFDs) with traditional

open-loop V/F control scheme fail to share the load under such conditions.

In this Thesis, two new methods are proposed to address the load sharing problems under an

internal disturbances (such as rotor resistance variations) and external disturbances (such as

wheel slippage due to snow/water/oil etc.). The new methods are shown to be effective in

sharing the load under disturbances. Moreover, the proposed methodologies may be readily

extended to an arbitrary number of motors driving a common mechanical load, and are easy

to implement with traditional/existing low-cost VFDs, which may be advantageous for many

existing or legacy applications.

iii

Preface

A version of Chapter 3 has been published in the following manuscript: Jaishankar Iyer,

Kamran Tabarraee, Sina Chiniforoosh, and Juri Jatskevich, “An improved V/F control

scheme for symmetric load sharing of multi-machine induction motor drives,” In proc.

24th

IEEE Canadian Conference on Electrical and Computer Engineering, Niagara Falls,

Ontario, Canada, 2011. I identified the problem, developed the Matlab/Simulink® models,

and wrote most of the manuscript, while the conducted research was supervised by Dr. Juri

Jatskevich. The manuscript was revised, iterated and discussed among all co-authors, my

fellow colleagues Kamran Tabarraee and Sina Chiniforoosh, and my supervisor Dr. Juri

Jatskevich.

A version of Chapter 4 has been published in the following manuscript: Jaishankar Iyer,

Mehrdad Chapariha, Kamran Tabarraee, Milad Gougani, and Juri Jatskevich, “Load Sharing

in V/F Speed Controlled Multi-motor Drives,” In proc. 7th

IEEE Vehicle Power and

Propulsion Conference, Chicago, IL, USA, 2011. I identified the problem, developed the

Matlab/Simulink® models, devised the solution and wrote most of the manuscript, while the

conducted research was supervised by Dr. Juri Jatskevich. The manuscript was revised,

iterated and discussed among all co-authors, my fellow colleagues Mehrdad Chapariha,

Kamran Tabarraee and Milad Gougani, and my supervisor Dr. Juri Jatskevich.

1

Table of Contents

Abstract .................................................................................................................................... ii

Preface ..................................................................................................................................... iii

Table of Contents .................................................................................................................... 1

List of Tables ........................................................................................................................... 4

List of Figures .......................................................................................................................... 6

Acknowledgements ............................................................................................................... 10

Dedication .............................................................................................................................. 11

1 Introduction ................................................................................................................. 12

1.1 Motor Load Applications in Industry ................................................................. 12

1.2 Variable Frequency Drives in Industrial Applications ....................................... 13

1.3 Multi-Motor Load Sharing .................................................................................. 16

1.4 Thesis Composition ............................................................................................ 19

2 Modeling of Induction Machines and Variable Frequency Drives ............................. 20

2.1 Modeling ............................................................................................................. 20

2.2 Induction Machine Modeling .............................................................................. 20

2.3 Variable Frequency Drive Modeling .................................................................. 24

3 Load Sharing under Rotor Resistance Variation ........................................................ 26

3.1 Introduction ......................................................................................................... 26

3.2 Induction Machine Steady State Torque ............................................................. 26

3.3 Rotor Resistance Variation and Load Sharing Disparity .................................... 31

3.4 Load Sharing Using Speed Reference Compensation Method Based on Rotor

Resistance ....................................................................................................................... 35

2

3.5 Load Sharing Using Speed Reference Compensation Method Based on Current

Feedback ......................................................................................................................... 40

3.6 Experimental Verification of the Proposed Load Sharing Scheme .................... 43

3.6.1 Physical test bench set-up ............................................................................... 43

3.6.2 Experimental procedure of load sharing and results from VFD interface ...... 48

3.6.3 Steady state measurements and calculations................................................... 52

3.6.4 Verification of model using simulation of the physical set-up ....................... 55

4 Load Sharing under Wheel Slippage in Vehicular Application .................................. 62

4.1 Motivation ........................................................................................................... 62

4.2 Concept of Torque Transfer and Wheel Slippage ............................................... 63

4.3 Adhesion, Tractive Force, and Vehicular Motion .............................................. 64

4.4 Induction Motor Load in a Gantry Crane Application........................................ 70

4.5 System Model and Performance under Wheel Slippage..................................... 73

4.5.1 System performance without load sharing ...................................................... 77

4.6 Proposed Methodology for Improved Load Sharing under Wheel Slippage ...... 80

4.6.1 Computer studies demonstrating the proposed methodology ......................... 83

5 Conclusion .................................................................................................................. 86

5.1 Summary ............................................................................................................. 86

5.2 Future Research .................................................................................................. 87

References .............................................................................................................................. 88

Appendices ............................................................................................................................. 94

Appendix A ..................................................................................................................... 94

Appendix B ..................................................................................................................... 96

3

Appendix C ..................................................................................................................... 97

Appendix D ..................................................................................................................... 98

4

List of Tables

Table 3-1 Electromagnetic torque developed by IM1 and IM2 under rotor

resistance variation using the conventional V/F scheme without

compensation. ................................................................................................. 34

Table 3-2 Electromagnetic torque developed by IM1 and IM2 under rotor

resistance variation using the proposed load sharing compensation

scheme............................................................................................................. 38

Table 3-3 Individual motor torques under different loading conditions for

conventional scheme without load sharing compensation scheme. ................ 40

Table 3-4 Individual motor torques under different loading conditions for

proposed load sharing compensation scheme. ................................................ 40

Table 3-5 Torque current read from the DriveExplorer® software interface: (a)

without compensation; and (b) with proposed compensation for load

sharing. ............................................................................................................ 49

Table 3-6 Torque current calculated from the measured data: (a) without

compensation; and (b) with proposed compensation. ..................................... 53

Table 3-7 Torque current calculated from the simulated results with and without

proposed load sharing compensation. ............................................................. 60

Table 4-1 Sample parameters of the gantry crane used in the simulation. ...................... 73

Table 4-2 Surface adhesion factor parameters for steel wheel on steel rail in dry

and slippery conditions. .................................................................................. 74

Table 4-3 Load on Wheel 1-IM1 and Wheel 2-IM2 under wheel slippage without

using the proposed load sharing compensation scheme. ................................ 79

5

Table 4-4 Load on Wheel 1-IM1 and Wheel 2-IM2 under wheel slippage using the

proposed load sharing compensation scheme. ................................................ 85

6

List of Figures

Figure 2.1 Role of machines in different types of industrial loads (a) roller table

(©Danieli Centro Combustion) [1]; (b) mill motors (©Eastport trading

co. Inc) [2]; (c) processing lines (©Danieli Wean United) [3], (d) crane

application (©Thyssenkrup Steel) [4]. ............................................................ 13

Figure 2.2 Torque-speed characteristics for a commanded speed of 188sec

rad for

an IM at different loading conditions.............................................................. 16

Figure 2.3 Different load sharing configurations: (a) multiple motors driven by

individual drives; and (b) multiple motors driven by a single drive unit........ 17

Figure 2.1 Control schematics for an induction model based on qd reference

frame. .............................................................................................................. 23

Figure 2.2 Control schematics for V/F controller. ........................................................... 25

Figure 3.1 Steady state equivalent circuit of an induction machine. ................................ 27

Figure 3.2 Torque-speed characteristics for parameter variation in a 3HP IM: (a)

rotor resistance; (b) stator resistance; (c) stator leakage inductance; and

(d) magnetizing inductance. ............................................................................ 29

Figure 3.3 Torque-speed characteristics for parameter variation in a 50HP IM: (a)

rotor resistance; (b) stator resistance; (c) stator leakage inductance; and

(d) magnetizing inductance. ............................................................................ 30

Figure 3.4 Block diagram of Volt / Hertz control scheme. .............................................. 32

Figure 3.5 Block diagram for load sharing between two V/F controlled induction

motors under conventional speed referencing. ............................................... 33

Figure 3.6 Torque-speed characteristics of two coupled induction motors, with

7

rotor resistance variation, sharing a common load without

compensation. ................................................................................................. 34

Figure 3.7 Block diagram of the proposed scheme for load sharing between two

V/F controlled induction motors. .................................................................... 37

Figure 3.8 Torque-speed characteristics of two coupled induction motors, with

rotor resistance variation, sharing a common load with compensation. ......... 37

Figure 3.9 Load sharing of two coupled IM’s with rotor resistance variation under

different loading conditions. ........................................................................... 39

Figure 3.10 Proposed load sharing compensation scheme under rotor resistance

variation. ......................................................................................................... 41

Figure 3.11 Mechanical load of 8.1 mN. shared between the coupled IM’s: (a)

without compensation; and using proposed speed compensation based

on (b) rotor resistances; and (c) current feedback ........................................... 42

Figure 3.12 Physical set-up for verification of the proposed scheme. ............................... 44

Figure 3.13 Load sharing motor test bench used for the practical observations. ............... 45

Figure 3.14 VFD’s used for powering the load sharing motors. ........................................ 46

Figure 3.15 PLC used to control the drives running the load sharing motors. ................... 47

Figure 3.16 Torque and flux component of the motor current. .......................................... 48

Figure 3.17 Screenshots of the DriveExplorer® software interface for the VFD 1

and VFD 2 without load sharing compensation. ............................................. 50

Figure 3.18 Screenshots of the DriveExplorer® software interface for the VFD 1

and VFD 2 with load sharing compensation. .................................................. 51

Figure 3.19 Measured line currents for Motor 1 (1HP) and Motor 2 (5HP): (a)

8

without compensation; and (b) with proposed load sharing

compensation. ................................................................................................. 52

Figure 3.20 Phasor diagram of voltage and current for Motor 1 (1HP) with and

without the proposed load sharing compensation. .......................................... 54

Figure 3.21 Phasor diagram of voltage and current for Motor 2 (5HP) with and

without the proposed load sharing compensation. .......................................... 54

Figure 3.22 Measured and simulated line voltages and currents for Motor 1 (1HP)

without load sharing compensation. ............................................................... 55

Figure 3.23 Measured and simulated line voltages and currents for Motor 2 (5HP)

without load sharing compensation. ............................................................... 56

Figure 3.24 Measured and simulated line voltages and currents for Motor 1 (5HP)

with load sharing compensation...................................................................... 57

Figure 3.25 Measured and simulated line voltages and currents for Motor 2 (5HP)

with load sharing compensation...................................................................... 58

Figure 3.26 Simulation results for the load sharing without compensation and with

the proposed compensation. ............................................................................ 60

Figure 4.1 Gantry crane running on a set of rails with IM driven wheels. ....................... 64

Figure 4.2 Graph depicting general relationship between surface adhesion factor

a and slip-speed for different road conditions. ............................................ 66

Figure 4.3 Graph depicting general relationship between speed correction factor

c and vehicle speed. ...................................................................................... 67

Figure 4.4 Diagram showing different speeds and forces acting on the wheel. ............... 68

Figure 4.5 Slip-stick phenomenon at the contact surface of wheel and rail. .................... 69

9

Figure 4.6 Top view of the gantry crane showing the different speeds and tractive

forces. .............................................................................................................. 71

Figure 4.7 Block diagram for conventional load sharing between two V/F

controlled induction motors under resilient or stochastic coupling. ............... 72

Figure 4.8 Surface adhesion factor vs. slip speed for parameters listed in Table 4-2. ..... 75

Figure 4.9 Block diagram of the simulation model for the wheel and vehicle

dynamics of the gantry crane. ......................................................................... 76

Figure 4.10 Results of wheel slip under conventional V/F control without the

proposed load sharing scheme: (a) wheel and vehicle speed; (b) total

tractive effort; (c) surface adhesion factor of Wheel 1 and Wheel 2; and

(d) load torque on Wheel 1-IM1 and Wheel 2-IM2. ....................................... 78

Figure 4.11 Moment of force vector on the axle under wheel slip with conventional

V/F control without the proposed load sharing scheme. ................................ 79

Figure 4.12 Trace of adhesion at different rail conditions vs. slip speed. .......................... 81

Figure 4.13 Proposed change in the speed referencing of the drive powering the

wheels of a gantry crane under wheel slippage. ............................................. 82

Figure 4.14 Block diagram of the proposed scheme for improved load sharing

between two V/F controlled induction motors under wheel slippage............. 82

Figure 4.15 Results of wheel slip under the proposed load sharing scheme: (a) wheel

and vehicle speed; (b) total tractive effort; (c) surface adhesion factor of

Wheel 1 and Wheel 2; and (d) load torque on Wheel 1-IM1 and Wheel

2-IM2. ............................................................................................................. 84

10

Acknowledgements

I would like to express my deepest appreciation and gratitude to my research supervisor, Dr.

Juri Jatskevich, for allowing me to conduct research under him and whose strong academic

support and dedication to his students have been the most precious assets. I am also very

thankful for the financial support of my thesis project through Dr. Juri Jatskevich’s research

grants, which made it both possible and relevant to many practical and industrial

applications.

I also would like to thank Dr. Dommel and Dr. Dunford, who have accepted to be on the

examining committee and dedicated their time and effort for evaluating my thesis. I owe a

huge debt to my mom and dad who have supported and guided me throughout my life. My

special thanks also go to my friends and colleagues at the UBC’s Electrical Energy and

Power Systems Group who have always supported me and gave their valuable comments and

feedback for my research. My previous three-year experience at Siemens Ltd., also helped

me to look at the problems from the system level while keeping in mind that a practical

solution should be simple and cost effective to find its way into implementation.

Last and but not the least, thanks to all my friends and everyone who intentionally or

unintentionally played a part in my life and helped me mold myself into the person I am

today.

11

Dedication

Mom and Dad,

I Love you, this one is for you.

12

1 Introduction

1.1 Motor Load Applications in Industry

Industrial loads vary in sizes, type of functionality, range of operation, nature of

surroundings, etc. The type of motors used varies as per the application. Main-Mill motors,

auxiliary motors, pump motors, roller table or conveyor motors, crane motors, high precision

/ position controlled motors, etc., may be realized using synchronous motors, induction

motors, conventional brushed DC motors and permanent magnet brushless DC motors.

Figure 1.1 shows different types of industrial applications, wherein multiple motors are used.

Of all the types of motors used in industrial applications, the induction machines (IM) are the

most widely used because of their simple but yet rugged construction and low cost. The

squirrel cage design is the commonly used type of IMs because of the simple construction of

the rotor winding, which makes them robust and requires low maintenance. The squirrel cage

induction machines are easy to manufacture as compared to the wound-rotor type. For these

reasons, the conventional squirrel cage IMs are generally preferred by the manufacturers and

the end-users for many applications.

13

Figure 1.1 Role of machines in different types of industrial loads (a) roller table (©Danieli Centro

Combustion) [1]; (b) mill motors (©Eastport trading co. Inc) [2]; (c) processing lines

(©Danieli Wean United) [3], (d) crane application (©Thyssenkrup Steel) [4].

1.2 Variable Frequency Drives in Industrial Applications

The IM on its own is difficult to control under the fixed frequency source. The steady state

torque-speed characteristic is very nonlinear over the entire speed region and is typically

usable only in the region close to the synchronous speed. Hence, an IM cannot be used alone

(a) (b)

(c) (d)

14

in many industrial applications which require wide range of controlled motion. Several

simple power-electronic-based control systems are employed in industry to control the

operation of induction machines. The variable frequency drives (VFDs) provide the most

efficient and effective way of motor control. The aim of control is usually mechanical speed

or output torque of the machine. The VFDs can range from advanced vector-controlled

schemes wherein the torque control may be achieved almost instantaneously, to the

conventional Volts-per-Hertz (V/F) scalar control which relies on steady-state torque-speed

relationship of the machine to deliver the required speed or torque, which may also be used

either in open-loop or in a closed-loop with speed regulator.

Vector controlled VFDs are advantageous because of their capability of delivering both

speed and torque control with remarkable accuracy which can be used to implement

advanced load sharing schemes such as torque-follower or trim control [5]. For example, the

Allen Bradley PowerFlex 700 series vector controlled drives from M/s Rockwell Automation

have speed regulation of around 0.1% to 0.001% in speed control mode and a torque

regulation of ±5% without feedback to ±2% with feedback in torque mode [6]. Hoever, such

advanced VFDs are typically very expensive and may not be financially justified for many

applications. The choice of the drive is dependent on the type of application. Main mill

motors, tension controller, etc., may require high precision torque control and hence would

typically need the vector-controlled VFDs.

The advanced control strategies make the vector drive an expensive choice [7] and hence

these drives are not popular for normal applications which form a large percentage of

15

industrial processes. It is not financially viable to use vector-controlled VFDs for these

applications because it will involve a huge capital investment. The applications such as roller

tables, conveyor belts, cooling fans, crane wheel motors, and etc. still make use of traditional

volts/hertz control because of its low cost. The basic V/F VFD controllers however only

work in speed control mode where the output speed is regulated through a speed feedback,

but such VFDs are generally low-cost. The V/F VFD is a speed controller which takes

advantage of induction machines torque-speed characteristic in its stable region. In this

region, the machine mechanical speed is close to the electrical speed of the voltage which the

machine is fed with. The drive control sets the frequency, and then based on that frequency

adjust the voltage to prevent the saturation while maintaining flux. The drive varies the

voltage and frequency input to alter the torque-speed characteristics such that the torque-

speed characteristic intersects the load curve at the commanded speed. Figure 1.2 shows how

the torque-speed curve of a 5HP IM (Hyundai® Inverter Shield ™ Premium Efficiency.

Specifications are given in Appendix A) is changed to meet the various load requirements at

a particular rotor speed of 188 sec

rad . We can see that the base frequency changes along

with the loading of the IMs. This can be seen by looking at the machine speed at zero torque,

i.e. the synchronous speed. As the loading is increased the frequency is increased, however

the V/F ratio is maintained.

16

Figure 1.2 Torque-speed characteristics for a commanded speed of 188sec

rad for an IM at

different loading conditions.

1.3 Multi-Motor Load Sharing

Some applications need multiple motors to work in tandem or in parallel. The reasons for

using multiple motors may vary from lack of space for big motors resulting in the use of

several coupled motors of smaller ratings in tandem, to process requirement of parallel

motors. Process such as Mills, conveyor belts, roller tables, cranes, etc., cannot work with

just one motor. They need more than one motor working in parallel to drive the common

mechanical load. In such applications, load sharing is naturally required, and it is important

to maintain the speed and the torque of the participating motors the same or in some

proportion as required by the process.

17

Load sharing is essentially an arrangement where a common load is shared by multiple

motor-drive sets [5], [8]. There are different possible configurations available for powering

the load sharing motors. Figure 1.3 shows two such different schemes in multi-motor

applications. In Figure 1.3(a), a multiple motor-drive set (motors driven by individual

dedicated drive) is used to share the load. In Figure 1.3(b), multiple motors driven by single

VFD are used; hence individual control of the motors is not possible and the load sharing

occurs naturally and uncontrollable. However, in Figure 1.3(a), it is seen that the motors can

be individually controlled by the corresponding VFDs. Hence, only the configuration of

Figure 1.3 (a) can be used for effective re-distribution of the load among the motors and

achieving effective load sharing under various disturbances. Therefore, this configuration is

considered in this thesis.

IMn

LOAD

VFD1

VFD2

VFDn

(a)

IM2

IM1

Speed feedback

IMn

IM1

IM2

VFD

(b)

LOAD

Speed feedback

Figure 1.3 Different load sharing configurations: (a) multiple motors driven by individual drives;

and (b) multiple motors driven by a single drive unit.

In multi-motor applications, even if the overall control scheme aims to maintain and control

the speed, the internal torque control might be required to share the torque between several

18

motors in order to prevent overloading, over-heating and malfunction of a single motor or the

whole system. While the greater part of the drives used in industry are using standard V/F

control scheme, it will be required to study the methods to share the torque among such

drives in different situation including variations of machine parameters, different motors, or

different loading conditions, etc. Thus, this thesis considers the most common type V/F

VFDs, unless otherwise explicitly mentioned.

Under load sharing using V/F controller, the torque delivered by the individual participating

motor depends on the motor parameters, the command speed and the load on that motor, etc.

Without loss of generality, this thesis considers a system with two IMs sharing a common

mechanical load. Under ideal conditions, the motor parameters are identical, the commanded

speeds are the same, and the loading on each motor would be equal. If the IMs are not

identical but are of different rating, then their load may need to be split proportionally to their

power rating, which would be a more general scenario. But when the conditions deviate from

ideal, e.g. changing rotor resistance or a change in the individual loading, etc., then the

torque delivered by the IM will also differ. The machines would become unequally loaded

with one motor getting overloaded. The research in my thesis is mainly focused on two such

instances where the load sharing is changed due to the following:

1. Variations in the parameters of one of the motors (e.g. rotor resistance) due to

temperature variations, use of a replacement motor with different rotor parameters,

defective rotor, etc. These variations constitute internal disturbance.

2. The load distribution among the motors may be affected due to changes in external

conditions (e.g. wheel slippage). These variations constitute external disturbance.

19

1.4 Thesis Composition

The thesis is comprised of the following Chapters:

Chapter 2 presents the concept of various motor drives and presents the basic model that

is used for the studies in this thesis.

Chapter 3 discusses the problem of load sharing between induction motors with different

rotor resistances which may be caused by parameter deviations. It provides a solution to

improve the load sharing under such variation. The Chapter also shows results from an

experimental set-up used to verify the proposed scheme.

Chapter 4 discusses the problem of load sharing among induction motors in vehicular or

crane applications, where the wheel slippage may occur. A new methodology is presented

to improve the load sharing under the considered disturbances.

Chapter 5 concludes the thesis by summarizing the contributions of conducted research

and briefly mentions the future research directions that may be taken beyond my thesis.

The parameters of all induction motors, VFD specifications, software specification and

digital power meter specification are all summarized in Appendices in appropriate Sections.

20

2 Modeling of Induction Machines and Variable Frequency Drives

2.1 Modeling

There are various simulation packages available today that can be used very effectively to

model the electrical components and networks [9], [10], [11], [12], [13], [14], and many of

which can be used for modeling the induction motor drives. The computer simulations, if the

models and parameters are correct, should produce results very similar to actual system but at

the same time should be fast and simple to execute [15], [16]. The simulation can then be

used as a very effective tool for designing and improving the actual physical motor drive

systems and their applications. The models developed in this Chapter will be used to analyze

the load sharing phenomenon and verify the proposed methodologies presented in the

subsequent Chapters.

2.2 Induction Machine Modeling

The classical model for induction machines is the qd model [17], which has been well-

known and used for many years, and is considered sufficient in terms of its assumptions and

accuracy for the purpose of this thesis. The model is based on the reference frame theory

[18], [19], [20], [21], [22]. In this thesis, a symmetrical squirrel cage induction motor is

considered, wherein the zero sequence is neglected due to the assumed Y-connection of the

stator winding with floating neutral point. The corresponding voltage equations in qd

reference frame can be expressed as

qdsdqsqdssqds pλλirv ,

(2.1)

21

0qdrdqrrqdrrqdr pλλirv ,

(2.2)

where the voltage, current and flux linkages are represented in vectors such that

Tdqqd fff , where f can be voltage, current or flux linkages. The stator and rotor

resistance matrix are represented by ssss rrrdiagr , and rrrr rrrdiag r . In (2.1)

and (2.2), Tqddq λ and p denotes operator dt

d. The remaining variables are

defined as follows:

qsv , and dsv are the voltages at q axis, and d axis of the stator,

qrv , and drv are the voltages at q axis, and d axis of the rotor,

sr , and rr are the stator and rotor resistances,

qsi , and dsi are the currents at the q axis, d axis of the stator,

qri , and dri are the currents at the q axis, d axis of the rotor,

qs , and ds are the flux linkages at the q axis, d axis of the stator,

qr , and dr are the flux linkages at q axis, d axis of the stator,

, and r are the electrical speeds of the reference frame and rotor speed.

The flux linkages used in the above equations can be expressed as :

qdrqdsMqdslsqds LL iiiλ ,

(2.3)

qdrqdsMrqdlrqd LL

riiiλ

00 ,

(2.4)

where lsL , lrL , and ML are the stator and rotor leakage inductances and the magnetizing

inductance. The leakage inductance and magnetizing inductance are combined to

22

give Mls LLL . The inductances are converted into the corresponding reactances by

LX b . The flux linkages in the equations (2.1) to (2.4) can be rewritten in flux linkages

per second using variable and base frequency, fb 2 , as

bqdqd λψ .

(2.5)

where the flux linkages per second are represented in vectors such that Tdsqsqds ψ .

The developed electromagnetic torque is calculated as

dsqsqsds

b

e iiP

T

1

2

3

2. (2.6)

The real power at the machine terminals is calculated as

dsdsqsqse ivivP

2

3. (2.7)

The above equations are realized in the qd model of the induction machine as shown in

Figure 2.1

23

Figure 2.1 Control schematics for an induction model based on qd reference frame.

24

2.3 Variable Frequency Drive Modeling

To study the operation of multi-motor systems with VFDs, modeling is indispensable [17].

The basic VFD with V/F control is used in the industry in most of the cases because to its

low cost, and this drive is assumed in this thesis. The control operates under two principles:

1. The rotor speed in the motoring region of an IM is proportional to the input electrical

frequency

2. To avoid machine saturation, the voltage-per-frequency ratio input to the motor

should be constant (uncompensated approach).

These principles result in the following relationships for the voltage and frequency:

*

e

b

b

s

VV

, (2.8)

here **

2rme

P ,

(2.9)

where bV and b are the rated base voltage and base electrical frequency of the IM; *

e and

*

rm are the commanded electrical frequency and approximate mechanical speed. The model

considered in this thesis is implemented according to the methodology defined in [[17],

Chap. 14] and the diagram shown in Figure 2.2.

25

Figure 2.2 Control schematics for V/F controller.

26

3 Load Sharing under Rotor Resistance Variation

3.1 Introduction

The traditional/basic V/F IM drives operate only using speed command signals, and the

developed torque is consequently determined according to the torque-speed characteristics of

the machine. As the developed torque is a function of rotor resistance, in load-sharing

applications, particularly, deviations among the rotor resistance values is probable and will

result in disproportionate sharing of the mechanical load and hence overloading of one or

several machines. In this thesis, a solution for the above issue is presented in the form of an

improved V/F scheme, which compensates for the parameter change by adjusting the

command speed reference signals accordingly. The proposed method is shown to be effective

and easy to implement, and may be readily extended to an arbitrary number of motors or to

the case where dissimilar motors are coupled and the mechanical torque is intentionally

distributed unevenly among the machines according to their ratings.

3.2 Induction Machine Steady State Torque

The steady state electromagnetic torque developed by an IM is given by [23]

22

2

23

lrthrth

r

e

the

XXsrR

srVPT

, (3.1)

where thV , thR , and thX are the Thevenin equivalent circuit parameters obtained from the

steady state equivalent circuit of Figure 3.1 and s is the rotor slip.

27

rs Lls

VsThevenin

Equivalent

Llr

Lm

'rr

s

Is I'r

Im

Figure 3.1 Steady state equivalent circuit of an induction machine.

The stator side of the induction machine can be combined with the magnetizing inductance

using Thevenin equivalence. The resulting voltage, resistance and reactance can be

calculated as follows:

Mlss

Msth

XXjr

XjVV

, (3.2)

Mls

Ms

thXX

XrR

, (3.3)

Mls

Mls

thXX

XXX

, (3.4)

where sV is the voltage input (per phase) to the IM stator; and e is the stator electrical

frequency.

In the motoring region, where the slip is typically low, (3.1) may be approximated as

re

th

r

r

e

the

r

sVP

sr

srVPT

2

2

2

23

23 . (3.5)

Equation (3.5) shows that the torque has strong dependence on the rotor resistance and slip

and the Thevenin voltage. Changes in these variables will affect the developed torque. Slip is

28

mechanical load dependent. The next step would be to find the sensitivity of the torque

toward a change in the remaining electrical parameters thV and rr , the two variables in (3.5).

The Thevenin voltage thV depends on the motor parameters sr , lsX , MX and the source

voltage sV as seen in (3.2). The source voltage sV is normally regulated by the drive and

hence can be considered as constant. Thus to measure the sensitivity dependence of eT on

thV and rr , the effects of variation of the motor parameters sr , rr , lsX , and MX on eT have

to be studied. The parameters of 3HP and 500HP IM’s (given in the Appendix A) from [17]

and [24] were considered here, and the steady-state torque speed curves were plotted for

parameter variations of 130% to 70%. The parameters were changed sequentially and the

results are plotted in Figure 3.2 and Figure 3.3.

29

Figure 3.2 Torque-speed characteristics for parameter variation in a 3HP IM: (a) rotor resistance;

(b) stator resistance; (c) stator leakage inductance; and (d) magnetizing inductance.

30

Figure 3.3 Torque-speed characteristics for parameter variation in a 50HP IM: (a) rotor

resistance; (b) stator resistance; (c) stator leakage inductance; and (d) magnetizing

inductance.

31

In Figure 3.2 and Figure 3.3, it is seen that in the motoring region, rotor resistance variation

had the most noticeable effect with the operating torque increasing with the decrease in the

rotor resistance. This is seen in Figure 3.2 (a) and Figure 3.3 (a). Similar studies were also

done on 50HP and 2250HP IMs, which also showed comparable results. Thus, it can be

deduced that rotor resistance variation has the most observable impact on the motoring

torque and hence this variation was considered for the thesis. The variations in the rotor

resistance may naturally occur due to temperature variations, replacement of motors with

previously repaired motors, use of non-identical motors, etc.

The sensitivity of the torque also depends on the slope of the torque-speed curve in the

motoring region. The IMs with smaller rotor resistance and steeper slopes have higher

sensitivity and hence are more vulnerable to large torque fluctuations under small changes in

the rotor resistances. Therefore, motors with higher rotor resistance are preferred for load

sharing applications as they have higher slip and hence much gentler slope in the motoring

region [25]. However, high-slip motors have higher copper loss and are less efficient.

Instead, machines with lower rotor resistance are generally preferred to reduce the losses, and

such IMs have steeper slopes in the motoring region.

3.3 Rotor Resistance Variation and Load Sharing Disparity

The rotor resistance of the two rigidly-coupled IMs may not be similar. It is highly unlikely

that even the motors coming from the same manufacturer will have exactly the same rotor

resistances. Moreover, the rotor resistance changes with loading and temperature. The

equivalent rotor resistance also changes with the frequency of the rotor currents and slip due

32

to the deep-rotor-bar effect, which depends on the rotor design [23], [26].

The diagram of Figure 2.2 is simplified here and depicted in Figure 3.4. The ramp, PI

controller and the speed limit blocks of Figure 2.2 is masked under the “Speed-Control-

Regulator” block. The VSI block is the actual hardware of the drive consisting of the

switching devices which was shown as “ qd to abc transformation block” in Figure 2.2.

V/F ControlSpeed Command IM

Speed

Control

Regulator

VSI

Speed feedback

Figure 3.4 Block diagram of Volt / Hertz control scheme.

A conventional scheme of multi-motor speed referencing is shown in Figure 3.5. Two motors

are rigidly coupled to share the common mechanical load. The input to the V/F control block

is the PI controlled difference between the speed feedback and the speed command. In rigidly

coupled multi-motor applications, all motors are coupled to each other and hence have a

common speed feedback. The PI corrected speed commands for both the VFDs are the same

and similar voltages and frequencies are injected into the coupled IMs. Thus, the similarity in

the torque developed by the two motors will depend on the rotor resistance of each IM.

33

LOAD

V/F ControlSpeed Command

V/F Control

IM1

IM2

Speed feedback

Speed

Control

Regulator

Speed

Control

Regulator

VSI

VSI

Figure 3.5 Block diagram for load sharing between two V/F controlled induction motors under

conventional speed referencing.

In the following discussion, two IMs rated 1HP each (as per Appendix A) are simulated to

share a mechanical load of mN.1.8 at sec

188 rad . The V/F drive and IM are modeled using

(2.1) to (2.9). The inertia of the load is considered to be 2.02.0 mkg . The machines (without

rotor resistance variation) are both rated to generate a full load torque of mN.05.4 . Both IMs

are identical in all respects, except the rotor resistances which are set to 06.5 and 41.7

for IM1 and IM2, respectively. The resultant torque-speed characteristic of each IM is shown

in Figure 3.6. It is observed that, as predicted by (3.5), the motor with the smaller rotor

resistance, IM1, carries a higher percentage of the load than the other motor. The values of

electromagnetic torque developed by the machines are provided in Table 3-1. It can be seen

that IM1 is overloaded to 118% whereas IM2 is operating below the rated torque by 18%.

The problem may become more severe from the process point of view, because the

overloading may force one or more IMs to operate closer to the breakdown region. In this

case, the entire process may become susceptible to breakdown as there is a possibility that

the overloaded machine would be isolated either by circuit tripping or by breakdown. The

34

rest of the system might not be able to carry the extra load and leading to stoppage of the

production line.

Figure 3.6 Torque-speed characteristics of two coupled induction motors, with rotor resistance

variation, sharing a common load without compensation.

Table 3-1 Electromagnetic torque developed by IM1 and IM2 under rotor resistance variation

using the conventional V/F scheme without compensation.

IM1 ( 06.51rr ) IM2 ( 41.72rr )

NmTe1 1

1

rated

e

T

T NmTe2

2

2

rated

e

T

T

4.77 118% 3.33 82%

35

3.4 Load Sharing Using Speed Reference Compensation Method Based on Rotor

Resistance

In the previous Section, it was shown that the electromagnetic torque is sensitive to the rotor

resistance, the input voltage and the input frequency. Thus, the participating torques in the

load sharing are seldom even or constant. In order to keep the torques of the coupled motors

equal under rotor resistance variation, we should change the input voltage and frequency

equivalently to compensate the system. This Section describes a methodology of changing

the input frequency (the speed reference) so as to vary the torque-speed curve and thus

achieve balanced load sharing among the coupled IMs. It is assumed that the rotor resistance

variation is known or can be estimated using either temperature-dependent look-up tables or

the online estimation methods [23]. Various methods have been proposed in the literature for

estimating the rotor resistance, but otherwise such methods are outside of the scope of this

thesis.

For two coupled IMs with different rotor resistances, (3.5) can be written as

11

1 1

2

11

23

re

th

er

sVPT

, (3.6)

22

2 2

2

22

23

re

th

er

sVPT

.

(3.7)

Herein, the suffix 1 and 2 correspond to IM1 and IM2, respectively. From (3.6) and (3.7) we

can see that when 21 rr rr , the operating torques of these IMs are not the same. For these

IMs to have the same operating torque, the right hand side of (3.6) and (3.7) should be equal.

36

2

2

2

2

2

1

1

1

2

1

23

23

re

th

re

th

r

sVP

r

sVP

. (3.8)

Solving (2.8), (3.2) and (3.8) for the electrical frequency of the second drive, 2e , we get:

r

S

S

r

r

M

Mree

X

X

r

r

X

X

1

2

1

2

2

112 , (3.9)

where r is the rotor electrical frequency, and lsMS XXX .

If (3.9) is satisfied then both the IMs will generate the same electromechanical torque and

equally share the load. Then, (3.9) is used to generate the corrected reference speed for the

second drive in the proposed load sharing scheme. The new scheme is shown in Figure 3.7

where the “Speed reference compensation block” is formed using (3.9). The second drive is

now operating without the speed control regulator block and the actual speed feedback is

taken to the “Speed reference compensation block”. The speed reference to the second drive

is varied as per the change in the rotor resistance. Employing the proposed approach, the

improved load sharing is shown in Figure 3.8. Notice that the maximum torque is now

different indicating that different voltages and frequencies are injected into the machines. It is

also observed that the machines are running with different synchronous speeds unlike the

case in Figure 3.6. Most importantly, the torque-speed characteristics of the machines now

intersect near the commanded speed which results in almost equal values for torque.

37

Speed Command IM1

IM2

Speed feedback

Speed feedback

Speed

Control

Regulator

Speed Reference

compensation block

V/F Control

V/F Control

VSI

VSI

LOAD

Figure 3.7 Block diagram of the proposed scheme for load sharing between two V/F controlled

induction motors.

Figure 3.8 Torque-speed characteristics of two coupled induction motors, with rotor resistance

variation, sharing a common load with compensation.

38

Comparing the torque values in Table 3-2 with those of Table 3-1, it is seen that, using the

proposed scheme, the load sharing between the machines has become more symmetrical and

the overloading on IM1 is removed. Each of the motors now shares approximately 50% of

the load. The proposed scheme can be readily extended to multiple motors (more than two).

It can be realized in practice, by implementing the “Speed reference compensation block” in

a PLC or similar logical device (assuming that the equivalent rotor resistance may be

appropriately estimated online). The first drive is speed referenced as per the required speed

and the second drive is speed referenced by the “Speed reference compensation block”.

Table 3-2 Electromagnetic torque developed by IM1 and IM2 under rotor resistance variation

using the proposed load sharing compensation scheme.

IM1 ( 06.51rr ) IM2 ( 41.72rr )

NmTe1 1

1

rated

e

T

T

NmTe2 2

2

rated

e

T

T

4.1 101% 4 99%

It is well understood that (3.5) holds true only when the slip is small and the machines

operate near the synchronous speed. As load and slip increases, the torque-speed curve

gradually loses its linearity. It is then expected that the performance of the proposed load

sharing scheme would be very good under lighter loads and will start to deteriorate under

heavily loads. In order to investigate the above mentioned characteristic, the IMs considered

in this paper are subjected to 25%, 50% and 100% loading. The torque developed by the

machines using the conventional and proposed V/F schemes has been superimposed in

Figure 3.9.

39

As seen in this figure, using the proposed load sharing scheme, the loading of the machines is

essentially equal at 25% load and has a difference of 2% at full load. However, using the

conventional/uncompensated method, the load is never shared equally and the difference

ranges from 10% at 25% load to 36% at full load. The results are summarized Table 3-3 and

Table 3-4. As can be seen in these tables, the proposed compensation scheme significantly

improves the load balancing between the considered IMs under light and heavy loads.

Figure 3.9 Load sharing of two coupled IM’s with rotor resistance variation under different

loading conditions.

40

Table 3-3 Individual motor torques under different loading conditions for conventional scheme

without load sharing compensation scheme.

Loading IM1 ( 06.51rr ) IM2 ( 41.72rr )

NmTe1 1

1

rated

e

T

T

NmTe2 2

2

rated

e

T

T

25% 1.21 30% 0.82 20%

50% 2.40 59% 1.65 41%

100% 4.77 118% 3.33 82%

Table 3-4 Individual motor torques under different loading conditions for proposed load sharing

compensation scheme.

Loading IM1 ( 06.51rr ) IM2 ( 41.72rr )

NmTe1 1

1

rated

e

T

T

NmTe2 2

2

rated

e

T

T

25% 1.01 25% 1.01 25%

50% 2.03 50% 2.02 50%

100% 4.10 101% 4.00 99%

3.5 Load Sharing Using Speed Reference Compensation Method Based on Current

Feedback

The scheme described above provides very good accuracy in torque sharing but requires

rotor resistance estimation using various methods [23], which would add to the complexity

and cost of the VFDs. A more practical and simpler approach may be required to share the

torque under the rotor resistance variations. A simple but practical approach may be derived

based equating the real component of the phase current (which sometimes is referred to as

the torque current). The torque currents of the individual motors can be taken as a feedback

and the signal can be used to alter the speed referencing of the drives. As the generated

torque is approximately proportional to the torque current (real component of the phase

41

current), adjusting the torque current can control the generated torque of the IMs. A block

diagram depicting this approach is shown in Figure 3.10.

IM2 current

IM1 current

LOAD

V/F ControlSpeed Command

V/F Control

IM1

IM2

Speed feedback

Speed

Control

Regulator

Speed

Control

Regulator

VSI

VSI

Speed feedback

PID

Torque

current

estimator

Torque

current

estimator

Figure 3.10 Proposed load sharing compensation scheme under rotor resistance variation.

Under normal operation, both motors IM1 and IM2 have equal rotor resistances and take

equal torque currents. When the rotor resistance of IM1 drops from the rated 41.7rr to

06.5rr , it starts taking higher percentage of the load. The difference in the currents

(error current) are fed back to alter the speed reference of the VFDs such that the error

current decreases. The simulation results are plotted in Figure 3.11. Also, in Figure 3.11 we

have plotted the results from the speed compensation using resistance block scheme. In the

considered study, the motors are assumed to be working with the same rotor resistance till

sec5t . At sec5t , the rotor resistance of IM1 decreases from 41.7rr to

06.5rr . In practice, this may be a much slower change, but the study is focused on

steady state before and after the change. It is seen that when this happens under the

traditional method the motor torques start differing away from each other leading to

42

unbalanced loading. However, with the proposed compensation methods, the IMs remain in

good balancing throughout the study.

Figure 3.11 Mechanical load of 8.1 mN. shared between the coupled IM’s: (a) without

compensation; and using proposed speed compensation based on (b) rotor resistances;

and (c) current feedback

43

3.6 Experimental Verification of the Proposed Load Sharing Scheme

3.6.1 Physical test bench set-up

To check the validity of the proposed load sharing compensation scheme, we used the

following experimental set up available in the Alpha Technology Lab, Kaiser 3075. The

overview schematic of the test bench is depicted in Figure 3.12. In the considered motor

bench with three machines shown in detail in Figure 3.13, two IMs rated 1HP and rated 5HP

were coupled on a common shaft and assumed to be driving a common mechanical load

emulated by the remaining third motor. The proposed scheme is implemented by using one

of the motors, Motor 3 (1HP), as a load and the other motors (Motor 1 (1HP) and Motor 2

(5HP)) for driving this load. As two identical motors with dissimilar rotor resistances were

not available, we used two dissimilar motors, 1HP and rated 5HP, for the experiment. These

motors are powered using VFDs which are run in V/F control. The specifications of the

VFDs used in the set-up are summarized in the Appendix B. The PLC is used to emulate the

control as explained in the previous sections. The details of the PLCs hardware and software

are listed in Appendix C. The experimental set up of the VFDs and PLC boxes are shown in

Figure 3.14, and Figure 3.15, respectively.

In the considered configuration, Motor 1 (1HP) and Motor 2 (5HP) are speed referenced with

1507.3 rpm anti-clockwise direction; while the Motor 3 (1HP) is torque referenced to run at

100% loading clockwise to emulate a common mechanical load of 4.05 mN. . The excess

energy from Motor 3 (1HP) is being dumped through the VFD 3 into an auxiliary breaking

resistor box. However, as the PLC was not programmed during the course of the experiment,

the above control (changing speed reference) was done manually using a computer

44

(Programming Station) over Ethernet/IP. A customized Rockwell Automation Software

DriveExecutive and DriveExplorer were used for online monitoring of the drive parameters.

Figure 3.12 Physical set-up for verification of the proposed scheme.

45

Figure 3.13 Load sharing motor test bench used for the practical observations.

Motor #1

Motor #2 Motor #3

46

Figure 3.14 VFD’s used for powering the load sharing motors.

47

Figure 3.15 PLC used to control the drives running the load sharing motors.

48

3.6.2 Experimental procedure of load sharing and results from VFD interface

The current taken in by an IM comprises of a reactive component and a real component. The

reactive component of the current is due to the leakage flux and magnetizing current,

whereas the real component of the current is spend on the losses in the resistances and the

rotor current which produces the torque (torque current). The real current is in-phase with the

supplied voltage as depicted in Figure 3.16. In the following simplified analysis, it is

assumed that the IM torque is generated by the real component of the current. Hence, to share

the load, the Motor 1 (1HP) and Motor 2 (5HP) should carry the same torque current.

Figure 3.16 Torque and flux component of the motor current.

To emulate the needed conditions, the experimental set-up is run twice: once with identical

speed reference for both the drives without the proposed load sharing scheme; and second

time with the proposed improved load sharing scheme. To implement the proposed scheme,

the speed reference of Motor 2 (5HP) is decreased to a point where the torque currents of

both motors are similar. The torque currents are monitored in the DriveExplorer software

(see Figure 3.17 and Figure 3.18). Based on results shown in Figure 3.17, we can see that

initially both the VFDs were referenced with the same speed, and the individual load torque

current for the Motor 1 (1HP) and Motor 2 (5HP) are unequal with second motor taking more

load. The results of this study are summarized in Table 3-5, which shows that torque current

49

of Motor 2 (5HP) is 0.9A, whereas the torque current of Motor 1 (1HP) is around 0.2 A. This

happens because in the motoring region of the torque speed curve at a shaft speed, the Motor

2 (5HP) has higher electromagnetic torque compared to the Motor 1 (1HP).

In the second study, with the speed reference compensation, these motors run with different

operating frequency. The frequency change brings about a change in the torque-speed curve

of the IMs. It is seen from Figure 3.18 that the load is now better shared between Motor 1

(1HP) and Motor 2 (5HP) and the torque currents are equalized. The motors now take 0.6 A

and 0.7 A of the real currents, respectively. Please note that the total phase current of each

motor will be different even with the proposed scheme due to the dissimilar motors that

require different flux current. Another interesting observation is that initially the power-

factor of Motor 1 and Motor 2 were 0.16 and 0.29, respectively. With the proposed load

sharing, the power-factor of Motor 1 (1HP) has improved to 0.49 due to the increase in the

torque current of the motor, and Motor 2 (5HP) power-factor has dropped to 0.21 doe to

reduction in load.

Table 3-5 Torque current read from the DriveExplorer® software interface: (a) without

compensation; and (b) with proposed compensation for load sharing.

Motor 1 (1HP) Motor 2 (5HP)

Speed

Reference

( rpm )

Torque

Current

(A)

Speed

Reference

( rpm )

Torque

Current

(A)

Shaft Speed

( rpm )

Without

compensation 1507.3 0.2 1507.3 0.9 1490

With

compensation 1507.3 0.6 1478.0 0.7 1460

50

Figure 3.17 Screenshots of the DriveExplorer® software interface for the VFD 1 and VFD 2 without

load sharing compensation.

51

Figure 3.18 Screenshots of the DriveExplorer® software interface for the VFD 1 and VFD 2 with

load sharing compensation.

52

3.6.3 Steady state measurements and calculations

The individual motor currents were measured using Yokogawa WT1600 (specification is

summarized in the Appendix D). The measured phase currents were captured, saved, and are

plotted in Figure 3.19 for the steady state conditions without and with the proposed

compensation method. As we can see in Figure 3.19, the currents in the Motor 1 (1HP)

increases and the currents in the Motor 2 (5HP) decreases when the proposed speed reference

compensation is enabled to improve the load sharing. However, in the given experimental

set-up, the currents should not be equal to each other as the machines and their magnetizing

currents are different.

Figure 3.19 Measured line currents for Motor 1 (1HP) and Motor 2 (5HP): (a) without

compensation; and (b) with proposed load sharing compensation.

53

To further validate the results, we have calculated the real component of the measured

currents. This is done by calculating the phase difference between the respective phase

voltages and phase currents and then calculating that component of the current which is in

phase with the phase voltage. The results are summarized in Table 3-6. These results show

that the balance between the torque currents and subsequently the load sharing has improved.

Table 3-6 Torque current calculated from the measured data: (a) without compensation; and (b)

with proposed compensation.

Motor 1 (1HP) Motor 2 (5HP)

Speed

reference

( rpm)

Torque

current (A)

Speed

reference

( rpm)

Torque

current (A)

Shaft Speed

( rpm )

Without

compensation 1507.3 0.3 1507.3 1.4 1490

With

compensation 1507.3 0.7 1478.0 1.1 1460

The corresponding voltage and current phasors are also plotted for Motor 1 (1HP) and Motor

2 (5HP) with and without the proposed compensation. The plots are shown in Figure 3.20

and Figure 3.21, respectively. As the torque sharing improves, the load on the previously

lightly loaded Motor 1 (1HP) increases. This increases the real current of the machine,

improving the power factor of the machine. This can be seen in Figure 3.20, where the angle

between the voltage and current phasor corresponding to a particular phase has decreased

from 1 to 2 . Thus, the proposed scheme, if used wisely, can improve the sharing and also

improve the power factor.

54

Figure 3.20 Phasor diagram of voltage and current for Motor 1 (1HP) with and without the

proposed load sharing compensation.

Figure 3.21 Phasor diagram of voltage and current for Motor 2 (5HP) with and without the

proposed load sharing compensation.

55

3.6.4 Verification of model using simulation of the physical set-up

In this Section the previously developed model of the multi-motor drive system with verified

against the physical set-up for two dissimilar motors. A load of 4.05 Nm equivalent to the

load used in the physical set-up is used to load Motor 1 (1HP) and Motor 2 (5HP). The motor

parameters are exactly equal to the ones used in the actual set-up. The measured and

simulated voltage and current waveforms are shown in Figure 3.22 through Figure 3.25. It is

seen that the simulated results match the measured data very well.

Figure 3.22 Measured and simulated line voltages and currents for Motor 1 (1HP) without load

sharing compensation.

56

Figure 3.23 Measured and simulated line voltages and currents for Motor 2 (5HP) without load

sharing compensation.

57

Figure 3.24 Measured and simulated line voltages and currents for Motor 1 (5HP) with load sharing

compensation.

58

Figure 3.25 Measured and simulated line voltages and currents for Motor 2 (5HP) with load sharing

compensation.

The simulation results are shown in Figure 3.26 and the corresponding values of the torques

and currents are summarized in Table 3-7. Initially, the motors are assumed to run from the

VFDs without the proposed compensation. Both the motors’ VFDs are speed referenced with

1507.3 rpm , similar to the physical set-up. It is seen that Motor 2 (5HP) takes most of the

load and gets 3.5 mN. ; whereas the Motor 1 (1HP) gets loaded to 0.5 mN. . The torque

59

current of the motors are calculated using the Fourier transform of the current signal and then

calculating the component of the current that is in phase with the voltage. These values are

close to the ones observed from the test bench tabulated in Table 3-6. At sec2t the

proposed load sharing scheme is switched on. It is seen that the frequency input for Motor 2

(5HP) decreases until the load torques are matched. The load sharing compensator changes

the speed reference of the Motor 2 (5HP) such that the torque speed curve at the motoring

region is changed and the motors start sharing the load between them equally. It is seen in

Figure 3.26 that with enabled proposed control, the revised speed reference for the second

motor has changed to 1484.3 rpm and the torque balancing is improved significantly. The

load on the Motor 2 (5HP) reduces whereas the 1HP motor load increases to achieve the

desired balance. The revised speed reference is not exactly equal to the ones in the set-up

because in the physical model the speed is manually changed using the DriveExecutive

software where the speed change is restricted to step size of around 15 rpm .

The motor real power mostly comprise of the resistive losses and the electromagnetic torque.

Thus the real power reflects the torque loading of the machines. It is seen that the real power

of the machines are different without compensation as seen in Figure 3.26. But when the

compensator is switched on, the set-up starts to share the load. The real power of the Motor 2

(5HP) decreases as Motor 1 (1HP) becomes equally loaded.

60

Table 3-7 Torque current calculated from the simulated results with and without proposed load

sharing compensation.

Motor 1 (1HP) Motor 2 (5HP)

Speed

Reference

( rpm )

Torque

Current (A)

Speed

Reference

( rpm )

Torque

Current (A)

Shaft

Speed

( rpm )

Without

compensation 1507.3 0.3 1507.3 1.2 1500

With

compensation 1507.3 0.7 1484.3 0.7 1480

Figure 3.26 Simulation results for the load sharing without compensation and with the proposed

compensation.

61

Based on the simulation studies and the experimental results, the proposed method is seen to

not only improve the load sharing between similar motors but also dissimilar motors. The

scheme also improves the power-factor of the system which is a considerable contribution.

The proposed scheme should be wisely used when implementing for dissimilar motors

keeping in mind the loading capacity of the individual motors. One way to generalize the

proposed scheme is to share the load in relative proportion to the capacity of each

participating IMs.

62

4 Load Sharing under Wheel Slippage in Vehicular Application

4.1 Motivation

It was seen in Chapter 3 that load sharing is a function of individual motor parameters, the

load distribution among the motors, and the commanded speed of each motor. In this Chapter

we extend the concept of load sharing control under the change in the load distribution that

may occur in multi-motor systems such as vehicular platforms, rail cranes, etc. due to

external factors such as wheel slippage.

IMs driven by basic Volts/Hertz controller are commonly used for driving the wheels of

gantry cranes such as the one shown in Figure 1.1(d) and many other industrial applications.

The torque developed by the propulsion motors generates the tractive force that moves the

vehicular or a crane platform. If the contact between the surface or rail and the driving wheel

is not the same among all participating wheels, then the adhesion and the tractive force

generated by each wheel will be different leading to unequal loading of the driving IMs. In

addition to the degradation of the vehicular/platform/crane performance, the result is

undesirable leading to some motors being under loaded and others overloaded. In this

Chapter, a method is proposed for sharing the torques equally between the wheels of a gantry

crane, driven by IMs with basic VFDs operating in V/F mode. The proposed control strategy

is explained for two coupled motors but may be readily extended to a number of coupled

motors and other similar applications where the coupling between the motors is not rigid and

the torque passed to each IM may vary by the virtue of adhesion.

63

4.2 Concept of Torque Transfer and Wheel Slippage

The torque generated by the IM needs a medium to get transferred from the machine to the

load. The medium can be in the form of [27]:

1. Rigid mechanical coupling between the load and the motor,

2. Resilient connection or viscous damping coupling, where the interconnection is either

by long shafts, chains or belts, or by the material being processed where twisting and

elongation becomes significant, and

3. Friction-based tractive coupling in which changing mechanical surfaces influence the

values of the tractive parameters and forces.

The problem discussed in Chapter 3 considered a rigid coupling between the load and the IM.

In such coupling, the loss of mechanical torque is minimal as there exists a direct coupling.

However, some application makes use of resilient or friction coupling in which the medium

of transfer is a contact surface between the machine and the material. Rolling Mill

(Steel/Paper/etc.), tube mill, gantry crane wheel motion, roller table application etc. are some

of the applications that make use of such coupling. The torque generated by the IM is

transferred to the material or the ground/rail by the virtue of contact between the two

surfaces. Hence, to have efficient torque transfer, the surfaces should not be slippery and

remain always be in contact with each other.

Without loss of generality, in this thesis a gantry crane operation shown in Figure 4.1 is

considered. The gantry crane runs on steel rails and typically has multiple wheels driven by

IMs. For effective motion of the gantry crane, the torque generated by the wheels should be

64

transferred to the rail to generate the propulsion force. For this to happen there should be

active bonding between the wheels and the rail. Such a bonding between the two surfaces is

known as adhesion. If the bonding breaks, then the torque does not get transferred and the

crane may stop moving in the desired direction with the wheels spinning rapidly (wheel

slippage). The bonding can break when the crane is accelerating from standstill or is trying to

stop rapidly, for example. The bonding may also break because of wear-out of the wheels

and the rails or some external contamination like water or oil spillage, etc.

Induction

MotorSteel Wheel

Steel Rail

Trolley hook for

lifting loads

Figure 4.1 Gantry crane running on a set of rails with IM driven wheels.

4.3 Adhesion, Tractive Force, and Vehicular Motion

The total adhesion coefficient can be considered as a bonding between the wheel and the

rail. The bonding is dependent on two factors, namely on the surface adhesion factor a ,

and the speed correction factor c . Both factors changes the total adhesion coefficient as

follows

65

ca , (4.1)

where a is the surface adhesion factor, and c is the speed correction factor.

During the normal operation, the gantry (bridge) crane speed is very close but never equal to

the linear speed of the wheel. The difference in the speeds is known as the slip-speed , and

is given by

tw VV , (4.2)

where wV is the linear circumferential wheel velocity and given by www rV ; and tV is the

vehicular velocity; and wr is the radius of the wheel.

The slip-speed λ , along with other environmental factors [28], determines the surface

adhesion factor a , between the wheel and the surface. The surface adhesion coefficient

determines the amount of tractive force that can be transferred from the wheel onto the rail

without sliding [29]. Higher coefficient of surface adhesion factor means better transfer with

less energy loss in sliding. Surface adhesion factor points out to the phenomena of bonding

between the surfaces in contact. This is a surface phenomenon and is highly dependent on the

nature of the surface; such as its roughness, contamination, hardness, chemical and physical

composition, etc. The relationship between the surface adhesion factor and the slip-speed is

not theoretical and hence there is no standard equation encapsulating this relationship.

Significant research has been done to generalize this relationship and today many empirical

formulas exist to show this relationship [30], [31]. This relationship is defined for different

surfaces in contact and hence there exists more than one equation formulizing this

relationship. A sample graph for tire-road adhesion on dry and wet road condition is shown

66

in Figure 4.2. The pattern can be divided into two regions:

1. Stable region (where the adhesion increases with increase in slip also known as Creep

Region)

2. Unstable region (where the adhesion decreases with increase in slip know as

Slip/Spin Region)

Dry Condition

Wet Condition - 1

Wet Condition - 2

Stable Unstable

Slip-speed λ (m/s)

Su

rfac

e ad

hes

ion

fac

tor μ

a

Figure 4.2 Graph depicting general relationship between surface adhesion factor a and slip-

speed for different road conditions.

It was also noticed in series of conducted experiments that the total adhesion coefficient

decreased with increase in the material speed / vehicle velocity [31]. This is because as the

vehicular speed is increased the dwell time is decreased, decreasing the molecular level

interlocks and hence decreasing the adhesion energy required to break the interlock. This

factor is known as the speed correction factor c . Similar to the relationship between surface

adhesion factor and slip speed, the relationship between the adhesion coefficient and the

vehicle speed could only be stated empirically. A sample pattern is as shown in Figure 4.3.

This relationship was seen prominent under high velocities.

67

Vehicle speed - Vt (m/s)

Sp

eed

co

rrec

tio

n f

acto

r μ

c

Figure 4.3 Graph depicting general relationship between speed correction factor c and vehicle

speed.

The total adhesion coefficient defined in (4.1) is responsible for the generation of traction

force

NFT , (4.3)

where N is the normal force due to mass on the driving wheel.

For the purpose of further discussion, a wheel with mass M is considered to be rolling on a

flat surface as depicted in Figure 4.4. The wheel is rolling with a linear speed of tv and a

linear circumferential wheel velocity given by www rV , under a tractive effort of TF given

by (4.3). This tractive effort produces vehicular motion against the rolling resistance RollingR .

This motion can be described by the following differential equation

Rollingt

T Rdt

dvMF . (4.4)

68

If the rail surface were on a slope with respect to the ground, (4.4) would need to include the

gravitational component, sinMg , which is neglected for our studies as we consider the

normal operation where the gantry crane is running on a perfect horizontal rail.

The rolling resistance RollingR consists of different resistive forces. These forces can be in

form of micro-slip (adhesion component), surface deformations (hysteresis component) due

to the compressive force of the body [32], [33], [34] and also due to the aerodynamics [35],

[36]. The rolling resistance, RollingR in (4.4), is thus a combination of different resistive forces.

airndeformatioadhesionRolling RRRR . (4.5)

Figure 4.4 Diagram showing different speeds and forces acting on the wheel.

Adhesion is important in transfer of generated torque to the rail to overcome the surface

friction. Adhesion and friction are related and it is helpful to have an overview of the relation

between the Adhesion and Friction. Many papers, e.g., [37] and [38], have explained the

relationship between adhesion and friction in greater depths. To put it in simpler term,

friction can be defined as an undesirable opposition to motion of the body while adhesion can

69

be defined as a force of attraction between the two surfaces [29],[39], [40].

Although (4.4) suggests that increase in tractive effort will result in higher linear velocity of

the vehicle, there is an upper limit beyond which the wheel will start spinning and the vehicle

will lose its linear velocity. “Spin” is a phenomenon where the vehicle wheel accelerates

more than the vehicle; whereas “Slip” is a phenomenon where the vehicle wheel decelerates

more than the vehicle [41]. When a wheel moves on a surface, it undergoes micro-slip.

Micro-slip, as the name suggests, is a phenomena where the contact surface of the wheel

undergoes random slip and stick. The distribution of this slip and stick instances depend on

the slip-speed . A sample slip-stick phenomenon is plotted against the slip-speed in Figure

4.5. When the tractive effort is rapidly increased, the vehicle speed cannot keep up with the

wheel speed due to inertia and the slip-speed increases. If the difference is too high, then the

slip region in the slip-stick region increases and the vehicle starts slipping [39], [42].

ST

ICK SLIPSTICK SLIP SLIP

Low Slip SpeedModerate Slip

SpeedSliding Motion

Rolling Direction Rolling Direction Rolling Direction

Figure 4.5 Slip-stick phenomenon at the contact surface of wheel and rail.

70

4.4 Induction Motor Load in a Gantry Crane Application

The angular motion of the wheel is generated by the wheel that is driven by IM. In this

Section, we discuss the role of an IM in the vehicular motion. The top view of the general

case of gantry crane of Figure 4.1 is reproduced in Figure 4.6 for better clarity. For the

purpose of this thesis, the gantry crane is assumed to have four wheels, out of which two

wheels are driving wheels (Wheel 1 and Wheel 2) coupled to the two separate IMs (IM 1 and

IM 2), and the remaining two are passive driven wheels (Wheel 3 and Wheel 4). The total

vehicle mass M is considered to be distributed equally amongst the four wheels, with each

wheel carrying an equivalent mass of 4

M . Let 1M , and 2M be the mass acting on the

Wheel 1 and Wheel 2. The vehicle is considered to be moving linearly on a perfect plane

surface with a linear speed of tV . The wheels have linear speed of 1wV (Wheel 1) and 2wV

(Wheel 2) with a total adhesion of 1 and 2 for Wheel 1 and Wheel 2, respectively. Each

wheel contributes a tractive force 1TF (Wheel 1) and 2TF (Wheel 2), where each force is

gMFT 111 , (4.6)

gMFT 222 .

(4.7)

It should be noted that only the driving wheels generates the tractive force. This means that

for the gantry crane in the Figure 4.6, the tractive effort of the total vehicle will be

2

1

221121

i

iiTTtotalT gMgMgMFFF . (4.8)

71

Driving

Wheel 1

Driving

Wheel 2

Driven

Wheel 3

Driven

Wheel 4

Vw1

Vw2

Vt

FT1

FT2

FT total

IM 1

IM 2

Figure 4.6 Top view of the gantry crane showing the different speeds and tractive forces.

The tractive force TF acts as load torque given by wTload rFT . Thus the individual traction

loads will be given by the following

wTload rFT 11 , (4.9)

wTload rFT 22 .

(4.10)

The traction loads along with the individual frictional torque 1fricT and 2fricT , and the inertia

1J and 2J act as a load on the connected IMs. The torque of IM 1 and IM 2 can be given by

dt

dJTTT rm

fricloade

1

111

, (4.11)

dt

dJTTT rm

fricloade

2

222

,

(4.12)

where wr is the radius of the driving wheel; and 1rm , and 2rm are the rotational speeds of

the IM 1 and IM 2. The motor torques 1eT and 2eT produces the angular motion of the wheels

which helps in generating the micro-slip and further generates the tractive effort as explained

72

in Section 4.3.

Assuming equal mass distribution and an ideal condition where the adhesion under each

wheel is the same and neglecting the frictional load, the load on each IM will be equal ((4.11)

and (4.12)). However, in reality it is highly unlikely that the adhesion will be the same for

both the wheels because of its dependency on various variables. A difference in surface

adhesion factor under the wheels (oil/water spillage, snow, surface deformity and abrasion)

during the process is also inevitable and will result in a change in tractive effort and thus a

change in the loading of the IMs ((4.9) and (4.10)). The loading of the IMs is hence highly

susceptible and depends a great deal on the external environmental conditions. The

conventional scheme of powering the IMs for the gantry crane application is shown in Figure

4.7. It is seen that similar to Figure 3.5, the speed referencing of both VFDs is the same and

hence the input voltage and frequency to both the IMs is the same. Under the conventional

scheme, it is impossible to achieve equal load sharing between the wheel motors. In most

cases, slip occurs temporarily because of occasional oil slippage or occurrence of

water/snow. Though temporarily, such random occurrence of slip can overload the respective

IM high enough for circuit tripping and stoppage of the process.

Figure 4.7 Block diagram for conventional load sharing between two V/F controlled induction

motors under resilient or stochastic coupling.

WHEEL-1V/F ControlSpeed Command

V/F Control

IM1

IM2

Speed feedback

Speed

Control

Regulator

Speed

Control

Regulator

VSI

VSI WHEEL-2

RAIL-1

RAIL-2

73

4.5 System Model and Performance under Wheel Slippage

A slow moving gantry crane is considered for the study in this thesis. The gantry crane is

considered to be moving with a speed of 0.5 s

m or 30min

m . The simulation parameters

are listed in Table 4-1. The model used for the simulation is shown in Figure 4.9 and is

simulated in Matlab/Simulink® [12], [13]. In the model, the Coriolis-effect of the gantry

crane hook and the suspended body, the thermal dependence of adhesion energy and

frictional parameters are neglected. For steel wheel on steel rail, the rolling friction is due to

the plastic deformation of the contact surfaces and is scarcely affected by lubricants [33].

Hence, the rolling friction is considered constant. Assuming that the gantry crane is moving

on planar surface, we can also neglect the effect of gravity. The rolling resistance thus is

considered constant at 0.0025/ mN. on each wheel.

Table 4-1 Sample parameters of the gantry crane used in the simulation.

Simulation Parameters

Mass (kg) M 16,000 kg

Moment of inertia J 0.12mkg

Wheel radius / gear ratio G

rw

0.05 m

Linear speed of the crane tV

0.5s

m

Total number of wheels 4

Number of driving motors (Specifications

are given in Appendix A) 2 x 5HP

74

The surface adhesion factor for the wheel-rail system considered here is modeled as [43]

ba

a dece , (4.13)

where a , b , c , and d are the parameters defining the surface adhesion factor depending

on the surface condition. For the same considered wheel-rail system, the speed correction

factor is modeled as [31]

vc

8100

824.0

, (4.14)

where v is the vehicle linear speed in h

km .

The typical parameters needed for (4.13) to represent the dry and slippery conditions [43] are

listed in Table 4-2, and the resultant adhesion is plotted against the slip speed in Figure 4.8.

Table 4-2 Surface adhesion factor parameters for steel wheel on steel rail in dry and slippery

conditions.

Rail Condition a b c d

Dry 0.54 1.2 0.29 0.29

Slippery 0.54 1.2 1.0 1.0

75

Figure 4.8 Surface adhesion factor vs. slip speed for parameters listed in Table 4-2.

76

Figure 4.9 Block diagram of the simulation model for the wheel and vehicle dynamics of the gantry

crane.

77

4.5.1 System performance without load sharing

To study the system performance in this Subsection, it is assumed that the driving conditions

of one of the wheels, Wheel 1, is changed from dry to slippery for a period of time, and then

is changed to dry again. This situation may emulate accidental appearance of ice, oil, etc. on

one of the rails, which is passed by the crane platform. The model is run with a speed

reference of 10sec

rad to have a linear speed of 0.5s

m . At time sec8t , Wheel 1

encounters slippage. This is modeled by changing the surface adhesion factor parameters as

shown in Table 4-2 from dry to slippery. This condition prevails for the next 7secs, and at

sec15t , the rail condition changes back to dry. The results of such a drop in surface

adhesion factor predicted by the model are shown in Figure 4.10. Figure 4.10(a) shows that

the vehicle speed decreases when the adhesion on Wheel 1 drops. This is because the tractive

effort totalTF momentarily falls as shown in Figure 4.10(b) b the driving force is reduced and

the vehicle speed drops as per (4.4). The corresponding surface adhesion factor change is

shown in Figure 4.10(c). The slip speed of both wheels increases identically as both the IMs

are referenced with the same speed command signal. As seen in Figure 4.10(c), the increased

slip speed also increases the surface adhesion factor on the Wheel 2. The difference in the

adhesion between the wheels gives rise to a variation in the load torque on the motors as seen

in Figure 4.10(d). Table 4-3 summarizes the difference in the load torques during this

scenario. From Table 4-3, we can see that during the course of disturbance the motor on

Wheel 2 becomes overloaded to around 150% while the load on the Wheel 1 motor drops to

around 50%, respectively.

78

Figure 4.10 Results of wheel slip under conventional V/F control without the proposed load sharing

scheme: (a) wheel and vehicle speed; (b) total tractive effort; (c) surface adhesion factor

of Wheel 1 and Wheel 2; and (d) load torque on Wheel 1-IM1 and Wheel 2-IM2.

79

Table 4-3 Load on Wheel 1-IM1 and Wheel 2-IM2 under wheel slippage without using the

proposed load sharing compensation scheme.

Adhesion a Load torque eT ( Nm )

Time Wheel 1 Wheel 2 Wheel 1-IM1 Wheel 2-IM2

sec8 0.01 0.01 19.6 19.6

sec15sec8 0.005 0.015 8.82 30.38

sec15 0.01 0.01 19.6 19.6

Moreover, the difference in the tractive force (~431N) between the wheels will generate a

deformation torque defT around the center of the axle connecting the two wheels given by

lFFT TTdef 21 , (4.15)

where l is the distance of the wheels from the center of the axle. The formation of

deformation torque defT is shown in Figure 4.11. This torque will generate a sideward stress

on the rail and the wheel, potentially causing faster wear or even blocking of the crane cart in

between the rails, which may be catastrophic for the system.

Td

ef =

0 N

m

FT1

FT2

ℓ

Axle

FT1=FT2 FT1≠FT2

FT1

FT2

Axle

Td

ef >

0 N

m

Figure 4.11 Moment of force vector on the axle under wheel slip with conventional V/F control

without the proposed load sharing scheme.

80

4.6 Proposed Methodology for Improved Load Sharing under Wheel Slippage

In a simple V/F control technique, the VFD only has control over the speed of the IM. Thus

the reference speed is the only controllable variable that can be taken into consideration. In

this Section, a methodology for changing the speed reference of the VFDs to achieve load

sharing during wheel slippage is discussed and implemented. The considered adhesion is

plotted against the slip speed in Figure 4.12. The adhesions at the different steady state slip

speed are indicated with points a1 and b1 , a2 and b2 , and a3 and b3 , respectively. In

particular, for the considered points we have:

1. Point a1 and b1 : Steady state operating points of Wheel 1 and Wheel 2 before the

slip occurs,

2. Point a2 and b2 : Steady state operating points of Wheel 1 and Wheel 2 after the slip

occurred,

3. Point a3 and b3 : Desired steady state operating points for the Wheel 1 and Wheel 2.

It is desirable for the wheels to have the same adhesion hence the same torque after

the slip occurs.

81

Figure 4.12 Trace of adhesion at different rail conditions vs. slip speed.

When both VFDs have the same speed reference, the slip-speeds of both the wheels are

identical. From Figure 4.12, it can be seen that when this happens point a2 and b2 gives

different adhesion because of dissimilar characteristics of the rail under each wheel. To have

similar adhesion from different road characteristics, we need to alter the wheel speeds

differently to give slips (point a3 and b3 ) corresponding to the same adhesion.

From Figure 4.12, it is clear that adhesion from the two rail surfaces can be made equal only

by increasing the slip of the Wheel 1 while at the same time decreasing the slip of the Wheel

2. When this is achieved, point a2 moves to a3 while b2 moves to b3 in Figure 4.12. The

wheel slip is increased or decreased by increasing or decreasing the wheel speed. The desired

speed reference would try to reduce the difference in torque which demonstrates the idea of

proposed method for adjusting the speed reference. The resulting proposed control scheme is

82

depicted in Figure 4.13. In this approach, the speed loop alters the reference speed of each

wheel to achieve equal torques. In practice, torque may be estimated from measured currents

and voltages. The control block diagram of Figure 4.13 is added to Figure 4.9 across the

points “A” and “B” to give final proposed control scheme shown in Figure 4.14.

Figure 4.13 Proposed change in the speed referencing of the drive powering the wheels of a gantry

crane under wheel slippage.

WHEEL-1V/F ControlSpeed Command

V/F Control

IM1

IM2

Speed feedback

Speed

Control

Regulator

Speed

Control

Regulator

VSI

VSI WHEEL-2

RAIL-1

RAIL-2

Speed feedback

Motor

Torque-1

Motor

Torque-2

controller

Figure 4.14 Block diagram of the proposed scheme for improved load sharing between two V/F

controlled induction motors under wheel slippage.

83

4.6.1 Computer studies demonstrating the proposed methodology

The proposed methodology is implemented using the block diagram depicted in Figure 4.14

and the conditions similar to the previous case, wherein the Wheel 1 slipping at time

sec8t . The results achieved by the proposed method predicted by the simulation are

shown in Figure 4.15. From Figure 4.15(a), it is seen that the slip velocity of the wheels are

different unlike in Figure 4.10(a). The slip velocity is automatically adjusted such that the

surface adhesion factors [see Figure 4.15(c)] for both the wheels remains the same. Although

the wheels are running with different velocities due to the difference in the slip-speed and the

road conditions, the adhesion under Wheel 1 and Wheel 2 are the same. Thus, the tractive

force for both wheels are equal, which assures that the load torques on both wheels are

properly shared as shown in Figure 4.15(d). The results are also summarized in Table 4-4.

84

Figure 4.15 Results of wheel slip under the proposed load sharing scheme: (a) wheel and vehicle

speed; (b) total tractive effort; (c) surface adhesion factor of Wheel 1 and Wheel 2; and

(d) load torque on Wheel 1-IM1 and Wheel 2-IM2.

85

Table 4-4 Load on Wheel 1-IM1 and Wheel 2-IM2 under wheel slippage using the proposed load

sharing compensation scheme.

Adhesion a Load torque ( Nm )

Time Wheel 1 Wheel 2 Wheel 1-IM1 Wheel 2-IM2

sec8 0.01 0.01 19.6 19.6

sec15sec8 0.01 0.01 19.6 19.6

sec15 0.01 0.01 19.6 19.6

To further modify the proposed methodology, the torque signal in Figure 4.13 can be

replaced by the real components of the phase current (the torque current). This would be

similar to the methodology described in Chapter 3. Also, since the IMs are typically of the

same base rating with the same magnetizing current, it may be possible to simply use the rms

currents of each motor and use these signals to implement a similar torque balancing

approach. It is seen that with the proposed load sharing scheme, the load balancing between

the motors has improved significantly even under the wheel slippage. The proposed scheme

is simple to implement on existing VFDs with minimal additional hardware.

86

5 Conclusion

In this thesis, two practical cases of load sharing in systems with multiple induction motor

drives where studied and their solutions were discussed in detail. The provided solutions

have the element of novelty, are simple and cost-effective to implement considering the same

existing basic equipment and V/F VFDs, which may be appealing to many industrial

applications.

5.1 Summary

Chapter 3 gave analyzes the load sharing among rigidly-coupled induction motors with

variations of internal parameters such as rotor resistance, and proposes a solution for load

improving sharing under rotor resistance variations. The rigidly-coupled induction motors are

common in industrial applications such as roller table, conveyor belts, etc. The proposed

solution was designed assuming a basic V/F control VFD which is widely used in the

industry and was intended to give a cost effective economical solution to a generic problem.

Chapter 4 extended the problem of load sharing to a practical case of moving vehicular or

crane platform with multiple wheels driven by several induction motors and corresponding

VFDs. In such common applications, oil / water spillage, occurrence of snow, etc., may cause

variations in adhesion and tractive forces. Slipping and/or spinning of wheels are a common

phenomenon in such applications leading to uneven distribution of load passed to the

individual induction motors. Under traditional V/F divers it was not possible to maintain load

balancing under such conditions. A simple solution was provided to improve the load/torque

sharing among the participating induction motors, which may be practically realized based

87

on current measurements. Although, the proposed method was developed and presented for a

gantry crane application, the proposed methodology with appropriate modifications can be

extended to other applications with similar properties, e.g., trains, trolley, vehicles, etc.

5.2 Future Research

Chapter 3 considered knowledge of the rotor resistance variation. In practice, this method

may be more difficult to realize effectively. The solution can be suitably modified to include

the online parameter identification to identify the rotor resistances and other parameter

variations and then change the speed reference accordingly. The online parameter

identification is a vast topic of research [44], [45], [46], [47]. A further research would be

required to find the most suitable and at the same time simple-to-implement approaches that

can be considered together with the existing basic VFDs. The alternative approach proposed

in Chapter 3 uses the current measurement which may be more practical for implementation

and applicable to larger number of applications with similar problem. This approach can be

further generalized to include proportional load sharing among dissimilar motors.

Chapter 4 dealt with load sharing between the motors under wheel slippage. The general

idea can be also studied from a point of view of operating the motor at the peak of the

adhesion-slip curve (Figure 4.8). This ensures the maximum use of available adhesion

resulting in maximizing the tractive effort. This property may be particular desirable for in

automotive applications for maximizing the vehicular acceleration for the given surface and

improving the driving traction and stability of the vehicles under different road conditions.

This involves online identification of the surface adhesion [48], [49], [50].

88

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Appendices

Appendix A

Motor Specification

A. 5HP Hyundai, 460 V, 60 Hz, 1750 rpm , 4 Pole,

Model: HNV413-CC-DBLS, Type: HJS184SR235-HNV413-CC-DBLS,

503.1sr , 147.1rr , 665.3lsX , 786.4lrX , 38.101mX ,

mNTrated .25.20 , mNT .75.60max , 2.105.0 mkgJ .

B. 1HP Baldor Reliance, 460 V, 60 Hz, 1725 rpm , 4 Pole,

Catalogue No.: CM3546, Spec No.: 34G795X269,

98.6sr , 41.7rr , 84.11lsX , 03.11lrX , 23.207mX ,

mNTrated .05.4 , mNT .15.17max , 2.00261.0 mkgJ .

C. 3HP, 220 V, 60 Hz, 1710 rpm , 4 Pole,

435.0sr , 816.0rr , 754.0lsX , 754.0lrX , 13.26mX ,

2.089.0 mkgJ .

D. 3HP, 460 V, 60 Hz, 1705 rpm , 4 Pole,

087.0sr , 228.0rr , 302.0lsX , 302.0lrX , 08.13mX ,

2.662.1 mkgJ .

E. 500HP, 2300 V, 60 Hz, 1773 rpm , 4 Pole,

95

262.0sr , 187.0rr , 206.1lsX , 206.1lrX , 02.54mX ,

2.06.11 mkgJ .

F. 2250HP, 2300 V, 60 Hz, 1786 rpm , 4 Pole,

029.0sr , 022.0rr , 226.0lsX , 226.0lrX , 04.13mX ,

2.87.63 mkgJ .

96

Appendix B

Variable Frequency Drive Specification

Motor

Rating Drive Rating Specifications

1HP

5 HP Normal

Duty, 3 HP

Heavy Duty

PowerFlex700 AC Drive, 480 VAC, 3 PH, 8 Amps, 5 HP

Normal Duty, 3 HP Heavy Duty, IP20 / Type 1, No HIM

(Blank Plate), Brake IGBT Installed, Without Drive

Mounted Brake Resistor, Second Environment Filter per

CE EMC directive (89/336/EEC), No Communication

Module, Vector Control with 120V I/O, No Feedback

Input Voltage 480 VAC, 3 PH

Current Rating 8 Amps

Enclosure IP20 / Type 1

Frame Size Frame Size 0

Output Current Information Output Amps: 8A Cont,

8.8A 1 Min, 12A 3 Sec

I/O Options Vector Control with 120V

I/O

Brake IGBT Brake IGBT Installed

Filter Options

Second Environment

Filter per CE EMC

directive (89/336/EEC)

5HP

10 HP Normal

Duty, 7.5 HP

Heavy Duty

PowerFlex700 AC Drive, 480 VAC, 3 PH, 14 Amps, 10

HP Normal Duty, 7.5 HP Heavy Duty, IP20 / Type 1, No

HIM (Blank Plate), Brake IGBT Installed, Without Drive

Mounted Brake Resistor, Second Environment Filter per

CE EMC directive (89/336/EEC), No Communication

Module, Vector Control with 24V I/O, No Feedback

Input Voltage 480 VAC, 3 PH

Current Rating 14 Amps

Enclosure IP20 / Type 1

Frame Size Frame Size 1

Output Current Information Output Amps: 14A Cont,

16.5A 1 Min, 22A 3 Sec

I/O Options Vector Control with 24V

I/O

Brake IGBT Brake IGBT Installed

Filter Options

Second Environment

Filter per CE EMC

directive (89/336/EEC)

97

Appendix C

Software details

Name: DriveExecutive

Description: This software is an online/offline drive and adapter configuration tool that

leverages Windows Explorer-style navigation, built-in html product help, and handy

diagnostic and setup wizards. A state-of-the-art comparison tool lets you look at differences

and make two devices/files the same.

Source: Rockwell Automation

Link: http://www.ab.com/en/epub/catalogs/36265/1323285/9616672/9616694/index.html

Name: DriveExplorer Description: DriveExplorer™ Software is an easy-to-use, cost effective application for

monitoring and online configuration of your PowerFlex® drives and communication

adapters. It makes drive set-up easy and faster than using a Human Interface Module (HIM).

Source: Rockwell Automation

Link: http://ab.rockwellautomation.com/Drives/Software/9306-DriveExplorer

98

Appendix D

Yokogawa WT1600 Digital Power Meter

Description: The WT1600 is power meter designed for measurement of extremely small

currents in energy-saving equipment, as well as measurement of large currents for evaluating

large-sized loads. The WT1600 works with voltages ranging from 1.5 V up to 1000 V,

supporting a wide range of applications. Because it can accept signal inputs for up to six

phases, a signal WT1600 unit can measure I/O signals on inverters.

Source: Yokogawa

Link: http://tmi.yokogawa.com/discontinued-products/digital-power-analyzers/digital-power-

analyzers/wt1600-digital-power-meter/