an improved vf control scheme for symmetric load sharing of multi-machine induction motor drives1

7/27/2019 An Improved VF Control Scheme for Symmetric Load Sharing of Multi-machine Induction Motor Drives1

1/4

AN IMPROVED V/F CONTROL SCHEME FOR SYMMETRIC LOAD SHARING OF

MULTI-MACHINE INDUCTION MOTOR DRIVES

Jaishankar Iyer, Kamran Tabarraee, Sina Chiniforoosh, and Juri Jatskevich

Electrical and Computer Engineering, University of British Columbia, Vancouver, Canada

ABSTRACT

The traditional low-cost Volts-per-Hertz (V/F) induction

motor (IM) drives typically operate based on speed

command, whereas the developed torque is consequently

determined according to the torque-speed characteristics of

the machine. In multi-machine load-sharing applications, it

is preferred to have number of identical IMs; whereas in

practice, deviations among motor parameters is probable

and will result in disproportionate sharing of the mechanicalload and even overloading one or several machines. In this

paper, an improved V/F scheme is presented, which

compensates for possible variations in the motor parameter

(e.g. rotor resistance) and balances the load accordingly.

The new method is shown to be effective and easy to

implement, and may be readily extended to an arbitrary

number of motors driving a common load.

Index Terms induction motors, V/F control, load

sharing, variable frequency drives.

1. INTRODUCTION

Multi-motor-driven loads can be found in a wide range of

applications in industry such as conveyor belts for

transportation of raw material, mill motors used in iron and

pulp and paper industries, mining drills, etc. The term load

sharing is commonly used when describing such systems

wherein typically a number of mechanically-coupled

induction motors (IMs) are fed by corresponding variable

frequency drives (VFDs) as shown in Figs. 1(a) and (b) [1].

These VFDs range from the more advanced and expensive

vector-controlled schemes, wherein the torque control may

be achieved practically instantaneously, to the conventional

Volts-per-Hertz (V/F) control which relies on steady-state

analysis and is often used along with a closed-loop speed

regulator as shown in Fig. 1(c). The former is advantageousbecause it is capable of both speed and torque control and

can implement load sharing schemes such as torque-

follower or trim control [1]. Nevertheless, the latter is

widely used in many industrial applications mainly because

of simplicity and low cost.

The properties of a load sharing system also depend on

the type of coupling used between the motors [2].The focus

in this paper is on the cases that the load sharing is carried

IMn

LOAD

VFD1

VFD2

VFDn

(a)

IM2

IM1

Speed feedback

IMn

IM1

IM2

VFD

(b)

LOAD

(c)

Speed feedback

V/F ControlSpeed Command IM1Speed

Control

RegulatorVSI

Speed feedback

Fig. 1. Different load sharing configurations: (a) multiple motors driven byindividual drives; (b) multiple motors driven by a single drive unit; and (c)block diagram of a conventional V/F speed control scheme.

out merely through rigid couplings, although the proposed

concepts may be extended to other cases.

As seen in Fig. 1, generally, the machines may be fedfrom either a set of drive units (a) or a single drive unit (b).

In its strictest sense, however, a load sharing scheme

requires that the fraction of torque applied to the load by

each motor can be dictated by the drive-motor set [1], [3].

From this viewpoint, the configuration of Fig. 1(b) is not

deemed effective since therein the torque developed by each

machine is determined according to the corresponding

torque-speed characteristics.

For the purpose of this paper, the V/F control depicted

in Fig. 1 is assumed to operate only in speed control mode.

Here, the speed command and feedback signals are fed into

the speed regulator block as seen in Fig. 1(c). The resulting

speed reference is then converted to the voltage referenceaccording to the following equation [4]:

refb

bs

VV

= . (1)

Here, the base voltage and base angular frequency of the

machine have been denoted by bV and b , respectively.

The torque-speed characteristic of the IM depends on the

applied voltage, frequency and the rotor resistance. In

practice, the equivalent rotor resistance values of two

IEEE CCECE 2011 - 001487


2/4

similar machines may not be equal even if they come from

the same manufacturer. 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 to the deep-rotor-bar effect, which

depends on the rotor design [5], [6]. In a load sharing

system composed of several machines, such variations in the

value of rotor resistance results into different torque-speed

characteristics for the machines and hence different values

of developed electromagnetic torque. In other words, the

load will not be equally shared among the motors and/or the

symmetry might gradually deteriorate due to changes in

loading, temperature, etc. This issue is further discussed in

the next section and a new and improved V/F control

scheme is proposed to ensure a symmetric load sharing

among the motors despite.

2. PROBLEM DEFINITION AND MOTIVATION

Herein, two identical IMs are considered to be mechanically

coupled and fed by VFDS with corresponding V/F controlas seen in Fig. 2. The analysis, however, may be further

extended to any number of machines. The steady state

operating torque developed by each IM is given by [5]

( ) ( )22

2

23

rthrth

r

e

the

XXsrR

srVPT

+++

=

, (2)

where thV , thR , and thX are the Thevenin equivalent

circuit parameters obtained from the equivalent circuit of

Fig. 3, and e is the electrical frequency of the source. In

the motoring region where the slip is typically low, (2) may

be approximated by

( ) reth

r

r

e

the

rsVP

srsrVPT =

2

2

2

23

23 . (3)

As seen in (3), the torque-speed characteristic isapproximated by a linear equation in the low-slip region.

The dependency of the developed torque on the voltage,

frequency, and rotor resistance is evident in (2) and (3). In

the V/F controlled scheme of Fig. 2, the voltage andfrequency are dictated by the speed control regulator block

according to (1) and the actual and command speed signals.

Since these speed signals are the same for both drives, the

same voltages and frequencies will be injected into bothmachines. Therefore, if the rotor resistance values aredifferent, the corresponding amounts of electromagnetic

torque developed by the machines will be different, and theload will not be equally shared between the machines.

As a result of this, one machine will be responsible for

carrying a higher fraction of the load.

The above-mentioned problem is clarified in the torque-speed characteristics depicted in Fig. 4 for the induction

machines with parameters given in the Appendix. Here, the

two machines are identical except the rotor resistance,

which are 06.5 and 41.7 for IM1 and IM2,

respectively. A mechanical load of mN.1.8 has been

applied to the machines atsec

188 rad . It is observed that,

as predicted by (3), the motor with the smaller rotor

resistance, IM1, carries a higher percentage of the load thanmotor IM2.

Fig. 2. Load sharing between two V/F controlled induction motors.

'

rr

s

Fig. 3. Equivalent circuit of an Induction Machine.

Fig. 4. Torque-speed characteristics of IM1 and IM2 using the conventionalV/F scheme.

The values of electromagnetic torque developed by the

machines are provided in Table I. It can be seen that IM1 isoverloaded by 18% whereas the other machine is operating

below the rated torque. The problem could become more

severe if a larger number of machines are interconnected.

The asymmetry in the load sharing is even more pronouncedfor the IMs with a low rotor resistance where the slope of

the torque-speed characteristic becomes higher in magnitudeand the characteristic is very steep in the low-slip region

according to (3). Indeed, high-slip motors are preferred for

load sharing in applications such as conveyor belts to reduce

IEEE CCECE 2011 - 001488


3/4

the effects of belt stretch and improve the load sharing

among belt-coupled drums [7]. However, high-slip motors

have higher copper loss and lower efficiency. Therefore,using the traditional method for load sharing has the trade-

off between the symmetric load sharing and high efficiency.

This is the motivation for modifying the traditional V/F

scheme in order to achieve a symmetric load sharing among

possibly different motors.

Table I. Electromagnetic torque developed by IM1 and IM2 using the

conventional V/F scheme.

IM1 ( = 06.5rr ) IM2 ( = 41.7rr )

( )eT Nm e

rated

T

T ( )eT Nm

e

rated

T

T

4.77 118% 3.33 82%

3. PROPOSED SCHEME

The torque generated in the motoring region is a

function of voltage, electrical frequency and rotor resistance(see (3)). For the IMs, with different rotor resistances, inorder to have the same operating torque, the voltage and the

frequency fed to the machines should be different. This inturn requires different speed references. For the torques to

be equal, the following equation should be satisfied:

2

2

2

22

1

1

1

21 .

23

23

re

th

re

th

r

sVP

r

sVP

= . (4)

Solving (4) results in

( )r

S

S

r

r

M

M

reeX

X

r

r

X

X +

=

1

2

1

2

2

1

12, (5)

where e is the electrical frequency, MX is the magnetizing

inductance,S

X is the stator self inductance. The suffix 1 and

2 denotes IM1 and IM2. This equation will be used to

generate the reference speed for the second drive. The new

scheme is shown in Fig. 5 where the Speed referencecorrection block is formed using (5). The second drive is

now operating without the speed control regulator block and

the actual speed feedback is taken as the Speed reference

correction block. From (5), it is seen that the speed

reference to the second drive is varied as per the change in

the rotor resistance. Therefore, the motors will be operatingwith different voltages and synchronous speeds.

Employing the proposed approach, the improved load

sharing for the case discussed in the previous section isshown in Fig. 6. Notice that the maximum torque is nowdifferent for the motors indicating that different voltages and

frequencies are injected into the machines. It is alsoobserved that the machines are running with different

synchronous speeds unlike the case in Fig. 4. Most

importantly, the torque-speed characteristics of the

machines now intersect near the commanded speed which

results in almost equal values for torque. It should be noted,

however, that the intersection does not take place exactly at

the commanded speed. This is of course due to using the

approximation (3) in the model.

Fig. 5. Block diagram of the proposed improved V/F scheme.

Fig. 6. Torque-speed characteristics of IM1 and IM2 using the proposedimproved V/F scheme.

Table II. Electromagnetic torque developed by IM1 and IM2 using theproposed improved V/F scheme.

IM1 ( = 06.5rr ) IM2 ( = 41.7rr )

( )eT Nm e

rated

T

T ( )eT Nm

e

rated

T

T

4.1 101% 4 99%

Comparing the torque values in Table II with those of

Table I, it is seen that, using the proposed scheme, the loadsharing has become symmetrical between the machines and

the overloading is removed. Each of the motors now shares

roughly 50% of the load. Consequently, a lower-slip motor

can be used, if desired, to increase the efficiency of thesystem without the risk of overloading and possible

breakdown.

The above scheme can be readily extended to multiplemotors (more than two). It can be realized in practice, by

implementing the Speed reference correction block in a

PLC or similar logical device. The first drive is speed

referenced as per the required speed and the second drive is

speed referenced by the Speed reference correction block.

IEEE CCECE 2011 - 001489


4/4

4. OPERATION UNDER INCREASED LOADING

It is well understood that (3) only holds when the slip issmall and the machine operates near the synchronous speed.

With the increased loading, as slip increases, the torque-speed curve gradually loses its linearity. It is then expected

that the performance of the proposed scheme would be

superior under lighter loads and deteriorate as the machine

gets more heavily loaded.In order to investigate the above-mentioned

characteristic, the IMs considered in this paper have been

subjected to 25%, 50% and 100% loading. The torque

developed by the two machines using the conventional and

proposed V/F schemes has been superimposed in Fig. 7.

Fig. 7. Load sharing under different loading conditions.

As seen in this figure, using the proposed scheme the

loading of the machines is essentially equal at 25% load andhas a difference of 2% at full loading. However, using the

conventional method, the load is never shared equally

among the machines and the difference ranges from 10% at

25% loading to 36% at full loading.

The percentage of loading for the motors at differentloading conditions is shown in Table III. It is seen that in the

conventional scheme, IM1 is overloaded when the system is

subjected to the full loading. At the same time, this is

completely avoided using the proposed scheme.

Table III. Comparison of the conventional (a) and proposed (b) schemesunder different loading conditions.

(a)

Loading IM1 IM2

( )eT Nm e

rated

T

T ( )eT Nm

e

rated

T

T

25% 1.21 30% 0.82 20%

50% 2.40 59% 1.65 41%

100% 4.77 118% 3.33 82%

(b)

Loading IM1 IM2

( )eT Nm e

rated

T

T ( )eT Nm

e

rated

T

T

25% 1.01 25% 1.01 25%

50% 2.03 50% 2.02 50%

100% 4.10 101% 4.00 99%

5. CONCLUSION

A new and improved V/F scheme was proposed for

symmetric load sharing between mechanically-coupled

induction motors. It is assumed that the trend in the rotorresistance variation with respect to slip is known. The

proposed scheme has better load sharing under different

loading conditions compared to the traditional method. The

possibility of load sharing among drives under V/F control

using measurable parameters like stator currents andvoltages is under study and will be the topic of further

research.

6. APPENDIX

Induction Machines (IM 1 and 2) Parameters:Baldor Reliance, 1 hp, 480 V, 60 Hz, 1750 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= .

7. REFERENCES

[1] P, Rockwell Automation-Load Sharing Applications for AC DrivePublication Number DRIVES-WP001A-EN-P June 2000

[2] Jeftenic, B.; Bebic, M.; Statkic, S.; , "Controlled multi-motor drives,"Power Electronics, Electrical Drives, Automation and Motion, 2006.SPEEDAM 2006. International Symposium on , vol., no., pp.1392-1398, 23-26 May 2006

[3] N. Mitrovic, V. Kostic, M. Petronijevic, B. Jeftenic, "Multi-MotorDrives for Crane Application," Advances in Electrical and ComputerEngineering, vol. 9, no. 3, pp. 57-62, 2009.

[4] P. Krause, O. Wasynczuk, S. Sudhoff, Analysis of ElectricMachinery and drive system Second Edition ISBN 9812-53-150-5

[5] P. C. Sen, Principles of electric machines and power electronics,2nd Edition, John Wiley & Sons, 1996.

[6] Foroosh, S.C.; Liwei Wang; Jatskevich, J.; , "A simple inductionmachine model for predicting low frequency dynamics," Electricaland Computer Engineering, 2008. CCECE 2008. CanadianConference on , vol., no., pp.001655-001660, 4-7 May 2008

[7] Paulson, G. E. Motor Selection for Belt-Conveyor Drives presentedat the Tenth CIM Maintenance/Engineering Conference, Saskatoon,Saskatchewan September 13-16, 1998.

IEEE CCECE 2011 - 001490

an improved vf control scheme for symmetric load sharing of multi-machine induction motor drives1

Documents