A Modified Torque Control Approach for Load Sharing Application

Using V/F Induction Motor Drives

Abstract: The volt-per-Hertz (V/F) drives of induction motors (IMs) are widely used in industrial applications because these drives are simple and cost effective. V/F drives operation is based on speed command and unable to toque control. In industrial applications the IMs are coupled to feed heavy loads. Coupling the IMs in addition to economic advantage leads to reduction of energy consumption. When the load becomes heavier the number of IMs that feed the load will be increased and vice versa. However with coupled IMs, the load is not shared properly and some of the IMs may be overloaded. For a proportional load sharing using of the torque control drives seems to be necessary, but these drives are complicated and expensive. This paper describes a torque control approach for coupled IMs V/F drives which is accurate and inexpensive and also uses minimum number of motor parameters.

Keywords: induction motors, V/F control, load sharing,

variable frequency drives

1. Introduction

Mechanically coupled induction motors (IMs) are

widely used in industrial applications such as conveyor

belts for transportation of raw material, mill motors used

in iron and pulp and paper industries, mining drills, etc.

“Load sharing” is a term used by many to describe a

system where multiple drive and motor sets are coupled

and used to run one mechanical load. In the strictest

sense, load-sharing means that the amount of torque

applied to the load from each motor is prescribed and

carried out by each drive and motor set. [1], [3]. Each

drive and motor set must provide its proportional share of

power to the driven load. In load sharing, for torque

control possibility of individual motors, each motor must

have an individual drive set. The drive sets must be

interconnected, interconnecting the drive sets make it

possible to have a comparison between the drives and

generate an error signal, which is used to compensate

unbalanced load sharing of the drive sets.

The drive sets of motors range from the more

advanced and expensive vector-controlled schemes to the

conventional Volts-per-Hertz (V/F) control. The vector-

controller is capable to speed and torque control and can

implement load sharing schemes such as torque-follower

or trim control; hence this controller excels to the others

[1]. Therefore, the V/f controller is widely used in many

industrial applications mainly due to its simplicity and

low cost. Since a volts/hertz drive does not have the

ability to run in “torque mode”, a more loose

interpretation of the term “load sharing” is sometimes

used. Load sharing on a volts/hertz drive is much less

controllable and to a large extent dependent on the motor

and type of load coupling.

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 out merely through rigid couplings, although the

proposed concepts may be extended to other cases.

Fig. 1: block diagram of a conventional V/F speed control scheme

General diagram of the conventional V/F drive is

shown in Fig. 1. Reference and actual speeds are applied

to speed control block, then resultant speed reference is

converted to the voltage reference according to the

following equation [4]:

bs ref

b

VV

(1)

Where, bV and b are the base voltage and base angular

frequency of the machine respectively.

The torque-speed characteristic of the IM depends on

the applied voltage, frequency and the rotor resistance. In

practice, the rotor resistance changes with load variations,

temperature and frequency of rotor current [5], [6].

Furthermore the equivalent rotor resistances may be

different even in two identical motors. Consequently the

torque-speed characteristics of two identical machines

may be non-identical. Different torque-speed

characteristics cause improper load sharing of the IMs. In

Mohammad Amiri*, Mohammad Reza Feyzi **, and Hossein Saberi*** *University of Tabriz, m_amiri89@ms.tabrizu.ac.ir

** University of Tabriz, feyzi@tabrizu.ac.ir

*** University of Tabriz, h_saberi89@ms.tabrizu.ac.ir

a load sharing system composed of several machines,

such deviations in the rotor resistance value has undesired

effects in the load sharing.

A modified scheme for decreasing motor parameter

deviation effect is proposed in [8]. This scheme relies on

output torque equation in steady state and can decrease

deviation effect and consequently an approximated

balance load sharing is achieved. It should be noted that

this scheme is based on approximated equation of output

torque that can be used just in low slip values. This

equation is also dependent to motor parameters and so

accurate values of motor parameters are needed in this

scheme. When heavy loads are applied to the system, slip

increases and causes large error in the approximated

equation of torque output. This error results in improper

load sharing between the motors. The problem can be

more severe if a number of various machines with

different parameters are interconnected. This issue is

further discussed in the next section and a new and

modified V/F control scheme is proposed to ensure a

proportional load sharing of the motors with respect to

their rated power

2. Problem Definition

The V/F drives are generally investigated in steady

state, where the torque equation is given by [5] 2

2 2

/3

2 ( / ) ( )

th re

e th r th r

V r sPT

R r s X X

(2)

thV , thR and thX are the Thevenin equivalent circuit

parameters and is the electrical frequency of the source.

Two IMs and V/F drives are considered to provide the

mechanically coupled load as shown in Fig. 2. From (2)

the IM output toque relies on its parameters and rated

values. Impressing the same reference speed to V/F

drives will apply voltages with the same magnitude and

frequency to the motors. The IMs with different

parameters which have same speed reference, have

different torque speed characteristics. Coupling IMs with

different torque speed characteristics yields to different

torque values for the IMs. The torque value is determined

based on motor parameters therefore it is not proportional

to the rated power of the IMs. Consequently one or some

of the IMs may be overloaded.

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

motors

Fig. 3: Torque-speed characteristics of IM1 and IM2 using the

conventional V/F scheme

In this paper, two 5 and 10 horse power (hp) IMs are

considered. The parameters and rated values of each IM

are given in the appendix. A mechanical load of 60 N.m

is applied to the machines at the speed of 184.9 rad/sec.

The difference between motor outputs is shown in the

Fig. 3. The torque values of the IMs are given in Table II.

As shown in Table II, the 10 hp IM is overloaded by

5.05% but the 5 hp IM is operating 11.1 % below the

rated torque.

In load sharing applications to assimilate the IMs

parameters which lead to assimilation of torque speed

characteristics, the identical IMs have to be used.

When two low resistance motors with low slip in

operation region are coupled mechanically, small

differences in motor speeds result in large differences in

motor torques and consequently one of the motors will be

overloaded quickly. In other words, in high slip motors

the characteristic slope in operation region is lower than

high slip motors and changes in speed and torque are

small and load sharing can be implemented better. Hence

for load sharing applications, the high slip motors are

preferred [7]. On the other hand, high-slip motors have

higher copper loss and lower efficiency. Therefore, using

the traditional method for load sharing has the trade-off

between the proportional load sharing and high

efficiency.

Clearly load sharing has several advantages. Some of

the advantages include: limitless increasing of the power

and consequently increasing the effectiveness, optimum

energy consumption, and generally economic benefits.

However using identical, high slip and low efficiency

motors are the shortcomings of the traditional load

sharing methods. These shortcomings are originated from

this fact that a simple V/F drive is not able to torque

control. However drives with torque control ability are

complicated and expensive and sometimes the traditional

methods are preferred in trade off between traditional

methods and drives with torque control ability. This is a

reason for modifying the V/F drives in order to achieve

proportional load sharing among any number of different

motors with comparative price.

3. Proposed Scheme

n the proposed approach IMs torque control and load

sharing is performed by modifying the reference speed of

the IM drives. If different speed references are applied to

the IMs, different voltages with different frequencies will

be fed to the IMs and consequently from (2) the IM

torque values will be changed. So with increasing the

speed reference of the IM, which is operating below the

rated torque, contribution of the IM from load torque will

be increased and vice versa. In this method to determine

final speed reference of the IMs a speed correction block

is located next to the regulator block.

Speed correction block needs the speed reference

which is determined by speed regulator block and torque

values of IMs which are obtained from torque estimation

methods [9] to calculates the final speed reference for the

IMs. In this method just one speed regulator and speed

correction block is used to torque control of a number of

IMs and share the load proportional to their rated power.

It should be noted that the speed correction block just

needs the rated power of the IMs for load sharing and

does not rely on any motor parameter. However when

torque estimation methods are used the stator resistance

will be needed. Stator resistance value is almost a

constant value and simple to determine.

The new scheme is shown in Fig. 4. The speed

regulator block is used for adjusting the IM speed to the

speed command. In speed regulator block the speed

command is compared to IM speed feedback and an error

signal is generated. The PI controller converts the error

signal to a suitable reference speed. The obtained

reference speed is delivered to speed correction block. In

speed correction block, the total torque developed by the

IMs is calculated. Then the torque reference for each IM

proportional to its rated power is obtained from

aggregated torque. The torque reference of each IM is

compared to its developed torque and an error signal is

generated. A PI controller converts the error signal to

speed reference adjustment signal. The signal adjusts the

speed reference to suitable speed reference that shares the

load proportionally as shown in Fig. 5.

Fig. 4: Block diagram of the proposed improved V/F scheme.

Fig. 5: Torque-speed characteristics of IM1 and IM2 using the proposed

improved V/F scheme.

The output torque values of the motors by using

proposed approach are given in Table III. Comparison of

Table II and III, shows capability of proposed scheme.

This method can be readily extended to several different

motor. As it is mentioned, this method does not need the

motor parameters and so it has impressive accuracy and

flexibility. The proposed method is very simple and easy

to implement.

4. Simulation Results

To provide a benchmark for evaluating the

performance of proposed scheme simulation results are

presented in two different parts. In the first section, two 5

and 10 hp IMs are considered. In the second section, the

simulation is done with three 5, 10 and 20 hp IMs.

The simulations are performed in MATLAB\Simulink

environment. The parameters and rated values of the IMs

are given in the appendix. In each section two types of

diagrams are presented as follow: (1) reference speed and

actual speed of the IMs, with and without the proposed

scheme (2) developed torque of each IM with and without

the proposed scheme.

4.1 Section 1

This section investigates the accuracy and performance

of the proposed approach and sharing the load between

different IMs. Two 5 and 10 hp IMs, IM1 and IM2

respectively, are considered. A mechanical load of 60

N.m has been applied to the machines in second one. The

simulation results are presented in Fig. 6-8.

0.5 1 1.51600

1650

1700

1750

1800

1850

1900

1950

2000

Time (sec)

Speed (

rpm

)

Actual Speed

Reference Speed

(a)

0.5 1 1.5

1600

1700

1800

1900

2000

Time (sec)

Speed (

rpm

)

Actual Speed

Reference Speed

(b)

0.5 1 1.51600

1700

1800

1900

2000

Time (sec)

Speed (

rpm

)

Actual Speed

Reference Speed

(c)

Fig. 6: Speed diagram of: (a) IM1and IM2 using the traditional V/F scheme; (b) IM1 using the proposed improved V/F scheme; and (c) IM2

using the proposed improved V/F scheme

0.5 1 1.5-10

0

10

20

30

40

Time (sec)

Torq

ue (

Nm

)

(a)

0.5 1 1.5-20

0

20

40

60

80

Time (sec)

Torq

ue (

Nm

)

(b)

Fig. 7: Torque diagram using the traditional V/F scheme for: (a) IM1;

and (b) IM2.

0.5 1 1.5-10

0

10

20

30

40

Time (sec)

Torq

ue (

Nm

)

(a)

0.5 1 1.5-20

0

20

40

60

80

Time (sec)

Torq

ue (

Nm

)

(b)

Fig. 8: Torque diagram using the proposed improved V/F scheme

for: (a) IM1; and (b) IM2.

Table I Reference speed of im1 and im2

IM No. Power (hp)

Speed reference using the traditional scheme (rpm))

Speed reference using the proposed scheme (rpm

1 5 1841 1845.5

2 10 1841 1839

Table II Electromagnetic torque developed by IM1 and IM2 using the

traditional V/F scheme.

IM No. Power (hp) Te (Nm) e

rated

T

T

1 5 17.95 89.75%

2 10 42.05 105.125

Table III Electromagnetic torque developed by IM1 and IM2 using the

proposed improved V/F scheme.

IM No. Power (hp) Te (Nm) e

rated

T

T

1 5 20 100%

2 10 40 100%

A meaningful and concise abstract is required. The

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reflecting the subject matter.

4.2 Section 2

This section demonstrates ability of the proposed

approach for extending to any number of different IMs

with any arrangement. In this section, three IMs, 5, 10

and 20 hp are considered as shown in Fig. 9.

Fig. 9: Block diagram of the proposed improved V/F scheme.

A mechanical load of 140 N.m has been applied to the

machines in second one. The results are shown in Fig. 10-

12.

0.5 1 1.51600

1650

1700

1750

1800

1850

1900

1950

2000

Time (sec)

Speed (

rpm

)

(a)

0.5 1 1.51600

1650

1700

1750

1800

1850

1900

1950

2000

Time (sec)

Speed (

rpm

)

Actual Speed

Reference Speed

(b)

0.5 1 1.51600

1650

1700

1750

1800

1850

1900

1950

2000

Time (sec)

Speed (

rpm

)

Actual Speed

Reference Speed

(c)

0.5 1 1.51600

1650

1700

1750

1800

1850

1900

1950

2000

Time (sec)

Speed (

rpm

)

Actual Speed

Reference Speed

(d)

Fig. 10: Speed diagram of (a) IM, IM2, and IM3 using the traditional

V/F scheme; (b) IM1 using the proposed improved V/F scheme; (c) IM2

using the proposed improved V/F scheme; and (d) IM3 using the proposed improved V/F scheme.

0.5 1 1.5-20

-10

0

10

20

30

40

50

Time (sec)

Torq

ue (

Nm

)

(a)

0.5 1 1.5-20

0

20

40

60

80

Time (sec)

Torq

ue (

Nm

)

(b)

0.5 1 1.5-50

0

50

80

100

150

200

Time (sec)

Torq

ue (

Nm

)

(c)

Fig. 11: Torque diagram using the traditional V/F scheme for: (a) IM1;

(b) IM2; and (c) IM3

0.5 1 1.5-40

-20

0

20

40

60

Time (sec)

Torq

ue (

Nm

)

(a)

0.5 1 1.5-40

-20

0

20

40

60

80

Time (sec)

Torq

ue (

Nm

)

(b)

0.5 1 1.5-100

0

80100

200

Time (sec)

Torq

ue (

Nm

)

(c)

Fig. 12: Torque diagram using the proposed improved V/F scheme for:

(a) IM1; and (b) IM2.

Table IV Reference speed of IM1 and IM2

IM No. Power (hp)

Speed reference using the traditional scheme (rpm))

Speed reference using the proposed scheme (rpm

1 5 1832 1845.2

2 10 1832 1838

3 20 1832 1827.7

Table V Electromagnetic torque developed by IM1 and IM2 using the

traditional V/F scheme.

IM No. Power (hp) Te (Nm) e

rated

T

T

1 5 14.28 71.4%

2 10 33.85 84.625%

3 20 91.87 114.84%

Table VI Electromagnetic torque developed by IM1 and IM2 using the

proposed improved V/F scheme.

IM No. Power (hp) Te (Nm) e

rated

T

T

1 5 20 100%

2 10 40 100%

3 20 80 100%

The results and torque values given in Table IV-VI,

show the development ability of proposed approach. As

shown, by using the proposed scheme the load is shared

proportional to the IMs rated power with an impressive

accuracy. Also in this method gain values of the PI

controllers are constant and they should not be adjusted

with any change in arrangement and type of IMs. This is

another advantage of this approach

5. Conclusion

A new approach to torque control of induction motors

in load sharing application with V/F drives is proposed.

Performance and accuracy of proposed method for load

sharing between different IMs is investigated. Simulation

results verify effectiveness, accuracy and flexibility of

proposed method in different arrangement. This method

is more accurate and demonstrates better load sharing

than the previous methods.

The independency of the approach to motor

parameters is specified. Also it is mentioned that if the

torque estimation methods are used, the stator resistance

value will be needed. This parameter is almost a constant

value and simple to determine.

Feature works will devote to energy consumption

reduction and optimization. In feature schemes, the

quantity of load will determine the motor types which

provide the load. So with increasing the load the number

of IMs which provide load is increased and vice versa.

Appendix

Induction Machines Parameters:

A. IM1

5 hp, 460 V, 60 Hz, 1750 rpm, 4 Pole.

rs=1.115 Ω, rr=1.083 Ω, Xls=2.25 Ω, Xlr=2.25 Ω,

Xm=76.793 Ω, Treated=20 N.m, , J=0.02 N.m

B. IM2

10 hp, 460 V, 60 Hz, 1760 rpm, 4 Pole.

rs=0.6837 Ω, rr=0.451Ω, Xls=1.5653 Ω, Xlr=1.5653 Ω,

Xm=56.021 Ω, Treated=40 N.m, , J=0.05N.m

C. IM3

20 hp, 460 V, 60 Hz, 1760 rpm, 4 Pole.

rs=0.2761 Ω, rr=1645 Ω, Xls=0.826 Ω, Xlr=0.826 Ω,

Xm=28.7 Ω,Treated=80 N.m, , J=0.1N.m

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