introduction to industrial drives

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INTRODUCTION To ELECTRICAL DRIVES Presented by, Vinay Shreyas K.V Lecturer, Dept. of EEE H.K.B.K.C.E Bangalore – 045. Chapter - 1

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Page 1: Introduction to Industrial Drives

INTRODUCTION To

ELECTRICAL DRIVES

Presented by,

Vinay Shreyas K.VLecturer, Dept. of EEE

H.K.B.K.C.E Bangalore – 045.

Chapter - 1

Page 2: Introduction to Industrial Drives

INTRODUCTION•Motion control is required in large number of industrial and domestic applications. Ex: Robot, fans, washing m/c, mills etc.Drives – systems employed for motion control are called as drives.

Motion Control – Prime Movers. •Diesel or petrol engines, gas or steam turbines, steam engines, hydraulic motors and electric motors .•Also for supplying mechanical energy for motion control.

Electric Drives – Drives employing Electric Motor as Prime Movers.

Motion Control

Prime Movers

Electric Drives Electric Motors has Prime Movers

Page 3: Introduction to Industrial Drives

ELECTRIC DRIVES

An electric drive is defined as a machine equipment designed to convert electrical energy into mechanical energy and provide electrical control of this process.

(Or)

An electric drive can be defined as an electromechanical device for converting electrical energy into mechanical energy to impart motion to different machines and mechanisms for various kinds of process control.

Page 4: Introduction to Industrial Drives

ADVANTAGES OF ELECTRIC DRIVESThey have flexible control characteristics. The steady state and dynamic characteristics of electric drives can be shaped to satisfy the load requirements.

Drives can be provided with automatic fault detection systems. Programmable logic controller and computers can be employed to automatically control the drive operations in a desired sequence.

Available in wide range of speed, torque and power.

High efficiency, lower noise, low maintenance requirements, no load losses and short time overloading capability.

Can operate in all the four quadrants of speed-torque plane. Electric braking gives smooth deceleration. Regenerative braking is possible.

Page 5: Introduction to Industrial Drives

ADVANTAGES OF ELECTRIC DRIVESElectric energy can be generated and transported to the desired point economically and efficiently.

Do not pollute environment.

They can be started instantly and can immediately be fully loaded

They are adaptable to almost any operating conditions such as explosive and radioactive environments

Page 6: Introduction to Industrial Drives

CONVENTIONAL ELECTRIC DRIVE SYSTEM

•A typical conventional electric drive system for variable speed application employing multi-machine system is shown in Figure.

• The system is obviously bulky, expensive, inflexible and require regular maintenance.

•In the past, induction and synchronous machines were used for constant speed applications – this was mainly because of the unavailability of variable frequency supply.

Page 7: Introduction to Industrial Drives

Block diagram of Electric Drive System

•Electric drives is multi-disciplinary field. Various research areas can be sub-divided from electric drives as shown in Figure 3.

Page 8: Introduction to Industrial Drives

MODERN ELECTRIC DRIVE SYSTEM

With the advancement of power electronics, microprocessors and digital electronics, typical electric drive systems nowadays are becoming more compact, efficient, cheaper and versatile .

The voltage and current applied to the motor can be changed at will by employing power electronic converters.

AC motor is no longer limited to application where only AC source is available, however, it can also be used when the power source available is DC or vice versa

Page 9: Introduction to Industrial Drives

BASIC BLOCK DIAGRAM ELECTRIC DRIVE SYSTEM

A modern electrical drive system has the following components1. Electrical machines and loads 2. Power Modulator or Processor

3. Sources 4. Control unit 5. Sensing unit

PowerSource

Power Processor(Power

ElectronicConverters)

Control Unit

Motor Load

Feed

bac

k

Control

Page 10: Introduction to Industrial Drives

BASIC BLOCK DIAGRAM ELECTRIC DRIVE SYSTEM – POWER SOURCE

• Regulated (i.e., utility) or Un-regulated (i.e., renewable)

• DC Source Batteries Fuel Cell Photovoltaic

• AC Source Single or three phase utility Wind generator.

Page 11: Introduction to Industrial Drives

BASIC BLOCK DIAGRAM ELECTRIC DRIVE SYSTEM – MOTOR

They convert energy from electrical to mechanical - therefore can be regarded as energy converters.

In braking mode, the flow of power is reversed.

Depending upon the type of power converters used, it is also possible for the power to be fed back to the sources rather than dissipated as heat.

There are several types of motors used in electric drives – choice of type used depends on applications, cost, environmental factors and also the type of sources available..

Page 12: Introduction to Industrial Drives

BASIC BLOCK DIAGRAM ELECTRIC DRIVE SYSTEM – MOTOR

Broadly, they can be classified as either DC or AC

•DC motors (wound or permanent magnet) •AC motors •Induction motors – squirrel cage, wound rotor •Synchronous motors – wound field, permanent magnet •Brushless DC motor – require power electronic converters •Stepper motors – require power electronic converters •Synchronous reluctance motors or switched reluctance motor – require power electronic converters

Page 13: Introduction to Industrial Drives

BASIC BLOCK DIAGRAM ELECTRIC DRIVE SYSTEM – POWER MODULATOR

Since the electrical sources are normally uncontrollable, it is therefore necessary to be able to control the flow of power to the motor – this is achieved using power processor or power modulator.

With controllable sources, the motor can be reversed, brake or can be operated with variable speed.

Conventional methods used, for example, variable impedance or relays, to shape the voltage or current that is supplied to the motor – these methods however are inflexible and inefficient.

Modern electric drives normally used power electronic converters to shape the desired voltage or current supplied to the motor.

In other words, the characteristic of the motors can be changed at will.

Page 14: Introduction to Industrial Drives

BASIC BLOCK DIAGRAM ELECTRIC DRIVE SYSTEM – POWER MODULATOR

Power electronic converters have several advantages over classical methods of power conversion, such as

1)More efficient – since ideally no losses occur in power electronic converters 2)Flexible – voltage and current can be shaped by simply controlling switching functions of the power converter. 3) Compact – smaller, compact and higher ratings solid–state power electronic devices are continuously being developed – the prices are getting cheaper

Converters are used to convert and possibly regulate (i.e. using closed-loop control) the available sources to suit the load i.e. motors.

These converters are efficient because the switches operate in either cut-off or saturation modes.

Page 15: Introduction to Industrial Drives

BASIC BLOCK DIAGRAM ELECTRIC DRIVE SYSTEM – POWER MODULATOR In the electric drive system, the power modulators can be

any one of the following

• Controlled rectifiers (ac to dc converters)• Inverters (dc to ac converters)• AC voltage controllers (AC to AC converters)• DC choppers (DC to DC converters)• Cyclo converters (Frequency conversion)

Page 16: Introduction to Industrial Drives

Basic Components of Electric Drives – Power Processing Unit

Page 17: Introduction to Industrial Drives

Basic Components of Electric Drives – Power Processing Unit

Page 18: Introduction to Industrial Drives

BASIC BLOCK DIAGRAM ELECTRIC DRIVE SYSTEM – CONTROL UNIT

The complexity of the control unit depends on the desired drive performance and the type of motors used.

A controller can be as simple as few op-amps and/or a few digital ICs, or it can be as complex as the combinations of several ASICs and digital signal processors (DSPs).

The types of the main controllers can be

• Analog - which is noisy, inflexible. However analog circuit ideally has infinite bandwidth.

Page 19: Introduction to Industrial Drives

BASIC BLOCK DIAGRAM ELECTRIC DRIVE SYSTEM – CONTROL UNIT

•Digital – immune to noise, configurable. The bandwidth is obviously smaller than the analog controller's – depends on sampling frequency. Einstein College of Engineering .

•DSP/microprocessor – flexible, lower bandwidth compared to above. DSPs perform faster operation than microprocessors (multiplication in single cycle).

Page 20: Introduction to Industrial Drives

Choice (or) Selection of Electrical Drives

Choice of an electric drive depends on a number of factors. Some of the important factors are.

1. Steady State Operating conditions requirementsNature of speed torque characteristics, speed regulation, speed range, efficiency,

duty cycle, quadrants of operation, speed fluctuations if any, ratings etc2. Transient operation requirementsValues of acceleration and deceleration, starting, braking and reversing

performance.3. Requirements related to the sourceTypes of source and its capacity, magnitude of voltage, voltage fluctuations, power

factor, harmonics and their effect on other loads, ability to accept regenerative power

4. Capital and running cost, maintenance needs life.5. Space and weight restriction if any.6. Environment and location.7. Reliability.

Page 21: Introduction to Industrial Drives

CLASSIFICATION OF ELECTRIC DRIVEIn general, electric drives may be classified into three categories: Group drive, Individual drive & Multimotor drive.

GROUP ELECTRIC DRIVE•This drive consists of a single motor, which drives (actuates) several mechanisms by means of one or more line shafts supported on bearings.

•The line shaft may be fitted with either pulleys and belts or gears, by means of which a group of machines or mechanisms may be operated. It is also some times called as SHAFT DRIVES.

Advantages• A single large motor can be used instead of number of small motors.•The rating of single large motor may be appropriately reduced taking into account the diversity factor of load.

Page 22: Introduction to Industrial Drives

CLASSIFICATION OF ELECTRIC DRIVE

Disadvantages

•There is no flexibility. If the single motor used develops fault, the whole process will be stopped.

•Addition of an extra machine to the main shaft is difficult.

•The level of noise produced at the worksite is quite high.

•Considerable power loss take place in the energy transmitting mechanisms.

Page 23: Introduction to Industrial Drives

CLASSIFICATION OF ELECTRIC DRIVEIndividual Electric Drive

•In this drive each individual machine is driven by a separate motor. •This motor also imparts motion to various parts of the machine.

Multi Motor Electric Drive

•In this drive system, there are several drives, each of which serves to actuate one of the working parts of the drive mechanisms.

E.g.: •Complicated metal cutting machine tools•Paper making industries,•Rolling machines etc.

Page 24: Introduction to Industrial Drives

CLASSIFICATION OF LOAD TORQUES:Various load torques can be classified into broad categories.

Active load torques

•Load torques which has the potential to drive the motor under equilibrium conditions are called active load torques.

•Such load torques usually retain their sign when the drive rotation is changed. (reversed)

Eg: •Torque due to force of gravity.•Torque due tension.•Torque due to compression and torsion etc

Page 25: Introduction to Industrial Drives

CLASSIFICATION OF LOAD TORQUES:

Passive load torques

•Load torques which always oppose the motion and change their sign on the reversal of motion are called passive load torques.

Eg: •Torque due to friction, cutting, fans, pumps, lathes etc.

Page 26: Introduction to Industrial Drives

Components of Load Torques:

The load torque Tl can be further divided in to following components.

(i) Friction Torque (TF)

•Friction will be present at the motor shaft and also in various parts of the load.

•TF is the equivalent value of various friction torques referred to the motor shaft.

(ii) Windage Torque (TW)

•When motor runs, wind generates a torque opposing the motion. This is known as windage torque.

Page 27: Introduction to Industrial Drives

Components of Load Torques:

(iii) Torque required to do useful mechanical work (TL)

•Nature of this torque depends upon particular application.

• It may be constant and independent of speed.

•It may be some function of speed, it may be time invariant or time variant, its nature may also change with the load’s mode of operation.

Page 28: Introduction to Industrial Drives

Friction torque with speed is shown in figure below

•Its value at stand still is much higher than its value slightly above zero speed.

•Friction at zero speed is called stiction or static friction.

•In order to start the drive the motor should at least exceed stiction.

Page 29: Introduction to Industrial Drives

Friction torque can be resolved into three components

•Viscous Friction (TV)

•Coulomb Friction (TC)

•Static Friction (TS)

Page 30: Introduction to Industrial Drives

Friction torque can be resolved into three components

•Component Tv varies linearly with speed is called VISCOUS friction and is given by•Where B is viscous friction co-efficient.

•Another component TC, which is independent of speed, is known as COULOMB friction.

•Third component Ts accounts for additional torque present at stand still.• Since Ts is present only at stand still it is not taken into account in the dynamic analysis.

Page 31: Introduction to Industrial Drives

Components of Load Torques:

•Windage torque, TW which is proportional to speed squared is given by•C is a constant•From the above discussions, for finite speed.

•If there is a torsional elasticity in shaft coupling the load to the motor, an additional component of load torque known as coupling torque will be present.

Page 32: Introduction to Industrial Drives

Characteristics of Different types of Loads

One of the essential requirements in the section of a particular type of motor for driving a machine is the matching of speed-torque characteristics of the given drive unit and that of the motor.

Therefore the knowledge of how the load torque varies with speed of the driven machine is necessary.

Different types of loads exhibit different speed torque characteristics.

Page 33: Introduction to Industrial Drives

Characteristics of Different types of Loads

However, most of the industrial loads can be classified into the following four categories.

• Constant torque independent of speed.

• Torque proportional to speed (Generator Type load)

• Torque proportional to square of the speed (Fan type load)

• Torque inversely proportional to speed (Constant power type load)

Page 34: Introduction to Industrial Drives

Constant Torque characteristics:•Most of the working machines that have mechanical nature of work like shaping, cutting, grinding or shearing, require constant torque irrespective of speed. •Similarly cranes during the hoisting and conveyors handling constant weight of material per unit time also exhibit this type of characteristics.

Page 35: Introduction to Industrial Drives

Torque Proportional to speed:

•Separately excited dc generators connected to a constant resistance load, eddy current brakes have speed torque characteristics given by T=kω

Page 36: Introduction to Industrial Drives

Torque proportional to square of the speed:

•Another type of load in practice is the one in which load torque is proportional to the square of the speed.Eg: Fans rotary pumps, compressors and ship propeller

Page 37: Introduction to Industrial Drives

Torque Inversely proportional to speed:

•Certain types of lathes, boring machines, milling machines, steel mill coiler and electric traction load exhibit hyperbolic speed-torque characteristics

Page 38: Introduction to Industrial Drives

SPEED TORQUE CONVENTIONS AND MULTI QUADRANT OPERATIONS

• The speed is assumed to be “+”, if the direction of rotation is anticlockwise or in such a way to cause an “upward” or “forward” motion of the drive.– For reversible drive “+” direction of the speed can be assumed arbitrarily either

clockwise or anticlockwise.

•The motor torque is “+”, if it produce increase in speed in the “+” sense (acceleration). But the load torque is assigned the “+” sign when it is directed against the motor torque.

- The motor torque is considered “-” if it produces deceleration.

• A motor operates in two modes i.e., motoring and braking.–Motoring: It converts electrical energy to mechanical energy, which supports its motion.– Braking: It works as a generator, converts mechanical energy to electrical energy, opposes the motion.

Note: Motor can provide motoring and braking operations for both forward and reverse directions.

Page 39: Introduction to Industrial Drives

SPEED TORQUE CONVENTIONS AND MULTI QUADRANT OPERATIONS

•Power developed by the motor is given by the product of speed and torque.–For motoring operations power developed is “+”.–For braking operations power developed is “-”.

•Plot of speed torque characteristics of the load/motor for all four quadrant of operation is known as quadrant diagram.

Page 40: Introduction to Industrial Drives

MULTI QUADRANT OPERATIONS

Page 41: Introduction to Industrial Drives

Torque-Speed Quadrant of Operation

T

• Direction of positive (forward) speed is arbitrary chosen

• Direction of positive torque will produce positive (forward) speed

m

Te

Te

m

Tem

Te

m

Quadrant 1Forward motoring

Quadrant 2Forward braking

Quadrant 3Reverse motoring

Quadrant 4Reverse braking

Figure shows the torque and speed co-ordinates for both forward (positive) & reverse (negative) motions.

Page 42: Introduction to Industrial Drives

Torque-Speed Quadrant of Operation

•In quadrant I, developed power is positive, hence machine works as a motor supplying mechanical energy.

•Operation in quadrant I is therefore called Forward Motoring.

•In quadrant II, power developed is negative. Hence, machine works under braking opposing the motion.

•Therefore operation in quadrant II is known as forward braking.

•Similarly operation in quadrant III and IV can be identified as reverse motoring and reverse braking since speed in these quadrants is negative.

Page 43: Introduction to Industrial Drives
Page 44: Introduction to Industrial Drives

Torque-Speed Quadrant of Operation

•For better understanding of the above notations, let us consider operation of hoist in four quadrants as shown in the figure. •Direction of motor and load torques and direction of speed are marked by arrows.•A hoist consists of a rope wound on a drum coupled to the motor shaft.• One end of the rope is tied to a cage which is used to transport man or material from one level to another level.• Other end of the rope has a counter weight. •Weight of the counter weight is chosen to be higher than the weight of empty cage but lower than of a fully loaded cage. •Forward direction of motor speed will be one which gives upward motion of the cage.

Page 45: Introduction to Industrial Drives

Torque-Speed Quadrant of Operation

•Load torque line in quadrants I and IV represents speed-torque characteristics of the loaded hoist.

This torque is the difference of torques due to loaded hoist and counter weight.

•The load torque in quadrants II and III is the speed torque characteristics for an empty hoist.

•This torque is the difference of torques due to counter weight and the empty hoist.

•Its sigh is negative because the counter weight is always higher than that of an empty cage.

Page 46: Introduction to Industrial Drives

Torque-Speed Quadrant of Operation

•The quadrant I operation of a hoist requires movement of cage upward, which corresponds to the positive motor speed which is in counter clockwise direction here.

•This motion will be obtained if the motor products positive torque in CCW direction equal to the magnitude of load torque.

•Since developed power is positive, this is forward motoring operation.

Page 47: Introduction to Industrial Drives

Torque-Speed Quadrant of Operation

•Quadrant IV is obtained when a loaded cage is lowered. Since the weight of the loaded cage is higher than that of the counter weight .

•It is able to overcome due to gravity itself.

•In order to limit the cage within a safe value, motor must produce a positive torque must have opposite polarity with respect to rotation and acts as a brake.

•The motor torque sign is positive, but as both power and speed are negative, drive is operating in reverse braking operation.

Page 48: Introduction to Industrial Drives

Torque-Speed Quadrant of Operation

•Operation in quadrant II is obtained when an empty cage is moved up.

•Since a counter weigh is heavier than an empty cage, its able to pull it up.

•In order to limit the speed within a safe value, motor must act in the opposite direction of rotation or motor torque must be negative.

•The power will be negative though the speed is positive, so this quadrant is known as forward braking quadrant operation.

Page 49: Introduction to Industrial Drives

Torque-Speed Quadrant of Operation

•Operation in quadrant III is obtained when an empty cage is lowered. (i.e., represents the downward motion of the empty cage)

•Since an empty cage has a lesser weight than a counter weight, the motor should produce a torque in CW direction.

•Since speed is negative and developed power is positive, this is reverse motoring operation.

Page 50: Introduction to Industrial Drives
Page 51: Introduction to Industrial Drives
Page 52: Introduction to Industrial Drives

DYNAMICS OF MOTOR LOAD SYSTEM Fundamentals of Torque Equations•A motor generally drives a load (Machines) through some transmission system. While motor always rotates, the load may rotate or undergo a translational motion.•Load speed may be different from that of motor, and if the load has many parts, their speed may be different and while some parts rotate others may go through a translational motion.•Equivalent rotational system of motor and load is shown in the figure.

Te , m

TL

J

Page 53: Introduction to Industrial Drives

DYNAMICS OF MOTOR LOAD SYSTEMNotations Used:•J = Moment of inertia of motor load system referred to the motor shaft kg − m2•ωm = Instantaneous angular velocity of motor shaft, rad/sec.

•T = Instantaneous value of developed motor torque, N-m

•Tl = Instantaneous value of load torque, referred to the motor shaft N-m•Load torque includes friction and windage torque of motor.•Motor-load system shown in figure can be described by the following fundamental torque equation.

Equation (1) is applicable to variable inertia drives such as mine winders, reel drives, Industrial robots.

Page 54: Introduction to Industrial Drives

DYNAMICS OF MOTOR LOAD SYSTEM

•For drives with constant inertia

•Equation (2) shows that torque developed by motor is counter balanced by load torque Tl and a dynamic torque.

•Torque component is called dynamic torque because it is present only during the transient operations.

Note:•Energy associated with dynamic torque is stored in the form of kinetic energy given by

Page 55: Introduction to Industrial Drives

EQUIVALENT VALUES OF DRIVE PARAMETERS

INTRODUCTION

1. Different parts of load may be coupled through different mechanisms like gears, v-belts etc.

2. Parts may have different speeds and types of motions like rotational and translational.

This section provides equivalent moment of inertia and torque components of motor load system, all referred to motor-shaft.

Page 56: Introduction to Industrial Drives

LOADS WITH ROTATIONAL MOTION

• Motor

• Te

• Load 1, TL0

• Load 2, TL1

• J

0

• J

1

• m

• m

• m

1

• n

• n

1

Consider a motor driving two loads, one coupled directly to its shaft and other through gear with n and n1 teeth as shown below.

Loads with Rotational Motion

•Jo = moment of inertia of motor and load directly coupled to its shaft.

•Motor speed & torque coupled directly to load be ωm and Tlo .

• Moment of inertia, speed & torque of the load coupled through a gear be J1, ωm , Tl1.

Page 57: Introduction to Industrial Drives

LOADS WITH ROTATIONAL MOTIONIf the losses in transmission is neglected, then kinetic energy due to equivalent inertia must be the same as kinetic energy of various moving parts.Therefore, --------------------------(1)

Divide by in equation (1) -----------------------------------------(2)

Gear Teeth Ratio = -------------------------------------(3)

Power at the loads and motor must be same. If transmission efficiency of the gears be η1

Then, --------------------------------------(4)

Page 58: Introduction to Industrial Drives

LOADS WITH ROTATIONAL MOTIONDivide by ωm .

Therefore, -----------------------------------------(5)

If there are m other loads with moment of inertia J1, J2…………..Jm and gear teeth ratios of a1, a2, ………….am then,

If m loads with torques Tl1, Tl2…………..Tlm are coupled through gears with teeth ratios a1, a2, ………….am and transmission efficiencies η1, η2,………ηm in addition to one directly coupled, then

Page 59: Introduction to Industrial Drives

LOADS WITH TRANSLATIONAL MOTIONConsider a motor driving two loads, one coupled directly to its shaft and other through transmission system converting rotational motion to linear motion.

Mass, Velocity and Force of the load coupled through a gear be M1 (Kg), V1 (m/sec),F1 (N).

If the losses in transmission is neglected, then kinetic energy due to equivalent inertia must be the same as kinetic energy of various moving parts.

MotorTe

Load 1, TL0

Load 2, TL2

J0

m

v1

Rotational to linear motion transmission

Mass M1 force F1

Page 60: Introduction to Industrial Drives

LOADS WITH TRANSLATIONAL MOTION

---------------------------------------(1)

Divide by in equation (1)

Power at the loads and motor must be same. If transmission efficiency of the gears be η1

If there are m other loads with translational motion with velocities V1,V2…………..Vm and masses M1, M2, ………….Mm respectively, then

If m loads with torques Tl1, Tl2…………..Tlm are coupled through gears with teeth ratios a1, a2, ………….am and transmission efficiencies η1, η2,………ηm in addition to one directly coupled, then

Page 61: Introduction to Industrial Drives

STEADY STATE STABILITY

The question : •What is the criterion for steady state stability of an electric drive?

•Starting from fundamentals, derive a relationship between load torque and motor torque for steady state stability.

Page 62: Introduction to Industrial Drives

STEADY STATE STABILITY OF AN ELECTRIC DRIVE

•The drive is said to be in equilibrium if the torque developed by the motor is exactly equal to the load torque.

•The stability of the motor load combination is defined as the capacity of the system which enables it to develop forces of such a nature as to restore equilibrium after any small departure therefore.

•Equilibrium state of the drive mainly disturbs because of the following two types of disturbances,

1.Changes from the state of equilibrium takes place slowly therefore the effect of inertia of the rotating masses is insignificant2.Sudden and fast changes from the equilibrium state, as a result of which the effect of both inertia and inductance can not be neglected.

Page 63: Introduction to Industrial Drives

STEADY STATE STABILITY OF AN ELECTRIC DRIVE

The system is said to be stable - sometimes after the appearance of disturbance it attains a new equilibrium condition.

The system is said to be unstable - comes to rest or continuous increase in speed following disturbance i.e sysem is unable to take up a new equilibrium position

Page 64: Introduction to Industrial Drives

Steady state stability of an electric drive

• The equilibrium point will be termed as stable state when the operation will be restored to it

• Let the disturbance causes a reduction of ∆ωm

in speed.

• At new speed, electrical motor torque TM is greater than the load torque, motor will accelerate and operation will be restored to point A.

• similarly an increase in ∆ωm speed caused by a disturbance will make load torque greater than the motor torque, resulting in deceleration and restore the operation to point A.

Therefore, drive is steady state stable at point A.Consider the speed-torque

characteristics at the equilibrium point be A.

Page 65: Introduction to Industrial Drives

Steady state stability of an electric drive

•Now consider equilibrium point B which is obtained when the same motor drives another load as shown in the figure.

•A decrease in speed causes the load torque to become greater than the motor torque, electric drive decelerates and operating point moves away from point B.

•Similarly when working at point B and increase in speed will make motor torque greater than the load torque, which will move the operating point away from point B

Page 66: Introduction to Industrial Drives

Steady state stability of an electric drive

From the above discussions: A machine is stable if its load speed torque curve are such that for

i) A decrease in speed, TM > TL

ii) A increase in speed, TL > TM

Page 67: Introduction to Industrial Drives

Steady state stability of an electric drive

Let the equilibrium of the torques and speed is TM, TL and ω and the small deviations are ∆TM, ∆TL and ∆ω.

After the displacement from the equilibrium state the torque equation becomes, the torque equation becomes

Page 68: Introduction to Industrial Drives

Steady state stability of an electric drive

Considering the small deviation, changes can be expressed as a linear function of change in speed,

From the torque equation, where all quantities are expressed in terms of their deviations from the equilibrium,

Page 69: Introduction to Industrial Drives

Steady state stability of an electric drive

Solution is,

Where ∆ωm, is the initial value of the deviation in speed. For the stable system the exponent must be negative, so speed increment will disappear with time. The exponent will always be negative if,

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