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INTRODUCTION TO ELECTRICAL DRIVES

Drives are employed for systems that require motion control – e.g. transportation system, fans, robots, pumps, machine tools, etc. Prime movers are required in drive systems to provide the movement or motion and energy that is used to provide the motion can come from various sources: diesel engines, petrol engines, hydraulic motors, electric motors etc. Drives that use electric motors as the prime movers are known as electrical drives. It is estimated that about half of electricity generated is converted to mechanical energy and this conversion is performed using electric drives. There are several advantages of electrical drives:

a. Flexible control characteristic – This is particularly true when power electronic converters are employed where the dynamic and steady state characteristics of the motor can be controlled by controlling the applied voltage or current.

b. Available in wide range of speed, torque and power; they are available in mW up to MW range.

c. High efficiency, low noise, low maintenance requirements and cleaner operation d. Electric energy is easy to be transported over long distances. e. Adaptable to various operating conditions: explosive, submerged in liquid, various types

of mounting, etc f. Can be started instantly and can be fully loaded immediately (no need to warm-up or re-

fueling the motor) A typical conventional electric drive system for variable speed application employing multi-machine system is shown in Figure 1, which also known as the Ward-Leonard system. The variable speed of the load is obtained by varying the terminal voltage of the DC motor, which is fed by the DC generator. The AC motor is mechanically coupled to the DC generator and hence runs at constant speed. Subsequently, the field excitation of the DC generator is adjusted in order to provide the adjustable DC voltage to the DC machine. If the DC generator voltage is adjusted to be lower than the back EMF voltage of the DC motor, the ‘motor’ will be operated in regenerative braking mode. In other words, 4-quadrant operation is possible with this configuration. Obviously, the system is bulky, expensive, inflexible and require regular maintenance due to the present of the DC machines. In the past, for constant speed application, induction and synchronous motors were widely. An efficient variable speed operation of AC motors is only possible if both the frequency and magnitude of the 3-phase supply voltage are adjustable; unfortunately this is used to be almost impossible.

Figure 1 Conventional variable speed electrical drive system With the advancement in power electronics, microprocessors and digital electronics, typical electric drive systems nowadays are becoming more compact, efficient, cheaper and versatile – this is shown in Figure 2. The voltage and current (magnitude and frequency) applied to the motor can be changed at will by employing power electronic converters. AC motor is no longer limited to applications where only AC source is available, however, it can also be used when the power source available is DC or vice versa

AC motor

DC generator

variable DC DC

motor

variable speed

Load

fixed speed

If

Ia

2

Figure 2 Modern Electric drive system employing power electronic converters Like other power electronic systems, modern electric drives is a multi-disciplinary field. The drive systems can be broken into several different research areas, as depicted in Figure 3.

Figure 3 Multi-disciplinary nature of electric drive system

Components of Electrical Drives The main components of a modern electrical drive are the motor, power processor, control unit electrical source and the mechanical load. These components are different from one drive system to another drive system, depending upon the applications, cost, available electrical source, etc. These are briefly discussed below. a) Motors

Motors obtain power from electrical sources. 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

Power Source

Control

feedback

Power Processor

(Power electronic Converters)

Control Unit

Motor Load

• Machine design • Speed sensorless • Machine theory

• Non-linear control • Real-time control • DSP application • PFC • sensors • Speed sensorless • Power electronic converters

• Utility interface • Renewable energy

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the power to be fed back to the sources (regenerative braking) rather than dissipated as heat (dynamic braking). There are several types of motors used in electric drives – the choice of the type to be used depends on applications, cost, environmental factors and also on the type of sources available. Broadly, they can be classified as either DC or AC motors: 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

b) Power processor or power modulator

Typically, electrical sources are uncontrollable. For instance, if it is an AC source, the frequency and magnitude are fixed (from the utility company), or maybe both are varying randomly (such as obtained from wind generator). It is therefore necessary to provide an interface between the available electrical source and the motor so that the power flow between the source and the motor, hence the speed of the motor or the torque can be systematically regulated and controlled -– this is achieved by using power processor or power modulator. With controllable sources, the motor can be reversed, brake or can even be operated with variable speed. Conventional power processor (non- power electronics approached) used, for example, variable impedance or relays, to shape the voltage or current that is supplied to the motor – these methods are inflexible, inefficient and have limited control capability. In modern electric drive systems, power electronic converters are used to shape the desired voltage or current that is supplied to the motor. The power converters are commonly used to convert one form of electrical power to another (e.g. AC to DC, DC to AC, etc). The main advantage of using power electronic converters is because of their high efficiency. With power electronic converters, characteristic of the motors can be changed at will to adapt the load requirements. Power electronic converters have several advantages over classical methods of power conversion, such as : • More efficient – since ideally no losses occur in power electronic converters • Flexible – voltage and current can be shaped by simply controlling the switching

functions of the power converter • Compact – smaller, compact and higher ratings solid–state power electronic devices are

continuously being developed – the prices are getting cheaper.

Power electronic converters are typically consists of power semiconductor devices and passive elements, such as inductors and/or capacitors. The losses in power semiconductor devices are minimized since they are always operated in either cut-off or saturated modes. The conversion of electrical power from one form to another can be performed with either single-stage conversion or multiple-stage conversion. For example a conversion from AC to DC can be performed in two stages (ACàDCàDC) or it can be performed with single stage conversion, i.e. ACàDC. The choice of which one to choose, in general, depends on application requirements, such as control bandwidth, output voltage or current ripples, cost, etc. AC to DC conversion

Diode rectifier

DC-DC converter

control

Controlled rectifier

control AC DC AC AC DC

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DC to AC DC to DC AC to AC

c) Control Unit

Control unit is used to generate the switching signals to the power switches of the power converters. The switching signals are generated depending on the control scheme adopted, which 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 controllers can be constructed from/using: • analog circuit - which is noisy, inflexible. However, analog circuit ideally can provide

infinite control bandwidth. • digital circuit – immune to noise, configurable. The bandwidth is obviously limited that

depends on the sampling frequency. Field Programmable Gate Arrays (FPGA) devices are gaining popularity due to their re-configurable features. However implementation of sophisticated control algorithm and observers can be very difficult and complex.

• DSP/microprocessor – flexible, lower bandwidth compared to the digital circuit. DSPs perform faster operation than microprocessors (multiplication in a single cycle). With a DSP/microprocessor, complex estimations and observers can be easily implemented.

Inverter (PWM)

control

DC-DC converter

control

Inverter (six-step)

control

DC-DC Converter

control

Controlled Rectifier

control

Inverter (six-step)

control

Diode Rectifier

control

Inverter (PWM)

Matrix Converter

control

DC DC AC DC AC

DC DC

AC DC AC AC DC AC

AC AC

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Most of the time, the control unit has to be electrically isolated from the power converters using opto-coupler or pulse transformers, for the following reasons:

• Malfunction in power circuit may damage control circuit if no electrical isolation is present.

• Safety for the operator – the high voltage and/or high current faulty condition in the power circuit can be conducted to the control circuit normally maintained by an operator/user

• Avoid conduction of harmonic to control circuit. Power electronic converters generate harmonics that can conduct to the control circuit thus interfering with its operation.

d) Source

Electrical sources or power supplies provide the energy to the electrical motors. Power sources can be of AC or DC in nature and normally are uncontrollable, i.e. their magnitudes and frequencies are either fixed or varying, depending on the sources of energy such as battery, power utility, fuel cell, etc. Fixed frequency and fixed magnitude AC source is normally obtained from power utility and can be either three-phase or single-phase; 3-phase sources are normally for high power applications. In order to efficiently control the motor, regardless of whether it is a DC or AC source (and depending on the type of the motor), it has to be regulated using power electronics converters before being fed to the motor. Power electronics converters typically have poor input power factor and it is sometimes necessary for the power converters to be operated with high power factor; if this is needed, power factor correction circuit has to be introduced.

e) Sensors Sensors for voltage, current, speed or torque are required for closed-loop operation and protections in electrical drive systems. Signals from these sensors have to be isolated from the control unit for the same reasons as explained before. Electrical isolation in voltage and current sensors are obtained using, for example, Hall-ffect sensors/devices. For high performance drive system, the speed is obtained from high-resolution speed encoders or resolvers. The terms ‘sensorless drive’ is normally referred to a drive system that does not need a mechanical speed sensor but rather the speed is estimated using motor terminal variables i.e. voltages and currents.

There can be several factors that affect the selection of different configuration of electrical drive system such as:

a) Torque and speed profile - determine the ratings of converters and the quadrant of operation required.

b) Capital and running cost – Drive systems will vary in terms of start-up cost and running cost, e.g. maintenance.

c) Space and weight restrictions d) Environment and location

Comparison between DC and AC drives Motors :

• DC require maintenance, heavy, expensive, speed limited by mechanical construction • AC less maintenance, light, cheaper, robust, high speed (esp. squirrel–cage type)

Control unit:

• DC drives: Simple control – decoupling torque and flux by mechanical commutator – the controller can be implemented using simple analog circuit even for high performance torque control. This means that cheaper cost for the controller.

• AC drives, the types of controllers to be used depend on the required drive performance – obviously, cost increases with performance. Scalar control drives technique does not

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require fast processor/DSP whereas in Field Oriented Control (FOC) or Direct Torque Control (DTC) drives, DSPs or fast processors are normally employed.

Performance:

• In DC motors, flux and torque components are always magnetically perpendicular to one another thanks to the mechanical commutator and brushes. The torque is controlled via the armature current while maintaining the field component constant. Fast torque and decouple control between flux and torque components can be achieved easily.

• In AC machines, in particular the induction machines, magnetic coupling between phases and between stator and rotor windings makes the modeling and torque control difficult and complex. Control of the steady state operating conditions is accomplished by controlling the magnitude and the frequency of the applied voltage; which is known as the scalar control technique. This is satisfactory for some applications, however for a more demanding applications such as elevators, electric vehicles, machine tools, it unacceptable because of the poor transient response and poor precision. The transient response and precision can be improved by applying the vector control technique; the decoupling between the torque and flux components is achieved through frame transformations. Implementation of this control technique is complex thus requires fast processors such as DSPs.

Overview of AC and DC drives The advancement in electric drive system is very much related to the development in the power semiconductor devices technology. The introduction of the Silicon-Controlled Rectifier (SCR) in 1957 has initiated the application of solid state devices in power converters. The development of the electrical drives systems can be divided into three stages Before power semiconductor devices were introduced: AC drives were used for fixed speed operation. Generating an AC voltage with variable frequency was only possible by using rotary converters, which are bulky and inflexible. Although it is possible to use variable voltage with fixed frequency sources (for example using transformers) to control the speed of AC motors, the efficiency of the drive system will be very poor especially at low speeds. On the other hand, variable DC supply can be produced using multi-machine configuration (Ward Leonhard system) and hence could be used to control the armature voltage of the DC motors. Consequently, DC drives are widely used for variable speed operation, whereas AC machines were used mainly for fixed speed applications. After power semiconductor devices were introduced in 1950s Although self-turnoff devices (Bipolar Junction Transistor – BJT) were available in the 1950s their voltage ratings were too low which make them inappropriate to be used in power circuit. Silicon-Controlled Rectifier (SCR) was introduced in 1957. The higher ratings of SCR compared to the solid state transistor at that time, has made it possible for it to be used in static frequency converters or inverters for high power applications. Speed control with AC motor can be performed because variable frequency AC supply can be generated using inverters. However, since the switching frequency of an SCR was low which require commutation circuit in order to turn-off, square wave inverters were mainly used in AC drive system. In early 1960s, the improvement in the fabrication of BJT along with the introduction of pulse width modulation (PWM) control technique has significantly contributed to the improvement in the AC motor drives. Transient torque control to some extend was nearly achieved to the expense of a very complex algorithm with numerous approximations. The true high performance torque control similar to DC drives was still not achievable due to the complex magnetic coupling between phases in the stator and rotor of the AC machines. Nevertheless, DC drives were gradually being replaced with AC drives in medium performance variable speed applications. Applications requiring precise and fast torque control were still dominated by DC drives. After semiconductor devices were introduced in 1980s In 1972, Prof. Blashke published his approach of AC motor control, to what is now known as Field Oriented Control (FOC) or vector control. FOC control basically transformed the

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control of AC motors to the one similar to DC motor control. In other words, the high performance torque control can be achieved using AC motors. This is possible through complex frame transformations and algorithm. However not until in the early 80s, where faster microprocessors were available, the algorithm used for FOC was not practically realizable. In 1980s, increasing number of applications utilizing FOC control could be found in industries. Applications which were previously possible only with DC drives were gradually being replaced with FOC of AC drives. It was predicted that the AC drives will eventually replace the DC drives in the near future. Four-quadrant operation of a drive system

The quadrant of operation of a drive system is defined by the speed and the torque of the motor; this can be illustrated using the ω-T graph shown in Figure 4. The circles in each of the quadrant can be considered to represent the rotor or shaft of the rotating machine. The plane is divided into 4 quadrants, thus 4 modes of operation, based on the directions of the speed and torque. The quadrants are marked as I, II, III and IV. The positive or forward speed is arbitrarily chosen in counterclockwise direction (it can also be chosen as clockwise). The positive torque is in the direction that will produce acceleration in forward speed. Most of the rotating electric motors can operate in all quadrants, i.e. capable of operating in forward and reverse directions. On the other hand, not all power converters can operate in all quadrants; some class of converters can operate only in single quadrant, some in 2 quadrants and some in 4 quadrants. In order for a drive system to be able to operate in all 4 quadrants, both, the motor and power converter, must be capable of operating in 4 quadrants. Quadrants of operation for power converters are discussed in the next section.

Figure 4 Four-quadrant operation of a drive system Quadrant I Both torque and speed are positive – the motor rotates in forward direction, which is in the same direction as the motor torque. The power of the motor is the product of the speed and torque (P = Teω), therefore the power of the motor is positive. Energy is converted from electrical form to mechanical form, which is used to rotate the motor. The mode of operation is known as forward motoring.

ω ω

ω ω

ω

T

I II

III IV

Te Te

Te Te

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Quadrant II The speed is in forward direction but the motor torque is in opposite direction or negative value. The torque produced by the motor is used to ‘brake’ the forward rotation of the motor. The mechanical energy accumulated during the braking, is converted to electrical energy – thus the flow of energy is from the mechanical system to the electrical system. However the flow of energy back to the source is only possible if the power converter is capable of doing so. The product of the torque and speed is negative thus the power is negative, implying that the ‘motor’ operates as a generator, i.e. in braking mode. The mode of operation is known as forward braking. Example: In DC motor drive (separately excited or permanent magnet) for example, forward braking is initiated when the armature terminal voltage of a motor rotating in forward direction is reduced lower than the back EMF of the motor. This forces the current to flow in reverse direction thus implying a negative torque (2nd quadrant). The motor speed reduces to a new steady state speed and again operates in the quadrant 1. Quadrant III The speed and the torque of the motor are in the same direction but are both negative. The reverse electrical torque is used to rotate the motor in reverse direction. The power, i.e. the product of the torque and speed, is positive implying that the motor operates in motoring mode. The energy is converted from electrical form to mechanical form. This mode of operation is known as reverse motoring. Example: If the motor initially operates in quadrant 1 (forward speed), it will have to operate in forward braking first before the speed can be reversed (quadrant 3). In order to move from quadrant 1 to quadrant 3, the voltage applied to the motor terminal has to be reversed. Quadrant IV The speed is in reverse direction but the torque is positive. The motor torque is used to ‘brake’ the reverse rotation of the motor. The mechanical energy gained during the braking is converted to electrical form – thus power flow is from the mechanical system to the electrical system. The product of the speed and torque is negative implying that the ‘motor’ operates as a generator, i.e. in braking mode. This mode of operation is known as reverse braking. Torque Equations For Rotating Systems The Newton’s Law states that, the net force acting on a body of mass M equals to the rate of change of its mechanical momentum, which is the product of its mass and its velocity in the direction of the net force. In the equation form, this is given by

dtdM

vdtdv

Mdt)Mv(

dF +== (1)

where F is the net force acting on the body, M is the mass of the body and v is its velocity. This is illustrated by Figure 5.

Figure 5 Translational motion With constant mass, (1) can be written as

M

x

v

Fp Ff dt

dvMF =

fp FFF −=

9

dtdv

MF =

For rotational motion (which is the case for rotating electrical machines), the force, the mass and the linear velocity in translational motion are equivalent to the torque, the moment of inertia and the angular velocity, respectively. Equation (1) can therefore be written as

dtdJ

dtd

Jdt)J(

dT ω+ω

=ω

= (3)

where T is the net torque, J is the moment of inertia and ω is the angular velocity. The rotational system which is analogous to the translational system of Figure 5 is shown in Figure 6.

Figure 6 Rotational motion For most of the cases, J is constant thus reducing (3) to

dtd

JTω

= (4)

In terms of the angular position, θ, this can be written as

2

2

dtd

JTθ

= (5)

For rotating electrical machines, the net torque is given by

dtd

JTTT le

ω=−= (6)

where Te is the internal electrical torque produced by the motor, Tl is the load torque and/or the internal friction of the motor. T is the available torque at the shaft and is responsible for accelerating the inertia of the motor. T is also known as the dynamic torque and it only exists during the transient (i.e. acceleration and deceleration). In order to accelerate in forward direction, Te –Tl must be positive; which means that the applied electrical torque must be larger than the load torque. In order to decelerate, the net torque must be negative; the electrical torque must be made smaller than the load torque and the motor operates in braking mode – more on this later. Note that the speed is always continuous. A discontinuity in speed (i.e. step change in speed) theoretically will require an infinite torque. This is analogous to the voltage and current across a capacitor in which discontinuity in capacitor voltage is not allowed as it corresponds to an infinite capacitor current. Equation (4) relates the torque and the mechanical speed (or position) of the machine. For a given electrical torque profile, with the known moment of inertia and the load torque, the speed profile of the drive system can be determined. In a torque-controlled drive system, the speed is

ω, Te TL

θ le TTT −=

J dtd

JTω

=

10

governed by the load. If the load torque comprise of only the frictional torque which is proportional to the speed, (4) can be written as

ω+ω

= Bdtd

JTe (7)

Equation (7) can be easily simulated using SIMULINK as shown in Figure 7. In the simulation, a square wave torque is applied.

Torque

speed

To Workspace2

pos

To Workspace1

tref

To Workspace

1s

Integrator1

1s

Integrator

-K-

B

Add

-K-

1/J

Figure 7 Dynamic simulation of mechanical system Usually in a cascaded closed-loop control system in which the speed is to be controlled, the reference torque will be generated by the speed controller. In such cases, the torque will be governed by the speed. If we multiply (7) with the angular speed, we obtain an equation describing the power balance,

(8)

Where pD = ωmTe is the driving power, pL = ωmTl is the load power and dtdJ m

mω

ω is the change in

kinetic energy. Integrating the equation with time and setting the initial speed ω(0) = 0, we obtain the following:

(9) The last term of (9) is the stored kinetic energy of the system. It is analogous to the energy

stored in a capacitor )Cv( 221 or an inductor )Li( 2

21 . Similar to a capacitor voltage or an

dtdJTT m

mlmemω

ω+ω=ω

dtdJpp m

mLDω

ω+=

ττω

ω+τ=τ= ∫∫∫ dddJdpdpw

t

0

mm

t

0L

t

0DD

m0

mLD dJww ωω+= ∫ω

2mLD J

21

ww ω+=

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-10

0

10

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5-200

0

200

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

50

100

torq

ue

spee

d

pos

itio

n

11

inductor current, an angular velocity ω must be continuous. An abrupt (discontinuous) change in ω will results in an infinite power. Relation between translational and rotational motions

In most applications of the drive systems, the translational and rotational motions are inter-related. For instance the prime mover may be a rotational motor but the mechanical load that needs to be driven may be has a translational motion. To consider the relationship between the rotational and translational motions, a system shown in Figure 8 will be used.

Figure 8 Translational and rotational motions The relation between the torques and the linear forces are given by

Tl = rFl, Tm = rFm .

Also, v = rω

If the mass M is constant, we can write

dtdv

MFF lm =− ⇒ dt)r(d

MrT

rT lm ω

=−

dt)(d

MrTT 2lm

ω=− (10)

Equation (10) states that the equivalent moment of inertia of the translational motion referred to the axis of the pulley is given by Jequ = Mr2

System with gears

It was found out that machines designed to operate at low speeds are large in size compared to the ones which are designed to operate at high speeds. In order to avoid the unnecessary large size machines, high speed operations are normally preferred. However, in some applications, slow motion with high torque is required. Consequently for such applications, gears which reduce speed but amplify the torque, are commonly employed. An example of the hoist drive employing gears is shown in Figure 9.

M

Fm Fl

r r

v

Tm

Tl

ω

12

Figure 9 Hoist drive with gears The hoist drive system shown in Figure 9 can be represented by an equivalent system similar to Figure 5. In order to do that, we need to obtain the equivalent moment of inertia and load torque. If the mass M3 is considered being moved upwards, with the negligible frictional torque, it can be shown that the torque equation for the equivalent system is given by

331

31em gMrdtd

JTωω

+ω

= (11)

where [ ]2333

2

1

32

2

1

21e rMJJJJ +⎟⎟

⎠

⎞⎜⎜⎝

⎛

ωω

+⎟⎟⎠

⎞⎜⎜⎝

⎛

ω

ω+=

Eg1: conveyor belt system Figure 10 shows a belt conveyor drive system which is used to move load A which has a mass of 5 kg. Given that the frictional torque between the rollers and the belt is 25 Nm and the moment of inertia of the rollers and motor are 250 × 10-3 kg-m2 and 300 × 10-3 kg-m2 respectively. The radius of the roller is 0.2 m. The steady state speed of the motor is 1000 rpm and it is required that the steady state speed of box A to be v = 3 m/s .

(i) What is the required gear ratio? (ii) What is the equivalent moment of inertia as seen by the motor shaft? (iii) What is the equivalent load torque as seen by the motor shaft?

J1

J2

M3

J3

ω1, Tm ω2

ω3

2r3 Los

s-fr

ee

gear

Gear system Motor

X

Roller

v 2r m

belt

Figure 10 Conveyor belt

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(iv) Calculate the electrical torque needed to accelerate box A from 0 m/s (standstill) to 3 m/s in 2 second.

Solution

(i) 3 m/s à 15 rad/s. The speed of the shaft is 1000 rpm = 104.72 rad/s. Hence ratio n1/n2 =

0.1432 (ii) Moment of inertia as seen by the motor’s shaft is due to the roller, load A and motor. Jequ = 300 × 10-3 + (0.1432)2 (250 × 10-3 + 5 × 0.22) = 0.3644 kg-m2 (iii) The load torque is due to the frictional torque of 25 Nm only. Tequ = (0.1432)×25 = 3.58 Nm (iv) Using the equivalent rotating system, Te = Tequ + Jequ (dω/dt) = 3.58 + 0.3644 (104.72/2) = 22.67 Nm

Steady state operating speed The characteristics of the motor and load are normally described based on their torque versus speed graph or T-ω characteristics. The steady state T-ω characteristic of a motor corresponds to the variation of its torque versus its speed, with all other variables including the voltage (or current) and frequency (for AC motor) are kept constant. Typical shape of T-ω characteristics of different motors are shown in Figure 11.

Figure 11 Typical T-ω characteristic for different types of motors The loads on the other hand will have their own T-ω characteristics. It is the intersection between the motor and the load T-ω characteristics that determines the steady state speed. This can be seen from (6) where at steady state dω/dt = 0 and Te = Tl. The steady state torque-speed characteristic of the motor depends on the applied voltage or current. Hence, by changing the point of intersections between the motor and load torque-speed curves, different steady-state speeds can be achieved (Figure 12).

Synchronous motor Separately excited DC motor

Induction motor Series DC motor

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Figure 12 Different steady state speeds (Tl = Te) for different motor’s T-ω characteristics It should be noted that the graph in Figure 12 only displayed the steady state characteristics of the load and motor. The transient responses before these steady state speeds are reached have to be dealt with using the dynamic characteristics of the load and motor. Components of Load Torque, Tl

In general, the load torque Tl can be classified into two types: the passive load torque (frictional torque) and the active load torque. Frictional toque exists only when there is motion. It always opposes the motion and changes its sign when the direction of rotation changes. Active load torque on the other hand, is independent of the direction of motion. Active loads normally retain their sign even when the drive changes its direction. Frictional torque Moving parts of the motor and load constitute the frictional torque. There are several types of frictional as described in Figure 13 and explained below:

• Coulomb friction – exists in bearings, gears, coupling and brakes. It is almost independent of speed.

• Viscous friction – exist in lubricated bearings due to the laminar flow of the lubricant. It is directly proportional to the speed.

• Windage friction – occurs due the turbulent flow of air or liquid. It is directly proportional to the square of speed

In practical drive system consisting of load and motor, all components of friction described above exist simultaneously. However, in most of the cases, only one or two components are dominating. For instance, a fan or a propeller will typically have the windage friction dominating, whereas in paper mill and machine tools, the dominating one could be the viscous friction.

Torque

speed

Torque-speed characteristic of the load, Tl

Different steady-state torque-speed characteristics of the motor, Te

ω1 ω2 ω3

Different motor speeds

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Constant torque (active load) The direction of constant load torque is independent of speed – it retains the direction even when the direction of rotation reverses or changes, e.g. gravity, tension or compression undergone by elastic body. This type of torque is capable of driving the motor under equilibrium and is said to be an active torque. Some examples of load torques

a. Load torques which are independent of the speed Typical example would be the load caused by gravitational pull. The load does not change sign even when the direction of motion changes.

b. Torques which are dependent on speed - Proportional to the speed – e.g. load torque due to the laminar flow of the lubricant

known as viscous friction - Proportional to the square of the speed – e.g. fan, blowers and pumps where

turbulent flow of liquid or air occurs. - Inversely proportional to the speed – this type of load consumes constant power.

Large torque required at low speed and small torqued required at high speed. E.g. coiler used in steel strip or paper mills.

T

ω

Viscous

Coulomb

Windage

Speed

Torque

Gravitational torque

FL

α

TL

gM

TL = rFL = r g M sin α

Te

Figure 13 Frictional torque

Figure 14 Constant load torque: gravitational force

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Thermal considerations The losses in the machines contribute to the temperature increase in the machine. The various parts of the machine have different temperature limits. Particularly important is the insulation used for the windings which give rise to the different classes of machines. If the temperature goes beyond the allowable temperature, it will cause an immediate breakdown (short circuit in the winding) or it will deteriorate the quality and hence reduces the lifetime of the insulation material. Allowable power losses are higher for materials which can withstand higher temperature which translates to higher costs. The classes of the insulator used for the winding in electrical machines are shown in Table 1.

Table 1 Classification of insulators

Class Max safe temperature (oC)

V 90 A 105 E 120 B 130 F 155 H 180 C >180

Three main cause of power losses are:

Conductor losses (i2R) Exist in the windings, cables, brushes, slip rings, commutator, and etc. Core losses Mainly due to eddy current and hysteresis losses Friction and windage losses Mainly due to ball bearings, brushes, ventilation losses

The constructions of the machines are very complex; normally built from various types of materials (heterogeneous) with complex geometrical shapes. To exactly predict the heat flow and hence the temperature distribution is extremely difficult. Based on the assumptions that the temperature limits of all parts does not exceed the temperature limits under certain operating conditions, the motors can therefore adequately modeled as homogeneous bodies. Obviously, this assumption cannot determine the specific internal thermal conditions for the motors.

Figure 15 Homogeneous body

Thermal capacity, C (Ws/oC) Surface A, (m2) Surface temperature, T (oC) Ambient temperature, To

p1 INPUT POWER (losses)

p2 OUTPUT POWER (convection)

17

Let us assume that a homogeneous body shown in Figure 15 represents a motor which has a thermal capacity C. The input power, which is the losses incurred in the motor, is represented by p1 whereas the output power, which is the power released as heat by convection, is represented by p2. The output power due to radiation is assumed negligible because of the low operating temperature and back radiation. Under a steady state condition, the input power equals the output power; this is when the steady state temperature is reached. The equation describing the power balance is given by

21 ppdtdT

C −= (12)

The heat dissipated by convection is given by

p2= αA (T − To) (13) where α is the coefficient of heat transfer. If we let ΔT = T − To , equation (12) can be written as

1p)T(AdtTd

C =Δα+Δ

or

Ap

)T(dtTd 1

T α=Δ+

Δτ (14)

where τT = C/(αA) is the thermal time constant. With ΔT(0)=0 and a step change in the power input p1 from 0 to ph at t=0, the solution for ΔT is

(15) At steady state, ΔT(∞) = ph/(αA) During cooling, i.e. when heat is removed at t=0, the temperature of the body decays to the ambient temperature.

(16)

( )τ−−α

=Δ /th e1A

pT

TΔ

t τ

A

phα

τ−⋅Δ=Δ /te)0(TT

Heating transient

18

Figure 16 Heating and cooling transients If the thermal time constant is large, a temporary overload is therefore possible without exceeding the temperature limits. Three typical modes of operation are:

- Continuous duty - Short time intermittent duty - Periodic intermittent duty

(i) Continuous duty

The motor is loaded continuously. Obviously the rating of the motor must at least equal the continuous loading of the machine. Normally, motor with next higher power rating from commercial available rating is selected. (ii) Short time intermittent duty

The time of operation is considerably less than the thermal time constant. The motor is allowed to cool to ambient temperature before the new load cycle is applied. The motor is allowed to be overloaded provided that the maximum temperature is not exceeded. However, the application of much higher power than the rated power is subject to the available torque of the machine. For DC machine this is limited due the sparking between the brushes and the commutator. In induction machine, this is limited by its pull-out torque. (iii) Periodic intermittent duty

The load cycle is repeated periodically. The machine is not allowed to cool to ambient when the next load cycle is applied. The temperature will fluctuate and the mean value will eventually settle to a steady state value. The machine can be overloaded and amount of overloading depends on the duty cycle of the load. The heating and cooling time constant may be different depending whether the machine is self-cooled or forced-cooled. Ratings of converters and motors In order to accelerate to a given reference value, the motor torque has to be larger than the load torque. According to (1), the difference between Tl and Te determines how fast the angular acceleration is. For example, the speed and torque responses for a closed-loop speed control DC drive with two different torque limit setting (10 Nm and 15 Nm) is shown in Figure 17. The higher the torque during the speed transient, the faster is the speed gets to its reference.

t τ

TΔ

)0(TΔ Cooling transient

19

0.19 0.2 0.21 0.22 0.23 0.24 0.25-200

-100

0

100

200

spee

d (ra

d/s)

0.19 0.2 0.21 0.22 0.23 0.24 0.250

5

10

15

20

torq

ue (N

m)

Figure 17 Speed response with different torque limit settings

In most cases, the torque during this transient condition can be up to 3 times the rated torque of the motor (for servo motor, it can be as high as 8 to 10 times the rated value). This momentary high torque is possible due to the large thermal capacity of the motor with suitable insulators used for the winding. The converter, which conducts the motor current, must be able to sustain this condition. However since the thermal capacity of the converters (i.e. switching devices) is small, the current cannot be higher than its rated value even for a short time. Consequently, the current rating of the converter is normally set to equal the maximum allowable motor current and this can be as high as the 3 times the motor rated current. The maximum allowable torque during transient of a drive system is determined by the current rating of the converter used whereas the continuous torque limit depends on the current rating of the motor. The operating area of a 4-quadrant motor drive is shown in Figure 18. The converter is normally protected from the over-current condition by the current limiter mechanism within the converter system, which means that sustained overloads on the motor has to be protected by an additional thermal protection mechanism. Above the base speed, ωb, the toque is limited by the maximum allowable power, which depends on whether the transient or continuous torque limit is considered. The speed limit basically depends on the mechanical limitation of the motor.

Torque

Speed

Power limit for transient torque

Power limit for continuous torque

Transient torque limit

Continuous torque limit

Maximum speed limit

ωb - ωb

Figure 18 Limits for torque, speed and power for drive system

20

Steady-state stability The motor will operate at the steady-state speed (point where Tl = Te) provided that the speed is of stable equilibrium. The stable equilibrium speed is investigated using steady-state torque-speed characteristics of the load and motor. A disturbance in any part of the drive will result in a speed to depart from the steady state speed. However, if the steady-state speed is of stable equilibrium, the speed will return to the stable equilibrium speed. On the other hand, if the speed is not of the stable equilibrium, the disturbance will results in the speed to drift away from the equilibrium speed. It can be shown that the condition for stable equilibrium is:

0ddT

ddT el >

ω−

ω (17)

(a) (b)

Figure 19 Steady state stability Let us take an example of Figure 19(a). Assume that there is a disturbance that causes the steady state point to move away from the equilibrium point Q1, such that an increase in speed occurs. A new load torque and motor torque at this new speed (ω1) which is according to Figure 9(a) are Tl1 and Te1 respectively. Clearly from the figure, Tl1 > Te1 and according to the equation of motion for torque, the motor will decelerate. The deceleration will cause the motor to return to its initial equilibrium point. Therefore point Q1 is said to be steady state stable. In Figure 19(b), point Q2 on the other hand, is steady state unstable. At ω2, the electrical torque is larger than the load torque and this causes the system to accelerate further away from Q2. It should be noted that in electrical drive system with power electronic converters, the system can be brought back to Q2 by altering the T-ω characteristic of the motor. This is typically done for example using the closed-loop speed control system. References

Te Tl

Motor will decelerate back to equilibrium since Tl > Te

Δω Δω

Motor will accelerate away from equilibrium since Te > Tl

Torque

speed

Torque

speed

Tl Te

Q2

Tln

Ten Tl2

Te2

ω1 ω2

Q1

21

G.K. Dubey, “Fundamental of Electrical Drives”, Narosa, 1994. W. Leonhard, “Control of Electrical Drives”, Springer-Verlag, 2001