A1 Reasons For Adopting A Simplified Approach

The aim of this Appendix is to help the readers who are not familiar with closed-loop control and feedback to feel confident when they meet such ideas in the drives context. In line with the remainder of the book, the treatment avoids mathematics where possible, and in particular it makes only passing reference to transform techniques. This approach is chosen deliberately, despite the limitations it imposes, in the belief that it is more useful for the reader to obtain a sound grasp of what...

A21 Erroractivated feedback systems

An everyday example of a feedback system is the lavatory cistern (Figure A.1), where the aim is to keep the water level in the tank at the full mark. The valve through which water is admitted to the tank is controlled by the position of the arm carrying a ball that floats in the water. The steady-state condition is shown in diagram (a), the inlet valve being closed when the arm is horizontal. When the WC is flushed (represented by the bottom valve being opened - see diagram (b)), the water...

A3 Steadystate Analysis Of Closedloop Systems

A typical closed-loop system is shown in block diagram form in Figure A.3. As explained in the introduction, our aim is to keep the mathematical treatment as simple as possible, so each of the blocks contains a single symbol that represents the ratio of output to input under steady-state conditions, i.e. when any transients have died out and all the variables have settled. Figure A.3 Typical arrangement of negative-feedback closed-loop control system A useful question to pose whenever a new...

A5 Steadystate Error Integral Control

An important criterion for any closed-loop system is its steady-state error, which ideally should be zero. We can return to the op-amp example studied above to examine how the error varies with loop gain, the error being the difference between the reference signal and the feedback signal. If we make the reference signal unity for the sake of simplicity, the magnitudes of the output and error signals will be as shown in Figure A.7, for the three values of forward gain listed in Table A.1. At the...

Answers To Numerical Review Questions

15) (a) 0.70 V rad s 7.0 Nm (b) 56.06 A (c) 0.2 V 11.5 V (d) 1588 rev min 22.27 Nm 87.3 17) 5.8 V 0.485 m Nm 1.04 x 105 rad s2 30) 519.075 V 17 W 9603 W 88.2 Nm 1077.44 rev min 352.81 A 176.3 Nm 17.5 3) 1728 rev min 2.4 Hz 72 rev min 1800 rev min 9) 30 0.71 mm 10) 1.053 2.217 18) 458 V 20.8 kW 1450 rev min 21) 22.2 kW 11) 1380 rev min, 0.08 60 rev min, 0.67 7) 15 7.5 1.8 9) 72 rev min 8) 4-pole 5.5 kW 1380 rev min 9) 12.88 kgm2 101.85 kJ 100 kJ 10) 2

Brushless Dc Motors

Much of the impetus for the development of brushless d.c. motors came from the computer peripheral and aerospace industries, where high performance coupled with reliability and low maintenance are essential. Very large numbers of brushless d.c. motors are now used, particularly in sizes up to a few hundred watts. The small versions (less than 100 W) are increasingly made with all the control and power electronic circuits integrated at one end of the motor, so that they can be directly...

Cage rotor

For small values of slip, i.e. in the normal running region, the lower we make the rotor resistance the steeper the slope of the torque-speed curve becomes, as shown in Figure 6.9. We can see that at the rated torque (shown by the horizontal dotted line in Figure 6.9) the full-load slip of the low-resistance cage is much lower than that of the high-resistance cage. But we saw earlier that the rotor efficiency is equal to (1 s), where s is the slip. So, we conclude that the low-resistance rotor...

Chopper drive

The basic circuit for one phase of a VR motor is shown in the upper part of Figure 9.15 together with the current waveforms. A high-voltage power supply is used in order to obtain very rapid changes in current when the phase is switched-on or off. The lower transistor is turned on for the whole period during which current is required. The upper-transistor turns on whenever the actual current falls below the lower threshold (shown dotted in Figure 9.15) and it turns off when the current exceeds...

Constanttorque load

A constant torque load implies that the torque required to keep the load running is the same at all speeds. A good example is a drum-type hoist, where the torque required varies with the load on the hook, but not with the speed of hoisting. An example is shown in Figure 11.3. The drum diameter is 0.5 m, so if the maximum load (including the cable) is say 1000 kg, the tension in the cable (mg) will be 9810 N, and the torque applied by the load at the drum will be given by force x radius 9810 x...

Constantvoltage drive

This is the simplest possible drive the circuit for one of the three phases is shown in the upper part of Figure 9.13, and the current waveforms at low and high stepping rates are shown in the lower part of the figure. The d.c. voltage V is chosen so that when the transistor is on, the steady Figure 9.13 Basic constant-voltage drive circuit and typical current waveforms current (equal to V R if we neglect the on-state voltage drop across the transistor) is the rated current as specified by the...

Control Arrangements For Inverterfed Drives

For speed control manufacturers offer options ranging in sophistication from a basic open-loop scheme which is adequate when precise speed holding is not essential, through closed-loop schemes with tacho or encoder feedback, up to vector control schemes which are necessary when optimum dynamic performance is called for. The variety of schemes is much greater than for the fully matured d.c. drive, so we will look briefly at some examples in the remainder of this section. The majority of drives...

Controlledspeed Synchronous Motor Drives

As soon as variable-frequency inverters became a practicable proposition it was natural to use them to supply synchronous motors, thereby freeing the latter from the fixed-speed constraint imposed by mains-frequency operation and opening up the possibility of a simple open-loop controlled speed drive. The obvious advantage over the inverter-fed induction motor is that the speed of the synchronous motor is exactly determined by the frequency, whereas the induction motor always has to run with a...

Converter output impedance overlap

So far we have tacitly assumed that the output voltage from the converter was independent of the current drawn by the motor, and depended only on the delay angle a. In other words we have treated the converter as an ideal voltage source. In practice the a.c. supply has a finite impedance, and we must therefore expect a volt-drop which depends on the current being drawn by the motor. Perhaps surprisingly, the supply impedance (which is mainly due to inductive leakage reactances in transformers)...

Currentforced drive

The initial rate of rise of current in a series R-L circuit is directly proportional to the applied voltage, so in order to establish the current more quickly at switch-on, a higher supply voltage (Vf) is needed. But if we simply increased the voltage, the steady-state current (Vf R) would exceed the rated current and the winding would overheat. To prevent the current from exceeding the rated value, an additional 'forcing' resistor has to be added in series with the winding. The value of this...

Dc Servo Drives

The precise meaning of the term 'servo' in the context of motors and drives is difficult to pin down. Broadly speaking, if a drive incorporates 'servo' in its description, the implication is that it is intended specifically for closed-loop or feedback control, usually of shaft torque, speed, or position. Early servomechanisms were developed primarily for military applications, and it quickly became apparent that standard d.c. motors were not always suited to precision control. In particular...

Discontinuous current

We can see from Figure 4.2 that as the load torque is reduced, there will come a point where the minima of the current ripple touches the zero-current line, i.e. the current reaches the boundary between continuous and discontinuous current. The load at which this occurs will also depend on the armature inductance, because the higher the inductance the smoother the current (i.e. the less the ripple). Discontinuous current mode is therefore most likely to be encountered in small machines with low...

Drive Circuits And Pullout Torquespeed Curves

Users often find difficulty in coming to terms with the fact that the running performance of a stepping motor depends so heavily on the type of drive circuit being used. It is therefore important to emphasise that in order to meet a specification, it will always be necessary to consider the motor and drive together, as a package. There are three commonly used types of drive. All use transistors, which are operated as switches, i.e. they are either turned fully on, or they are cut-off. A brief...

Duty cycle and rating

This is a complex matter, which in essence reflects the fact that whereas all motors are governed by a thermal (temperature rise) limitation, there are different patterns of operation which can lead to the same ultimate temperature rise. Broadly speaking the procedure is to choose the motor on the basis of the r.m.s. of the power cycle, on the assumption that the losses (and therefore the temperature rise) vary with the square of the load. This is a reasonable approximation for most motors,...

Dynamic behaviour and timeconstants

The use of the terms 'surge' and 'sudden' in the discussion above would have doubtless created the impression that changes in the motor current or speed can take place instantaneously, whereas in fact a finite time is always necessary to effect changes in both. (If the current changes, then so does the stored energy in the armature inductance and if speed changes, so does the rotary kinetic energy stored in the inertia. For either of these changes to take place in zero time it would be...

Fourquadrant operation and inversion

So far we have looked at the converter as a rectifier, supplying power from the a.c. mains to a d.c. machine running in the positive direction and acting as a motor. As explained in Chapter 3, this is known as one-quadrant operation, by reference to quadrant 1 of the complete torque-speed plane shown in Figure 3.16. But suppose we want to run the machine as a motor in the opposite direction, with negative speed and torque, i.e. in quadrant 3 how do we do it And what about operating the machine...

Full speed regenerative reversal

To illustrate more fully how the voltage has to be varied during sustained regenerative braking, we can consider how to change the speed of an unloaded motor from full speed in one direction to full speed in the other, in the shortest possible time. At full forward speed the applied armature voltage is taken to be + V (shown as 100 in Figure 3.17), and since the motor is unloaded the no-load current will be very small and the back e.m.f. will be almost equal to V. Ultimately, we will clearly...

Further Reading

Acarnley, P.P. (2002) Stepping Motors A Guide to Modern Theory and Practice (4th ed.). IEE Publishing, London. ISBN 085296417x. A comprehensive treatment at a level which will suit both students and users. Beaty, H.W. and Kirtley, J.L. (1998) Electric Motor Handbook. New York McGraw- Comprehensive analytical treatment including chapters on motor noise and servo controls. Hindmarsh, J. (1985) Electrical Machines and their Applications (4th ed.). Oxford Pergamon. Hindmarsh, J. (1984) Electrical...

Generating And Braking

Having explored the torque-speed curve for the normal motoring region, where the speed lies between zero and just below synchronous, we must ask what happens if the speed is above the synchronous speed, or is negative. A typical torque-speed curve for a cage motor covering the full range of speeds, which are likely to be encountered in practice, is shown in Figure 6.15. We can see from Figure 6.15 that the decisive factor as far as the direction of the torque is concerned is the slip, rather...

Inductive motor load

As mentioned above, motor loads are inductive, and we have seen earlier that the current cannot change instantaneously in an inductive load. We must therefore expect the behaviour of the converter with an inductive load to differ from that with a resistive load, in which the current can change instantaneously. The realisation that the mean voltage for a given firing angle might depend on the nature of the load is a most unwelcome prospect. What we would like to say is that, regardless of the...

Influence Of Rotor Current On Flux

Up to now all our discussion has been based on the assumption that the rotating magnetic field remains constant, regardless of what happens on the rotor. We have seen how torque is developed, and that mechanical output power is produced. We have focused attention on the rotor, but the output power must be provided from the stator winding, so we must turn attention to the behaviour of the whole motor, rather than just the rotor. Several questions spring to mind. Firstly, what happens to the...

Limitations imposed by motor

The standard practice in d.c. drives is to use a motor specifically designed for operation from a thyristor converter. The motor will have a laminated frame, will probably come complete with a tachogenerator, and - most important of all - will have been designed for through ventilation and equipped with an auxiliary air blower. Adequate ventilation is guaranteed at all speeds, and continuous operation with full torque (i.e. full current) at even the lowest speed is therefore in order. By...

Limitations imposed by the inverter constant power and constant torque regions

The main concern in the inverter is to limit the currents to a safe value as far as the main switching devices are concerned. The current limit will be at least equal to the rated current of the motor, and the inverter control circuits will be arranged so that no matter what the user does the output current cannot exceed a safe value. The current limit feature imposes an upper limit on the permissible torque in the region below base speed. This will normally correspond to the rated torque of...

Load Requirements Torquespeed Characteristics

The most important things we need to know about the load are the steady-state torque-speed characteristic, and the effective inertia as seen by the motor. In addition, we clearly need to know what performance is required. At one extreme, for example, in a steel-rolling mill, it may be necessary for the speed to be set at any value over a wide range, and for the mill to react very quickly when a new target speed is demanded. Having reached the set speed, it may be essential that it is held very...

Magnetic circuits in motors

The reader may be wondering why so much attention has been focused on the gapped C-core magnetic circuit, when it appears to bear little resemblance to the magnetic circuits found in motors. We will now see that it is actually a short step from the C-core to a magnetic motor circuit, and that no fundamentally new ideas are involved. The evolution from C-core to motor geometry is shown in Figure 1.10, which should be largely self-explanatory, and relates to the field system of a d.c. motor. We...

Maximum output power

We have seen that if the mechanical load on the shaft of the motor increases, the speed falls and the armature current automatically increases until equilibrium of torque is reached and the speed again becomes steady. If the armature voltage is at its maximum (rated) value, and we increase the mechanical load until the current reaches its rated value, we are clearly at full-load, i.e. we are operating at the full speed (determined by voltage) and the full torque (determined by current). The...

Measurement Of Parameters

The tests used to obtain the equivalent circuit parameters of a cage induction motor are essentially the same as those described for the transformer in Section 7.4.5. To simulate the 'open-circuit' test we would need to run the motor with a slip of zero, so that the secondary (rotor) referred resistance (R2 s) became infinite and the rotor current was absolutely zero. But because the motor torque is zero at synchronous speed, the only way we could achieve zero slip would be to drive the rotor...

Methods Of Starting Cage Motors Direct Starting Problems

Our everyday domestic experience is likely to lead us to believe that there is nothing more to starting a motor than closing a switch, and indeed for most low-power machines (say up to a few kW) - of whatever type - that is indeed the case. By simply connecting the motor to the supply we set in train a sequence of events which sees the motor draw power from the supply while it accelerates to its target speed. When it has absorbed and converted sufficient energy from electrical to kinetic form,...

Operating characteristics and control

If the d.c. input voltage to the inverter is kept constant and the motor starts from rest, the motor current will be large at first, but will decrease with speed until the motional e.m.f. generated inside the motor is almost equal to the applied voltage. When the load on the shaft is increased, the speed begins to fall, the motional e.m.f. reduces and the current increases until a new equilibrium is reached where the extra motor torque is equal to the load torque. This behaviour parallels that...

Optimum acceleration and closedloop control

There are some applications where the maximum possible accelerations and decelerations are demanded, in order to minimise point-to-point times. If the load parameters are stable and well defined, an open-loop approach is feasible, and this is discussed first. Where the load is unpredictable, however, a closed-loop strategy is essential, and this is dealt with later. To achieve maximum possible acceleration calls for every step command pulse to be delivered at precisely optimised intervals...

Outline of approach

So far in this book we have not referred to the parallels between the induction motor and the transformer, not least because the former is designed to convert energy from electrical to mechanical form, while the latter converts electrical power from one voltage to another. Physically, however, the construction of the wound-rotor induction motor has striking similarities with that of the 3-phase transformer, with the stator and rotor windings corresponding to the primary and secondary windings...

Polechanging motors

For some applications continuous speed control may be an unnecessary luxury, and it may be sufficient to be able to run at two discrete speeds. Among many instances where this can be acceptable and economic are pumps, lifts and hoists, fans and some machine tool drives. We established in Chapter 5 that the pole number of the field was determined by the layout and interconnection of the stator coils, and that once the winding has been designed, and the frequency specified, the synchronous speed...

Power Range For Motors And Drives

The diagrams (Figures 11.1 and 11.2) give a broad indication of the power range for the most common types of motor and drive. Because 10 W 100 W 1 kW 10 kW 100 kW 1 MW 10 MW 10 W 100 W 1 kW 10 kW 100 kW 1 MW 10 MW Figure 11.1 Continuous power rating for various types of motor Figure 11.1 Continuous power rating for various types of motor the power scales are logarithmic it would be easy to miss the exceptionally wide power range of some types of motor induction and d.c. motors, for example,...

Production of rotating magnetic field

Now that we have a picture of the field, we turn to how it is produced. If we inspect the stator winding of an induction motor we find that it consists of a uniform array of identical coils, located in slots. The coils are in fact connected to form three identical groups or phase windings, distributed around the stator, and symmetrically displaced with respect to one another. The three-phase windings are connected either in star (wye) or delta (mesh), as shown in Figure 5.2. The three-phase...

Real transformer noload condition flux and magnetising current

In modelling the real transformer at no-load we take account of the finite resistances of the primary and secondary windings the finite reluctance of the magnetic circuit and the losses due to the pulsating flux in the iron core. Figure 7.7 Equivalent circuit of real transformer under no-load conditions, allowing for presence of magnetising current and winding resistances The winding resistances are included by adding resistances R1 and R2, respectively in series with the primary and secondary...

Reduction of flux by rotor current

We should begin by recalling that we have already noted that when the rotor currents are negligible (s 0), the e.m.f. that the rotating field induces in the stator winding is very nearly equal to the applied voltage. Under these conditions a reactive current (which we termed the magnetising current) flows into the windings, to set up the rotating flux. Any slight tendency for the flux to fall is immediately detected by a corresponding slight reduction in e.m.f., which is reflected in a...

Reluctance and airgap flux densities

If we neglect the reluctance of the iron parts of a magnetic circuit, it is easy to estimate the flux density in the air-gap. Since the iron parts are then in effect 'perfect conductors' of flux, none of the source MMF (NI) is used in driving the flux through the iron parts, and all of it is available to push the flux across the air-gap. The situation depicted in Figure 1.7 therefore reduces to that shown in Figure 1.8, where an MMF of NI is applied directly across an air-gap of length g. To...

Requirements of drive

The basic function of the complete drive is to convert the step command input signals into appropriate patterns of currents in the motor windings. This is achieved in two distinct stages, as shown in Figure 9.10, which relates to a 3-phase motor. The 'translator' stage converts the incoming train of step command pulses into a sequence of on off commands to each of the three power stages. In the one-phase-on mode, for example, the first step command pulse will be routed to turn on phase A, the...

Resistive load

Thyristors T1 and T4 are fired together when terminal A of the supply is positive, while on the other half-cycle, when B is positive, thyristors T2 and T3 are fired simultaneously. The output voltage waveform is shown by the solid line in Figure 2.8. There are two pulses per mains cycle, hence the description 'two-pulse' or full-wave. At every instant the load is either connected to the mains by the pair of switches T1 and T4, or it is connected the other way up by the pair of switches T2 and...

Resultant field

The layout of coils for the complete 4-pole winding is shown in Figure 5.6(a). The go sides of each coil are represented by the capital letters (A, B, C) and the return sides are identified by bars over the letters (A, B, C). (For the sake of comparison, a 6-pole winding layout that uses the same stator slotting is shown in Figure 5.6(b) here the pole-pitch is six slots and the coils are short-pitched by one slot.) Returning to the 4-pole winding, we can see that the windings of phases B and C...

Review Questions

The first ten questions are designed to reinforce understanding by means of straightforward calculations, while the remainder are more demanding and involve some extension of the basic ideas. 1) At what frequency must a 4-pole motor be supplied so that its synchronous speed is 1200 rev min 2) The nameplate of a standard 50 Hz induction motor quotes full-load speed as 2950 rev min. Find the pole number and the rated slip. 3) A 4-pole, 60 Hz induction motor runs with a slip of 4 . Find (a) the...

Rotor currents and torque large slip

As the slip increases, the rotor e.m.f. and rotor frequency both increase in direct proportion to the slip. At the same time the rotor inductive reactance, which was negligible at low slip (low rotor frequency) begins to be appreciable in comparison with the rotor resistance. Hence, although the Figure 5.17 Magnitude of current induced in rotor over the full range of slip Figure 5.17 Magnitude of current induced in rotor over the full range of slip induced current continues to increase with...

Rotor currents and torque small slip

When the slip is small (say between 0 and 10 ), the frequency of induced e.m.f. is also very low (between 0 and 5 Hz if the supply frequency is 50 Hz). At these low frequencies the impedance of the rotor circuits is predominantly resistive, the inductive reactance being small because the rotor frequency is low. The current in each rotor conductor is therefore in time phase with the e.m.f. in that conductor, and the rotor current wave is therefore in space phase with the rotor e.m.f. wave, which...

Shadedpole motors

There are several variants of this extremely simple, robust and reliable cage motor, which predominate for low-power applications such as hairdryers, oven fans, tape decks, office equipment, display drives, etc. A 2-pole version from the cheap end of the market is shown in Figure 6.23. The rotor, typically between 1 and 4 cm diameter, has a die-cast aluminium cage, while the stator winding is a simple concentrated coil wound round the laminated core. The stator pole is slotted to receive the...

Shunt motor steadystate operating characteristics

A basic shunt-connected motor has its armature and field in parallel across a single d.c. supply, as shown in Figure 3.12(a). Normally, the voltage will be constant and at the rated value for the motor, in which case the steady-state torque speed curve will be similar to that of a separately excited motor at rated field flux, i.e. the speed will drop slightly with load, as shown by the line ab in Figure 3.12(b). Over the normal operating region the torque-speed characteristic is similar to that...

Shunt Series And Compound Motors

Before variable-voltage supplies became readily available, most d.c. motors were obliged to operate from a single d.c. supply, usually of constant voltage. The armature and field circuits were therefore designed either for connection in parallel (shunt), or in series. As we will see shortly, the operating characteristics of shunt and series machines differ widely, and hence each type tends to claim its particular niche shunt motors were judged to be good for constant-speed applications, while...

Singleconverter reversing drives

We will consider a fully controlled converter supplying a permanentmagnet motor, and see how the motor can be regeneratively braked from full speed in one direction, and then accelerated up to full speed in reverse. We looked at this procedure in principle at the end of Chapter 3, but here we explore the practicalities of achieving it with a converter-fed drive. We should be clear from the outset that in practice, all the user has to do is to change the speed reference signal from full forward...

Speed Control

We have seen that to operate efficiently an induction motor must run with a small slip. It follows that any efficient method of speed control must be based on varying the synchronous speed of the field, rather than Figure 6.17 Torque-speed curve for d.c. injection braking of cage motor Figure 6.17 Torque-speed curve for d.c. injection braking of cage motor the slip. The two factors that determine the speed of the field, are the supply frequency and the pole number (see equation (5.1)). The pole...

Speed control of woundrotor motors

The fact that the rotor resistance can be varied easily allows us to control the slip from the rotor side, with the stator supply voltage and frequency constant. Although the method is inherently inefficient it is still used in many medium and large drives such as hoists, conveyors and crushers because of its simplicity and comparatively low cost. Figure 6.19 Influence of external rotor resistance (R) on torque-speed curve of wound-rotor motor Figure 6.19 Influence of external rotor resistance...

Stardelta wyemesh starter

This is the simplest and most widely used method of starting. It provides for the windings of the motor to be connected in star (wye) to begin with, thereby reducing the voltage applied to each phase to 58 (1 v 3) of its DOL value. Then, when the motor speed approaches its running value, the windings are switched to delta (mesh) connection. The main advantage of the method is its simplicity, while its main drawbacks are that the starting torque is reduced (see below), and the sudden transition...

Starting from rest

The rate at which the motor can be started from rest without losing steps is known as the 'starting' or 'pull-in' rate. The starting rate for a given motor depends on the type of drive, and the parameters of the load. This is entirely as expected since the starting rate is a measure of the motor's ability to accelerate its rotor and load and pull into synchronism with the field. The starting rate thus reduces if either the load torque, or the load inertia are increased. Typical pull-in...

Stator Currentspeed Characteristics

In the previous section, we argued that as the slip increased, and the rotor did more mechanical work, the stator current increased. Since the extra current is associated with the supply of real (i.e. mechanical Figure 5.20 Phasor diagrams showing stator current at no-load, part-load and full-load. The resultant current in each case is the sum of the no-load (magnetising) current and the load component Figure 5.20 Phasor diagrams showing stator current at no-load, part-load and full-load. The...

Steadystate stability pullout torque and stalling

We can check stability by asking what happens if the load torque suddenly changes for some reason. The load torque shown by the dotted line in Figure 6.8 is stable at speed X, for example if the load torque increased from Ta to Tb, the load torque would be greater than the motor torque, so the motor torque would decelerate. As the speed dropped, the motor torque would rise, until a new equilibrium was reached, at the slightly Figure 6.8 Torque-speed curve illustrating stable operating region...

Summary

When the stator is connected to a 3-phase supply, a sinusoidally distributed, radially directed rotating magnetic flux density wave is set up in the air-gap. The speed of rotation of the field is directly proportional to the frequency of the supply, and inversely proportional to the pole number of the winding. The magnitude of the flux wave is proportional to the applied voltage, and inversely proportional to the frequency. When the rotor circuits are ignored (i.e. under no-load conditions),...

Switched Reluctance Motor Drives

The switched reluctance drive was developed in the 1980s to offer advantages in terms of efficiency, power per unit weight and volume, robustness and operational flexibility. The motor and its associated power-electronic drive must be designed as an integrated package, and optimised for a particular specification, e.g. for maximum overall efficiency with a Plate 10.1 Switched reluctance motors. The motors with finned casings are TEFVfor use in general-purpose industrial controlled speed drives,...

The Ideal Transformer

Because we are dealing with balanced 3-phase motors we can achieve considerable simplification by developing single-phase models, it being understood that any calculations using the equivalent circuit (e.g. torque or power) will yield 'per phase' values which will be multiplied by three to give the total torque or power. A quasi-circuit model of an iron-cored transformer is shown diagram-matically in Figure 7.2. This represents the most common application of the transformer, with the primary...

The Rotating Magnetic Field

Before we look at how the rotating field is produced, we should be clear what it actually is. Because both the rotor and stator iron surfaces are smooth (apart from the regular slotting), and are separated by a small air gap, the flux produced by the stator windings crosses the air gap radially. The behaviour of the motor is dictated by this radial flux, so we will concentrate first on establishing a mental picture of what is meant by the 'flux wave' in an induction motor. The pattern of flux...

Torque control

For applications requiring the motor to operate with a specified torque regardless of speed (e.g. in line tensioning), we can dispense with the outer (speed) loop, and simply feed a current reference signal directly to the current controller (usually via the 'torque ref terminal on the control board). This is because torque is directly proportional to current, so the current controller is in effect also a torque controller. We may have to make an allowance for accelerating torque by means of a...

Torque prediction and control

If the iron in the magnetic circuit is treated as ideal, analytical expressions can be derived to express the torque of a reluctance motor in terms of the rotor position and the current in the windings. In practice, however, this analysis is of little real use, not only because switched reluctance motors are designed to operate with high levels of magnetic saturation in parts of the magnetic circuit, but also because, except at low speeds, it is not practicable to achieve specified current...

Torque Production

In this section we begin with a brief description of rotor types, and introduce the notion of 'slip', before moving onto explore how the torque is produced, and investigate the variation of torque with speed. We will find that the behaviour of the rotor varies widely according to the slip, and we therefore look separately at low and high values of slip. Throughout this section we will assume that the rotating magnetic field is unaffected by anything which happens on the rotor side of the...

Toy Motors

The motors used in model cars, trains etc. are rather different in construction from those discussed so far, primarily because they are designed to be cheap to make. They also run at high speeds, so it is not important for the torque to be smooth. A typical arrangement used for rotor diameters from 1 cm to perhaps 3 cm is shown in Figure 3.18. The rotor, made from laminations with a small number (typically three or five) of multi-turn coils in very large 'slots,' is simple to manufacture, and...

Transient Performance Step response

It was pointed out earlier that the single-step response is similar to that of a damped second-order system. We can easily estimate the natural frequency vn in rad s from the equation 2 slope of torque angle curve vn - - - Knowing vn, we can judge what the oscillatory part of the response will look like, by assuming the system is undamped. To refine the estimate, and to obtain the settling time, however, we need to estimate the damping ratio, which is much more difficult to determine as it...

Transient torque control

We have seen previously that in both the induction motor and the d.c. motor, torque is produced by the interaction of currents on the rotor with the radial flux density produced by the stator. Thus to change the torque, we must either change the magnitude of the flux, or the rotor current, or both and if we want a sudden (step) increase in torque, we must make the change (or changes) instantaneously. Since every magnetic field has stored energy associated with it, it should be clear that it is...

Variable reluctance motor

A simplified diagram of a 30 per step VR stepping motor is shown in Figure 9.5. The stator is made from a stack of steel laminations, and has six equally spaced projecting poles, or teeth, each carrying a separate coil. The rotor, which may be solid or laminated, has four projecting teeth, of the same width as the stator teeth. There is a very small air-gap -typically between 0.02 and 0.2 mm - between rotor and stator teeth. When no current is flowing in any of the stator coils, the rotor will...

Voltage control of highresistance cage motors

Where efficiency is not of paramount importance, the torque (and hence the running speed) of a cage motor can be controlled simply by altering the supply voltage. The torque at any slip is approximately proportional to the square of the voltage, so we can reduce the speed of the load by reducing the voltage. The method is not suitable for standard low-resistance cage motors, because their stable operating speed range is very restricted, as shown in Figure 6.18(a). But if special high-rotor...

Hybrid motor

A cross-sectional view of a typical 1.8 hybrid motor is shown in Figure 9.6. The stator has eight main poles, each with five teeth, and each main pole carries a simple coil. The rotor has two steel end-caps, each with 50 Figure 9.6 Hybrid (200 steps per revolution) stepping motor. The detail shows the rotor and stator tooth alignments, and indicates the step angle of 1.8 Figure 9.6 Hybrid (200 steps per revolution) stepping motor. The detail shows the rotor and stator tooth alignments, and...

Rotor induced emf current and torque

The rate at which the rotor conductors are cut by the flux - and hence their induced e.m.f. - is directly proportional to the slip, with no induced e.m.f. at synchronous speed (s 0) and maximum induced e.m.f. when the rotor is stationary (s 1). Figure 5.12 Variation of rotor induced e.m.f and frequency with speed and slip The frequency of rotor e.m.f. is also directly proportional to slip, since the rotor effectively slides with respect to the flux wave, and the higher the relative speed, the...

Chopperfed Dc Motor Drives

If the source of supply is d.c. (for example in a battery vehicle or a rapid transit system) a chopper-type converter is usually employed. The basic operation of a single-switch chopper was discussed in Chapter 2, where it was shown that the average output voltage could be varied by periodically switching the battery voltage on and off for varying intervals. The principal difference between the thyristor-controlled rectifier and the chopper is that in the former the motor current always flows...

Rotor construction

Two types of rotor are used in induction motors. In both the rotor 'iron' consists of a stack of steel laminations with evenly spaced slots punched around the circumference. As with the stator laminations, the surface is coated with an oxide layer, which acts as an insulator, preventing unwanted axial eddy currents from flowing in the iron. The cage rotor is by far the most common each rotor slot contains a solid conductor bar and all the conductors are physically and electrically joined...

Scaling down the excitation problem

We can get to the essence of the matter by imagining that we take a successful design and scale all the linear dimensions by half. We know that to fully utilise the iron of the magnetic circuit we would want the air-gap flux density to be the same as in the original design, so because the air-gap length has been halved the stator MMF needs to be half of what it was. The number of coils and the turns in each coil remains as before, so if the original magnetising current was Im, the magnetising...

Steadystate operation Importance of achieving full flux

Three simple relationships need to be borne in mind to simplify understanding of how the inverter-fed induction motor behaves. Firstly, we established in Chapter 5 that for a given induction motor, the torque developed depends on the strength of the rotating flux density wave, and on the slip speed of the rotor, i.e. on the relative velocity of the rotor with respect to the flux wave. Secondly, the strength or amplitude of the flux wave depends directly on the supply voltage to the stator...

Selfsynchronous closedloop operation

In the open-loop scheme outlined above, the frequency of the supply to the motor is under the independent control of the oscillator driving the switching devices in the inverter. The inverter has no way of knowing whether the rotor is correctly locked-on to the rotating field produced by the stator, and if the pull-out torque is exceeded, the motor will simply stall. In the self-synchronous mode, however, the inverter output frequency is determined by the speed of the rotor. More precisely, the...

Significance of equivalent circuit parameters

If the study of transformers was our aim, we would now turn to some numerical examples to show how the equivalent circuit was used to predict performance for example, we might want to know how much the secondary voltage dropped when we applied the load, or what the efficiency was at various loads. But our aim is to develop an equivalent circuit to illuminate induction motor behaviour, not to become experts at transformer analysis, so we will avoid quantitative study at this point. On the other...

Power Electronic Converters For Motor Drives

In this chapter we look at examples of the power converter circuits which are used with motor drives, providing either d.c. or a.c. outputs, and working from either a d.c. (battery) supply, or from the conventional a.c. mains. The treatment is not intended to be exhaustive, but should serve to highlight the most important aspects which are common to all types of drive converters. Although there are many different types of converters, all except very low-power ones are based on some form of...

Torque per unit volume

For motors with similar cooling systems, the rated torque is approximately proportional to the rotor volume, which in turn is roughly proportional to the overall motor volume. This stems from the fact that for a given cooling arrangement, the specific and magnetic loadings of machines of different types will be more or less the same. The torque per unit length therefore depends first and foremost on the square of the diameter, so motors of roughly the same diameter and length can be expected to...

Performance of chopperfed dc motor drives

We saw earlier that the d.c. motor performed almost as well when fed from a phase-controlled rectifier as it does when supplied with pure d.c. The chopper-fed motor is, if anything, rather better than the phase-controlled, because the armature current ripple can be less if a high chopping frequency is used. Typical waveforms of armature voltage and current are shown in Figure 4.13(c) these are drawn with the assumption that the switch is ideal. A chopping frequency of around 100 Hz, as shown in...

Thyristor Dc Drives General

Drive Schematic Diagram

For motors up to a few kilowatts the armature converter can be supplied from either single-phase or three-phase mains, but for larger motors three-phase is always used. A separate thyristor or diode rectifier is used to supply the field of the motor the power is much less than the armature power, so the supply is often single-phase, as shown in Figure 4.1. The arrangement shown in Figure 4.1 is typical of the majority of d.c. drives and provides for closed-loop speed control. The function of...

Base speed and field weakening

Field Weakening Constant Power

Returning to our consideration of motor operating characteristics, when the field flux is at its full value the speed corresponding to full armature voltage and full current i.e. the rated full-load condition is known as base speed see Figure 3.10 . The motor can operate at any speed up to base speed, and at any torque current up to the rated value by appropriate choice of armature voltage. This full flux region of operation is indicated by the shaded area Oabc in Figure 3.10, and is often...

Double cage rotors

Double cage rotors have an outer cage made up of relatively high resistivity material such as bronze, and an inner cage of low resistivity, usually copper, as shown in Figure 6.10. The inner cage is sunk deep into the rotor, so that it is almost completely surrounded by iron. This causes the inner bars to have a much higher leakage inductance than if they were near the rotor surface, so that under starting conditions when the induced rotor frequency is high their inductive reactance is very...

A8 Disturbance Rejection Example Using Dc Machine

Motor Block Diagram Torque Disturbance

We will conclude our brief look at the benefits of feedback by considering an example that illustrates how a closed-loop system combats the influence of inputs or disturbances that threaten to force the output of the system from its target value. We already referred to the matter qualitatively in Section A.2.2, when we looked at how we would drive a car at a constant speed despite variations in wind or gradients. Throughout this book the self-regulating properties of electric motors have been...

Armature reaction

In addition to deliberate field-weakening, as discussed above, the flux in a d.c. machine can be weakened by an effect known as 'armature reaction'. As its name implies, armature reaction relates to the influence that the armature MMF has on the flux in the machine in small machines it is negligible, but in large machines the unwelcome field weakening caused by armature reaction is sufficient to warrant extra design features to combat it. A full discussion would be well beyond the needs of most...

Cycloconverter Drives

Cyclo Convertor Output Voltage Waveform

We conclude this chapter with a discussion of the cycloconverter variable-frequency drive, which has never become very widespread but is sometimes used in very large low-speed induction motor or synchronous motor drives. Cycloconverters are only capable of producing acceptable output waveforms at frequencies well below the mains frequency, but this, coupled with the fact that it is feasible to make large induction or synchronous motors with high-pole numbers e.g. 20 means that a very low-speed...

Ideal transformer noload condition flux and magnetising current

Ideal Transformer

We will begin by asking how the ideal transformer behaves when its primary winding is connected to the voltage source as shown in Figure 7.2, but the secondary is open circuited. This is known as the no-load Figure 7.2 Single-phase transformer supplying secondary load Z Figure 7.2 Single-phase transformer supplying secondary load Z Figure 7.3 No-load condition i.e. secondary open-circuited , with secondary winding omitted for the sake of clarity Figure 7.3 No-load condition i.e. secondary...

Field produced by each phase winding

Crompton Phase Motor Under Binding

The aim of the winding designer is to arrange the layout of the coils so that each phase winding, acting alone, produces an MMF wave and hence an air-gap flux wave of the desired pole number, and with a sinusoidal variation of amplitude with angle. Getting the desired pole number is not difficult we simply have to choose the right number and pitch of coils, as shown by the diagrams of an elementary 4-pole winding in Figure 5.3. In Figure 5.3 a we see that by positioning two coils each of which...

Graphical interpretation via phasor diagram

Locus Diagram Circuit

We will look at the current phasor diagram as the slip is varied, for two motors, both having the same leakage reactance, XT. One motor will be representative of the 'low-resistance' end of the scale R2 0.1 XT while the other will represent the 'high-resistance' end R2 XT . As before, the voltage and frequency are constant throughout. The reason for choosing total leakage reactance as the common factor linking the two motors is simply that the current loci see below are then very similar, and...

Torquespeed Characteristics Constant Vf Operation

When the voltage at each frequency is adjusted so that the ratio V f is kept constant up to base speed, and full voltage is applied thereafter, a family of torque-speed curves as shown in Figure 8.3 is obtained. These curves are typical for a standard induction motor of several kW output. As expected, the no-load speeds are directly proportional to the frequency, and if the frequency is held constant, e.g. at 25 Hz in Figure 8.3, the speed drops only modestly from no-load point a to full-load...

Series motor steadystate operating characteristics

The series connection of armature and field windings Figure 3.13 a means that the field flux is directly proportional to the armature current, and the torque is therefore proportional to the square of the current. Reversing the direction of the applied voltage and hence current therefore leaves the direction of torque unchanged. This unusual property is put to good use in the universal motor, but is a handicap when negative braking torque is required, since either the field or armature...

A22 Closedloop systems

Closed Loop Speedometer Block Diagram

To illustrate the origin and meaning of the term 'closed-loop' we will consider another familiar activity, that of driving a car, and in particular we will imagine that we are required to drive at a speed of exactly 50 km h, the speed to be verified by an auditor from the bureau of standards. The first essential is an accurate speedometer, because we must measure the output of the 'process' if we are to control it accurately. Our eyes convey the 'actual speed' signal from the speedometer dial...

Deep bar rotors

Deep Bar Rotor

The deep bar rotor has a single cage, usually of copper, formed in slots which are deeper and narrower than in a conventional single-cage design. Construction is simpler and therefore cheaper than in a double cage rotor, as shown in Figure 6.11. The deep bar approach ingeniously exploits the fact that the effective resistance of a conductor is higher under a.c. conditions than under d.c. conditions. With a typical copper bar of the size used in an induction motor rotor, the difference in...

Conventional Dc Motors

Upper Brush Motor

Until the 1980s the conventional brushed d.c. machine was the automatic choice where speed or torque control is called for, and large numbers remain in service despite a declining market share that reflects the move to inverter-fed induction motors. Applications range from steel rolling mills, railway traction, to a very wide range of industrial drives, robotics, printers, and precision servos. The range of power outputs is correspondingly wide, from several megawatts at the top end down to...

Autotransformer starter

A 3-phase autotransformer is usually used where star delta starting provides insufficient starting torque. Each phase of an autotransformer consists of a single winding on a laminated core. The mains supply is connected across the ends of the coils, and one or more tapping points or a sliding contact provide a reduced voltage output, as shown in Figure 6.3. The motor is first connected to the reduced voltage output, and when the current has fallen to the running value, the motor leads are...

Real transformer approximate equivalent circuit

The justification for the approximate equivalent circuit see Figure 7.11 a rests on the fact that for all transformers except very small ones i.e. for all transformers that would cause serious harm if they fell on ones foot the series elements in Figure 7.10 b are of low impedance and the parallel elements are of high impedance. Actually, to talk of low or high impedances without qualification is nonsense. What the rather loose language in the paragraph above really means is that under normal...

Real transformer on load exact equivalent circuit

Transformer Equivalent Circuit

The equivalent circuit showing the transformer supplying a secondary load impedance Z2 is shown in Figure 7.10 a . This diagram has been annotated to show how the ideal transformer at the centre imposes the relationships between primary and secondary currents. Provided that we know the values of the transformer parameters we can use this circuit to calculate all the voltages, currents and powers when either the primary or secondary voltage are specified. However, we seldom use the circuit in...

Fourquadrant Operation And Regenerative Braking

Quadrant Motor

As we saw in Section 3.4, the beauty of the separately excited d.c. motor is the ease with which it can be controlled. Firstly, the steady-state speed is determined by the applied voltage, so we can make the motor run at any desired speed in either direction simply by applying the appropriate magnitude and polarity of the armature voltage. Secondly, the torque is directly proportional to the armature current, which in turn depends on the difference between the applied voltage V and the back...

Phasor diagram and Powerfactor control

Synchronous Motor Phasor Diagram

To see how the magnitude of the e.m.f. influences behaviour we can examine the phasor diagrams of a synchronous machine operating as a motor, as shown in Figure 10.4. The first point to clarify is that our sign convention is that motoring corresponds to positive input power to the machine. The power is given by VI cos f, so when the machine is motoring positive power the angle f lies in the range 90 . If the current lags or leads the voltage by more than 90 the machine will be generating....

Step position error and holding torque

In the previous discussion the load torque was assumed to be zero, and the rotor was therefore able to come to rest with its poles exactly in line with the excited stator poles. When load torque is present, however, the rotor will not be able to pull fully into alignment, and a 'step position error' will be unavoidable. The origin and extent of the step position error can be appreciated with the aid of the typical torque-displacement curve shown in Figure 9.8. The true step position is at the...