## 10 Synchronous Brushless Dc And Switched Reluctance Drives

Synchronous Motors Excited-rotor motors Equivalent circuit of excited-rotor synchronous motor Phasor diagram and Power-factor control Starting Permanent magnet synchronous motors Hysteresis motors Reluctance motors Controlled-Speed Synchronous Motor Drives Open-loop inverter-fed synchronous motor drives Self-synchronous (closed-loop) operation Operating characteristics and control Switched Reluctance Motor Drives 358 Torque prediction and control 360 Power converter and overall drive Power...

## 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...

## A4 Importance Of Loop Gain Example

To illustrate the significance of the forward and feedback paths on the overall gain of a closed-loop system we will look at an operational amplifier of the type frequently used in analogue control. In their basic form these amplifiers typically have very high gains, but the gain can vary considerably even amongst devices from a single batch. We will see that as normally employed (with negative feedback) the unpredictability of the open-loop gain is not a problem. The op-amp itself is...

## 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...

## A6 Pid Controller

We saw in Section A.3 that the simplest form of controller is an amplifier the output of which is proportional to the error signal. A control system that operates with this sort of controller is said to have 'proportional' or 'P' control. An important feature of proportional control is that as soon as there is any change in the error, proportionate action is initiated immediately. We have also seen in Section A.5 that in order to completely eliminate steady-state error we need to have an...

## 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

## Approximate Equivalent Circuits

This section is devoted to what can be learned from the equivalent circuit in simplified form, beginning with the circuit shown in Figure 7.16, in which the magnetising branch has been moved to the left-hand side. This makes calculations very much easier because the current and power in the magnetising branch are independent of the load branch. The approximation involved in doing this are greater than in the case of a transformer because for a motor the ratio of magnetising reactance to leakage...

## Armature voltage feedback and IR compensation

In low-power drives where precision speed-holding is not essential, and cost must be kept to a minimum, the tachogenerator is dispensed with and the armature voltage is used as a 'speed feedback' instead. Performance is clearly not as good as with tacho feedback, since whilst the steady-state no-load speed is proportional to armature voltage, the speed falls as the load (and hence armature current) increases. We saw in Chapter 3 that the drop in speed with load was attributable to the armature...

## Behaviour with a mechanical load

Suppose that, with the primitive linear motor up to its no-load speed we suddenly attach the string carrying the weight, so that we now have a steady force (T mg) opposing the motion of the conductor. At this stage there is no current in the conductor and thus the only force on it will be T. The conductor will therefore begin to decelerate. But as soon as the speed falls, the back e.m.f. will become less than V, and current will begin to flow into the conductor, producing an electromagnetic...

## Behaviour with no mechanical load

In this section we assume that the hanging weight has been removed, and that the only force on the conductor is its own electromagnetically generated one. Our primary interest will be in what determines the steady speed of the primitive motor, but we must begin by considering what happens when we first apply the voltage. With the conductor stationary when the voltage V is applied, the current will immediately rise to a value of V R, since there is no motional e.m.f. and the only thing which...

## 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...

## Comparison with dc drive

The initial success of the inverter-fed induction motor drive was due to the fact that a standard induction motor was much cheaper than a Plate 8.1 Inverter-fed induction motor with inverter mounted directly onto motor. (Alternatively the inverter can be wall-mounted, as in the upper illustration, which also shows the user interface module.) (Photo courtesy of ABB) comparable d.c. motor, and this saving compensated for the relatively high cost of the inverter compared with the thyristor d.c....

## 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...

## 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)...

## Current control

The closed-loop current controller, or current loop, is at the heart of the drive system and is indicated by the shaded region in Figure 4.11. The purpose of the current loop is to make the actual motor current follow the current reference signal (Iref) shown in Figure 4.11. It does this by comparing a feedback signal of actual motor current with the current reference signal, amplifying the difference (or current error), and using the resulting amplified current error signal (an analogue...

## 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...

## Dependence of pull out torque on motor parameters

The aim here is to quantify the dependence of the maximum or pull-out torque on the rotor parameters, for which we make use of the simplest possible (but still very useful) model shown in Figure 7.17. The magnetising branch and the stator resistance are both ignored, so that there is only one current, the referred rotor current l2 being the same as the stator current I1. Of the two forms shown in Figure 7.17, we will focus on the one in Figure 7.17(b), in which the actual and fictitious rotor...

## Digitally Controlled Drives

As in all forms of industrial and precision control, digital implementations have replaced analogue circuitry in many electric drive systems, but there are few instances where this has resulted in any real change to the structure of existing drives, and in most cases understanding how the drive functions is still best approached in the first instance by studying the analogue version. There are of course important systems which are predominantly digital, such as PWM inverter drives (see Chapter...

## 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...

## Doubleconverter reversing drives

Where full four-quadrant operation and rapid reversal is called for, two converters connected in anti-parallel are used, as shown in Figure 4.8. One converter supplies positive current to the motor, while the other supplies negative current. The bridges are operated so that their d.c. voltages are almost equal thereby ensuring that any d.c. circulating current is small, and a reactor is placed between the bridges to limit the flow of ripple currents which result from the unequal ripple voltages...

## 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...

## Dynamic braking

A simpler and cheaper but less effective method of braking can be achieved by dissipating the kinetic energy of the motor and load in a resistor, rather than returning it to the supply. A version of this technique is employed in the cheaper power electronic converter drives, which have no facility for returning power to the mains. When the motor is to be stopped, the supply to the armature is removed and a resistor is switched across the armature brushes. The motor e.m.f. drives a (negative)...

## Elementary motor stationary conditions

The primitive linear machine is shown pictorially in Figure 1.13 and in diagrammatic form in Figure 1.14. It consists of a conductor of active2 length l which can move horizontally perpendicular to a magnetic flux density B. It is assumed that the conductor has a resistance (R), that it carries a d.c. current (I), and that it moves with a velocity (v) in a direction perpendicular to the field and the current (see Figure 1.14). Attached to the conductor is a string which passes over a pulley and...

## Enclosures and cooling

There is clearly a world of difference between the harsh environment faced by a winch motor on the deck of an ocean-going ship, and the comparative comfort enjoyed by a motor driving the drum of an office photocopier. The former must be protected against the ingress of rain and seawater, while the latter can rely on a dry and largely dust-free atmosphere. Classifying the extremely diverse range of environments poses a potential problem, but fortunately this is one area where international...

## Energy Conversion Motional

We now turn away from considerations of what determines the overall capability of a motor to what is almost the other extreme, by examining the behaviour of a primitive linear machine which, despite its obvious simplicity, encapsulates all the key electromagnetic energy conversion processes that take place in electric motors. We will see how the process of conversion of energy from electrical to mechanical form is elegantly represented in an 'equivalent circuit' from which all the key aspects...

## Equivalent Circuit

We can represent the electrical relationships in the primitive machine in an equivalent circuit as shown in Figure 1.15. The resistance of the conductor and the motional e.m.f. together represent in circuit terms what is happening in the conductor (though in reality the e.m.f. and the resistance are distributed, not lumped as separate items). The externally applied source that drives the current is represented by the voltage V on the left (the old-fashioned battery symbol being deliberately...

## Equivalent circuit of excitedrotor synchronous motor

Predicting the current and power-factor drawn from the mains by a cylindrical-rotor synchronous motor is possible by means of the very simple per-phase a.c. equivalent circuit shown in Figure 10.3. In this circuit Xs (known as the synchronous reactance) represents the effective inductive reactance of the stator phase winding R is the stator winding resistance V the applied voltage and E the e.m.f. induced in the stator winding by the rotating field produced by the d.c. current on the rotor....

## Equivalent Circuit Under Variablefrequency Conditions

The beauty of the conventional equivalent circuits we have explored is that everything happens at supply frequency, and there is no need for us to bother with the fact that in reality the rotor currents are at slip frequency. In addition there are well-established approximations that we can make to simplify analysis and calculations, such as moving the magnetising branch to the left-hand side, and ignoring the stator resistance in all calculations except efficiency. But more and more induction...

## Excitation power and VA

The setting up of the travelling wave by the magnetising current amounts to the provision of'excitation' for the motor. Some energy is stored in the magnetic field, but since the amplitude remains constant once the field has been established, no power input is needed to sustain the field. We therefore find that under the conditions discussed so far, i.e. in the absence of any rotor currents, the power input to the motor is very small. (We should perhaps note that the rotor currents in a real...

## Excitedrotor motors

The rotor carries a 'field' winding which is supplied with direct current via a pair of sliprings on the shaft, and is designed to produce an air-gap field of the same pole number and spatial distribution (usually sinusoidal) as that produced by the stator winding. The rotor may be more or less cylindrical, with the field winding distributed in slots (see Figure 10.2(a)), or it may have projecting ('salient') poles around which the winding is concentrated (see Figure 10.2(b)). As the discussion...

## Force on a conductor

We now return to the production of force on a current-carrying wire placed in a magnetic field, as revealed by the setup shown in Figure 1.1. The direction of the force is shown in Figure 1.1 it is at right angles to both the current and the magnetic flux density. With the flux density horizontal and to the right, and the current flowing out of the paper, the force is vertically upward. If either the field or the current is reversed, the force acts downwards, and if both are reversed, the force...

## 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...

## Generating region overhauling loads

For negative slips, i.e. when the rotor is turning in the same direction, but at a higher speed than the travelling field, the 'motor' torque is in fact negative. In other words the machine develops a torque that which opposes the rotation, which can therefore only be maintained by applying a driving torque to the shaft. In this region the machine acts as an induction generator, converting mechanical power from the shaft into electrical power into the supply system. Many cage induction machines...

## Generation of step pulses and motor response

The step pulses may be produced by an oscillator circuit, which itself is controlled by an analogue voltage, digital controller or microprocessor. When a given number of steps is to be taken, the oscillator pulses are gated to the drive and the pulses are counted, until the required number of steps is reached, when the oscillator is gated off. This is illustrated in Figure 9.2, for a six-step sequence. There are six-step command pulses, equally spaced in time, and the motor takes one step...

## Half stepping

We have already seen how to step the motor in 30 increments by energising the phases one at a time in the sequence ABCA, etc. Although this 'one-phase-on' mode is the simplest and most widely used, there are two other modes, which are also frequently employed. These are referred to as the 'two-phase-on' mode and the 'half-stepping' mode. The two-phase-on can provide greater holding torque and a much better damped single-step response than the one-phase-on mode and the half-stepping mode permits...

## High inertia loads overheating

Apart from accelerating slowly, high inertia loads pose a particular problem of rotor heating, which can easily be overlooked by the unwary user. Every time an induction motor is started from rest and brought up to speed, the total energy dissipated as heat in the motor windings is equal to the stored kinetic energy of the motor plus load. (This matter is explored further via the equivalent circuit in Chapter 7.) Hence with high inertia loads, very large amounts of energy are released as heat...

## Highspeed running and ramping

The discussion so far has been restricted to operation when the step command pulses are supplied at a constant rate, and with sufficiently long intervals between the pulses to allow the rotor to come to rest between steps. Very large numbers of small stepping motors in watches and clocks do operate continuously in this way, stepping perhaps once every second, but most commercial and industrial applications call for a more exacting and varied performance. To illustrate the variety of operations...

## Ideal transformer noload condition voltage ratio

We now consider the secondary winding to be restored, but leave it disconnected from the load so that its current is zero, in which case it can clearly have no influence on the flux. Because the magnetic circuit is perfect, none of the flux set up by the primary winding leaks out, and all of it therefore links the secondary winding. We can therefore apply Faraday's law and make use of equation (7.3) to obtain the secondary induced e.m.f. as There is no secondary current, so there is no...

## Ideal transformer on load

We now consider what happens when we connect the secondary winding to a load impedance Z2. We have already seen that the flux is determined solely by the applied primary voltage, so when current flows to the load it can have no effect on the flux, and hence because the secondary winding resistance is zero, the secondary voltage remains as it was at no-load, given by equation (7.7). (If the voltage were to change when we connected the load we could be forgiven for beginning to doubt the validity...

## 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...

## Inertia matching

There are some applications where the inertia dominates the torque requirement, and the question of selecting the right gearbox ratio has to be addressed. In this context the term 'inertia matching' often causes confusion, so it worth explaining what it means. Suppose we have a motor with a given torque, and we want to drive an inertial load via a gearbox. As discussed previously, the gear ratio determines the effective inertia as 'seen' by the motor a high step-down ratio (i.e. load speed much...

## Introduction

Judged in terms of fitness for purpose coupled with simplicity, the induction motor must rank alongside the screwthread as one of mankind's best inventions. It is not only supremely elegant as an electromechanical energy converter, but is also by far the most important, with something like one-third of all the electricity generated being converted back to mechanical energy in induction motors. Despite playing a key role in industrial society, it remains largely unnoticed because of its workaday...

## 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...

## Line current

To find the line current we must find the effective impedance looking in from the supply, so we first find the impedances of the rotor branch and the magnetising (air-gap) branches. Expressed in 'real and imaginary' and also 'modulus and argument' form these are Rotor branch impedance, Zr 7.5 + j1 7.57 7.6 V Magnetising branch impedance, Zm 6.25 + j'39.0 39.5 80.9 V The parallel combination of these two branches has an effective impedance of 6.74 + j2.12 or 7.07 17.5 . At roughly 7 V, and...

## 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

So far we have assumed that the source of the magnetic field is a permanent magnet. This is a convenient starting point as all of us are familiar with magnets, even if only of the fridge-door variety. But in the majority of motors, the working magnetic field is produced by coils of wire carrying current, so it is appropriate that we spend some time looking at how we arrange the coils and their associated iron 'magnetic circuit' so as to produce high magnetic fields which then interact with...

## 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...

## Magnetic field and magnetic flux

When a current-carrying conductor is placed in a magnetic field, it experiences a force. Experiment shows that the magnitude of the force depends directly on the current in the wire, and the strength of the magnetic field, and that the force is greatest when the magnetic field is perpendicular to the conductor. In the set-up shown in Figure 1.1, the source of the magnetic field is a bar magnet, which produces a magnetic field as shown in Figure The notion of a 'magnetic field' surrounding a...

## Magnetic flux density

Along with showing direction, the flux plots also convey information about the intensity of the magnetic field. To achieve this, we introduce the idea that between every pair of flux lines (and for a given depth into the paper) there is a same 'quantity' of magnetic flux. Some people have no difficulty with such a concept, while others find that the notion of quanti fying something so abstract represents a serious intellectual challenge. But whether the approach seems obvious or not, there is...

## Magnetomotive force MMF

One obvious way to increase the flux density is to increase the current in the coil, or to add more turns. We find that if we double the current, or the number of turns, we double the total flux, thereby doubling the flux density everywhere. We quantify the ability of the coil to produce flux in terms of its magnetomotive force (MMF). The MMF of the coil is simply the product of the number of turns (N) and the current (I), and is thus expressed in ampere-turns. A given MMF can be obtained with...

## Magnitude of rotating flux wave

We have already seen that the speed of the flux wave is set by the pole number of the winding and the frequency of the supply. But what is it that determines the amplitude of the field To answer this question we can continue to neglect the fact that under normal conditions there will be induced currents in the rotor. We might even find it easier to imagine that the rotor conductors have been removed altogether this may seem a drastic assumption, but will prove justified later. The stator...

## Magnitude of torque

Returning to our original discussion, the force on each conductor is given by equation 1.2, and it follows that the total tangential force Fdepends on the flux density produced by the field winding, the number of conductors on the rotor, the current in each, and the length of the rotor. The resultant torque or couple1 (T) depends on the radius of the rotor (r), and is given by We will develop this further in Section 1.5, after we examine the remarkable benefits gained by putting the conductors...

## 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...

## Maximum speed and speed range

We saw in Chapter 1 that as a general rule, for a given power the higher the base speed the smaller the motor. In practice, there are only a few applications where motors with base speeds below a few hundred rev min are attractive, and it is usually best to obtain low speeds by means of the appropriate mechanical speed reduction. Speeds over 10 000 rev min are also unusual except in small universal motors and special-purpose inverter-fed motors. The majority of medium-size motors have base...

## Measurement of parameters

Two simple tests are used to measure the transformer parameters - the open-circuit or no-load test and the short-circuit test. We will see later that very similar tests are used to measure induction motor parameters. In the open-circuit test, the secondary is left disconnected and with rated voltage (V1) applied to the primary winding, the input current (I0) and power (W0) are measured. If we are seeking values for the three-element model in Figure 7.11(b), we would expect no power at no load,...

## 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,...

## Modelling the electromechanical energy conversion process

In Chapters 5 and 6 we saw that the behaviour of the motor was determined primarily by the slip. In particular we saw that if the motor was unloaded, it would settle at almost the synchronous speed (i.e. with a very small slip), with very little induced rotor current, at very low frequency. As the load torque was increased the rotor slowed relative to the travelling flux the magnitude and frequency of the induced rotor currents increased the rotor thereby produced more torque and the stator...

## Motor current waveforms

For the sake of simplicity we will look at operation from a single-phase (2-pulse) converter, but similar conclusions apply to the 6-pulse converter. The voltage (Va) applied to the motor armature is typically as shown in Figure 4.2(a) as we saw in Chapter 2, it consists of rectified 'chunks' of the incoming mains voltage, the precise shape and average value depending on the firing angle. The voltage waveform can be considered to consist of a mean d.c. level (Vdc), and a superimposed pulsating...

## Motor operation with converter supply

The basic operation of the rectifying bridge has been discussed in Chapter 2, and we now turn to the matter of how the d.c. motor behaves when supplied with 'd.c.' from a controlled rectifier. By no stretch of imagination could the waveforms of armature voltage looked at in Chapter 2 (e.g. Figure 2.12) be thought of as good d.c., and it would not be unreasonable to question the wisdom of feeding such an unpleasant looking waveform to a d.c. motor. In fact it turns out that the motor works...

## Openloop inverterfed synchronous motor drives

This simple method is attractive in multi-motor installations where all the motors must run at exactly the same speed. Individually the motors (permanent magnet or reluctance) are more expensive than the equivalent mass-produced induction motor, but this is offset by the fact that speed feedback is not required, and the motors can all be supplied from a single inverter, as shown in Figure 10.7. The inverter voltage-frequency ratio will usually be kept constant (see Chapter 8) to ensure that the...

## Openloop position control

A basic stepping motor system is shown in Figure 9.1. The drive contains the electronic switching circuits, which supply the motor, and is discussed later. The output is the angular position of the motor shaft, while the input consists of two low-power digital signals. Every time a Plate 9.1 Hybrid 1.8 stepping motors, of sizes 34 (3.4 inch diameter), 23 and 17. (Photo courtesy of Astrosyn) Plate 9.1 Hybrid 1.8 stepping motors, of sizes 34 (3.4 inch diameter), 23 and 17. (Photo courtesy of...

## 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...

## Operating temperature and cooling

The cooling arrangement is the single most important factor in determining the output from any given motor. Plate 1.2 Steel frame cage induction motor, 150 kW (201 h.p.), 1485 rev min. The active parts are totally enclosed, and cooling is provided by means of an internal fan which circulates cooling air round the interior of the motor through the hollow ribs, and an external fan which blows air over the case. (Photograph by courtesy of Brook Crompton.) Plate 1.2 Steel frame cage induction...

## 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

To understand how an induction motor operates, we must first unravel the mysteries of the rotating magnetic field. We shall see later that the rotor is effectively dragged along by the rotating field, but that it can never run quite as fast as the field. When we want to control the speed of the rotor, the best way is to control the speed of the field. Our look at the mechanism of the rotating field will focus on the stator windings because they act as the source of the flux. In this part of the...

## Overall operating region

A standard drive with field-weakening provides armature voltage control of speed up to base speed, and field-weakening control of speed thereafter. Any torque up to the rated value can be obtained at any speed below base speed, and as explained in Chapter 3 this region is known as the 'constant torque' region. Above base speed, the maximum available torque reduces inversely with speed, so this is known as the 'constant power' region. For a converter-fed drive the operating region in quadrant 1...

## Performance Prediction Example

The per-phase equivalent circuit parameters (referred to the stator) of a 4-pole, 60 Hz, 440 V three-phase delta-connected induction motor are as follows Stator and rotor leakage reactances, X1 X21 j1.0 V Rotor resistance, R2 0.3 V Magnetising reactance, Xm j40 V Iron-loss resistance, Rc 250 V. The mechanical frictional losses at normal speed amount to 2.5 kW. We will calculate the input line current, the output power and the efficiency at the full-load speed of 1728 rev min. The per-phase...

## Permanent magnet synchronous motors

Permanent magnets are used on the rotor instead of a wound field typical 2-pole and 4-pole surface-mounted versions are shown in Figure 10.5, the direction in which the magnets have been magnetised being represented by the arrows. Motors of this sort have outputs ranging from about 100 W up to perhaps 100 kW. For starting from a fixed-frequency supply a rotor cage is required, as discussed above. The advantages of the permanent magnet type are that no supply is needed for the rotor and the...

## Phasor diagram

It is instructive to finish by looking at the phasor diagrams showing the principal voltages and currents under full-load conditions, as shown in Figure 7.15, which is drawn to scale. From the voltage phasor diagram, we note that in this motor the voltdrop due to the stator leakage reactance and resistance is significant, in that the input voltage of 440 V is reduced to 408.5 V, i.e. a reduction of just over 7 . The voltage across the magnetising branch determines the magnetising current and...

## Plug reversal and plug braking

Because the rotor always tries to catch up with the rotating field, it can be reversed rapidly simply by interchanging any two of the supply leads. The changeover is usually obtained by having two separate 3-pole contactors, one for forward and one for reverse. This procedure is known as plug reversal or plugging, and is illustrated in Figure 6.16. The motor is initially assumed to be running light (and therefore with a very small positive slip) as indicated by point A on the dotted...

## Position control

As mentioned earlier many servo motors are used in closed-loop position control applications, so it is appropriate to look briefly at how this is achieved. Later (in Chapter 8) we will see that the stepping motor provides an alternative open-loop method of position control, which can be cheaper for some applications. In the example shown in Figure 4.15, the angular position of the output shaft is intended to follow the reference voltage (Uref), but it should be clear that if the motor drives a...

## Power converter and overall drive characteristics

An important difference between the SR motor and all other self-synchronous motors is that its full torque capability can be achieved without having to provide for both positive and negative currents in the phases. This is because the torque does not depend on the direction of current in the phase-winding. The advantage of such 'unipolar' drives is that because each of the main switching devices is permanently connected in series with one of the motor windings (as in Figure 9.15), there is no...

## Power factor and supply effects

One of the drawbacks of a converter-fed d.c. drive is that the supply power factor is very low when the motor is operating at high torque (i.e. high current) and low speed (i.e. low armature voltage), and is less than unity even at base speed and full load. This is because the supply current waveform lags the supply voltage waveform by the delay angle a, as shown (for a 3-phase converter) in Figure 4.9, and also the supply current is approximately rectangular (rather than sinusoidal). Figure...

## 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,...

## Power relationships conductor moving at constant speed

Now let us imagine the situation where the conductor is moving at a constant velocity (v) in the direction of the electromagnetic force that is propelling it. What current must there be in the conductor, and what voltage will have to be applied across its ends We start by recognising that constant velocity of the conductor means that the mass (m) is moving upwards at a constant speed, i.e. it is not accelerating. Hence from Newton's law, there must be no resultant force acting on the mass, so...

## Principle Of Motor Operation

The principle on which stepping motors are based is very simple. When a bar of iron or steel is suspended so that it is free to rotate in a magnetic field, it will align itself with the field. If the direction of the field is changed, the bar will turn until it is again aligned, by the action of the so-called reluctance torque. (The mechanism is similar to that of a compass needle, except that if a compass had an iron needle instead of a permanent magnet it would settle along the earth's...

## Principle of operation

If one of the leads of a 3-phase motor is disconnected while it is running light, it will continue to run with a barely perceptible drop in speed, and a somewhat louder hum. With only two leads remaining there can only be one current, so the motor must be operating as a single-phase machine. If load is applied the slip increases more quickly than under Plate 6.1 Single-phase capacitor-run induction motor. Output power range is typically from about 70 W to 2.2 kW, with pole-numbers from 2 to 8....

## Producing Rotation

Nearly all motors exploit the force which is exerted on a current-carrying conductor placed in a magnetic field. The force can be demonstrated by placing a bar magnet near a wire carrying current (Figure 1.1), but anyone trying the experiment will probably be disappointed to discover how feeble the force is, and will doubtless be left wondering how such an unpromising effect can be used to make effective motors. We will see that in order to make the most of the mechanism, we need to arrange a...

## 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...

## Properties Of Induction Motors

We have started with the exact circuit in Figure 7.12 because the air-gap in the induction motor causes its magnetising reactance to be lower than a transformer of similar rating, while its leakage reactance will be higher. We therefore have to be a bit more cautious before we make major simplifications, though we will find later that for many purposes the approximate circuit (with the magnetising branch on the left) is actually adequate. In this section, we concentrate on what can be learned...

## Pullout torque under constantcurrent conditions

If the phase currents are taken to be ideal, i.e. they are switched-on and switched-off instantaneously, and remain at their full-rated value during each 'on' period, we can picture the axis of the magnetic field to be advancing around the machine in a series of steps, the rotor being urged to follow it by the reluctance torque. If we assume that the inertia is high enough for fluctuations in rotor velocity to be very small, the rotor will be rotating at a constant rate, which corresponds...

## Real transformer leakage reactance

In the ideal transformer it was assumed that all the flux produced by the primary winding linked the secondary, but in practice some of the primary flux will exist outside the core (see Figure 1.7) and will not link with the secondary. This leakage flux, which is proportional to the primary current, will induce a voltage in the primary winding whenever the primary current changes, and it can therefore be represented by a 'primary leakage inductance' (l1) in series with the primary winding of...

## 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...

## Regenerative operation and braking

All motors are inherently capable of regenerative operation, but in drives the basic power converter as used for the 'bottom of the range' version will not normally be capable of continuous regenerative operation. The cost of providing for fully regenerative operation is usually considerable, and users should always ask the question 'do I really need it ' In most cases it is not the recovery of energy for its own sake, which is of prime concern, but rather the need to achieve a specified...

## Relative magnitudes of V and E and efficiency

Invariably we want machines which have high efficiency. From equation 1.20, we see that to achieve high efficiency, the copper loss (I2R) must be small compared with the mechanical power (EI), which means that the resistive volt-drop in the conductor (IR) must be small compared with either the induced e.m.f. (E) or the applied voltage (V). In other words we want most of the applied voltage to be accounted for by the 'useful' motional e.m.f., rather than the wasteful volt drop in the wire. Since...

## 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...