where f = supply frequency in Hertz, and

p = number of pole pairs

    Note: A 2-pole motor has 1 pole pair.

Voltage—frequency relationship: If it is desired to convert a constant speed motor operating direct-on-line to a variable speed drive using an inverter it is necessary to consider the effect of frequency on flux and torque. An induction motor on a normal supply operates with a rotating field set up by three-phase currents in the stator winding. The magnitude of the field is controlled broadly by the voltage impressed upon the winding by the supply. This is because the resistance of the windings results in only a small voltage drop, even at full load current, and therefore in the steady-state the supply voltage must be balanced by the e.m.f. induced by the rotating field. This e.m.f. depends on the product of three factors:

Exactly the same factors are valid for transformer design, except that the field is pulsating instead of rotating. For inverter operator the speed of field rotation for which maximum voltage is appropriate is known as the ‘base speed’.

The consequence of reducing the supply frequency can readily be deduced from the relationship described above. For the same flux the induced e.m.f. in the stator winding will be proportional to frequency, hence the voltage supplied to the machine windings must be correspondingly reduced in order to avoid heavy saturation of the core. This is valid for changes in frequency over a wide range. The voltage/frequency relationship should therefore be linear if a constant flux is to be maintained within the machine, as the designer intended. If flux is constant so is the motor torque for a given stator current, hence the drive has a constant torque characteristic.

Although constant V/f control is an important underlying principle, it is appropriate to point out departures from it which are essential if a wide speed range is to be covered. Firstly, operation above base speed is easily achieved by increasing the output frequency of the inverter above the normal mains frequency; two or three times base speed is easily obtained. The output voltage of an inverter cannot usually be made higher than its input voltage therefore the V/f characteristic is typically like that shown in Figure 19.6(a). Since V is constant above base speed, the flux will fall as the frequency is increased after the output voltage limit is reached. The machine flux falls (Figure 19.6(b)) in direct proportion to the actual V/f ratio. Although this greatly reduces the core losses, the ability of the machine to produce torque is impaired and less mechanical load is needed to draw full load current from the inverter. The drive is said to have a constant-power characteristic above base speed. Many applications not requiring full torque at high speeds can make use of this extended speed range.

The second operating condition where departure from a constant V/f is beneficial is at very low speeds, whereby the voltage drop arising from the stator resistance becomes significantly large. This voltage drop is at the expense of flux, as shown in Figure 19.6(b). To maintain a truly constant flux within the machine the terminal voltage must be increased above the constant V/f value to compensate for the stator resistance effect. Indeed, as output frequency approaches zero, the optimum voltage becomes the voltage equal to the stator IR drop. Compensation for stator resistance is normally referred to as ‘voltage boost’ and almost all inverters offer some form of adjustment so that the degree of voltage boost can be matched to the actual winding resistance. It is normal for the boost to be gradually tapered to zero as the frequency progresses towards base speed. Figure 19.6(c) shows a typical scheme for tapered boost. It is important to appreciate that the level of voltage boost should increase if a high starting torque is required, since in this case the IR drop will be greater by virtue of the increased stator current. In this case automatic load-dependent boost control is useful in obtaining the desired low speed characteristics. Such a strategy is referred to as constant V/f (or V/Hz) control and is a feature of most commercially available a.c. drives though more advanced open-loop strategies are now becoming more available.

So far the techniques described have been based on achieving constant flux within the air gap of the machine or, if that is not possible, then the maximum flux. Constant flux is the ideal condition if the largest capability of torque is required because the load cannot be predicted with certainty, or if the most rapid possible acceleration time is desired. A large number of inverters are used however for variable air volume applications where control of airflow is obtained by variable speed fans. The torque required by a fan follows a square law characteristic with respect to speed and reducing the speed of a fan by 50% will reduce its torque requirement to only 25% of rated. As the load is entirely predictable there is no need for full torque capability and hence flux to be maintained, and higher motor efficiency can be obtained by operating at a reduced flux level. A further benefit is that acoustic noise, a major concern in air conditioning equipment, is significantly reduced. It is therefore common for inverters to have an alternative square law V/f characteristic or, ideally, a self-optimising economy feature so that rapid acceleration to meet a new speed demand is followed by settling to a highly efficient operating point.

Slip ring induction motor: The wound rotor or slip-ring a.c. machine whilst introducing the negative aspect of brushes does address some of the disadvantages of the cage induction motor but with the handicap of cost compared to the equivalent rated d.c. shunt-wound machine.

With the correct value of (usually) resistance inserted in the rotor circuit, near-unity relationship between torque and supply current at starting can be achieved, i.e. 100% full load torque, with 100% full load current, 200% FLT with 200% FLC etc., (i.e. comparable with the starting capability of the d.c. machine). Not only the high starting efficiency but also the smooth controlled acceleration historically gave the slip-ring motor great popularity for lift, hoist and crane applications. It has had similar popularity with fan engineers, to provide a limited range of air volume control, either 2:1 or 3:1 reduction, at constant load, by the use of speed regulating variable resistances in the rotor circuit. Although a fan possesses a square law torque–speed characteristic, so that motor currents fall considerably with speed, losses in the rotor regulator at lower motor speeds are still relatively high, severely limiting the useful speed range.

Rotor slip-ring systems, used with this type of motor, offer a similar service life to that of the d.c. motor commutator system.

Efficient variable speed control of slip-ring motors can be achieved by converters based upon the slip energy recovery principle first proposed by Krammer. Such schemes are based upon converting the slip frequency on the rotor to supply frequency. It is also possible to retrofit variable frequency inverters to existing slip-ring motors. This can be done simply by shorting out the slip-ring terminations (ideally on the rotor thereby eliminating the brushes) and treating the motor as a cage machine.

Variable voltage control of slip-ring motors has been used extensively, notably in crane and lift applications, though these are now largely being replaced by flux vector drives and will therefore not be considered further.

Stationary torque characteristics: A motor which uses permanent magnets to supply the field flux is represented by the simple equivalent circuit of Figure 19.8. This is a series circuit of the armature resistance, R_a, and back e.m.f., E.

If we ignore the voltage drop across the transistors, the equation for the voltage is

K_e is known as the back-e.m.f. constant of the motor. The armature current I_a is

Therefore, from above, the torque T is

K_t is known as the torque constant of the motor.

Figure 19.9 shows the relation between T (torque) and Ω (rotational speed) at two different voltages. The torque decreases linearly as the speed increases. The slope of this function is a constant K_tK_e/R_a and is independent of the terminal voltage and the speed. Such characteristics make the speed or position control of a d.c. motor relatively easy.

The starting torque and the no load speed (assuming no bearings friction and windage loss) are given by

Summary of characteristics: Table 19.1 shows the salient characteristics of the three-phase a.c. to d.c. converters described above.

Practical effects: The characteristics in Table 19.1 have, for the most part, been based upon idealised conditions of negligible a.c. inductance and constant d.c. current. Whilst these assumptions provide a convenient means for compassion they are not often valid in practice. It is not practicable to consider all such effects here. The effect of d.c. link current ripple on a.c. supply harmonics is of great practical industrial importance mainly in relation to 3-phase bridges (ignoring single-phase traction requirement). Practical experience has led to the adoption by many of the following values:

In general, the amplitudes of higher harmonics are rarely of significance, in regard to supply distortion. Under conditions of very high d.c. current ripple, the 5th harmonic can assume a considerably higher value than that quoted above. A practical example would be an application with a very capacitive d.c. load (e.g. a voltage source inverter) in such a case where no smoothing choke is used I₅ could be as high as 0.5I₁.

Single converter drives: Figure 19.13 shows a single-converter d.c. drive.

In its most basic form the motor will drive the load in one direction only without braking or reverse running. It is said to be a ‘single-quadrant drive’, only operating in one quadrant of the torque-speed characteristic.

Such drives have wide application from simple machine tools to fans, pumps, extruders, agitators, printing machines etc.

If the drive is required to operate in both the forward and reverse directions and/or provide regenerative braking a single fully-controlled converter can still be used however, some means of reversing either the field or armature connections, as shown in Figure 19.14, must be added.

Reversal of armature current can involve bulky (high current) reversing switches but due to the low inductance of the armature circuit can be completed in typically 0.2 seconds. Field current reversal takes longer, typically in the order of 1 second, however lower cost reversing switches may be used. The field reversal time can be reduced by using higher voltage field converters to force the current. Forcing voltages up to 4 per unit are used but care must be taken not to overstress the machine. Obviously this increased voltage cannot be applied continuously and requires either a switched a.c. supply or a controlled field converter.

Armature and field reversal techniques are used where torque reversals are infrequent such as hoists, presses, lathes and centrifuges.

Dual-converter drives: When a four quadrant drive is required to change the direction of torque rapidly, the delays associated with reversing switches described above may be unacceptable. A dual converter comprising two fully controlled power converters connected in inverse-parallel can be used as shown in Figure 19.15. Bridge 1 conducts when the armature current I_a is required to be positive, bridge 2 when it is required to be negative.

There are two common forms of dual converter. In the first, both bridges are controlled simultaneously to give the same mean output voltage. However, the instantaneous voltages from the rectifying and inverting bridges cannot be identical, and reactors L_p are included to limit the current circulating between them. The principal advantage of this system is that when the motor torque, and hence current, is required to change direction (polarity), there need be no delay between the conduction of one bridge and the other. This is the dual converter bridge with circulating current.

In the other, the circulating current-free dual converter only one bridge at a time is allowed to conduct. The cost and losses associated with the L_p reactors can then be eliminated, and economies can also be made in the drive control circuits. However, the penalty is a short time delay, as the current passes through zero, while it is ensured that the thyristors in one bridge have safely turned off before those in the second are fired. This delay introduces a ‘torque-free’ period of typically 10 ms. Speed reversal for a 3 kW drive of this type from −1500 to +1500 rev/min can still be achieved in approx 200 ms.

This circulating current-free dual converter is by far the most common industrial four-quadrant drive and is used in many demanding applications—paper, plastics and textile machines where rapid control of tension is required, are good examples.

Field control: The output power of a motor is the product of torque and speed. If torque reduces in proportion to speed increases, the motor is said to have a constant power characteristic.

In applications where material is coiled or uncoiled at constant tension, the torque required to produce that tension varies in proportion to coil diameter, whilst rotational speed required to maintain a constant peripheral speed (and therefore line speed) is inversely proportional to diameter. A motor having a constant power characteristic is well suited to this type of application, the advantage being that a smaller motor can be used than would otherwise be the case. Machine tool drives also make use of constant power operation, since loads are small at high speeds, whilst heavy work is done at low speed.

The torque produced by a d.c. motor is proportional to the product of armature current and field flux. By weakening the field as speed increases, a constant power characteristic can be achieved.

In practice there are two major techniques for field weakening both of which rely on a field controller which itself is a simple thyristor converter operating in a current control mode.

In the first method, suitable for coiler and uncoiler applications, the field current reference is arranged to be inversely proportional to coil diameter (measured directly, or calculated from the ratio of line speed to motor speed). Since flux is not strictly proportional to field current, this method does not give a true constant-power characteristic unless compensation for the non-linear part of the motor field curve is applied.

The second method is to use the field controller with an outer, voltage loop having a fixed reference, and to use motor armature voltage as the feedback signal. At low speeds, the voltage loop saturates, providing maximum field current, since armature voltage is below the set value. As speed increases, the armature voltage rises to the point where it matches the preset reference in the field controller. Above that speed, an error signal is produced by the voltage loop, which causes the field controller to weaken the motor field current and thereby restore armature voltage to the setpoint level. The resulting characteristics are shown in Figure 19.16.

As regenerative braking depends on the return of power from the motor to the mains, it cannot work if the mains supply fails due to a blown fuse or a power cut. Dynamic braking of 4Q drives is often encountered as a fail-safe means of stopping the motor and its load, and as the only means of (reverse) braking of single-ended drives. This involves switching in a resistor across the d.c. motor.

Since the kinetic energy of the motor and its load is converted into heat by the braking resistor, it is important to rate it correctly for the duty it is expected to perform, taking account of load inertia and the number of stops per hour.

• The inability of a thyristor to interrupt current means that an alternating supply is necessary to commutate the converter—this precludes operation from a d.c. supply. This is a common requirement on battery vehicles and d.c. fed rail traction.

• The d.c. ripple frequency is determined by the a.c. and is, for a 50 Hz supply frequency, 100 Hz for single-phase and 300 Hz for three-phase fully-controlled bridges. This means that additional smoothing components are often required when using high speed machines, permanent magnet motors or other special motors with low armature inductance.

• As a result of the delay inherent in thyristor switching (3.3 ms in a 50 Hz 3-phase converter) the current control loop band width of the converter is limited to approximately 100 Hz, which is too low for many servo drive applications.

• Thyristor controlled a.c.–d.c. converters have an inherently poor input power factor at low output voltages. (Near unity power factor can be achieved using an uncontrolled rectifier feeding a d.c.–d.c. converter).

• Electronic short-circuit protection is not economically possible with thyristor converters. Protection is normally accomplished by fuses.

Single-quadrant d.c.–d.c. converter: The most basic d.c. to d.c. converter is shown in Figure 19.17. The output voltage is changed by pulse-width modulation (PWM)—that is, by varying the time for which the transistor T is turned on. The voltage applied to the motor is therefore in the form of a square wave of varying periodicity. Because the motor is inductive the current waveform is smoothed, the flywheel diode D carrying the current whilst the transistor is turned off.

The basic formulae relating the variables in this circuit are as follows:

The circuit is only capable of supplying unidirectional current and voltage to the motor and is therefore not capable of four-quadrant operation, that is reversing or regenerating.

Applications for this circuit are normally limited to drives below 5 kW and simple variable-speed applications.

Two-quadrant d.c.–d.c. converter: In order to achieve full four-quadrant operation a converter must be capable of supplying reversible voltage and current to the motor. A circuit that is capable of two-quadrant operation—that is motoring and braking in one direction only—is shown in Figure 19.18. This converter is able to reverse the current flow to the motor but unable to reverse the motor terminal voltage and hence the speed. During motoring, the converter operates as the basic ‘chopper’ with T1 and D2 carrying the current. During braking (or regeneration) T1 is inoperative and T2 controls the current. During its on-periods, motor current builds up negatively, limited by motor inductance L. When T2 turns off, the only path for the current is via D1 back into the supply; hence the circuit is regenerative.

Since this circuit is not capable of motor speed reversal it is normally only used in unidirectional applications. However because of its simplicity it is sometimes used in traction applications where reversing is carried out by means of a changeover switch to reverse the armature or field supply.

Four-quadrant d.c.–d.c. converter: Figure 19.19 shows a basic four-quadrant converter capable of supplying reversible voltage and current i.e. of reversing and regeneration.

During motoring, positive output transistors T1 and T4 are switched on during the on-period, whilst diodes D2 and D4 conduct during the off-period. When D2 and D4 conduct, the motor supply is reversed and consequently the voltage is reduced to zero at 50% duty cycle. Any reduction of duty cycle below 50% will cause the output voltage to reverse but with current in the same direction; hence the speed is reversed and the drive is regenerating. With transistors T2 and T3 conducting, the current is reversed and hence the full four-quadrant operation is obtained.

One disadvantage of this converter is that the amplitude of the output ripple voltage is twice that of the simple converter—and the current ripple is therefore worse. This problem can be overcome by a technique known as double-edged modulation. With this technique the flywheel current is circulated via a transistor and a diode during the off-period. For example, after T1 and T4 have been conducting, T4 is turned off and T3 on, so that the flywheel current circulates via T1 and D3. The net effect is a reduction in ripple voltage and a doubling of ripple frequency.

These four-quadrant converters are widely used in high performance d.c. drives such as servos.

General characteristics: The fixed frequency mains supply is a voltage source behind an impedance. Voltage source inverters can be similarly considered, and consequently are very flexible in their application. Major inherent features included:

Six step square wave inverter: A typical d.c. link square wave voltage-fed inverter drive is shown in Figure 19.21. The three-phase a.c. supply is converted to d.c. in the phase-controlled rectifier stage. The rectified d.c. power is then filtered and fed to the inverter. Note that the d.c. link reactor is small compared to that used in current source designs. Indeed in drives up to about 4 kW it is not practically necessary. Some manufacturers omit the reactor in designs to 400 kW and above, however this has a significant effect upon supply harmonics and unduly stresses the rectifier and filter capacitor.

The inverter switching elements shown as transistors TR1 to TR6 are gated at 60° intervals in the sequence in which they are numbered in the diagram, and each transistor conducts for 180°. The feedback diodes D1 to D6 are connected in inverse-parallel with the transistors, and permit the return of energy from reactive or regenerative loads through the inverter to the d.c. link.

For a star-connected motor, synthesis of inverter output voltage waveforms is shown in Figure 19.22. The phase-to-neutral voltage of the inverter has six-step waveshape while the corresponding phase-to-phase voltage has 120° conduction angle. The output frequency is controlled by the rate at which the inverter transistors are triggered into conduction by the inverter control circuitry. Reversing the firing sequence of transistors in the inverter changes the direction of rotation of the motor, and no switching of power leads, either on the incoming supply or to the motor itself, is necessary.

The phase-controlled rectifier regulates the d.c. link voltage and this, in turn, determines the magnitude of the output voltage from the inverter. Thus, the output voltage/frequency relationship may be controlled to regulate the motor flux in the desired manner.

The advantages of the square-wave inverter are high efficiency (98%), suitability to standard motors, potential good reliability and high-speed capability. However, it suffers from low-speed torque pulsations and possible low-speed instability.

In a square wave inverter, each harmonic voltage amplitude is inversely proportional to the harmonic order and hence there are no pronounced high-order harmonics. These are filtered by the motor leakage inductances.

Very high speed motor operation is possible by increasing the output frequency. Faster switching devices such as MOS transistors and insulated gate bipolar transistor (IGBT) can be used to achieve this performance.

It is known that the square wave inverter gives objectionable torque pulsation at low frequency operation, below approximately 5 Hz. This pulsating torque is due to the interactions of low order harmonics with the fundamental voltage, causing a stepping or cogging motion to the rotor running at low speed. Hence, the pulsating torque limits the low frequency operation of the square wave inverter. Appropriate feedback control techniques or flux weakening can attenuate the low speed pulsating torque problems.

The existence of a phase-controlled rectifier to control the voltage of the inverter as illustrated in Figure 19.21 is an inherent weakness of this circuit. The phase-controlled rectifier will present a low power factor to the a.c. supply, at low speeds, and the d.c. link filter capacitor is large and reduces the response time of the system to voltage and hence speed changes. If the drive system is one for which regenerative braking operation is a requirement, the rectifier has to be of inverse-parallel type. The input power-factor and response time of the drive can be improved by replacing the phase-controlled rectifier with a diode rectifier feeding a d.c. chopper which regulates the input voltage to the inverter. For recovering regenerative energy of the load, a two-quadrant chopper will be necessary. The alternative supply converter arrangement of a diode bridge plus chopper also provides a fixed voltage link which is more economically buffered if mains dip ride-through is required.

The voltage-fed square-wave drive is usually used in low power industrial applications where the speed range is limited to 10 to one and dynamic performance is not important. Recently, this type of drive has largely been superseded by PWM type voltage-fed inverters. Nevertheless, the voltage-fed square wave inverter can be easily adapted to multimotor drives where the speed of a number of induction motors can be closely tracked. It is also used in some high frequency (> 1 kHz) and some high power applications.

Pulse width modulated (PWM) inverter: In the PWM inverter drive, the d.c. link voltage is uncontrolled and derived from a simple diode bridge. The output voltage can be controlled electronically within the inverter by using PWM techniques. In this method, the transistors are switched on and off many times within a half cycle to generate a variable-voltage output which is normally low in harmonic content.

A PWM waveform is illustrated in Figure 19.23.

A large number of PWM techniques exist each having different performance notably in respect to the stability and audible noise of the driven motor.

Using the PWM technique, low-speed torque pulsations are virtually eliminated since negligible low-order harmonics are present. Hence, this is an ideal solution where a drive system is to be used across a wide speed range.

Since voltage and frequency are both controlled with the PWM quick response to changes in demand voltage and frequency can be achieved. Furthermore, with a diode rectifier as the input circuit a high power-factor, approaching unity, is offered to the incoming a.c. supply over the entire speed and load range.

PWM inverter drive efficiency typically approaches 98% but this figure is heavily affected by the choice of switching frequency—the higher the switching frequency the higher the losses in the drive. In practice the maximum fundamental output frequency is usually restricted to 100 Hz in the case of gate turn-off thyristors (GTO) or about 1 kHz for a transistor based system. The upper frequency limit may be improved by making a transition to a less sophisticated PWM waveform with a lower switching frequency and ultimately to a square wave if the application demands it. However, with the introduction of faster-switching power semiconductors, these restrictions to switching frequency and minimum pulse-width have been eased.

In general, a motor with a large leakage reactance is desirable to limit the flow of harmonic currents and thereby minimise losses.

Converter-fed synchronous machine: Once rotating a synchronous machine generates a.c. voltages which can be used for the natural commutation of a converter connected to its terminals. Indeed the connected synchronous machine behaves as the mains in respect of the a.c to d.c converters described earlier.

Figure 19.24 shows the basic components of the drive system. A low-impedance or ‘stiff’ d.c. current source is required and is obtained from a controlled rectifier and a series reactor. With a stiff current source, the output current wave is not greatly affected by the magnitude of the load.

The synchronous machine can be approximately represented by a counter-emf in series with an equivalent leakage inductance. The d.c. current is switched through the inverter thyristors so as to establish three-phase, six-stepped symmetrical line current waves. Each thyristor conducts for 120° and at any instant one upper thyristor and one lower thyristor remain in conduction.

It is necessary to maintain an approximately constant angular relationship between the rotor and stator m.m.f.s and hence automatically maintain the correct inverter frequency. This is an important point. The inverter does not impose a frequency upon the machine, rather the machine itself determines the frequency. The motor cannot therefore pole-slip. The drive is accelerated by increasing the current fed to the drive which then accelerates and thereby increases the frequency.

As in the d.c. drives, the a.c. supply power factor is poor at low speeds. Full four-quadrant operation is possible without additional components.

Special procedures are necessary for starting these drives since at standstill the machine voltage is not available to commutate the current. In essence this is usually achieved by momentarily switching off the d.c. link current every sixth of a cycle. This allows the thyristors in the inverter to turn off so that the next pair can be fired. Above approximately 5% of rated speed the machine generates sufficient voltage for natural commutation and control is undertaken in a similar manner to that of a d.c. drive.

Applications for this type of drive fall into two main catagories. Firstly, starting converters for large synchronous machines, the converter being rated only for a fraction of the machine rating. Secondly, as large high power (and sometimes high speed) variable speed drives for a variety of applications. Power ratings, typically from 1.5 to 30 MW at speeds up to 8000 rpm are available. Also of import is the fact that high voltage drives are offered with supply voltages up to 5 kV typical, but systems up to 25 kV are in service where the high voltage converter technology is similar to that used for HVDC power converters.

Converter-fed induction motor drive: Unlike the Synchronous machine, the induction motor is unable to provide the VARs, or terminal voltage to commutate a converter connected to its terminals. Commercial schemes are available however which are closely based upon the converter fed synchronous machine drive having additional components to provide VAR compensation.

Figure 19.25 shows a basic power circuit. The diagram somewhat belies the potential complexity of the VAR compensator. In its simplest form this could comprise capacitors plus appropriate switches. Control of such a system is somewhat involved. It is often better to use a cycloconverter or even an auxiliary synchronous machine to provide the commutation, and motor VARs.

This system is only appropriate for high power drives, generally above 4 MW where an induction motor is preferred.

Forced commutated induction motor drive: This is the most widely used current source inverter at power levels in the range 50–3500 kW at voltages up to normally 690 V. (High voltage versions 3.3 kV/6.6 kV have been developed however they have not proved to be economically attractive.)

Figure 19.26 shows the inverter and motor of the drive. The d.c. link current I_d, taken from a ‘stiff’ current source is sequentially switched at the required frequency into the stator windings of the induction motor. The motor voltage waveform is approximately sinusoidal apart from the superposition of voltage spikes caused by the rise and fall of machine current at each commutation. Further distortion is caused by the effects of slot ripple and d.c. current ripple.

The operating frequency range is typically 5-60 Hz, the upper limit being set by the relatively slow commutation process. Special motors with low leakage inductance do offer advantage with this converter and allow reduced capacitance in the inverter and/or higher operating frequency. Below 5 Hz, torque pulsations can be problematic but PWM of the current can be used at low frequencies to ease the problem.

This system is most commonly used for single motor applications such as fans, pumps, extruders, compressors etc. where very good dynamic performance is not necessary and a supply power factor which decreases with speed is acceptable.

Static Kramer drive: The static Kramer drive is shown in Figure 19.27. The drive comprises a slip-ring (wound rotor) induction motor together with an uncontrolled converter, d.c. smoothing reactor and a fully-controlled converter in the rotor circuit.

The diode bridge gives an output voltage V_d which is proportional to the slip of the motor. V_d is opposed by the d.c. voltage of the fully-controlled bridge, a small potential difference being sufficient to circulate current corresponding to the required load torque. Ideally, neglecting losses, the fully-controlled bridge d.c. voltage sets the speed to which the motor will accelerate. Control is therefore very similar to a d.c. drive.

Power can flow in only one direction via the diode bridge which means that motoring torque can be developed only at subsynchronous speeds. For reverse running it is necessary to reverse the phase sequence of the stator supply.

This drive can be very economic when designed for operation over a limited speed range below synchronous speed—this is the useful operating region for fans, pumps etc. The converter bridges required for such limited speed range operation need only be rated at a fraction of that of the machine it is controlling. It is necessary in such designs to provide a starter, usually a resistance to run the motor up to the lowest controllable speed. This means that should there be a fault with the converter equipment, the system can be easily designed to run at full speed without the controller.

Note that the supply harmonic currents and VARS associated with the converter part of the drive may be substantially reduced by adopting a limited speed range solution.

The static Kramer drive finds application mainly at ratings between 1 and 20 MW, with induction motors with 4 or more poles. (Stability problems exist with 2-pole motors which can only be resolved with care.) Speed ranges of 30% are typical (i.e. 70–100% rated speed). The induction motor stator can be wound for any conventional voltage e.g. 6.6 kV, 11 kV.

Flux controller: The field converter is either a half or fully controlled thyristor converter. The half controlled converter can only apply positive voltage to the field winding, and so the current in the winding can be increased quickly, but decays slowly. The fully controlled converter can apply positive or negative voltages, and so the performance is the same whether the current is increasing or decreasing. When the motor is rotating at a speed below base speed the field current reference is constant at the rated level for the motor, and so the motor armature voltage increases with speed. The armature voltage reaches its rated level at base speed, and above this speed the flux controller reduces the field current reference, i^*_F to keep the voltage at the rated level as the speed increases further. The armature voltage feedback can include armature resistance compensation to avoid the effects of the armature resistance drop on the voltage control loop.

Torque controller: For four-quadrant operation two thyristor bridges are used as shown in Figure 19.31(b). Both bridges can apply positive or negative voltage to the motor, but the positive bridge can only supply positive current and the negative bridge negative current. Therefore the positive bridge conducts when positive torque is required and the negative bridge when negative torque is required. The bridges are phase controlled to apply the voltages required by the reference, V_A^*, to the motor. Due to the high voltage ripple in the converter output and the unidirectional nature of thyristors, the current in the armature can be continuous or discontinuous. While the current is continuous the relationship between the voltage reference and the actual applied voltage is a cosine function and the voltage reference can be used directly to control the firing angle of the converter. When the current is discontinuous the relationship is highly non-linear and varies with the voltage level applied to the motor. The drive stores the relationship between the firing angle and motor current for different output voltage levels, and during discontinuous current operation the correct firing angle is selected by the firing angle prediction block for a given current reference. Any errors are trimmed out by an integrator operating on the current error.

When a change in direction of torque is required one bridge must stop conducting and the other bridge must become active. It is clear from the power circuit diagram that only one bridge must conduct at a time during this changeover to avoid a short circuit across the armature supply. It is important that this changeover occurs as quickly as possible to give good dynamic torque control. Modern microprocessor controlled drives enable intelligent methods to be used to keep the bridge changeover delay as short as possible.

Performance and applications: The performance characteristics of a d.c. motor drive can be summarised as:

Performance and applications: The performance characteristics of the open-loop drive control system applied to an induction motor can be summarised as:

Performance and applications: The performance characteristics of the closed-loop induction motor drive can be summarised as:

Closed-loop induction motor drives are used in many applications where good dynamic performance is required and especially where an induction motor drive is required to give full torque at standstill. The following are some examples of applications where this type of drive is used:

Operation without position feedback: The control system described above requires incremental rotor position feedback, but it is possible to implement the scheme without any physical feedback device. This can be done by estimating the rotor position from information available to the drive through the motor voltages and currents. One class of methods used to determine the rotor position, referred to as model based methods, use a model of the motor to calculate the rotor speed and hence the incremental rotor position. When a physical position feedback device is used the drive gives good dynamic performance and operates with full torque even at standstill. When a position estimator is used the dynamic performance is reduced and the minimum speed for full torque operation is similar to that of the open-loop drive. However a closed-loop induction motor drive without position feedback does have the following advantages and disadvantages when compared to an open-loop induction motor drive.

Advantages:

Performance and applications: The performance characteristics of the permanent magnet servo drive can be summarised as:

The following are some examples of applications where permanent magnet servo drives are used:

• Although the inverter allows power flow in either direction, the diode rectifier only allows power to flow from the supply into the drive. Therefore the chopper circuit must be used to dissipate unwanted energy in the resistor when braking power is fed from the motor to the drive.

• The currents taken from the supply generally contain significant harmonics.

• The voltage at the inverter input is theoretically limited to the peak line voltage of the supply. In practice this is reduced further by voltage drops in the converter. This limits the maximum output voltage without over-modulation to less than the supply voltage.

Performance and applications: The performance characteristics of the four-quadrant drive described here can be summarised as:

Four-quadrant drives are used in applications where good quality input waveforms are required and/or significant braking energy can be returned to the supply. The following are some examples of applications where this type of drive is used:

• The calculations for the current controllers, reference frame translation and space vector modulator are more complex than the direct torque control hysteresis comparators and switching table. However the sample rate required for direct torque control (typically 40 kHz) is much higher than that for a space vector modulator (6–12 kHz), because direct torque control uses a hysteresis method.

• As well as supplying a single induction motor, most induction motor drives can also supply more than one motor in parallel where the motors are different sizes, or the drive can be used as a general purpose variable frequency/variable voltage power supply. Direct torque control cannot be used in these applications, and so a direct torque control drive must also be able to operate with space vector modulation for these applications.

• Because direct torque control is based on hysteresis controllers the inverter has a continuously variable switching frequency. This is considered to be an advantage in spreading the spectrum of the audible noise from the motor, but the range must be controlled so that it does not exceed the maximum allowed by the power electronics of the inverter. Care must also be taken with direct torque control to ensure that changes from one voltage vector to another more than 60° away do not occur repetitively as this can increase the stress on motor insulation. • A direct torque control drive inherently delivers a change in torque in the shortest possible time within the limits of the sample rate. Because of the sampling and calculation delays usually associated with space vector modulator based systems a change in torque can take several samples. However, deadbeat type algorithms can be used with a space vector modulator systems giving performance which compares well to that of direct torque control.