# Induction Motor

Lightly loaded induction motors are particularly guilty of producing low power factors since the reactive power does not change with the load on the motor.

## Drivers

Grant Musgrove, ... Matt Taher, in Compression Machinery for Oil and Gas, 2019

### Variable Frequency Drives

Induction and synchronous motors are designed for a specific voltage per frequency ratio (V/Hz). Voltage is the supply voltage to the motor, and frequency is the supply frequency. The V/Hz ratio is directly proportional to the amount of magnetic flux in the motor magnetic material (stator and rotor core laminations). The torque developed on motor shaft is proportional to the strength of the rotating flux. The type and the amount of magnetic material used in motor construction are factors to define motor power rating.

With constant supply power frequency, higher voltage causes higher V/Hz ratio and higher flux. With constant supply voltage, lower supply frequency would cause higher V/Hz ratio and higher flux. Higher flux increases the motor torque capability. When motor operates at higher V/Hz than rated, the overfluxing occurs, which may cause saturation of the stator and rotor magnetic core. Saturation causes overheating and can lead to motor failure. When motor operates at lower V/Hz than rated, the magnetic flux is reduced. Reduced flux reduces the torque capability and affects the motor ability to handle the load.

When motors are supplied directly from the power network, the supply power frequency is constant, while voltage and current change during motor starting. During motor acceleration to synchronous speed (synchronous motors) or close to synchronous speed (induction motors), the current would initially rise to multiple times the rated current and cause voltage drop. Lower voltage while supply frequency is constant means lower V/Hz ratio and lower flux which affects the torque. Once the motor accelerates, the voltage recovers to close to rated value and the torque available at the motor shaft is at the rated value. The speed of the motor is then constant and synchronous (synchronous motors) or close to synchronous (induction motors). With motors connected directly to power network, the speed is dictated by the fixed network frequency and cannot be controlled. To manage the speed when necessary, additional mechanical systems are used: dampers, valves, gear boxes, brakes, etc. Mechanical systems reduce the overall system efficiency. In addition, as explained previously, induction motors consume reactive power, so maintaining the power factor may be a challenge with induction motors. Synchronous motors do not cause issues with the power factor, they can actually help.

There are four categories of challenges with motors connected directly to the power supply network: high starting current, torque control, speed control, and power factor (only with the induction motors). One of the effective ways to address the challenges is to use VFDs. When VFDs are used, the drive is supplied from the power network, and the motor is supplied from the drive.

VFDs control the motor speed and motor torque by controlling the frequency and magnitude of voltages and currents supplied to the motor. Each VFD has three sections: rectifier, filter with energy storage, and inverter. Typical conceptual configuration is shown in Fig. 7.22.

Rectifier takes the fixed frequency and magnitude voltage sinusoid from the grid and rectifies it into DC waveform.

Filter takes the DC waveform from rectifier and provides almost pure linear DC. Energy storage is used to support instantaneous energy balance. If with balanced three-phase load, the total power remains constant from instant to instant and with the ideal converter, the energy storage would not be required. In practice, converters require energy storage to store sufficient energy to supply the motor during the brief intervals when load power is greater than the input power. Capacitors and inductors are used for energy storage.

Inverter inverts the DC power back to AC through a set of electronic switches (MOSFET (metal-oxide semiconductor field-effect transistor), IGBT (insulated-gate bipolar transistor), IGCT (integrated gate-commutated thyristor), GTO (gate turn-off thyristor), etc.). These switches, by opening and closing at certain speeds and durations, can invert DC and recreate output currents and voltage waveforms that mimic sinusoidal AC waveforms. The motor is then supplied from the output of the inverter.

The output waveforms are pulse width modulated (PWM) waveforms. They are called PWM waveforms because they are created by multiple pulses of the switches at short intervals. The magnitude and frequency of PWM voltage waveforms are adjustable. By varying the time, the pulses are on and which switches are firing, the frequency can be increased or decreased. By changing the width and duration of the pulses, the average voltage to the motor can be increased and decreased. Typical PWM waveform with sinusoid being approximated is shown in Fig. 7.23.

With an induction motor used as an example, the induction motor can run efficiently only at close to synchronous speed of the rotating field. The speed control requires continuous variation of the rotating field speed, which requires variation of frequency.

When the inverter output voltage at each inverter output frequency is controlled so that the V/Hz ratio is kept constant up to the rated speed, a family of torque-speed curves can be derived similar to Fig. 7.24.

Point “a” in Fig. 7.24 corresponds to no load torque and no load speed at inverter supplied frequency of 25 Hz. From no load in point “a” to full load in point “b,” the speed will drop slightly. If it is required to maintain the constant speed from point “a,” the VFD control would raise the frequency so that the full load operating point moves to point “c.” The VFD control would also raise the voltage proportionally to the frequency increase, to maintain the constant V/Hz ratio at the full load, and thus maintain the full load torque.

From Fig. 7.24, it can be observed that the pullout torque is constant at all points below the rated speed, except at low frequencies. At low frequencies, the pullout torque is reduced because of the effect of stator resistance. As the frequency approaches zero, the voltage drop due to stator resistance becomes important, and flux reduction that causes the torque reduction becomes prominent. This effect is known and easily mitigated by low-speed voltage boosting: increasing the V/f ratio at low frequencies to restore the flux. Fig. 7.25 shows a typical set of torque-speed curves for a drive with low-speed voltage boosting.

Beyond rated speed, V/Hz ratio cannot be kept constant anymore because voltage cannot increase beyond rated voltage of the motor to avoid motor insulation breakdown. The increase in frequency beyond rated frequency is possible and will produce higher speed but with voltage kept at rated voltage, and consequently reducing V/Hz ratio, the flux density will reduce and the torque will reduce.

The advantage of VFD supplied motors is that the motor can supply the same maximum torque from zero speed to rated speed. This area of the motor torque-speed characteristic is called “constant torque” area. Continuous operation at peak torque is not done in practice because of the heat limitations. The upper torque limit equal to motor rated torque is usually set in the controller.

With VFD supplied motors and with their availability of high torque at low speeds, the starting problems common to fixed frequency operations (initial high slip, high starting current, voltage drop, and torque reduction) are avoided. The VFD-driven motor starts with low frequency, which is gradually increased. The slip speed of the rotor is always small and the rotor continuously operates in the optimum torque condition. Rated torque is available at low speeds and starting current does not exceed the rated full load current. The motor can start from a week power supply system without causing voltage disturbances in the supply network.

As mentioned previously, the VFD-driven motor can develop any torque up to rated torque at any speed up to rated speed. This area is called “constant torque” area. Above rated speed, V/Hz will reduce because voltage is kept constant at rated motor voltage, stator, and rotor current are also kept constant and speed and frequency are increasing, so the flux density will reduce and the torque will reduce inversely with the frequency. This area in the motor torque-speed characteristic is called “constant power” area. Constant power area is up to approximately twice the rated speed. Beyond constant power area is the high-speed area where current limit coincides with the pullout torque limit, which reduces inversely with the square of the frequency, so the constant power cannot be maintained any further. Constant torque, constant power, and high-speed areas are shown in Fig. 7.26.

In VFD supplied motor applications, it is important to note that torque-speed curves show the torque the motor can produce for each frequency, but not for how long and if motor can operate in each condition continuously. If in a VFD supplied motor application, a standard induction motor is used, heat limitations need to be taken into consideration. Standard industrial motor is usually an enclosed with an external shaft mounted fan which blows air over the finned external case. The standard design and motor cooling is for the continuous operation for the fixed network supplied frequency and rated speed. When standard industrial motor operates connected to a VFD which produces low frequency and runs the motor at low speed, the motor cooling becomes an issue. The motor will be capable to produce rated torque at low speed, but in those conditions, it will operate at higher temperature which may significantly impact the service life of the motor or cause overheating and motor failure.

When motor is used in VFD applications, it is important to specify operating scenarios, design the cooling accordingly, and use motors suitable for inverter duty.

Other than cooling, there are other considerations that must be considered in the design when VFD-driven motors are used, such as impact of the harmonics from the VFD to the network, cable configuration and sizing from the VFD to the motor, etc.

URL: https://www.sciencedirect.com/science/article/pii/B9780128146835000079

## Electrical submersible pumps

James F. LeaJr, Lynn Rowlan, in Gas Well Deliquification (Third Edition), 2019

### 12.2.1Electric submersible pump induction and permanent magnet motor RPM

IM or PMM synchronous RPM is defined by the following equation:

(12.1)${\mathrm{RPM}}_{\mathrm{SYNC}}=\frac{\text{Hertz}×120}{\mathrm{Motor}\phantom{\rule{.5em}{0ex}}\mathrm{poles}}$

The IM, when connected to a 60-Hz power system, or a variable frequency drive (VFD) operating at an output frequency of 60 Hz, has a synchronous RPM of 3600 but the actual RPM will be less. The IM rotor must slip or rotate slower than the rotating magnetic field produced by the stator windings to induce current into the rotor, which develops the rotor’s magnetic field. The IM RPM is defined in the following equation:

(12.2)${\mathrm{RPM}}_{\mathrm{IM}}={\mathrm{RPM}}_{\mathrm{SYNC}}-{\mathrm{RPM}}_{\mathrm{SLIP}}$

where the slip RPM will vary from 180 to 50 depending on the load imposed by the pump, seal and intake load, and the motor diameter. The IM’s full load RPM, when 60 Hz power is applied, will be approximately 3420 RPM.

The full voltage, 60 Hz, composite curve for a 562 IM is shown in Fig. 12.3A. This motor is 5.62 in. in diameter and the length will vary from 6 ft. (40 HP) to 35.5 ft. (450 HP). The average HP per foot is about 10.5. The average HP density is about 62 HP per cubic foot.

The relationship between HP, voltage, amperage, efficiency, and power factor is defined in the following equation:

(12.3)$\mathrm{Output}\phantom{\rule{.25em}{0ex}}\text{HP}=\frac{\mathrm{voltage}×\mathrm{amperage}×\sqrt{3}×\mathrm{efficiency}×\mathrm{power}\phantom{\rule{.25em}{0ex}}\mathrm{factor}}{746\phantom{\rule{.25em}{0ex}}\mathrm{W}/\text{HP}}$

At 100% load the RPM is 3490, the amperage is at 100% of nameplate, the efficiency is 87% (0.87), and the power factor is 81% (0.81). At 50% load the RPM is 3555, the amperage is at 65% of nameplate, the efficiency is 82.5% (0.825), and the power factor is 66% (0.66).

Reducing the load on the motor to 50% of nameplate will reduce the efficiency from 87% to 82.5% or a 5.2-point reduction in efficiency.

The full voltage, 60 Hz, composite curve for a 456 IM is shown in Fig. 12.3B. This motor is 4.56 in. in diameter and the length will vary from 5 ft. (10 HP) to 31.2 ft. (120 HP). The average HP per foot is about 3.2. The average HP density is about 33 HP per cubic foot.

At 100% load the RPM is 3430, the amperage is at 100% of nameplate, the efficiency is 81% (0.81), and the power factor is 85% (0.85).

At 50% load the RPM is 3510, the amperage is at 60.5% of nameplate, the efficiency is 77% (0.77), and the power factor is 75.5% (0.755).

Reducing the load from 100% to 50% will reduce the efficiency from 81% to 77% or a 4.9-point reduction in motor efficiency will occur.

The four-pole, synchronous PMM must be operated with a variable speed drive (VSD), also called a VFD. When operated at 120 Hz, the motor will rotate at a synchronous RPM (3600 RPM). There is no RPM slip associated with the PMM since the rotor magnetic field is supplied by the permanent magnets on the rotor. Since there are no rotor losses in the PMM, it is 10%–12% more efficient than a comparable IM. The PMM uses rare earth magnets to generate a strong rotor magnetic field. This field is stronger than the electrically generated field of an IM. As a result, a PMM can generate three to five times the power of an equivalently sized IM. This translates into the horsepower density being increased three to five times. Owing to their higher horsepower density, PMMs may eliminate the need for tandem or triple tandem IMs. The required power may be delivered in one PM motor section.

Fig. 12.4A and B is PM performance curves for a 4.56 in. diameter (456 series) and 5.62 in. diameter (562 series) motor, respectively. Note the higher efficiency as compared to the IMs in Fig. 12.3A and B. Also efficiency is a function of the applied motor voltage as the loading changes just as it did with the IMs. Since the PM motors are operated using a VSD, the motors can be adjusted to the most efficient level by manually or automatically, adjusting the volt per hertz coming out of the VSD as the well conditions change causing the motor loading to change.

URL: https://www.sciencedirect.com/science/article/pii/B9780128158975000123

## Reciprocating Compressors

Justin Hollingsworth, ... Franzisko Maywald, in Compression Machinery for Oil and Gas, 2019

### Induction Motors

An induction motor develops torque by inducing current to the rotor, which is proportional to the differential speed of the rotor and the rotating magnetic field in the stator. For NEMA design B motors the differential speed (called slip) is between 1% and 2% at full load. Due to the torque variation at each revolution the instantaneous speed will vary. For example, if the speed variation was 0.8% so the slip would vary between 0.6% and 1.4% giving a torque variation of 60% torque to 140% torque. But the power factor would vary with load so at 60% power it might be 80% amps and at 140% load 140% amps for an average of 110% amps. Note how the power is at 100% but the amps are at 110%, that is, in an overload situation by amps but not by power. The heating effect in the motor is primarily governed by the motor amps so at 110% amps it is likely that the motor winding temperatures would be excessive. In this case the current pulsation is (140  80)/100 = 60% NEMA MG1 limits the current pulsation to 66% API-618 limits the current pulsation to 40%. It is recommended that the API 618 limits be applied to induction motors because the NEMA pulsation limits are not adequate to protect against overloading the motor.

URL: https://www.sciencedirect.com/science/article/pii/B9780128146835000055

## Process Drives and Starting Requirements

Geoff Macangus-Gerrard, in Offshore Electrical Engineering Manual (Second Edition), 2018

### Reciprocating Pumps and Compressors

If an induction motor is used to drive a large reciprocating pump or compressor, the heavy cyclic torque fluctuations demanded from the motor will in turn demand heavy current fluctuations from the supply. When the motor load is a significant part of the installation generating capacity, instability of voltage and power may result.

An alternative is to use a synchronous motor with a squirrel-cage damping winding imbedded in the rotor. If a steady torque is being developed by the machine, the load angle would remain in an equilibrium position. As the rotor of a synchronous motor running in synchronism with the supply experiences a torque proportional to its angular displacement from the equilibrium position and also possesses rotational inertia, it constitutes an oscillatory system similar to the balance wheel of a clock. If J is the moment of inertia of the rotor in kilogram metre squared, then it can be shown that natural frequency of the rotor will be

$f=\frac{1}{2\pi }\sqrt{\text{Ts}/\text{J}×\left(\text{No}\text{.}\phantom{\rule{0.25em}{0ex}}\text{of}\phantom{\rule{0.25em}{0ex}}\text{pole}\phantom{\rule{0.25em}{0ex}}\text{pairs}\right)}\phantom{\rule{0.25em}{0ex}}\text{Hz}$

where Ts = 3 VI/cos θ nm; V, the system voltage; I, current produced by the field induced voltage; θ, the load angle.

Synchronous motors driving reciprocating machinery receive torque impulses of a definite frequency and for satisfactory operation the natural frequency of the rotor must be at least 20% higher or lower than the frequency of the torque impulses (Fig. 2.12.2).

The imbedded squirrel-cage damping windings, used for starting, will produce some corresponding current fluctuation with torque, but this is not excessive as can be the case with an equivalent induction motor. Such windings produce damping torques proportional to the angular velocity of any rotor oscillation and hence reduce the synchronous motor’s tendency to hunt because of the alternating currents induced in the other windings and current paths of the rotor, giving rise to destabilising torques.

URL: https://www.sciencedirect.com/science/article/pii/B9780123854995000145

## Electric Machines, Drives

Zivan Zabar, in Encyclopedia of Physical Science and Technology (Third Edition), 2003

### II.F.2Braking of Induction Motors

A slip-ring induction motor has a greater variety of braking mode controls than a squirrel-cage motor. This is due to the additional flexibility in controlling the resistance of the rotor circuit.

Dynamic braking is usually obtained by switching over the stator winding to a dc voltage source. In order to limit the current magnitude and to control the braking rate, one can either vary the dc voltage or, if the rotor has slip rings, connect it to external resistors (Fig. 12).

The dc current in the stator generates a stationary magnetic flux in the motor air gap. Rotation of the rotor in this field induces ac currents in its windings. The frequency of these currents decreases with rotor speed so as to set up a magnetic field that is stationary with respect to the stator. The interaction of the two fields creates a braking torque whose magnitude depends on the dc field generated by the stator, the rotor resistance, and the speed of the rotor. The braking torque T as a function of the slip S given by Eq. (81) of “Electric Machines, Rotating, Construction and Theory”, with Tmax proportional to the square of the dc current, and S = ω/ω0 (where ω is the rotor shaft speed and ω0 is the synchronous speed of the motor). This braking mode is applied mainly to hoisting and crane machines.

Regenerative braking can take place only when the rotor rotates in the same direction as that of the stator magnetic field but faster than its synchronous speed ω0. Several torque–speed characteristics are plotted inFig. 13, where the different resistance values refer to a slip-ring rotor. The curve Rr = 0 is the natural motor characteristic, which is the only one realizable with a squirrel-cage motor.

Any increase in the rotor speed ω above ω0, ω > ω0, due to some external torque, will force the motor to operate in a generating mode. When ω > ω0, the slip S becomes negative. Therefore, rewriting Eq. (78) of “Electric Machines, Rotating, Construction and Theory,”

(21)${\overline{\text{I}}}_{2}^{\prime }=\frac{{\overline{\text{V}}}_{1}{\text{R}}_{2}^{\prime }\text{S}}{{\left({\text{R}}_{2}^{\prime }\right)}^{2}+{\left({\omega }_{1}{\text{L}}_{\text{sc}}\text{S}\right)}^{2}}-\text{j}\frac{{\overline{\text{V}}}_{1}{\omega }_{1}{\text{L}}_{\text{sc}}{\text{S}}^{2}}{{\left({\text{R}}_{2}^{\prime }\right)}^{2}+{\left({\omega }_{1}{\text{L}}_{\text{sc}}\text{S}\right)}^{2}},$

the active component of the current Ī′2 reverses direction while the reactive one stays in the same direction. This means that the motor operates as a generator connected in parallel with the utility network and returns electrical energy to it while drawing reactive power for its excitation. This braking mode is used in drives with pole-changing motors, as well as in hoisting mechanisms, and so on.

Countercurrent braking is widely used in drive practice, mainly when the motor is of the wound-rotor type. The reason is that the presence of slip rings permits the introduction of resistances in the rotor circuit to limit the magnitude of the current and to control the braking rate (Fig. 14).

This plugging condition can be set up by interchanging any two phases of the stator winding so as to reverse the direction of the rotating magnetic field in the motor air gap while the rotor still rotates in the initial direction. Since the speed has a negative sign, the slip S is larger than 1, S > 1. The torque, which is given by Eq. (77) of “Electric Machines, Rotating, Construction and Theory,” is relatively small. Since it acts in the opposite direction to the rotor motion, the latter begins to slow down (curve B inFig. 14). When the speed drops to zero (point C on curve B), the motor should be deenergized; otherwise, it will begin to rotate in the reverse direction.

URL: https://www.sciencedirect.com/science/article/pii/B0122274105009170

## Pumping; Electrical Plant; Control and Instrumentation

Don D. Ratnayaka, ... K. Michael Johnson, in Water Supply (Sixth Edition), 2009

### 17.19The Induction Motor

The induction motor comprises a stator which incorporates a distributed winding, connected to the three phase electrical supply, and a laminated steel rotor which in its simplest form has embedded large section bars which are short-circuited at each end. The motor thus consists of two electrically separate windings which are linked by a magnetic field forming a transformer, with an air gap magnetic circuit. The three phase current in the stator winding produces a smoothly rotating magnetic field whose rotational speed N (synchronous speed in rpm) is given by the equation:

Thus for a supply frequency of 50 Hz a 2-pole motor has a field speed of 3000 rpm, a 4-pole motor 1500 rpm, and a 6-pole motor 1000 rpm and so on.

The rotating magnetic field cuts the rotor bars and induces a current in them. The rotor current produces a magnetic field which interacts with the stator field, producing an accelerating torque. The motor will run up to a speed at which the developed torque is equal to the torque required by the driven load, including that required to overcome friction and windage losses.

In practice, the rotor cannot reach synchronous speed with the magnetic field when loaded, because under such a condition no current would be induced in the rotor conductors and hence no magnetic flux and torque would be produced. This explains why, for example, a loaded 4-pole motor may actually run at say 1440 rpm. The difference between the actual speed of rotation and synchronous speed with the magnetic field is termed the slip. The slip increases with the load and is normally expressed as a percentage of the synchronous speed. The slip at full load typically varies from about 6% for small motors to 2% for large motors. The starting torque and speed characteristics of the cage induction motor of basic standard design are shown in Figure 17.9.

The cage induction motor has a rotor core which is made up of laminations and conductors of aluminium, copper or copper-alloy non-insulated bars in semi-enclosed slots, the bars being short-circuited at each end by rings. For the smaller motors, the rotor bars and end rings are often cast. The advantages are simple construction, low cost and low maintenance. The limitations of the cage induction motor of basic standard design are low breakaway torque and high starting current, the former typically ranging from 0.5 to 2.0 times and the latter 3 to 7 times rated values, depending on motor rating and number of poles. These limitations can be improved by the use of motors with multi-cage rotors. The multi-cage rotor, in its simplest form, comprises a low reactance and high resistance outer or starting cage, whose influence predominates during the starting period and results in increased torque and reduced current, and an inner cage of lower resistance which is dominant under running conditions.

The wound rotor induction motor design incorporates a three phase, star configuration rotor winding connected to slip rings, to which external resistance is connected for starting. This type of motor is used when high starting torque, reduced starting current and controlled acceleration characteristics are required. The magnitude of starting torque and current, and acceleration period are determined by the value of the external resistance. Under running conditions the slip rings are shorted-out. Disadvantages of the wound rotor motor are higher cost and additional slip ring and brush gear maintenance.

#### Rated Output, Starting Torque and Start Frequency

The rated output of an induction motor is for the designated duty when the ambient temperature of the coolant air does not exceed 40°C or, for a water cooled motor, when the temperature of the water entering the heat exchanger does not exceed 25°C, both at a height above sea level not exceeding 1000 m. The supply voltage is allowed to deviate between 95% and 105% of the rated voltage of the motor without affecting the rated output.

When the motor is operated in conditions different from the reference values, motor rated output will be affected. This must be considered at the time of motor selection (EN 60034, BS 4999). The normal requirement is for the motor to operate continuously at voltages not differing from the rated value by more than plus and minus 5%. When the motor is required to operate under varying and cyclic load conditions, which may include periods of either no-load or standstill, reference must be made to the manufacturer giving details of the load inertia and the load/time duty sequence.

Starting torque. The standard cage induction motor is designed to produce a starting torque over the range between standstill and that at which pull-out (minimum) torque occurs, which is not less than 1.3 times a torque characteristic which varies as the product of the square of the unit speed and the rated torque. This is representative of the run-up characteristic of a typical centrifugal pump. The factor of 1.3 is chosen to allow for a voltage of 90% rated value at the motor terminals during the starting period. The load and motor torque characteristic during the starting period must be considered at the time of motor selection. This is especially important where the motor is required to start with a voltage drop greater than 10%, typically for direct-on-line starting control.

Frequency of starting. The standard cage induction motor is designed to allow two starts in succession (running to rest between starts) from cold or one start from hot after running at rated conditions. Further starting is permissible only if the motor temperature does not exceed the steady state temperature at rated load. Because the number of starts directly affects motor service life, they should be kept to a minimum. More onerous starting requirements must be considered at the time of motor selection. For the wound-rotor induction motor, the starting frequency is generally dictated by the short-time rating of the starting resistor.

URL: https://www.sciencedirect.com/science/article/pii/B9780750668439000251

## Pumping, Electrical Plant, Control and Instrumentation

Malcolm J. Brandt BSc, FICE, FCIWEM, MIWater, ... Don D. Ratnayaka BSc, DIC, MSc, FIChemE, FCIWEM, in Twort's Water Supply (Seventh Edition), 2017

### Rated Output, Starting Torque and Start Frequency

The rated output of an induction motor is defined for the designated duty when the ambient temperature of the coolant air does not exceed 40°C or, for a water-cooled motor, when the temperature of the water entering the heat exchanger does not exceed 25°C, both at a height above sea level not exceeding 1000 m. The supply voltage is allowed to deviate between 95% and 105% of the rated voltage of the motor without affecting the rated output. VSD operation of the motor actually varies the motor voltage to improve the efficiency of the drive system.

When the motor is operated in conditions different from the reference values, motor rated output will be affected. This must be considered at the time of motor selection. The normal requirement is for the motor to operate continuously at voltages not differing from the rated value by more than 5%. When the motor is required to operate under varying and cyclic load conditions, which may include periods of either no-load or standstill, reference must be made to the manufacturer giving details of the load inertia and the load/time duty sequence.

Starting torque. The standard cage induction motor is designed to produce a starting torque over the range between standstill and that at which pull-out (minimum) torque occurs, which is not less than 1.3 times a torque characteristic which varies as the product of the square of the unit speed and the rated torque. This is representative of the run-up characteristic of a typical centrifugal pump. The factor of 1.3 is chosen to allow for a voltage of 90% rated value at the motor terminals during the starting period. The load and motor torque characteristic during the starting period must be considered at the time of motor selection. This is especially important where the motor is required to start with a voltage drop greater than 10%, typically for direct-on-line starting control.

Frequency of starting. The standard cage induction motor is designed to allow two starts in succession (running to rest between starts) from cold or one start from hot after running at rated conditions. Further starting is permissible only if the motor temperature does not exceed the steady state temperature at rated load. Because the number of starts directly affects motor service life, they should be kept to a minimum. More onerous starting requirements must be considered at the time of motor selection. For the wound rotor induction motor, the starting frequency is generally dictated by the short-time rating of the starting resistor. When using the standard cage induction motor with an electronic VSD these limitations are reduced since the starting conditions are less onerous. The mechanical stress on the motor and the windings is also reduced.

URL: https://www.sciencedirect.com/science/article/pii/B9780081000250000193

## Electric Machines, Design

Enrico Levi, in Encyclopedia of Physical Science and Technology (Third Edition), 2003

### II.AEvaluation of Inductances

If one expresses all quantities in per unit of their rated values, the overload capability of induction motors is, according to Section IV.c of Electric Machines, Rotating, Construction and Theory,

(1)$\text{OC}=\frac{{\text{T}}_{\text{max}}}{{\text{T}}_{\text{R}}}\sim \frac{1/\left(2{\text{x}}_{\text{sc}}\right)}{\text{cos}{\varphi }_{1\text{R}}}.$

This relation determines the values of x1 = x2 = xsc/2 corresponding to the specified values of OC and cos ϕ1 R. The magnetizing reactance xm can then be determined with the help of the phasor diagram of Fig. 28 of Electric Machines, Rotating, Construction and Theory. One observes that the per-unit magnetizing current is

(2)$|{\text{i}}_{\mu }|=1/\left({\text{x}}_{\text{m}}+{\text{x}}_{1}\right)=|\text{sin}{\varphi }_{1\text{R}}|-|{\text{i}}_{2}\text{sin}{\varphi }_{2\text{R}}|,$

and since

(3)$\begin{array}{l}|{\text{i}}_{2}\text{cos}{\varphi }_{2\text{R}}|=|\text{cos}{\varphi }_{1\text{R}}|,\hfill \\ \phantom{\rule{2.75em}{0ex}}|{\text{i}}_{\mu }|=|\text{sin}{\varphi }_{1\text{R}}|-|\text{tan}{\varphi }_{2\text{R}}|\text{cos}{\varphi }_{1\text{R}},\hfill \end{array}$

where ∣ tan ϕ2 R = xsc/(r2/SR)  xsc.

For synchronous motors and neglecting the small contribution of the variable reluctance if the poles are salient, one obtains from Eq. (56) of Electric Machines, Rotating, Construction and Theory

$\begin{array}{l}\text{OC}=\frac{{\text{i}}_{\text{f}}}{\text{cos}{\varphi }_{\text{aR}}}\hfill \\ \phantom{\rule{1.75em}{0ex}}=\frac{1}{\text{cos}{\varphi }_{\text{aR}}}\sqrt{{\text{i}}_{\mu }^{2}-2|{\text{i}}_{\mu }|\text{sin}{\varphi }_{\text{aR}}+1},\hfill \end{array}$

where

(4)$|{\text{i}}_{\mu }|=\frac{1}{{\text{x}}_{\text{m}}\left(1+{\text{x}}_{\text{a}}/{\text{x}}_{\text{m}}\right)},$

if is the per-unit field current, and xa/xm can be assumed to be approximately equal to 0.1. Similar relations can be obtained for synchronous generators where the regulation is

$\text{Reg}=\left({\text{V}}_{0}-{\text{V}}_{\text{R}}\right)/{\text{V}}_{\text{R}}={\text{x}}_{\text{m}}{\text{i}}_{\text{f}}-1$

or

(5)$\sqrt{{\left(\frac{1}{1+{\text{x}}_{\text{a}}/{\text{x}}_{\text{m}}}\right)}^{2}-2\frac{{\text{x}}_{\text{m}}\text{sin}{\varphi }_{\text{aR}}}{1+{\text{x}}_{\text{a}}/{\text{x}}_{\text{m}}}+{\text{x}}_{\text{m}}^{2}-1}$

and the short-circuit ratio is

(6)$\text{SCR}=|{\text{i}}_{\mu }|.$

The conditions imposed by the performance specifications on the design of machines operating at adjustable frequency through the interposition of a power conditioner are much less stringent. The dc machines belong to this group. They are essentially synchronous machines in which the frequency is controlled by a closed, feedback loop that senses the position of the brushes and therefore that of the poles. Thus, they differ from adjustable-frequency synchronous-machine drives only with respect to the power conditioner, which is mechanical instead instead of electrical.

Up to this point the rotating machine has been considered as a block in the system diagram, or a “black box.” The next step in the design is to provide the details of its physical realization in terms of topology, geometry, and materials.

URL: https://www.sciencedirect.com/science/article/pii/B0122274105009182

## Electric Motors

Anibal de Almeida, Steve Greenberg, in Encyclopedia of Energy, 2004

### 3.2.3Electric Transportation

#### 3.2.3.1Rail

Due to the availability of powerful and compact inverters, there is an increasing tendency to use AC induction motors with inverter drives rather than DC drives. In the future, high-speed rail will include magnetic levitation trains (using magnetic repulsion to float the cars above the guideway) that use a linear motor to propel the cars along the guideway.

Electric and hybrid electric vehicles use sophisticated water-cooled drives that include regenerative braking to increase energy efficiency. Some designs use AC induction motors and some use permanent-magnet motors. These will continue to evolve as hybrid vehicles move from internal combustion engines to fuel cells as the primary power source.

#### 3.2.3.3Air

The National Aeronautics and Space Administration in the United States is flying unmanned airplanes powered by numerous electric motors that gather their electricity from onboard solar–electric panels and fuel cells. These can fly at very high altitudes for long periods and could eventually perform many of the functions of satellites at much lower cost.