**Introduction**

Induction machines, either motors or generators, are very important for our modern society. Industry, rural and household applications, use induction motors for 85% or more applications in rotating systems. They dominate the market of electrical motors and consume more than 60% of total industrial electricity in industrialized countries. The main reasons are a very strong low-cost design with reliability and inexpensive maintenance. There are no permanent magnets, consequently the manufacturability is only constrained by the availability of iron, copper, machinery for punching the magnetic steel sheets, and electromechanical people capable of understanding how to do winding and assembling. During the 21st century there will be furhter more concerns on energy savings, sustainability and global economics. Therefore, the use of induction machines as either motors or generators become of primordial importance, regarding sustainability and widespread manufacturability. Until 1980’s there were concerns about starting-up induction motors with direct connection to the utility grid, and also constraints on how much reactive power would be needed to maintain the magnetization of those machines. Those machines would operate at constant speed plus/minus the slip variation around the synchronous speed, so they were initially considered constant nominal speed operation. There were some developments in the 70’s and 80’s regarding soft-start control, controlling torque by the rotor winding (for slip-rings machines with rotor connection), with some promises with thyristor based forced-commutation McMurray topologies. Towards the end of 80’s and throughout the 1990’s there were tremendous developments of power electronics-based control of induction motors, with further and better scalar and then vector control schemes, development of direct torque schemes, continuous applications of digital signal processors (DSPs), ASICS, then FPGAs. There were a lot of R&D in advanced control techniques in adaptive control, state observers, flux observers, on-line estimation or parameters, sensorless control, neural network based control, high frequency signal injection for parameter and robustness improvements. This chapter lays out some foundations, based on d-q instantaneous theory transient modeling of induction machines with their fundamental controls. The principles are explained to allow implementation of scalar and vector control approaches for induction machines operating as motors drives.

Long time ago induction motors were considered to be “fixed frequency devices”, i.e. they were connected to the ac supply, then some transient and inrush current would develop and down to a constant electrical frequency of operation, rotating at a shaft speed (RPM) that would depend on the number of poles, there would be a slight variation around the synchronous speed that would depend on the mechanical torque, since the slip frequency increases for increasing torque. Then during the 1960’s it was found that induction could have variable frequency – it could not change rapidly – sluggish methods were employed, thyristors -based circuits were often employed, if they were on natural commutation a lot of constraints were dependent on the overall circuit parameters, thyristor on natural commutation could change the voltage on the machine (with a lot of harmonics), but such a variable voltage operation was not fast, not reliable, and the machine could easily collapse of lack of magnetization. The idea of Volt/Hz control is that flux is proportional to the integral of voltage minus leakages, for example a stator-flux-oriented vector control of an induction motor drive will have the estimation of stator flux by the time integration of the terminal voltage subtracted of the stator resistance. In the magnetic modeling of an induction machine the air-gap flux will be the stator flux subtract by the stator leakage (across the magnetizing inductance), and the rotor flux will be further in the machine by subtracting the rotor leakage. Therefore, a simple dimension analysis gives a unit of [volts*seconds] for flux. It is simple to assume that Volts/Hertz means a constant volts*seconds, i.e. a constant flux.McMurray proposed a forced-commutation SCR based circuit where the voltage would programmed proportionaly to the frequency variation (V/f operation) and with careful slowing down or ramping up frequency it could make possible the first variable frequency drives.

**Early Developments of Induction Motor Drives**

In the 1960 there was a flourishing beginning of power electronics. Professor BK Bose published a paper “Electronic Speed Control of Motors” J. IE (India), pp. 172-182, Sept. 1962, which was essentially a dc-drive using thyratrons. General Electric had a lot of resources and devoted electrical engineers to work with the newly invented device silicon-controller rectifier (SCR) also called thyristor. The early 1960’s induction motors could be controlled with thyristors (SCRs) by controlling the impressed machine voltage using natural commutation, so there were many low-frequency harmonics creating shaft torque pulsations, as well as by only controlling voltage, at constant fundamental frequency, the machine flux was not maintained, and it could easily fall of their electromagnetic stability. In 1961, William McMurray (who is considered to be the ΄founding father΄ and guru of power electronics invented forced commutation techniques: the McMurray and the McMurray–Bedford inverter, later the ac-switched commutation in 1980. It is a fact that there has been no analytical paper nor any known report on how Volts/Hertz was initally proposed in the 1960’s, so for all practical purposes, the V/f control of voltage-fed IM drive was invented by McMurray, although it is not mentioned clearly in literature. There were studies and implementations of cycloconverters and ac voltage control by thyristors in the 1960’s literature.

Sinusoidal PWM (SPWM) technique was invented by Schonung and Stemmler in 1964, but around that time only thyristors were devices for high voltage, bipolar junction transistors were available only for radio applications, very small power rating, very low frequency of operation, so still took 20 more years until SPWM became applicable in transistors-based inverters. In 1965 McMurray deployed thyristors to essentially start the revolution towards variable-frequency motor drives, and open-loop volts/hertz control technique became very popular; by keeping V/Hz constant, with some machine performance measurement in order to fine tune a look-up table it could be possible to maintain the flux nearly constant for variable speed drive operation, greatly enhancing the bandwith of the control dynamics, as well as keeping a good torque per ampere performance. Then it was possible to extend the speed range for higher than the synchronous frequency by imposing a flux weakening for increasing speed, and constrained voltage at the machine terminals, typically using 120 degrees phase-shifted square-wave operation on induction machines with their floating-neutral, in order to avoid circulation of 3rd harmonics and keeping harmonics and sub-harmonics somewhat under control.

During the 70’s closed-loop speed control with slip and flux regulation was implemented mostly on analog control circuits. William McMurray working for the General Electric developed in the 60’s the forced commutation of thyristors in voltage-fed inverter, and assuming square-wave 6-step waveforms for machines with floating neutral he developed for the first time induction motor drives in volts/Hz with speed control. During the 1960’s and 1970’s the early stage of induction motor drives was dominated by voltage-fed square-wave 6-step inverter where forced commutation of thyristors was used and the frequency control was simple to implement in voltage-fed inverter. Before PWM was implemented in inverters, the dc-link voltage could be controlled by a front-end thyristor bridge rectifier.

Park (in 1929) as well as Kron and Stanley (1938) made original contributions on quadrature two-fluxes reaction theory of electrical machinery, but the area of induction machines control was enhanced when in 1969 Hasse introduced the direct vector-control (DVC), in such a thesis there was a decoupled system achieved with flux measurements in the air-gap of the induction machine. The indirect vector-control (IVC) was introduced by Blaschke in 1972. The analysis on the rotor d-q currents in the rotating reference framce made possible the vector control with analysis of the synchronous reference frame and stationary reference frame dynamic models of the machine, nowadays such IVC conditions are defined as ” Blaschke equations”. Throughout the 70’s only analog circuits with operational amplifiers were implemented for solving equations capable of controlling induction machines, and typically the power electronics modulation were based on hysteresis band controllers, those were easily implemented with Schmitt-trigger analog comparators. The first time the author of this chapter observed the implementation of an analog based (with op-amps) vector control implementation for an induction machine was in 1988. In the USA there was a solid introduction of the Texas Instruments digital signal processors (DSPs), allowing fast calcuations in real-time, the families C20 and C25 were integers and C30 was a floating-point DSP processor.

**Induction Machines Drives Features and Enhancements**

Variable speed induction motors are important for energy saving purposes. Most of industrial applications will have centrifugal load torque applications, the change is proportional to the square of speed, and consequently power changes in proportion with the cube of speed with energy varying at different speeds. Variable frequency drives manage energy consumption by changing the speed, and continuous speed control is desirable for a variety of applications, moving air, fluids, heating and ventilation, lifting water, moving belts, loads in container systems, providing energy efficiency, reliable dynamics, and cost efficiency for a variety of shaft rotating applications.

Variable frequency drives can have speed feedback when precision of speed measurement is fundamental, compounded machines for construction, transportation, electric vehicles. Speed control is important on a shaft where on the other side of the shaft there is some mover that impresses constant torque. On the other hand, if the device on the shaft imposes constant speed, the motor drive will mostly have to impress a torque control, and induction motor drives can be programmed for either torque or speed closed loop control.

The induction machine may also have estimation methodologies, for example to avoid speed sensors, or some other variables may be measured to estimate other ones. This class of motor drives are normally defined as sensorless motor drives control. In order to have sensorless motor drives, the estimation techniques will depend on a mathematical model. The model will need most certainly voltage and current feedback, or only current signals, to estimate the speed and or the torque. The model will have influence on accuracy of the machine parameters, and then, measurement of motor parameters will be important, or some class of parameter identification will have to be implemented. The chain of the system is : a motor drive may depend on speed or torque measurement, which can be estimated with a model that depends on measuring voltage and or current variables, which will require parametric identification of the machine in advance, or in real-time. The overall stability of the induction motor drives scheme will be affected by how this control chain is implemented, then advanced control (analog and/or digital) will be required for mathematical implementation in real-time.

After adaptive control and model reference control were developed for induction machines in the 1990’s, there was a period of studying how the system would behave with high frequency signal injection: the induction machine is made of copper, iron, and magnetic fluxes circulating in a real material that is not perfect, and probably anisotropic, then a carrier signal superimposed on the PWM waveforms may help with frequency tracking signal to noise ratio detection, spectral classification, which will then require advanced signal processing algorithms. At the time period of the first decade of the 21st century there was a lot of implementation of advanced motor drives control with higher layers of system management. For example, an induction machine can serve as a wind turbine or as a hydropower turbine energy conversion from a prime mover that could be powered by some sort of energy resource, then a power balance control from the mechanical side, towards the drive, and maybe going forwards into another inverter connected to a grid would require more layers of control and signal processing than a simple motor drive. In recent years there has been “green energy policies” in several countries for the installation of small- or medium-power Distributed Energy Resources (DER), including renewable or alternative energy sources and storage elements. Those units will have power electronics interfaces and maybe some induction machines or induction generators connected to solutions “intelligent power sources”. Those intelligent power sources cooperate to meet the energy demand by exploiting renewable energy at the maximum extent, making possible smart grids where there is enhanced information technology throughout the whole system with capabilities, with impact on environment, science and technology, economics and lifestyle. The use and operation of induction machines as motors or generators have been very popular for renewable energy sources. In the past there were concerns of reactive power consumption and poor voltage regulation under varying speeds for directly connected induction machines, but the advance and developments in power electronics, real-time control, and application of modeling and signal processing have been facilitating contemporary use and retrofit of modern adjustable speed and torque control of induction machines for smart-grid applications.

We are in in age of energy transformation, from fossil fuel to renewable energy, and sustainability and circular economy of the whole society must be considered. Therefore, in such perspective it is important to understand how the manufacturability of induction machines is accessible to nearly all, anywhere: they have simple and robust construction, the materials utilized are mostly iron and copper, maybe some aluminum, resins, and any industrial base of tools and shop supplies are mostly sufficient as raw resources. For induction machines applications it is necessary to keep electrical engineering solid as a technological framework, students with an understanding of electromagnetism, energy conversion, electrical circuits, and with some hands-on skills can learn everything needed to design an induction machine from scratch, order magnetic steel lamination, and with help of mechanical technicians and someone trained in wiring transformers and electrical motors can make one induction machine with indigenous grass-roots, even spinning further local economy developments with possible new labor and crafts. Therefore, induction machines are certainly a present and a future solution that should be a humanity treasure kept in our electrical engineering schools and communities as sustainability cultural resource.

**Electromechanical Considerations**

Induction machines have a robust construction and relative low manufacturing cost. Induction machines are more economical when compared to synchronous machines. For high power applications such a difference is less perceptive because high power machines are typically custom made. But for medium and small sizes the difference in price is dramatic, reaching 80% of difference, i.e. for most of residential, rural and some small-commercial sizing, induction machines are less expensive than any other machine. For same kVA rating, induction machines are somewhat larger than synchronous machines, because the magnetizing current circulates through the stator, so a part of the magnetic iron is for excitation of the machine (while permanent magnet machines are of course more compact). In applications as induction generators, when they are connected to the grid they have less less constraints on the turbine speed control, and naturally stable, with very low maintenance requirements. There are three constraints for grid connected induction generators : (1) starting-up, and (2) reactive power requirements to be provided by the grid connection, or from an inverter based control, and (3) directly connected induction generators will not have a variable shaft speed to optimize any turbine mechanical performance (unless they are doubly-fed with converters on the rotor side). A long time ago the US National Electrical Manufacturers Association (NEMA) standardized the variations in torque-speed characteristics and frame sizes assuring physical interchangeability between motors of competing manufacturers, thereby making them a commercial success and available for integral horsepower ratings with typical voltages ranging from 110 V to 4160 V. The only perceived weakness of induction machines would be lower efficiency (since the rotor dissipates power) and the need of reactive power in the stator. The induction machine is made up of two major components: (i) the stator consisting of steel laminations mounted on a frame in such a manner that slots are formed on the inside diameter of the assembly very similar to a synchronous machine assembly, and (ii) the rotor consisting of a structure of steel laminations mounted on a shaft with two possible configurations classified as wound rotor or cage rotor. It is recommended the book by the author of this chapter, titled ” Modeling and Analysis with Induction Generators – 3rd Edition” and published by Taylor and Francis / CRC Press for construction details.

The induction machine will have a external case providing the magnetic path for the three phase stator circuits, with bearings providing the mechanical support for the shaft clearance (air gap) between the rotor and stator cores, for a wound rotor a group of brush holders and carbon brushes, for connection to the rotor windings. The winding of a wound rotor could be three-phase type with the same number of poles than the stator, generally connected in Y with three terminal leads connected to the slip rings by means of carbon brushes. Wound rotors are usually made for very large power machines, where power electronic circuits will control the rotor winding currents. For industrial and commercial applications typically squirrel cage rotors are used. Squirrel cage rotor windings consist of solid bars of conducting material embedded in the rotor slots and shorted at the two ends by conducting rings. In large machines the rotor bars are made of copper alloy brazed to the end rings, when rotors are sized up to about 20 inches in diameter they are usually stacked in a mold made to aluminum casting, enabling a structure combining the rotor bars, end rings and cooling fan. Induction machines are very simple, rugged , and very reasonable in manufacturing costs. Some variations on the rotor design are used to alter the torque speed features, and when machines are used for induction generators they are optimized for better efficiency, less magnetizing circulating current, higher-leakage inductance (to boost their output voltage and filter out harmonics), and with cooling capable to keep low overall temperature of operation even for very low shaft speeds and internal and enclosed environments.

**Scalar-Control and Field-Oriented Control**

We can understand induction machines based on foundations and principles of electrical engineering, physics, electromagnetism, using differential equations for the equivalent circuits. The use of quadrature d-q axis transformations, from three-phase to stationary frame, and then from stationary frame to rotating reference frame allow more compact formulation in addition of achieving an hypothetical equivalent dc-machine on the rotating reference frame. For parameter estimation, model-reference-controk, and induction generator applications, typically the rotating-reference-frame does not capture the requirements, and either d-q stationary of the traditional abc three-phase formulation is used for such adaptive control methodologies, or self-excited induction generators modeling and control. The differential equations can be restated as the state space model. In terms of feedback signals, input currents and voltages are measured for use in control loop. Speed is another measurement quantity, but it is sometimes undesirable because speed sensors are fragile and may fail, so sensorless induction machine drives have been developed.

The first approach ever used for induction motor drives was a direct machine terminal voltage control (with thyristors), then a proportional open-loop configuration where machine voltages and currents would be variable in frequency, in order to maintain a pretty much constant ratio of impressed voltage by frequency (Volts/Hz) allowed the first generation of motor drives defined as Scalar Control. Therefore, scalar control of induction motors/generators refers to the control of the magnitude of voltage and frequency in order to achieve suitable torque and speed with an impressed slip (slip is the angular speed of the machine flux subtracted by the equivalent shaft speed in the machine flux rotating reference frame). Scalar control can be easily understood based on the fundamental principles of induction machine steady-state modeling. The use of a power electronic system is either for a series connection of inverters and converters between the induction generator and the grid, or for a parallel path system capable of providing reactive power for isolated operation. Scalar control disregards the coupling effect on the generator, i.e. the voltage will be set to control the flux and the frequency in order to control the torque. However, flux and torque are also functions of frequency and voltage, respectively. On the other hand, vector control, also called field oriented control, has mathematical transformations from the machine abc three-phase model towards a rotating-reference-frame virtual dc model, then proper alignment of a chosen field orientation will be made, either on d or on the q axis. You can find on other technical references the formulation based on the abc and quadrature notations. The vector control orientation has been initially develop for the rotor flux aligned with the d-axis for the indirect vector control, then the stator flux aligned with the d-axis for the direct vectro control. It is possible also to have universal field orientation, where any flux can be aligned to any rotating-reference frame axis.

Scalar control is different than vector control such that both magnitude and phase alignment of the vector variables are controlled. Scalar control drives give somewhat inferior performance, but they are easy to implement and are very popular for pumping and industrial applications. The importance of scalar control has diminished recently because of the superior performance of the vector-controlled drives and the introduction of high performance inverters. High performance inverters offer prices competitive to scalar control based inverters (volts/Hertz inverters), although they are cheap and widely available. The main constraint to use a scalar control method for induction motor/generators is related to the transient response. If shaft torque and speed are bandwidth limited and torque varies slowly to track required speed variations (within hundreds of milliseconds up to the order of almost a second), scalar control may work appropriately. Hydropower and wind power applications have slower mechanical dynamics than such a timing constraint. Therefore, it seems that scalar control is still a good approach for renewable energy type applications.

Field oriented control uses dynamic model of the IM where the voltages, currents and ﬂuxes are expressed in space vector forms. Since the IM is described by differential equations, the model accounts for both steady state and transient dynamics of the IM. Therefore, field oriented control can achieve excellent performance in transient and steady state conditions. In the rotating rotor flux frame, quantities rotating at synchronous speed appear as DC quantities. With the ﬂux aligned to the d axis of the reference frame, d component of the stator current represents the flux and q component of the stator current represents the torque. Therefore, the control of IM is reduced to a simple control scheme. The simplicity is resulted from the fact that torque and flux components are decoupled in the adopted reference frame. Two types of field oriented control are defined based on the position of the rotor flux: indirect and direct. By adding the slip position to the measured rotor position, the flux position in indirect field oriented control is obtained. The flux position in direct field oriented control is calculated based on the terminal variables and rotor speed. Since field oriented control stems from a frame transformation that requires rotor speed, the knowledge of rotor position needs to be acquired accurately in order to perform such transformation. The accuracy of the rotor position estimate has a significant impact on the performance of field oriented control. If such estimate is not accurate enough, the satisfactory level of decoupling of the torque and flux will not be achieved. Therefore, field oriented control is dependent on having good machine parameter characterization, in addition of excellent sensor monitoring and feedback of the required machine variables, plus a power microcontroller, or DSP based processor for very fast real-time computation with quick PWM methodology, good protection against over-currents or over-voltages, making possible that an inverter controlling the induction machine impress current-control capabilities in a closed loop speed control, or in a closed-loop torque control.