# Electric machine

In electrical engineering, electric machine is a general term for machines using electromagnetic forces, such as electric motors, electric generators, and others. They are electromechanical energy converters: an electric motor converts electricity to mechanical power while an electric generator converts mechanical power to electricity. The moving parts in a machine can be rotating (rotating machines) or linear (linear machines). While transformers are occasionally called "static electric machines", since they do not have moving parts, generally they are not considered "machines", but as electrical devices "closely related" to the electrical machines.
Electric machines, in the form of synchronous and induction generators, produce about 95% of all electric power on Earth (as of early 2020s), and in the form of electric motors consume approximately 60% of all electric power produced. Electric machines were developed beginning in the mid 19th century and since that time have been a ubiquitous component of the infrastructure. Developing more efficient electric machine technology is crucial to any global conservation, green energy, or alternative energy strategy.

## Operating Principle

The main operating principles of electric machines take advantage of the relationship between electricity and magnetism, specifically that changes in one can create changes in the other. For example, moving a bar magnet around a wire to induce a voltage across it, or running current through a wire in a magnetic field to generate a force. With proper orientation of magnets, wires, voltages, and currents, an electric machine can convert electric energy (electricity) to mechanical energy (motion) and vice-versa.
This is largely based off of Maxwell's Equations and is analytically and mathematically complex, especially since most electric machines rotate to couple electricity and motion. However, a Linear DC machine, with its simple operation and orientation of components, makes this analysis more straightforward.

### Theory

An example Linear DC machine is shown below, consisting of an electric circuit partially overlapping a magnetic field. The electric circuit is made up of a battery $V_{B}$, a resistor $R$, a switch $S$, and two wires. The wires extend out and lie in a constant magnetic field ${\vec {B}}$ and have a small bar of length $l$ laying across them that is able to move freely. The machine's operation is governed by 4 principles:
* The Lorentz Force, a force generated due to current flowing in a magnetic field. For a wire with current $i$ flowing within magnetic field ${\vec {B}}$, the force is ${\vec {{F}_{ind}}}=i*({\vec {l}}\times {\vec {B}})$, where ${\vec {l}}$ is the unit vector in the direction of current flow.
* Faraday's Law of Induction, a voltage induced due to movement within a magnetic field. For a wire of length ${\vec {l}}$ moving in a magnetic field ${\vec {B}}$ with velocity ${\vec {v}}$, the induced voltage is ${e}_{ind}=({\vec {v}}\times {\vec {B}})\cdot {\vec {l}}$.
* Kirchhoff's Voltage Law (KVL), the sum of voltages around a loop is zero. For a series circuit of $N$ elements, the summation of voltage drops $V_{k}$ is equal to zero $0=\sum _{k=1}^{N}V_{k}$.
* Newton's Laws of Motion, an applied force on an object is equal to its mass by its acceleration. For an applied force ${\vec {F}}$ accelerating a mass $m$, this force is ${\vec {F}}=m*{\vec {a}}$.
In the design shown, as all the vectors are all orthogonal to each other, the direction is simplified to either left or right (for velocity and forces) or up and down (for current). The table below shows these 4 equations simplified.
| Equation | Description | Magnitude | Direction |
| 1 | Lorenz Force | ${F}_{ind}=ilB$ | Left or Right |
| 2 | Induced Voltage | ${e}_{ind}=vBl$ | |
| 3 | KVL | ${V}_{B}=iR+{e}_{ind}$ | Up or Down (current) |
| 4 | Law of Motion | ${F}=ma$ | Left or Right |

### Machine Starting

With the switch open, there is no closed electric circuit, and the battery supplies no current. With no current flowing within the magnetic field, no force is generated, the bar does not move, and no voltage is induced across it.
The machine can be started by closing switch $S$, which forms a closed electric circuit. From equation (3) the current supplied can be determined, however as the bar is not moving yet the induced voltage ${e}_{ind}=0$ and the starting current is determined only by the series resistance $R$.
$i={V_{B}-{e}_{ind} \over R}\longrightarrow {i}_{start}={V_{B} \over R}$
With current now flowing through the bar and within the magnetic field ${\vec {B}}$, a force is induced, and the bar begins moving. With the magnetic field oriented into the page, and current flowing from top to bottom through the bar, the right-hand rule shows that the force generated is to the right. From Newton's law of motion in equation (4), the bar will begin accelerating to the right proportional to its mass.
As the bar starts moving in the magnetic field, a voltage is induced across the bar from (2). With the motion of the bar to the right and the magnetic field into the page, the magnitude of ${e}_{ind}$ is positive. With ${e}_{ind}>0$, the current flowing will be reduced, which in turn reduces the induced force and reduces the acceleration of the bar. While the acceleration decreases, the speed still increases, which increases the magnitude of ${e}_{ind}$. This feedback continues until the induced voltage rises to the full battery voltage, ${e}_{ind}=V_{B}$, resulting in no current flow, which results in no induced force, and no acceleration. The bar settles into its steady-state speed equal to
$V_{B}={e}_{ind}={v}_{ss}Bl\longrightarrow {v}_{ss}={{e}_{ind} \over Bl}$
This is referred to as the No-Load speed. The bar will continue to move at this speed until it is disturbed, and as long as the wires and magnetic field extend out far enough. It also assumes that there is no friction and the bar has no mass.

### Motor Action

Assuming the bar has a mass $m$, when the switch is closed and current begins to flow through the bar in the magnetic field, a force will be induced. However, $F_{ind}$ will now be opposed by the force from the weight of $m$ from gravity $g$. Defining this as $F_{load}$ the net force on the bar then becomes
$F_{net}=F_{ind}-F_{load}=F_{ind}-mg$
As the net force is less than the induced force at No-Load, the bar will experience less acceleration, resulting in the induced voltage decrease, which causes more current to be drawn, ultimately increasing the induced force. This continues until the induced force is equal to the load force, resulting in no net force and no acceleration. Unlike the ideal case at no-load, the circuit now draws some current to produce enough force to offset the load force and settles at a speed lower than the no-load stead-state speed. If a mass $M$ were placed in front of the bar, the electric machine would draw additional current to move both masses at a constant, lower speed. As the motor adjusts to reach a net force of zero, the ultimate induced force the machine produces is
$F_{ind}=F_{load}=g(m+M)$

### Generator Action

If the switch is closed, the electric machine will draw enough current to move the mass of the bar at a constant speed, slightly below the theoretical no-load speed. If instead of opposing motion, a force is applied in the same direction of the moving bar, the net force becomes
$F_{net}=F_{ind}+F_{app}$
As the net force is now greater than the induced force, the bar will begin accelerating and the speed will increase. As the speed increases in the magnetic field, the induced voltage across the bar will increase. With the induced voltage already near the battery voltage, the applied force causes it to rise above the battery voltage, causing the current to reverse direction and flow into the battery.
$i={V_{B}-{e}_{ind} \over R}\longrightarrow -i={{e}_{ind}-V_{B} \over R}$
When the current changes directions, the induced force changes direction and begins to oppose the applied force. This slows the bar down, lowering the induced voltage and current drawn. This continues until the induced force is equal to the applied force, but in the opposite direction, with the bar moving at a constant speed above the steady-state speed.
With the current flowing the opposite direction, the electric machine charges the battery with the power from the force applied to the bar and acts as a generator. This shows an unintuitive aspect of most electric machines: a machine changing between acting as a motor and generator does not result in its direction of motion (or rotation) changing.

### Power Conversion and Losses

Power is defined as work per unit time $P={dW \over dt}$, and an electric machine converts electrical power to mechanical power (as a motor) or mechanical power to electrical power (as a generator). Mechanically, if a constant force $F$ is applied to an object across a distance $x$, the work done is defined as $F\cdot x$, and thus the power as $F\cdot v$. Electrically, power is defined as voltage across an element multiplied by its current $V\cdot I$, given the definitions of voltage being work per unit charge ${dW \over dQ}$ and current as charge per unit time ${dQ \over dt}$. These equations are summarized in the table below.
| Description | Simplified |
| Power (mechanical) | ${P}_{mech}={dW \over dt}={d \over dt}(F\cdot x)=F\cdot {dx \over dt}=F\cdot v$ |
| Power (electrical) | ${P}_{elec}={dW \over dt}={dW \over dQ}\cdot {dQ \over dt}=V\cdot I$ |
For the linear DC machine, the power converted is the electrical power delivered to the moving power, which is equal to the mechanical power of the bar. This takes the form of
$P_{conv}=e_{ind}\cdot i=F_{ind}\cdot v$
An electric machine also transfer power to losses, generally in the form of heat. While this is not desirable behavior, it is the nature of electric machines and all thermodynamic systems.
Electrically, the resistance in the circuit dissipates some power as heat, taking the form
$P_{loss,elec}=i^{2}R$
Mechanically, some power is also lost due to the friction between the moving bar and load and the rails, taking the form
$P_{loss,mech}=F_{f}v=(\mu F_{N})v=(\mu g[m+M])v$
The total power produced by the machine is the sum of the converted power and the losses. When operating as a motor, the battery provides the total power and when operating as a generator the applied force provides the total power.
These power equations are shown in the table.
| Description | Simplified |
| Converted Power | $P_{conv}=e_{ind}\cdot i=F_{ind}\cdot v$ |
| Electrical Losses | $P_{loss,elec}=i^{2}R$ |
| Mechanical Losses | $P_{loss,mech}=F_{f}v=(\mu F_{N})v=(\mu g[m+M])v$ |
| Total Power | $P_{total}=P_{conv}+P_{loss,elec}+P_{loss,mech}$ |
| Motor total power | $P_{total}=V_{B}\cdot i$ |
| Generator total power | $P_{total}=F_{app}\cdot v$ |

## Generator

An electric generator is a device that converts mechanical energy to electrical energy. A generator forces electrons to flow through an external electrical circuit. It is somewhat analogous to a water pump, which creates a flow of water but does not create the water inside. The source of mechanical energy, the prime mover, may be a reciprocating or turbine steam engine, water falling through a turbine or waterwheel, an internal combustion engine, a wind turbine, a hand crank, compressed air or any other source of mechanical energy.
The two main parts of an electrical machine can be described in either mechanical or electrical terms. In mechanical terms, the rotor is the rotating part, and the stator is the stationary part of an electrical machine. In electrical terms, the armature is the power-producing component and the field is the magnetic field component of an electrical machine. The armature can be on either the rotor or the stator. The magnetic field can be provided by either electromagnets or permanent magnets mounted on either the rotor or the stator. Generators are classified into two types, AC generators and DC generators.

### AC generator

An AC generator converts mechanical energy into alternating current electricity. Because power transferred into the field circuit is much less than power transferred into the armature circuit, AC generators nearly always have the field winding on the rotor and the armature winding on the stator.
AC generators are classified into several types.
* In an induction generator, the stator magnetic flux induces currents in the rotor. The prime mover then drives the rotor above the synchronous speed, causing the opposing rotor flux to cut the stator coils producing active current in the stater coils, thus sending power back to the electrical grid. An induction generator draws reactive power from the connected system and so cannot be an isolated source of power.
* In a Synchronous generator (alternator), the current for the magnetic field is provided by a DC current source, either separate or rectified from the output of the machine using a full bridge rectifier.

### DC generator

A DC generator is a machine that converts mechanical energy into Direct Current electrical energy. A DC generator generally has a commutator with split ring to produce a direct current instead of an alternating current.

## Motor

An electric motor converts electrical energy into mechanical energy. The reverse process of electrical generators, most electric motors operate through interacting magnetic fields and current-carrying conductors to generate rotational force. Motors and generators have many similarities and many types of electric motors can be run as generators, and vice versa. Electric motors are found in applications as diverse as industrial fans, blowers and pumps, machine tools, household appliances, power tools, and disk drives. They may be powered by direct current or by alternating current which leads to the two main classifications: AC motors and DC motors.

### AC motor

An AC motor converts alternating current into mechanical energy. It commonly consists of two basic parts, an outside stationary stator having coils supplied with alternating current to produce a rotating magnetic field, and an inside rotor attached to the output shaft that is given a torque by the rotating field. The two main types of AC motors are distinguished by the type of rotor used.
* Induction (asynchronous) motor, the rotor magnetic field is created by an induced current. The rotor must turn slightly slower (or faster) than the stator magnetic field to provide the induced current. There are three types of induction motor rotors, which are squirrel-cage rotor, wound rotor and solid core rotor.
* Synchronous motor, it does not rely on induction and so can rotate exactly at the supply frequency or sub-multiple. The magnetic field of the rotor is either generated by direct current delivered through slip rings (exciter) or by a permanent magnet.

### DC motor

The brushed DC electric motor generates torque directly from DC power supplied to the motor by using internal commutation, stationary permanent magnets, and rotating electrical magnets. Brushes and springs carry the electric current from the commutator to the spinning wire windings of the rotor inside the motor. Brushless DC motors use a rotating permanent magnet in the rotor, and stationary electrical magnets on the motor housing. A motor controller converts DC to AC. This design is simpler than that of brushed motors because it eliminates the complication of transferring power from outside the motor to the spinning rotor. An example of a brushless, synchronous DC motor is a stepper motor which can divide a full rotation into a large number of steps.

## Other electromagnetic machines

Other electromagnetic machines include the Amplidyne, Synchro, Metadyne, Eddy current clutch, Eddy current brake, Eddy current dynamometer, Hysteresis dynamometer, Rotary converter, and Ward Leonard set. A rotary converter is a combination of machines that act as a mechanical rectifier, inverter or frequency converter. The Ward Leonard set is a combination of machines used to provide speed control. Other machine combinations include the Kraemer and Scherbius systems.

## Electromagnetic-rotor machines

Electromagnetic-rotor machines are machines having some kind of electric current in the rotor which creates a magnetic field which interacts with the stator windings. The rotor current can be the internal current in a permanent magnet (PM machine), a current supplied to the rotor through brushes (Brushed machine) or a current set up in closed rotor windings by a varying magnetic field (Induction machine).

### Permanent magnet machines

PM machines have permanent magnets in the rotor which set up a magnetic field. The magnetomotive force in a PM (caused by orbiting electrons with aligned spin) is generally much higher than what is possible in a copper coil. The copper coil can, however, be filled with a ferromagnetic material, which gives the coil much lower magnetic reluctance. Still the magnetic field created by modern PMs (Neodymium magnets) is stronger, which means that PM machines have a better torque/volume and torque/weight ratio than machines with rotor coils under continuous operation. This may change with introduction of superconductors in rotor.
Since the permanent magnets in a PM machine already introduce considerable magnetic reluctance, then the reluctance in the air gap and coils are less important. This gives considerable freedom when designing PM machines.
It is usually possible to overload electric machines for a short time until the current in the coils heats parts of the machine to a temperature which cause damage. PM machines can less tolerate such overload, because too high current in the coils can create a magnetic field strong enough to demagnetise the magnets.

### Brushed machines

Brushed machines are machines where the rotor coil is supplied with current through brushes in much the same way as current is supplied to the car in an electric slot car track. More durable brushes can be made of graphite or liquid metal. It is even possible to eliminate the brushes in a "brushed machine" by using a part of the rotor and stator as a transformer that transfers current without creating torque. Brushes must not be confused with a commutator. The difference is that the brushes only transfer electric current to a moving rotor while a commutator also provides switching of the current direction.
There is iron (usually laminated steel cores made of sheet metal) between the rotor coils and teeth of iron between the stator coils in addition to black iron behind the stator coils. The gap between rotor and the stator is also made as small as possible. All this is done to minimize the magnetic reluctance of the magnetic circuit which the magnetic field created by the rotor coils travels through, something which is important for optimizing these machines.
Large brushed machines which are run with DC to the stator windings at synchronous speed are the most common generator in power plants, because they also supply reactive power to the grid, because they can be started by the turbine and because the machine in this system can generate power at a constant speed without a controller. This type of machine is often referred to in the literature as a synchronous machine.
This machine can also be run by connecting the stator coils to the grid and supplying the rotor coils with AC from an inverter. The advantage is that it is possible to control the rotating speed of the machine with a fractionally rated inverter. When run this way the machine is known as a brushed double feed "induction" machine. "Induction" is misleading because there is no useful current in the machine which is set up by induction.

### Induction machines

Induction machines have short circuited rotor coils where a current is set up and maintained by induction. This requires that the rotor rotates at other than synchronous speed, so that the rotor coils are subjected to a varying magnetic field created by the stator coils. An induction machine is an asynchronous machine.
Induction eliminates the need for brushes which is usually a weak part in an electric machine. It also allows designs which make it very easy to manufacture the rotor. A metal cylinder will work as rotor, but to improve efficiency a "squirrel cage" rotor or a rotor with closed windings is usually used. The speed of asynchronous induction machines will decrease with increased load because a larger speed difference between stator and rotor is necessary to set up sufficient rotor current and rotor magnetic field. Asynchronous induction machines can be made so they start and run without any means of control if connected to an AC grid, but the starting torque is low.
A special case would be an induction machine with superconductors in the rotor. The current in the superconductors will be set up by induction, but the rotor will run at synchronous speed because there will be no need for a speed difference between the magnetic field in stator and speed of rotor to maintain the rotor current.
Another special case would be the brushless double fed induction machine, which has a double set of coils in the stator. Since it has two moving magnetic fields in the stator, it gives no meaning to talk about synchronous or asynchronous speed.

## Reluctance machines

Reluctance machines have no windings on the rotor, only a ferromagnetic material shaped so that "electromagnets" in stator can "grab" the teeth in rotor and advance it a little. The electromagnets are then turned off, while another set of electromagnets is turned on to move rotor further. Another name is step motor, and it is suited for low speed and accurate position control. Reluctance machines can be supplied with permanent magnets in the stator to improve performance. The "electromagnet" is then "turned off" by sending a negative current in the coil. When the current is positive the magnet and the current cooperate to create a stronger magnetic field which will improve the reluctance machine's maximum torque without increasing the currents maximum absolute value.

## Polyphase AC machines

The armature of polyphase electric machines includes multiple windings powered by the AC currents offset one from another by equal phasor angles. The most popular are the 3 phase machines, where the windings are (electrically) 120° apart.
The 3-phase machines have major advantages of the single-phase ones:
* steady state torque is constant, leading to less vibration and longer service life (the instantanous torque of a single-phase motor pulsates with the cycle)
* power is constant (the power consumption of the single-phase motor varies over the cycle);
* smaller size (and thus lower cost) for the same power;
* the transmission over 3 wires need only 3/4 of the metal for the wires that would be required for a two-wire single-phase transmission line for the same power;
* better power factor.

### Sequence

The winding phases of the 3-phase motor must be energized in a sequence for a motor to rotate, for example the phase V lagging phase U by 120°, and phase W lagging the phase V (U > V > W, normal phase rotation, positive sequence). If the sequence is reversed (W < V < U), the motor will rotate in the opposite direction (negative sequence). The common current through all three windings is called zero sequence. Any combination of the AC currents in the three windings can be expressed as a sum of three symmetrical currents, corresponding to positive, negative, and zero sequences.

## Electrostatic machines

In electrostatic machines, torque is created by attraction or repulsion of electric charge in rotor and stator.
Electrostatic generators generate electricity by building up electric charge. Early types were friction machines, later ones were influence machines that worked by electrostatic induction. The Van de Graaff generator is an electrostatic generator still used in research today.

## Homopolar machines

Homopolar machines are true DC machines where current is supplied to a spinning wheel through brushes. The wheel is inserted in a magnetic field, and torque is created as the current travels from the edge to the centre of the wheel through the magnetic field.

## Electric machine systems

For optimized or practical operation of electric machines, today's electric machine systems are complemented with electronic control.