Electric machine

In electrical engineering, electric machine is a general term for a machine that makes use of electromagnetic forces and their interactions with voltages, currents, and movement, such as motors and generators. They are electromechanical energy converters, converting between electricity and motion. The moving parts in a machine can be rotating (rotating machines) or linear (linear machines). While transformers are occasionally called "static electric machines", they do not have moving parts and are more accurately described as electrical devices "closely related" to electrical machines.

An electric machine separated into its moving portion (rotor) and its stationary portion (stator and base). Pictured, and AC induction motor.

Electric machines, in the form of synchronous and induction generators, produce about 95% of all electric power on Earth (as of early 2020s). In the form of electric motors, they consume approximately 60% of all electric power produced. Electric machines were developed in the mid 19th century and since have become a significant component of electric infrastructure. Developing more efficient electric machine technology is crucial to global conservation, green energy, and 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.

This is largely based off of Maxwell's Equations and can be analytically and mathematically complex, especially since most electric machines rotate to couple electricity and motion. However, most electric machines are governed by the same 4 principles:

1. 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.
2. 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 ${e}_{ind}=({\vec {v}}\times {\vec {B}})\cdot {\vec {l}}$.
3. 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 $0=\sum _{k=1}^{N}V_{k}$.
4. 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 ${\vec {F}}=m*{\vec {a}}$.

As current flows within a magnetic field, a force is induced that causes movement. With this movement also within the magnetic field, a voltage is induced in the machine. This induced voltage affects the current, which in turn affects the force, speed, and induced voltage. This feedback tends to drive the machine to an equilibrium so that the electrical energy and mechanical energy are matched (plus losses). With proper orientation of magnetic fields, wires, voltages, and currents, an electric machine can convert electric energy (electricity) to mechanical energy (motion) and vice-versa.

Electric machines typically separate their moving and non-moving portions, and identifying them uniquely. In rotating machines, the stationary portion is called the stator, while the rotating portion is the rotor. The stator and rotor may having windings (wire wound around them) to carry the current on the electrical side and/or to help create the magnetic field. The current carrying winding is called the armature winding while the magnetic field winding is called the field winding. All rotating machines have armature windings, but not all machines have field windings (i.e. if the magnetic field is created by a permanent magnet instead of the electromagnet created by the field winding). The armature winding and field winding (if applicable) can be on either the stator or rotor, depending on the machine design, however they are rarely on the same part.

Characteristics of Electric Machines

While electric machines have their differences, they share many traits, and are often grouped by some part of their construction or intended operation. Below are some of the common characteristics common to most electric machines.

Motors and Generators

If an electric machine converts mechanical energy into electrical energy, it is referred to as a generator, while machines that are convert electricity to motion are called motors.

Generators that produce alterating current (AC) are called alternators, while direct current (DC) generators are called dynamos. Motors are referred to as pumps when their motion is used to move a fluid, such as water.

Theoretically, most electric machines can be used as either a generator or a motor, however in practice it is common for machines to be spealized to one or the other. Generator's power is generally rated in kilowatts (kW) while motors are rated in terms of horsepower (hp).

AC vs DC

One of the most common ways to divide electric machines is by the electrical system they are connected to, either DC or AC, with AC often divided into single phase or three phase. With rare exceptions, such as universal motors, machines cannot switch between electric systems. AC machines are largely either synchronous generators or induction motors.

DC machine is somewhat of a misnomer, as all DC machines use alternating voltages and currents to operate. Most DC machines contain a device called a commutator, which allows the windings within the DC machine to periodically change their connections to the DC system as the machine rotates, effectively alternating the direction of voltages and currents.

Brushed vs Bushless

If an electric machine has an electric circuit on its rotor, it needs a means to power the circuit, even while the rotor is rotating. One method of doing this is to attach metallic brushes to the stator and have them held under tension against the rotor. The brushes are then energized on the stationary stator side, and transfer electricty to the moving rotor. The part of the rotor that contact the brushes is called slip rings, and is designed to withstand both the electricity being passed through it, and the mechanical wear of continuously spinning against the brushes. The brushes are generally made of carbon, for its strength and conductivity. Brushes wear down and need replacing throughout the life of the machine.

Another common technique of powering the electric circuit on the rotor is through electromagnetic induction, as the rotor is already moving and meets one of the main requirements of induction (varying magnetic field). This technique is very common for induction motors, but is also used in bushless synchronous machines.

If the winding on the rotor is a field winding, its purpose it to act as an electromagnet and generate a magnetic field that rotates. This can be replaced with a permanent magnet, which removes the need for brushes or slip rings and simplifies the design of the machine. Large permanent magnetics are expensive and do not always allow for a machine to act as both a motor and generator, so PM machines tend to be limited to small power motors.

Speed and Torque

Electric motors convert electricity to motion, and are able to move increasing larger mechanical loads by drawing more electrical energy, however this comes at a cost. With the Lorenz Force defining the speed of the machine, if the force has to overcome a larger mechanical load, the speed of the machine slows down. In rotating motors, the forces are viewed as torques, and the behavior is referred to as the speed-torque curve of the machine.

In most electric motors there are two magnetic fields: the one produced from the armature winding connected to the electrical power, and another from the field winding (or PM). The interaction of these two magnetic fields induce a torque in the machine, similar to how two bar magnets will rotate to align with each other. This induced torque is used to rotate the rotor, and in a motor, rotate the mechanical load attached to the rotor. As the induced torque is based on the magnetic fields, it is related to the induced Lorenz force and the speed of the machine. Electric motors denote speed in terms of revolutions per minute (RPM).

The shape of the speed-torque curve depends on the design of the motor. In DC motors, the speed-torque curve is linear, with maximum torque occurring with zero speed (stall torque) and maximum speed occuring at zero torque (no-load speed). In AC motors, the torque-speed curve is a more complex shape, beginning at the starting torque associated with the locked-rotor current and no speed, gradually increasing with speed until peaking at the breakdown torque, and finally rapidly falling to zero at the no-load speed. The exact shape of the curve depends on the AC motor design.

Some AC motors produce a none-zero starting torque but others, most notably single-phase induction motors, produce zero torque at zero speed and cannot self-start to move even an unloaded rotor. The reasons behind this are due to induction motors operating based on a rotating magnetic field on the stator, which single phase power do not produce. None self-starting induction motors require starting circuits, the most common being the capacitive-start design.

Synchronous vs Asynchronous

In AC electric machines, one magnetic field rotates around the machine due to the electrical system while the other magnetic field rotates with the rotor's physical motion. If these two magnetic fields rotate at the same speed, the machine is said to be a synchronous machine, and operates at synchronous speed. If the magnetic fields rotate at different speeds the machine is asynchronous, or more commonly an induction machine, with a speed either abover or below synchronous speed. If the rotors field is slower than the stator field, the machine acts as a motor, it is faster it acts as a generator. Induction machines cannot operate at synchronous speeds.

DC machines are not classified as either synchronous or asynchronous, as the magnetic fields do not rotate. The field winding magnetic field is stationary, and the armature winding has its polarity reversed by communtation.

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

Main article: Symmetrical components

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.

Example: Linear DC Machine

Most electrical machines are complex to analyze, however a simple Linear DC machine can be used to see how the operating principles relate. 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.

A simple Linear DC machine, consisting of an electric circuit overlapping a constant magnetic field.

In the design shown, as all the vectors are all orthogonal to each other, the direction of the vectors are simplified to either left or right (for velocity and forces) or up and down (for current). The table below shows the 4 operating 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	$P_{total}=F_{app}\cdot v$