9
Electric Powertrains
An electric vehicle (EV) is similar to an engine‐powered vehicle except that the engine‐powertrain is now replaced by an electric machine, and the onboard fuel (gasoline or diesel) is replaced by an electric energy storage device, such as a battery pack.
9.1 Basics of Electric Vehicles
Figure 9.1 shows the basic structure of an EV. In this configuration, the battery stores energy in a chemical form. The most popular is a lithium‐ion battery at the present time. The battery is charged from an electric outlet with an electric charger either carried on board or installed at the charging station. Typically, a low power charger is carried on board (3.3 kW, 6.6 kW) and fast chargers are installed at charge stations. The inverter converts the battery’s DC voltage to a multi‐phase AC to drive the electric machine. The inverter can change the amplitude and frequency of the power flow into the motor so that the torque, speed, and direction of the motor are controlled to drive the vehicle in the desired operation mode. During braking of the vehicle, the battery is charged by regenerative energy recovered from the kinetic energy of the vehicle which is converted from mechanical energy to electric energy by the electric motor, acting as a generator. Due to the characteristics of the electric machines, the mechanical transmission is usually simpler for an EV than in a conventional vehicle. Many EVs use a single speed gear reduction to satisfy all the driving needs, while some others use two‐speed automated transmissions for the purpose similar to the CVT in a conventional vehicle. EVs generally do not need a multiple‐speed automatic transmission as used in conventional vehicles. There may be a DC‐DC converter between the battery and the inverter in some cases, in order to match the voltage of the battery to the inverter/motor voltage.
Figure 9.1 Basic structure of an EV.
Figure 9.2 shows a typical electric drivetrain which consists of an electric motor, a power electronics converter, and a gearbox.
Figure 9.2 Electric system of a passenger car, which includes a PM motor, a power electronics inverter, and a gearbox.
9.2 Current Status and Trends for EVs
EVs have many advantages and challenges. Electricity is more efficient than the combustion process in a car. Well‐to‐wheel studies show that, even if the electricity is generated from petroleum, the equivalent miles that can be driven by 1 gallon (3.8 liter) of gasoline is 108 miles (173 km) in an electric car, compared to 33 miles (53 km) in an internal combustion engine (ICE) car [6–8]. In a simpler comparison, it costs 2 cents per mile to use electricity (at USD 0.12 per kWh) but 10 cents per mile to use gasoline (at USD 3.30 per gallon) for a compact car. Since electricity can be generated through renewable sources, such as hydroelectric, wind, solar, and biomass, EVs can be cleaner and more sustainable than combustion‐based vehicles. On the other hand, the current electricity grid has extra capacity available at night when usage of electricity is off‐peak. It is therefore ideal to charge EVs at night when the grid has extra energy capacity available. This is particularly so when differentiated pricing structures are available where the price at night is significantly cheaper. The batteries on board an electric vehicle can also potentially be used for electric grid support, such as peak shaving, frequency regulation, backup power, and other purposes.
However, there are many challenges for EVs. High cost, limited driving range, and long charging time are the main shortcomings for battery‐powered EVs. Electric energy storage is currently the bottleneck for mass penetration of EVs due to the unsatisfactory energy density, power density, lifespan, and cost.
EVs were invented in 1834, that is, about 60 years earlier than gasoline‐powered cars, which were invented in 1895. By 1900, there were 4200 automobiles sold in the USA, of which 40% were electric cars (http://sites.google.com/site/petroleumhistoryresources/Home/cantankerous‐combustion). In the USA, there were a number of electric car companies in the 1920s, with two of them dominating the EV markets – Baker of Cleveland and Woods of Chicago. Both car companies offered hybrid electric cars. However, the hybrid cars were more expensive than gasoline cars and sold poorly. Electric vehicles and hybrid electric vehivles (HEVs) had faded away by 1930 and the electric car companies all failed. There were many reasons leading to the disappearance of EVs.
It was not until the Arab oil embargo in 1973 that the soaring price of gasoline sparked new interest in EVs. The US Congress introduced the Electric and Hybrid Vehicle Research, Development, and Demonstration Act in 1976 recommending the use of EVs as a means of reducing oil dependency and air pollution. In 1990, the California Air Resource Board (CARB), in consideration of the smog affecting Southern California, passed the zero emission vehicle (ZEV) mandate, which required 2% of vehicles sold in California to have no emissions by 1998 and 10% by 2003. California car sales is approximately10% of the total car sales in the United States. Major car manufacturers were afraid that they might lose the California car market without a ZEV. Hence, every major automaker developed EVs and HEVs. Fuel cell vehicles were also developed during this period. Many EVs were made, such as GM’s EV1, Ford’s Ranger pickup EV, Honda’s EV Plus, Nissan’s Altra EV, and Toyota’s RAV4 EV.
In 1993, the US Department of Energy set up the Partnership for Next Generation Vehicle (PNGV) program to stimulate the development of EVs and HEVs. The partnership was a cooperative research program between the US government and major auto corporations, aimed at enhancing vehicle efficiency dramatically. Under this program, three US car companies demonstrated the feasibility of a variety of new automotive technologies, including an HEV that could achieve 70 MPG. This program was cancelled in 2001 and was transitioned to the Freedom CAR (Cooperative Automotive Research), which was responsible for the HEV, plug‐in HEV (PHEV), and battery research programs under the US Department of Energy.
Unfortunately, the EV program faded away by 2000, with thousands of EV programs terminated by the auto companies. This is due partially to the fact that consumer acceptance was not overwhelming, and partially to the fact that the CARB relaxed its ZEV mandate.
From 1997 to 2009, the US market was mostly focused on hybrid cars. Many models were available to the consumer, with the best‐selling car being the Toyota Prius, which sold nearly 4 million units worldwide from 1997 to 2016.
EVs reemerged in the USA and other parts of the world around 2009 when several policies and incentive programs were established by the US government partially to stimulate the economy after the 2008 economic crisis. In particular, Tesla Motors was established in 2003 and produced its first battery‐powered pure electric sports car, Roadster, in 2008, and sold to more than 30 countries. A total of 2450 Roadsters were sold in 2008. This was the first EV that had a range of more than 200 miles per charge, and was also the first EV to use a lithium‐ion battery pack. As of September 2016, Tesla has sold more than 160,000 battery electric cars worldwide, including Model S (145,000 units), Model X (16,000 units). The latest model, Model 3, has already taken orders of more than 500,000 with an expected delivery of 2018.
GM’s Chevrolet Volt is the all‐time best‐selling plug‐in electric car in the world with over 117,000 units sold from 2012 to September 2016. The Volt is not a pure EV, rather, it is a plug‐in hybrid car with the pure‐electric driving capability using the battery energy for 40 miles. The Chevrolet Bolt, a purely battery‐powered EV from GM, was available in late 2016. It has a driving range of 238 mile per charge and is the only all‐electric car under $50,000 that is capable of more than 200 miles per charge as of October 2016. The starting price in the US is $37,495.
Nissan produced its Leaf EV in 2010. The Leaf has a range of 84 miles (with a 24 kWh battery pack) to 107 miles per charge (with a 30 kWh battery pack). It sold more than 230,000 units from 2010 to July 2016, ranking it the best‐selling all‐electric car in history.
Ford released its Focus EV in 2011, with a 23 kWh liquid‐cooled lithium‐ion battery pack which delivers a range of 76 miles on a single charge. The production of the Ford Focus is limited, and sales have been in the hundreds to less than 2000 a year.
The Fiat 500e is a pure‐electric vehicle produced by Fiat Chrysler Automotive Group (FCA). It is powered by an 83 kW, 199 Nm permanent‐magnet motor, and a 24 kWh liquid‐cooled/heated li‐ion battery pack which delivers a range of 80 miles (130 km), and up to 100 mi (160 km) in city driving, according to FCA.
Recently, Toyota announced its all‐new Prius Prime; unlike the Prius, which has a hybrid powertrain, the Prius Prime is similar to the Chevy Volt. Toyota said that the car will offer 640 miles of range per charge/refuel and will achieve 133 MPG equivalent (MPGe), the highest MPGe of all electric and plug‐in electric cars, better than the Tesla Model X (289 miles range and 89 MPGe) and Chevy Bolt (238 miles range and 119 MPGe) by a large margin.
The US was the largest EV market in 201, but in 2015, China took over the first place. In 2015 and 2016, China sold more than 350,000 electric vehicles per year (including passenger, light‐duty trucks, delivery vehicles, and buses) and approximately 300,000 low‐speed electric cars. The estimated highway‐capable electric vehicle sales will reach 450,000 in 2017, predicted by many. Government incentive plays a crucial role in the growth of EV manufacturing and sales. In 2015, even though the reported sales topped 300,000, there were extensive frauds, faking the EV sales to obtain the government subsidy, according to China’s National Development and Reform Commission (NDRC).
9.3 Output Characteristic of Electric Machines
Electric machines have many unique characteristics that are especially suited for automotive powertrain applications. There are many kinds of electric machines, such as brushed DC machines, induction machines (IM), synchronous machines (SM), permanent magnet machines (PM), and switched reluctance machines (SRM). However, due to the space, weight, cost, and other limitations, EV powertrain applications are dominated by just three: induction machines, brushless DC machines, and permanent magnet synchronous machines. The SRM and other machines have been proposed for EV applications but have not become popular up to now.
When using electric motors for EV powertrain applications, there are a few possible configurations. Today’s electric motors, combined with inverters and associated controllers, have a wide speed range of operations, which covers a normal range for constant torque operations, and an extended speed range for constant power operations, which makes the design of the powertrain much easier. The powertrain motor needs to be able to provide the required torque and speed for all driving conditions of an EV. Hence, the size of the motor will be fairly large, usually rated at 100 kW or more for highway‐capable passenger cars. Traditional automatic transmissions or continuously variable transmissions (CVT) used in conventional cars are no longer required for EVs. However, a two‐speed automatic transmission may be beneficial in reducing vehicle energy consumption.
Electric motors are extensively discussed in various textbooks and many technical publications. In this chapter, we will first briefly discuss the principles of DC motors, induction motors, and permanent magnet machines, and then focus on a few unique aspects of electric motors that are specific to traction applications.
Depending on the type of current supplied and the principle of operation, electric machines can be classified to various categories as shown in Figure 9.3. Typically, electric machines consist of direct current (DC) and alternative current (AC) machines. Within DC machines, there are brushed and brushless DC machines, then AC machines are further classified into induction, synchronous, and switched reluctant machines, based on their principle of operations. For synchronous machines, the magnetic field can be created either by permanent magnets (hence, PM synchronous machines) or by a coil (hence, electrically excited synchronous machines).
Figure 9.3 Classification of electric machines.
Traditionally, electric machines, including brushed DC machines, induction machines, and electrically excited synchronous machines, are widely used in industrial and residential applications with a fixed speed or a limited range of operating speeds for a given power supply. With the advances in power electronics, microcomputers, and control, variable‐speed drives have become more popular today.
9.4 DC Machines
Due to the availability of variable‐speed drives, DC machines are no longer popular in industrial and residential applications, due to their bulky size and high maintenance cost. However, DC machines are often used to illustrate the principle of electric machines because of their simplicity and controllability. In particular, many variable‐speed AC machines, such as induction machines and PM synchronous machines, can be controlled to behave in a similar way to DC machines.
9.4.1 Principle of DC Machines
Figure 9.4 shows the basic principle and operation of a DC machine. The DC machine includes a stator, a rotor with commutators, and a pair of brushes. In the given space, we fix two permanent magnets on the stator, which will generate a magnetic field between the two magnets. A rectangular coil with its two sides perpendicular to the magnetic fields are placed inside the space between the two magnets. To increase the magnetic field strength as well as the mechanical strength, we put the steel rotor inside the two magnets and attach the coil to the surface of the rotor.
Figure 9.4 Principle of DC machines (cross‐sectional view).
The stator consists of the magnet, a housing that holds the magnet, bearings, and connectors. The rotor consists of the winding, a steel cylinder that is usually made of laminated silicon steel which has slots to fill the windings. The rotor that contains the winding is also called the armature. The laminated steel is used to reduce the magnetic losses due to the time‐varying magnetic field.
The coil or armature is powered by a DC source. Assuming the DC power has a voltage of V, the coil has a resistance of R as shown in Figure 9.5, and both the magnets and coil are stationary, then the current will form in the coil, as expressed as (here, the inductance is neglected due to the DC voltage):
Figure 9.5 Equivalent circuit when stationary.
Now, since the current is under the magnetic field, a few things will happen sequentially. First, a force will be generated on the two sides of the coil which can be expressed as:
where B is the magnetic field generated by the magnets, and l is the side length of the coil under the magnetic field. The force of the coils will generate a torque T since it is wound on the surface of the rotor. Assume there are N conductors inside the magnet, and the diameter of the rotor is D, the torque is (Figure 9.4 has two conductors, with each side of the coil is considered a conductor):
This torque will move the coil to rotate around the center of the rotor. Assume the angular speed of the coil is ω, the inertia of the rotor is J, and the torque (including friction of the rotor and shaft, and any load that is connected to the shaft) is TL, then we have,
The linear speed of the coil (the surface of the rotor) is 
, where D is the diameter of the rotor.
From the Lorentz law, the rotating coil will generate a back electromotive force (emf), or an internal voltage by each conductor, which can be expressed as
The total voltage on the coil, assume it has N conductors, will be
Now, the current in the coil will be different from the one when the rotor is in a standstill condition. The new current, as shown in Figure 9.6, can be expressed as:
The total flux under each magnet can be expressed as:
Therefore, we can replace the above equations as:
where k = N/π.
Figure 9.6 Equivalent circuit when rotating.
The above expressions are derived from Figure 9.4 where only one pair of poles is shown. DC machines can be made of one pair or multiple pairs of poles. Also, the number of conductors are assumed to be all in series in the above derivations. In DC motor designs, the conductors can be designed to be connected in series or parallel depending on the number of poles. Therefore, for a more generic formula, we assume that the DC motor has p pairs of poles, and the N conductors have 2a branches in parallel. Each parallel branch will only get I/2a current. Therefore, the following equations are derived. Only the constant k changes with the introduction of parallel circuits 2a and number of pole pairs, p:
where 
In the steady state, the voltage Eq. (9.11) still holds for multiple pairs of poles. Plugging Eqs (9.13) and (9.14) to (9.11), the torque–speed relationship can be expressed as:
The torque–speed relationship can be plotted as shown in Figure 9.7. In Figure 9.7, when there is no load connected to the motor shaft, the speed of the motor is 
. When the motor shaft speed is zero – in other words, when the motor shaft is locked – the back emf is also 0, therefore, the shaft torque is 
.
Figure 9.7 Torque–speed relationship of DC machines and the operating points when driving a typical vehicle.
In Figure 9.7, we also plotted the torque–speed of the traction force of a vehicle for three different grades. The vehicle resistance torque can be express as
where Tvehicle is the vehicle resistive torque on the motor shaft, r is the radius of the wheel, g is the gear ratio from the wheel to the motor shaft (which includes the final drive and the transmission), Froll is the rolling resistance, FAD is the aerodynamic resistance, Fgrade is the hill climbing resistance, m is the mass of the vehicle, and a is the acceleration of the vehicle.
Three vehicle resistance torque curves are plotted in Figure 9.7, for grades of 0°, 15°, and 30° as examples. The cross points of the motor curve with the vehicle resistive torque curves indicate the operating points of the motor. The difference between the motor torque and the resistive torque indicates how much acceleration force is available at a certain vehicle speed.
Equation (9.16) can also be rewritten as a speed–torque relationship:
Figure 9.8 shows the speed–torque relation expressed by Eq. (9.15). The motor speed will decrease as the torque increases, with a slope of R/(kΦ)2. The load torque in Figures 9.7 and 9.8 represents a typical vehicle resistance force. When the motor (or vehicle) starts, the vehicle speed is zero, so the back emf is zero. The motor produces a current of V/R (neglecting the inductances), so a large torque is produced, shown as the cross point of motor torque with the vertical axis in Figure 9.7. This torque is to overcome the vehicle resistance and provide a large acceleration needed to accelerate the vehicle. Depending on the slope of the road, the acceleration can be calculated. As the vehicle speed increases, the emf will increase, hence the stator current will decrease, which results in the decrease of stator current and less torque. At a certain speed, depending on the slope of the road, the motor torque is equal to the vehicle resistive torque and a maximum speed is reached, shown as the cross points of the motor torque curve and the vehicle resistive curve in Figure 9.8.
Figure 9.8 Motor speed–torque relationship and as a function of load torque.
The motor will have a number of losses before it transfers the electric power to the shaft as mechanical power. Figure 9.9 shows the power flow and types of losses in a typical electric machine. First, when current flows in the stator windings, it creates conduction losses in the winding, also known as copper losses. Second, the magnetic field will generate eddy currents and hysteresis losses in the rotor material, which is typically composed of laminated silicon steel. Third, when the rotor spins, it introduces frictional losses in the bearing and windage loss due to wind resistance acting on the rotor.
Figure 9.9 Power flow in a DC machine.
The power balance equations are:
P1 is the input power from the voltage supply; Pem is the electromagnetic power transferred from the stator to the rotor; Pmec is the total mechanical power on the rotor shaft; P2 is the output power to the load connected to the shaft; pcu1 is the copper loss of the rotor winding; piron is the iron loss of the stator core; pfw is the frictional and windage loss; and pad is the stray load loss.
The efficiency is the ratio of output mechanical power and the input electrical power.
The typical efficiency of an electric machine ranges from 50% for very small motors to 99% for large motors. The typical efficiency for EV powertrain motors – which may be rated at tens of kilowatts to over 100 kW – is about 85–95%. The power loss in the machine needs to be dissipated to the surrounding air or cooling medium through air, liquid, or natural convection.
9.4.2 Excitation Types of DC Machines
The magnetic field is the key to generating torque in an electric machine. In DC motors, the magnetic field can be generated through excitation by an external voltage source, in parallel or series with the main DC supply, or from a separate DC power source, or using permanent magnets. The four different types of excitation of DC machines are shown in Figure 9.10.
Figure 9.10 Excitation of DC motors: (a) parallel‐excited or shunt DC machine; (b) separately excited DC machines; (c) Series‐excited DC machines; (d) Permanent magnet DC machines.
Figure 9.10a shows the equivalent circuit of a parallel‐excited or shunt DC motor, in which the field winding is in parallel with the armature winding and shares the same DC source. The field winding usually has a large number of turns and a large resistance. So the field winding current is typically small, in the order of less 5% of the armature current. A variable resistor can be connected in series with the field winding to adjust the magnetic field to adjust the speed of the motor.
Figure 9.10b shows the equivalent circuit of a separately excited DC motor. In this arrangement, the field winding has its own supply voltage, separate from the main power source. It is convenient to adjust the field winding voltage to adjust the motor speed.
Figure 9.10c shows the equivalent circuit of a series‐wound DC motor. In this setup, the field winding is in series with the armature winding. Hence the field winding and the armature winding share the same current. To reduce losses in the field winding, the field winding usually has a very small number of turns and a small resistance. It is difficult to adjust the motor speed since the current is the same for both field and armature windings.
Figure 9.10d shows the equivalent circuit of a permanent magnet DC motor. The field is generated by the magnets, hence, it is not possible to adjust the magnetic flux. However, since there is no electrical loss for the generation of the magnetic field, the efficiency of permanent magnet DC motors are typically 3–5% higher than electrically excited DC motors. Flux weakening is possible in PM machines, in which case an electric current in the stator is controlled to generate a magnetic field that is in the opposite direction of the stator magnetic field, so as to reduce the total air‐gap magnetic flux.
9.4.3 Speed Control of DC Machines
From Eq. (9.18), we can see that, for a given load torque, the DC motor’s speed is related to three important parameters: the total flux ф, the stator resistance R, and the supply voltage. Hence, we can change the speed of a DC motor in three different ways, namely, adjusting the terminal voltage; adjusting the magnetic field flux, and adjusting the stator resistance.
9.4.3.1 Adjust Terminal Voltage
From Eq. (9.15), we can see that, by adjusting the terminal voltage, the steady‐state motor speed will change for a given load torque characteristics, as shown in Figure 9.11. With the reduction of terminal voltage, the operating speed will decrease. The control of terminal voltage can be realized via power electronics circuits, namely, a buck converter, a half‐bridge converter, or a full bridge converter.
Figure 9.11 Motor speed–torque control by adjusting terminal voltage.
In Figure 9.12, the motor is controlled by a buck converter. The DC supply, Va, is connected via a semiconductor switch, which opens and closes at a very high frequency (in the kilohertz range). When the switch closes, current flows from the power supply Va to the motor terminal, where the armature inductance will limit the rate of increase of current into the stator. When the switch opens, the current in the stator will continue to flow through the diode, which is called a freewheeling diode. In the steady state, the average voltage at the motor terminal is determined by how much the switch closes during one period, which is also defined as the duty ratio:
where ton is the time of the switch is turned on, Ts is the switching cycle, toff is the time the switch is turned off during one period, and D is the duty ratio of the switch. It is apparent that when the switch is open all the time, there will be no current flowing to the motor terminal, hence the motor speed will be zero. When the switch is closed all the time, the motor will have the maximum current and the speed will reach its maximum.
Figure 9.12 Voltage control of DC motors via a buck converter.
In the circuit in Figure 9.12, the motor can only rotate in one direction because the range of voltage applied to the motor is from 0 (when D = 0) to Va (when D = 1). Another disadvantage of the circuit is that the motor cannot send power back to the source due to the unidirectional power flow of the power switch.
Figure 9.13 shows a motor controlled by a half bridge converter, also referred to as a two‐quadrant chopper. The half bridge converter can control the motor in one direction and also realize energy feedback to the source. In Figure 9.13, switch S2 is open all the time during motoring while S1 is controlled to open and close at a certain frequency. During motoring, when switch S1 is closed, current flows to the motor through S1. When S1 is open, motor current continues to flow through D2 for freewheeling. The motor speed is proportional to the duty ratio of S1. During regenerative braking, S1 is kept open all the time, while S2 is controlled. When S2 is closed, the motor terminal forms a short circuit through S2. Due to the back emf and inductance of the motor, the current will flow out of the motor through S2 with a certain rate limited by the inductance. Once the current reaches a certain amount, controlled by the duty ratio of S2, S2 opens, the current that originally flows out of the motor through S2 is now forced to flow through D1 to the source, hence the energy is fed back to the supply.
Figure 9.13 Voltage control of DC motors via a half bridge converter.
The two‐quadrant chopper can control the motor in motoring and regenerative braking but can only rotate in one direction. To overcome the issues of a buck converter and two‐quadrant chopper, a full bridge converter can be used, as shown in Figure 9.14. In Figure 9.14, when S1 and S4 close, S2 and S3 will open. When S1 and S4 open, S2 and S3 will close. So, when S1 and S4 close all the time, the motor gets a positive voltage and rotates in the positive direction at its maximum speed. When S2 and S3 close all the time, the motor gets a negative voltage and rotates in the negative direction with its maximum speed. If S1/S4 and S3/S4 both opens and closes 50% of the time, the average voltage at the motor is zero, hence the motor will not rotate.
Figure 9.14 Voltage control of DC motors via a full bridge converter.
Each switch is also paralleled with a freewheeling diode which is to conduct current in the opposite direction to the switch. Hence, the full bridge can operate the motor in all four conditions: positive direction motoring (forward driving); positive direction generating (driving while braking); negative direction motoring (vehicle backing up), negative direction generating (braking when reversing the vehicle).
Controlling the terminal voltage, whether through a buck or two‐quadrant chopper or a full bridge converter, the motor terminal voltage will reach its maximum value when the duty ratio reaches 1. Hence, the motor speed will reach its maximum value. Therefore, the motor speed can be only controlled below its rated speed when controlling the armature voltage.
9.4.3.2 Adjust Magnetic Flux
The second method of controlling the motor speed is to control the magnetic flux. Depending on the type of excitation, the flux can be controlled by adjusting the voltage of the excitation (separately excited machines), or the resistance in the excitation branch (parallel excited machines), or by flux weakening (PM machines). When the flux is adjusted, the speed–torque will change so the speed is adjusted, as shown in Figure 9.15. When controlling the field winding resistance in a DC machine, the increase of field resistance will result in the decrease of magnetic flux. Hence the speed of the motor will increase for a given load torque. So typically, DC motor speed can be controlled above the rated speed by adjusting the magnetic flux. Field weakening has the same effect, that is, the motor speed can be increased by reducing the total flux.
Figure 9.15 Motor speed–torque control by adjusting magnetic flux.
9.4.3.3 Adjust Stator Resistance
The last method, adjusting the armature resistance, although it is not popular, can also be used. From Eq. (9.15), when an external resistance is connected in series with the armature winding, the slope of the speed–torque will change, hence the speed will change for a given load torque, as shown in Figure 9.16. The motor speed can be controlled to go down, as shown in Figure 9.16. Note too that, since the resistance will share the same armature current, it will consume a lot of power. So the efficiency of the motor for this method will be compromised. Hence, this method is no longer prevalent in the motor speed control, partially due to the advance of power electronics technology.
Figure 9.16 Motor speed–torque control by armature resistance.
9.5 Induction Machines
Induction motors are a popular choice for traction applications due to their robust construction, low cost, wide field weakening range, and high reliability. Especially for EVs, PHEVs, and HEVs that require a high‐power motor, induction motors can provide more reliable operation than other types of electric motors [21–37]. However, when compared to PM motors, induction motors have lower efficiency and less torque density.
One typical induction motor used for traction applications is the squirrel cage induction motor. An inverter is used to control the motor so that the desired torque can be delivered for a given driving condition at a certain speed. Advanced control methodologies, such as vector control, direct torque control, and field‐oriented control, are popular in induction motor control for traction applications.
9.5.1 Principle of Induction Motors
The basic structure of an induction machine is shown in Figure 9.17. The two main parts of an induction motor are the stator (which houses the winding) and the rotor (which houses the squirrel cage). Both stator and rotor are made out of laminated silicon steel with a thickness of 0.35, 0.5, or 0.65 mm. The laminated steel sheets are first stamped with slots and are then stacked together to form the stator and rotor, respectively. Windings are put inside the stator slots while the rotor is cast in aluminum.
Figure 9.17 An induction motor: (a) rotor and stator assembly; (b) rotor squirrel cage; (c) cross‐sectional view of an ideal induction motor with six conductors on the stator.
There are some additional components to make up the whole machine: the housing that encloses and supports the whole machine, the shaft that transfers torque, the bearing, an optional position sensor, and a cooling mechanism (such as a fan or liquid cooling tubes).
In Figure 9.17c, AX is phase a, BY is phase b, and CZ is phase c. The direction of the phase currents is for a particular moment ωt = 60 electric degrees; “+” indicates positive and “–” indicates negative. It can be seen that conductor AZB forms one group and XCY forms another group. Together they create a magnetic field at 30° NW–SE. The direction of the field will change as the current changes over time.
The stator windings shown in Figure 9.17c are supplied with a three‐phase AC sinusoidal current. Assuming that the amplitude of the currents is Im amperes, and the angular frequency of the current is ω radians per second, then the three‐phase currents can be expressed as:
Since the currents of each of the three phases are functions of time, the direction of current as shown in Figure 9.17c will change with time. If we mark the direction of the current at any given time, we can see the magnetic field generated by the stator current with its peak changing position over time.
Mathematically, we can derive this magnetic field. Each of the three phase currents will generate a magnetic field. Since the three windings are located 120° from each other in space along the inside surface of the stator, the field generated by each phase can be written as follows, assuming the spatial magnetic field distribution in the air gap due to winding currents is sinusoidal by design:
where K is a constant. Using Equations (9.1) and (9.2), considering that 
and cos(ωt + θ) + cos(ωt + θ − 240°) + cos(ωt + θ − 480°) = 0, we get
Equation (9.21) shows that the magnetic field is a traveling wave along the inner surface of the stator. In other words, the total magnetic field is a sinusoidal field with its peak rotating at an angular speed ω rad/s.
Since ω = 2πf, the rotational speed of the field will be the same as the supply frequency: f revolutions per second or nS = 60f revolutions per minute (RPM). Noting that the above derivation is based on one pair of poles, a more general equation for the field speed (or synchronous speed) of an induction machine can be given as
where p is the number of pairs of poles. Figure 9.18 shows the arrangement of a four‐pole squirrel‐cage induction motor with flux distribution.
Figure 9.18 Flux distributions of a four‐pole induction motor during transient finite element analysis.
Assuming initially that the rotor is stationary, an electromotive force (emf) will be induced inside the rotor bars of the squirrel cage. A current is therefore formed inside the rotor bars through the end rings. Similarly, since the field is rotating, this current will generate a force on the rotor bars (the rotor bar current is inside the stator magnetic field). If the force (or torque) is sufficiently large, the rotor will start to rotate.
The maximum speed of the rotor will be less than the synchronous speed because, if the rotor reaches the synchronous speed, there will be no relative movement between the rotor bars and the stator field, hence no emf or force will be generated. The difference between the rotor speed and the synchronous speed is defined as slip s, that is, s = (nS − nm)/nS = (ωS − ωm)/ωS, where nm and ωm are the rotor speeds in RPM and radians per second, respectively. Typical slips of induction motors are within 1–3%.
9.5.2 Equivalent Circuit of Induction Motors
We can represent the induction motor by two separate circuits, one for the stator and one for the rotor. Since the three phases are symmetrical, we only need to analyze one phase as shown in Figure 9.19. We use phasors for the analysis of the AC circuit. Here we have defined the direction of current flow using the transformer convention. It is worth noting that the rotor and the stator quantities will have different frequencies except when the rotor is stationary.
Figure 9.19 Stator and rotor circuits of an induction machine.
The voltage equation of the primary and the secondary circuit can be written as:
where V is the phase voltage, I the phase current, R the phase resistance, and L the leakage inductance of the winding. The subscripts S and R represent the stator and rotor respectively.
Since the field is rotating at synchronous speed ωS and the rotor is rotating at speed ωm, the speed of the magnetic field relative to the rotor bar is ωS − ωm = sωS = sω/p, and ωR = psωS = sω is the frequency of the rotor current.
If we multiply both sides equation (9.24) by k and then divide by s, we get
The rotor has AC quantities a slipping frequency ωR = sω. By using the following, 
, we have
We will choose k such that 
.We can then redraw the equivalent circuit of the induction motor as shown in Figure 9.20a. Here we neglected the magnetic loss in the stator core. If we include the magnetic loss, then the equivalent circuit can be illustrated as in Figure 9.20b.
Figure 9.20 Modified equivalent circuit of an induction machine: (a) neglecting iron loss; (b) considering iron loss.
In the equivalent circuit in Figure 9.20, for a given voltage supply the current of the circuit can be written as:
To simplify the analysis, we can neglect Rm + jωXm. Under this assumption, the electromagnetic power transferred from the stator to the rotor is:
Noting that electromagnetic power or rotor power has two parts, namely, the loss of the rotor winding and the power transferred to its shaft, Eq. (9.28) can be rewritten as:
The first term represents the rotor copper loss and the second term the mechanical power on the shaft. The electromagnetic torque of the motor can be written as:
We can plot torque Tem as a function of slip s from Eq. (9.30) and obtain the torque–speed characteristics of an induction motor as shown in Figure 9.21.
Figure 9.21 Torque–speed characteristics of an induction motor for a constant frequency and constant voltage supply.
9.5.3 Speed Control of Induction Machine
The speed of an induction motor, in RPM, can be expressed as:
Hence, we will have three approaches to change the speed of an induction motor: change the number of poles, change the frequency, and change the slip:
- Change number of poles: The stator winding is designed such that, by changing the winding configuration, the number of poles will change. For example, some induction motors are designed as 4/6, 6/8, or 4/8 pole capable. While changing the number of poles has been used in controlling the induction motor speed in the past, it is used less and less today due to the complexity of the stator winding configuration and low efficiency.
- Change frequency of the supply voltage: This is the most popular method for controlling induction motor speed in modern drive systems, including traction drives. This will be discussed in more detail in the next section.
- Change slip: Since the electromagnetic torque of an induction motor is closely related to slip as shown in Eq. (9.31), there are a few ways to change the slip to control induction motor speed:
- Change the magnitude of the supply voltage: As shown in Figure 9.22, as the voltage is changed, the speed of the motor is also changed. However, this method provides limited variable speed range since the torque is proportional to the square of voltage.
- Change stator resistance or stator leakage inductance: This can be done by connecting a resistor or inductor in series with the stator winding.
- Change rotor resistance or rotor leakage inductance: This is only applicable to wound‐rotor induction motors.
- Apply an external voltage to the rotor winding: This voltage has the same frequency as the rotor back emf or rotor current. Modern, doubly fed wind power generators belong to this group. This method is only applicable to wound‐rotor induction motors.
Figure 9.22 Adjusting the speed of an induction motor by varying the terminal voltage.
When an external resistance is in series with the stator or rotor winding, there is loss associated with this resistor. Hence the system efficiency is compromised. When an external inductor is in series with the stator or rotor, the power factor is compromised. Hence, adding resistance or inductance is no longer a popular method in modern electric drive systems.
9.5.4 Variable Frequency, Variable Voltage Control of Induction Motors
Varying the frequency of power supply is by far the most effective and most popular method of adjusting the speed of an induction motor. If we neglect the stator resistance, leakage inductance, and the magnetic loss, the stator voltage equation can be written as:
where kS is the machine constant and Φ is the total flux. Hence, when changing the frequency, the stator voltage should also be changed proportionally in order to maintain a relatively constant flux so that the stator and rotor core do not get saturated, while the output torque can be maintained constant:
When the frequency and voltage are adjusted, the torque–speed characteristics are as shown in Figure 9.23. Although the above expression is generally true, three observations can be made:
- For low‐frequency operations, the voltage drop across the stator resistance and inductance are no longer negligible, so the stator voltage has to be increased to compensate.
- The motor speed corresponding to the rated frequency and rated voltage is called the rated speed or base speed.
- When the stator voltage reaches its rated supply (maximum), in order to further increase frequency (or speed), the stator flux must be reduced in order to satisfy Eq. (9.33). This is called the flux weakening operation. The ratio of the maximum speed to the rated base speed of the motor is defined as the adjustable speed range or X. Modern induction motors can achieve up to X = 5 adjustable speed range.
Figure 9.23 Adjusting induction motor speed using variable frequency supply. In this example, the rated speed is 6000 RPM, and the maximum speed is 12,000 RPM. The adjustable speed range X = 2.
9.5.5 Efficiency and Losses of Induction Machine
The losses in an induction machine are shown in Figure 9.24. The losses include: (1) copper loss in the stator winding; (2) magnetic loss in the stator iron (or core loss or iron loss); (3) copper loss in the rotor winding; (4) windage loss due to the rotation of the rotor and frictional loss in the bearing; and (5) additional losses that cannot be accounted for by the above components, also called additional loss or stray load loss.
Figure 9.24 Losses in an induction motor.
The power balance equations are:
P1 is the input power from the voltage supply; Pem is the electromagnetic power transferred from the stator to the rotor; Pmec is the total mechanical power on the rotor shaft; P2 is the output power to the load connected to the shaft; pcu1 is the copper loss of the stator winding; pcu2 is the copper loss of the rotor; piron is the iron loss of the stator core; pfw is the frictional and windage loss; and pad is the stray load loss.
The efficiency can be expressed as:
One aspect of traction motors for modern HEVs is high‐speed operation. Traditionally, laminated silicon steel sheets were designed for use at low frequencies (50 or 60 Hz), and today’s traction drives typically operate at about 6000–15,000 RPM. With four‐pole designs, the operating frequency is 500 Hz. Some traction motors operate at frequencies as high as 800–1200 Hz. Since eddy current loss and hysteresis loss are proportional to frequency or the square of the frequency, the core loss will be significant at high frequencies. In order to keep the core loss within a reasonable range, the magnetic flux in the iron has to be relatively lower than that used in low‐speed motors, and the thickness of the silicon steel sheets may have to be reduced as well.
The second aspect is that the inverter‐operated induction motor will contain harmonics in its voltage and current. These harmonics will introduce additional losses in the winding and stator and rotor core. As is well known, the eddy current loss can be doubled in many induction motors due to the pulse width modulated (PWM) supply. These additional losses may cause excessive temperature rise which must be considered during the design and analysis of induction motors.
9.5.6 Field‐Oriented Control of Induction Machine
With field‐oriented control, an induction machine can perform somewhat like a DC machine. This section explains the theory and implementation of the field‐oriented control of an induction machine [42].
When expressed in phasors, the voltage equation for a three‐phase induction machine with three symmetrical stator windings is given as:
where p is the differential operand d/dt, and V, I, and λ are phasors of voltage, current, and flux linkage respectively. Subscript S relates to stator quantities and R refers to rotor quantities. Equations (9.36) and (9.37) are expressed in stator and rotor coordinates respectively. Therefore, stator frame S is stationary and rotor frame R is rotational (rotor quantities are at rotor frequency or slip frequency).
Suppose there is a frame B, and the angle between the stator and this frame B is δ, therefore the angle between the rotor and this frame is (δ − θ). Multiplying Eq. (9.36) by e−jδ and Equation 37 by e−j(δ−θ), we get:
Let:
By employing the equation:
Or:
Equations (9.41) and (9.42) can then be transferred to a general frame B, where all space phasors are expressed in frame B with the superscript (B) as:
The superscript (B) will be omitted further in this section for convenience. When expressed in phasors, the flux linkage can be expressed as:
where Lm is the stator inductance and L1σ and L2σ are the stator and rotor leakage inductance respectively.
Note that although the phasors are in a different frame, the stator flux and rotor flux are rotating at the same speed.
For squirrel cage induction machines, the rotor current iR is not accessible. Therefore, a fictitious rotor magnetizing current imr is defined such that the rotor flux can be expressed in terms of this fictitious rotor magnetizing current and stator inductance in the same way as in Eq. (9.45):
The rotor current can then be expressed as a function of magnetizing current and stator current from Eq. (9.46):
where:
Substituting Eqs (9.47) and (9.48) into Eq. (9.44) and considering that VR is normally set to 0 for squirrel cage induction motors, the rotor equation can be rewritten as:
where Tr is the rotor time constant which can be expressed as:
As stated above, the rotor magnetizing current is a fictitious current. The magnitude of this current can be observed through the following approach. If the rotor equation is written in the stator frame then δ = 0, pθ is equal to the speed of the rotor ω, and Eq. (9.50) has the following form:
Since this equation is written in the stator frame, we can find the α and β components of phasors iS and imr:
Therefore Eq. (9.52) becomes:
Stator current can be easily transferred from the abc system to the αβ system. Eq. (9.54) can be implemented discretely in the time domain, therefore, imrα and imrβ can be observed. Once this has been done, imr and δr can finally be calculated:
where δr is the angle between the fictitious current imr and the stator current iSα as shown in Figure 9.25.
Figure 9.25 Stator and rotor current in α, β coordinates.
If the frame is chosen such that B is aligned with λR as shown in Figure 9.26, imr will only have real components. Therefore this rotor equation can then be decomposed into its direct and quadrature components as:
Figure 9.26 Stator current in d, q and α, β coordinates.
From Eq. (9.45), when is is decomposed to d, q components, the equation can be written as:
From Eq. (9.57) it can be seen that imr is only related to isd. Therefore, imr can be controlled by controlling isd.
The torque in the machine is:
which has to be balanced with the load and acceleration torque:
where Tq is the developed torque, TL is the load torque, and ω is the angular speed of the motor. If θ is the angle between the stator and the rotor, then ω = pθ.
It can also be proved that isq is directly related to motor torque as follows. By substituting iS and iR into the torque in Eq. (9.59), the torque can be derived:
Magnetizing current imr can be controlled by controlling the real component of stator current, and torque control are achieved by controlling the imaginary component of the stator current.
For ease of implementing control, we will introduce the per‐unit system. A per‐unit system is essentially a system of dimensionless parameters occurring in a set of wholly or partially dimensionless equations. This kind of system can extensively simplify the phenomena of problems. The parameters of the machines fall in a reasonably narrow numerical range when expressed in a per‐unit system related to their ratings and therefore this is extremely useful in simulating machine systems and implementing the control of electric machine by digital computers. Generally, rated power and frequency can be chosen respectively as the base values of power and frequency for normalization, whereas the peak values of rated phase current and phase voltage may be chosen respectively as the base values of current and voltage. Derived base values of impedance, inductance, and flux leakage are as follows (with subscript B indicating the variable as base value):
Normalized torque can be expressed as:
The torque equation can then be normalized. Dividing Eq. (9.61) by Eq. (9.63), we get:
where superscript * donates the normalized value. For convenience, superscript * will be omitted in further derivations. To implement the control strategy, a technique has to be developed to identify the magnitude of the magnetizing current imr and the angle δr.
There are two ways to implement the flux observer of Eq. (9.54). One way is to take the Laplace transform of Eq. (9.49) and apply a bilinear transformation to convert the Laplace transform to the z transform. The inverse z transform can be used to obtain imrα and imrβ in the discrete time domain. An alternative method is to discretize Eq. (9.49) directly in the time domain. Assuming that the sample time is Ts, then the following equation can be obtained from Eq. (9.54):
Therefore imrα and imrβ can be derived from Eq. (9.60):
where κ is the ratio of sampling time to rotor constant:
The time variables can also be made dimensionless by multiplying both sides of the equations by ωB. Therefore both Ts and Tr are expressed in per‐unit values in Eqs (9.66) and (9.67). A block diagram of the flux observer is shown in Figure 9.27. The flux observer takes the phase currents and speed as input and calculates imr, cos α, and sin α.
Figure 9.27 Block diagram of the rotor flux observer.
It has been shown in the previous sections that it is possible to control the magnetizing component and torque component of the stator current separately. A PI controller is one way to implement control. The numerical expression for a PI controller is:
where Vo is the output of the PI controller and &ip.eop; is the error signal of input Vi (here Vi can be the measured current or torque of the motor, and Vo can be the PWM signal). In order to get the time domain discrete expression, we differentiate Eq. (9.68):
Further implementation is straightforward:
where K1 and K2 can be expressed as:
For example, if the gain is chosen as KPI = 50, TPI = 0.02 seconds, sampling time Tr = 0.02 seconds, and Ts = 0.67 ms, then the constants K1 and K2 are K1 = 1.0168, K2 = 0.9671.
The purpose of field‐oriented control is to control an induction machine in such a way that it behaves like a DC motor. A block diagram is shown in Figure 9.28 and the flowchart is shown in Figure 9.29. An incremental encoder is used to measure the speed of the motor. As shown in Eq. (9.54), the magnetizing current does not change instantaneously with isd as it does in a DC motor. Rather, the magnetizing current lags a time constant Tr corresponding to the change of isd.
Figure 9.28 Field‐oriented control of an induction machine.
Figure 9.29 Flowchart of the closed‐loop control of an induction machine.
In this setup, the flux observer uses the speed signal of an incremental encoder and the current measurement through two external current sensors. Only the currents of two phases are needed to perform the coordinate transformations due to symmetry.
9.6 Permanent Magnet Motor Drives
PM motors are the most popular choices for EV and HEV powertrain applications due to their high efficiency, compact size, high torque at low speeds, and ease of control for regenerative braking [43–90]. The PM motor in an HEV powertrain is operated either as a motor during normal driving or as a generator during regenerative braking and power splitting, as required by the vehicle operations and control strategies. PM motors with higher power densities are also now increasingly the choice for aircraft, marine, naval, and space applications.
The most commercially used PM material in traction drive motors is neodymium‐ferrite‐boron (Nd–Fe–B). This material has a very low Curie temperature and high‐temperature sensitivity. It is often necessary to increase the size of magnets to avoid demagnetization at high temperatures and high currents. On the other hand, it is advantageous to use as little PM material as possible in order to reduce the cost without sacrificing the performance of the machine.
9.6.1 Basic Configuration of PM Motors
When PMs are used to generate the magnetic field in an electric machine, it becomes a PM motor. Both DC and AC motors can be made with PMs. Only PM synchronous motors and PM brushless DC motors are chosen for modern traction drives. We will primarily explain the operation of PM synchronous motors in this book.
A PM synchronous motor contains a rotor and a stator, with the stator similar to that of an induction motor, and the rotor contains the PMs. From the section on induction motors, we know that the three‐phase winding, with three‐phase symmetrical AC supply, will generate a rotating magnetic field. To generate a constant average torque, the rotor must follow the stator field and rotate at the same synchronous speed. This is also why these machines are called PM synchronous motors.
There are different ways to place the magnets on the rotor, as shown in Figure 9.30. If the magnets are glued to the surface of the rotor, it is called a surface‐mounted PM motor (SPM). If the magnets are inserted inside the rotor in the pre‐cut slots, then it is called an interior permanent magnet motor (IPM).
Figure 9.30 Surface‐mounted magnets and interior magnets: left, SPM motor; right, IPM motor. 1 – magnet; 2 – iron core; 3 – shaft; 4 – non‐magnetic material; 5 – non‐magnetic material.
For an SPM motor, the rotor can be a solid piece of steel since the rotor iron core itself is not close to the air gap, hence the eddy current loss and hysteresis loss due to slot/tooth harmonics can be neglected. For the IPM motor, the rotor needs to be made out of laminated silicon steel since the tooth/slot harmonics will generate eddy current and hysteresis losses.
Due to the large air gap as well as the fact that the magnets have a permeability similar to that of air, SPM motors have similar direct‐axis reactance xd and quadrature‐axis reactance xq. On the other hand, IPM motors have different xd and xq. This difference will generate a so‐called reluctance torque. It is worth pointing out that although there is a reluctance torque component, it does not necessarily mean that an IPM motor will have a higher torque rating than an SPM motor for the same size and same amount of magnetic material used. This is because, in IPM motors, in order to keep the integrity of the rotor laminations, there are so‐called “magnetic bridges” that will have leakage magnetic flux. So for the same amount of magnet material used, an SPM motor will always have higher total flux. There are many different configurations for IPM motors as shown in Figure 9.31. The exploded view of a PM synchronous motor is shown in Figure 9.32.
Figure 9.31 Four commonly used IPM rotor configurations: (a) circumferential‐type magnets suitable for brushless DC or synchronous motor; (b) circumferential‐type magnets for the line‐start synchronous motor; (c) rectangular slots IPM motor; (d) V‐type slots IPM motor.
Figure 9.32 Exploded view of a PM motor for EV powertrain applications.
9.6.2 Basic Principle and Operation of PM Motors
The no‐load magnetic field of PM machines is shown in Figure 9.33. When the rotor is driven by an external source (such as an engine), the rotating magnetic field will generate a three‐phase voltage in the three‐phase windings. This is the generator mode operation of the PM machine.
Figure 9.33 Magnetic field distribution of PM machines at no‐load conditions (the stator current is zero): (a) a four‐pole SPM motor; (b) an eight‐pole symmetrical IPM motor; (c) a four‐pole unsymmetrical IPM configuration.
When operated as a motor, the three‐phase windings, similar to those of an induction motor, are supplied with either a trapezoidal form of current (brushless DC) or sinusoidal current (synchronous AC). These currents generate a magnetic field that is rotating at the same speed as the rotor or synchronous speed. By adjusting the frequency of the stator current, the speed of the rotor or the synchronous speed can be adjusted accordingly.
The torque is the attraction between the rotor magnetic field and the stator magnetic field in the circumferential direction. Hence, under no‐load conditions, the rotor and the stator field are almost lined up. When the angle between the rotor field and the stator field reaches 90 electric degrees, the maximum torque is reached in SPM motors. For IPM motors, the maximum torque occurs at an angle slightly larger than 90°, due to the existence of reluctant torque.
Figure 9.34 illustrates how a PM motor operates in different modes. The stator winding generates a rotating field that attracts the rotor magnets. If the two fields are lined up, the attraction between the two magnetic fields is in the radial direction, hence there is no electromagnetic torque. When the stator field is leading the rotor field, the stator will attract the rotor magnets. The machine then operates as a motor. When the stator field is lagging the rotor field, the machine becomes a generator.
Figure 9.34 Operation of a PM synchronous machine: (a) no load; (b) operating as generator; (c) operating as motor.
At no load, the rotor magnetic field will generate a back emf Eo in the stator windings. When a voltage with the same frequency is applied to the stator windings, then a current will be generated and the voltage equation can be written as;
where R is the stator resistance and X is the synchronous impedance. The phasor diagram is shown in Figure 9.35 when neglecting the stator resistance. From the diagram, the term jIX can be further decomposed into two components: jIdXd and jIqxq. In fact, in IPM motors, the d axis and q axis will have different reactances. By using Figure 9.35, Eq. (9.73) can be rewritten for IPM motors as:
The real power can be calculated, since from Figure 9.35, ϕ = δ + θ:
Figure 9.35 Phasor diagram of PM synchronous motors: (a) SPM; (b) IPM; (c) flux weakening mode of IPM.
where ϕ is the power factor angle (the angle between the voltage and current), θ is the angle between the voltage and back emf, and δ is the inner power angle (the angle between the back emf and the voltage). From Figure 9.35:
Therefore, the power of PM motors can be expressed as:
The torque can be derived by dividing Eq. (9.77) by the rotor speed as shown in Figure 9.36, where the torque–speed characteristics of a typical PM motor are shown. For SPM motors, since Xd = Xq, the second term of Eq. (9.77) is zero. For IPM motors, the q axis has less reluctance due to the existence of soft iron in its path, and the d axis has magnets in its path which has larger reluctance. Therefore Xq is much larger than Xd.
Figure 9.36 Power of IPM motor as a function of inner power angle.
On the other hand, from Eq. (9.75), and neglecting losses, we can see that:
Therefore, when inner power angle δ = 0, for a given stator current, the torque of the motor reaches its maximum. In this condition, the stator current is in phase with the back emf Eo, and:
Hence, the stator voltage must be proportional to frequency to satisfy Eq. (9.79) and maintain maximum torque output at the same time. This operation is also called constant torque operation. It can also be seen from Eq. (9.77) that for a given θ, the power is inversely proportional to the frequency, since V, Xd, and Eo are all proportional to frequency ω. This is similar to the V/f control of induction motors.
When stator voltage reaches its maximum, Eq. (9.79) can no longer be maintained. As ω increases, V becomes constant, and a current in the d axis direction must be supplied, as shown in Figure 9.35c. The relationship between the voltage and frequency can be expressed as
This operation is also called the flux weakening operation region because the d axis current generates a magnetic flux in the opposite direction to the PM field. Note that, due to constraints such as the current limit of the inverter, the q axis current may have to be decreased from its rated value so that the total current from the inverter is kept the same. Additional losses at higher speeds may make it necessary to further reduce the torque output. It can also be seen from Eq. (9.77) that for a given θ, the first term is constant since V is constant, and both Xd and Eo are proportional to frequency ω. In theory, the torque is inversely proportional to frequency in this operation, so the power is constant. Hence this mode is also referred to as the constant power operation range.
The torque–speed characteristics can be plotted as shown in Figure 9.37.
Figure 9.37 Torque–speed characteristics of a typical PM motor.
The efficiency of PM motors is typically higher than induction motors since they do not need excitation for the magnetic field, while it is needed for induction and DC motors. The losses in a PM machine are shown in Figure 9.38. The losses include: (1) copper loss in the stator winding; (2) magnetic loss in the stator iron (or core loss or iron loss); (3) magnetic loss in the rotor magnet as well as losses of the rotor steel; (4) windage loss due to the rotation of the rotor and frictional loss in the bearing; and (5) additional losses that cannot be accounted for by the above components, also called additional loss or stray load loss.
Figure 9.38 Losses in PM motor.
The power balance equations are:
where P1 is the input power from the voltage supply, Pem is the electromagnetic power transferred from the stator to the rotor, Pmec is the total mechanical power of the rotor shaft, P2 is the output power to the load connected to the shaft, pcu1 is the copper loss of the stator winding, pmag is the loss of the rotor magnet and rotor steel, piron is the iron loss of the stator core, pfw is the frictional and windage loss, and pad is the stray load loss.
The efficiency can be expressed as:
The typical efficiency of a PM motor is plotted in Figure 9.39.
Figure 9.39 Efficiency map of a typical EV motor.
9.7 Switched Reluctance Motors
Both switched reluctance motors and synchronous reluctance motors have attracted attention in traction applications due to their simple structure, not needing a squirrel cage or magnets on the rotor, very little loss on the rotor, and ease of control [93–114].
Although they have many advantages, PM motors and induction motors both have their own limitations. For example, PM motors face the possibility of demagnetization at extremely high temperature, limited speed range, and difficulty in protecting the powertrain during a fault condition. Induction motors have limited torque capability at low speeds, lower torque density and lower efficiency, noise due to stator/rotor slot combinations, and so on.
From the previous section we have seen that the torque of a synchronous motor has two terms, one related to Eo and Xd, which is induced by the rotor PM field, and one related to V, Xd, and Xq, which is induced by the difference in reactance of the d axis and q axis. In other words, even if the magnets are removed, an IPM motor can still generate torque with a sinusoidal supply due to the existence of salience of the rotor. This is called a synchronous reluctance motor. The stator and the rotor of a synchronous reluctance motor have the same number of poles.
Switched reluctance or synchronous reluctance motors do not use magnets or a squirrel cage. They simply use the difference in d axis and q axis reactance to produce reluctant torque. Therefore, they are similar to a synchronous motor without excitation and are therefore known as a switched reluctance motor. Hence only the second term of Eq. (9.77) exists. The torque of a switched reluctance motor with sinusoidal supply is:
In order to increase the torque of a switched reluctance motor, the q axis and d axis reactance is designed to have a large difference. A cross‐section of a synchronous motor is shown in Figure 9.40.
Figure 9.40 synchronous reluctance motor.
Switched reluctance motors are similar to synchronous motors but will have different numbers of poles on the stator and the rotor. Figure 9.41 shows the cross‐section of a switched reluctance motor and its control circuit.
Figure 9.41 Cross‐section of a 6/8‐pole switched reluctance motor (top) and its control circuit (bottom).
9.8 EV Transmissions
As discussed earlier in this chapter, EVs usually do not need a multiple‐speed transmission due to the wide speed range of electric motors. However, in order to reduce the size and cost of the EV drivetrain, EV motors are often designed to operate at a relatively high speed. Hence, a speed‐reduction gearbox is necessary for EVs. In some applications, a two‐speed transmission may be employed to increase the overall efficiency of the EV system.
A reverse gear is not needed in EV powertrains since the motor can be controlled to turn in both directions.
9.8.1 Single‐Speed EV Transmission
A single‐speed transmission is the most popular choice for EVs. A single‐speed can be made with multi‐stage gears, or with a planetary‐gear. Figures 9.42 and 9.43 shows the two configurations, respectively.
Figure 9.42 A multi‐stage gear based single‐speed transmission for EVs.
Figure 9.43 A planetary gear based single‐speed transmission for EVs.
In Figure 9.42, a two‐stage gear is used to realize the high ratio transmission. The speed relationship is;
where N1, N2, N3, and N4 are the number of teeth of each of the gears.
In Figure 9.43, the sun gear is connected to the electric motor, the planetary carrier is fixed to the case, and the output shaft is connected to the ring gear. The speed relationship of the gear train can be expressed as:
Since the carrier is grounded, the actual speed relation between the motor and the output shaft is:
For example, if the ring gear has 72 teeth and the sun gear has 28 teeth, then the speed ratio from the motor to the output shaft is 72/28 = 2.57, which is a very large gear ratio.
It is also possible to fix the sun gear or ring gear in the planetary based transmission. In these cases, the speed ratio can be expressed as follows. When the ring gear is fixed and the sun gear is used as the output:
When the sun gear is fixed and the ring gear is used as the output:
9.8.2 Multiple Ratio EV Transmissions
Two‐speed automatic transmissions have been proposed for electric powertrain applications. Even though an electric motor can provide a large speed range to satisfy the operational needs of typical cars without the need of a multiple‐speed transmission, there are imperfections in this arrangement.
With a single ratio reduction box, the requirement for the motor increases. The motor will need to provide a large stall torque (Torque generated at zero and very low speeds) and a large speed range at the same time. The efficiency of the motor will be compromised due to the wide operation range. Therefore, with a properly designed multiple‐speed transmission, the system will provide many advantages. Figure 9.44 shows a two‐speed transmission with automatic shifting.
Figure 9.44 Single‐ratio speed reduction gearbox for EV applications.
First, the stall torque requirement is reduced due to the large gear ratio available. This will potentially reduce the size of the motor, which can result in the reduction of size, weight, and cost of the motor. It also reduces the requirements on the inverter (less current will be needed).
Second, the motor can be controlled to operate in its more efficient region by changing the gear ratios like the ones used for an internal combustion engine.
Last, the top speed of the motor can be reduced due to a lower gear ratio being available. This will reduce the bearing requirement, losses in the steel, operation frequencies, and cost of the motor.
Studies have shown that a two‐speed transmission can fulfill the above purposes and at the same time provide energy savings of at least 5–10% while improving the acceleration, gradability, and top speed of the vehicle. However, one designing an EV powertrain with a multiple speed transmission, it needs to consider that the added cost should be reasonable or minimal. The total mass of the powertrain should remain the same. The gear shifting must be simple and smooth and no torque interruption should occur during gear shifting.
Traditional CVTs generally do not meet the above requirements because they are usually bulky, expensive, and inefficient. A special design of the transmission is therefore needed. For example, there are two methods for realizing the two‐speed transmission for EV: an automatic gearbox based two‐speed transmission and a planet gear based two‐speed transmission.
9.8.2.1 Automatic Gearbox Based Two‐Speed Transmission
Figure 9.45 shows the principle and internal structure of a typical two‐speed EV transmission based on an automatic gearbox. There are three parallel shafts in the gearbox: input, output, and grooved shafts. For the input shaft, there are two gear wheels, labeled as the first and second wheel, and a synchronizer installed on it. The two gear wheels have different sizes and gear ratios that are used to provide different speed variable ratios to the output shaft. The synchronizer can be connected to the input shaft and be spinning at the same speed, which is used to realize the speed shift between the two gear wheels.
Figure 9.45 Structure of a two‐speed EV transmission based on automatic gearbox.
The synchronizer is an important intermediate device in this gearbox, and it is flexible to move along the input shaft, resulting in three working positions: first gear, second gear, and neutral gear. As shown in Figure 9.45, when the synchronizer moves to the left, it can connect the first gear wheel with the input shaft through a spline. Then, the transmission ratio is determined by the first gear wheel. Similarly, when the synchronizer moves to the right, it can connect the second gear wheel with the input shaft through another spline. Then, the transmission ratio is determined by the second gear wheel. Considering the different size of the gear wheels, the transmission ratio is therefore regulated. When the synchronizer is arranged in the middle, it has no connection with the gears, which is named as the neutral gear position. In this case, there is no direct power transmission between the input and output shafts.
The grooved shaft is in parallel with the input shaft and placed above it as shown in Figure 9.45. The spin of this groove shaft is driven by a motor, and its main function is to adjust the position of the synchronizer to achieve the shifting of the transmission. In the working process, the groove shaft is connected to a selector rod, which contains a shifting fork that allows the synchronizer to rotate. The shifting fork can move to the left and right to connect different gear wheels. When it is maintained at the direction around the grooved shaft, the neutral gear position is realized.
The output shaft is also in parallel with the input shaft, and two gear wheels, named as the third and fourth gear wheels, are connected to it. The third and fourth gear wheels can engage with the first and second gear wheels on the input shaft, respectively, and the selection of engagement is achieved by the synchronizer. There is also a measurement device on the output shaft to measure the rotational speed. The measured signals are then processed to acquire the vehicle speed, and the vehicle controller can react to optimize the driving status based on these data.
This proposed transmission has two‐speed shifting. The first speed aims at the normal driving status. In this situation, the two gear wheels with smaller reduction ratio can provide higher speed. The second speed is more suitable for acceleration and gradability. In this situation, the reduction ratio of the gear wheels is higher, and larger torque can be provided for heavy‐duty working scenarios. The reduction ratios are optimized based on the output property of the motor and the power requirement of the vehicle. Hence, the lacking of power in the heavy‐duty mode and the waste of power in the normal driving mode are both solved. The switching of the two working modes is determined by an automatic controller, and the process is optimized based on the real‐time status of the vehicle, which contributes to improving the performance of the electric vehicle. In addition, the shifting is realized by a low‐power motor instead of by direct involvement of the driver, which can avoid any manual mistake and provide effectiveness and convenience.
This proposed gearbox‐based two‐speed transmission has three main advantages. First, the shifting performance and lift‐time are significantly improved. There are two shifting steps in this system, and the neutral position is between them. The speed control of the rotating motor can be achieved in the neutral status to make its speed consistent with the following gear wheel. The synchronizing process is only performed when their speeds are exactly the same. Therefore, the shifting process is more effective and smoother. The wear and tear on the synchronizer can be alleviated and its lift‐time can be extended.
Second, the power provided by the motor can perfectly match the power required by the driving profile. The reduction ratio of the gear wheels is automatically selected by the vehicle controller, and the reaction speed of the controller can be really fast. The shifting process can be much smoother since the speed of the synchronizer can be regulated at the neutral position. All these processes do not need the attention of the driver, which also makes this design friendly for the general public.
Third, the structure of this design is simple, which can also reduce the system cost and weight. Since this transmission system needs to be installed on the vehicle side, it is important to reduce its cost and weight for practical applications. The good news is that this design uses a minimum number of components to realize the speed shifting function without sacrificing any technical performance of the vehicle. Compared to existing transmission systems for electric vehicles, the proposed system has a significant cost–performance advantage. In addition, since this design considers the characteristic and output performance of the motor, the size is also reduced, which is suitable for the onboard installation.
9.8.2.2 Planet Gear based Two‐Speed Transmission
Figure 9.46 shows the simplified structure of a planet gear based two‐speed transmission system, which consists of four parts: input shaft, planet gear wheel system, synchronizer, and output shaft. Similar to the previous gearbox based transmission system, the input shaft is directly connected to the motor as the power input, and the output shaft is connected to the vehicle wheels as the power output. This system can provide two speed‐reduction ratios, and a synchronizer is utilized to achieve the speed shifting as well. The difference from the previous system is that the planet gear wheel system is used to replace the previous automatic gearbox system, and the outside case of the system also contributes to the transmission process. The transmission ratio depends on the connection of the planet gear wheel system with the synchronizer. The unique function of the planet gear wheel system is explained in details as follows.
Figure 9.46 Structure of a two‐speed EV transmission based on planet‐gear.
The planet gear wheel system consists of four parts: sun wheel, planet wheel, planet carrier, and ring gear. The sun wheel is in the center of the gear system, and it is connected to the input shaft, which is also the center of rotation. The planet carrier is connected to the output shaft, which determines the output rotation. The ring gear is at the outer edge of the planet wheels, and there is a spline connected to it. Note that the ring gear can rotate, and its speed depends on different working modes. The planet wheels are arranged inside of the ring gear, and usually there are three planet wheels, which have engagements with both the sun wheel and the ring gear. When the system is working, the planet wheels are not only self‐rotating but also move around the sun wheel.
The structure of the synchronizer in this planet wheel system is similar to that in the gearbox system. The synchronizer is connected to the grooved shaft through a spline, and this connection can make the ring gear rotate together with the synchronizer. The synchronizer can move along the direction that is in parallel with the input shaft, resulting in three positions: first shifting position, second shifting position, and neutral position. A selector rod and shifting fork are used to fix the synchronizer in different positions. For example, in Figure 9.46, when the synchronizer moves to the left, the shifting fork is connected to the outer side case, which is defined as the first shifting position. When the synchronizer moves to the right, the shifting fork is connected to the planet carrier, which is also the output shaft. Therefore, the reduction ratio is different from the previous case, and it is defined as the second shifting position. When the synchronizer moves to the middle, it has no connection with either the input or the output shaft, which is defined as the neutral position.
The working principle of this planet gear based transmission is similar to the previous gearbox based system. The two shifting positions can provide different reduction ratios in the transmission. The first position is used for the normal driving status of the electric vehicle because it can provide a relatively high speed. The second position is used for the acceleration and gradability scenarios because it can provide a large rotation torque. The switch of these two shifting positions is controlled by an automatic controller, which can optimize the power output of the motor and improve the driving performance. In addition, in the neutral shifting position, the speed of the synchronizer can be controlled by a motor to smooth the shifting switch transient.
The planet gear based transmission also has three advantages over the gearbox based system. First, the size and weight of the transmission system are relatively small. Since all planet gear wheels are placed inside the ring gear, the internal space is fully used and the system structure is more compact. Therefore, the required size and usage of metal can be significantly reduced.
Second, the transmission performance is improved. The input and output shafts are on the same line. Considering the symmetrical structure of the planet gear wheels, the distribution of multiple planet wheels can balance the force on the sun gear and the bearings, which can help increase the transmission efficiency. Also, because there are more engagements of gears, the system can rotate more smoothly and be more robust to external shock and vibration.
Third, the range of transmission ratio can be increased. The planet gear system can realize the composition and decomposition of motion. With a proper design of dimensions, the planet gear system can achieve a high transmission ratio with a limited number of gear wheels. Especially in electric vehicle applications, the high transmission ratio can contribute to increasing the maximum achievable torque of the motor, which can further improve the acceleration and gradability performance.
9.9 Conclusions
Electric motors and associated controllers are one of the key enabling technologies for electric, hybrid electric, and plug‐in hybrid electric vehicles. Various types of electric motors and drive systems are available for the powertrain of electric vehicles. Traction motors and drives experience very harsh environmental conditions, such as a wide temperature range (−30 to 60 °C), severe vibration and shock, high electromagnetic noise, size and weight constraints, and stringent safety and reliability requirements. As a result, there are many unique aspects in the design, development, analysis, manufacturing, and research of electric motors and drives for traction applications which are all important aspects but cannot all be covered in this chapter. Readers could consult the references below for further reading. For example, more in‐depth studies about synchronous reluctance motor design and optimization can be found in [114] and studies of the uncontrolled generation in PM drive motors are covered in [140, 141].
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