AIM

To create a Simulink model of an EV.

INTRODUCTION OF ELECTRIC VEHICLES:

INTRODUCTION OF ELECTRIC VEHICLES:

Electric vehicles (EVs) use an electric motor for traction, and chemical batteries, fuel cells, ultracapacitors, and/or flywheels for their corresponding energy sources. The electric vehicle has many advantages over the conventional internal combustion engine vehicle (ICEV), such as an absence of emissions, high efficiency, independence from petroleum, and quiet and smooth operation. The operational and fundamental principles in EVs and ICEVs are similar. There are, however, some differences  between ICEVs and EVs, such as the use of gasoline tanks vs. batteries, ICE vs. electric motor, and different transmission requirements. [1]

The concept of the battery electric vehicle is essentially simple. The vehicle consists of an electric battery for energy storage, an electric motor, and a controller. The battery is normally recharged from mains electricity via a plug and a battery charging unit that can either be carried onboard or fitted at the charging point. The controller will normally control the power supplied to the motor, and hence the vehicle speed, in forward and reverse. This is normally known as a Two-quadrant controller, forwards and backwards. It is usually desirable to use regenerative braking both to recoup energy and as a convenient form of frictionless braking. When in addition the controller allows regenerative braking in forward and reverse directions it is known as a Four-quadrant controller.[2]

Previously, the EV was mainly converted from the existing ICEV by replacing the internal combustion engine and fuel tank with an electric motor  drive and battery pack while retaining all the other components. Drawbacks such as its heavy weight, lower flexibility, and performance degradation have caused the use of this type of EV to fade out. In its place, the modern EV is built based on original body and frame designs. This satisfies the structure requirements unique to EVs and makes use of the greater flexibility of electric propulsion. A modern electric drive train is conceptually illustrated in Figure 1. The drive train consists of three major subsystems: electric motor propulsion, energy source, and auxiliary. The electric propulsion subsystem is comprised of a vehicle controller, power electronic converter, electric motor, mechanical transmission, and driving wheels. The energy source subsystem involves the energy source, the energy management unit, and the energy refueling unit.

Figure 1. Modern Electric Drivetrain.

The auxiliary subsystem consists of the power steering unit, the hotel climate control unit, and the auxiliary supply unit. Based on the control inputs from the accelerator and brake pedals, the vehicle controller provides proper control signals to the electronic power converter, which functions to regulate the power flow between the electric motor and energy source. The backward power flow is due to the regenerative braking of the EV and this regenerated energy can be restored to the energy source, provided the energy source is receptive. Most EV batteries as well as ultracapacitors and flywheels readily possess the ability to accept regenerated energy. The energy management unit cooperates with the vehicle controller to control the regenerative braking and its energy recovery. It also works with the energy refueling unit to control the refueling unit, and to monitor the usability of the energy source. The auxiliary power supply provides the necessary power at different voltage levels for all the EV auxiliaries, especially the hotel climate control and power steering units. [1]

ELECTRIC VEHICLE PROPULSION:

[1] Electric propulsion systems are at the heart of electric vehicles (EVs) and hybrid electric vehicles (HEVs). They consist of electric motors, power converters, and electronic controllers. The electric motor converts the electric energy into mechanical energy to propel the vehicle, or, vice versa, to enable regenerative braking and/or to generate electricity for the purpose of charging the onboard energy storage. The power converter is used to supply the electric motor with proper voltage and current. The electronic controller commands the power converter by providing control signals to it, and then controls the operation of the electric motor to produce proper torque and speed, according to the command from the drive. The electronic controller can be further divided into three functional units — sensor, interface circuitry, and processor. The sensor is used to translate measurable quantities such as current, voltage, temperature, speed, torque, and flux into electric signals through the interface circuitry. These signals are conditioned to the appropriate level before being fed into the processor. The processor output signals are usually amplified via the interface circuitry to drive power semiconductor devices of the power converter. The functional block diagram of an electric propulsion system is illustrated in Figure 2.

Figure 2. Functional block diagram of typical electric propulsion system.

Differing from the industrial applications of motors, the motors used in EVs and HEVs usually require frequent starts and stops, high rates of acceleration/ deceleration, high torque and low-speed hill climbing, low torque and high-speed cruising, and a very wide speed range of operation. The motor drives for EVs and HEVs can be classified into two main groups, namely the commutator motors and commutator-less motors as illustrated in Figure 3.

COMMUTATOR MOTORS: These motors mainly are the traditional DC motors, which include series excited, shunt excited, compound excited, separately excited, and permanent magnet (PM) excited motors. DC motors need commutators and brushes to feed current into the  armature, thus making them less reliable and unsuitable for maintenance-free operation and high speed. In addition, winding excited DC motors have low specific power density. Nevertheless, because of their mature technology and simple control, DC motor drives have been prominent in electric propulsion systems. Technological developments have recently pushed commutator-less electric motors into a new era. Advantages include higher efficiency, higher power density, lower operating cost. They are also more reliable, and maintenance free compared to commutator DC motors. Thus, commutator-less electric motors have now become more attractive.

Figure 3. Classification of electric motor drives for EV and HEV application.

INDUCTION MOTORS: These are widely accepted as a commutator-less motor type for EV and HEV propulsion. This is because of their low cost, high reliability, and maintenance-free operation. However, conventional control of induction motors such as variable-voltage variable-frequency (VVVF) cannot provide the desired performance. With the advent of the power electronics and microcomputer era, the principle of field-oriented control (FOC) or vector control of induction motors has been accepted to overcome their control complexity due to their nonlinearity. However, these EV and HEV motors using FOC still suffer from low efficiency at low light loads and limited constant-power operating range.

PM SYNCHRONOUS MOTORS: By replacing the field winding of conventional synchronous motors with PMs, PM synchronous motors can eliminate conventional brushes, slip rings, and field copper losses. Actually, these PM synchronous motors are also called PM brushless AC motors, or sinusoidal-fed PM brushless motors, because of their sinusoidal AC current and brushless configuration. Since these motors are essentially synchronous motors, they can run from a sinusoidal or pulsed waveform modulation supply (PWM supply) without electronic commutation. When PMs are mounted on the rotor surface, they behave as non-salient synchronous motors because the permeability of PMs is similar to that of air. By burying those PMs inside the magnetic circuit of the rotor, the saliency causes an additional reluctance torque, which leads to facilitating a wider speed range at constant power operation. On the other hand, by abandoning the field winding or PMs while purposely making use of the rotor saliency, synchronous reluctance motors are generated. These motors are generally simple and inexpensive, but with relatively low output power. Similar to induction motors, these PM synchronous motors usually use FOC for high-performance applications. Because of their inherently high-power density and high efficiency, they have been accepted as having great potential to compete with induction motors for EV and HEV applications. By virtually inverting the stator and rotor of PM DC motors (commutator), PM brushless DC motors are generated. It should be noted that the term “DC” may be misleading since it does not refer to a DC current motor. Actually, these motors are fed by rectangular AC current, and are hence also known as rectangular-fed PM brushless motors.40 The most obvious advantage of these motors is the removal of brushes. Another advantage is the ability to produce a large torque because of the rectangular interaction between current and flux. Moreover, the brushless configuration allows more cross-sectional area for the armature windings. Since the conduction of heat through the frame is improved, an increase in electric loading causes higher power density. Different from PM synchronous motors, these PM brushless DC motors generally operate with shaft position sensors. Recently, sensor less control technologies have been developed in the Power Electronics and Motor Drive Laboratory at Texas A&M University.

SWITCHED RELUCTANCE MOTORS: Switched reluctance (SR) motors have been recognized to have considerable potential for EV and HEV applications. Basically, they are direct derivatives of single-stack variable-reluctance stepping motors. SR motors have the definite advantages of simple construction, low manufacturing cost, and outstanding torque–speed characteristics for EV and HEV applications. Although they possess simplicity in construction, this does not imply any simplicity of their design and control. Because of the heavy saturation of pole tips and the fringe effect of pole and slots, their design and control are difficult and subtle. Traditionally, SR motors operate with shaft sensors to detect the relative position of the rotor to the stator. These sensors are usually vulnerable to mechanical shock and sensitive to temperature and dust. Therefore, the presence of the position sensor reduces the reliability of SR motors and constrains some applications. Recently, sensor less technologies have been developed in the Power Electronics and Motor Drive Laboratory — again at Texas A&M University. These technologies can ensure smooth operation from zero speed to maximum speed.

POWER CONVERTER CIRCUITS IN EV’s:

[2] The voltage from all sources of electrical power varies with time, temperature, and many other factors, especially current. Battery voltage is actually quite well regulated, but frequently there will be a requirement for a change in the voltage to a lower or higher value, usually to control the speed of a motor. Most electronic and electrical equipment requires a fairly constant voltage. This can be achieved by dropping the voltage down to a fixed value below the operating range of the fuel cell or battery or boosting it up to a fixed value. In other cases, it would be desirable to produce a variable voltage (e.g., for a motor) from the more-or-less fixed voltage of a battery. Therefore, a change is required, and it is done using ‘switching’ or ‘chopping’ circuits, which are described below.

[1] Choppers are used for the control of DC motors because of a number of advantages such as high efficiency, flexibility in control, light weight, small size, quick response, and regeneration down to very low speeds. Presently, the separately excited DC motors are usually used in traction, due to the control flexibility of armature voltage and field. For a DC motor control in open-loop and closed-loop configurations, the chopper offers a number of advantages due to its high operation frequency. High operation frequency results in high-frequency output voltage ripple and, therefore, less ripples in the motor armature current and a smaller region of discontinuous conduction in the speed–torque plane. A reduction in the armature current ripple reduces the armature losses. A reduction or elimination of the discontinuous conduction region improves speed regulation and the transient response of the drive.

SINGLE-QUADRANT CHOPPER: The power electronic circuit and the steady-state waveform of a DC chopper drive are shown in Figure 4. A DC voltage source, V, supplies an inductive load through a self-commutated semiconductor switch S. The symbol of a self-commutated semiconductor switch has been used because a chopper can be built using any device among thyristors with a forced commutation circuit: GTO, power transistor, MOSFET, and IGBT. The diode shows the direction in which the device can carry current.

Figure 4. Principle of operation of a step down (or class A) basic chopper circuit.

The diode shows the direction in which the device can carry current. A diode D_F is connected in parallel with the load. The semiconductor switch S is operated periodically over a period T and remains closed for a time t_on = δT with 0 < δ < 1. The variable δ = t_on/T is called the duty ratio or duty cycle of a chopper. Figure 2., also shows the waveform of control signal i_c. Control signal i_c will be the base current for a transistor chopper, and a gate current for the GTO of a GTO chopper or the main thyristor of a thyristor chopper. If a power MOSFET is used, it will be a gate to the source voltage. When the control signal is present, the semiconductor switch S will conduct, if forward biased. It is assumed that the circuit operation has been arranged such that the removal of i_c will turn off the switch.

During the on interval of the switch (0  t  δT), the load is subjected to a voltage V and the load current increases from i_a1 to i_a2. The switch is opened at t = δT. During the off period of the switch (δT  t 1), the load inductance maintains the flow of current through diode D_F. The load terminal voltage remains zero (if the voltage drop on the diode is ignored in comparison to V) and the current decreases from ia2 to ia1. The internal 0  t δT is called the duty interval and the interval δT  t  T is known as the free-wheeling interval. Diode D_F provides a path for the load current to flow when switch S is off, and thus improves the load current waveform. Furthermore, by maintaining the continuity of the load current at turn off, it prevents transient voltage from appearing across switch S, due to the sudden change of the load current. The source current waveform is also shown in Figure 5(e). The source current flows only during the duty interval and is equal to the load current. The direct component or average value of the load voltage Va is given by:

Figure 5. Waveforms from (b) to (e) for a step-down basic chopper (class A).

By controlling δ between 0 and 1, the load voltage can be varied from 0 to V; thus, a chopper allows a variable DC voltage to be obtained from a fixed voltage DC source. The switch S can be controlled in various ways for varying the duty ratio δ. The control technologies can be divided into the following categories:

• Time ratio control (TRC). [Constant frequency TRC: The chopper period T is kept fixed and the on period of the switch is varied to control the duty ratio δ. Varied frequency TRC: Here, δ is varied either by keeping ton constant and varying T or by varying both t_on and T.]
• Current limit control (CLC).

The following important points can be noted from the waveform of Figure 5:

1. The source current is not continuous but flows in pulses. The pulsed current makes the peak input power demand high and may cause fluctuation in the source voltage. The source current waveform can be resolved into DC and AC harmonics. The fundamental AC harmonic frequency is the same as the chopper frequency. The AC harmonics are undesirable because they interfere with other loads connected to the DC source and cause radio frequency interference through conduction and electromagnetic radiation. Therefore, an L-C filter is usually incorporated between the chopper and the DC source. At higher chopper frequencies, harmonics can be reduced to a tolerable level by a cheaper filter. From this point, a chopper should be operated at the highest possible frequency.
2. The load terminal voltage is not a perfect direct voltage. In addition to a direct component, it has harmonics of the chopping frequency and its multiples. The load current also has an AC ripple.

The chopper of Figure 4 is called a class A chopper. It is one of a number of chopper circuits that are used for the control of DC motors. This chopper is capable of providing only a positive voltage and a positive current. It is therefore called a single-quadrant chopper, capable of providing DC separately excited motor control in the first quadrant, positive speed, and positive torque. Since it can vary the output voltage from V to 0, it is also a step-down chopper or a DC-to-DC buck converter. The basic principle involved can also be used to realize a step-up chopper or DC to DC boost converter. The circuit diagram and steady-state waveforms of a step-up chopper are shown in the Figure 6. This chopper is known as a class B chopper. The presence of control signal i_c indicates the duration for which the switch can conduct if forward-biased.

During a chopping period, T, it remains closed for an interval 0 t  δT and remains open for an interval δT  t T. During the on period, i_S increases from i_S1 to i_S2, thus increasing the magnitude of energy stored in inductance L. When the switch is opened, current flows through the parallel combination of the load and capacitor C. Since the current is forced against the higher voltage, the rate of change of the current is negative. It decreases from i_S2 to i_S1 in the switch’s off period. The energy stored in the inductance L and the energy supplied by the low-voltage source are given to the load. The capacitor C serves two purposes.

Figure 6. Principle of operation of a step up (or class B) basic chopper circuit.

At the instant of opening of switch S, the source current, i_S, and load current, i_a, are not the same. In the absence of C, the turn off of S will force the two currents to have the same values. This will cause high induced voltage in the inductance L and the load inductance. Another reason for using capacitor C is to reduce the load voltage ripple. The purpose of the diode D is to prevent any flow of current from the load into switch S or source V. For understanding the step-up operation, capacitor C is assumed to be large enough to maintain a constant voltage V_a across the load. The average voltage across the terminal a, b is given as:

The average voltage across the inductance L is:

The source voltage is:

Substituting from equations (2) and (3) into (4) gives:

According to (5), theoretically the output voltage V_a can be changed from V to ∞ by controlling δ from 0 to 1. In practice, V_a can be controlled from V to a higher voltage, which depends on the capacitor C, and the parameters of the load and chopper.

The main advantage of a step-up chopper is the low ripple in the source current. While most applications require a step-down chopper, the step-up chopper finds application in low-power battery-driven vehicles. The principle of the step-up chopper is also used in the regenerative braking of DC motor drives.

Figure 7. Waveforms from (b) to (d) for a step-up basic chopper (class B).

TWO-QUADRANT CONTROL OF FORWARD MOTORING AND REGENERATIVE BRAKING: A two-quadrant operation consisting of forward motoring and forward regenerative braking requires a chopper capable of giving a positive voltage and current in either direction. This two-quadrant operation can be realized in the following two schemes.

Figure 8. Speed–torque profiles of multi-quadrant operation.

SINGLE CHOPPER WITH A REVERSE SWITCH: The chopper circuit used for forward motoring and forward regenerative braking is shown in Figure 9, where S is a self-commutated semiconductor switch, operated periodically such that it remains closed for a duration of δT and remains open for a duration of (1 - δ)T. C is the manual switch. When C is closed and S is in operation, the circuit is similar to that of Figure 6, permitting the forward motoring operation. Under these conditions, terminal a is positive and terminal b is negative.

Figure 9. Forward motoring and regenerative braking control with a single chopper.

Regenerative braking in the forward direction is obtained when C is opened and the armature connection is reversed with the help of the reversing switch RS, making terminal b positive and terminal a negative. During the on-period of the switch S, the motor current flows through a path consisting of the motor armature, switch S, and diode D₁, and increases the energy stored in the armature circuit inductance. When S is opened, the current flows through the armature diode D₂, source V, diode D1 and back to the armature, thus feeding energy into the source. During motoring, the changeover to regeneration is done in the following steps. Switch S is deactivated, and switch C is opened. This forces the armature current to flow through diode D₂, source V, and diode D₁. The energy stored in the armature circuit is fed back to the source and the armature current falls to zero. After an adequate delay to ensure that the current has indeed become zero, the armature connection is reversed, and switch S is reactivated with a suitable value of d to start regeneration.

CLASS C TWO-QUADRANT CHOPPER: In some applications, a smooth transition from motoring to braking and vice versa is required. For such applications, the class C chopper is used as shown in Figure 10. The self-commutated semiconductor switch S₁ and diode D₁ constitute one chopper and the self-commutator switch S₂ and diode D₂ form another chopper. Both the choppers are controlled simultaneously, both for motoring and regenerative braking.

Figure 10. Forward motoring and regenerative braking control using class C two-quadrant chopper circuit.

The switches S₁ and S₂ are closed alternately. In the chopping period T, S₁ is kept on for a duration δT, and S₂ is kept on from δT to T. To avoid a direct, short-circuit across the source, care is taken to ensure that S₁ and S₂ do not conduct at the same time. This is generally achieved by providing some delay between the turn off of one switch and the turn on of another switch. The waveforms of the control signals v_a i_a and i_s and the devices under conducting during different intervals of a chopping period are shown in Figure 11. In drawing these waveforms, the delay between the turn off of one switch and the turn on of another switch has been ignored because it is usually very small. The control signals for the switches S₁ and S₂ are denoted by i_c1 and i_c2, respectively. It is assumed that a switch conducts only when the control signal is present, and the switch is forward biased.

The following points are helpful in understanding the operation of this two-quadrant circuit:

1. In this circuit, discontinuous conduction does not occur, irrespective of its frequency of operation. Discontinuous conduction occurs when the armature current falls to zero and remains zero for a finite interval of time. The current may become zero either during the freewheeling interval or in the energy transfer interval. In this circuit, freewheeling will occur when S₁ is off, and the current is flowing through D₁. This will happen in interval δT t  T, which is also the interval for which S₂ receives the control signal. If i_a falls to zero in the freewheeling interval, the back EMF will immediately drive a current through S₂ in the reverse direction, thus preventing the armature current from remaining zero for a finite interval of time. Similarly, energy transfer will be present when S₂ is off and D₂ is conducting — that is, during the interval 0  t  δT. If the current falls to zero during this interval, S1 will conduct immediately because i_c is present and V > E. The armature current will flow, preventing discontinuous conduction.

Figure 11. Forward motoring and regenerative braking control using class C two-quadrant chopper waveforms.

2. Since discontinuous conditions are absent, the motor current will be flowing all the time. Thus, during the interval 0 t  δT, the motor armature will be connected either through S₁ or D₂. Consequently, the motor terminal voltage will be V and the rate of change of i_a will be positive because V>E. Similarly, during the interval δT  t  T, the motor armature will be shorted either through D₁ or S₂. Consequently, the motor voltage will be zero and the rate of change of i_a will be negative.
3. During the interval 0 t  δT, the positive armature current is carried by S₁ and the negative armature current is carried by D₂. The source current flows only during this interval and it is equal to i_a. During the interval δT  t  T, the positive current is carried by D₁ and the negative current is carried by S₂.
4. From the motor terminal voltage waveform of Figure 11, V_a = δV. Hence,

Equation (6) suggests that the motoring operation takes place when δ > E/V, and that regenerative braking occurs when δ < E/V. The no-load operation is obtained when δ = E/V.

 

FOUR-QUADRANT OPERATION: The four-quadrant operation can be obtained by combining two class C choppers (Figure 10) as shown in Figure 12, which is referred to as a class E chopper. In this chopper, if S₂ is kept closed continuously and S₁ and S₄ are controlled, a two-quadrant chopper is obtained, which provides positive terminal voltage (positive speed) and the armature current in either direction (positive or negative torque), giving a motor control in quadrants I and IV. Now if S₃ is kept closed continuously and S₁ and S₄ are controlled, one obtains a two-quadrant chopper, which can supply a variable negative terminal voltage (negative speed) and the armature current can be in either direction (positive or negative torque), giving a motor control in quadrants II and III.

Figure 12. Class E four-quadrant chopper.

This control method has the following features: the utilization factor of the switches is low due to the asymmetry in the circuit operation. Switches S₃ and S₂ should remain on for a long period. This can create commutation problems when the switches use thyristors. The minimum output voltage depends directly on the minimum time for which the switch can be closed, since there is always a restriction on the minimum time for which the switch can be closed, particularly in thyristor choppers. The minimum available output voltage, and therefore the minimum available motor speed, is restricted. To ensure that switches S₁ and S₄, or S₂ and S₃ are not on at the same time, some fixed time interval must elapse between the turn off for one switch and the turn on of another switch. This restricts the maximum permissible frequency of operation. It also requires two switching operations during a cycle of the output voltage.

POWER ELECTRONICS:

[3] Power electronics involves the study of electronic circuits intended to control the flow of electrical energy. These circuits handle power flow at levels much higher than the individual device ratings. All power electronic circuits manage the flow of electrical energy between some sort of source and a load. The parts in a circuit must direct electrical flows, not impede them. A general power conversion system is shown in Figure 13. The function of the power converter positioned at the middle is that of controlling energy flow between a given electrical source and a given load. For our purposes, the power converter will be implemented with a power electronic circuit. As a power converter appears between a source and a load, any energy used within the converter is lost to the overall system. A crucial point emerges—to build a power converter, we should consider only lossless components. A realistic converter design must approach 100% efficiency.

Figure 13. General system for electric power conversion.

A power converter connected between a source and a load also affects system reliability. If the energy source is perfectly reliable (it is on all the time), then a failure in the converter affects the user (the load) just as if the energy source had failed. An unreliable power converter creates an unreliable system. A converter must be even better than this if system degradation is to be prevented. An ideal converter implementation will not suffer any failures over its application lifetime. In many cases, extremely high reliability can be a more difficult objective than that of high efficiency.

A circuit built from ideal switches will be lossless. As a result, switches are the main components of power converters, and many people equate power electronics with the study of switching power converters. Magnetic transformers and lossless storage elements such as capacitors and inductors are also valid candidates for use in power converters. The complete concept, shown in Figure 14, illustrates a power electronic system. Such a system consists of an energy source, an electrical load, a power electronic circuit, and control functions. The power electronic circuit contains switches, lossless energy storage elements, and magnetic transformers. The controls take information from the source, load, and designer and then determine how the switches operate to achieve the desired conversion. The controls are usually built up with conventional low-power analog and digital electronics.

Figure 14. A basic power electronic system.

Switching devices are selected based on their power handling rating—the product of their voltage and currents ratings— rather than on power dissipation ratings. This is in contrast to other applications of electronics, in which power dissipation ratings dominate. When the

devices are used as switches instead, the power levels increase considerably, as suggested by the following examples.

1. The 2N2222A is a popular bipolar transistor with a rated collector-emitter breakdown voltage of 30 V, a maximum collector current of 0.8 A, and rated power dissipation of 0.5W. In a conventional analog circuit, it usually handles energy within its 0.5W power dissipation rating. In principle, this device can manipulate the flow of 0.8 A in a 30 V circuit and so a power electronics engineer would list its power handling rating as 24W. The ability to control up to 24W, combined with good switching characteristics, makes this device common as an auxiliary element in power supplies.
2. The MTW20N50 is a metal-oxide-semiconductor field-effect transistor (MOSFET) with a drain current rating of 20 A, a maximum drain-source breakdown voltage of 500 V, and rated power dissipation of 250W. The power handling rating is 10kW. Several manufacturers have developed power electronic controllers for domestic refrigerators, air conditioners, and even electric vehicles based on this device and its relatives.

The second part of the definition of power electronics points out that the circuits handle power at levels much higher than that of the ratings of individual devices. In the first Example (i), a 2N2222A might be used to handle 24W—as compared with its individual rating of 0.5W. The MTW20N50 is used to handle up to 10kW, compared to its rating of 250W.

RELIABILITY OF POWER ELECTRONICS AND THE ISSUES:  High-power applications lead to interesting issues. For example, in an inverter the semiconductors often manipulate 40 times their rated power or more. A small design error, unexpected thermal problem, or minor change in layout could alter this somewhat, perhaps to a factor of 45. This small change puts large additional stresses on the devices and can lead to quick failure. The first issue for reliability in power electronic circuits is that of managing device voltage, current, and power dissipation levels to keep them well within rating limits. This can be challenging when power handling levels are high.

The second issue for reliability is simplicity. It is well established in military electronics that the more parts there are in a system, the more likely it is to fail. Power electronic circuits tend to have few parts, especially in the main energy flow paths. Necessary operations must be carried out through shrewd use of these parts. Often, this means that sophisticated control strategies are applied to seemingly simple conversion circuits.

The third issue for reliability is integration. One way to avoid the reliability–complexity tradeoff is to integrate multiple components and functions on a single substrate. A microprocessor, for example, might contain more than a million gates. As all interconnections and signals flow within a single chip, the reliability is nearly that of a single part. An important parallel trend in power electronic devices involves the integrated module. Manufacturers seek ways to package several switching devices, with their interconnections and protection components together as a unit. Control circuits for converters are also integrated as much as possible to keep reliability high.

The package itself becomes a fourth issue for reliability, and one that is as yet only partly understood. Semiconductor packages include small bonding wires that can be susceptible to thermal or vibration damage. The small geometries tend to enhance electromagnetic interference among the internal circuit components.

SWITCH MATRIX OF POWER ELECTRONICS: The most readily apparent difference between a power electronic circuit and other types of electronic circuits is the switch action. In contrast to a digital circuit, the switches do not indicate a logic level. Control is affected by determining the times at which switches should operate. Whether there is just one switch or a large group, there is a complexity limit: If a converter has m inputs and n outputs, even the densest possible collection of switches would have a single switch between each input line and each output line. The m x n switches in the circuit can be arranged according to their connections. The pattern suggests a matrix, as shown in the Figure 15.

Figure 15. The general switch matrix.

Power electronic circuits fall into two broad classes:

1. Direct switch matrix circuits. In these circuits, energy storage elements are connected to the matrix only at the input and output terminals. The storage elements effectively become part of the source or load. A rectifier with an external lowpass filter is an example of a direct switch matrix circuit. In the literature, these circuits are sometimes called matrix converters.
2. Indirect switch matrix circuits, also termed embedded converters. These circuits, like the polarity-reverser example, have energy storage elements connected within the matrix structure. There are usually very few storage elements. Indirect switch matrix circuits are most commonly analyzed as a cascade connection of direct switch matrix circuits with the storage in between.

The switch matrices in realistic applications are small. A 2 x 2 switch matrix, for example, covers all possible cases with a single-port input source and a two-terminal load. The matrix is commonly drawn as the H-bridge shown in Figure 16.

Figure 16. H-bridge configuration of a 2 x 2 switch matrix.

A more complicated example is the three-phase bridge rectifier shown in Figure 16. There are three possible inputs, and the two terminals of the dc circuit provide outputs, which give a 3 x 2 switch matrix. In a personal computer power supply, there are commonly five separate dc loads, and the switch matrix is 2 x 10. Very few practical converters have more than ≈24 switches, and most designs use fewer than 12. A switch matrix provides a way to organize devices for a given application. It also helps to focus the effort into three major task areas. Each of these areas must be addressed effectively in order to produce a useful power electronic system.

1. The Hardware Task: Build a switch matrix. This involves the selection of appropriate semiconductor switches and the auxiliary elements that drive and protect them.
2. The Software Task: Operate the matrix to achieve the desired conversion. All operational decisions are implemented by adjusting switch timing.

• The Interface Task: Add energy storage elements to provide the filters or intermediate storage necessary to meet the application requirements. Unlike most filter applications, lossless filters with simple structures are required.

In a rectifier or other converter, we must choose the electronic parts, how to operate them, and how best to filter the output to satisfy the needs of the load.

 

Figure 16. Three-phase bridge rectifier circuit, a 3 x 2 switch matrix.

IMPLICATIONS OF KIRCHOFF’S VOLTAGE AND CURRENT LAWS: A major challenge of switch circuits is their capacity to ‘‘violate’’ circuit laws. Consider first the simple circuits of Figure 17. The circuit of Figure 17(a) is something we might try for ac-dc conversion. This circuit has problems. Kirchhoff ’s voltage law (KVL) tells us that the ‘‘sum of voltage drops around a closed loop is zero.’’ However, with the switch closed, the sum of voltages around the loop is not zero. In reality, this is not a valid result. Instead, a very large current will flow and cause a large I . R drop in the wires. The KVL will be satisfied by the wire voltage drop, but a fire or, better yet, fuse action, might result. There is, however, nothing that would prevent an operator from trying to close the switch. The KVL, then, implies a crucial restriction: A switch matrix must not attempt to interconnect unequal voltage sources directly. Notice that a wire, or dead short, can be thought of as a voltage source with V = 0, so KVL is a generalization for avoiding shorts across an individual voltage source.

Figure 17. Hypothetical power converters: (a) Possible ac-dc converter.

A similar constraint holds for Kirchhoff ’s current law (KCL). The KCL states that ‘currents into a node must sum to zero.’’ When current sources are present in a converter, we must avoid any attempts to violate KCL. In Fig. 17(b), if the current sources are different and the switch is opened, the sum of the currents into the node will not be zero. In a real circuit, high voltages will build up and cause an arc to create another current path. This situation has real potential for damage, and a fuse will not help. The KCL implies a restriction in which a switch matrix must not attempt to interconnect unequal current sources directly. An open circuit can be thought of as a current source with I = 0, so KCL applies to the problem of opening an individual current source.

Figure 17. Hypothetical power converters: (b) Possible dc-dc converter.

In contrast to conventional circuits, in which KVL and KCL are automatically satisfied, switches do not ‘‘know’’ KVL or KCL. If a designer forgets to check, and accidentally shorts two voltages or breaks a current source connection, some problem or damage will result. On the other hand, KVL and KCL place necessary constraints on the operating strategy of a switch matrix. In the case of voltage sources, switches must not act to create short-circuit paths among dissimilar sources. In the case of KCL, switches must act to provide a path for currents. These constraints drastically reduce the number of valid switch operating conditions in a switch matrix, and lead to manageable operating design problems.

Figure 18. Short-term KVL and KCL problems in energy storage circuits: (a) An inductor cannot sustain dc voltage indefinitely; (b) A capacitor cannot sustain dc current indefinitely.

When energy storage is included, there are interesting implications for the current law restrictions. Figure 18 shows two ‘‘circuit law problems.’’ In Fig. 7(a), the voltage source will cause the inductor current to ramp up indefinitely because V = L di/dt. We might consider this to be a ‘‘KVL problem,’’ since the long-term effect is similar to shorting the source. In Fig. 7(b), the current source will cause the  capacitor voltage to ramp toward infinity. This causes a ‘‘KCL problem’’; eventually, an arc will form to create an additional current path, just as if the current source had been opened. Of course, these connections are not problematic if they are only temporary. However, it should be evident that an inductor will not support dc voltage, and a capacitor will not support dc current. On average over an extended time interval, the voltage across an inductor must be zero, and the current into a capacitor must be zero.

REOLUTION OF HARDWARE PROBLEMS IN SEMICONDUCTOR DEVICES: A switch is either on or off. An ideal switch, when on, will carry any current in any direction. When off, it will never carry current, no matter what voltage is applied. It is entirely lossless, and changes from its on state to its off state instantaneously. A real switch can only approximate an ideal switch. Those aspects of real switches that differ from the ideal include the following:

1. limits on the amount and direction of on-state current.
2. a nonzero on-state voltage drop (such as a diode forward voltage).
3. some level of leakage current when the device is supposed to be off.
4. limitations on the voltage that can be applied when off; and
5. operating speed. The time of transition between the on and off states can be important.

The degree to which properties of an ideal switch must be met by a real switch depends on the application. For example, a diode can easily be used to conduct dc current; the fact that it conducts only in one direction is often an advantage, not a weakness. Many different types of semiconductors have been applied in power electronics. In general, these fall into three groups:

1. Diodes: which are used in rectifiers, dc-dc converters, and in supporting roles.
2. Transistors: which in general are suitable for control of single-polarity circuits. Several types of transistors are applied to power converters. The most recent type, the insulated gate bipolar transistor (IGBT) is unique to power electronics and has good characteristics for applications such as inverters.
3. Thyristors: which are multijunction semiconductor devices with latching behavior. Thyristors in general can be switched with short pulses, and then maintain their state until current is removed. They act only as switches. The characteristics are especially well-suited to controllable rectifiers, although thyristors have been applied to all power conversion applications.

Some of the features of the most common power semiconductors are listed in Table 1. This table shows a wide variety of speeds and rating levels. As a rule, faster speeds apply to lower ratings. For each device type, cost tends to increase both for faster devices and for devices with higher power-handling capacity.

Table 1. Some modern semiconductor switch types and their basic characteristics

Conducting direction and blocking behavior are fundamentally tied to the device type, and these basic characteristics constrain the choice of device for a given conversion function. Consider again a diode. It carries current in only one direction and always blocks current in the other. Ideally, the diode exhibits no forward voltage drop or off-state leakage current. Although it lacks all the features of an ideal switch, the ideal diode is an important switching device. Other real devices operate with polarity limits on current and voltage and have corresponding ideal counterparts. It is convenient to define a special type of switch to represent this behavior: the restricted switch.

A restricted switch is an ideal switch with the addition of restrictions on the direction of current flow and voltage polarity. The ideal diode is one example of a restricted switch. The diode always permits current flow in one direction, while blocking flow in the other. It therefore represents a forward conducting reverse-blocking restricted switch and operates in one quadrant on a graph of device current vs voltage. This FCRB function is automatic—the two diode terminals provide all the necessary information for switch action. Other restricted switches require a third gate terminal to determine their state. Consider the polarity possibilities given in Table 2.

Table 2. Some modern semiconductor switch types and their basic characteristics

Additional functions such as bidirectional- conducting reverse-blocking can be obtained simply by reverse connection of one of the five types in the table. The quadrant operation shown in the table indicates polarities. For example, the current in a diode will be positive when on and the voltage will be negative when off. This means diode operation is restricted to the single quadrant comprising the upper vertical (current) axis and the left horizontal (voltage) axis. The other combinations appear in the table. Symbols for restricted switches can be built up by interpreting the diode’s triangle as the current-carrying direction and the bar as the blocking direction. The five types can be drawn as in Table 2. Although the symbols are used infrequently, they are valuable for showing the polarity behavior of switching devices. A circuit drawn with restricted switches represents an idealized power converter.

Restricted switch concepts guide the selection of devices. For example, consider an inverter intended to deliver ac load current from a dc voltage source. A switch matrix built to perform this function must be able to manipulate ac current and dc voltage. Regardless of the physical arrangement of the matrix, we would expect bidirectional-conducting forward-blocking switches to be useful for this conversion. This is a correct result: Modern inverters operating from dc voltage sources are built with FETs or with IGBTs arranged with reverse-parallel diodes. As new power devices are introduced to the market, it is straightforward to determine what types of converters will use them.

RESOLVING SOFTWARE PROBLEM – SWITCHING FUNCTIONS: The physical m x n switch matrix can be associated with a mathematical m x n switch state matrix. Each element of this matrix, called a switching function, shows whether the corresponding physical device is on or off.

A switching function q(t) has a value of unity when the corresponding physical switch is on and 0 when it is off. Switching functions are discrete-valued functions of time, and control of switching devices can be represented with them.

Figure 19. A generic switching function with period T; duty ratio D; and time reference t₀.

Figure 19 shows a typical switching function. It is periodic, with period T, representing the most likely repetitive switch action in a power converter. For convenience, it is drawn on a relative time scale that begins at 0 and draws out the square wave period-by-period. The actual timing is arbitrary, so the center of the first pulse is defined as a specified time t0 in the figure. In many converters, the switching function is generated as an actual control voltage signal that might drive the gate of either a MOSFET or some other semiconductor switching device.

The timing of switch action is the only alternative for control of a power converter. As switch action can be represented with a discrete-valued switching function, the timing can be represented within the switching function framework. Based on Figure 19, a generic switching function can be characterized completely with three parameters:

1. The duty ratio D is the fraction of time during which the switch is on. For control purposes the pulse width can be adjusted to achieve a desired result. We can term this adjustment process pulse-width modulation (PWM), perhaps the most important process for implementing control in power converters.
2. The frequency f_switch = 1/T (with radian frequency ω = 2pf_switch) is most often constant, although not in all applications. For control purposes, frequency can be adjusted. This is unusual in power converters because the operating frequencies are often dictated by the application.
3. The time delay t₀ or phase ф₀ = ωt₀. Rectifiers often make use of phase control to provide a range of adjustment. A few specialized ac-ac converter applications use phase modulation.

With just three parameters to vary, there are relatively few possible ways to control any power electronic circuit. The dc-dc converters usually rely on duty ratio adjustment (PWM) to alter their behavior. Phase control is common in controlled rectifier applications. Pulse-width modulation is used formally for many types of inverters. Switching functions are very powerful tools for general representation of converter action. The most widely used control approaches derive from averages of switching functions. Their utility comes from their application in writing circuit equations.

LOSSES IN POWER ELECTRONICS: [4]The two types of losses that occur in the power electronics are as detailed below:

• Conduction Losses: when the transistor shown in the Fig. 20(a), is OFF, it carries a leakage current (I_LEAK). The power loss associated with the leakage current is as follows:

 

Figure 20. ON and OFF Condition of a Transistor.

However, since the leakage current is quite small and does not vary significantly with the voltage, it is usually neglected and thus the transistor power loss is essentially zero. When the transistor is ON, as in the Figure 10(b), it has a small voltage drop across it. This voltage is called the Saturation Voltage V_CE(SAT). The transistor’s power dissipation or conduction loss due to the saturation voltage is given as follows:

  

Where,

The equation (2) gives the power loss due to the condition if the switch remains ON indefinitely. However, to control the power for a given application, the switch is turned ON and OFF in a periodic manner. Therefore, to find the voltage power loss, one must consider the duty cycle as:

 

 Similarly,

 

Here, the duty cycle ‘d’ is defined as the percentage of the cycle in which the switch is ON:

•  Switching Losses: In addition to the conduction loss, a real switch has switching losses because it cannot change from ON state to the OFF state (or vice versa) instantaneously. A real switch takes a finite time t_SW(ON) to turn ON and t_SW(OFF) to turn OFF. These times not only introduce power dissipation but also limit the highest switching frequency possible. The transition times t_SW(ON) and t_SW(OFF) for real switches are usually not equal, with the t_SW(ON) generally being larger. However, in this condition, it is assumed that t_SW(ON) is equal to t_SW(OFF). The Figure 21 shows the switching waveforms for (a) voltage across the switch and (b) the current through it. When the switch is OFF, the voltage across it is equal to the source voltage. During the turn-ON, which takes a finite time, the voltage across the switch decreases to zero. During the same time, the current through the switch increases from zero to I_C. The transistor has a current through it and a voltage across it during the switching time, therefore, it has a power loss.

  

Figure 21. Waveforms during the switching operation: (a) voltage across the switch, (b) current through the switch and (c) power dissipated in the switch.

 

To find the power dissipated in the transistor during the switching interval, the instantaneous value of I_C is multiplied to the corresponding value of V_CE. The instantaneous power curve is shown in the Figure 21(c). The energy dissipated in the switch is equal to the area under the power waveform. Note that the maximum power is dissipated when both the current and the voltage are passing through their midpoint values. Therefore, the maximum power loss when switching from the OFF state to the ON state is given as:

  

It is interesting to note that the power curve looks essentially like a rectified sine wave. The average value of this waveform is:

 

 (OR)

 

The energy loss (power x time) during the turn ON will be P_SWON(AVG) x t_SW(ON).

 

A similar analysis gives the energy loss during the turn OFF condition as follows:

 

The total energy loss in one cycle due to switching is given as follows:

 

The average power dissipation in the switch will be equal to:

 

 

Where T is the switching period and ‘f’ is the pulse repetition rate (frequency of the switching). It is important to not the following:

 

If we let,

 

On substituting (16) in (14), we get:

  

The total power loss in the switch is:

 

 

FORCES ACTING ON THE VEHICLE:

[5] The fundamentals of vehicle design involve the basic principles of physics, especially the Newton's second law of motion. According to Newton's second law the acceleration of an object is proportional to the net force exerted on it. Hence, an object accelerates when the net force acting on it is not zero. In a vehicle several forces act on it and the net or resultant force governs the motion according to the Newton's second law. The propulsion unit of the vehicle delivers the force necessary to move the vehicle forward. This force of the propulsion unit helps the vehicle to overcome the resisting forces due to gravity, air, and tire resistance. The acceleration of the vehicle depends on:

• the power delivered by the propulsion unit,
• the road conditions,
• the aerodynamics of the vehicle and
• the composite mass of the vehicle.

GENERAL DESCRIPTION OF VEHICLE MOVEMENT: The vehicle motion can be completely determined by analyzing the forces acting on it in the direction of motion. The forces acting on a vehicle, moving up a grade, are shown in Figure 22. The tractive force (Ft) in the contact area between the tires of the driven wheels and the road surface propels the vehicle forward. The tractive force (Ft) is produced by the power plant and transferred to the driving wheels via the transmission and the final drive. When the vehicle moves, it encounters a resistive force that tries to retard its motion. The resistive forces are:

• Rolling resistance
• Aerodynamic drag
• Uphill resistance

Figure 22. Forces acting on a vehicle moving uphill.

Using the Newton's second law of motion, the vehicle acceleration can be expressed as:

where V is the vehicle speed,  is the total tractive effort (Nm) ,  is the total resistance (Nm) , M is the mass of the vehicle (kg) ,  is the mass factor for converting the rotational inertias of the rotating components into translational mass.

ROLLING RESISTANCE:  The rolling resistance of tires on hard surfaces is due to hysteresis in the tire material. In Figure 23, a tire at standstill is shown. On this tyre a force ( P ), is acting at its center. The pressure in the contact area between the tire and the ground is distributed symmetrically to the center line and the resulting reaction force (Pz) is aligned along P.

Figure 23. Pressure distribution in contact area.

The deformation, z, versus the load P, in the loading and unloading process is shown in Figure 24. From this figure it can be seen that, due to the hysteresis, the force (P) for the same deformation (z) of the tire material at loading is greater than at during unloading. Hence, the hysteresis causes an asymmetric distribution of the ground reaction forces.

Figure 24. Force acting on a tyre vs. deformation in loading and unloading.

The scenario of a rolling tire is shown in Figure 7. When the tire rolls, the leading half of the contact area is loading, and the trailing half is unloading. Thus, the pressure on the leading half is greater than the pressure on the trailing half (Figure 25a). This phenomenon results in the ground reaction force shifting forward. The shift in the ground reaction force creates a moment that opposes rolling of the wheels. On soft surfaces, the rolling resistance is mainly caused by deformation of the ground surface, (Figure 25b). In this case the ground reaction force almost completely shifts to the leading half.

Figure 25a: Force acting on a tyre vs. deformation in loading and unloading on a hard surface.

The moment produced by forward shift of the resultant ground reaction force is called rolling resistance moment (Figure 25a), and can expressed as:

Where T_r is the rolling resistance (Nm), P is the normal load acting on the center of the rolling wheel (N), M is the mass of the vehicle (kg), g is the acceleration due to gravity (m/s²) and a is the deformation of the tyre (m).

Figure 25b : Force acting on a tyre vs. deformation in loading and unloading on a soft surface.

To keeps the wheel rolling, a force Fr, acting on the center of the wheel is required to balance this rolling resistant moment. This force is expressed as:

Where T_r is the rolling resistance (Nm), P is the normal load acting on the center of the rolling wheel (N), r_dyn is the dynamic radius of the tyre (m) and f_r is the rolling resistance coefficient.

The rolling resistance moment can be equivalently replaced by horizontal force acting on the wheel center in the direction opposite to the movement of the wheel. This equivalent force is called the rolling resistance and its magnitude is given by:

Where P is the normal load acting on the center of the rolling wheel (N), f_r is the rolling resistance coefficient.

When a vehicle is moving up a gradient, the normal force (P), is replaced by the component that is perpendicular to the road surface. Hence, above equation is rewritten as:

Where P is the normal load acting on the center of the rolling wheel (N), f_r rolling resistance coefficient and  is the road angle (radians).

The rolling resistance coefficient, f_r, is a function of tire material, tire structure, tire temperature, tire inflation pressure, tread geometry, road roughness, road material and presence of absence of liquids on the road. The typical values of the rolling resistance coefficient (f_r) are given in the table below.

Table 3. Reference values for rolling resistance coefficient.

The values given in table above do not consider the variation of f_r with speed. Based on experimental results, many empirical formulas have been proposed for calculating the rolling resistance on a hard surface. For example, the rolling resistance coefficient of a passenger car on a concrete road may be calculated as:

Where V is the speed of the vehicle (km/hr).

In vehicle performance calculation, it is sufficient to consider the rolling resistance coefficient as a linear function of speed. For most common range of inflation pressure, the following equation can be used for a passenger car on a concrete road:

Where V is the speed of the vehicle (km/hr) and using this equation one can predict the values of f_r with acceptable accuracy for speeds up to 128 km/hr.

AERODYNAMIC DRAG: A vehicle traveling at a particular speed in air encounters a force resisting its motion. This force is known as aerodynamic drag. The main causes of aerodynamic drag are:

• Shape Drag: The shape drag is due to the shape of the vehicle. The forward motion of the vehicle pushes the air in front of it. However, the air cannot instantaneously move out of the way and its pressure is thus increased. This results in high air pressure in the front of the vehicle. The air behind the vehicle cannot instantaneously fill the space left by the forward motion of the vehicle. This creates a zone of low air pressure. Hence, the motion of the vehicle creates two zones of pressure. The high-pressure zone in the front of the vehicle opposes its movement by pushing. On the other hand, the low-pressure zone developed at the rear of the vehicle opposes its motion by pulling it backwards.
• Skin effect: The air close to the skin of the vehicle moves almost at the speed of the vehicle while the air away from the vehicle remains still. Between these two layers (the air layer moving at the vehicle speed and the static layer) the molecules move at a wide range of speeds. The difference in speed between two air molecules produces friction. This friction results in the second component of aerodynamic drag and it is known as skin effect.

The aerodynamic drag is expressed as:

Where  is the density of the air (kg/m³), A_f is the frontal area (m²), V is the vehicle speed (m/s) and C_D is the drag coefficient.

The aerodynamic drag coefficients and the frontal area for different vehicle types is given in the Table 4.

Table 4. Reference values for drag coefficient (C_D) and the frontal area (A_f  in m²) for some vehicle types.

GRADING RESISTANCE: When a vehicle goes up or down a slope, its weight produces a component of force that is always directed downwards, Figure 26. This force component opposes the forward motion, i.e., the grade climbing. When the vehicle goes down the grade, this force component aids the vehicle motion. The grading resistance can be expressed as:

Where M is the mass of the vehicle (kg), g is the acceleration due to gravity (m/s²) and  is the road angle (radians).

In order to simplify the calculation, the road angle a, is usually replaced by the grade value, when the road angle is small. The grade value is defined as (Figure 26):

In some literature, the tire rolling resistance and the grading resistance taken together and are called road resistance. The road resistance is expressed as:

Where M is the mass of the vehicle (kg), g is the acceleration due to gravity (m/s²) and  is the rolling resistance coefficient.

Figure 26. Vehicle going up a grade.

 

ACCELERATION RESISTANCE: In addition to the driving resistance occurring in steady state motion, inertial forces also occur during acceleration and braking. The total mass of the vehicle and the inertial mass of those rotating parts of the drive accelerated or braked are the factors influencing the resistance to acceleration:

Where M is the mass of the vehicle (kg), J_rot is the inertia of rotational components (kg/m²), V is the vehicle speed (km/hr) and r_dyn is the dynamic radius of the tyre (m).

The rotational component is a function of the gear ratio. The moment of inertia of the rotating drive elements of engine, clutch, gearbox, drive shaft, etc., including all the road wheels are reduced to the driving axle. The acceleration resistance can be expressed as:

Where λ is the rotational inertia constant, M is the mass of the vehicle (kg), V is the vehicle speed (m/s).

TOTAL DRIVING RESISTANCE: The traction force (Ft) required at the drive wheels is made up of the driving resistance forces and is defined as:

This is further simplified as follows:

 

The above equation may be used to calculate the power required as follows:

 

PROBLEM SPECIFICATION AND SOLVING:

PROBLEM STATEMENT :

Create a MATLAB model of electric car which uses a battery and a dc motor. Choose suitable blocks from powertrain block set.

MODELLING AN ELECTRIC VEHICLE:

The modelling of an electric vehicle requires mathematically appropriate congregation of driving system, vehicle body parameter and corresponding system, electrical systems involved in the functioning of the vehicle and the power producing system. The schematic diagram of the model layout is as shown below in the Figure 27.

Figure 27. Layout of the model of the EV. [6]

The problem statement requires the usage of a DC motor as the source of propulsion energy. A permanent magnet DC motor is employed in the model to be constructed. The theory of the DC motor with permanent magnet is as follows:

[2] The classical DC electric motor is shown in Figure 28. It is a DC motor, equipped with permanent magnets and brushes. This simplified motor has one coil, and the current passing through the wire near the magnet causes a force to be generated in the coil. The current flows through brush X, commutator half ring A, round the coil, and out through the other commutator half ring B and brush Y (XABY). On one side (as shown in the diagram) the force is upwards, and in the other the force is downwards, because the current is flowing back towards the brushes and commutator. The two forces cause the coil to turn. The coil turns with the commutator, and once the wires are clear of the magnet the momentum carries it on round until the half rings of the commutator connect with the brushes again. When this happens, the current is flowing in the same direction relative to the magnets, and hence the forces are in the same direction, continuing to turn the motor as before. However, the current will now be flowing through brush X, half ring B, round the coil to A and out through Y, so the current will be flowing in the opposite direction through the coil (XBAY). The commutator action ensures that the current in the coil keeps changing direction, so that the force is in the same direction, even though the coil has moved.

Figure 28. Diagram to explain the operation of the simple permanent magnet DC motor.

Clearly, in a real DC motor there are many refinements over the arrangement of Figure 29. The most important of these are as follows:

• The rotating wire coil, often called the armature, is wound round a piece of iron, so that the magnetic field of the magnets does not have to cross a large air gap, which would weaken the magnetic field.
• More than one coil will be used, so that a current-carrying wire is near the magnets for a higher proportion of the time.
• This means that the commutator does not consist of two half rings (as in Figure 29) but several segments, two segments for each coil.
• Each coil will consist of several wires, so that the torque is increased (more wires, more force). More than one pair of magnets may be used, to further increase the turning force.

Figure 29. (a) Cross-section through a four-pole DC motor. The dotted lines show the magnetic flux. The motor torque is clockwise. (b) shows the convention used to indicate the direction of current flow in wires drawn in cross-section

As per the figure, the power converter implemented in the model of the EV is a H-bridge. The description of the H-bridge is as follows:

[7] An H-bridge is an electronic circuit that switches the polarity of a voltage applied to a load. These circuits are often used in robotics and other applications to allow DC motors to run forwards or backwards. Most DC-to-AC converters (power inverters), most AC/AC converters, the DC-to-DC push–pull converter, isolated DC-to-DC converter most motor controllers, and many other kinds of power electronics use H bridges. In particular, a bipolar stepper motor is almost always driven by a motor controller containing two H bridges.

Figure 30(a). Two basic states of an H-Bridge.

 

Figure 30(b). Structure of an H-Bridge (highlighted in red)

The H-bridge arrangement is generally used to reverse the polarity/direction of the motor but can also be used to 'brake' the motor, where the motor comes to a sudden stop, as the motor's terminals are shorted, or to let the motor 'free run' to a stop, as the motor is effectively disconnected from the circuit. The following table summarizes operation, with S1-S4 corresponding to the diagram above in Figure 30(b).

S1	S2	S3	S4	Result
1	0	0	1	Motor moves right
0	1	1	0	Motor moves left
0	0	0	0	Motor coasts
1	0	0	0
0	1	0	0
0	0	1	0
0	0	0	1
0	1	0	1	Motor brakes
1	0	1	0
x	x	1	1	Short circuit
1	1	x	x

Table 5. Operation of H-bridge.

EXPLANATION AND OBSERVATION OF THE EV:

• The model is created by incorporating the different subsystems as mentioned in the modelling section, are as follows:
• Vehicle subsystem
• Electrical subsystem
• Battery subsystem, and
• Driving subsystem
• The modelling of the subsystems is done in the same schematic order as mentioned above.

VEHICLE SUBSYSTEM:

• The vehicle subsystem consists of the vehicle body and its corresponding physical attributes.
• Initially, a vehicle body block is selected, and the parameters are set accordingly. The description of the Vehicle Body block is as follows:

VEHICLE BODY BLOCK: [8] The Vehicle Body block represents a two-axle vehicle body in longitudinal motion. The vehicle can have the same or a different number of wheels on each axle. For example, two wheels on the front axle and one wheel on the rear axle. The vehicle wheels are assumed identical in size. The vehicle can also have a center of gravity (CG) that is at or below the plane of travel. The block accounts for body mass, aerodynamic drag, road incline, and weight distribution between axles due to acceleration and road profile. Optionally include pitch and suspension dynamics. The vehicle does not move vertically relative to the ground.

The block has an option to include an externally-defined mass and an externally-defined inertia. The mass, inertia, and center of gravity of the vehicle body can vary over the course of simulation in response to system changes. The Vehicle Body block lets you model only longitudinal dynamics, parallel to the ground and oriented along the direction of motion. The vehicle is assumed to be in pitch and normal equilibrium. The block does not model pitch or vertical movement. As such, the equations assume that the wheels never lose contact. This constraint can result in negative normal forces.

Representation:

Figure 31. Representation of Vehicle Body block in SIMULINK.

• The following table describes in detail about the different ports of the vehicle body block along with specific implications of the input and output ports. The values assumed during the modelling of the electric vehicle using the Vehicle body block have also been detailed in the table mentioned below:

 

PORT	DESCRIPTION	VALUE/CONNECTION
Headwind speed (W) (m/s) - INPUT	Physical signal input port for headwind speed.	1.38889 m/s value is fed using a constant block and a Simulink-PS connector.
Road incline angle (beta) (radians) - INPUT	Physical signal input port for road incline angle.	0.0698132 rad value is fed using a constant block and a Simulink-PS connector.
Centre of gravity (CG) (m) - INPUT	Physical signal input port for the center of gravity, in m, of the externally-defined mass relative to the CG of the vehicle body.	0.5 m
Mass (M) (kg) - INPUT	Physical signal input port for the mass, in kg, of the externally-defined mass.	900 kg
External moment of Inertia (J) (kg m2) - INPUT	Physical signal input port for the moment of inertia, in kg m2, of the externally-defined mass.	Not employed in this model.
Longitudinal velocity (V) (m/s) - OUTPUT	Physical signal output port for vehicle longitudinal velocity.	Output is collected by the Goto block
Front Axle Normal Force (NF) (N) – OUTPUT	Physical signal output port for normal force on the front axle. Wheel forces are considered positive if acting downwards.	Connected to the N ports of the front tires.
Rear Axle Normal Force (NR) (N) - OUTPUT	Physical signal output port for normal force on the rear axle. Wheel forces are considered positive if acting downwards.	Connected to the N ports of the rear tires.
Horizontal motion (H) - CONSERVING	Conserving port associated with the horizontal motion of the vehicle body. Connect tire traction motion to this port.	Connected to the H ports of the tires and to the Ideal translational motion sensor.

Table 6. Ports of vehicle body block in SIMULINK.

 

• The other values of the input for the vehicle body block are as follows:

Parameter	Value
Number of wheel per axle	2
Horizontal distance from CG to front axle	1.4 m
Horizontal distance from CG to rear axle	1.6 m
Externally defined additional mass	…
Gravitational acceleration	9.81 m/s2
Frontal area	2 m2
Drag coefficient	0.19
Air density	1.25 kg/m3
Pitch dynamics	OFF

Table 7. Other parameters of the vehicle body block in SIMULINK.

 

• The given model of the electric vehicle is constructed as a rear wheel drive. Four wheels are considered. Tire (Magic Formula) block is used to represent the tires of the electric vehicle. The description of the Tire (Magic Formula) block is as follows:

TIRE (MAGIC FORMULA): [9] The Tire (Magic Formula) block models a tire with longitudinal behavior given by the Magic Formula [1], an empirical equation based on four fitting coefficients. The block can model tire dynamics under constant or variable pavement conditions. The longitudinal direction of the tire is the same as its direction of motion as it rolls on pavement. This block is a structural component based on the Tire-Road Interaction (Magic Formula) block. To increase the fidelity of the tire model, you can specify properties such as tire compliance, inertia, and rolling resistance. However, these properties increase the complexity of the tire model and can slow down simulation. Consider ignoring tire compliance and inertia if simulating the model in real time or if preparing the model for hardware-in-the-loop (HIL) simulation. The Tire (Magic Formula) block assumes longitudinal motion only and includes no camber, turning, or lateral motion. Tire compliance implies a time lag in the tire response to the forces on it. Time lag simulation increases model fidelity but reduces simulation performance.

Representation:

Figure 32. Representation of Tire (Magic Formula) block in SIMULINK.

• The description of different ports of the Tire (Magic Formula) block is as follows:

PORT	DESCRIPTION	VALUE/CONNECTION
Normal Force (N) (N) - INPUT	Physical signal input port associated with the normal force acting on the tire. The normal force is positive if it acts downward on the tire, pressing it against the pavement.	For front tires, these ports are connected to NF of the Vehicle body block and for the rear tires, this is connected to the NR of the vehicle body block.
Magic Formula coefficients (M) - INPUT	Physical signal input port associated with the Magic Formula coefficients. Provide the Magic Formula coefficients as a four-element vector, specified in the order [B, C, D, E].	Not employed in this model.
Slip (S) - OUTPUT	Physical signal output port associated with the relative slip between the tire and road.	Each tire is connected to a display to understand the slip value between the respective tire and the road.
Axle (A) - CONSERVING	Mechanical rotational port associated with the axle that the tire sits on.	Front tires are connected to each other while the rear tires axles are connected to the differential.
Hub (H) -CONSERVING	Mechanical translational port associated with the wheel hub that transmits the thrust generated by the tire to the remainder of the vehicle.	The H ports of the four tires are connected to the H port of the vehicle body.

Table 8. Ports of Tire (Magic Formula) block in SIMULINK.

 

• The other values of the input for the Tire (Magic Formula) block are as follows:

Parameter	Value
Parameterized by	Peak Longitudinal force and corresponding slip
Rated Vertical Load	2500 N
Peak longitudinal force at rated load	2500 N
Slip at peak force at rated load (percent)	10
Rolling radius	0.2 m
Dynamics	No compliance (suitable for HIL simulation) and no inertia
Rolling resistance model	Constant coefficient
Constant coefficient	0.005
Velocity threshold	0.001 m/s

Table 9. Other parameters of the Tire (Magic formula) block in SIMULINK.

 

• The axle ports of the rear tires are connected to the differential unlike the axle ports of the front tires. This is due to the fact that the vehicle is constructed as a rear axle drive. The description of the differential is as follows:

DIFFERENTIAL: [10] The Differential block represents a gear mechanism that allows the driven shafts to spin at different speeds. Differentials are common in automobiles, where they enable the various wheels to spin at different speeds while cornering. Ports D, S1, and S2 represent the longitudinal driveshaft and the sun gear shafts of the differential, respectively. Any one of the shafts can drive the other two. The block models the differential mechanism as a structural component based on the Simple Gear and Sun-Planet Bevel Simscape™ Driveline™ blocks. To increase the fidelity of the gear model, specify properties such as gear inertia, meshing losses, and viscous losses. By default, gear inertia and viscous losses are assumed to be negligible. The block enables you to specify the inertias of the gear carrier and internal planet gears. To model the inertias of the outer gears, connect Simscape Inertia blocks to ports D, S1, and S2. The gears are assumed to be rigid. Coulomb friction slows down simulation.

Representation:

Figure 33. Representation of Differential block in SIMULINK.

• The description of different ports of the differential block is as follows:

PORT	DESCRIPTION	VALUE/CONNECTION
Drive shaft (D) - CONSERVING	Rotational mechanical conserving port associated with the longitudinal driveshaft.	Connected to the output of the simple gear block.
Sun gear 1 (S1) - CONSERVING	Rotational conserving port associated with sun gear 1.	Connected to the A port of the rear left tire.
Sun gear 2 (S2) - CONSERVING	Rotational conserving port associated with sun gear 2.	Connected to the A port of the rear right tire.
Heat flow (H) - CONSERVING	Thermal conserving port associated with heat flow	Not employed.

Table 10. Ports of Differential block in SIMULINK.

• The other values of the input for the differential block are as follows:

Parameter	Value
Crown gear located	To the right of the centerline
Carrier (C ) to driveshaft (D) teeth ratio (NC/ND)	2
Friction model	No meshing losses – suitable for HIL simulation
Viscous loss coefficients of sun-carrier and drive shaft casing	[0 Nm/(rad-s), 0 Nm/(rad-s)]
Carrier inertia	0.001 kg-m2
Planet gear inertia	0.001 kg-m2

Table 11. Other parameters of the Differential block in SIMULINK.

 

• A simple gear block is connected to the differential input port D. the description of the Simple gear block is as follows:

SIMPLE GEAR BLOCK: [11] The Simple Gear block represents a gearbox that constrains the connected driveline axes of the base gear, B, and the follower gear, F, to corotate with a fixed ratio that you specify. You choose whether the follower axis rotates in the same or opposite direction as the base axis. If they rotate in the same direction, the angular velocity of the follower, ω_F, and the angular velocity of the base, ω_B, have the same sign. If they rotate in opposite directions, ω_F and ω_B have opposite signs. Gear inertia is assumed to be negligible. Gears are treated as rigid components. Coulomb friction slows down simulation.

Representation:

Figure 34. Representation of Simple Gear block in SIMULINK.

 

• The description of different ports of the Simple gear block is as follows:

PORT	DESCRIPTION	VALUE/CONNECTION
Base (B) - CONSERVING	Rotational mechanical conserving port associated with the base, or input, shaft.	Connected to the R port of the DC Motor block.
Follower  (F) - CONSERVING	Rotational mechanical conserving port associated with the follower, or output, shaft.	Connected to the A port of the rear right tire.
Heat flow (H) - CONSERVING	Thermal conserving port associated with heat flow	Not employed.
External Fault trigger (T) - INPUT	Physical signal input port for an external fault trigger.	Connected to the output of the simple gear block.

Table 12. Ports of Simple gear block in SIMULINK.

 

• The other values of the input for the Simple gear block are as follows:

Parameter	Value
Follower (F) to base (B) teeth ratio (NF/NB)	3
Output shaft rotates	In same direction to input shaft.
Meshing losses friction model	Constant efficiency of 80 %
Follower power threshold	0.001 W
Viscous loss coefficients of base (B) and Follower (F)	[0 Nm/(rad-s), 0 Nm/(rad-s)]
Faults	OFF

Table 13. Other parameters of the Simple gear block in SIMULINK.

 

• Therefore, the vehicle subsystem comprises of the above-mentioned blocks connected in a schematic arrangement as shown in the figure below:

Figure 35. Representation of Vehicle Subsystem in SIMULINK.

 

 

ELECTRICAL SUBSYSTEM:

• The electrical subsystem consists of the electrical devices that promote the required flow of current and maintains desired amount of voltage in the circuit. This subsystem is the heart of the electrical vehicle.
• A DC motor is employed to produce the required mechanical energy output from the electrical input. The description of the DC motor block is as follows:

DC MOTOR BLOCK: [12] The DC Motor block represents the electrical and torque characteristics of a DC motor using the following equivalent circuit model as shown in the figure below.

Figure 36. Representation of equivalent circuit of the DC motor under consideration.

One can specify the equivalent circuit parameters for this model when the user sets the Model parameterization parameter to By equivalent circuit parameters. The resistor R corresponds to the resistance the user specifies in the Armature resistance parameter. The inductor L corresponds to the inductance the user specifies in the Armature inductance parameter. The torque-speed characteristic for the DC Motor block is related to the parameters in the preceding figure. When the user sets the Model parameterization parameter to By stall torque & no-load speed or By rated power, rated speed & no-load speed, the block solves for the equivalent circuit parameters. It is not always possible to measure rotor damping, and rotor damping is not always provided on a manufacturer datasheet. An alternative is to use the no-load current to infer a value for rotor damping. The value for rotor damping, whether specified directly or in terms of no-load current, is taken into account when determining equivalent circuit parameters for Model parameterization options By stall torque and no-load speed and By rated power, rated speed and no-load speed.

When a positive current flows from the electrical + to - ports, a positive torque acts from the mechanical C to R ports. The DC Motor block allows you to model two types of faults:

• Armature winding fault — The armature winding fails and goes open circuit.
• Field winding fault — The field winding that creates the magnetic field fails and goes open circuit.

The block can trigger fault events:

• At a specific time (temporal fault).
• When a current limit is exceeded for longer than a specific time interval (behavioral fault).

The user can enable or disable these trigger mechanisms separately. One can choose whether to issue an assertion when a fault occurs, by using the Reporting when a fault occurs parameter. The assertion can take the form of a warning or an error. By default, the block does not issue an assertion.

Representation:

Figure 37. Representation of DC Motor block in SIMULINK.

 

• The description of different ports of the DC Motor block is as follows:

PORT	DESCRIPTION	VALUE/CONNECTION
Positive Terminal (+) - CONSERVING	Electrical conserving port associated with the DC motor positive terminal.	Connected to a positive terminal of the H bridge through current sensor block.
Negative terminal  (-) - CONSERVING	Electrical conserving port associated with the DC motor negative terminal.	Connected to the negative terminal of H bridge and is grounded using electrical reference
Motor case (C) - CONSERVING	Mechanical rotational conserving port associated with the DC motor case.	Connected to Mechanical Rotational reference block
Motor Rotor (R) - CONSERVING	Mechanical rotational conserving port associated with the DC motor rotor.	Connected to the base  (B) port of the Simple gear block.
Positive Field (F+) – CONSERVING	Electrical conserving port associated with the positive field winding.	Not applicable.
Negative Field (F-) – CONSERVING	Electrical conserving port associated with the negative field winding.	Not applicable.
Thermal port (H) – CONSERVING	Thermal port.	Not applicable.

Table 14. Ports of DC Motor block in SIMULINK.

• The other values of the input for the DC Motor block are as follows:

Parameter	Value
DC Motor field type	Permanent Magnet
Model parameterization	By rated load and speed
Armature inductance	12e-06 H
No load speed	10,000 rpm
Rated speed (at rated load)	8000 rpm
Rated load (mechanical power0	100 kW
Rated DC supply voltage	500 V
Rotor damping parameterization	By no-load current
Mechanical rotor inertia	0.01 g-cm2
Initial rotor speed	0 rpm
Armature winding open circuit faults	Not enabled

Table 15. Other parameters of the DC Motor block in SIMULINK.

 

• The positive terminal of the DC Motor is connected to current sensor and the description of the current sensor block is as follows:

CURRENT SENSOR: The Current Sensor block represents an ideal current sensor, that is, a device that converts current measured in any electrical branch into a physical signal proportional to the current. Connections + and – are electrical conserving ports through which the sensor is inserted into the circuit. Connection I is a physical signal port that outputs the measurement result.

Representation:

Figure 38. Representation of Current sensor block in SIMULINK.

 

• The description of different ports of the Current sensor block is as follows:

PORT	DESCRIPTION	VALUE/CONNECTION
(+) - CONSERVING	Electrical conserving port associated with the sensor positive terminal.	Connected to a positive terminal of the H bridge
(-) - CONSERVING	Electrical conserving port associated with the sensor negative terminal.	Connected to the positive terminal of DC Motor
(I) - OUTPUT	Physical signal output port for current.	Connected to the Controlled current source in the battery subsystem and to the scope using PS-Simulink converter.

Table 16. Ports of Current sensor block in SIMULINK.

 

• The power converted employed in this electric vehicle model is a H-bridge. The H-bridge block is described as follows:

H-BRIDGE BLOCK: [13] The H-Bridge block represents an H-bridge motor driver. The block has the following two Simulation mode options:

PWM — The H-Bridge block output is a controlled voltage that depends on the input signal at the PWM port. If the input signal has a value greater than the Enable threshold voltage parameter value, the H-Bridge block output is on and has a value equal to the value of the Output voltage amplitude parameter. If it has a value less than the Enable threshold voltage parameter value, the block maintains the load circuit using one of the following three Freewheeling mode options:

• Via one semiconductor switch and one freewheeling diode
• Via two freewheeling diodes
• Via two semiconductor switches and one freewheeling diode

The first and third options are sometimes referred to as synchronous operation. The signal at the REV port determines the polarity of the output. If the value of the signal at the REV port is less than the value of the Reverse threshold voltage parameter, the output has positive polarity; otherwise, it has negative polarity. Averaged — This mode has two Load current characteristics options:

• Smoothed
• Unsmoothed or discontinuous

The current will be smooth if the PWM frequency is large enough. Synchronous operation where freewheeling is via a bridge arm back to the supply also helps smooth the current. For cases where the current is not smooth, or possibly discontinuous (that is, it goes to zero between PWM cycles), use the Unsmoothed or discontinuous option. For this option, the user must also provide values for the Total load series resistance, Total load series inductance, and PWM frequency. During simulation, the block uses these values to calculate a more accurate value for H-bridge output voltage that achieves the same average current as would be present if simulating in PWM mode.

Set the Simulation mode parameter to Averaged to speed up simulations when driving the H-Bridge block with a Controlled PWM Voltage block. One must also set the Simulation mode parameter of the Controlled PWM Voltage block to Averaged mode. This applies the average of the demanded PWM voltage to the motor. The accuracy of the Averaged mode simulation results relies on the validity of the made assumption about the load current. If specified that the current is Unsmoothed or discontinuous, then the accuracy also depends on the values provided for load resistance and inductance being representative. This mode also makes some simplifying assumptions about the underlying equations for the case when current is discontinuous. For typical motor and bridge parameters, accuracy should be within a few percent. To verify Averaged mode accuracy, run the simulation using the PWM mode and compare the results to those obtained from using the Averaged mode.

Braking mode is invoked when the voltage presented at the BRK port is larger than the Braking threshold voltage. Regardless of whether in PWM or Averaged mode, when in braking mode the H-bridge is modeled by a series combination of two resistances R1 and R2 where:

• R₁ is the resistance of a single bridge arm, that is, half the value of the Total bridge on resistance parameter.
• R₂ is the resistance of a single bridge arm in parallel with a diode resistance, that is, R₂ = R₁ R_d / ( R₁ + R_d ), where R_d is the diode resistance.

To model the demands placed on the DC supply, you can choose to expose the power supply ports of the H-Bridge block by setting the Power supply parameter to External. If the power supply ports are exposed, then only PWM simulation mode is supported.

Representation:

Figure 39. Representation of H-Bridge block in SIMULINK.

 

• The description of different ports of the H-bridge block is as follows:

PORT	DESCRIPTION	VALUE/CONNECTION
Positive load connection port (+) - CONSERVING	Electrical conserving port associated with the positive load connection.	Connected to the positive terminal of the current sensor.
Negative load connection port  (-) - CONSERVING	Electrical conserving port associated with the negative load connection.	Connected to the negative terminal of the DC motor and electrical reference.
Pulse Width Modulated signal (PWM) – CONSERVING	Electrical conserving port associated with the pulse-width modulated signal. The voltage is defined relative to the REF port.	Connected to the PWM port of the Controlled PWM voltage block.
Reference (REF) – CONSERVING	Electrical conserving port associated with the floating zero volt reference.	Connected to the REF port of the Controlled PWM Voltage block and in turn to the negative terminal of the Controlled Voltage source 2 block.
REV (REV) – CONSERVING	Electrical conserving port associated with the voltage that controls when to reverse the polarity of the H-Bridge block output. The voltage is defined relative to the REF port.	Connected to the ‘ref-‘ port of the Controlled PWM Voltage block and in turn to negative terminals of Controlled Voltage source 1 block and Controlled Voltage source 2 block.
BRK (BRK) – CONSERVING	Electrical conserving port associated with the voltage that controls when to short circuit the H-Bridge block output. The voltage is defined relative to the REF port.	Connected to the positive terminal of the Controlled Voltage source 2 block.
THERMAL (H)	Thermal port	Not applicable.
Positive supply connection (V+) - CONSERVING	Electrical conserving port associated with the positive electrical supply connection.	Not applicable.
Negative supply connection (V-) - CONSERVING	Electrical conserving port associated with the negative electrical supply connection.	Not applicable.

Table 17. Ports of H-bridge block in SIMULINK.

 

• The other values of the input for the H-bridge block are as follows:

Parameter	Value
Power supply	Internal
Simulation mode	Averaged
Regenerative Braking	Always enabled (suitable for linearization)
Load current characteristics	Smoothed
Enabled threshold voltage	2.5 V
PWM Signal amplitude	5 V
Reverse threshold voltage	2.5 V
Braking threshold voltage	2.5 V
Bridge Output Voltage amplitude	500 V
Total bridge on resistance	0.1 ohm
Freewheeling diode on resistance	0.05 ohm

Table 18. Other parameters of the H-Bridge block in SIMULINK.

 

• The Controlled PWM voltage source is connected to the PWM port of the H-bridge. The description of the Controlled PWM voltage source is as follows:

CONTROLLED PWM VOLTAGE BLOCK: [14] The Controlled PWM Voltage block represents a pulse-width modulated (PWM) voltage source. The block has two modeling variants, accessible by right-clicking the block in your block diagram and then selecting the appropriate option from the context menu, under Simscape -Block choices:

• Electrical input ports — The block calculates the duty cycle based on the reference voltage across its ref+ and ref- ports. This modeling variant is the default.
• PS input — Specify the duty cycle value directly by using an input physical signal port.

Assumptions and limitations:

• The REF output of this block is floating, it is not tied to the Electrical Reference. One consequence of this is that if one connects the PWM and REF electrical ports directly to the PWM and REF electrical ports of an H-bridge or a gate driver, the user must attach an Electrical Reference block to the REF connection line.
• Do not connect the Controlled PWM block directly to a semiconductor gate, because this omits the gate driver output impedance that determines switching dynamics. Use a Gate Driver or a Half-Bridge Driver block to set the gate-source or the gate-emitter voltage.
• Do not use the Controlled PWM block to drive a motor block directly. A PWM motor driver goes open circuit in between pulses. Use the H-Bridge block to drive a motor block.
• When driving a motor via the H-Bridge block, set the Simulation mode parameter to Averaged to speed up simulations. One must also set the Simulation mode parameter of the H-Bridge block to Averaged mode. This applies the average of the demanded PWM voltage to the motor. The Averaged mode assumes that the impedance of the motor inductive term is small at the PWM frequency. To verify this assumption, run the simulation using the PWM mode and compare the results to those obtained from using the Averaged mode.
• If the model is linearizing model, set the Simulation mode parameter to Averaged and ensure the specified operating point of the block correctly. One can only linearize the block for inputs corresponding to a duty cycle greater than zero and less than 100 percent.

Representation:

Figure 40. Representation of Controlled PWM Voltage block in SIMULINK.

 

• The description of different ports of the Controlled PWM Voltage block is as follows:

PORT	DESCRIPTION	VALUE/CONNECTION
Positive terminal (ref+) - CONSERVING	Positive electrical reference voltage.	Connected to the positive terminal of the Controlled Voltage source 1 block.
Negative terminal  (ref-) - CONSERVING	Negative electrical reference voltage	Connected to REV port of H0bridge and negative terminal of Controlled Voltage source 1 block.
Pulse Width Modulated signal (PWM) – CONSERVING	Electrical conserving port associated with the pulse-width modulated signal.	Connected to PWM port of H-bridge.
Floating zero volt reference (REF) – CONSERVING	Electrical conserving port associated with the floating zero volt reference.	Connected to the REF port of the H-bridge and negative terminal of Controlled Voltage Source 2 block.
Control signal, unitless (u) -INPUT	Input physical signal that specifies the duty cycle.	Not applicable.

Table 19. Ports of Controlled PWM Voltage block in SIMULINK.

• The other values of the input for the Controlled PWM Voltage block are as follows:

Parameter	Value
PWM frequency	1000 Hz
Simulation mode	Averaged
Input voltage for 0% duty cycle	0 V
Input voltage for 100% duty cycle	5 V
Output Voltage amplitude	500 V

Table 20. Other parameters of the Controlled PWM Voltage block in SIMULINK.

 

• Controlled Voltage sources are used to maintain the constant value of the voltage while feeding the voltage to the Controlled PWM voltage source and to the BRK port of the H-bridge. The functions performed by the two blocks depend on the voltage of the signal received. The description of the Controlled Voltage source blocks is as follows:

CONTROLLED VOLTAGE SOURCE BLOCK: [15] The Controlled Voltage Source block represents an ideal voltage source that is powerful enough to maintain the specified voltage at its output regardless of the current flowing through the source. The output voltage is V = Vs, where Vs is the numerical value presented at the physical signal port.

Representation:

Figure 41. Representation of Controlled Voltage Source block in SIMULINK.

 

• The description of different ports of the Controlled Voltage Source block is as follows:

PORT	DESCRIPTION	VALUE/CONNECTION
(+) - CONSERVING	Electrical conserving port with the sensor positive terminal.	Connected to a positive terminal of the H bridge
(-) - CONSERVING	Electrical conserving port with the sensor negative terminal.	Connected to the positive terminal of DC Motor
(I) - OUTPUT	Physical signal output port for current.	Connected to AccelCmd and DeccelCmd ports of longitudinal driver block.

Table 21. Ports of Controlled Voltage source block in SIMULINK.

 

• Therefore, the layout of the electrical subsystem is as follows:

Figure 42. Representation of Electrical Subsystem in SIMULINK.

 

BATTERY SUBSYSTEM:

• The lifeline of the Electric Vehicle is the perfect and long-lasting battery system. The battery subsystem in the present model uses a single battery of high voltage. In reality, the batteries of lower voltages are arranged in series and in parallel to result in large voltage input to the electric motor.
• The battery in the model uses a battery block which is described as follows:

BATTERY BLOCK: [16] The Battery block represents a simple battery model. The block has four modeling variants, accessible by right-clicking the block in block diagram and then selecting the appropriate option from the context menu.

• Uninstrumented | No thermal port — Basic model that does not output battery charge level or simulate thermal effects. This modeling variant is the default.
• Uninstrumented | Show thermal port — Model with exposed thermal port. This model does not measure internal charge level of the battery.
• Instrumented | No thermal port — Model with exposed charge output port. This model does not simulate thermal effects.
• Instrumented | Show thermal port — Model that lets the user measure internal charge level of the battery and simulate thermal effects. Both the thermal port and the charge output port are exposed.

If the user selects Infinite for the Battery charge capacity parameter, the block models the battery as a series resistor and a constant voltage source. If one selects Finite for the Battery charge capacity parameter, the block models the battery as a series resistor and a charge-dependent voltage source. In the finite case, the voltage is a function of charge and has the following relationship:

where:

SOC (state-of-charge) is the ratio of current charge to rated battery capacity. V₀ is the voltage when the battery is fully charged at no load, as defined by the Nominal voltage, V_nom parameter. β is a constant that is calculated so that the battery voltage is V1 when the charge is AH1. Specify the voltage V1 and ampere-hour rating AH1 using block parameters. AH1 is the charge when the no-load (open-circuit) voltage is V1, and V1 is less than the nominal voltage.

The equation defines an approximate relationship between voltage and remaining charge. This approximation replicates the increasing rate of voltage drop at low charge values and ensures that the battery voltage becomes zero when the charge level is zero. The advantage of this model is that it requires few parameters, which are readily available on most datasheets.

Representation:

Figure 43. Representation of battery block in SIMULINK.

 

• The description of different ports of the differential block is as follows:

PORT	DESCRIPTION	VALUE/CONNECTION
Positive terminal (+) - CONSERVING	Electrical conserving port associated with the battery positive terminal.	Connected to the electric port of the Controlled Current source.
Negative terminal (-) - CONSERVING	Electrical conserving port associated with the battery negative terminal.	Connected to the electric port of the Controlled current source and also to the electrical reference.
Battery charge level (q) (C) - OUTPUT	Use this output port to change load behavior as a function of charge, without the complexity of building a charge state estimator.	Not applicable.
Battery thermal Mass (H) – CONSERVING	When this port is exposed, provide additional parameters to define battery behavior at a second temperature.	Not applicable.

Table 22.  Ports of Battery block in SIMULINK.

  

• The other values of the input for the Battery block are as follows:

Parameter	Value
Nominal Voltage	500 V
Current directionality	Disabled
Internal resistance	1 ohm
Battery charge capacity	Infinite
Open-circuit measurement temperature	298.15 K
Charge dynamics	Not employed
Variables	Not employed

Table 23. Other parameters of the Battery block in SIMULINK.

 

• The positive terminal of the battery is connected to the Controlled Current source block that receives a physical current signal from the current sensor block located in the Electrical subsystem. The description of the Controlled Current Source block is as follows:

CONTROLLED CURRENT SENSOR BLOCK: [17] The Controlled Current Source block represents an ideal current source that is powerful enough to maintain the specified current through it regardless of the voltage across the source. The output current is I = I_s, where I_s is the numerical value presented at the physical signal port. The positive direction of the current flow is indicated by the arrow.

Representation:

Figure 44. Representation of Controlled Current Source block in SIMULINK.

 

• The description of different ports of Controlled Current Source block is as follows:

PORT	DESCRIPTION	VALUE/CONNECTION
Positive terminal (+) - CONSERVING	Electrical conserving port associated with the battery positive terminal.	Connected to the positive terminal of the battery
Negative terminal (-) - CONSERVING	Electrical conserving port associated with the battery negative terminal.	Connected to the battery negative terminal  source and also to the electrical reference.
Physical Signal (arrow head symbol) - OUTPUT	Physical signal input port is used to accept the signal in appropriate format.	Connected to the Current sensor from the Electrical Subsystem.

Table 24.  Ports of Controlled Current Source block in SIMULINK.

• In this case, the battery is assumed to provide 50Ah.This value is useful in the calculation of the Sate of Charge of the battery system employed to run the electric vehicle.
• In this model, battery block which implements a generic dynamic model that represents most popular types of rechargeable batteries could be used. That directly gives the SOC. In this model, the SOC is calculated using few blocks. This method is employed to gain more interaction with different blocks in Simulink.
• To find the value of SOC, the following arrangement is made:

Figure 45. Schematic representation of blocks to calculate SOC in SIMULINK.

 

• The block named Rate Transition is used to take input from the current input from the current sensor located in the Electrical subsystem. The current signal is a physical signal and Rate transition bock is a Simulink, therefore, a PS to Simulink converter is used. The description of the Rate Transition block is as follows:

RATE TRANSITION BLOCK: [18] The Rate Transition block transfers data from the output of a block operating at one rate to the input of a block operating at a different rate. Use the block parameters to trade data integrity and deterministic transfer for faster response or lower memory requirements.

Representation:

Figure 46. Representation of Rate Transition block in SIMULINK.

  

• The description of different ports of the Rate Transition block is as follows:

PORT	DESCRIPTION	VALUE/CONNECTION
Port_1 - INPUT	Input signal to transition to a new sample rate, specified as a scalar, vector, matrix, or N-D array.	Connected to the converted signal from Current sensor using PS-Simulink converter
Port_1 - OUTPUT	Output signal is the input signal converted to the sample rate you specify. The default configuration ensures safe and deterministic data transfer.	Connected to the gain block.

Table 25.  Ports of Rate Transition block in SIMULINK.

 

• The other values of the input for the Rate Transition block are as follows:

Parameter	Value
Ensuring data integrity during data transfer	ON
Ensuring deterministic data transfer (maximum delay)	ON
Initial conditions	0
Specified output port sample time	-1

Table 26. Other parameters of the Rate Transition block in SIMULINK.

 

• The Gain block is used to perform mathematical calculation on the input signal using Ah produced by the battery considered in the EV model. The following is the description of the Gain block:

GAIN BLOCK: [19] The Gain block multiplies the input by a constant value (gain). The input and the gain can each be a scalar, vector, or matrix. One can specify the value of gain in the Gain parameter. The Multiplication parameter lets you specify element-wise or matrix multiplication. For matrix multiplication, this parameter also lets the user indicate the order of the multiplicands. Gain is converted from doubles to the data type specified in the block mask offline using round-to-nearest and saturation. The input and gain are then multiplied, and the result is converted to the output data type using the specified rounding and overflow modes.

Representation:

Figure 47. Representation of Gain block in SIMULINK.

  

• The description of different ports of the Gain block is as follows:

PORT	DESCRIPTION	VALUE/CONNECTION
Port_1 - INPUT	The Gain block accepts real or complex-valued scalar, vector, or matrix input. The Gain block supports fixed-point data types. If the input of the Gain block is real and gain is complex, the output is complex.	Connected to the Rate Transition block output port.
Port_1 , Input multiplied by gain - OUTPUT	The Gain block outputs the input multiplied by a constant gain value. When the input to the Gain block is real and gain is complex, the output is complex.	Connected to the Discrete time integrator block.

Table 27.  Ports of Gain block in SIMULINK.

 

• The input signal from the Rate Transition block is multiplied by battery’s Ah in terms of A in seconds. The other values of the input for the Gain block are as follows:

Parameter	Value
Gain	1/(50*3600)
Multiplication	Element wise (k.*u)
Signal attributes	Unaltered default values
Parameter attributes	Unaltered default values

Table 28. Other parameters of the Gain block in SIMULINK.

 

• The Gain block’s output i.e., the multiplied input current signal is then subjected to integration in discrete time integrator. The description of the Discrete Time Integrator block is as follows:

DISCRETE TIME INTEGRATOR BLOCK: [20] The Discrete-Time Integrator block is used in place of the Integrator block to create a purely discrete model. With the Discrete-Time Integrator block, the user can define initial conditions on the block dialog box or as input to the block, define an input gain (K) value, output the block state, define upper and lower limits on the integral and reset the state with an additional reset input.

Representation:

Figure 48. Representation of Discrete Time Integrator block in SIMULINK.

 

• The description of different ports of the Discrete Time Integrator block is as follows:

 

PORT	DESCRIPTION	VALUE/CONNECTION
Port_1 - INPUT	Input signal, specified as a scalar, vector, or matrix	Connected to the Gain block to receive multiplied signal.
Initial conditions of state (IC)- INPUT	Initial conditions of the states, specified as a finite scalar, vector, or matrix.	Not applicable.
Port_1 - Discrete time integration or accumulation of input -OUTPUT	Discrete-time integration or accumulation of the input signal, specified as a scalar, vector, or matrix.	Connected to the Add block to get the output subtracted from a constant block bearing value 1.
Port_2 – Saturation OUTPUT	Signal indicating when the state is being limited, specified as a scalar, vector, or matrix. The signal has one of three values: 1 indicates that the upper limit is being applied. 0 indicates that the integral is not limited. -1 indicates that the lower limit is being applied.	Not applicable.
Port_3 – State OUTPUT	Block states, output as a scalar, vector, or matrix. By default, the block adds this port to the top of the block icon. Use the state port when:   The output of the block is fed back into the block through the reset port or the initial condition port, causing an algebraic loop.	Not applicable.

Table 29.  Ports of Discrete Time Integrator block in SIMULINK.

 

• The other values of the input for the Discrete Time Integrator block are as follows:

Parameter	Value
Integrator Method	Forward Euler
Gain value	1.0
External reset	None
Initial condition source	Internal
Initial condition	0
Initial condition setting	Auto
Sample time (-1 for inherited)	-1
Limit output	NO
Signal attributes	Remained unchanged from default
State attributes	Remained unchanged from default

Table 30. Other parameters of the Discrete Time Integrator block in SIMULINK.

 

• The output from the add block, which subtracts the signal value from the discrete time integrator from the value borne by the constant block, which is 1, to calculate the SOC that is achieved in the cycle for given run time. The result is displayed in the display block and the variation of the SOC from the start to the end of the simulation is captured in scope block.
• Therefore, the layout of the battery subsystem is as follows:

 

Figure 49. Schematic representation of Battery Subsystem in SIMULINK.

 

  

DRIVING SUBSYSTEM

 

• The driving system is the virtual segment of the real time driving scenario that incorporates the driver who responds to the real time traffic scenarios and gives the appropriate inputs. The decision of acting on the acceleration and braking depends on the driver and the driving conditions.
• To mimic these realistic responses, longitudinal driver block is chosen. The description of the Longitudinal Driver block is as follows:

LONGITUDINAL DRIVER BLOCK: [21] The Longitudinal Driver block implements a longitudinal speed-tracking controller. Based on reference and feedback velocities, the block generates normalized acceleration and braking commands that can vary from 0 through 1. You can use the block to model the dynamic response of a driver or to generate the commands necessary to track a longitudinal drive cycle. Use the The External Actions parameters are used to create input ports for signals that can disable, hold, or override the closed-loop acceleration or deceleration commands. The block uses this priority order for the input commands: disable (highest), hold, override. The control type i.e., cntrlType parameter to specify options that are available to produce necessary control actions. The Proportional-integral (PI) controls with tracking windup and feed-forward gains. The shift type parameter ‘none’ is used which indicates no transmission. Block outputs a constant gear of 1. This setting is used to minimize the number of parameters the user needs to generate acceleration and braking commands to track forward vehicle motion. This setting does not allow reverse vehicle motion.

Representation:

Figure 50. Representation of Longitudinal driver block in SIMULINK.

 

• The description of different ports of the Longitudinal driver block is as follows:

PORT	DESCRIPTION	VALUE/CONNECTION
Reference Vehicle Velocity (VelRef) - INPUT	Reference velocity, vref, in m/s.	Connected to the Drive Cycle Source block.
Longitudinal Vehicle Velocity (VelFdbk)- INPUT	Longitudinal vehicle velocity, U, in the vehicle-fixed frame, in m/s.	Connected to the Actual Velocity output from Vehicle body block in Driver subsystem
Road Grade Angle (Grade) -INPUT	Road grade angle, θ or γ, in deg.	Connected to a constant bearing the value of 0.0698132.
Enable Acceleration Command Overdrive (EnblAccelOvr) - INPUT	Enable acceleration command override.	Not applicable.
Acceleration Overdrive Command (AccelOvrCmd) - INPUT	Acceleration override command, normalized from 0 through 1.	Not applicable.
Acceleration Hold (AccelHld) - INPUT	Boolean signal that holds the acceleration command at the current value.	Not applicable.
Disable Acceleration Command (AccelZero) – INPUT	Disable acceleration command.	Not applicable.
Enable Deccelerration Command Overdrive (EnblDecelOvr) – INPUT	Enable deceleration command override.	Not applicable.
Deceleration Overdrive Command (DecelOvrCmd) -INPUT	Deceleration override command, normalized from 0 through 1.	Not applicable.
Deceleration Hold (DecelHld) - INPUT	Boolean signal that holds the deceleration command at the current value.	Not applicable.
Disable Deceleration Command (DecelZero) - INPUT	Disable deceleration command.	Not applicable.
Gear (ExtGear) -INPUT	Park : 80 Reverse : -1 Neutral : 0 Drive : 1 Gear: Gear number	Not applicable.
Commanded Vehicle Acceleration (AccelCmd) -OUTPUT	Commanded vehicle acceleration, yacc, normalized from 0 through 1.	Connected to the physical signal port of Controlled Voltage source 1 block in Electrical subsystem through  Simulink – PS converter.
Bus Signal (Info) -OUTPUT	Bus signal containing these block calculations: Accel, Decel, Gear, Clutch, Err, ErrSqrSum, ErrMax, ErrMin, ExtActions.	This is connected to a Bus Signal and then to two scopes that represent acceleration and deceleration of the vehicle.
Commanded Vehicle Deceleration (DecelCmd) - OUTPUT	Commanded vehicle deceleration, ydec, normalized from 0 through 1.	Connected to the physical signal port of Controlled Voltage source 2 block in Electrical subsystem through  Simulink – PS converter.
Commanded Vehicle Gear (GearCmd) -OUTPUT	Integer value of commanded vehicle gear: Park : 80 Reverse : -1 Neutral : 0 Drive : 1 Gear: Gear number	Not applicable.

Table 31.  Ports of Longitudinal Driver block in SIMULINK.

 

• The other values of the input for the Longitudinal Driver block are as follows:

Parameter	Value
External Actions	None
Control Type	PI
Shift Type	None
Reference and feedback units (Velocity)	m/s
Output gear signal	Not applied
Nominal Proportional Gain Kp	15
Integral Gain Ki	1
Velocity feed-forward Kff	0.05
Grade angle feed-forward Kg	0.01 degree-1
Nominal speed Vnom	100
Anti-windup Kaw	0.1
Error Filter time constant tauerr	0.03 sec

Table 32. Other parameters of the Discrete Time Integrator block in SIMULINK.

• The drive cycle is given as an input to the longitudinal driver. Therefore, a block named Drive Cycle source is used to fulfill this purpose. The description of the Drive Cycle Source block is as follows:

DRIVE CYCLE SOURCE BLOCK: [22] The Drive Cycle Source block generates a standard or user-specified longitudinal drive cycle. The block output is the specified vehicle longitudinal speed, which you can use to:

• Predict the engine torque and fuel consumption that a vehicle requires to achieve desired speed and acceleration for a given gear shift reference.
• Produce realistic velocity and shift references for closed loop acceleration and braking commands for vehicle control and plant models.
• Study, tune, and optimize vehicle control, system performance, and system robustness over multiple drive cycles.

Identify the faults within tolerances specified by standardized tests, including:

• EPA dynamometer driving schedules
• Worldwide Harmonised Light Vehicle Test Procedure (WLTP) laboratory tests

For the drive cycles, the user can:

• Drive cycles from predefined sources. By default, the block includes the FTP–75 drive cycle. To install additional drive cycles from a support package, see Install Drive Cycle Data. The support package has drive cycles that include the gear shift schedules, for example JC08 and CUEDC.
• Workspace variables that define your own drive cycles.
• .mat, .xls, .xlsx, or .txt files.
• Wide open throttle (WOT) parameters, including initial and nominal reference speed, deceleration start time, and final reference speed.

Representation:

Figure 51. Representation of Drive Cycle Source block in SIMULINK.

  

• The description of different ports of the Drive Cycle Source block is as follows:

PORT	DESCRIPTION	VALUE/CONNECTION
Vehicle Reference Speed (RefSpd) - OUTPUT	Vehicle reference speed, in units that you specify. To specify the units, use the Output velocity units parameter.	Connected to the ‘VelRef’ port of the Longitudinal Driver.
Vehicle reference Acceleration (RefAcc)- OUTPUT	To calculate the acceleration, the block implements Savitzky-Golay differentiation using a second-order polynomial with a three-sample point filter.	Not applicable.
Vehicle Gear (Gear) -OUTPUT	To enable this port: Specify a drive cycle that contains a gear shift schedule. You can use: o   A support package to install standard drive cycles that include the gear shift schedules, for example JC08 and CUEDC. o   Workspace variables. o   .mat, .xls, .xlsx, or .txt files. Select Output gear shift data.	Not applicable.
Bus Signal  (Info) - OUTPUT	Bus signal containing these block calculations: Reference Speed, Reference Accel, Gear, Fault.	Not applicable.
Vehicle Longitudinal Speed (VelFdbk) - INPUT	Longitudinal vehicle speed.	Not applicable.

Table 33.  Ports of Drive Cycle Source block in SIMULINK.

 

• The other values of the input for the Drive Cycle Source block are as follows:

Parameter	Value
Drive Cycle Source	FTP75
Output Velocity units	m/s
Output sample period dt	0 sec
Fault tracking	disabled

Table 34. Other parameters of the Discrete Time Integrator block in SIMULINK.

• The layout of the Driving system is as follows:

Figure 52. Schematic representation of Driving subsystem in SIMULINK.

 

• A Goto block is created to capture the velocity from the drive cycle i.e., reference velocity. The Goto block is named Drivecycle_velocity and its tag visibility is set to global.
• The output velocity from the Vehicle body in the Vehicle Subsystem and the Drivecycle velocity from the Goto block are collected in the Output Subsystem as follows:

Figure 53. Schematic representation of Output subsystem in SIMULINK.

 

• The actual velocity and the drive cycle velocity are collected in the same scope block to understand the variations. A Goto block is connected to the actual velocity and is used to calculate aerodynamic drag.
• The output velocity from the vehicle body is in ‘m/s’ and therefore to obtain the distance travelled by the vehicle for given time of simulation, the integrator is connected to the actual velocity. Display block is connected to show the numerical value of the distance travelled.
• Apart from the velocity calculations, the various forces that act on the vehicle are also calculated. The formulae used to calculate the aerodynamic drag, rolling resistance force and hill climbing force are mentioned in the earlier section. The product block is used for multiplying the values, the block add is used to add the values.
• The sum of aerodynamic drag force, rolling resistance force and hill climbing force yields the total force required by the vehicle to move. On multiplying this force with the velocity yields the power required to run the vehicle.
• The values of forces and power are thoroughly understood by connecting them to the scope.
• Therefore, the total layout of the model of an Electric Vehicle is as follows:

 

Figure 54. Schematic representation of model of an EV in SIMULINK.

•  By setting the simulation time to 2474 sec, which is suggested under the drive cycle FTP75, the results are obtained and are detailed in the next section titled ‘Results’.

 

RESULTS

• On setting the simulation time to 2474 sec, the model of an Electric Vehicle is calculated and simulated. The electric vehicle is assumed to run on the drive cycle FTP75 with PI control system which doesn’t produce the effect of reverse gearing. The entire vehicle is assumed to weigh 900 kg (kerb weight). The road angle is maintained at 4^o taken in radians. The following is the layout of the variation of the actual velocity obtained from the vehicle body block in Vehicle subsystem and the drive cycle velocity which is the reference velocity obtained from the Drive cycle source block in the Driving subsystem:

Figure 55. Schematic representation of variation of actual velocity and drive cycle velocity.

The blue curve represents actual velocity whereas the yellow curve represents the drive cycle velocity. It can be observed that the drive cycle FTP75 is valid till 1367 sec and then it takes 622 seconds approximately to recur. These velocities have same units i.e. m/s.

Figure 56. Exaggerated view of variation of velocities.

The variation of the velocity is almost miniscule which is a desirable effect while manufacturing a vehicle. The global maximum value of the drive cycle velocity is recorded as 25.347 m/s in 239.995 sec from the start whereas, the global maximum velocity obtained by the vehicle body is 25.335 m/s in 239.995 sec. The drive cycle velocity is 0.012 m/s greater than the actual velocity. This is due the fact of occurrence of friction and resistive force along with miscellaneous quantities that effect the velocity of the vehicle.  The superimposition of the two curves is very close due to the close tolerances. The variation is extremely small and can be ignored as shown in the figure 56.

On the whole, the variation of the velocity observed in the present model is suitable for manufacturing.

 

• From the figure shown below, the total distance travelled by the vehicle for the time period of 2474 sec is shown below:

Figure 57. Representation of the total distance travelled by the electric vehicle in 2474 sec.

It can be observed that the vehicle was capable of running for 17.77 km for 2474 sec. The actual velocity shown in the figure 57 is the velocity at the end of the drive cycle. The average speed cannot be calculated using the formula of the ratio of total distance over total time as the result achieved are a part of the drive cycle and the drive cycle is at rest for certain amount of time in the simulation.

 

• The acceleration and the deceleration of the vehicle can be identified by the scope in the driving subsystem. The scope details on the variation of acceleration and deceleration during the entire drive cycle. The following figures shows the variation of the acceleration and deceleration of the electric vehicle that runs on FTP75 drive cycle for 2474 sec:

Figure 58. Representation of the variation of the acceleration and deceleration of the EV.

From the figure 58, the yellow curve indicated the acceleration of the vehicle and the blue curve represents the deceleration of the vehicle. It can be observed that the deceleration spikes at random time intervals where as the acceleration varies in the close range. Sudden spikes are not observed in the acceleration curve as they are observed in the deceleration curve. The global maximum acceleration of the vehicle is observed at 277.511 sec from the start and its value is 0.0415 m/s². While the deceleration is highest at 552.011 sec from the start at a value of 0.0452 m/s2. In the present scenario, the value of the highest acceleration is less than the value of deceleration. It can also be observed that in 1.455 seconds the deceleration reaches it maximum value and returns to the state zero starting from zero.

Mathematical calculation of the braking distance:

deceleration = 0.0452 m/s²

Actual velocity of the vehicle at 551.974 sec = 0.381 m/s

To calculate the stopping time, the following formula is incorporated:

 

Therefore, the stopping time is 8.43 sec.

Assuming that the driver’s delay in acting is 1 sec, total reaction time is 9.43 sec.

To calculate the distance travelled by the vehicle to halt is:

Where g is the grade (decimal) and is positive for uphill and negative for downhill and f is the average friction factor which is 0.6 for the dry surface and 0.3 for wet surface and g is the acceleration due to gravity i.e., 9.81 m/s².

Assuming that the vehicle moves uphill at 4^o  which is 0.0698132 and the surface is dry therefore the average friction factor is 0.6, and since the final velocity is considered to be zero due to the effect of braking, the braking distance is calculated as:

  

Therefore, the braking system can produce the braking distance of 0.011 m in a time interval of 9.43 sec.

Although the distance calculations are not presented in Simulink, but it is safe to assume from the mathematical calculations, that the braking system of car is very good and passenger safe. In reality, this might not be possible to bring the vehicle to stop in 1.1 cm.

 

 

• The variation of the State of Charge of the battery is depicted in the following curve plotted by the scope block in the Battery subsystem:

Figure 59. Representation of the variation of the SOC of the battery of the  EV.

From the above figure, it can be noted that the value of the SOC at the end of the 2474 sec of simulation is at 0.1664 which is a low value. Ideally, the SOC must not be maintained below 20%. In the working EVs, once the SOC hits the vehicle designed least value of SOC, the battery stops functioning and the vehicle may stop altogether indicating the user to recharge the battery. In case of HEV, the propulsion shifts to IC engine where a part of the power generated is redirected to charging the vehicle which is commonly termed as regenerative braking. Since, the present model is an EV, it is advisable to set the least value of SOC to 30% which is observed nearly at 2104.229 sec from the start of the vehicle. Therefore, the vehicle will run for 2105 sec without any issue with the battery and the power producing system.

In this model, the if the least threshold SOC is to be set, it is advisable to be set at 30%.  Based on the set SOC value, the vehicle is assumed to run about 13.08 km for 2015 sec.

 

 

• In the electrical subsystem, the PWM port of the H-bridge is connected to the PWM port of the Controlled PWM voltage block. This ensures the regenerative braking in the electrical vehicle. But this model does not produce regenerative braking as it is dependent on the type of the longitudinal driver selected. The output from the power converter H-Bridge is passed through a current sensor. The current sensor converts current measured in the electrical branch joining the power converter H-bridge and the electric permanent magnet type DC Motor, into a physical signal proportional to the current. The physical signal output from the current sensor dictates the battery output. The battery takes the input from the current sensor through a controlled current source which maintains a specified value of current irrespective of the voltage in the system. As a result, the battery discharges based on the requirement of the power generated as produced by the drive cycle whose inputs are given to the electrical subsystem. The variation of the current as observed in the current sensor which is the input to the DC motor is as follows:

Figure 59. Representation of the variation of the current in the Current Sensor.

The variation of the current through the current sensor is observed in the figure 59 and it can be concluded that the variation in the current is almost periodic. Initially, the value of the current at 0 sec is 6.981 nA which is almost 0 A. The global maximum value of the current is observed at 568.116 sec bearing a value of 189.986 A and the global minimum value of the current is -48.611 A which occurs at 612.093 sec from the start. At the global  maximum velocity, the value of SOC is 80.15 % and the value of SOC at global minimum current is 78.18 %.

 

 

• The output subsystem not only defines the variation of the actual velocity with respect to the reference theoretical velocity but also details the values of the forces that collectively act on the vehicle. The aerodynamic drag force that acts on the vehicle is calculate based on the general formula mentioned in the previous section. To calculate the aerodynamic drag force, the actual velocity is used that varies throughout the simulation time. Therefore, the variation of the aerodynamic drag is studied with the help of the scope block as shown below:

Figure 60. Representation of the variation of Aerodynamic Drag Force on EV.

The global maxima of the Aerodynamic drag occurs at 239.995 sec with the value of 109.8kN. The global minima occurs at maximum actual velocity which is 25.335 m/s. This is a clear indication that the aerodynamic drag is proportional to the square of the velocity of the body i.e., electric vehicle. The minimum velocity is 0 m/s and hence the least value of the aerodynamic drag is also 0 N. the value of Rolling resistance force is constant and takes the value of 44.15 N. similarly, the hill climbing force is 615.9 N. Therefore, the total maximum force acting on the vehicle is given as follows:

 

Therefore, the maximum total force acting on the vehicle is 110.46 kN and the minimum value of the total force is 660 N which occurs in the absence of aerodynamic force. The total force in Simulink is not a constant value as the value of the aerodynamic drag force keeps changing with the velocity of the vehicle. Hence, the plot of the total force is as follows:

Figure 61. Representation of the variation of Total Force on EV.

The maximum value of the total force is 110.4 kN and it occurs at 240.293 sec from the start of the simulation. Since the minimum value of actual velocity is zero, the aerodynamic force becomes zero when velocity is minimum. In those cases, only two forces act on the vehicle which are rolling resistance force and hill climbing force. Therefore, the total force in such circumstances is 660 N. On clear observation, it is evident that the dominant contributing force to the total force is the aerodynamic drag force and therefore, the variation of the total force is similar to the variation of the aerodynamic drag force. The power required to run the vehicle is obtained by multiplying the total force acting on the vehicle with the actual velocity of the vehicle. The following is the variation of the power of the vehicle working on FTP75 drive cycle:

Figure 62. Representation of the variation of Power on EV.

The maximum value of the power is 2.798 MW which occurs at 240.665 sec from the start. This is because, the value of the total is maximum at that point and so is the velocity. The minimum value of the power required to run the vehicle is 0W since the actual velocity obtains the value of 0 m/s at certain points in the drive cycle. Once the vehicle hits the value of 0W of power, the vehicle propels due to inertia to the next time step where the velocity is increased as the power is produced by the engine takes over. Therefore, despite having the least values of power, the vehicle still propels accordingly (as guided by the graph).

 

CONCLUSION

The model that has been constructed uses basic DC motor employing a permanent magnet with a simple power generator block incorporating H-bridge. Most of the inertial effects and other miscellaneous effects acting on the vehicle body has not been considered. The vehicle in the current model doesn’t undergo regenerative braking nor changes gears. This model is the most simplistic model of an EV. This model is capable of travelling 17.77km in 2474 sec with 16.64% of SOC remaining. To avoid the excessive draining of the battery the vehicle is safe to travel a distance of 13.08 km for 2015 sec with 30% remaining SOC. The maximum speed attained by the vehicle under consideration is 25.335 m/s. The maximum power required to propel the vehicle is 2.798 MW and maximum total resistive forces acting on the vehicle is 110.4 kN and minimum total resistive force on the vehicle is 660.05 N. The current model can be developed further including gear shifting schemes, varied drive cycles, different motor parameters and so on to understand the dynamics of the working of the EV.

BIBLIOGRAPHY

1. ‘Modern Electric, Hybrid Electric, and Fuel Cell Vehicles – Fundamentals, Theory, and Design”, Mehrdad Ehsani, Yimin Gao, Sebastian E.Gay, Ali Emadi, Power electronics and applications series, ISBN 0-8493-3154-4, CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida.
2. “Electric Vehicle Technology Explained”, James Larminie, John Lowry, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England. ISBN 0-470-85163-5.
3. ‘Power Electronics Handbook’, Muhammad H. Rashid, ISBN 9780128114070, https://doi.org/10.1016/B978-0-12-811407-0.09997-9.
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13. https://in.mathworks.com/help/physmod/sps/ref/hbridge.html?s_tid=doc_ta
14. https://in.mathworks.com/help/physmod/sps/ref/controlledpwmvoltage.html?s_tid=doc_ta
15. https://in.mathworks.com/help/physmod/simscape/ref/controlledvoltagesource.html?s_tid=doc_ta
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17. https://in.mathworks.com/help/physmod/simscape/ref/controlledcurrentsource.html?searchHighlight=CONTROLLED%20CURRENT%20SOURCE&s_tid=srchtitle
18. https://in.mathworks.com/help/simulink/slref/ratetransition.html
19. https://in.mathworks.com/help/simulink/slref/gain.html?s_tid=doc_ta
20. https://in.mathworks.com/help/simulink/slref/discretetimeintegrator.html?s_tid=doc_ta
21. https://in.mathworks.com/help/autoblks/ref/longitudinaldriver.html?s_tid=doc_ta
22. https://in.mathworks.com/help/autoblks/ref/drivecyclesource.html?s_tid=doc_ta