Sunday, April 19, 2009

SEPIC Converters Solve Automotive Power NeedsPart 1

Single-ended primary inductance converter (SEPIC) topology is a good choice for automotive power systems that require an output voltage between the low and high values of the input voltage. SEPIC topology fits this application because its duty ratio can be varied around 50% to provide an output voltage that is either below or above the input voltage. Additionally, compared to flyback converters, SEPIC converters avoid the problems with leakage inductance and snubbers.
Fig. 1 shows the basic SEPIC topology. In the steady-state during the switch (SW) on-time, energy is stored in inductor L1. The inductor currents IL1 and IL2 ramp up at a slope determined by the input voltage and the inductances L1 and L2. The L2 inductor current ramps up at the same rate through coupling capacitor CS and SW. The CS positive terminal is at ground potential, and the voltage across L2 is VIN, which is the same as the voltage across L1. At this point in time, the output capacitors supply the load current while diode D is reverse biased. When the SW turns off, diode D is forward biased, and it conducts the energy stored in both inductors to the load while also charging the output capacitor. The voltages across the inductors are clamped to output voltage with the same inductor down-slope currents.


Current-mode PWM controllers, such as the MAX15004/15005, operate over an automotive input voltage range from 4.5 V to 40 V (load-dump). The input voltage can go down as low as 2.5 V (cold-crank) after startup if VCC is supplied by an external bias voltage. The controllers integrate all the building blocks necessary for implementing fixed-frequency SEPIC converters. By operating the converters at a high switching frequency, designers can use smaller power components. Additionally, the converters include easy slope compensation, synchronization, hiccup-up current limit and overvoltage protection features to reduce the number of external components needed in the system.
To optimize SEPIC converter performance, let's examine the design procedures to select the component values for the controller and evaluate the performance with some measurements in a practical design. The typical specifications are used to demonstrate the actual design. The system specs are VIN = 6 V to 40 V and VOUT = 12 V/1 A; the input voltage can go down as low as 2.5 V in cold-crank condition once VCC is supplied through VOUT. With VIN as low as 2.85 V, the circuit delivers 85% of its rated output power. Fig. 2 shows the schematic developed with the above specifications that can power an automotive infotainment display.








POWER SECTION DESIGN



Voltage-mode control was passed over in favor of current-mode control, because current-mode control responds immediately to line voltage changes and provides inherent overcurrent protection for the switching device. Due to its simpler dynamics and inherent protection features, a peak current-mode control architecture is used in the MAX15005A. Peak current-mode control compares the amplified output-voltage error with the primary inductor current signal. Using the MAX15005A pulse-width modulator (PWM), the primary inductor current ramp is compared against the amplified output-voltage error.
The inner current control loop contains a small current-sense resistor that senses the primary switch current. The resistor transforms this current waveform into a voltage signal that is fed directly into the inverting input of the PWM comparator. The slope-compensated voltage is summed inside the chip and then fed to the PWM comparator to avoid subharmonic oscillations when duty ratios are greater than 50%. This inner loop determines the response to input voltage changes. The outer voltage control loop involves comparing a portion of the output voltage to a reference voltage at the input of the internal error amplifier. The amplified error voltage is then connected to the noninverting input of the PWM comparator. The PWM comparator output drives a MOSFET driver after overcurrent, overvoltage and thermal-protection logic.
Peak current-mode control requires simpler compensation, has pulse-by-pulse current limiting, and has better dynamic line regulation. In order to limit peak currents through components, continuous conduction mode (CCM) was chosen. In the CCM, RMS currents in the coupled inductor, the switch and the diode can be half as compared to the currents in discontinuous conduction-mode operation, requiring the larger components. Because the output ripple current is less than it would be if discontinuous mode were used, the output capacitors also are smaller. Continuous conduction mode, however, requires higher magnetizing inductances to stay in CCM throughout the entire operating range and maintain a right-half-plane zero in its transfer function.
Selecting the switching frequency is the foundation of the optimization and design compromise flow to determine all the component values. A higher switching frequency leads to smaller component sizes with fair efficiency, while lower frequency increases the achievable efficiency but will require slightly bulkier components. The MAX15005A switching frequency (FS) is programmable from 15 kHz to 1 MHz using an external resistor (RT) and capacitor (CT) network. Ideally, FS can be set below 150 kHz so that the third harmonics can remain below AM band, thus minimizing RF noise (interference). Some applications, such as VFD converters, require very low EMI and prefer switching frequencies as low as 20 kHz. The converter switching frequency (FS) is externally synchronizable to further assist in keeping the EMI low and away from the tuned AM band.
After selecting the power circuit topology, the next decision is to determine the maximum duty cycle (DMAX) of the switch, Q, in Fig. 2. The duty cycle is the ratio of on-time of Q to total period (D = TON /T). In a CCM SEPIC converter, the maximum duty cycle will determine the component current ratings and impact the maximum voltage stress on the switching elements. The MAX15005A can provide a maximum duty cycle of 85% with a minimum on time of 100 ns.
The dc transfer function of a CCM SEPIC converter is given by Eq. 1 and Eq. 2 in Fig-EQ:




Fig-EQ : Figure of All Equations.


Where:
VOUT = Output voltage
VD = Diode drop
RL = Inductor DCR value.
The maximum duty cycle occurs at VINMIN and is determined to be 84.5% when the minimum on-time of the switch is 1.08 µs (both of these values are within the limits of the IC). Fig. 3 shows the RTCT oscillator waveform, gate drive waveform and output voltage at 6-V input, 12-V output and 1-A output.







INDUCTOR SELECTION



In SEPIC converters, both the inductors are subject to the same voltages and same ripple currents. Thus, both inductors have the same values. However, peak current rating would be different. These days, coupled inductors are readily available with 1-to-1 turn ratios with a coupling factor nearly equal to 1. This saves board space and eliminates the need for a snubber. With coupled inductors, the value of inductance will be half of the individual inductors. The coupled inductance value is selected using Eq. 3 in Fig-EQ .
Where:
ΔIL = Acceptable inductor ripple.
Due to the dc isolation capacitor between input and output, average inductor currents IL1, IL2 are equal to the input current and the load current, respectively. Use the following equation to calculate and ensure the peak inductor current (ILPK) is lower than the saturating current specification of the coupled inductor:
Where:
η = assumed efficiency.
The required RMS current rating of the inductors that causes the heat losses and temperature rise is given by Eq. 5 in Fig-EQ:
Where:
This design uses a 15-µH MSD1278-153ML coupled inductor from CoilCraft.





INPUT AND OUTPUT CAPACITORS SELECTION


The input currents in SEPIC architectures are continuous. The inductor reduces the ripple currents as well as the required input capacitance. However, a higher value for the input capacitor may be necessary to ensure better impedance interaction with the source input. RMS current rating and the capacitor value needed to maintain specified input ripple are given by Eq. 6 and Eq. 7, respectively in Fig-EQ.
Where :
ΔVIN is the acceptable input ripple. The ESR ripple is given by Eq. 8.
Where:
ESRCIN = maximum ESR value.


The SEPIC output capacitor has to supply the full load current when SW is ON (and the inductors are charging). The output capacitor thus sees large ripple currents, and it must be able to handle the RMS current given by Eq. 9 in Fig-EQ:
Additionally, the output capacitor value should be selected to maintain the specified output voltage ripple, which includes both ESR ripple and capacitive ripple given by Eq. 10 and Eq. 11 in Fig-EQ.
The waveforms in Fig. 4 show the output and input voltage ripples at 6-V input and 1-A output current. Output peak-to-peak ripple is 128 mV and input peak-to-peak ripple is 25 mV, which are less than 1% of their final values.





COUPLING CAPACITOR SELECTION

The coupling capacitor, CS, provides dc isolation between input and output. Because the load is isolated from input, the total supply shutdown current can be reduced below 10 µA by turning off the MAX15004/5 through its ON/OFF pin. The coupling capacitors need to carry large ripple currents. Thus, nonpolar ceramic capacitors, which have excellent ESR, ESL and ripple current ratings, are best suited to the task. The value of the coupling capacitor depends on the maximum ripple across it. The RMS current flowing through these coupling capacitors is given by Eq. 12 in Fig-EQ.Multiple ceramic capacitors may be paralleled to improve the performance further.

Because it carries large ripples, the capacitor of choice should be a low ESR, low ESL ceramic-type device. The value of the coupling capacitor depends on the maximum ripple across it and can be calculated using Eq. 13 Fig-EQ:
The peak voltage across CS is equal to the input voltage plus a difference voltage, ΔVCS. This ΔVCS is set to a value between 2% and 5% of the minimum input voltage. Therefore, the voltage rating should be greater than maximum input voltage. Due to presence of CS, SEPIC is best suited for low power applications where ripple currents are less.

Conducted EMI filter design


Conducted EMI filter design for SMPS
• Introduction
• EMI in SMPS
• Common Mode(CM) noise
• Differential Mode(DM) noise
• Minimizing EMI in SMPS design
• Measuring conducted EMI
• EMI filter design
• Emi filter components
• Emi filter topology
• Calculating CM filter component values
• Calculating DM filter component values
• Determining filter corner frequencies
• Design steps
• Conclusions




Introduction
• The threat of generating EMI from the fast switching pulses in SMPS has always been a
serious concern
• Thus achieving the electromagnetic compatibility (EMC) has become a requirement as
important as meeting the power conversion specifications
• EMI includes three elements
• Source of the electromagnetic emission
• Coupling path
• A receiver of the EMI (victim)
• Conducted emissions 150kHz-30MHz
• Common mode(CM) measured between each power line and ground
• Differential mode measured between power lines
• Radieted emissions 30MHz-1GHz


EMI in SMPS
• Because of the fast switching in SMPS they generate large amount of electromagnetic
interferences and that’s usually the reason for SMPS not to comply the EMC standards
• EMI filter is usually needed in the input of the SMPS to achieve the required standards
• Conducted emissions 150kHz-30MHz
– CM common mode emissions :
paracitic capacitances and the switching voltage waveform across the switch
– DM differential emissions:
The swiching action causes current pulses at the input
Thus switching spikes exist as a differential mode noise source
• Radiated emissions 30MHz-1GHZ
– Magnetic and Elecric fields


EMI in SMPS
• Operation conditions also affects to the filter design
• The worst case should be always considered
– Highest input voltage leads to peak du/dt value
→CM noise will be maximum
– Lowest input voltage and maximum load current would lead to peak di/dt value
→DM noise will be maximum


EMI in SMPS Sources of CM noise


EMI in SMPS Sources of DM noise

• The switching action of the power mosfet causes current pulses at the input and voltage ripple at the output

LINEAR INDUCTION MOTOR

Abstract

Linear induction motors (LIM) are used in many different applications, from slow moving sliding doors to high-speed trains around the world. Anything that requires linear motion will require a LIM. The primary goal is to analyze a small laboratory sized single sided linear induction motor (SLIM) for educational aid.

The idea of a LIM had been suggested in 1895 and was first developed by an English Electrical Engineer, Eric Laithwaite. He spent the rest of his career investigating these special machines. His colleagues are currently designing a launch system with linear motors, which is a more efficient alternative to the rockets used to launch spacecrafts.

Lim operates on the same principle as the conventional rotary motor. The rotary motor is cut out and laid flat to from the equivalent lim. Nothing has changed; only the direction of motion has changed.

Conventional motor Linear motor

This report describes the basic concept and control of linear induction motor. The stator winding and reaction plate design are very important.

Chapter 1 INTRODUCTION

1.1 Objective and goals: -

The aim of this report is to understand a basic of linear induction motor for educational purposes. The main goal of this report is to study of linear induction motor.

1.2 Overview of report: -

The report is divided up into several chapters. The chapters follow each other logically to explain the overview of LINEAR INDUCTION MOTOR.

Chapter 1: Provides an introduction to the report, defines the objectives and goals.

Chapter 2: This chapter is the literature review, which provides a working knowledge of the LIM, gathered from various resources.

Chapter 3: Explains the operating properties associating with LIM.

Chapter 4: Describes the various effects regarding LIM.

Chapter 5: Describes the control of Linear Induction Motor.

Chapter: -2 CONSTUCTION AND WORKING OF LIM

This chapter includes a working knowledge of the linear induction motor, its characteristics, and types of linear induction motor.

2.1 History: -

The idea of a linear induction motor had been suggested in 1895, and was first developed by an English Electrical Engineer, Eric Laithwaite. Laithwaite discovered that it is possible to arrange two linear motors back to back, to produce a continuous oscillation without the use of any switching devices. In 1946, the first large scale linear motor was built by westinghhouse corporation, which was an aircraft launcher. This is no new technology regarding LIM, but merely designed in a different form. Only the way it produces motion and shape is changed.

2.2 Application: -

Wherever straight-line motion or reciprocating forces are needed, the lim is superior to provide such service. They are typically used in applications where accurate positioning is not required. The linear induction motor has proven itself in many unusual applications, ranging from a small sliding door right to steam catapults used on aircraft carriers. Table illustrates some typical application where LIM are used.

Fig 2.1 Linear machine

Typical Application.

  • Sliding Doors
  • Sewage Distributors
  • Automated Warehousing
  • Aluminium can propulsion
  • Crane drives
  • Stage curtain movement
  • Mixer stirrer drives
  • Scrap sorting movement
  • Revolving doors
  • Baggage handling
  • Flat circular motors
  • Linear accelerators
  • Flexible manufacturing systems
  • Personal rapid transport system
  • Ship test tank drives
  • Bogie drives
  • Turntable drives
  • Target movement
  • Steel tube movement
  • Wire winding
  • Slewing drives
  • Sheet metal movement
  • Pallet drives
  • Research machines
  • Automated postal systems
  • Multi motor in track systems
  • Theme park rides
  • Extrusion pullers
  • Robotic systems
  • People movers
  • Lover profile drives
  • Conveying systems
  • Airport carousels

2.3 Linear induction motor: -

A linear induction motor is basically a rotating squirrel cage induction motor opened out flat. Instead of producing rotary torque from a cylindrical machine it produces linear force from a flat one. Depending on the size and ratings of the LIM, they can produce thrust up to several thousands Newton. The speed of the LIM is determined by the winding design and supply frequency.

Conceptually all types of motors can have possible linear configurations (dc induction, synchronous, and reluctance). The dc motor and synchronous motor require double excitation (field and armature). This makes the hardware application rather complex. The reluctance motor produces poor thrust, since it has no secondary excitation. It can be seen why most of the attention is diverted to linear induction motors.

Linear induction motors can have various configurations: the air gap can be flat or cylindrical, and the flux can be longitudinal or transverse. A lim can be either a short primary or a short secondary lim, depending on whether the primary or the secondary is the shorter. In each case, either the primary or the secondary can be the moving member. Finally, the motor can either be single sided or a double sided. This report will be concerned with designing a sho0rt primary (moving member), flat air gap, longitudinal flux and single sided motor.

Fig 2.2 LIM with transverse flux.

2.4 Operation: -

The linear motor operates on the same principal as a rotary squirrel cage induction motor. The rotary induction motor becomes a linear induction motor when the coils are laid out flat. The reaction plate in the LIM becomes the equivalent rotor. This is made from a non-magnetic highly conductive material. The induced field maximized by backing up the reaction plate with an iron plate (conducting sheet). The iron plate serves to amplify the magnetic field produced in the coil. The air gap between the stator and the reaction plate must typically be very small, much smaller than the allowable gap for the synchronous motor, otherwise the amount of current required for stator coils becomes unreasonable.

When supplying an ac current to the coils, a traveling magnetic wave is produced. Swapping the phases reverse the direction of travel. Currents induced in the reaction plate by the traveling magnetic wave create a secondary magnetic field. It is not necessary to kept the field of motion synchronized to the position of the reaction plate, since the second field is induced by the stator coil. A linear thrust is produced with the reaction between these two fields.


2.5 LIM Components: -

The LIM consists of two main components.


1) 3-phase coil assembly:

The coil assembly consists of a 3-phase winding that is wound into a steel lamination stack. These laminations are insulated from one another with very fine materials, such as paper or adhesive glue. The entire assembly can be encapsulated with thermally conductive epoxy for insulation and stability. The coil assembly will require some form of mounting to ensure stability during operation. The single sided configuration consists of a single coil assembly that is used in conjunction with an aluminium or copper plate backed by a steel reaction plate. The coil assembly can be directly connected to the ac line for single speed applications.

2) Reaction plate: -

A suitable reaction plate is required for proper operation of the LIM. The reaction plate is made from standard steel, aluminium, and or copper. For single sided operation, the required reaction plate consists of a .125” [3 mm] thick aluminium or a .080” [2 mm] thick copper plate that is backed by a .25” [6mm] thick ferrous steel plate. The steel plate can be omitted put the force will be dramatically reduced.

Fig 2.3 Reaction Plate


Chapter 3 PROPERTY OF LINEAR INDUCTION MOTOR


This chapter describes the various properties associated with LIM. When comparing the properties of the LIM to the properties of the conventional rotary motor, these two are basically identical to one another. The equations formulated for rotary machines can be applied directly to LIMs with a few minor adjustments.

3.1 Linear Synchronous Speed: -


Consider a conventional rotary motor, it is possible to lay a section of the stator out flat without affecting the shape or speed of the magnetic field. Hence, the flat stator would produce a magnetic field that moves at constant speed. The linear synchronous speed is given by:

Vs=2pf (3.1)

Where
Vs = linear synchronous speed [m/s].
p = width of one pole-pitch [m].
f = frequency [hz].

It is important to note that the linear speed does not depend upon the number of poles but only depend on the pole-pitch width. By this logic, it is possible to for a 2-pole linear machine to have the same linear synchronous speed as that of a 6-pole linear machine, provided that they have the same pole- pitch-pitch width.
To further clarify, consider two machines where the radii are R and 2R respectively (Figure 3.1a). The rotational field speed for is w0 for both of them, while the linear speeds are different.



FIG 3.1: Linear and rotary corresponding gap sizes: a) Effective radius R: b) Effective radius 2R: c) travel length 2JR: d) travel length 4JR

For case (a), for case (b)

Vs = w0R vs = 2 w0R
= 2ÿfR = 4ÿfR
=2f* pole pitch =2f* pole pitch.

For each one cycle of current the field travels two pole pitches. In figure 3.1 (b), the pole pitch is twice that of figure 3.1 (a). The results clearly indicate that linear synchronous speed does not depend on the number of poles, but depend on the pole pitch.

To increase the linear synchronous speed of the LIM, the designer could either.
(a) Design a longer pole pitch.
(b) Increased the supply frequency.


3.2 SLIP: -

The slip formula of LIM is identical to conventional rotary machine. The slip is defined as, “ slip (s) of an induction motor is the difference between the synchronous speed and rotor speed, expressed as a percentage (or per unit) of synchronous speed.” The per unit of slip can be expressed by
S = (vs-v)/vs.

Where

S = slip.
Vs = synchronous linear speed [m/s].
V = speed of rotor (or stator) [m/s].


3.3 FORCES: -

The main forces involved with the LIM are thrust, normal and lateral. Thrust is what this Report is interested in, and its relationship with the other adjustable parameters. The normal force is perpendicular to the stator in the z- direction. Lateral forces are side forces that are undesirable, due to the orientation of the stator.


Fig 3.2 Forces associated with LIMs.

3.3.1 THRUST: -

Under normal operation, the LIM develops a thrust proportional to the square of the applied voltage (Figure 3.3), and this reduces as the slip is reduced similarly to that of an induction motor with a high rotor resistance.

The air gap for a typical LIM machine is 2mm, variations up to "20 % are considered acceptable. The effect of the air gap on thrust and current line is shown in figure 3.4.

Fig 3.3 Thrust - line voltage characteristic

Fig 3.4 Air gap on thrust and current characteristic.
The amount of thrust produced by a LIM is as follows.

F = Pr/Vs

Where

F = thrust [N].
Pr = power transmitter to the rotor [w].
Vs = linear synchronous speed [m/s].

The equivalent circuit of the LIM is exactly the same as of a conventional 3-phase rotary machine. The power output is as follows:

Power output = 3(I1) 2 Rs/s (1-s) W

Referring to equation, if F is the amount of thrust produced in newtons and vs is the linear synchronous speed in m/s then:

Fvs = 3(I1) 2 Rs/s (1-s)

If the iron loss is very small, thus:

Power output = power input - 3(I1) 2 Rp

The power input can be approximately related to the mechanical input of the machine.

Fig 3.5 LIM Equivalent Circuit.
3.3.2 NORMAL FORCE: -

In a double-sided linear induction motor (DLIM) configuration, the reaction plate is centrally located between the two primary stators. The normal force between one stator and the reaction plate is equal and opposite to that of the second stator. Therefore the resultant normal force is zero. A net normal force will only occur if the reaction plate is placed asymmetrically between the two stators. This force tends to center the reaction plate. A small displacement of the reaction plate from the center is directly proportional to the displacement.

In a SLIM configuration in which there is a rather large net force between the primary and secondary. This is because of the fundamental asymmetrical topology. At synchronous speed, the force is an attractive force and its magnitude is reduced as the speed is reduced. At certain speeds the force will become repulsive, especially at high frequency operation.
Fig 3.6 Normal Force in LIM
3.3.3 LATERAL FORCE: -

Lateral force moves in the y-direction as shown in figure. These occur due to the asymmetric positioning of the stator in a LIM. Any displacement from central positioning will result in an unstable system. Generally, small displacements will only result in very small lateral force. At high frequency operation, the lateral force can be become quite chaotic. A set of guided mechanical wheel track is sufficient to eliminate small lateral force.

3.3.4 THE GOODNESS FACTOR: -

Induction motors draw current from its primary source and then transfer it to the secondary circuit crossing the air gap by induction. The difference between the power transferred across the air gap and the rotor losses is available as the mechanical energy to drive the load. In prospective of energy conversion, the primary resistance and the leakage reactances of the primary and the secondary circuit are not essential. The energy conversion efficiency can be improved as the mutual reactance Xm of the motor is increased and the secondary circuit resistance R2 is decreased. The goodness factor is G = Xm/ R2 for a basic motor. As the value of g increases, the performance of the machine gets better.

The goodness factor for a linear motor can be defined as

G = (2Ffp2)/(prrg)
= (m0/prr) * vs (p/g).
Where

f = source frequency.
p = pole pitch of the primary winding.
rr = surface resistivity of the secondary conduction sheet.
g = air gap.
m0 = permittivity of free space.
Vs = linear synchronous speed.

From above formula, it can be seen that a linear motor is a better energy conversion device at high synchronous speeds and also when the ratio (p/g) is large. This can be explained in terms from a more fundamental point of view. For example, a linear motor, just like any other electromagnetic device, has an inherent force density limitation imposed on it by the design constraints of electric and magnetic loadings. With the resulting thrust limitations, high power for a given sized of motor is only possible at very high speeds. When the ratio (p/g) is small, the primary leakage flux is large, and consequently the effective magnetic coupling is reduced and the LIM shows poor performance. The air gap is determined coupling is reduced and the LIM shows poor performance. The air gap is determined by mechanical considerations and hence, for a given linear synchronous speed, the pole pitch an therefore the ratio (p/g) are reduced as frequency is increased. Low frequency motors therefore perform much better than high frequency ones.

3.3.5 TRAVELLING WAVES: -


Since the length of the LIM does not join up upon itself, one might think that when the flux reaches the end of the stator, there must be a delay before it returns to restart once more at the beginning. In fact, this is not the case. The traveling waves of flux produced by the LIM, move smoothly from one end of the stator to the other. Figure 3.7 shows the movement of flux from left to right in a 2-pole LIM. At the extremities A and B of the stator, the flux cuts off sharply. No matter how fast the N or S pole disappears at the right, it builds up again at the left.
Figure 3.7: shape of the magnetic field created by a 2- pole, 3-phase linear stator, over one complete cycle. The successive frames are separated by an interval of time equal to 1/6 cycle.
Chapter 4 VARIOUS EFFECT OF LIM

This chapter describes the various effects of LIM. These effects must be minimized as much as possible when designing LIM, so that they do not drastically affect performance. Some effects can be eliminated while others are unavoidable.

4.1 END EFFECT: -

One obvious difference between LIM and conventional rotary machines is that the fact that LIM has ends. This means that the traveling magnetic field cannot join up on itself, and introduces end effects. The end effects can result in characteristics that are much different from rotary machines.

The end effect is clearly exhibited in the form of a non-uniform flux density distribution along the length of the motor. For a LIM supplied with a constant current, typical variation of the normal flux density with slip and position along the length is illustrated in fig 4.1. With constant primary current, its magnetizing component and consequently the air gap flux decreases as the load component increases with increasing slip. This is true for any induction motor, with or without end effect. For a given slip, the flux density builds up along the LIM length, beginning with a small flux density at the entry end. Depending on the length of penetration of the entry end effect wave, the flux density may not even reach the nominal level that would be found in a motor without end effect.
Fig 4.1 Normal flux density distribution in LIM.
The theoretical evaluation of these effects is much too complicated to explain, but the results can be stated fairly simply. Laithwaite states that, “ if the total number of pole pitches on the shorter member (either short stator or short rotor) exceeds four, the additional effect of the transients due to the edges is likely to be so small that it can be neglected, except in large, powerful machine.”


4.2 EDGE EFFECT: -

The edge effect is generally described as the effect of having finite width for a linear motor. This effect is more evident with lower values of width to air gap ratio. Figure 4.2 illustrates the variation of the normal flux density in the transverse direction. The figure shows a dip at the center due to the edge effect, and the dip is more obvious at higher slips.

Fig 4.2 Edge effect in LIM
As a result, the edge effect will increase the secondary resistivity, lateral instability due to the uneven secondary overhangs and a reduction in performance.
4.3 GAP EFFECT: -

Conventional rotary machine has a small air gap, in the order of 2mm or less. This allows a high gap flux density. For LIM, the air gap can be as large as 5cm for one operating on a traction system. The magnetic circuit reluctance is much higher for large air gaps, in which the magnetizing current is also higher. There is a rather large leakage flux that further reduces the operating power factor. The gap density is less than for the rotary counterpart, and consequently iron losses form a smaller part of the total loss.

Figure shows the effect of air gap to the attraction force. Figure 4.3 and Figure 4.4 shows the effect of air gap on thrust and line current.
Fig 4.3 Attraction/ air gap characteristics.
Fig 4.4 Effect of air gap on thrust and line current.
CHAPTER 5 CONTROL STRATAGERIES IN LINEAR INDUCTION MOTOR

Following are the name of various methods by which we can control the speed of linear induction motor.

1. Variable frequency variable voltage method.

2. Direct torque and flux control method.

3. Vector control method.

All above methods are similar to Induction Motor with small modification and same equations can be applied to Linear Induction Motor.















































































































































































































AC VOLTAGE CONTROLLER CIRCUITS

AC voltage controllers (ac line voltage controllers) are employed to vary the RMS value of the alternating voltage applied to a load circuit by introducing Thyristors between the load and a constant voltage ac source. The RMS value of alternating voltage applied to a load circuit is controlled by controlling the triggering angle of the Thyristors in the ac voltage controller circuits.
In brief, an ac voltage controller is a type of thyristor power converter which is used to convert a fixed voltage, fixed frequency ac input supply to obtain a variable voltage ac output. The RMS value of the ac output voltage and the ac power flow to the load is controlled by varying (adjusting) the trigger angle ‘a’

There are two different types of thyristor control used in practice to control the ac power flow

· On-Off control
· Phase control

These are the two ac output voltage control techniques.
In On-Off control technique Thyristors are used as switches to connect the load circuit to the ac supply (source) for a few cycles of the input ac supply and then to disconnect it for few input cycles. The Thyristors thus act as a high speed contactor (or high speed ac switch).

PHASE CONTROL
In phase control the Thyristors are used as switches to connect the load circuit to the input ac supply, for a part of every input cycle. That is the ac supply voltage is chopped using Thyristors during a part of each input cycle.
The thyristor switch is turned on for a part of every half cycle, so that input supply voltage appears across the load and then turned off during the remaining part of input half cycle to disconnect the ac supply from the load.


By controlling the phase angle or the trigger angle ‘a’ (delay angle), the output RMS voltage across the load can be controlled.

The trigger delay angle ‘a’ is defined as the phase angle (the value of wt) at which the thyristor turns on and the load current begins to flow.


Thyristor ac voltage controllers use ac line commutation or ac phase commutation. Thyristors in ac voltage controllers are line commutated (phase commutated) since the input supply is ac. When the input ac voltage reverses and becomes negative during the negative half cycle the current flowing through the conducting thyristor decreases and falls to zero. Thus the ON thyristor naturally turns off, when the device current falls to zero.


Phase control Thyristors which are relatively inexpensive, converter grade Thyristors which are slower than fast switching inverter grade Thyristors are normally used.

For applications upto 400Hz, if Triacs are available to meet the voltage and current ratings of a particular application, Triacs are more commonly used.


Due to ac line commutation or natural commutation, there is no need of extra commutation circuitry or components and the circuits for ac voltage controllers are very simple.
Due to the nature of the output waveforms, the analysis, derivations of expressions for performance parameters are not simple, especially for the phase controlled ac voltage controllers with RL load. But however most of the practical loads are of the RL type and hence RL load should be considered in the analysis and design of ac voltage controller circuits.





TYPE OF AC VOLTAGE CONTROLLERS
The ac voltage controllers are classified into two types based on the type of input ac supply applied to the circuit.
· Single Phase AC Controllers.
· Three Phase AC Controllers.
Single phase ac controllers operate with single phase ac supply voltage of 230V RMS at 50Hz in our country. Three phase ac controllers operate with 3 phase ac supply of 400V RMS at 50Hz supply frequency.
Each type of controller may be sub divided into
· Uni-directional or half wave ac controller.
· Bi-directional or full wave ac controller.
In brief different types of ac voltage controllers are
· Single phase half wave ac voltage controller (uni-directional controller).
· Single phase full wave ac voltage controller (bi-directional controller).
· Three phase half wave ac voltage controller (uni-directional controller).
· Three phase full wave ac voltage controller (bi-directional controller).

APPLICATIONS OF AC VOLTAGE CONTROLLERS
Lighting / Illumination control in ac power circuits.
Induction heating.
Industrial heating & Domestic heating.
Transformer tap changing (on load transformer tap changing).
Speed control of induction motors (single phase and poly phase ac induction motor control).
AC magnet controls.



PRINCIPLE OF ON-OFF CONTROL TECHNIQUE (INTEGRAL CYCLE CONTROL)
The basic principle of on-off control technique is explained with reference to a single phase full wave ac voltage controller circuit shown below. The thyristor switches and are turned on by applying appropriate gate trigger pulses to connect the input ac supply to the load for ‘n’ number of input cycles during the time interval . The thyristor switches and are turned off by blocking the gate trigger pulses for ‘m’ number of input cycles during the time interval . The ac controller ON time usually consists of an integral number of input cycles.

R=RL= Load Resistance
Fig.: Single phase full wave AC voltage controller circuit




Example
Referring to the waveforms of ON-OFF control technique in the above diagram,
Two input cycles. Thyristors are turned ON during for two input cycles.
One input cycle. Thyristors are turned OFF during for one input cycle


Fig.: Power Factor


Thyristors are turned ON precisely at the zero voltage crossings of the input supply. The thyristor is turned on at the beginning of each positive half cycle by applying the gate trigger pulses to as shown, during the ON time . The load current flows in the positive direction, which is the downward direction as shown in the circuit diagram when conducts. The thyristor is turned on at the beginning of each negative half cycle, by applying gating signal to the gate of , during . The load current flows in the reverse direction, which is the upward direction when conducts. Thus we obtain a bi-directional load current flow (alternating load current flow) in a ac voltage controller circuit, by triggering the thyristors alternately.


This type of control is used in applications which have high mechanical inertia and high thermal time constant (Industrial heating and speed control of ac motors). Due to zero voltage and zero current switching of Thyristors, the harmonics generated by switching actions are reduced.


For a sine wave input supply voltage,V
RMS value of input ac supply = = RMS phase supply voltage.
If the input ac supply is connected to load for ‘n’ number of input cycles and disconnected for ‘m’ number of input cycles, then