Induction Machine Speed Control 2 - Research in · PDF filePer phase equivalent circuit of...

Induction Machine Speed Control

Master Thesis in Electronics August 30

th, 2007

By

Lars-Göran Andersson [email protected]

Mälardalen University Department of Computer Science and Electronics

Supervisor Magnus Jansson

Bombardier Transportation

Company Supervisor Lars Hörnlund

LSI Svenska AB

Examiner Mikael Ekström

Mälardalen University Department of Computer Science and Electronics

Department of Computer Science and Electronics of 28

___________________________________________________________ Induction Machine Speed Control

Lars-Göran Andersson Mälardalen University

Abstract

This thesis work finds and presents an alternative method of motor speed control to the

voltage control method currently used by LSI Svenska AB, the constant Volt/Hertz method with sinusoidal Pulse Width Modulation (PWM) and shows the advantages and disadvantages that is possible to achieve with this new method compared with the currently used method.

Acknowledgement

I really appreciate the guidance and support given by my supervisor Magnus Jansson and my company supervisor Lars Hörnlund they have been quite dynamic through out my thesis work and contributed with quite invaluable ideas which really helped me to progress I acknowledge the Department of Computer Science and Electronics for providing enough resources to help me complete this thesis work.

Last but not the least I am thankful to my loved ones, my friends and colleagues who

supported me during my time at Mälardalen University.




Table of Contents

1 Introduction ........................................................................................................................ 5

1.1 Background ................................................................................................................ 5 2 Theoretical Background ..................................................................................................... 5

2.1 AC motor market........................................................................................................ 5 2.2 Induction motor theoretical basics ............................................................................. 5

2.2.1 Dynamical model ............................................................................................... 5 2.2.2 Power performance ............................................................................................ 6

2.3 Speed control systems for Induction Motors.............................................................. 8 3 Analysis of problem ........................................................................................................... 9

3.1 Comparison current ↔ new method .......................................................................... 9 3.1.1 Properties method currently used....................................................................... 9 3.1.2 New method requirements ................................................................................. 9

3.2 Model / method ........................................................................................................ 10 3.2.1 Creating a schematic in Pspice......................................................................... 10 3.2.2 Studying different control techniques .............................................................. 10

4 Solution ............................................................................................................................ 11 4.1 Deciding what model to be used .............................................................................. 11

4.1.1 Three-phase voltage source inverters with sinusoidal PWM ........................... 12 4.2 Building a model ...................................................................................................... 16

4.2.1 Simulation with Simulink / Matlab .................................................................. 16 4.3 Analysis of results .................................................................................................... 21 4.4 Future work .............................................................................................................. 21

4.4.1 Implementation with Digital Signal Processor (DSP)...................................... 21 5 Summary and conclusions................................................................................................ 22 6 References ........................................................................................................................ 23 7 Appendix .......................................................................................................................... 24

7.1 Simulink model ........................................................................................................ 24




List of figures

Figure 1. Per phase equivalent circuit of polyphase Induction Machine ................................... 6 Figure 2. Power flow in an induction motor .............................................................................. 8 Figure 3. Typical motor torque - load characteristic .................................................................. 8 Figure 4. Schematic LSI speed regulator ................................................................................. 10 Figure 5. 3-phase inverter......................................................................................................... 11 Figure 6. Three-phase inverter VLL/Vd as a function of ma ....................................................... 15 Figure 7. Three-phase sinusoidal PWM waveforms and harmonic spectrum.......................... 15 Figure 8. Voltage - frequency relation Induction Machine...................................................... 16 Figure 9. Induction machine..................................................................................................... 18 Figure 10. Dynamic T-equivalent circuit for the induction motor ........................................... 19 Figure 11. 3-phase PWM converter with DC-link ................................................................... 19 Figure 12. Simulation of Induction Machine start ................................................................... 21 Figure 13. Main Simulink model ............................................................................................. 24 Figure 14. Discrete PWM Generator 4 pulses.......................................................................... 24 Figure 15. IGBT Bridge ........................................................................................................... 25 Figure 16. Three-Phase Induction Machine (IM main)............................................................ 25 Figure 17. IM Sub. 1 ................................................................................................................ 26 Figure 18. IM Sub. 2 ................................................................................................................ 26 Figure 19. IM Sub. 3 ................................................................................................................ 27 Figure 20. IM Sub. 3.1 ............................................................................................................. 27 Figure 21. IM Sub. 3.2 ............................................................................................................. 28

List of tables

Table 1. Harmonics of VLL for a large and odd mf (mf a multiple of 3) .................................... 14 Table 2. Comparison of Adjustable Frequency Drives ............................................................ 20




1 Introduction

1.1 Background The method for Induction Machine (IM) speed control currently used by LSI Svenska AB

in Falun is limited to a maximum of four amperes current delivered to the motor due to excessive heat build up inside the speed control unit housing. They would like to increase the maximum allowed current of the speed control unit up to sixteen amperes thereby making it possible to sell their products to a wider range of customers with different needs for example control of pumps and more powerful fans, so here it is important to minimize the losses created in the machine/motor. If possible they would also want to decrease the number of steps (time) needed in the production line for each unit.

2 Theoretical Background

2.1 AC motor market Market analysis shows that most of all industrial motor applications uses AC induction

motors. The reasons for this include high robustness, reliability, low price and high efficiency, η > 90% is preferred in order to reduce costs of operation and to maximize long term profit gains for the user. However, the use of induction motors also has its disadvantages, these lie mostly in its difficult controllability, due to its complex mathematical model, its non linear behavior during saturation effect and the electrical parameter oscillation which depends on the physical influence of the temperature.

2.2 Induction motor theoretical basics

2.2.1 Dynamical model In the stationary reference frame (αβ-coordinates), the dynamic model of a 3-phase

induction motor can be described as

vbijaa

jaais

s

r

s

r

r

r

s

dtd

⎥⎦

⎤⎢⎣

⎡+

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎥⎥⎦

⎤

⎢⎢⎣

⎡

+

−=

⎥⎥⎦

⎤

⎢⎢⎣

⎡

02221

1211

φωρω

φ (2.1)

where:

Lb

aLa

LLLaL

Ra

ss

rr

m

rrs

m

rs

s

σ

ττ

τσστσ

σ

1

1

1

2221

1211

=

−==

=⎟⎟⎠

⎞⎜⎜⎝

⎛ −−−=




Rs , Rr : stator, rotor resistance per phase respectively Ls , Lr : stator, rotor inductance per phase respectively Lm : magnetizing inductance per phase ωr : rotor angular speed τr : rotor time constant (= Lr / Rr) ρ : Lm / σ Ls Lr σ : leakage constant (= 1 – Lm

2 / Ls Lr) The input and state variables are as follows, stator current : is = isα + j isβ stator voltage : vs = vsα + j vsβ rotor flux : Φr = Φrα + j Φrβ

2.2.2 Power performance

Figure 1. Per phase equivalent circuit of polyphase Induction Machine

Where:

U1 = stator terminal voltage E1 = stator emf generated by resultant air-gap flux R1 = stator effective resistance X1 = stator leakage reactance Rm = iron core-loss resistance Xm = magnetizing reactance R'2 = rotor effective resistance referred to stator X'2 = rotor leakage reactance referred to stator urb = e.m.f due to the saturable iron bridges in the rotor slots I0 = sum of magnetizing I0X and core-loss I0R current components I1 = stator current I´2 = rotor current referred to stator

Some of the important steady-state performance characteristics of a polyphase induction motor include the variation of current, speed, and losses as the load-torque requirements change, and the starting and maximum torque. Performance calculations can be made from the equivalent circuit. All calculations can be made on a per-phase basis, assuming balanced operation of the machine. Total quantities can be obtained by using an appropriate multiplying factor.




The equivalent circuit of (Fig. 1), is usually employed for the analysis. The core losses, most of which occur in the stator, as well as friction, windage, and stray-load losses are included in efficiency calculations. The power-flow diagram for an induction motor is given in (Fig. 2), in which m1 is the number of stator phases, Φ1 is the power-factor angle between U1 and I1, Φ2 is the power-factor angle between E1 and I2´, T is the internal electromagnetic torque developed, ωs is the synchronous angular velocity in mechanical radians per second, and ωm is the actual mechanical rotor speed given by ωs(1 - S). The total power Pg in watts transferred across the air gap from the stator is the difference between the electrical power input Pi and the stator copper loss. Pg is thus the total rotor input power, which is dissipated in the resistance R2´ / S of each phase so that

( ) ω sg TSRImP ==

'2

2

1'2 (2.2)

where T is the internal electromagnetic torque developed by the machine, and ωs is the synchronous angular velocity in mechanical radians per second. Subtracting the total rotor copper loss, which is m1(I2´)2R2´=SPg, from (Eq. 2.2) for Pg, we get the internal mechanical power developed:

( ) ( ) ( )S

STS RImPP mgm

−==−=

1'21 '

2

2

1ω (2.3)

This much power is absorbed by a resistance of R2´(1-S)/S, which corresponds to the load.

From (Eq. 2.3), we can see that, of the total power delivered to the rotor, the fraction (1-S) is converted to mechanical power and the fraction S is dissipated as rotor copper loss. We can conclude then that an induction motor operating at high slip values will be inefficient.

The total rotational losses including the core losses can be subtracted from Pm to obtain the mechanical power output Po that is available in mechanical form at the shaft for useful work:

ωmorotmo TPPP =−= (2.4) The per-unit efficiency of the induction motor is then given by

PP

i

o=η (2.5)




Figure 2. Power flow in an induction motor

2.3 Speed control systems for Induction Motors The angular speed in rad / s of an induction AC machine mechanical speed is given by

( )ωω sm s−= 1 (2.6)

this shows us that there are two possibilities for speed regulation of an induction motor, altering the slip s (typical < 5%), or the synchronous speed ωs . When the motor is connected to mains with constant frequency the speed will be determined by the point of intersection between the motor and the load torque characteristic

Figure 3. Typical motor torque - load characteristic

Ignoring the stator resistance and the magnetizing impedance in the equivalent circuit model of an induction motor, which is usually a valid approximation for motors, gives a simple equation for the shaft torque in Nm

ssssTT

m

mee +

= max2 (2.7)

where the maximal torque and corresponding slip is given by




XU

Ts

eσω2

132

max = (2.8)

respectively

XRsm

σ

'2= (2.9)

3 Analysis of problem

3.1 Comparison current ↔ new method Try to find a suitable method making it possible to fulfill the needs of LSI Svenska AB.

3.1.1 Properties method currently used Benefits:

• Simple circuit • Few components • Low component cost • Reliable

Disadvantages: • Excessive heat build-up • Limited current (due to heat and losses)

• Needs extra hardware mounted on the machine

3.1.2 New method requirements • 16 A current supplied to the IM • Higher starting torque

• 3-phase output from inverter • Limited power loss (less heat) • Must handle EMC • Must compile with regulations




3.2 Model / method

3.2.1 Creating a schematic in Pspice

P22.2Meg

P11Meg

R310k

R210k

R1

330

C1

100nF

C2

150nF

C4

68nF

L1

1.0mH

1 2

V1B1

1 2

IM

IM

F2

128

F1

6.3A

P1 Potentiometer for speed regulationP2 Potentiometer for min current adjustment

D1

V21Vac0Vdc

Figure 4. Schematic LSI speed regulator

3.2.2 Studying different control techniques • VOLTAGE CONTROL (the model used by LSI Svenska AB) Unfortunately this is not an effective control. As the voltage decreases, the torque

decreases (the torque developed in an induction motor is proportional to the square of the terminal voltage). Practically this is confined to 80-100% control.

• FREQUENCY CONTROL This is by far the most efficient way to control the speed. However, one has to make sure

that the machine does not saturate. Since the flux is proportional to V/f, this control has to assure that the magnitude of the voltage is proportional to the speed. Power electronic circuits are best suited for this kind of control.

• VECTOR CONTROL The magnetizing current always lags (inductive) the voltage by 90° and the torque

producing current is always in phase with the voltage. In vector control the magnetizing current (Id) is controlled in one control loop and the torque producing current (Iq) in another. The two vectors Id and Iq which are always 90° apart, are then added (vector sum) and sent to the modulator, which turns the vector information into a rotating PWM modulated 3-phase system with the correct frequency and voltage. This will reduce torque pulsation and a robust control with fast dynamic response for the induction motor is achieved.




• CHANGING STATOR POLES For a stator witch has several independent windings, one can connect them is series for

starting, essentially building N*poles. The speed of the machine will be reduced by the same factor. As the machine speed increases, one can switch the stator connection to a parallel connection, hence reducing the amount of poles and hence accelerating the machine. This method is simple, but can really accommodate only 2 speeds.

• ROTOR RESISTANCE As seen for the starting, one can insert a variable resistance in the rotor (slip rings) and

hence cause the developed torque to vary, hence control the speed. • DOUBLY FED MOTOR A special application can be to inject a current in the rotor. Hence the air gap flux will

depend upon the difference of frequency between stator and rotor currents, and therefore the speed can be varied by varying the rotor frequency.

• KRAMER CIRCUIT With the method of variable resistor in the rotor circuit, a lot of power is dissipated in this

additional resistor. With the Kramer method, one takes the rotor windings, and feed a 3-phase rectifier. This DC voltage is then fed through an inverter back to the source. Here only the component losses are accounted for. The excess power not transformed in mechanical torque will be fed back to the source.

4 Solution

4.1 Deciding what model to be used The most frequently used three-phase inverter circuit consists of three legs, one for each

phase, as shown in (Fig. 5). The output of each leg, for example VAN (with respect to the negative dc bus), depends only on Vd and the switch status the output voltage is independent of the output load current since one of the two switches in a leg is always on at any instant. Here, I ignore the blanking time required in practical circuits by assuming the switches to be ideal. Therefore, the inverter output voltage is independent of the direction of the load current.

Figure 5. 3-phase inverter




4.1.1 Three-phase voltage source inverters with sinusoidal PWM Most motors are designed to for sine wave AC supply and the inverter output should be as

near to sinusoidal as possible. It is therefore best to choose the control wave with sine shape to give a PWM pattern in which the pulse width is sinudosially modulated throughout the half cycle. Pulse-width-modulated three-phase inverters shape and control the three-phase output voltages in magnitude and frequency with an essentially constant input voltage Vd. To obtain balanced three-phase output voltages in a three-phase PWM inverter, the same triangular voltage waveform is compared with three sinusoidal control voltages that are 120° out of phase, as shown in (Fig. 7) (which is drawn for modulation factor mf = 15).

ff

mcontrol

trif= (4.1)

It should also be noted from (Fig. 7b) that an identical amount of average DC component

is present in the output voltages VAN and VBN, which are measured with respect to the negative DC bus. These dc components are canceled out in the line-to-line voltages, for example in VAB shown in (Fig. 7b).

In a three-phase inverter, only the harmonics in the line-to-line voltages are of concern.

The harmonics in the output of any one of the legs, for example VAN in (Fig. 7b), only the odd harmonics exist as sidebands, centered around mf and its multiples, provided mf is odd. Only considering the harmonic at mf (the same applies to its odd multiples), the phase difference between the mf harmonic in VAN and VBN is (120 mf)°. This phase difference will be equivalent to zero (a multiple of 360°) if mf is odd and a multiple of 3. As a consequence, the harmonic at mf is suppressed in the line-to-line voltage VAB, The same argument applies in the suppression of harmonics at the odd multiples of mf if mf is chosen to be an odd multiple of 3 (where the reason for choosing mf to be an odd multiple of 3 is to keep mf odd and, hence, eliminate even harmonics). Thus, some of the dominant harmonics in the one-leg inverter can be eliminated from the line-to-line voltage of a three-phase inverter.

Sinusoidal PWM considerations are summarized as follows:

1. Small mf (mf ≤ 21): To eliminate the even harmonics, a synchronized PWM should be used and mf should be an odd integer. Moreover, mf should be a multiple of 3 to cancel out the most dominant harmonics in the line-to-line voltage.

2. Large mf (mf > 21): The amplitudes of subharmonics due to asynchronous PWM are small at large values of mf. Therefore, at large values of mf the asynchronous PWM can be used where frequency of the triangular waveform is kept constant, whereas the frequency of vcontrol varies, resulting in noninteger values of mf (so long as they are large). However, if the inverter is supplying a load such as an ac motor, the subharmonics at zero or close to zero frequency, even though small in amplitude, will result in large currents that will be highly undesirable. Therefore, the asynchronous PWM should be avoided.

3. Overmodulation (ma > 1.0): Regardless of the value of mf, the conditions pertinent to a small mf should be observed.




Modulation Index

The average output voltage can be affected by changing the modulation index, defined as voltage ratio between the fundamental of the control wave to the fundamental of the non-modulated carrier wave as ma modulation index (fig. 7a)

VVm

tri

controla

)1(

)1(= (4.2)

Linear Modulation (ma < 1.0)

In the linear region (ma < 1.0), the fundamental-frequency component in the output voltage varies linearly with the amplitude modulation ratio ma (fig. 6). The peak value of the fundamental frequency component in volts in one of the inverter legs is

2)ˆ(

1

VmV daAN = (4.3)

Therefore, the line-to-line rms voltage at the fundamental frequency, due to 120° phase displacement between phase voltages (ma ≤ 1.0), can be written as

VmVmVV dadaLL AN 612.022

323 )ˆ(

1≈== (4.4)

The harmonic content for the phase to phase voltage will be strongly dependent on the modulation index ma. A Fourier analysis on the output phase-to-phase waveform and in general the harmonic spectra will be given from

⎭⎬⎫

⎩⎨⎧

⎟⎠⎞

⎜⎝⎛ +⎟

⎠⎞

⎜⎝⎛=∑

= 2cos

2sin

4

1

δδπ α m

dh

mn nn

nVA (4.5a)

⎭⎬⎫

⎩⎨⎧

⎟⎠⎞

⎜⎝⎛ +⎟

⎠⎞

⎜⎝⎛=∑

= 2sin

2sin

4

1

δδπ α m

dh

mn nn

nVB (4.5b)

With n=kmf ± m k= 1, 2, 3, ... and m can be odd or even. These rms harmonic voltages are listed in Table 1 below.




ma

f

0.2 0.4 0.6 0.8 1.0

1 0.122 0.245 0.367 0.490 0.612 mf ± 2 0.010 0.037 0.080 0.135 0.195 mf ± 4 0.005 0.011 2mf ± 1 0.116 0.200 0.227 0.192 0.111 2mf ± 5 0.008 0.020 3mf ± 2 0.027 0.085 0.124 0.108 0.038 3mf ± 4 0.007 0.029 0.064 0.096 4mf ± 1 0.100 0.096 0.005 0.064 0.042 4mf ± 5 0.021 0.051 0.073 4mf ± 7 0.010 0.030

Table 1. Harmonics of VLL for a large and odd mf (mf a multiple of 3) Overmodulation (ma > 1.0)

In PWM overmodulation, the peak of the control voltage is allowed to exceed the peak of the triangular waveform. Unlike the linear region, in this mode of operation the fundamental-frequency voltage magnitude does not increase proportionally with mu. This is shown in Fig. 3, where the rms value of the fundamental-frequency line-to-line voltage VLL is plotted as a function of ma. Similar to a single-phase PWM, for sufficiently large values of ma, the PWM degenerates into a square-wave inverter waveform. This results in the maximum value of VLL equal to 0.78 Vd (fig. 6).

In the overmodulation region compared to the region with ma < 1.0, more sideband

harmonics appear centered around the frequencies of harmonics mf and its multiples. However, the dominant harmonics may not have as large amplitude as with ma < 1.0. Therefore, the power loss in the load due to the harmonic frequencies may not be as big in the overmodulation region as the presence of additional sideband harmonics would suggest. Depending on the nature of the load and on the switching frequency, the loss due to these harmonics in overmodulation may be even less than those in the linear region of the PWM.

Disadvantages with sinusoidal PWM

The biggest disadvantages with sinusoidal PWM are that the liner range is relatively small. There are many ways to extend it

• A third harmonic is added to the sine wave to make the waveform more flat topped. Adding a third harmonic does not constitute a problem as the third harmonic and multiples thereby will not been seen in the line-to-line voltage.

• The sine wave is replaced by a trapezoid or staircase wave to a flat top reference wave. • The carrier wave is only applied during the first and last 60◦ intervals per half cycle,

e.g. 0◦ to 60◦ and 120◦ to 180◦.




Figure 6. Three-phase inverter VLL/Vd as a function of ma

Figure 7. Three-phase sinusoidal PWM waveforms and harmonic spectrum




To me the frequency control model with flux proportional to V/f and voltage proportional

to the speed seems to bee the best solution. Building a solution with a rectifier, a DC link with LP-filter and a three-phase Pulse With Modulated (PWM) inverter feeding the motor. At first testing this approach with a computer model built in Simulink (Matlab) making simulations of the solution possible.

Figure 8. Voltage - frequency relation Induction Machine

4.2 Building a model

4.2.1 Simulation with Simulink / Matlab

4.2.1.1 Dynamic model for the IM Let us first consider the stator circuit. The resistance Rs of the stator winding is (for all

practical purposes) equal in all three phases. From the law of induction it follows that the part of the stator voltage which is not dissipated in the stator resistance will build up a flux in the stator winding. Hence, with vs

s as the stator voltage space vector, the following relation must hold:

0=−−dt

ds

ss

ss

s

s iRvψ

(4.6)

where is

s and ψss are the space vectors for stator current and stator flux linkage respectively.

The rotor circuit, with winding resistance Rr, can be treated in a similar way. Suppose that the rotor is observed from a coordinate system (rotor coordinates) which rotates with the same speed as the rotor ωr. Let us denote rotor coordinates with superscript "r". As the coordinate




system is rotor-fixed, there will be no induced voltage due to the rotation, so the same relation as for the stator must hold, but with “s → r”:

0=−−dt

dr

rs

sr

r

r iRvψ

(4.7)

Here vr

r, irr and ψr

r are the rotor voltage, current, and flux space vectors respectively. But the rotor winding is short-circuited, so vr

r = 0. Now, let us transform irr and ψr

r to stationary coordinates. This is a αβ transformation using the rotor position θr = ∫ ωr dt:

ψψ θθ r

r

js

r

r

r

js

r eiei rr == , (4.8)

Equation (4.7) is transformed as

0

0

00

=−−

⇒=⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛ ⎟⎠⎞⎜

⎝⎛

−−−

⇒=⎟⎠⎞⎜

⎝⎛

−−

−

−−

−

−

dt

dj

dt

dj

dt

d

s

rs

rr

s

rr

s

r

j

s

r

j

r

s

r

j

r

s

r

j

s

r

j

r

iR

eeieR

eieR

r

rr

r

r

ψψω

ψψω

ψ

θθθ

θθ

(4.9)

The induction motor is thus described by the following equations:

)(

)(

rotorjdt

d

statordt

d

iR

iRv

s

rr

s

rr

s

r

s

ss

s

s

s

s

−=

−=

ψωψ

ψ (4.10)




Figure 9. Induction machine

Let us now find a relation between the stator and rotor flux linkages. The rotor winding is referred to the stator, i.e., the rotor winding is represented by coils in the α and β directions, cf. (Fig. 9). Assuming linear magnetic conditions, the air gap flux ψαs can then be expressed as

iiiiL s

r

s

s

s

m

s

mm

s+== ,ψ α

(4.11)

where Lm is the mutual inductance between the stator and the rotor, which is also called the magnetizing inductance, and im

s, is the magnetizing current. The stator flux is the sum of the air gap flux and the stator leakage flux, the latter which under linear magnetic conditions is proportional to the stator current only. Similar reasoning for the rotor flux yields

iLiLiLiL

s

rrl

s

mm

s

r

s

ssl

s

mm

s

s

+=

+=

ψψ

(4.12)

where Lsl and Lrl are the stator and rotor leakage inductances, respectively. The leakage inductances are typically 10% of Lm or less. Alternatively, with Ls = Lm + Lsl and Lr = Lm + Lrt as the stator and rotor self-inductances, respectively, the relations can be expressed as

iLiLiLiL

s

rr

s

sm

s

r

s

rm

s

ss

s

s

+=

+=

ψψ

(4.13)

Combining (4.12) with (4.10), assuming constant inductances, yields

0

0

=−−−

=−−−

dtd

dtd

dtd

dtd

iLiLiRj

iLiLiRvs

mm

s

rrl

s

rr

s

rr

s

mm

s

ssl

s

ss

s

s

ψω (4.14)




These equations describe the dynamic equivalent circuit depicted in (Fig. 10). As there are three inductances configured in a “T”, this is known as the T-equivalent circuit.

Figure 10. Dynamic T-equivalent circuit for the induction motor

4.2.1.2 Simulink model I developed an AC/AC converter with DC-link in Simulink / Matlab (Appendix 7.1) with

a diode rectifier and a 3-phase PWM inverter controlling both the frequency and magnitude of the voltage output. The induction machine model was based on the equations of the dynamic induction machine model. For generation of PWM pulses the technique shown in Fig. (7.a-b) was used comparing sinusoidal control voltage (at the desired output frequency and proportional to the output voltage magnitude) with a triangular waveform at a selected switching frequency.

Figure 11. 3-phase PWM converter with DC-link

The harmonics in the output voltage appears as sidebands of the switching frequency and

its multiples in a PWM inverter. Therefore a high switching frequency results in an essentially sinusoidal current (plus a superimposed small ripple at a high frequency) in the motor.

Since the ripple current through the dc bus capacitor is at the switching frequency, the

input dc source impedance seen by the inverter would be smaller at higher switching: frequencies. Therefore, a small value of capacitance suffices in PWM inverters, but this capacitor must be able to carry the ripple current. A small capacitance across the diode rectifier also results in a better input current waveform drawn from the utility source. However, care should be taken in not letting the voltage ripple in the dc bus voltage become too large, which would cause additional harmonics in the voltage applied to the motor.




In a PWM inverter output voltage, since the harmonics are at a high frequency, the ripple

in the motor current is usually small due to high leakage reactances at these frequencies. Since these high-frequency voltage harmonics can have as high or even higher amplitude compared to the fundamental-frequency component, the iron losses (eddy current and hysteresis in the stator and the rotor iron) dominate. In fact, the total losses due to harmonics may even be higher with a PWM inverter than with a square-wave inverter. This comparison would of course depend on the motor design class, magnetic material property, and switching frequency. Because of these additional harmonic losses, it is generally recommended that a standard motor with a 5-10% higher power rating be used.

In a PWM drive, the pulsating torqueses developed are small in amplitude and are at high frequencies (compared to the fundamental). Therefore, as shown in (Eq. 4.10), they produce little speed pulsations because of the motor inertia.

inertiafrequencyripple

letorquerippofamplitudekespeedripplofAmplitude×

= (4.10)

Parameter PWM Square Wave CSIInput power factor + - - - Torque pulsation ++ - - Multi motor capability + + - Regeneration - - ++ Short-circuit protection - - ++ Open-circuit protection + + - Ability to handle undersized motor + + - Ability to handle oversized motor - - - Efficiency at low speeds - + + Size and weight + + - - Ride-trough capability + - -

Table 2. Comparison of Adjustable Frequency Drives




4.2.1.3 Simulation results

Figure 12. Simulation of Induction Machine start

4.3 Analysis of results The volt hertz (V/f) Pulse-Width-Modulation model seems to fulfill perhaps not all but

most of the requirement stated earlier in this document (3.1.2). Making an increase in the current supplied to the induction machine up to 16 amperes possible without big losses in the speed controller, thereby decreasing heat inside the enclosure. The 3-phase output gives a better feed to the induction machine without extra components needed on the motor and also produces a higher starting torque and reduced speed pulsation amplitude.

4.4 Future work

4.4.1 Implementation with Digital Signal Processor (DSP) Traditionally motor control was designed with analog components; they are easy to

design and can be implemented with relatively inexpensive components. However, there are several drawbacks with analog systems. Aging and temperature can bring about component variation causing the system to need regular adjustment, as the parts count increase the reliability of the system decreases. Analog components raise tolerance issues and upgrades are difficult as the design is hardwired. Digital systems offer improvements over analog




designs. Drift is eliminated since most functions are performed digitally, upgrades can easily be made in software and part count is also reduced since digital systems can handle several functions on chip.

Digital Signal Processors go on further to provide high speed, high resolution and sensor

less algorithms in order to reduce system costs. Providing a more precise control to achieve better consumption or radiation performances often means performing more calculations, the use of some 1-cycle multiplication & addition instructions included in a DSP speeds-up calculations.

Generally fixed point DSPs are preferred for motor control for two reasons. Firstly, fixed

point DSPs cost much less than the floating point DSPs. Secondly, for most application a dynamic range of 16 bits is enough. If and when needed, the dynamic range can be increased in a fixed-point processor by doing floating-point calculations in software.

5 Summary and conclusions It seem to me that switching from “volt control” to “frequency control (volt / hertz)”

method would make it possible to achieve the increase in current supplied to the induction motor requested by LSI Svenska AB without excessive heat buildup inside the speed controller housing. 3-phase output from the PWM inverter will reduce speed pulsation and produce a higher starting torque making it possible to reduce the size of the motor. There will be no need for manual adjustment of each unit, but the component cost and technical complicity are going in the wrong direction.

For the future Digital Signal Processors may be the best solution providing high speed,

high resolution and sensor less algorithms in order to reduce system costs. Upgrades can easily be made in software and part count is also reduced since digital systems can handle several functions on chip.




6 References I. Sadarangani, C., “Electrical Machines”,

Royal Institute of Technology, Stockholm, Sweden, (2000)

II. Mohan N, Undeland, T. M. and Robbins, W. P., “Power Electronics”, John Wiley & Sons Inc., USA, (2003)

III. Harnefors, L., “Control of Power Electronic Converters and Variable-Speed Drives”, Mälardalen University, Västerås, Sweden, (1999)

IV. Slemon, G. R, “Electric Machines and Drives”,

Addison-Wesley Publishing Company, USA, (1992)

V. Sarma, M. S, “Electrical Machines, Steady-State Theory and Dynamic Performance”, West Publishing Company, USA, (1994)

VI. El-Hawary, M. E, “Principled of Electric Machines with Power Electronic App.”, John Wiley & Sons Inc, USA, (2002)




7 Appendix

7.1 Simulink model

Continuous

pow ergui

v+-

Vab

Terminator1

TerminatorSelector

Scope I_Sw1 I_Sw2

Scope IM

Scope Fundamental

0

Multimeter

Tr1a

Tr1b

Tr2a

Tr2b

Vd+

A

B

Vd-

IGBT Bridge

5.77e-4*u^2

Fcn

In

Mag

Phase

Discrete Fourier1

In

Mag

Phase

Discrete Fourier

Tr1a

Tr1b

Tr2a

Tr2b

DiscretePWM Generator

4 pulsesDC 400V

C1

Tm is_abc

Te

wr

A

B

C

3 Phase IM

Vab

Is f und.

Vab f und.

I_Sw1 I_Sw2

is_abcis_abc

Te

wr

Figure 13. Main Simulink model

4Tr2b

3Tr2a

2Tr1b

1Tr1a

? ? ?

Triangular Wave

Tri

To Workspace5

Sinref

To Workspace4Sine Wave

Sign1

Sign

1

Constant

Figure 14. Discrete PWM Generator 4 pulses




4 Vd+ 3 Vd-

2 B 1 A

g

CE

IGBT4

g

CE

IGBT3

g

CE

IGBT2

g

CE

IGBT1

D4D3

D2D14Tr2b

3Tr2a

2Tr1b

1Tr1a

Figure 15. IGBT Bridge

3wr

2Te

1is_abc

3

C

2

B

1

A

v+-

v+-

Vsre

Vsim

Tm

is_abc

wr

Te

Sub3

Vab

Vbc

Vs

Sub2

is_abc

Va

Vb

Vc

Sub1

Re(u)Im(u)

1Tm

Figure 16. Three-Phase Induction Machine (IM main)




3Vc

2Vb

1Va

Terminator

s

-+

s

-+1

is_abc

Figure 17. IM Sub. 1

1Vs

u K

u K

u K 2/3

Gain

f(u)

f(u)

f(u)

2

Vbc

1Vab





3Te

2wr

1is_abc

rs

rs

rr

rr

p

p

Vsre

isre

rs

Vsim

isim

irre

rr

irim

Tm

J

Out

Sub2

FIs

FIr

is

ir

Te

Sub1

ReIm

ReIm

J

J

[Te]

[p]

[firi]

[firr]

[fisi]

[fisr]

[wr]

[firi]

[firr]

[fisi]

[Te]

[wr]

[fisr]

f(u)

f(u)

Re(u)Im(u)

Re(u)Im(u)

3Tm

2Vsim

1Vsre


Product4

3Te

2ir

1is

Product5

Product3

Product1

Procuct2

Ls

Ls

Lr

Lr

[p]

f(u)

Fcn1

Divide1

DivideIn1Out1

Conjugate

Im(u)

Lm

f(u)

2FIr

1FIs

Figure 20. IM Sub. 3.1




1Out

x' = Ax+Bu y = Cx+Du

[Te]

[p]

[wr]

[firi ]

[firr]

[wr]

f(u)

f(u)

f(u)

f(u)

f(u)

10J

9Tm

8irim

7rr

6irre

5isim

4Vsim

3rs

2isre

1Vsre

Figure 21. IM Sub. 3.2

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