Power electronic handbook

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1118 A. M. Trzynadlowski

Special Committee on Radio Interference (CISPR), both

already mentioned in the introduction to this chapter. The

series of IEC standards, IEC 61000-1 through IEC 61000-6,

covers all aspects of EMC. The FCC standards are harmonized

to IEC, as are the European Norms (EN) used in the European

Union (EU). Some speciﬁc EMC standards have also been

published by International Organization for Standardization

(ISO).

In 1992, the EU eliminated internal borders, necessitat-

ing a common system for establishing EMC standards and

accreditation, testing, and certiﬁcation procedures. The “New

Approach” and “Global Approach” have been initiated, whose

goal is to include EU directives into national laws of EU states,

harmonize national standards with the European standards,

and ensure validity of test reports and conformity certiﬁcates

between all Member States.

According to the “New Approach,” technical contents

have been removed from the European Directives and

entrusted to the European Standardization Bodies, which

are Comitè Europèen de Normalization (CEN), Comitè

Europèen de Normalization Electro-Technique (CENELEC),

and European Telecommunication Standards Institute (ETSI).

The key European Directive 89/336/EEC “Electromagnetic

Compatibility” gives only a general deﬁnition of the essen-

tial protection requirements for all electric and electronic

equipment and systems, while referring to CENELEC and

ETSI standards for technical details. The “Global Approach”

requires every product on the European market to have the

permanent “CE” marking, which indicates that the afﬁxer

declares, and takes full responsibility of, the conformity to all

applicable European directives.

The EMC Directive 89/336/EEC sets up emission and

immunity requirements. It deﬁnes (a) components, (b) sys-

tems, and (c) installations. The Directive applies only to

components performing direct function and to the systems.

Standards referred to in the Directive are divided into basic

standards, generic standards, and product standards. The basic

standards deﬁne general EMC requirements and testing pro-

cedures, without specifying any limit values or assessment

criteria. Generic standards specify the requirements for prod-

ucts in speciﬁc electromagnetic environments. For instance,

EN 50081-1 applies to emissions in residential, commercial,

and light industrial equipment, the latter including power

supplies for industrial equipment, and EN 50081-2 to emis-

sions in industrial environments. Respective immunity norms

are EN 50082-1 and EN 50082-2. Product standards address

EMC requirements for certain products and product families,

such as household appliances, information technology equip-

ment, or generic light industrial equipment, Various European

Norms are employed as the product standards.

The IEC 555-2 (EN 60555-2), IEC 1000-3-2 (EN 61000-

3-2), and IEC 1000-3-4 are emission standards for low-

frequency harmonics, closely associated with operation of

power electronic converters. Voltage ﬂuctuations and ﬂicker

(impression of unsteadiness of visual sensation induced by a light

stimulus whose luminance or spectral distribution ﬂuctuates in

time) emission limits are deﬁned in IEC 555-3 (EN 555-3),

IEC 1000-3-3 (EN 61000-3-3), and IEC 1000-3-5. IEC 61000-

4-7 and IEC 61000-4-15 deﬁne the required instrumentation

for EMI measurements. Radio-frequency conducted and radi-

ated emissions are dealt with in EN 55011, EN 55014, and

EN 55022, while CISPR 16 is the basic standard for radio-

interference measurements. Finally, IEC 1000-4-1 through IEC

1000-4-12 are immunity standards.

EMC standards are continuously being developed and

revised. Therefore, it is important to keep track of standards’

publication dates (DoP) and dates of withdrawal (DoW) of

conﬂicting earlier standards. Temporary EN standards are

called ENV. Numerous Internet resources are available, in

particular:

• American National Standards Institute (ANSI).

• Canadian Standards Association.

• Electronic Industries Association (EIA).

• European Telecommunications Standards Institute

(ETSI).

•

Federal Communications Commission (FCC).

•

IEEE Standards Association.

• International Electrotechnical Commission (IEC).

• International Organization for Standardization (ISO).

• National Institute of Standards and Technology (NIST).

• NSSN, A National Resource for Global Standards.

• Society of Automotive Engineers (SAE).

• Standards Australia.

• VCCI (Japanese EMC Regulation and Certiﬁcation).

• Verband Deutscher Elektrotechniker e. V. (VDE -

German standards).

For more EMC information links go to http://www.

dbtechnology.co.uk/links.htm. A comprehensive treatment of

contemporary EMC issues can be found in [13].

References

1. D. A. Weston, “Electromagnetic Compatibility: Principles and Appli-

cations,” 2nd Ed., Marcel Dekker, New York, 2001.

2. J. J. Carr, “The Technician’s EMI Handbook,” Nevnes Press, Woburn,

2000.

3. M. Mardiguian, “EMI Troubleshooting Techniques,” McGraw Hill,

New York, 1999.

4. C. R. Paul, “Introduction to Electromagnetic Compatibility,” John

Wiley, New York, 1992.

5. H. W. Ott, “Noise Reduction Techniques in Electronic Systems,” 2nd

Ed., John Wiley, New York, 1988.

6. L. Tihanyi, “Electromagnetic Compatibility in Power Electronics,”

IEEE Press, New York, 1995.

7. R. L. Ozenbaugh, “EMI Filter Design,” 2nd Ed., Marcel Dekker,

New York, 2001.

40 EMI Effects of Power Converters 1119

8. M. J. Nave, “Power Line Filter Design for Switched-Mode Power

Supplies,” Van Nostrand Reinhold, New York, 1991.

9. R. L. Kirlin, M. M. Bech, and A. M. Trzynadlowski, “Analysis of

Power and Power Spectral Density in PWM Inverters with Ran-

domized Switching Frequency,” IEEE Transactions on Industrial

Electronics, vol. 49, no. 2, pp. 486–499, Apr. 2002.

10. M. Vilathgamuwa, J. Deng, and K. J. Tseng, “EMI Suppression with

Switching Frequency Modulated DC-DC Converters,” IEEE Industry

Applications Magazine, vol. 5, no. 6, pp. 27–33, 1999.

11. A. M. Trzynadlowski, M. Zigliotto, and M. M. Bech, “Random

Pulse Width Modulation Quiets Motors, Reduces EMI,” PCIM Power

Electronics Systems Magazine, pp. 55–58, Feb. 1999.

12. G. L. Skibinski, R. J. Kerkman, and D. Schlegel, “EMI Emissions

of Modern PWM AC Drives,”IEEE Industry Applications Magazine,

vol. 5, no. 6, pp. 47–80, 1999.

13. L. Rosetto, P. Tenti, and A. Zuccato, “Electromagnetic Compatibility

Issues,” IEEE Industry Applications Magazine, vol. 5, no. 6, pp. 34–46,

1999.

Computer Simulation of Power

Electronics and Motor Drives

Michael Giesselmann, P. E.

Center for Pulsed Power and Power

Electronics, Department of

Electrical and Computer

Engineering, Texas Tech

University, Lubbock,

Texas, USA

41.1 Introduction ........................................................................................ 1121

41.2 Use of Simulation Tools for Design and Analysis........................................ 1121

41.3 Simulation of Power Electronics Circuits with PSpice



................................ 1122

41.4 Simulations of Power Electronic Circuits and Electric Machines.................... 1128

41.5 Simulations of AC Induction Machines Using Field Oriented (Vector) Control 1131

41.6 Simulation of Sensorless Vector Control Using PSpice



............................... 1135

41.7 Simulations Using Simplorer



................................................................ 1141

41.8 Conclusions ......................................................................................... 1144

References ........................................................................................... 1145

41.1 Introduction

This chapter shows how power electronics circuits, electric

motors, and drives, can be simulated with modern simula-

tion programs. The main focus will be on PSpice



, which

is one of the most widely used general-purpose simulation

programs and Simplorer



, which is more specialized towards

the power electronics and motor drives application area. Ali

Ricardo Buendia, who obtained his M.S.E.E. degree from Texas

Tech University, has created the examples for Simplorer



. The

PSpice



examples have been developed for the free student

version of OrCAD Capture 9.1 from Cadence. The author

found the use of examples that can be run on the student ver-

sion very beneﬁcial in an educational environment, since such

examples can be shared with students to enhance their under-

standing of the lecture material. This shall by no means lead to

the conclusion, that the programs and simulations presented

here cannot be used for serious professional work. In fact, the

author has used these tools with great success in many research

and consulting projects. In addition to the programs men-

tioned above, MathCAD



has been used to derive and present

the underlying equations. The advantage of using MathCAD



for this purpose is that in MathCAD



it is possible to check

equations by actually executing them.

The examples have been developed to illustrate advanced

techniques for simulation of systems from the power elec-

tronics and drives area but not to teach the basic features

of the individual programs. It is assumed, that the reader

will familiarize themself with the basics on how to run the

programs using the accompanying documentation. In addi-

tion, it is assumed, that the reader is familiar with the

basics of power electronics and electric machines, speciﬁ-

cally AC induction machines. For a review the reader shall be

referred to [1] for power electronics and [2, 3] for induction

machines.

41.2 Use of Simulation Tools for Design

and Analysis

It is appropriate to reﬂect upon the value of simulations and

its place in the design and analysis process before any in-depth

discussion of speciﬁc simulation examples. Computer simula-

tions enable engineers to study the behavior of complex and

powerful systems without actually building or operating them.

Simulations therefore have a place in the analysis of existing

equipment as well as the design of new systems. In addition,

computer simulations enable engineers to safely study abnor-

mal operating or fault conditions without actually creating

such conditions in the real environment.

However, the reader should be reminded that even the most

modern simulation programs cannot perfectly represent all

parameters and aspects of real equipment. The accuracy of the

1121

1122 M. Giesselmann

simulation results depends on the accuracy of the component

models and the proper identiﬁcation and inclusion of parasitic

circuit elements such as parasitic inductance, capacitance, and

mutual coupling. Accuracy of component models in this con-

text shall not mean that the model is actually faulty but rather

that the limitations of the model are exceeded. For exam-

ple, if the transformer inrush phenomenon were to be studied

using a linear model for a transformer, the simulation would

not yield useful results.

In particular, the precise prediction of voltage and current

traces during fast switching transitions in power electronics

circuits has been proven to be difﬁcult. To obtain useful

results, extensive experimental validation, advanced device

models (and the values for their parameters!), and detailed

knowledge of parasitic elements, including the ones of the

packaging of the circuit elements, are necessary. In addition,

numerical convergence is often a problem, if gate-drive signals,

with rise and fall times as steep as in real circuits, are applied.

Therefore, the exact prediction of waveforms during switch-

ing transitions shall be excluded from the discussions in this

chapter. Consequently, the author prefers to measure param-

eters such as voltage rise and fall times, over and undershoot

etc. on actual circuitry in the laboratory.

Sometimes, users of PSpice



claim that the convergence

problems are so severe, that it’s use for simulations of power

electronics circuits is just not possible or worth the effort.

However, this is absolutely not true and with the proper tech-

niques of gate signal generation, we can simulate just about any

given circuit with little or no convergence problems. In addi-

tion, if convergence problems are avoided, simulations run

much faster and larger numbers of individual transitions can

be studied. This is achieved by generating gate signals that are

slightly less steep than in real circuits using analog behavioral

elements. This gives a lot of insight into the cycle-by-cycle

as well as the system level behavior of a power electronics

circuit. In this fashion, the function of an existing, as well

as the expected performance of a new proposed circuit can be

studied. An excellent application for these cycle-by-cycle simu-

lations is the development and veriﬁcation of control strategies

for the power semiconductors.

Analog behavioral modeling (ABM) techniques included

in PSpice



can be used to study large and complex systems

like the control of induction machines using ﬁeld oriented

(also called vector) control techniques. Examples are given

that replace the power electronics inverter with an ABM

source that produces voltages, which represent the short-

term average (ﬁltering away the voltage components of the

switching frequency and above) of the output of a three-

phase inverter. These examples represent pure system level

simulations, which could have also been done using programs

like MatLab/Simulink



. However, circuit simulation programs

provide the option of studying actual circuit level details in

complex systems. To demonstrate this capability, the start-up

of an induction motor, fed by a three-phase metal oxide

semiconductor ﬁeld effect transistor (MOSFET) inverter, is

presented.

In all modeling cases, the user needs to deﬁne the goal of

the simulation effort. In other words, the user must answer the

question “What information shall be obtained through the

simulation of the circuit or system?” The user must then

select the appropriate simulation software and the appropri-

ate models. This process requires a detailed understanding of

the properties and limitations of the device models and the

sensitivity of the results to the model limitations. In order to

obtain such an understanding, it is often recommended and

necessary to perform numerous simulation test runs, carefully

scrutinize the results and compare them with measured data,

results from other simulation packages or otherwise known

facts.

41.3 Simulation of Power Electronics

Circuits with PSpice



The ﬁrst example of a power electronics circuit is a step-down

(also called buck) converter with synchronous rectiﬁcation.

For the purpose of synchronous rectiﬁcation, the diode, which

connects the inductor to ground in the regular circuit, is

replaced with a power MOSFET transistor. The beneﬁt of this

circuit is that the power MOSFET represents a purely resistive

channel in the on state. This channel does not have a residual,

current independent, voltage drop like the p–n junction of a

diode. Therefore, the voltage drop across the MOSFET can

be made lower than what can be achieved with diodes. The

results are reduced losses and increased efﬁciency. To achieve

this, the lower MOSFET must be turned on whenever the

upper MOSFET is turned off and the current in the induc-

tor is positive. If the current in the inductor is continuous,

the drive signal for the lower MOSFET is simply the inverted

drive signal for the upper MOSFET. However, if the current

in the inductor is discontinuous, the drive signal for the lower

MOSFET must be cut off as soon as the current in the inductor

goes to zero.

Figure 41.1 shows a simulation setup for a synchronous

buck converter that can operate correctly for continuous as

well as discontinuous inductor current. As mentioned before,

the key element of this example is the circuit for the genera-

tion of the gate-drive signals for the MOSFETs. For clarity, this

circuit has been realized using only standard elements from

the libraries of the evaluation version. The basic principle of

the operation of the gate-drive circuit is the well-known car-

rier based scheme, where a control voltage is compared with

a triangular carrier with ﬁxed amplitude. An “ABM” block,

shown in the lower left part of Fig. 41.1, generates the trian-

gular carrier. Equation (41.1) shown below gives the closed

form equation for the triangular carrier wave. The output

41 Computer Simulation of Power Electronics and Motor Drives 1123

0.5

Triangle

PWM

+15

−15

2 −

E −

IN–OUT −

IN–OUT +

EVALUE

2 +

1 −

1 +

E +

20uF

IC = 0V

Out

Rload

50V

Vin

IRF150

1−

2−

1mH

PARAMETERS:

SW = 10k

PI = 3.14159265

(1/Pi)*

Acos(Cos

(2*Pi*Fsw*Time

+Pi/2))

IF(V(%IN+)<

–2, IF(V(%IN–)>40m, –V(%IN+),0),0)

IF(V(%IN+)>2, V(%IN+),0)

FIGURE 41.1 Simulation setup for a synchronous buck converter.

range of the function shown in Eq. (41.1) is between 0.0

and 1.0.

Tri

(

)

acos



cos



2πFswt +



(41.1)

For the generation of the gate-drive signals, the carrier

wave is compared with a control signal that can have val-

ues between 0.0 and 1.0, corresponding to a duty cycle input

between 0 and 100%. Feeding the difference of the carrier

wave and the control signal into a soft comparator generates

the primary PWM signal. Careful inspection of the implemen-

tation of the soft-limiter element provided in the evaluation

version of PSpice



shows that it uses a scaled hyperbolic tan-

gent function. Figure 41.2 shows a plot of a hyperbolic tangent

function. It can easily be seen, that the result of the soft-limiter

is an output signal with smooth transitions, which is crucial

to avoid convergence problems in PSpice



. The soft-limiter

used here has an upper and lower limit of ±15 V and a gain

(steepness control for the tanh function) of 50.

Figure 41.3 shows the output of the simulation run for the

synchronous buck converter. The top-level graph shows the

generated triangle carrier. It has a frequency (Fsw, see param-

eter statement in Fig. 41.1) of 10 kHz. This frequency has been

chosen rather low to improve the readability of Fig. 41.3. In the

graph of the triangle voltage in Fig. 41.3, the gate-drive signals

are shown for both MOSFET transistors. Please note, that the

gate-drive signal for the lower MOSFET is vertically shifted

by 30 V in order to separate the traces for readability. The

graph below the gate-drive signals shows the inductor current.

It can be seen that the current is discontinuous after the initial

inrush peak. The inrush peak is caused by the fact that the

capacitor is initially discharged (IC = 0 V). It is evident, that

the gate-drive signal of the lower (synchronous rectiﬁcation)

MOSFET is appropriate for the inductor current. The bot-

tom trace shows the capacitor voltage, which has a steady-state

value of slightly more than 0.5 × 40 V (0.5 = 50% being the

duty cycle and 40 V being the input voltage) due to the fact that

the inductor current is slightly discontinuous even at steady-

state conditions. To test the gate-drive circuit for the lower

MOSFET, the load has been chosen such that the steady-state

current would be discontinuous. Following the soft-limiter are

two voltage-controlled voltage sources that generate isolated

gate-source voltages of 15 V for the on condition and 0 V for

the off condition of the MOSFETs. To enable operation with

discontinuous inductor current, the source “E−” in Fig. 41.1

also monitors the polarity of the inductor current through a

current-controlled voltage source “H1” with unity gain.

In addition to the cycle-by-cycle simulation of a DC–DC

converter, it is also possible to use a time-averaged replacement

for the MOSFET transistors used in the circuit in Fig. 41.1.

In fact, a common time-averaged model can be used for the

buck, the boost, the buck–boost, and the Cuk converter as

1124 M. Giesselmann

tanh - Function

1.1

–1.1

tanh(x)

–1

–6 –4 –2 0 2 4 6

FIGURE 41.2 Plot of a hyperbolic tangent function used to generate smooth PWM signals.

1.5V

1.0V

0.5V

20V

2.0A

–30V

SEL

4.0A

50.0V

37.5V

25.0V

12.5V

0s 0.5ms 1.0ms 1.5ms 2.0ms 2.5ms 3.0ms 3.5ms 4.0ms

Time

Output Voltage

Triangle Voltage

Gate Voltages

Inductor Current

V (Triangle)

V(1

+,1–)

I(L1)

V(Out) 25V

V(2

+,2–)–30

FIGURE 41.3 Output waveforms for the synchronous buck converter.

long as they operate with continuous inductor current. The

time-averaged model has the advantage that it can run much

faster since it does not have to follow each switching transi-

tion. It is also possible to perform DC and AC sweep analyses.

A DC sweep would sweep the duty cycle over a wide range

and show the output voltage as a function of the duty cycle.

An AC sweep analysis would sweep the frequency of an AC

signal, which is superimposed on top of the duty cycle bias

signal. The AC sweep allows the study of the behavior of the

converter, including a feedback control system, in the fre-

quency domain for traditional stability analysis and system

tuning. A detailed description of this time-averaged modeling

technique, including detailed examples is given in [4].

To illustrate the capabilities of the PSpice



simulation pro-

gram, the next example shows a complete three-phase inverter

bridge using six power MOSFETs. This circuit is shown in

Fig. 41.4. Note that free-wheeling diodes are an integral part

of every power MOSFET and are not shown separately. The

inverter drives a three-phase load, which could represent an

induction motor for a singular operating point. The load is

connected to the inverter output terminals with so-called con-

nection bubbles. Due to the number of elements involved, the

41 Computer Simulation of Power Electronics and Motor Drives 1125

PWM_Generator

Pos

M2M1

M4 M5

25 150mH

150mH

IRF150

IRF150IRF150

IRF150

Neg

150V

Vbus+

Vbus−

2−

1−

3−

5−

6−

4−

6−

5−

4−

3−

2−

1−

2−

3−

4−

5−

6−

PARAMETERS:

M_A = 0.8

AC_FREQ = 60

AC_AMP = {m_a}

FSW = 3.6k

PI = 3.14159265

R_load_a

R_load_b

R_load_c L_load_c

L_load_b

L_load_a

FIGURE 41.4 Circuit for a three-phase inverter with MOSFETs.

circuit for the gate drive-signal generation is contained in a

hierarchical block. Blocks like this are available from the main

toolbar in the schematic editor. Selecting “Descend Hierarchy”

for the block called “PWM_Generator” reveals the subcircuit

which is shown in Fig. 41.5.

The hexagonal shaped symbols named “1+,” “1−,” “2+,”

etc. are called interface ports. These interface ports provide the

connection between the subcircuit and the ports of the hierar-

chical block above. Here the connection is to the ports (dots)

on the “PWM_Generator” block. The interface ports are cre-

ated by simply drawing a wire up to the boundary of the block.

The name of the port is initially generic, “Px,” where x is a run-

ning number, but can be easily edited by double-clicking on

the generic name. After drawing a block and creating all the

ports, right-clicking the “Descend Hierarchy” will open up a

schematic page for the subcircuit which has all the appropri-

ately named interface ports already in it. Additional details on

hierarchical techniques can be found in [5].

The circuit shown in Fig. 41.5 is similar to the gate-drive

generation circuit discussed before. Circuits like the circuit

shown in Fig. 41.1, compare a triangular carrier with one or

more reference signals. In this case, three reference signals,

one for each phase, are used. The triangular carrier signal is

symmetrical with respect to the time axis. The values cover the

range from −1.0 to 1.0. The equation for the triangular carrier

for PWM modulation for AC reference signals is given by the

Eq. (41.2).

Tri

(

)

a sin



sin



2πf

t +



(41.2)

The three reference signals are sinusoidal signals with equal

amplitude and a relative phase shift of 120

◦

. For linear mod-

ulation, the amplitude range of the reference signals is limited

to the amplitude of the triangular carrier, e.g. 1 V. The ratio

of the reference wave amplitude and the (ﬁxed) carrier ampli-

tude is called amplitude modulation ratio “m_a.” In the circuit

shown in Fig. 41.4 “m_a” has a value of 0.8. This value is

deﬁned by a parameter symbol and represents a global param-

eter, which is visible throughout all levels of the hierarchy.

The phase to neutral voltage amplitude of each inverter leg

is equal to “Vbus+” (shown in Fig. 41.4) multiplied with the

amplitude modulation ratio. The frequency and waveshape of

the phase to neutral voltage of each phase leg is equal to the

reference waveform, if the high-frequency components result-

ing from the carrier wave are ﬁltered away. This way, each

inverter leg can be viewed as a linear power ampliﬁer for

its reference voltage. In fact, in drive applications, inverters

are often called “servo-ampliﬁers.” The load typically reacts

1126 M. Giesselmann

FREQ = {AC_freq}

PHASE = +120

VAMPL = {AC_amp}

FREQ = {AC_freq}

PHASE = −120

PHASE = 0

VAMPL = {AC_amp}

V_c

V_b

V_a

V_ref_c

V_ref_b

V_ref_a

Vtriangle

PWMc

PWMb

PWMa

500

+15

−15

500

+15

−15

3−Phase SPWM Generator:

Level Shifter and Driver

−

(2/Pi)*

Asin(Sin

(2*Pi*Fsw*Time

+Pi/2))

EVALUE

IF(V(%IN+)<–2.0, –V(%IN+),0)

IF(V(%IN+)>2.0, V(%IN+),0)

IF(V(%IN+)<–2.0, –V(%IN+),0)

IF(V(%IN+)>2.0, V(%IN+),0)

E_a+

1−

2−

3−

4−

5−

6−

IN−OUT−

IN−OUT+

IN−OUT−

IN−OUT+

IN−OUT−

IN−OUT+

IN−OUT−

IN−OUT+

IN−OUT−

IN−OUT+

IN−OUT−

IN−OUT+

E_b+

E_c+

E_a−

E_b−

E_c−

−

FIGURE 41.5 PWM generation subcircuit for a three-phase MOSFET inverter.

only to the low-frequency components of the inverter output

voltage. The high-frequency components, which include the

triangular carrier frequency (also called switching frequency)

and its harmonics, are typically “just a blur” for the load. This

is especially true in recent times, where switching frequencies

of 20 kHz and above are possible. As an added beneﬁt, audible

noise is avoided at these frequency levels.

The circuit involving the soft-limiter and level-shifter/high-

side driver in Fig. 41.5 is very similar to the circuit for the

synchronous buck converter, except for the fact that the load

current is not monitored. The control functions for the “E_x+,

E_x−” sources, where x denotes the phase, are chosen such

that the activation voltage levels are ±2 V. If the output voltage

of the soft-limiter is between −2 and +2 V, no MOSFET is

activated, and shoot-through, meaning a short circuit between

the positive and negative bus, is avoided.

Figure 41.6 shows the simulation results for the three-phase

inverter. The time scale is slightly stretched, to better show

the details of the PWM signals. The line-to-line voltage V

and the load current in all three phases are shown. Due to the

inductors contained in the load, the current cannot instan-

taneously change and follow the PWM signal. Therefore the

load currents are almost pure sinusoids with very little ripple.

This is representative of the real line currents in induction

motors.

Figure 41.7 shows an example where the MOSFETs in

Fig. 41.4 have been replaced with insulated gate bipolar tran-

sistor (IGBT). The particular IGBT shown here is included in

the library of the evaluation version. Note that free-wheeling

diodes are needed, if IGBTs are used. The free-wheeling diodes

carry the load current when the IGBTs are turned off to pro-

vide a continuous path for the current. This is very important,

since the load can have a substantial inductive component.

Whenever the diodes are conducting, energy ﬂows momen-

tarily back to the source. In the case of power MOSFETs, the

diodes (often called body diodes) are an integral part of the

device. In the symbol graphic of PSpice



these body diodes are

not shown for MOSFETs. For this circuit, the gate-drive circuit

and the results are the same as for the three-phase bridge with

power MOSFETs.

41 Computer Simulation of Power Electronics and Motor Drives 1127

400V

200V

–200V

–400V

SEL

4.0A

–4.0A

10ms 15ms 20ms 25ms 30ms

Time

I (R_load_a) I (R_load_b) I (R_load_c)

Line Currents in the Load:

Line to Line Voltage Vab:

V(A,B)

150

(V(PWM_Generator.V_ref_a) – V(PWM_Generator. V_ref_b))

FIGURE 41.6 Output waveforms of the three-phase inverter with MOSFETs.

PWM_Generator

150V

Vbus+

PARAMETERS:

M_A = 0.8

AC_AMP = {m_a}

AC_FREQ = 60

FSW = 3.6k

PI = 3.14159265

Neg

IGBT2

IGBT1

Pos

IGBT3

IGBT4 IGBT6

IGBT5

25 150mH

150mH

R_load_a

R_load_b

R_load_c L_load_c

L_load_b

L_load_a

1−

3−

2−

3−

4−

5−

6−

1−

2−

3−

4−

5−

6−

IXGH40N60 IXGH40N60

IXGH40N60IXGH40N60

IXGH40N60

−

4− 6−

5−

FIGURE 41.7 Three-phase inverter circuit with IGBTs.

1128 M. Giesselmann

41.4 Simulations of Power Electronic

Circuits and Electric Machines

In the following, the start-up of an induction motor, fed by

the three-phase inverter shown in Fig. 41.4, is presented. For

this purpose, the simple passive load in Fig. 41.4 is replaced

by an induction motor. For this and further discussions, it

is assumed that the reader is familiar with the theory of

induction machines. A number of excellent references are

given at the end of this chapter [2, 3, 6, 7]. The induc-

tion motor symbol represents the electro-mechanical model

of an induction motor. The model is suitable for studies of

electrical and mechanical transients as well as steady-state con-

ditions. The output pin on the motor shaft represents the

mechanical output. The voltage on this pin represents the

mechanical angular velocity using the relation 1 V = 1 rad/s.

In addition, any current drawn from or fed into this termi-

nal represents applied motor or generator torque according to

the relation 1 A = 1 Nm. Due to these deﬁnitions, the elec-

trical power associated with the voltage of the motor shaft

(with respect to ground) is identical to the mechanical power.

Following the well-known theory, the induction motor model

has been derived for a two-phase (direct and quadrature, D, Q)

PWM_Generator

Pos

200V

Vbus+

Vbus−

IRF150

IRF150 IRF150

IRF150

Motor1

R_sense_a

R_sense_b

R_sense_c

Neg

4−

2−

2+ 4+

1−

3−

5−

Torque

Omech

Ind_Motor

1−

2−

3−

4−

5−

6−

1−

2−

3−

4−

5−

6−

PARAMETERS:

FREQ_AC = 60

OMEGA = {2*Pi*Freq_AC}

PI = 3.14159265

Lin_Load1

4.0 Nm @

1765 RPM

6−

FIGURE 41.8 Induction motor start-up with three-phase inverter circuit.

equivalent motor. Attached to the motor is a bidirectional two-

phase to three-phase converter module. This module is voltage

and current invariant. This means that the voltage and current

levels in the two-phase and the three-phase machine are equal.

Consequently, the power in the two-phase machine is only two

third of the power in the three-phase circuit. This is accounted

for in the calculation of the electromagnetic torque (factor

3/2; see Eq. (41.4)). The internally generated torque can be

monitored on the output labeled “Torque” on top of the sleeve

around the motor shaft. The linear load in Fig. 41.8 is a symbol

that represents an appropriately sized resistor to ground.

In Fig. 41.8 the motor is represented by a custom symbol

called “Motor1.” A simple hierarchical block could have been

used for the motor, but a custom symbol has been created to

achieve a more realistic and pleasing graphical representation.

The symbol can be easily created with the symbol editor, which

is built into the regular schematics (capture) editor. The editor

provides standard graphical elements (lines, rectangles, circles

etc.) so that professional looking symbols can easily be created.

More details on this are shown in Figs. 41.19 and 41.20 and

the accompanying discussion. Parameters are passed onto the

subcircuit by using the name of the parameter preceded by a

‘@’ symbol. The advantage of passing parameters to subcircuits