Comparative Study of Various Computer Tools
in Electrical Engineering Courses1
Claudio A. Ca~nizares and Zeno T. Faur
University of Waterloo
Department of Electrical & Computer Engineering
Waterloo, ON, Canada N2L 3G1
Technical Report # 95-06, June 7, 1995
The work presented here was supported by the Oce of Teaching Resources and Continuing Education
(TRACE) at the University of Waterloo, through the TRACE Learning Technologies Research Grants.
Parts of this report were submitted on May 1995 for review and publication in the IEEE Transactions on
Education and the IEEE Transactions on Power Systems
1
Contents
1 Introduction
1
2 Description of the Study
3
1.1 Brief Literature Review : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :
1.2 Report Content : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :
2.1 Courses : : : : : :
2.2 Hardware : : : : :
2.3 Software : : : : : :
2.3.1 MATLAB :
2.3.2 MAPLE-V
2.3.3 EES : : : :
2.4 Tutorials : : : : : :
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3 Surveys
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1
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4 Examples and Comparisons
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5 Conclusions
24
A Final Survey
26
4.1 Transformer Dynamics : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 13
4.2 EES Modeling of AC/DC Rectier Bridge : : : : : : : : : : : : : : : : : : : : : : : 17
1
List of Figures
1
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7
8
9
Saturation curve for a two-winding lab transformer : : : : :
Transformer energization in EES format : : : : : : : : : : :
Transformer energization in MATLAB format, main le : :
Transformer energization in MATLAB format, equation le
Transformer energization in MAPLE-V format : : : : : : :
In-rush current in an unloaded single-phase transformer : :
Full-wave ac/dc rectier bridge : : : : : : : : : : : : : : : :
AC/DC rectier bridge in EES format : : : : : : : : : : : :
AC/DC rectier bridge output : : : : : : : : : : : : : : : :
2
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15
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23
List of Tables
1
2
Results of initial survey : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 10
Results of nal survey : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 11
3
Abstract
This report discusses dierent computer tools used to help deliver, administer and teach the material
covered in a second year machines course and a rst year circuits course. The computer facilities,
programs and tutorials developed are discussed, concentrating in the analysis of the results of using
these tools in the student learning process. The students' marks and the results of several student
surveys, as well as the teaching sta's observations, are used to evaluate the usefulness of the dierent
tools and determine their advantages and disadvantages. Some unexpected results regarding the
actual students' use of these tools are presented and thoroughly analyzed.
A comparison of three dierent simulation packages is also presented in this report, based on
their use as teaching tools for electromagnetic transients. The application of these programs to the
solution of a particular nonlinear problem in transformer dynamics is discussed in detail to highlight
the main dierences between them, particularly from the student's point of view. Finally, based on
the advantages and disadvantages of using these packages in the classroom, a simulation software is
recommended and used to simulate an ac/dc rectier bridge.
Chapter 1
Introduction
Computer tools to help professors and students alike in the teaching-learning process have become
very popular in the past decade or so. Scores of articles can be found in the technical and popular
literature referring to dierent software and hardware tools and the techniques to use them in learning
environments [1, 2, 3], probably due to the great leap forward in the last few years in software and
hardware development and their signicant reduced costs. Most of these papers mention many
advantages of using computer tools to improve the delivery of course material, and to presumably
help students with their retention and understanding of this information. A brief discussion of some
relevant papers follows.
1.1 Brief Literature Review
Simulation programs have been used with reasonable success in a variety of Electrical Engineering
courses throughout the world, from basic circuit analysis in freshmen courses to complex system
design and analysis at the senior and graduate levels [4, 5, 6, 7, 8]. In all of these papers, the
authors discuss several software and hardware tools and how they are used to teach dierent aspects
of Electrical Engineering. The author in [4] reports the results of a survey conducted at 82 universities
and colleges, showing a broad use of computers in the classroom and widespread use of simulation
software as an instructional tool for circuit analysis. In [5] and [6], the authors discuss in detail the
favorable use of several simulation packages as teaching aids in a variety of Electrical Engineering
courses. An in-house simulation program is presented in [7], reporting positive eects on the students'
understanding of a particular subject and improved problem solving abilities. Most of these papers
concentrate on discussing the positive aspects of simulation tools. In [8], however, the author
discusses both the advantages and disadvantages of using these tools in the classroom, concluding
that the negative aspects of using simulation packages are signicantly outweighed by the probable
benets.
1
CHAPTER 1. INTRODUCTION
2
In the area of electromagnetic transients, particularly machine transients, there are several simulation packages that have been proposed and used as teaching tools [9, 10, 11]. In [9], the authors
report on the instructional use in senior and graduate level machine courses of three dierent packages, comparing them on terms of their robustness and ease of use for the simulation of an induction
motor start-up; of these three packages, MATLAB [12] is used and discussed again in the present report. The authors in [10] demonstrate the advantages and feasibility of using symbolic-computation
packages for electromagnetic transient analysis. Although these types of programs have demonstrated to be very useful in the presentation and understanding of complex mathematical concepts
[1], they have not been widely used in electromagnetic transient studies. Nonetheless, in [11], the
author uses the symbolically based program MATHEMATICA [13] to study a series of transient and
steady state phenomena in electric machines.
1.2 Report Content
Based on their own experience and motivated by all the positive reports in the literature, particularly
on the usefulness of simulation packages for teaching electromagnetic transients, the authors of the
present report decided to use some of these programs as an integral part of two undergraduate
courses covering basic concepts in Electrical Engineering. Three packages easily accessible through
the campus PC-network were employed, namely, MATLAB [12], MAPLE-V [14], and EES [15], and
several self-explanatory tutorials were developed for these programs. To determine the eectiveness
and shortcomings of the computer tools, all students, regardless of their use of these tools, were
asked to ll several questionnaires throughout the term. Furthermore, the students' performance
was monitored and teaching sta's observations with regard to the students' use of the tools during
tutorials were recorded, in order to help draw some conclusions. This report presents the results
of the study, with the intention of giving other colleagues a more realistic view of the benets and
limitations of using computers in the classroom.
Chapter 2 describes in detail the complete set-up of the test that was carried out, i.e., the courses,
the software and hardware used, and the goals and means of using them. A brief description and
comparison of the simulation packages used to develop several computer tutorials, and the reason for
using them in the rst place, are also discussed in this chapter. Chapter 3 presents and analyzes the
surveys results, as well as the sta's observations and the students' performance in relation to their
use of the available computer tools. In Chapter 4, the results of using these programs to simulate
the energization of a single-phase transformer considering saturation are presented. In this chapter,
the use of EES to solve a nonlinear circuit problem, namely, the simulation of a single-phase rectier
bridge feeding an RL load, including capacitive ltering and detailed nonlinear models of the diodes,
is also shown. Conclusions and recommendations are presented in Chapter 5.
Chapter 2
Description of the Study
From the current literature, three areas of application for computer tools in the classroom were
primarily identied, namely, class administration, lecture delivery, and computer tutorials. In this
context, the software, hardware, and mechanisms for their use are discussed in this chapter, considering the courses where these tools were used.
2.1 Courses
Two undergraduate courses were used as the \testing ground." These were, in chronological order:
1. ME 269: Electromechanical Devices and Power Processing. This is a second year, rst term
course for Mechanical Engineering students, to introduce them to basic ideas in magnetic
circuits, electric machines and their controls. The material covered here is later used during
co-op terms, when the students work mostly in industry, and in a third year course in control
systems. The course has 3 lectures and a 2-hour tutorial class per week, with 3 lab sessions in
the term. The class attending the last oering was made up of approximately 85 students.
2. GEN E 123: Electrical Engineering. This is a rst year, second term, course for non-Electrical
Engineering students, to introduce them to basic issues in linear and non-linear circuits. It
is a prerequisite for ME 269 in Mechanical Engineering. The course has 3 lectures and a
1-hour tutorial class per week, with 4 lab sessions in the term. This course was oered to
approximately 85 Mechanical Engineering students.
The University of Waterloo Engineering program is a co-op program, with students alternating
between an academic term and a work term (4 months constitute a term), for a total of 6 working
terms in industry and 8 academic terms on campus [16]; students are usually required to take 5
courses during their academic terms. The Mechanical Engineering undergraduate program has high
3
CHAPTER 2. DESCRIPTION OF THE STUDY
4
admission standards, with a 1994 cuto average of 86% in 6 high-school advanced science courses
[17], which is considered high in Canada. Therefore, the students participating in the study can be
considered highly motivated.
The study was rst carried out with the second year class (ME 269), and then, with what was
learnt, it was modied for the rst year students (GEN E 123). The ME 269 students were compelled
to use the computer tutorials and learn a simulation package by requiring them to do a project, which
related to a transformer test done in the lab. On the other hand, the GEN E 123 students were
motivated to use the tutorials and learn the simulation package by asking them to do an optional
nal project for extra marks, in a subject that was not covered in lectures.
2.2 Hardware
All of the software used for this study is available in the campus PC-network, known as WATSTAR.
This is a DOS-based token-ring network with 1600 public and limited access terminals mostly dedicated to serve undergraduate students; 745 of these terminals are in Engineering [16, 18, 19].
WATSTAR has several ethernet gateways, so that it can reach and be reached through the Internet,
mostly for e-mail and ftp purposes, although remote access to UNIX or other servers is possible
through tcp/ip. It is interesting to highlight the fact that this network in Engineering, excluding
operating system calls, is mostly used for Word Processing (43%), followed by mail (16%), and programming (15%); only 8% of the software activity is related to math and scientic applications, i.e.,
simulation. A class disk, which typically is dedicated read-only disk space in a WATSTAR server,
was created to give students easy access to computer tutorials.
For presentations in class, a 486 PC-laptop and a LCD-screen were used mainly to discuss the
simulation packages and computer tutorials, so that these could be directly linked to the subject
presented in lectures. For the GEN E 123 class, tutorial sessions were run in a lab with computer
screens in each workbench, which made the discussion of the computer tutorials and simulation
packages easier to set up and follow than when using LCD-screens, as these have very specic
demands on lighting. After the rst experience with the ME 269 students, who were encouraged
to use the simulation packages and computer tutorials on their own time, the GEN E 123 students
were invited to work in a dedicated WATSTAR room during the tutorial sessions with the help of a
teaching assistant. Since these tutorial sessions are typically dedicated to solving previously assigned
problems with the help of teaching sta, the computer room was usually populated by students who
had solved their problems in advance, i.e., the \top" of the class.
CHAPTER 2. DESCRIPTION OF THE STUDY
5
2.3 Software
In order to help with the administration of the course, and in particular with the communication
between teaching sta and students, a news-group was created for easy access through WATSTAR.
The news-group was chosen due to its widespread use in Engineering, particularly Electrical Engineering, as this communication mechanism is less expensive than class e-mail lists, although is
certainly less personal. This news-group was mostly used to let students know in advance of issues
related to the course, such as course outlines, availability and mechanisms to access new computer
tutorials, etc. In particular, the news-group was very useful in the assignment of problems with the
corresponding answers, so that students could have extra time and a checking mechanism to work on
these problems before tutorial sessions. Students did not use the news-group to communicate with
the rest of the class or with the teaching sta, using instead e-mail for these purposes, apparently
due to the need for a more private medium.
Dierent simulation packages were chosen mostly due to easy accessibility through WATSTAR,
and also due to their proven popularity and usefulness for introducing students to dierent subjects
(e.g., [4, 5, 9]). A brief description of the three simulation packages and how and why they were
used, as well as their shortcomings and advantages, follows.
2.3.1 MATLAB
This is a powerful and versatile simulation software, very popular in industry and academia. It was
originally designed for numerical analysis of linear control systems; hence, it is very well suited for
numerical matrix manipulations. However, due to its exibility in allowing direct programming and
linking to FORTRAN and C routines, the package has grown immensely, with many added routines
to allow numerical simulations of nonlinear systems as well.
The major drawbacks of this program is its size and relative complexity; it takes some time to get
use to its language and become familiar with several of the main routines needed for basic simulations.
Equations must be handled in certain form and sequence, requiring the user to be familiar with the
phenomena being analyzed, making it somewhat complex for inexperienced users. Furthermore,
good comprehension of numerical analysis, linear algebra and linear systems is required, which
makes it somewhat inappropriate for rst year students, and sometimes dicult to understand for
second year students. For these reasons, this package was only used for the second year class, i.e.,
ME 269.
The University of Waterloo has a site-license for this program and related software, making it
readily accessible through WATSTAR. The Department of Computer Services (DCS) gives regular
introductory seminars to this package, so that students can easily learn the basics for its use in
various courses.
CHAPTER 2. DESCRIPTION OF THE STUDY
6
2.3.2 MAPLE-V
This is also a popular package, particularly at the University of Waterloo, where it has been developed
and improved. As with MATLAB, this package and related software is also easily accessible on
campus, with DCS giving regular seminars on its basic use.
The program is a very powerful package, mainly designed to do symbolic computations. It is
programmable and, therefore, very exible. Its numerical capabilities are adequate; however, these
cannot be considered its strong suit. One major problem is its complexity, particularly with regard
to notation, which is somewhat inconsistent and counterintuitive; it certainly takes a lot longer to
master than MATLAB. Furthermore, as in MATLAB, problems have to be solved in a given form,
i.e., the manner and order in which the equations are solved makes a dierence, requiring the user to
be familiar with the subject under study. Therefore, the package is not very adequate for freshmen
students, at least not for certain simulation purposes. This program was only used in ME 269.
2.3.3 EES
This is not a popular software, but it is certainly very adequate for simulation purposes. It was developed at the University of Wisconsin, as an \improvement" to an existent package called SOLVER-Q
[20]. This short program allows the user to numerically solve sets of nonlinear and/or dierential
equations simultaneously, with no regard to the order of the equations, which together with uncomplicated notation and simple to use pull-down menus makes it very easy to learn and use; the user
simply inputs the equations practically as he/she would write them on paper, and proceeds to solve
them through the use of menus. For all of these reasons, it was the preferred software by the ME 269
class, as reported below, and, consequently, it was chosen as the simulation package for the GEN E
123 group.
Although some programming can be done within the package, it is of limited scope. Other major
shortcomings are its limited graphics capabilities and its low reliability, i.e., it often crashes without
apparent reason. Some basic knowledge of numerical methods is required, although not fundamental;
for certain problems, it is important to understand how the program proceeds with its calculations
in order to be able to obtain a reasonable solution.
As with MATLAB and MAPLE, the University has a site-license, which makes the program
easily accessible.
2.4 Tutorials
Based on the simulation packages described above, several computer tutorials were designed for
each course. The main goal was to create self-contained tutorials that would allow the student to
review important equations and concepts discussed in lectures, through personal unsupervised use
CHAPTER 2. DESCRIPTION OF THE STUDY
7
and presentations in class. The tutorials below were developed for the ME-269 class in MATLAB,
MAPLE-V, and EES to give students a choice of simulation package and to allow the teaching sta
to determine the advantages and disadvantages of the dierent programs.
1. Phasor analysis: A simple R-L circuit was used to illustrate the advantages of phasor analysis
versus time domain simulation.
2. Transformer dynamics: The energization of a loaded single-phase transformer without considering saturation was discussed in this case. The parameters of the transformer were calculated
from the open-circuit and short-circuit tests. In this case, the dierential equations had to be
converted to matrix form for MATLAB and MAPLE-V.
3. Transformer saturation (project): This tutorial presented the energization of an unloaded
single-phase transformer considering saturation (in-rush currents). The core saturation was
modeled by both a piecewise-linear function and a continuous nonlinear function. Piecewiselinear saturation produced some numerical problems in EES, and was not possible to implement
in MAPLE-V. The data in this case was obtained from direct lab measurements.
4. Transformer eciency: Eciency versus load graphs were obtained for a single-phase transformer at dierent power factors. This problem was extracted directly from the textbook to
give the students a sense of a useful direct application of the simulation packages.
5. DC generator: V-I characteristics were obtained for a dc shunt generator using a piecewiselinear saturation curve.
6. Induction motor: In this tutorial, the steady state torque-speed characteristic of a three-phase
induction motor were computed.
Based on feedback from students and teaching sta of ME 269, only EES was used to develop
the computer tutorials described below for the rst year GEN E 123 class. This was the preferred
simulation package due to its simplicity and short learning curve, with enough computational power
to handle the type of simulations required.
1. Nonlinear equations: The parametric solution of a set of nonlinear equations was used to
introduce the main features of the simulation program, including tables and graphics, during
a tutorial session.
2. KVL and KCL: Voltages and currents of a textbook resistive circuit were calculated for dc and
ac voltage sources.
3. Dierential equations: A textbook R-L-C circuit was used to set up and solve the corresponding
dierential equations, for dc and ac sources, assuming zero initial conditions.
CHAPTER 2. DESCRIPTION OF THE STUDY
8
4. Circuit transients (optional project): An R-L-C dc circuit out of the textbook was used to
obtain the voltages and currents for a series of switching events.
5. Superposition: A resistive circuit from the textbook was used to demonstrate the principle of
superposition with ac and dc sources.
6. AC circuit: An R-L circuit was used to demonstrate the advantages of phasor analysis versus
time domain analysis.
7. Active lter: The output signal of an OPAMP band-pass lter was calculated at dierent
frequencies for a square-wave input voltage. The input signal was modeled using a nite
number of terms of the corresponding Fourier series.
8. AC/DC rectier: An ac/dc rectier bridge was solved using the basic nonlinear equation of a
Ge diode to obtain the voltage in an R-L load with capacitive ltering.
Chapter 3
Surveys
To determine how the computer tools were being used and whether these were actually helping
in the understanding of the course material, students were asked to answer several questionnaires
throughout the term. The ME 269 class was given three surveys, at the beginning, middle and end
of the term, whereas the GEN E 123 group was asked to ll out only two, one at the beginning and
one at the end of the course. The nal questionnaire for the ME 269 class is presented in Appendix
A, to give the reader a clear picture of the types of questions that were asked.
The surveys for both classes were rather similar. The rst one concentrated on determining the
students previous knowledge of software and computers, with particular interest in their familiarity
with and use of communication and simulation packages. The questionnaire included a question on
the students expectations of the use of these packages in the course, to later compare with their
actual observations and use of these tools. Table 1 shows the students' answers to the main questions
in the survey; observe the higher rate of response from the second year students, although this have
no bearing on the nal results.
Several important conclusions can be drawn from these survey results. First, the majority of
the students were familiar with the hardware, and a relative large number of them were used to
computer communications. However, few students had used simulation packages before, with these
few considering this type of software useful. Computers were mostly used for word processing, which
agrees with the actual use of WATSTAR on campus, as indicated before. Finally, the great majority
of the students felt that using the news-group and simulations packages in the course would be
helpful.
The results of the nal questionnaire are summarized in Table 2 for both courses. Notice again
the higher response from the second year students. Interesting conclusions can be extracted from the
students' answer, some of them somewhat unexpected, given the apparent positive disposition from
the students towards the use of computer tools in the course, as demonstrated on the rst survey.
First of all, familiarity with the hardware from their exposure to it through the course signicantly
9
CHAPTER 3. SURVEYS
10
Table 1: Results of initial survey in %
ME 269 GEN E 123
Participation
90
46
Familiar with WATSTAR
90
76
Familiar with e-mail
68
75
Familiar with news-groups
23
33
Familiar with EES
0
0
Familiar with MATLAB
2
5
Familiar with MAPLE-V
6
15
Simulation packages were helpful
88
91
Computer used for word processing
61
67
Computer used for programming
13
20
Computer used for data analysis
19
6
Computer tools would be helpful
90
100
improved, particularly for the rst year students who were also exposed to the network in other
courses. One can also observe that signicantly more second year students used the news-group
than rst year students, although only slightly more than half of both classes thought that it was
actually useful. However, these results could justify the use of news-groups in a regular basis in
future courses, since it does not require much time from teaching sta. Furthermore, it is clear from
the surveys' results that more ME 269 students used the simulation packages as opposed to the rst
year class, which could be reasonably attributed to the simulation project which was compulsory
for the ME 269 class and only optional in GEN E 123. Notice the clear preference of the second
year students for EES, even though no one was familiar with this software; this could be credited
to its relative simplicity, which was the main reason for choosing this package for GEN E 123. Half
of the group that used the simulation packages the most, i.e., the ME 269 class, considered these
programs helpful, as expected. The majority of GEN E 123 students felt that these programs were
not helpful, but a the same time they were not very familiar with the packages and tutorials. The
surveys' results also show that very few students plan on using the simulation packages in the future,
which is rather inconsistent with both their initial and future expectations of these programs.
With regard to the computer tutorials, more second year students were familiar with at least
one computer tutorial than the rst year students, which is to be expected due to the dierent
requirements in the project, and it is also consistent with their use of the simulation packages.
Also, about half of the ME 269 class thought that the computer tutorials were interesting and
helpful, whereas a lower number of GEN E 123 students felt that the tutorials were actually helpful.
This dierence could again be attributed to the distinct use of the simulations packages by both
classes. Finally, a relatively large number of students thought that the computer demonstrations and
discussions in class of the tutorials were interesting, with a smaller number of students thinking that
it was actually useful. These results were somewhat surprising, given the apparent attractiveness of
CHAPTER 3. SURVEYS
11
Table 2: Results of nal survey in %
ME 269 GEN E 123
Participation
73
60
More familiar with WATSTAR
71
92
Use WATSTAR in other courses
47
96
Use of news-group
70
44
News-group was helpful
56
51
Use of EES
82
60y
Use of MATLAB
5
|
Use of MAPLE-V
21
|
Plan to use simulation package in the future
10
16
Simulation packages were helpful
50
21
Familiar with at least one computer tutorial
79z
60y
Computer tutorials were interesting
46
50
Computer tutorials were helpful
55
37
Class demos were interesting
60
54
Class demos were helpful
44
50
Lack of time to use simulation tools
40
54
Not interested in using computer tools
8
9
Future use would be helpful
84
83
Tools should be used in other courses
66
74
y Estimate based on optional nal projects turned in.
z Tutorial closely related to required project.
computer presentations, assuming that the presentations were well structured and properly delivered;
however, the results could be explained based on the students' preference for trying to solve the
problems on their own, at their own pace.
Notice that a relatively large number of students complained of lack of time to use the computer
tools, whereas only a small group indicated no interest in them. This might justify the marked dierence between the actual students' use of the computer tools and their past and future expectations,
and brings out the issue of a probable overloaded curriculum.
It is important to mention that an intermediate questionnaire was given to the second year
students before the project was due, and the results indicated signicant less familiarity with the
simulation packages and tutorials than what it was observed in the nal survey. This might also
help explain some of the dierences one sees between the results of the nal survey for the ME 269
and GEN E 123 classes, since this survey was carried out for the rst year class before the optional
project was due.
In addition to the surveys, the teaching sta tried to monitor the students' performance in
relation to their use of the simulation packages, based mostly on observations and project marks.
These results were inconclusive, i.e., it was not possible to directly tie nal marks to the use of
the simulation packages. Nevertheless, the \top" students, which were people with marks above
CHAPTER 3. SURVEYS
12
90% and represented about 10% of the class, demonstrated interest in the computer tutorials and
consistently used the simulation packages throughout the term; however, one could not conclusively
argue that their performance would have been somewhat less stellar having not used these programs.
To nish this section it is appropriate to mention that a signicant number of person/hours were
dedicated to prepare the tutorials and set up some of the hardware and software used in this study.
To give the reader an idea, a computer tutorial took one person an average of 6 hours to set up and
check. Thus, if one considers the time expended in marking the simulation projects, preparing the
computer presentations in class, and supervising the use of the programs, the cost to benet ratio
most certainly becomes an issue when considering the use of these tools. In the study presented here,
research and funding were important motivational factors that are not always present. Moreover,
one should not forget that these tools also require extra time from the students, particularly in
learning the simulation packages and familiarizing themselves with each tutorial.
Chapter 4
Examples and Comparisons
Two examples of electromagnetic transient simulation are discussed in this chapter, to compare the
dierent simulation tools and recommend one of them for future use.
4.1 Transformer Dynamics
To illustrate the dierences and capabilities of the software packages described in this report, the
simulation of the energization of an unloaded single-phase 208/120V lab transformer with saturable
core is explained in detail in this section. This transient phenomenon is widely known in transformers
as the in-rush current problem.
The equations for a two-winding transformer when neglecting core losses are [21]:
d
v1 = R1i1 + 1
(1)
dt
d
v2 = R2i2 + 2
dt
1
2
= Ll1 i1 + m
= Ll2 i2 + a1 m
= f (im )
1
im = i1 + i2
a
N1
a =
N
m
2
where v1, v2, i1 , and i2 are the respective voltages and currents in the primary and secondary
windings; R1 and R2 are the windings' resistances; Ll1 and Ll2 are the windings' leakage inductances;
13
CHAPTER 4. EXAMPLES AND COMPARISONS
14
1 and 2 are the windings' ux linkages; a is the turn ration. To consider saturation, the magnetizing
ux linkage m can be represented as a nonlinear function f (im ) of the magnetizing current im as
follows (this function was originally proposed by Prof. F. Alvarado at the University of WisconsinMadison, USA):
ji j + b
(2)
m = f (im ) = k im m
jim j + c
where k, b and c are constants that can be calculated assuming that the function can be approximated
by a piecewise-linear function with two slopes, Lm1 and Lm2 , with Lm1 > Lm2 , i.e.,
! 1) Lm2 im )
f (im ! 0) Lm1 im )
f (im
k Lm2
b
k Lm1
c
(3)
Now, consider that at a threshold value io the two lines of the piecewise-linear approximation meet,
i.e.,
Lm1 io = Lm2 io + d
)
d = (Lm1
, Lm2 )io
(4)
Furthermore, the actual value of m at this point can be assumed to be a factor s < 1 of the
approximated piecewise-linear function value, i.e., m = s Lm1 io . Then, from equations (3), one can
estimate b to be
L
io
s m1 , 1
(5)
b 1 , s Lm2
Figure 1 illustrates the saturation curve for the transformer used in the simulations. Both
representations of the saturation curve are depicted, i.e., the nonlinear function (2) and the twoslope piecewise-linear approximation dened in equations (3) and (4). The values of Lm1 , Lm2 , io ,
and s needed for calculating the constants k, b, c, and d were obtained from lab measurements.
Equations (1) through (5) are all the equations needed to model the energization of the unloaded
transformer (i2 = 0) in EES, whether the saturation is represented with nonlinear or piecewiselinear functions. Figure 2 shows the set of EES instructions used to simulate the desired transient,
considering that the transformer parameters are given in terms of the short-circuit and open-circuit
lab tests. Notice that the transformer equations and saturation functions are written practically in
the same way as they are dened in equations (1) through (5).
For MATLAB and MAPLE, equations (1) must be transformed to the standard ordinary dierential equation (ODE) form. In order to do that, the ux linkages derivatives must be represented
in terms of the derivative of the windings' currents i1 and i2 , i.e.,
d1 = L di1 + @m dim
l1 dt
dt
@im dt
d2 = L di2 + 1 @m dim
l2 dt a @i dt
dt
m
CHAPTER 4. EXAMPLES AND COMPARISONS
15
2
1.5
Mag. flux linkage [Wb−turns]
1
0.5
0
−0.5
−1
−1.5
−2
−4
−3
−2
−1
0
im [A]
1
2
3
4
Figure 1: Saturation curve for a two-winding lab transformer. The solid line depicts the nonlinear
function used to represent m = f (im ), and the dashed line illustrates the approximation using a
piecewise-linear function.
CHAPTER 4. EXAMPLES AND COMPARISONS
{ Saturation is included by assuming that the magnetizing
flux linkage is a nonlinear function of the current im,
which can be approximated by two lines with different slopes,
Lm1 and Lm2, for values of im below and above a given
threshold io. Hence, the flux can represented in two ways:
a) A nonlinear function: }
FUNCTION fm_nl(im,Lm1,Lm2,io)
k := Lm2;
s := 0.63
b := 1/(1-s)*(s*Lm1/Lm2 - 1)*io;
c := k*b/Lm1
fm_nl := k*im*(abs(im)+b)/(abs(im)+c)
END
{
b) A function that approximates it using two lines: }
FUNCTION fm_l(im,Lm1,Lm2,io)
IF im>0 THEN b := (Lm1 - Lm2)*io ELSE b := (Lm2 - Lm1)*io
IF abs(im)<io THEN fm_l:=Lm1*im ELSE fm_l:=Lm2*im+b
END
{
{
{
{
{
{
{
{
{
{
{
{
{
The primary side (high voltage side) is assumed to be connected
to a sinusoidal voltage source: }
v1 = sqrt(2)*V1rms*sin(w*t)
where V1 is the nominal voltage: }
V1rms=208;
w= 2*pi*60
To solve this problem we need to the differential equation: }
v1 = Rhv*i1 + df1dt
since i2=0, where: }
f1 = Lhv*i1 + fm
fm = fm_nl(i1,Lm1,Lm2,io)
or}
{fm = fm_l(i1,Lm1,Lm2,io)}
Thus:
1. Calculate the parameters from the transformer oc and sc:
a) Open circuit test:
- Turns N1/N2 ratio -> }
a = 208/120
- Low V side measurements (no saturation) ->
}
Voc = 120; Ioc = 0.797; Poc = 32.6
Then: }
Qoc=sqrt((Voc*Ioc)^2 -Poc^2)
Xoc=Voc^2/Qoc
Xm1=a^2*Xoc;
Lm1=Xm1/w
And the values for Lm2 and io measured in the lab are: }
Lm2 = Lm1/5
io = sqrt(2)*Ioc/a
b) Short Circuit (assume Rhv = a^2 Rlv , Xhv = a^2 Xlv ):
- High V side measurements
->
}
Vsc =5.79; Isc = 5.26; Psc=25.5
Then: }
Rsc=Psc/(Isc^2);
Rhv=Rsc/2
Xsc=sqrt((Vsc/Isc)^2-Rsc^2)
Xhv=Xsc/2;
Lhv=Xhv/w
2. Solve the differential equation for about 10 cycles, assuming
that the transformer is in an initial "resting" state f1(0)=0}
f1 = integral(df1dt,t)
3. Plot i1. Notice the large current values. }
Figure 2: Simulation of transformer energization in EES format.
16
CHAPTER 4. EXAMPLES AND COMPARISONS
17
Hence, by dening the nonlinear function
m = @f (im )
(6)
=4 @
@im
@im
equations (1) can be transformed into the following ODE form:
" #
"
#,1 " # "
# " #!
Lm (im )=a
v1
R1 0
i1
d i1 = Ll1 + Lm (im )
,
(7)
2
dt i2
Lm (im )=a
Ll2 + Lm (im )=a
v2
0 R2
i2
Lm (im )
where im = i1 + i2=a. The function Lm (im ) can be calculated using equation (6) for the nonlinear
or piecewise-linear saturation functions respectively, i.e.,
ji j + b + k jim j + kji j jim j + b
Lm (im ) = k m
(8)
m (ji j + c)2
jim j + c jim j + c
m
Lm (im )
=
(
Lm1
Lm2
for jim j < io
for jim j io
(9)
Equations (7) plus functions (8) or (9) can be readily implemented in MATLAB and EES.
However, the discontinuous function (9) causes numerical problems in EES; hence, as EES does not
require the equations to be in standard ODE form, it is preferable to use the ux linkage equations
to carry out the simulation as shown in Figure 2. Figures 3 and 4 show the set of instructions needed
in MATLAB to simulate the transformer energization in ODE form with either denition of Lm (im ).
In MAPLE-V, it is not possible to dene conditional functions within ODE sets; therefore, the
discontinuous function (9) could not be implemented in this program. In this case, it is not necessary
to use function (8) to dene Lm (im ) in equations (7), as this program is able to symbolically compute
this function from the original denition (6). This is clearly shown in Figure 5, which illustrates the
instruction set needed to carry out the transformer simulation in MAPLE-V.
Figure 6 shows the expected results of the simulations, for both nonlinear and piecewise-linear
saturation functions. All three programs generated exactly the same curves, with the exception of
MAPLE-V which did not allow to model saturation with a piecewise-linear function.
Comparing the dierent set of instructions shown in Figures 2, 3, 4 and 5, one can clearly see that
EES is the easiest to understand and use by students, as there is no need for special manipulation
of the equations. Furthermore, all operations in EES are made through menu calls, rather than
hard-to-remember function calls as in MATLAB and MAPLE-V. For these reasons, plus its easy
availability and small size, about 80% of the second year students chose EES to do their projects.
4.2 EES Modeling of AC/DC Rectier Bridge
An ac/dc rectier bridge with capacitive ltering is solved here with the help of EES, using the basic
nonlinear equation of a Ge diode to obtain the voltage and current in an R-L load to give the reader
CHAPTER 4. EXAMPLES AND COMPARISONS
% The primary side (high voltage side) is assumed to be connected
% to a sinusoidal voltage source:
%
v1 = sqrt(2)*V1rms*sin(w*t)
% where V1 is the nominal voltage:
V1rms=208,
w= 2*pi*60
% To solve this problem we need to solve the differential equation:
%
v1 = Rhv*i1 + (Lhv+Lm)*di1/dt
% since i2=0. This equation in standard ODE form can be written as:
%
di1dt=(v1 - Rhv*i1(t))/(Lhv + Lm(i1(t)))
% and is defined in the MATLAB file "di1dt.m."
%
% Thus:
% 1. Calculate the parameters from the transformer oc and sc:
%
a) Open circuit test:
%
- Turns N1/N2 ratio ->
a = 208/120
%
- Low V side measurements (no saturation) ->
Voc = 120, Ioc= 0.797, Poc = 32.6
%
Then:
Qoc=sqrt((Voc*Ioc)^2 -Poc^2)
Xoc=Voc^2/Qoc
Xm1=a^2*Xoc
Lm1=Xm1/w
%
Saturation is included by assuming that the magnetizing
%
flux linkage is a nonlinear function of the current im=i1,
%
which can be approximated by two lines with different
%
slopes, Lm1 and Lm2, for values of im below or above a
%
given threshold io. The values for Lm2 and io measured
%
in the lab are:
Lm2 = Lm1/5
io = sqrt(2)*Ioc/a
%
Hence, Lm = dflux/di1, can be represented as a function
%
of im in two different ways:
%
1) A continuos function that comes from the derivative
%
of the flux.
%
2) A function that approximates the derivative by the
%
two slopes Lm1 and Lm2.
%
b) Short Circuit (assume Rhv = a^2 Rlv , Xhv = a^2 Xlv ):
%
- High V side measurements
->
Vsc=5.79, Isc = 5.26, Psc=25.5
%
Then:
Rsc=Psc/(Isc^2)
Rhv=Rsc/2
Xsc=sqrt((Vsc/Isc)^2-Rsc^2)
Xhv=Xsc/2
Lhv=Xhv/w
% 2. Solve the differential equation for about 10 cycles, assuming
%
that the transformer is in an initial "resting" state i1(0)=0,
i10=0;
to = 0;
tf = 0.1;
global V1rms w Rhv Lhv Lm1 Lm2 io saturation
saturation='nonlinear';
[t,i1] = ode23('di1dt',to,tf,i10);
% 3. Plot i1. Notice the large current values.
figure; plot(t,i1); xlabel('t [s]'); ylabel('i1 [A]');
Figure 3: Simulation of transformer energization in MATLAB format, main le.
18
CHAPTER 4. EXAMPLES AND COMPARISONS
19
function didt = di1dt(t,i1)
% File "di1dt.m" used to define the differential equation:
global V1rms w Rhv Lhv Lm1 Lm2 io saturation
v1 = sqrt(2)*V1rms*sin(w*t);
if strcmp(saturation,'nonlinear')
k = Lm2;
s = 0.63; b = 1/(1-s)*(s*Lm1/Lm2 - 1)*io;
c = k*b/Lm1;
i=abs(i1);
Lm=k*(i+b)/(i+c)+k*i/(i+c)-k*i*(i+b)/(i+c)^2;
else
if abs(im)<io, Lm = Lm1; else Lm = Lm2; end
end
didt = (v1 - Rhv*i1)/(Lhv + Lm);
Figure 4: Simulation of transformer energization in MATLAB format, equation le needed for the
numerical integration routines (ode23).
an idea of the capabilities of the preferred simulation program. The full rectier circuit is shown in
Figure 7, and the corresponding equations in EES format are shown in Figure 8. Figure 9 shows
the expected results of the simulation.
CHAPTER 4. EXAMPLES AND COMPARISONS
20
# The primary side (high voltage side) is assumed to be connected
# to a sinusoidal voltage source:
v1 := sqrt(2)*V1*sin(w*t);
# where V1 is the nominal voltage:
V1:=208;
w:= 2*Pi*60;
# To solve this problem we need to solve the differential equation:
#
v1 = Rhv*i1 + (Lhv+Lm)*di1/dt
# since i2=0. This equation in standard form can be written as:
di1dt:=('v1' - Rhv*i1(t))/(Lhv + Lm(i1(t)));
# Phasor analysis will not be able to detect the current transients
# that we are looking for. Thus :
# 1. Calculate the variables needed from the transformer oc and sc
#
tests:
#
a) Open circuit test:
#
- Turns N1/N2 ratio ->
a := 208/120;
#
- Low V side measurements (no saturation) ->
Voc := 120; Ioc := 0.797; Poc := 32.6;
#
Then:
Qoc:=sqrt('(Voc*Ioc)^2 -Poc^2');
Xoc:='Voc^2/Qoc' ;
Xm1:='a^2*Xoc' ;
Lm1:='Xm1/w';
#
Saturation is included by assuming that the magnetizing
#
flux linkage is a nonlinear function of the current im=i1
#
flowing through Lm, i.e.,
flux := k*i1*(abs(i1)+b)/(abs(i1)+c);
#
which can be approximated by two lines with different
#
slopes, Lm1 and Lm2, for values of im below or above a
#
given threshold io (in MAX values). The values for
#
Lm2 and io measured in the lab are:
Lm2 := 'Lm1/5';
io := sqrt(2)*'Ioc/a';
#
The constants k, b, and c can then be approximated by
k := 'Lm2';
s := 0.63;
b := '1/(1-s)*(s*Lm1/Lm2 -1)*io';
c := 'k*b/Lm1';
#
Thus, Lm can be represented as a function of im=i1,
#
since Lm = dflux/di1, i.e.,
dfluxdi1 := 'diff(flux,i1)';
Lm := unapply(dfluxdi1,i1);
#
b) Short Circuit (assume Rhv = a^2 Rlv , Xhv = a^2 Xlv ):
#
- High V side measurements
->
Vsc :=5.79; Isc := 5.26; Psc:= 25.5;
#
Then:
Rsc:='Psc/(Isc^2)';
Rhv:='Rsc/2' ;
Xsc:=sqrt('(Vsc/Isc)^2-Rsc^2');
Xhv:='Xsc/2' ;
Lhv:='Xhv/w' ;
# 2. Solve the differential equation for about 10 cycles, assuming
#
that the transformer is in an initial "resting" state i1(0)=0,
#
i.e., solve:
sys:={diff(i1(t),t)- 'di1dt' = 0, i1(0)=0};
sol:=dsolve(sys, i1(t) ,type=numeric):
# 3. Plot i1. Notice the large current values.
with(plots,odeplot):
p1:=odeplot(sol,[t,i1(t)],0..0.1,numpoints=80,color=red):
plots[display]({p1},labels=[`time [s]`, `i1`]);
Figure 5: Simulation of transformer energization in MAPLE-V format. Saturation could only be
modeled with a nonlinear function.
CHAPTER 4. EXAMPLES AND COMPARISONS
21
4
3.5
3
Current [A]
2.5
2
1.5
1
0.5
0
−0.5
0
0.01
0.02
0.03
0.04
0.05
time [s]
0.06
0.07
0.08
0.09
0.1
Figure 6: In-rush current in an unloaded single-phase transformer. The solid line corresponds to
the primary current i1 when saturation is modeled as a nonlinear function, whereas the dashed line
depicts the same current when saturation is represented by a piecewise-linear function.
iL
i d1
i d3
-
1
iC
-
3
+
vs
+
R
+
+
-
v
-
4
i d4
+
L
-
2
i d2
C
+
-
Figure 7: Full-wave ac/dc rectier bridge feeding an RL load with capacitive ltering.
CHAPTER 4. EXAMPLES AND COMPARISONS
{
This tutorial shows how EES can be used to solve circuits with
nonlinear elements, such as diodes. A single-phase full-wave
rectifier bridge is used to demonstrate the solution procedure.
1.- Define the nonlinear equation id=f(vd) for a all Ge diode,
i.e.,
vd/vdo
id = Is ( e
- 1)
based on a point (id0,vd0) in the id-vd plot. Assume that all
currents are given in mA; thus, the resistances must be defined
in kOhms, inductances in kH and capacitances in mF.
}
FUNCTION id(vd)
vd_Ge := 0.025 {V for Ge at 20 deg. C}
vd0 := 0.6 {V}
id0 := 2.8 {mA}
Is := id0 /( EXP(vd0/vd_Ge) - 1) {mA}
id := Is*( EXP(vd/vd_Ge) - 1) {mA}
END
{
2.- Define 2 V, 60 Hz source:
}
vs = 2*SIN(w*t) {V}
w = 2*PI*60
{
3.- Circuit equations for an R-L load, with capacitive filtering:
}
{ Capacitor => } v = 1/C*INTEGRAL(iC,t)
C = 0.05 {mF}
{ R-L load => } v = iL*R + vL {KVL}
iL= 1/L*INTEGRAL(vL,t)
R = 0.5 {kOhms}
L = 0.001 {kH}
{ Diodes
=> } vs = vd1 - vd3 {KVL}
vs = vd2 - vd4
-v = vd1 + vd4
id(vd1) + id(vd3) = iC + iL {KCL}
id(vd2) + id(vd4) = iC + iL
is = id(vd1) - id(vd4)
{
4.- Use a ParameTric Table to vary the time t from 0 to 40 ms
(200 points), and make different Plots after Solving the Table
(Calculate). }
Figure 8: AC/DC rectier bridge tutorial in EES format.
22
23
1.00
2.0
0.80
1.6
0.60
1.2
0.40
0.8
0.20
0.4
0.00
0.000
0.008
0.016
0.024
0.032
iL [mA]
v [V]
CHAPTER 4. EXAMPLES AND COMPARISONS
0.0
0.040
t
Figure 9: AC/DC rectier bridge output. The line with circles depicts the load voltage v, and the
solid line denotes the load current iL .
Chapter 5
Conclusions
A detailed description of a study to determine the advantages and disadvantages of using simulation
software in Electrical Engineering courses has been presented. The tools used to administer and
deliver lectures, and help students in their understanding of the course material have been discussed,
and, most importantly, the students' observations on the eectiveness of these tools and their actual
use of them are reported and analyzed in detail.
The report also presents a detailed comparison of three dierent simulation packages as tools for
teaching electromagnetic transients. The simulation of the energization of a saturable transformer
is used to highlight the dierences between the various programs, establishing that EES is the most
suitable of the three simulation programs for rst-year students, particularly due to its simplicity.
The usefulness of EES as a teaching tool is demonstrated further by means of a nonlinear circuit
simulation.
Although EES was shown to be a better simulation package than MATLAB and MAPLE-V to
introduce students to transient phenomena, the program presents two major drawbacks. First, EES
is not very reliable, crashing regularly without any warnings. Second, this program has limited range
of applications and graphic capabilities when compared to the other two packages. Based on these
two reasons mainly, one would not expect EES to become a popular tool, as opposed to MATLAB
and MAPLE-V which have become industry standards, limiting its value for students. Despite these
problems, the authors' experience has proved that EES is a economical and powerful research and
teaching tool on its own right.
Although one could argue that the survey results presented here show a relatively good acceptance
from students of computer tools in the classroom (40{50% range), it is clear that the majority of
the students seem to shy away from using them for a variety of reasons, but particularly due to a
probable overloaded curriculum; students seem to prefer standard ways of lecture delivery over new
mechanisms that require some extra work. The surveys show that there is a signicant dierence
between students' and teaching sta's expectations of the benets and use of computer resources
24
CHAPTER 5. CONCLUSIONS
25
in the teaching-learning process, and what it actually goes on in the classroom. These results also
demonstrate that the students' use of simulation tools do not just happen voluntarily as one would
expect, on the contrary, students have to be compelled to use them.
Based on the study results and the authors experience, one should consider carefully the use of
simulation packages in Engineering courses. The costs, in terms of time and resources, have to be
weighed against all probable benets, taking into consideration the large initial investment.
Appendix A
Final Survey
Final survey for second year students (ME 269):
1. Do you feel more comfortable now with WATSTAR?
YES
SOME
LITTLE
(Circle one.)
NO
2. Did you use WATSTAR in any of your other courses?
YES
NO
If yes, which course(s) and what program(s):______________________
__________________________________________________________________
3. For ME-269, which one of the following packages you used?
NO
LITTLE
SOME
REGULARLY
a) NEWS:
0
1
2
3
b) EES:
0
1
2
3
c) MATLAB:
0
1
2
3
d) MAPLE:
0
1
2
3
4. Do you think that the use of the news-group helped to improve the
communication with the Prof. and/or the administration of the
class?
YES
SOME
LITTLE
NO
5. Which one of the following simulation packages did you use for the
project?
EES
MATLAB
MAPLE
6. After using these programs, which simulation package you liked the
most (circle ONE):
26
APPENDIX A. FINAL SURVEY
EES
27
MATLAB
MAPLE
Because (circle your choices):
a)
User friendly
b)
Simple to understand
c)
Powerful (speed, graphic capabilities, etc.)
d)
Easily available
e)
Used in other course
f)
Plan to use it in the future
g)
Others:______________________________________________________
_________________________________________________________________
7. Did the use of these programs help you in better understanding the
material discussed in class?
YES
SOME
LITTLE
NO
8. Are you familiar with any of the following tutorials?
NO
LITTLE
SOME
YES
a) Phasors (I)
0
1
2
3
b) Transf. dynamics (II)
0
1
2
3
c) Transf. efficiency (III)
0
1
2
3
d) DC generator (IV)
0
1
2
3
e) Induction Motor (V)
0
1
2
3
f) Transf. Saturation (Proj.)
0
1
2
3
9. In general, you think that the tutorials were (circle one for each
category):
NO
LITTLE
SOME
YES
a) Understandable
0
1
2
3
b) Useful
0
1
2
3
c) Interesting
0
1
2
3
d) Challenging
0
1
2
3
e) Related to course
0
1
2
3
10. Did these tutorials help you understand better the material
discussed in class?
YES
SOME
LITTLE
NO
11. Were the class computer demos interesting?
YES
SOME
LITTLE
NO
12. Were these demos helpful in clarifying the material discussed in
APPENDIX A. FINAL SURVEY
28
class?
YES
SOME
LITTLE
NO
13. What were the major difficulties you had regarding the programs
and tutorials ?
(Circle your choices.)
a)
None
b)
Lack of time
c)
Too many programs
d)
Too many tutorials
e)
Difficult access to a computer
f)
WATSTAR too slow
g)
Not interested
h)
Others:______________________________________________________
_________________________________________________________________
14. Do you think that continuing the use of all these resources in
future ME 269 classes would be:
HELPFUL
SOME
LITTLE
WASTE
15. Would you like for the Profs. to use these resources in other
courses in a regular basis?
YES
SOME
LITTLE
NO
16. Any additional comments and suggestions would be appreciated.
We
are particularly interested in hearing any ideas that you may
have about how to improve the use of all these resources for
future classes.
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
_________________________________________________________________
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