INST 233 (Protective Relays), section 1
Lab
Protective Relay system: Question 91, completed objectives due by the end of day 4, section 2
Exam
Day 3 of next section
Specific objectives for the “mastery” exam:
• Electricity Review: Calculate voltages, currents, and phase shifts in an AC reactive circuit
• Match ANSI device number designations (40, 50, 51, 52, 79, 81, 86, 87) with descriptions of protective
relay functions
• Sketch proper wire connections to create a three-phase transformer bank from three independent power
transformers
• Calculate proper wire size for current transformer (CT) field wiring given burden ratings, CT
classification, and other relevant system parameters
• Calculate phasor magnitudes and angles in three-phase electrical circuits, given schematic or pictorial
diagrams of the components
• Determine the possibility of suggested faults in a simple protective relay circuit given a wiring diagram,
meter measurements, and/or reported symptoms
Recommended daily schedule
Day 1
Theory session topic: Power system components and electrical safety
Questions 1 through 20; answer questions 1-10 in preparation for discussion (remainder for practice)
Day 2
Theory session topic: Phasors
Questions 21 through 40; answer questions 21-30 in preparation for discussion (remainder for practice)
Day 3
Theory session topic: Instrument and power transformers
Questions 41 through 60; answer questions 41-50 in preparation for discussion (remainder for practice)
Day 4
Theory session topic: Overcurrent (50/51) protection
Questions 61 through 80; answer questions 61-68 in preparation for discussion (remainder for practice)
Feedback questions (81 through 90) are optional and may be submitted for review at the end of the day
1
How To . . .
Access the worksheets and textbook: go to the Socratic Instrumentation website located at
http://www.ibiblio.org/kuphaldt/socratic/sinst to find worksheets for every 2nd-year course section
organized by quarter, as well as both the latest “stable” and “development” versions of the Lessons In
Industrial Instrumentation textbook. Download and save these documents to your computer.
Maximize your learning: complete all homework before class starts, ready to be assessed as described
in the “Inverted Session Formats” pages. Use every minute of class and lab time productively. Follow all
the tips outlined in “Question 0” as well as your instructor’s advice. Make every reasonable effort to solve
problems on your own before seeking help.
Identify upcoming assignments and deadlines: read the first page of each course worksheet.
Relate course days to calendar dates: reference the calendar spreadsheet file (calendar.xlsx), found
on the BTC campus Y: network drive. A printed copy is posted in the Instrumentation classroom.
Locate industry documents assigned for reading: use the Instrumentation Reference provided by
your instructor (on CD-ROM and on the BTC campus Y: network drive). There you will find a file named
00 index OPEN THIS FILE.html readable with any internet browser. Click on the “Quick-Start Links” to
access assigned reading documents, organized per course, in the order they are assigned.
Study for the exams: Mastery exams assess specific skills critically important to your success, listed near
the top of the front page of each course worksheet for your review. Familiarize yourself with this list and pay
close attention when those topics appear in homework and practice problems. Proportional exams feature
problems you haven’t seen before that are solvable using general principles learned throughout the current and
previous courses, for which the only adequate preparation is independent problem-solving practice every day.
Answer the “feedback questions” (practice exams) in each course section to hone your problem-solving skills,
as these are similar in scope and complexity to proportional exams. Answer these feedback independently
(i.e. no help from classmates) in order to most accurately assess your readiness.
Calculate course grades: download the “Course Grading Spreadsheet” (grades template.xlsx) from
the Socratic Instrumentation website, or from the BTC campus Y: network drive. Enter your quiz scores,
test scores, lab scores, and attendance data into this Excel spreadsheet and it will calculate your course
grade. You may compare your calculated grades against your instructors’ records at any time.
Identify courses to register for: read the “Sequence” page found in each worksheet.
Receive extra instructor help: ask during lab time, or during class time, or by appointment.
Identify job openings: regularly monitor job-search websites. Set up informational interviews at
workplaces you are interested in. Participate in jobshadows and internships. Apply to jobs long before
graduation, as some employers take months to respond! Check your BTC email account daily, because your
instructor broadcast-emails job postings to all students as employers submit them to BTC.
Impress employers: sign the FERPA release form granting your instructors permission to share academic
records, then make sure your performance is worth sharing. Document your project and problem-solving
experiences for reference during interviews. Honor all your commitments.
Begin your career: participate in jobshadows and internships while in school to gain experience and
references. Take the first Instrumentation job that pays the bills, and give that employer at least two years
of good work to pay them back for the investment they have made in you. Employers look at delayed
employment, as well as short employment spans, very negatively. Failure to pass a drug test is an immediate
disqualifier, as is falsifying any information. Criminal records may also be a problem.
file howto
2
General Values and Expectations
Success in this career requires: professional integrity, resourcefulness, persistence, close attention to
detail, and intellectual curiosity. Poor judgment spells disaster in this career, which is why employer
background checks (including social media and criminal records) and drug testing are standard. The good
news is that character and clear thinking are malleable traits: unlike intelligence, these qualities can be
acquired and improved with effort. This is what you are in school to do – increase your “human capital”
which is the sum of all knowledge, skills, and traits valuable in the marketplace.
Mastery: You must master the fundamentals of your chosen profession. “Mastery” assessments challenge
you to demonstrate 100% competence (with multiple opportunities to re-try). Failure to complete any
mastery objective(s) by the deadline date caps your grade at a C−. Failure to complete by the end of the
next school day results in a failing (F) grade.
Punctuality and Attendance: You are expected to arrive on time and be “on-task” all day just as you
would for a job. Each student has 12 hours of “sick time” per quarter applicable to absences not verifiably
employment-related, school-related, weather-related, or required by law. Each student must confer with the
instructor to apply these hours to any missed time – this is not done automatically. Students may donate
unused “sick time” to whomever they specifically choose. You must contact your instructor and lab team
members immediately if you know you will be late or absent or must leave early. Absence on an exam day
will result in a zero score for that exam, unless due to a documented emergency.
Time Management: You are expected to budget and prioritize your time, just as you will be on the job.
You will need to reserve enough time outside of school to complete homework, and strategically apply your
time during school hours toward limited resources (e.g. lab equipment). Frivolous activities (e.g. games,
social networking, internet surfing) are unacceptable when work is unfinished. Trips to the cafeteria for food
or coffee, smoke breaks, etc. must not interfere with team participation.
Independent Study: Successful instrument technicians are able to learn on their own, because the
knowledge base of this field is broad, challenging, and ever-evolving. To build this skill, students learn
in an “inverted” model where independent study replaces lecture, and the instructor challenges students
during class time to explain what they have learned. Most students require a minimum of 3 hours daily
study time outside of school. Arriving unprepared (e.g. homework incomplete) is unprofessional and counterproductive. Question 0 of every worksheet lists practical study tips. The “Inverted Session Formats” pages
found in every worksheet outline the format and grading standards for inverted class sessions.
Independent Problem-Solving: The best instrument technicians are versatile problem-solvers. General
problem-solving is arguably the most valuable skill you can possess for this career, and it can only be built
through persistent effort. This is why you must take every reasonable measure to solve problems on your own
before seeking help. It is okay to be perplexed by an assignment, but you are expected to apply problemsolving strategies given to you (see Question 0) and to precisely identify where you are confused so your
instructor will be able to offer targeted help. Asking classmates to solve problems for you is folly – this
includes having others break the problem down into simple steps. The point is to learn how to think on your
own. When troubleshooting systems in lab you are expected to run diagnostic tests (e.g. using a multimeter
instead of visually seeking circuit faults), as well as consult the equipment manual(s) before seeking help.
Initiative: No single habit predicts your success or failure in this career better than personal initiative, which
is why your instructor will demand you do for yourself rather than rely on others to do for you. Examples
include setting up and using your BTC email account to communicate with your instructor(s), consulting
manuals for technical information before asking for help, regularly checking the course calendar and
assignment deadlines, avoiding procrastination, fixing small problems before they become larger problems,
etc. If you find your performance compromised by poor understanding of prior course subjects, re-read those
textbook sections and use the practice materials made available to you on the Socratic Instrumentation
website – don’t wait for anyone else to diagnose your need and offer help.
3
General Values and Expectations (continued)
Safety: You are expected to work safely in the lab just as you will be on the job. This includes wearing
proper attire (safety glasses and closed-toed shoes in the lab at all times), implementing lock-out/tag-out
procedures when working on circuits with exposed conductors over 30 volts, using ladders to access elevated
locations, and correctly using all tools. If you need to use an unfamiliar tool, see the instructor for directions.
Orderliness: You are expected to keep your work area clean and orderly just as you will be on the job.
This includes discarding trash and returning tools at the end of every lab session, and participating in all
scheduled lab clean-up sessions. If you identify failed equipment in the lab, label that equipment with a
detailed description of its symptoms.
Teamwork: You will work in instructor-assigned teams to complete lab assignments, just as you will work
in teams to complete complex assignments on the job. As part of a team, you must keep your teammates
informed of your whereabouts in the event you must step away from the lab or will be absent for any reason.
Any student regularly compromising team performance through lack of participation, absence, tardiness,
disrespect, or other disruptive behavior(s) will be removed from the team and required to complete all
labwork individually for the remainder of the quarter. The same is true for students found relying on
teammates to do their work for them.
Cooperation: The structure of these courses naturally lends itself to cooperation between students. Working
together, students significantly impact each others’ learning. You are expected to take this role seriously,
offering real help when needed and not absolving classmates of their responsibility to think for themselves or
to do their own work. Solving problems for classmates and/or explaining to them what they can easily read
on their own is unacceptable because these actions circumvent learning. The best form of help you can give
to your struggling classmates is to share with them your tips on independent learning and problem-solving,
for example asking questions leading to solutions rather than simply providing solutions for them.
Grades: Employers prize trustworthy, hard working, knowledgeable, resourceful problem-solvers. The grade
you receive in any course is but a partial measure of these traits. What matters most are the traits
themselves, which is why your instructor maintains detailed student records (including individual exam
scores, attendance, tardiness, and behavioral comments) and will share these records with employers if
you have signed the FERPA release form. You are welcome to see your records at any time, and to
compare calculated grades with your own records (i.e. the grade spreadsheet available to all students).
You should expect employers to scrutinize your records on attendance and character, and also challenge you
with technical questions when considering you for employment.
Representation: You are an ambassador for this program. Your actions, whether on tours, during a
jobshadow or internship, or while employed, can open or shut doors of opportunity for other students. Most
of the job opportunities open to you as a BTC graduate were earned by the good work of previous graduates,
and as such you owe them a debt of gratitude. Future graduates depend on you to do the same.
Responsibility For Actions: If you lose or damage college property (e.g. lab equipment), you must find,
repair, or help replace it. If you represent BTC poorly to employers (e.g. during a tour or an internship),
you must make amends. The general rule here is this: “If you break it, you fix it!”
Non-negotiable terms: disciplinary action, up to and including immediate failure of a course, will
result from academic dishonesty (e.g. cheating, plagiarism), willful safety violations, theft, harassment,
intoxication, destruction of property, or willful disruption of the learning (work) environment. Such offenses
are grounds for immediate termination in this career, and as such will not be tolerated here.
file expectations
4
Inverted session formats
The basic concept of an “inverted” learning environment is that the traditional allocations of student
time are reversed: instead of students attending an instructor-led session to receive new information and then
practicing the application of that information outside of the classroom in the form of homework, students
in an inverted class encounter new information outside of the classroom via homework and apply that
information in the classroom session under the instructor’s tutelage.
A natural question for instructors, then, is what their precise role is in an inverted classroom and how
to organize that time well. Here I will list alternate formats suitable for an inverted classroom session, each
of them tested and proven to work.
Small sessions
Students meet with instructors in small groups for short time periods. Groups of 4 students meeting for
30 minutes works very well, but groups as large as 8 students apiece may be used if time is limited. Each of
these sessions begins with a 5 to 10 minute graded inspection of homework with individual questioning, to
keep students accountable for doing the homework. The remainder of the session is a dialogue focusing on
the topics of the day, the instructor challenging each student on the subject matter in Socratic fashion, and
also answering students’ questions. A second grade measures each student’s comprehension of the subject
matter by the end of the session.
This format also works via teleconferencing, for students unable to attend a face-to-face session on
campus.
Large sessions
Students meet with instructors in a standard classroom (normal class size and period length). Each
of these sessions begins with a 10 minute graded quiz (closed-book) on the homework topic(s), to keep
students accountable for doing the homework. Students may leave the session as soon as they “check off”
with the instructor in a Socratic dialogue as described above (instructor challenging each student to assess
their comprehension, answering questions, and grading the responses). Students sign up for check-off on the
whiteboard when they are ready, typically in groups of no more than 4. Alternatively, the bulk of the class
session may be spent answering student questions in small groups, followed by another graded quiz at the
end.
Correspondence
This format works for students unable to attend a “face-to-face” session, and who must correspond with
the instructor via email or other asynchronous medium. Each student submits a thorough presentation of
their completed homework, which the instructor grades for completeness and accuracy. The instructor then
replies back to the student with challenge questions, and also answers questions the student may have. As
with the previous formats, the student receives another grade assessing their comprehension of the subject
matter by the close of the correspondence dialogue.
In all formats, students are held accountable for completion of their homework, “completion” being
defined as successfully interpreting the given information from source material (e.g. accurate outlines of
reading or video assignments) and constructive effort to solve given problems. It must be understood in an
inverted learning environment that students will have legitimate questions following a homework assignment,
and that it is therefore unreasonable to expect mastery of the assigned subject matter. What is reasonable to
expect from each and every student is a basic outline of the source material (reading or video assignments)
complete with major terms defined and major concepts identified, plus a good-faith effort to solve every
problem. Question 0 (contained in every worksheet) lists multiple strategies for effective study and problemsolving.
5
Inverted session formats (continued)
Sample rubric for pre-assessments
• No credit = Any homework question unattempted (i.e. no effort shown on one or more questions)
• Half credit = Evidence of confusion on any major concept clearly explained in the assigned reading;
answers shown with no supporting work; unable to explain the reading outline or solution methods
represented in written work; failure to follow clear instruction(s)
• Full credit = Every homework question answered; all important concepts from reading assignments
accurately expressed in the written outline and clearly articulated when called upon by the instructor
to explain
The minimum expectation at the start of every student-instructor session is that all students have made
a good-faith effort to complete 100% of their assigned homework. This does not necessarily mean all answers
will be correct, or that all concepts are fully understood, because one of the purposes of the meeting between
students and instructor is to correct remaining misconceptions and answer students’ questions. However,
experience has shown that without accountability for the homework, a substantial number of students will
not put forth their best effort and that this compromises the whole learning process. Full credit is reserved
for good-faith effort, where each student thoughtfully applies the study and problem-solving recommendations
given to them (see Question 0).
Sample rubric for post-assessments
• No credit = Failure to comprehend any important concept of the day; failure to apply logical reasoning
to the solution of any problem
• Half credit = Some misconceptions persist by the close of the session; problem-solving is inconsistent;
limited contribution to the dialogue
• Full credit = Socratic queries answered thoughtfully; effective reasoning applied to problems; ideas
communicated clearly and accurately; responds intelligently to questions and statements made by others
in the session; adds new ideas and perspectives
The minimum expectation is that each and every student engages with the instructor and with fellow
students during the Socratic session: posing intelligent questions of their own, explaining their reasoning
when challenged, and otherwise positively contributing to the discussion. Passive observation and listening
is not an option here – every student must be an active participant, contributing something original to every
dialogue. If a student is confused about any concept or solution, it is their responsibility to ask questions and
seek resolution.
If a student happens to be absent for a scheduled class session and is therefore unable to be assessed
on that day’s study, they may schedule a time with the instructor to demonstrate their comprehension at
some later date (before the end of the quarter when grades must be submitted). These same standards of
performance apply equally make-up assessments: either inspection of homework or a closed-book quiz for
the pre-assessment, and either a Socratic dialogue with the instructor or another closed-book quiz for the
post-assessment.
file format
6
Course Syllabus
INSTRUCTOR CONTACT INFORMATION:
Tony Kuphaldt
(360)-752-8477 [office phone]
(360)-752-7277 [fax]
tony.kuphaldt@btc.ctc.edu
DEPT/COURSE #: INST 233
CREDITS: 3
Lecture Hours: 10
Lab Hours: 50
Work-based Hours: 0
COURSE TITLE: Protective Relays
COURSE DESCRIPTION: In this course you will learn how to commission, test, and analyze basic
protective relays and instrument transformers used to protect equipment in electrical power systems. This
course also reviews phasor mathematics for three-phase electrical circuits. Pre/Corequisite course: INST232
(PLC Systems) Prerequisite course: MATH&141 (Precalculus 1) with a minimum grade of “C”
COURSE OUTCOMES: Configure, test, and analyze overcurrent protective relays and instrument
transformers.
COURSE OUTCOME ASSESSMENT: Protective relay configuration, testing, and analysis outcomes
are ensured by measuring student performance against mastery standards, as documented in the Student
Performance Objectives. Failure to meet all mastery standards by the deadline will result in a failing grade
for the course.
7
STUDENT PERFORMANCE OBJECTIVES:
• Without references or notes, within a limited time (3 hours total for each exam session), independently
perform the following tasks. Multiple re-tries are allowed on mastery (100% accuracy) objectives, each
with a different set of problems:
→ Calculate voltages, currents, and phase shifts in an AC reactive circuit, with 100% accuracy (mastery)
→ Match ANSI device number designations (40, 50, 51, 52, 79, 81, 86, 87) with descriptions of protective
relay functions, with 100% accuracy (mastery)
→ Sketch proper wire connections to create a three-phase transformer bank from three independent
power transformers, with 100% accuracy (mastery)
→ Calculate proper wire size for current transformer (CT) field wiring given burden ratings, CT
classification, and other relevant system parameters, with 100% accuracy (mastery)
→ Calculate phasor magnitudes and angles in three-phase electrical circuits, given schematic or pictorial
diagrams of the components, with 100% accuracy (mastery)
→ Determine the possibility of suggested faults in a simple protective relay circuit given a wiring
diagram, meter measurements, and/or reported symptoms, with 100% accuracy (mastery)
• In a team environment and with full access to references, notes, and instructor assistance, perform the
following tasks:
→ Demonstrate proper use of equipment to commission CT circuits
→ Demonstrate proper safety protocols for working with live CT circuits
→ Test an electromechanical instantaneous overcurrent (50) relay
→ Test an electromechanical time-overcurrent (51) relay
→ Determine phase rotation in a three-phase power system
• Independently perform the following tasks on a functioning bus-connected three-phase generating station
with 100% accuracy (mastery). Multiple re-tries are allowed with different specifications/conditions each
time):
→ Program an electronic overcurrent (50/51) relay as per specified system protection and instrument
transformer parameters, testing this relay’s operation to verify the correctness of those settings.
COURSE OUTLINE: A course calendar in electronic format (Excel spreadsheet) resides on the Y:
network drive, and also in printed paper format in classroom DMC130, for convenient student access. This
calendar is updated to reflect schedule changes resulting from employer recruiting visits, interviews, and
other impromptu events. Course worksheets provide comprehensive lists of all course assignments and
activities, with the first page outlining the schedule and sequencing of topics and assignment due dates.
These worksheets are available in PDF format at http://www.ibiblio.org/kuphaldt/socratic/sinst
• INST233 Section 1: 4 days theory and labwork
• INST233 Section 2: 2 days theory and labwork + 1 day for review and mastery exam + 1 day for
proportional exam
8
METHODS OF INSTRUCTION: Course structure and methods are intentionally designed to develop
critical-thinking and life-long learning abilities, continually placing the student in an active rather than a
passive role.
• Independent study: daily worksheet questions specify reading assignments, problems to solve, and
experiments to perform in preparation (before) classroom theory sessions. Open-note quizzes ensure
accountability for this essential preparatory work. The purpose of this is to convey information and basic
concepts, so valuable class time isn’t wasted transmitting bare facts, and also to foster the independent
research ability necessary for self-directed learning in your career.
• Classroom sessions: a combination of Socratic discussion, short lectures, small-group problem-solving,
and hands-on demonstrations/experiments review and illuminate concepts covered in the preparatory
questions. The purpose of this is to develop problem-solving skills, strengthen conceptual understanding,
and practice both quantitative and qualitative analysis techniques.
• Lab activities: an emphasis on constructing and documenting working projects (real instrumentation
and control systems) to illuminate theoretical knowledge with practical contexts. Special projects
off-campus or in different areas of campus (e.g. BTC’s Fish Hatchery) are encouraged. Hands-on
troubleshooting exercises build diagnostic skills.
• Tours and guest speakers: quarterly tours of local industry and guest speakers on technical topics
add breadth and additional context to the learning experience.
STUDENT ASSIGNMENTS/REQUIREMENTS: All assignments for this course are thoroughly
documented in the following course worksheets located at:
http://www.ibiblio.org/kuphaldt/socratic/sinst/index.html
• INST233 sec1.pdf
• INST233 sec2.pdf
9
EVALUATION AND GRADING STANDARDS: (out of 100% for the course grade)
• Completion of all mastery objectives = 50%
• Mastery exam score (first attempt) = 10%
• Proportional exam score = 30%
• Lab questions = 10%
• Quiz penalty = -1% per failed quiz
• Tardiness penalty = -1% per incident (1 “free” tardy per course)
• Attendance penalty = -1% per hour (12 hours “sick time” per quarter)
• Extra credit = +5% per project (assigned by instructor based on individual learning needs)
All grades are criterion-referenced (i.e. no grading on a “curve”)
100% ≥ A ≥ 95%
90% > B+ ≥ 86%
80% > C+ ≥ 76%
70% > D+ ≥ 66%
95% > A- ≥ 90%
86% > B ≥ 83%
76% > C ≥ 73%
66% > D ≥ 63%
83% > B- ≥ 80%
73% > C- ≥ 70% (minimum passing course grade)
63% > D- ≥ 60%
60% > F
Graded quizzes at the start of each classroom session gauge your independent learning. If absent or
late, you may receive credit by passing a comparable quiz afterward or by having your preparatory work
(reading outlines, work done answering questions) thoroughly reviewed prior to the absence.
Absence on a scheduled exam day will result in a 0% score for the proportional exam unless you provide
documented evidence of an unavoidable emergency.
If you fail a mastery exam, you must re-take a different version of that mastery exam on a different
day. Multiple re-tries are allowed, on a different version of the exam each re-try. There is no penalty levied
on your course grade for re-taking mastery exams, but failure to successfully pass a mastery exam by the
due date (i.e. by the date of the next exam in the course sequence) will result in a failing grade (F) for the
course.
If any other “mastery” objectives are not completed by their specified deadlines, your overall grade
for the course will be capped at 70% (C- grade), and you will have one more school day to complete the
unfinished objectives. Failure to complete those mastery objectives by the end of that extra day (except in
the case of documented, unavoidable emergencies) will result in a failing grade (F) for the course.
“Lab questions” are assessed by individual questioning, at any date after the respective lab objective
(mastery) has been completed by your team. These questions serve to guide your completion of each lab
exercise and confirm participation of each individual student. Grading is as follows: full credit for thorough,
correct answers; half credit for partially correct answers; and zero credit for major conceptual errors. All
lab questions must be answered by the due date of the lab exercise.
Extra credit opportunities exist for each course, and may be assigned to students upon request. The
student and the instructor will first review the student’s performance on feedback questions, homework,
exams, and any other relevant indicators in order to identify areas of conceptual or practical weakness. Then,
both will work together to select an appropriate extra credit activity focusing on those identified weaknesses,
for the purpose of strengthening the student’s competence. A due date will be assigned (typically two weeks
following the request), which must be honored in order for any credit to be earned from the activity. Extra
credit may be denied at the instructor’s discretion if the student has not invested the necessary preparatory
effort to perform well (e.g. lack of preparation for daily class sessions, poor attendance, no feedback questions
submitted, etc.).
10
REQUIRED STUDENT SUPPLIES AND MATERIALS:
• Course worksheets available for download in PDF format
• Lessons in Industrial Instrumentation textbook, available for download in PDF format
→ Access worksheets and book at: http://www.ibiblio.org/kuphaldt/socratic/sinst
• Ampacity ratings of wire from the National Electrical Code (NFPA 70) reference, available for free online
viewing at http://www.nfpa.org
• NFPA 70E “Standard for Electrical Safety in the Workplace”
• Spiral-bound notebook for reading annotation, homework documentation, and note-taking.
• Instrumentation reference CD-ROM (free, from instructor). This disk contains many tutorials and
datasheets in PDF format to supplement your textbook(s).
• Tool kit (see detailed list)
• Scientific calculator capable of performing complex-number arithmetic in both rectangular and polar
forms. TI-36X Pro, TI-83, or TI-84 recommended.
• Portable personal computer with Ethernet port and wireless. Windows OS strongly preferred, tablets
discouraged.
ADDITIONAL INSTRUCTIONAL RESOURCES:
• The BTC Library hosts a substantial collection of textbooks and references on the subject of
Instrumentation, as well as links in its online catalog to free Instrumentation e-book resources available
on the Internet.
• “BTCInstrumentation” channel on YouTube (http://www.youtube.com/BTCInstrumentation), hosts
a variety of short video tutorials and demonstrations on instrumentation.
• Instrumentation student club meets regularly to set up industry tours, raise funds for scholarships, and
serve as a general resource for Instrumentation students.
CAMPUS EMERGENCIES: If an emergency arises, your instructor may inform you of actions to
follow. You are responsible for knowing emergency evacuation routes from your classroom. If police or
university officials order you to evacuate, do so calmly and assist those needing help. You may receive
emergency information alerts via the building enunciation system, text message, email, or BTC’s webpage
(http://www.btc.ctc.edu), Facebook or Twitter. Refer to the emergency flipchart in the lab room (located
on the main control panel) for more information on specific types of emergencies.
ACCOMMODATIONS: If you think you could benefit from classroom accommodations for a disability
(physical, mental, emotional, or learning), please contact our Accessibility Resources office. Call (360)-7528345, email ar@btc.ctc.edu, or stop by the AR Office in the Admissions and Student Resource Center
(ASRC), Room 106, College Services Building
file INST233syllabus
11
Sequence of second-year Instrumentation courses
Core Electronics -- 3 qtrs
including MATH 141 (Precalculus 1)
(Only if 4th quarter was Summer: INST23x)
INST 200 -- 1 wk
Intro. to Instrumentation
Prerequisite for all INST24x,
INST25x, and INST26x courses
Summer quarter
Fall quarter
Winter quarter
Offered 1st week of
Fall, Winter, and
Spring quarters
Spring quarter
INST 230 -- 3 cr
INST 240 -- 6 cr
INST 250 -- 5 cr
INST 260 -- 4 cr
Motor Controls
Pressure/Level Measurement
Final Control Elements
Data Acquisition Systems
INST 231 -- 3 cr
INST 241 -- 6 cr
INST 251 -- 5 cr
INST 262 -- 5 cr
PLC Programming
Temp./Flow Measurement
PID Control
DCS and Fieldbus
INST 232 -- 3 cr
INST 242 -- 5 cr
INST 252 -- 4 cr
INST 263 -- 5 cr
Loop Tuning
Control Strategies
PLC Systems
Analytical Measurement
INST 233 -- 3 cr
CHEM&161 -- 5 cr
Protective Relays (elective)
Chemistry
ENGT 134 -- 5 cr
CAD 1: Basics
Prerequisite for INST206
All courses
completed?
Yes
INST 205 -- 1 cr
Job Prep I
No
INST 206 -- 1 cr
Job Prep II
Graduate!!!
12
Offered 1st week of
Fall, Winter, and
Spring quarters
The particular sequence of courses you take during the second year depends on when you complete all
first-year courses and enter the second year. Since students enter the second year of Instrumentation at four
different times (beginnings of Summer, Fall, Winter, and Spring quarters), the particular course sequence
for any student will likely be different from the course sequence of classmates.
Some second-year courses are only offered in particular quarters with those quarters not having to be
in sequence, while others are offered three out of the four quarters and must be taken in sequence. The
following layout shows four typical course sequences for second-year Instrumentation students, depending on
when they first enter the second year of the program:
Possible course schedules depending on date of entry into 2nd year
Beginning in Summer
July
Summer quarter
Beginning in Fall
Sept.
Motor Controls
Intro. to Instrumentation
Intro. to Instrumentation
Intro. to Instrumentation
INST 231 -- 3 cr
INST 240 -- 6 cr
INST 250 -- 5 cr
INST 260 -- 4 cr
PLC Programming
Pressure/Level Measurement
Final Control Elements
Data Acquisition Systems
Protective Relays (elective)
Fall quarter
Dec.
Jan.
INST 262 -- 5 cr
PID Control
DCS and Fieldbus
INST 242 -- 5 cr
INST 252 -- 4 cr
INST 263 -- 5 cr
Loop Tuning
Control Strategies
Analytical Measurement
CHEM&161 -- 5 cr
Winter quarter
INST 240 -- 6 cr
INST 250 -- 5 cr
Pressure/Level Measurement
INST 241 -- 6 cr
Mar.
April
Chemistry
Spring quarter
ENGT 134 -- 5 cr
June
July
CAD 1: Basics
Summer quarter
INST 230 -- 3 cr
Final Control Elements
INST 205 -- 1 cr
Job Prep I
INST 251 -- 5 cr
INST 260 -- 4 cr
INST 231 -- 3 cr
Temp./Flow Measurement
PID Control
Data Acquisition Systems
PLC Programming
INST 242 -- 5 cr
INST 252 -- 4 cr
INST 262 -- 5 cr
INST 232 -- 3 cr
Loop Tuning
DCS and Fieldbus
CHEM&161 -- 5 cr
INST 263 -- 5 cr
Chemistry
Control Strategies
Analytical Measurement
Winter quarter
Mar.
April
ENGT 134 -- 5 cr
Spring quarter
June
CAD 1: Basics
Motor Controls
PLC Systems
INST 233 -- 3 cr
Aug.
Sept.
Protective Relays (elective)
Fall quarter
Final Control Elements
INST 206 -- 1 cr
Job Prep II
INST 251 -- 5 cr
INST 260 -- 4 cr
INST 230 -- 3 cr
INST 240 -- 6 cr
PID Control
Data Acquisition Systems
Motor Controls
Pressure/Level Measurement
INST 252 -- 4 cr
INST 262 -- 5 cr
INST 231 -- 3 cr
INST 241 -- 6 cr
Loop Tuning
DCS and Fieldbus
PLC Programming
Temp./Flow Measurement
CHEM&161 -- 5 cr
INST 263 -- 5 cr
INST 232 -- 3 cr
Chemistry
Control Strategies
Spring quarter
INST 206 -- 1 cr
Job Prep II
July
Summer quarter
Sept.
Winter quarter
INST 206 -- 1 cr
Job Prep II
Fall quarter
INST 231 -- 3 cr
INST 240 -- 6 cr
INST 251 -- 5 cr
PLC Programming
Pressure/Level Measurement
PID Control
INST 241 -- 6 cr
INST 252 -- 4 cr
Temp./Flow Measurement
Loop Tuning
Motor Controls
INST 262 -- 5 cr
DCS and Fieldbus
INST 263 -- 5 cr
INST 232 -- 3 cr
PLC Systems
INST 233 -- 3 cr
Aug.
Jan.
Analytical Measurement
INST 250 -- 5 cr
Data Acquisition Systems
ENGT 134 -- 5 cr
Protective Relays (elective)
INST 242 -- 5 cr
Dec.
INST 206 -- 1 cr
Job Prep II
INST 230 -- 3 cr
Graduation!
INST 233 -- 3 cr
Aug.
INST 205 -- 1 cr
Job Prep I
Summer quarter
PLC Systems
CAD 1: Basics
INST 260 -- 4 cr
CAD 1: Basics
July
ENGT 134 -- 5 cr
June
Control Strategies
June
INST 251 -- 5 cr
Intro. to Instrumentation
INST 250 -- 5 cr
April
INST 241 -- 6 cr
Temp./Flow Measurement
INST 205 -- 1 cr
Job Prep I
INST 205 -- 1 cr
Job Prep I
Mar.
Spring quarter
INST 200 -- 1 wk
INST 200 -- 1 wk
Jan.
April
INST 200 -- 1 wk
INST 233 -- 3 cr
Dec.
Winter quarter
INST 200 -- 1 wk
PLC Systems
Sept.
Jan.
Fall quarter
Beginning in Spring
INST 230 -- 3 cr
INST 232 -- 3 cr
Aug.
Beginning in Winter
Final Control Elements
INST 242 -- 5 cr
Protective Relays (elective)
Dec.
Graduation!
Analytical Measurement
Graduation!
file sequence
13
CHEM&161 -- 5 cr
Mar.
Chemistry
Graduation!
General tool and supply list
Wrenches
• Combination (box- and open-end) wrench set, 1/4” to 3/4” – the most important wrench sizes are 7/16”,
1/2”, 9/16”, and 5/8”; get these immediately!
• Adjustable wrench, 6” handle (sometimes called “Crescent” wrench)
• Hex wrench (“Allen” wrench) set, fractional – 1/16” to 3/8”
• Optional: Hex wrench (“Allen” wrench) set, metric – 1.5 mm to 10 mm
• Optional: Miniature combination wrench set, 3/32” to 1/4” (sometimes called an “ignition wrench” set)
Note: when turning any threaded fastener, one should choose a tool engaging the maximum amount of
surface area on the fastener’s head in order to reduce stress on that fastener. (e.g. Using box-end wrenches
instead of adjustable wrenches; using the proper size and type of screwdriver; never using any tool that mars
the fastener such as pliers or vise-grips unless absolutely necessary.)
Pliers
• Needle-nose pliers
• Tongue-and-groove pliers (sometimes called “Channel-lock” pliers)
• Diagonal wire cutters (sometimes called “dikes”)
Screwdrivers
• Slotted, 1/8” and 1/4” shaft
• Phillips, #1 and #2
• Jeweler’s screwdriver set
• Optional: Magnetic multi-bit screwdriver (e.g. Klein Tools model 70035)
Electrical
• Multimeter, Fluke model 87-IV or better
• Alligator-clip jumper wires
• Soldering iron (10 to 40 watt) and rosin-core solder
• Resistor, potentiometer, diode assortments (from first-year lab kits)
• Package of insulated compression-style fork terminals (14 to 18 AWG wire size, #10 stud size)
• Wire strippers/terminal crimpers for 10 AWG to 18 AWG wire and insulated terminals
• Optional: ratcheting terminal crimp tool (e.g. Paladin 1305, Ferrules Direct FDT10011, or equivalent)
Safety
• Safety glasses or goggles (available at BTC bookstore)
• Earplugs (available at BTC bookstore)
Miscellaneous
• Simple scientific calculator (non-programmable, non-graphing, no conversions), TI-30Xa or TI-30XIIS
recommended. Required for some exams!
• Portable personal computer with Ethernet port and wireless. Windows OS strongly preferred, tablets
discouraged.
• Masking tape (for making temporary labels)
• Permanent marker pen
• Teflon pipe tape
• Utility knife
• Tape measure, 12 feet minimum
• Flashlight
An inexpensive source of tools is your local pawn shop. Look for tools with unlimited lifetime guarantees
(e.g. Sears “Craftsman” brand). Check for BTC student discounts as well!
file tools
14
Methods of instruction
This course develops self-instructional and diagnostic skills by placing students in situations where they
are required to research and think independently. In all portions of the curriculum, the goal is to avoid a
passive learning environment, favoring instead active engagement of the learner through reading, reflection,
problem-solving, and experimental activities. The curriculum may be roughly divided into two portions:
theory and practical.
Theory
In the theory portion of each course, students independently research subjects prior to entering the
classroom for discussion. This means working through all the day’s assigned questions as completely as
possible. This usually requires a fair amount of technical reading, and may also require setting up and
running simple experiments. At the start of the classroom session, the instructor will check each student’s
preparation with a quiz. Students then spend the rest of the classroom time working in groups and directly
with the instructor to thoroughly answer all questions assigned for that day, articulate problem-solving
strategies, and to approach the questions from multiple perspectives. To put it simply: fact-gathering
happens outside of class and is the individual responsibility of each student, so that class time may be
devoted to the more complex tasks of critical thinking and problem solving where the instructor’s attention
is best applied.
Classroom theory sessions usually begin with either a brief Q&A discussion or with a “Virtual
Troubleshooting” session where the instructor shows one of the day’s diagnostic question diagrams while
students propose diagnostic tests and the instructor tells those students what the test results would be
given some imagined (“virtual”) fault scenario, writing the test results on the board where all can see. The
students then attempt to identify the nature and location of the fault, based on the test results.
Each student is free to leave the classroom when they have completely worked through all problems and
have answered a “summary” quiz designed to gauge their learning during the theory session. If a student
finishes ahead of time, they are free to leave, or may help tutor classmates who need extra help.
The express goal of this “inverted classroom” teaching methodology is to help each student cultivate
critical-thinking and problem-solving skills, and to sharpen their abilities as independent learners. While
this approach may be very new to you, it is more realistic and beneficial to the type of work done in
instrumentation, where critical thinking, problem-solving, and independent learning are “must-have” skills.
15
Lab
In the lab portion of each course, students work in teams to install, configure, document, calibrate, and
troubleshoot working instrument loop systems. Each lab exercise focuses on a different type of instrument,
with a eight-day period typically allotted for completion. An ordinary lab session might look like this:
(1) Start of practical (lab) session: announcements and planning
(a) The instructor makes general announcements to all students
(b) The instructor works with team to plan that day’s goals, making sure each team member has a
clear idea of what they should accomplish
(2) Teams work on lab unit completion according to recommended schedule:
(First day) Select and bench-test instrument(s)
(One day) Connect instrument(s) into a complete loop
(One day) Each team member drafts their own loop documentation, inspection done as a team (with
instructor)
(One or two days) Each team member calibrates/configures the instrument(s)
(Remaining days, up to last) Each team member troubleshoots the instrument loop
(3) End of practical (lab) session: debriefing where each team reports on their work to the whole class
Troubleshooting assessments must meet the following guidelines:
• Troubleshooting must be performed on a system the student did not build themselves. This forces
students to rely on another team’s documentation rather than their own memory of how the system was
built.
• Each student must individually demonstrate proper troubleshooting technique.
• Simply finding the fault is not good enough. Each student must consistently demonstrate sound
reasoning while troubleshooting.
• If a student fails to properly diagnose the system fault, they must attempt (as many times as necessary)
with different scenarios until they do, reviewing any mistakes with the instructor after each failed
attempt.
file instructional
16
Distance delivery methods
Sometimes the demands of life prevent students from attending college 6 hours per day. In such cases,
there exist alternatives to the normal 8:00 AM to 3:00 PM class/lab schedule, allowing students to complete
coursework in non-traditional ways, at a “distance” from the college campus proper.
For such “distance” students, the same worksheets, lab activities, exams, and academic standards still
apply. Instead of working in small groups and in teams to complete theory and lab sections, though, students
participating in an alternative fashion must do all the work themselves. Participation via teleconferencing,
video- or audio-recorded small-group sessions, and such is encouraged and supported.
There is no recording of hours attended or tardiness for students participating in this manner. The pace
of the course is likewise determined by the “distance” student. Experience has shown that it is a benefit for
“distance” students to maintain the same pace as their on-campus classmates whenever possible.
In lieu of small-group activities and class discussions, comprehension of the theory portion of each course
will be ensured by completing and submitting detailed answers for all worksheet questions, not just passing
daily quizzes as is the standard for conventional students. The instructor will discuss any incomplete and/or
incorrect worksheet answers with the student, and ask that those questions be re-answered by the student
to correct any misunderstandings before moving on.
Labwork is perhaps the most difficult portion of the curriculum for a “distance” student to complete,
since the equipment used in Instrumentation is typically too large and expensive to leave the school lab
facility. “Distance” students must find a way to complete the required lab activities, either by arranging
time in the school lab facility and/or completing activities on equivalent equipment outside of school (e.g.
at their place of employment, if applicable). Labwork completed outside of school must be validated by a
supervisor and/or documented via photograph or videorecording.
Conventional students may opt to switch to “distance” mode at any time. This has proven to be a
benefit to students whose lives are disrupted by catastrophic events. Likewise, “distance” students may
switch back to conventional mode if and when their schedules permit. Although the existence of alternative
modes of student participation is a great benefit for students with challenging schedules, it requires a greater
investment of time and a greater level of self-discipline than the traditional mode where the student attends
school for 6 hours every day. No student should consider the “distance” mode of learning a way to have
more free time to themselves, because they will actually spend more time engaged in the coursework than
if they attend school on a regular schedule. It exists merely for the sake of those who cannot attend during
regular school hours, as an alternative to course withdrawal.
file distance
17
Metric prefixes and conversion constants
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Metric prefixes
Yotta = 1024 Symbol: Y
Zeta = 1021 Symbol: Z
Exa = 1018 Symbol: E
Peta = 1015 Symbol: P
Tera = 1012 Symbol: T
Giga = 109 Symbol: G
Mega = 106 Symbol: M
Kilo = 103 Symbol: k
Hecto = 102 Symbol: h
Deca = 101 Symbol: da
Deci = 10−1 Symbol: d
Centi = 10−2 Symbol: c
Milli = 10−3 Symbol: m
Micro = 10−6 Symbol: µ
Nano = 10−9 Symbol: n
Pico = 10−12 Symbol: p
Femto = 10−15 Symbol: f
Atto = 10−18 Symbol: a
Zepto = 10−21 Symbol: z
Yocto = 10−24 Symbol: y
METRIC PREFIX SCALE
T
tera
1012
G
M
giga mega
109
106
k
kilo
103
(none)
100
m
µ
milli micro
10-3 10-6
102 101 10-1 10-2
hecto deca deci centi
h
da
d
c
•
•
•
•
•
Conversion formulae for temperature
o
F = (o C)(9/5) + 32
o
C = (o F - 32)(5/9)
o
R = o F + 459.67
K = o C + 273.15
Conversion equivalencies for distance
1 inch (in) = 2.540000 centimeter (cm)
1 foot (ft) = 12 inches (in)
1 yard (yd) = 3 feet (ft)
1 mile (mi) = 5280 feet (ft)
18
n
nano
10-9
p
pico
10-12
Conversion equivalencies for volume
1 gallon (gal) = 231.0 cubic inches (in3 ) = 4 quarts (qt) = 8 pints (pt) = 128 fluid ounces (fl. oz.)
= 3.7854 liters (l)
1 milliliter (ml) = 1 cubic centimeter (cm3 )
Conversion equivalencies for velocity
1 mile per hour (mi/h) = 88 feet per minute (ft/m) = 1.46667 feet per second (ft/s) = 1.60934
kilometer per hour (km/h) = 0.44704 meter per second (m/s) = 0.868976 knot (knot – international)
Conversion equivalencies for mass
1 pound (lbm) = 0.45359 kilogram (kg) = 0.031081 slugs
Conversion equivalencies for force
1 pound-force (lbf) = 4.44822 newton (N)
Conversion equivalencies for area
1 acre = 43560 square feet (ft2 ) = 4840 square yards (yd2 ) = 4046.86 square meters (m2 )
Conversion equivalencies for common pressure units (either all gauge or all absolute)
1 pound per square inch (PSI) = 2.03602 inches of mercury (in. Hg) = 27.6799 inches of water (in.
W.C.) = 6.894757 kilo-pascals (kPa) = 0.06894757 bar
1 bar = 100 kilo-pascals (kPa) = 14.504 pounds per square inch (PSI)
Conversion equivalencies for absolute pressure units (only)
1 atmosphere (Atm) = 14.7 pounds per square inch absolute (PSIA) = 101.325 kilo-pascals absolute
(kPaA) = 1.01325 bar (bar) = 760 millimeters of mercury absolute (mmHgA) = 760 torr (torr)
Conversion equivalencies for energy or work
1 british thermal unit (Btu – “International Table”) = 251.996 calories (cal – “International Table”)
= 1055.06 joules (J) = 1055.06 watt-seconds (W-s) = 0.293071 watt-hour (W-hr) = 1.05506 x 1010
ergs (erg) = 778.169 foot-pound-force (ft-lbf)
Conversion equivalencies for power
1 horsepower (hp – 550 ft-lbf/s) = 745.7 watts (W) = 2544.43 british thermal units per hour
(Btu/hr) = 0.0760181 boiler horsepower (hp – boiler)
Acceleration of gravity (free fall), Earth standard
9.806650 meters per second per second (m/s2 ) = 32.1740 feet per second per second (ft/s2 )
19
Physical constants
Speed of light in a vacuum (c) = 2.9979 × 108 meters per second (m/s) = 186,281 miles per second
(mi/s)
Avogadro’s number (NA ) = 6.022 × 1023 per mole (mol−1 )
Electronic charge (e) = 1.602 × 10−19 Coulomb (C)
Boltzmann’s constant (k) = 1.38 × 10−23 Joules per Kelvin (J/K)
Stefan-Boltzmann constant (σ) = 5.67 × 10−8 Watts per square meter-Kelvin4 (W/m2 ·K4 )
Molar gas constant (R) = 8.314 Joules per mole-Kelvin (J/mol-K)
Properties of Water
Freezing point at sea level = 32o F = 0o C
Boiling point at sea level = 212o F = 100o C
Density of water at 4o C = 1000 kg/m3 = 1 g/cm3 = 1 kg/liter = 62.428 lb/ft3 = 1.94 slugs/ft3
Specific heat of water at 14o C = 1.00002 calories/g·o C = 1 BTU/lb·o F = 4.1869 Joules/g·o C
Specific heat of ice ≈ 0.5 calories/g·o C
Specific heat of steam ≈ 0.48 calories/g·o C
Absolute viscosity of water at 20o C = 1.0019 centipoise (cp) = 0.0010019 Pascal-seconds (Pa·s)
Surface tension of water (in contact with air) at 18o C = 73.05 dynes/cm
pH of pure water at 25o C = 7.0 (pH scale = 0 to 14)
Properties of Dry Air at sea level
Density of dry air at 20o C and 760 torr = 1.204 mg/cm3 = 1.204 kg/m3 = 0.075 lb/ft3 = 0.00235
slugs/ft3
Absolute viscosity of dry air at 20o C and 760 torr = 0.018 centipoise (cp) = 1.8 × 10−5 Pascalseconds (Pa·s)
file conversion constants
20
Question 0
How to get the most out of academic reading:
• Articulate your thoughts as you read (i.e. “have a conversation” with the author). This will develop
metacognition: active supervision of your own thoughts. Write your thoughts as you read, noting
points of agreement, disagreement, confusion, epiphanies, and connections between different concepts
or applications. These notes should also document important math formulae, explaining in your own
words what each formula means and the proper units of measurement used.
• Outline, don’t highlight! Writing your own summary or outline is a far more effective way to comprehend
a text than simply underlining and highlighting key words. A suggested ratio is one sentence of your
own thoughts per paragraph of text read. Note points of disagreement or confusion to explore later.
• Work through all mathematical exercises shown within the text, to ensure you understand all the steps.
• Imagine explaining concepts you’ve just learned to someone else. Teaching forces you to distill concepts
to their essence, thereby clarifying those concepts, revealing assumptions, and exposing misconceptions.
Your goal is to create the simplest explanation that is still technically accurate.
• Write your own questions based on what you read, as though you are a teacher preparing to test
students’ comprehension of the subject matter.
How to effectively problem-solve and troubleshoot:
• Study principles, not procedures. Don’t be satisfied with merely knowing how to compute solutions –
learn why those solutions work. In mathematical problem-solving this means being able to identify the
practical meaning (and units of measurement) of every intermediate calculation. In other words, every
step of your solution should make logical sense.
• Sketch a diagram to help visualize the problem. Sketch a graph showing how variables relate. When
building a real system, always prototype it on paper and analyze its function before constructing it.
• Identify what it is you need to solve, identify all relevant data, identify all units of measurement, identify
any general principles or formulae linking the given information to the solution, and then identify any
“missing pieces” to a solution. Annotate all diagrams with this data.
• Perform “thought experiments” to explore the effects of different conditions for theoretical problems.
When troubleshooting real systems, perform diagnostic tests rather than visually inspecting for faults.
• Simplify the problem and solve that simplified problem to identify strategies applicable to the original
problem (e.g. change quantitative to qualitative, or visa-versa; substitute easier numerical values;
eliminate confusing details; add details to eliminate unknowns; consider simple limiting cases; apply an
analogy). Often you can add or remove components in a malfunctioning system to simplify it as well
and better identify the nature and location of the problem.
• Work “backward” from a hypothetical solution to a new set of given conditions.
How to create more time for study:
• Kill your television and video games. Seriously – these are incredible wastes of time.
distractions (e.g. cell phone, internet, socializing) in your place and time of study.
Eliminate
• Use your “in between” time productively. Don’t leave campus for lunch. Arrive to school early. If you
finish your assigned work early, begin studying the next day’s material.
Above all, cultivate persistence. Persistent effort is necessary to master anything non-trivial. The keys
to persistence are (1) having the desire to achieve that mastery, and (2) realizing challenges are normal and
not an indication of something gone wrong. A common error is to equate easy with effective: students often
believe learning should be easy if everything is done right. The truth is that mastery never comes easy!
file question0
21
Creative Commons License
This worksheet is licensed under the Creative Commons Attribution 4.0 International Public
License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ or send a
letter to Creative Commons, 171 Second Street, Suite 300, San Francisco, California 94105, USA. The terms
and conditions of this license allow for free copying, distribution, and/or modification of all licensed works
by the general public.
Simple explanation of Attribution License:
The licensor (Tony Kuphaldt) permits others to copy, distribute, display, and otherwise use this
work. In return, licensees must give the original author(s) credit. For the full license text, please visit
http://creativecommons.org/licenses/by/1.0/ on the internet.
More detailed explanation of Attribution License:
Under the terms and conditions of the Creative Commons Attribution License, you may make freely
use, make copies, and even modify these worksheets (and the individual “source” files comprising them)
without having to ask me (the author and licensor) for permission. The one thing you must do is properly
credit my original authorship. Basically, this protects my efforts against plagiarism without hindering the
end-user as would normally be the case under full copyright protection. This gives educators a great deal
of freedom in how they might adapt my learning materials to their unique needs, removing all financial and
legal barriers which would normally hinder if not prevent creative use.
Nothing in the License prohibits the sale of original or adapted materials by others. You are free to
copy what I have created, modify them if you please (or not), and then sell them at any price. Once again,
the only catch is that you must give proper credit to myself as the original author and licensor. Given that
these worksheets will be continually made available on the internet for free download, though, few people
will pay for what you are selling unless you have somehow added value.
Nothing in the License prohibits the application of a more restrictive license (or no license at all) to
derivative works. This means you can add your own content to that which I have made, and then exercise
full copyright restriction over the new (derivative) work, choosing not to release your additions under the
same free and open terms. An example of where you might wish to do this is if you are a teacher who desires
to add a detailed “answer key” for your own benefit but not to make this answer key available to anyone
else (e.g. students).
Note: the text on this page is not a license. It is simply a handy reference for understanding the Legal
Code (the full license) - it is a human-readable expression of some of its key terms. Think of it as the
user-friendly interface to the Legal Code beneath. This simple explanation itself has no legal value, and its
contents do not appear in the actual license.
file license
22
Questions
Question 1
Read and outline the “Electrical Power Grids” section of the “Electric Power Measurement and Control”
chapter in your Lessons In Industrial Instrumentation textbook. Note the page numbers where important
illustrations, photographs, equations, tables, and other relevant details are found. Prepare to thoughtfully
discuss with your instructor and classmates the concepts and examples explored in this reading.
Alternatively, you may read the “Introduction to Power System Automation” section found in the same
chapter of the Lessons In Industrial Instrumentation textbook. This section gives a more comprehensive
overview of electrical power grids and associated instrumentation, as well as the single-line diagrams used
to document power grids.
file i03022
Question 2
Read and outline the “Single-line Electrical Diagrams” section of the “Electric Power Measurement
and Control” chapter in your Lessons In Industrial Instrumentation textbook. Note the page numbers
where important illustrations, photographs, equations, tables, and other relevant details are found. Prepare
to thoughtfully discuss with your instructor and classmates the concepts and examples explored in this
reading.
file i03023
Question 3
Read and outline the “Circuit Breakers and Disconnects” section of the “Electric Power Measurement
and Control” chapter in your Lessons In Industrial Instrumentation textbook. Note the page numbers
where important illustrations, photographs, equations, tables, and other relevant details are found. Prepare
to thoughtfully discuss with your instructor and classmates the concepts and examples explored in this
reading.
file i01245
23
Question 4
Read selected portions of “Informative Annex D – Incident Energy and Arc Flash Boundary Calculation
Methods” in the NFPA 70E document “Standard for Electrical Safety in the Workplace” and answer the
following questions:
Section D.2 (the “Ralph Lee Calculation Method”) and section D.3 (the “Doughty Neal Paper”) and
section D.4 (the “IEEE 1584 Calculation Method”) all reference the amount of clearing time for different
overcurrent protective devices. List those device types and comment on their relative operating times. What
kind of electrical fault do you think is being referred to in this Annex, opens or shorts?
The impedance of a power transformer or power system is mentioned throughout this section of the
NFPA document as a limiting factor in fault current and arc flash energy. Identify what causes impedance
in a power system, and whether a high percentage or a low percentage is more limiting to fault current.
Table D.4.7 lists different types of circuit breakers and their “Trip Unit Types”. Identify some of these
different trip unit types and how they work. Which of these trip unit types provides the smallest (i.e. safest)
arc flash boundary? Explain why this is so.
Suggestions for Socratic discussion
• Explain exactly why clearing time is a relevant parameter for calculating arc flash energy and arc flash
boundary size.
• An important safety policy at many industrial facilities is something called stop-work authority, which
means any employee has the right to stop work they question as unsafe. Describe a scenario involving
either arc flash or arc blast potential where one might invoke stop-work authority.
• When a substation operator closes circuit breakers to energize a bus, they typically begin with the
source having the greatest impedance. Explain why this is a wise choice.
file i03024
24
Question 5
Examine the single-line electrical diagram example contained in “Informative Annex D – Incident Energy
and Arc Flash Boundary Calculation Methods” of the NFPA 70E document “Standard for Electrical Safety
in the Workplace” and answer the following questions:
Identify how each of the following devices are represented in this diagram:
•
•
•
•
Transformers
Disconnects
Circuit breakers
Fuses
Several “tie breakers” are shown in this diagram, connecting bus segments together to form a larger bus.
Identify where these tie breakers are in the diagram, and explain their purpose in the power distribution
system.
Each transformer shown in this diagram bears a percentage rating. What, exactly, does this percentage
rating refer to?
Suppose the 5 MVA transformer feeding bus 2B suffers a catastrophic internal short-circuit. Identify the
points at which power will be automatically disconnected from this failed transformer, either by fuses or by
circuit breakers tripped by protective relays. Is it possible to restore power to bus 2B while this transformer
is still out of service? If so, explain how this could be accomplished.
Suppose the 2.5 MVA transformer feeding bus 7A suffers a catastrophic internal short-circuit. Identify
the points at which power will be automatically disconnected from this failed transformer, either by fuses
or by circuit breakers tripped by protective relays. Is it possible to restore power to bus 7A while this
transformer is still out of service? If so, explain how this could be accomplished.
Suggestions for Socratic discussion
• Should tie breakers and tie switches typically be left in their open or closed states? Explain your
reasoning.
• Calculate the maximum bolted-fault current for a three-phase transformer rated at 480 volt output and
1.5 MVA, with 6% impedance.
• Note the tie breaker arrangement between busses 1A and 1B: there is a direct tie breaker in parallel
with an inductor having its own pair of breakers. When initially connecting these two busses together,
the protocol is to close the direct tie breaker last, relying on the other two breakers and the associated
inductor to make the first connection between the busses. Explain why this is so.
file i03034
25
Question 6
Examine this single-line diagram of a power system and answer the following questions:
Power plant generators
Gen
Gen
Gen
A
B
C
13.8 kV
13.8 kV
13.8 kV
115 kV
115 kV
115 kV
D
E
F
Bus
G
H
Transmission line
Transmission line
J
K
Substation
Bus A
115 kV
Bus B
2
115 kV
6
13.8 kV
13.8 kV
Load A
1
Load B
Load C
3
11
7
Load D
Load E
8
Load F
4
9
Load G
Load H
12
Load I
5
10
Bus C
Load J
Load K
Load L
Suppose Load F fails in such a way that it draws far more current than it should. Identify which circuit
breaker(s) must trip in order to interrupt the fault current while maintaining power to as many other loads
as possible.
Suppose circuit breaker #5 fails to trip when commanded. Identify which other circuit breaker(s) must
trip in order to de-energize breaker #5 while maintaining power to as many loads as possible.
Suppose one of the high-voltage insulators on Bus C fails, causing a high amount of current to flow into
that bus. Identify which circuit breakers must trip in order to de-energize that bus while maintaining power
to as many loads as possible.
file i02864
26
Question 7
Read selected portions of the sales brochure for the Siemens model 3AP1 DTC high-voltage circuit
breaker and answer the following questions:
This particular model of circuit breaker is a “dead tank” design. Explain what this phrase means.
This particular model of circuit breaker not only has current-interrupting contacts, but also disconnect
and “earthing” switch contacts as well. Identify where each of these contacts is located in the assembly and
explain their functions.
file i03036
Question 8
Read selected portions of the sales brochure for the Siemens model 3AP1/2 live-tank high-voltage circuit
breakers and answer the following questions:
Explain what the phrase “live tank” means with regard to a circuit breaker, referencing illustrations or
photographs in the document to aid in your explanation.
Identify at least two different styles of high-voltage circuit breakers described in this document, showing
where power goes in and out of the breaker units.
Explain how the spring mechanism works to store mechanical energy to trip and close the circuit breaker
contacts. Note that the diagram shows different colored arrows to designate the “opening” and “closing”
directions.
Compare the following current ratings of a 550 kV model 3AP2 circuit breaker, and explain why each
one is different:
• Rated normal current =
• Rated peak withstand current =
• Rated short-circuit breaking current =
• Rated short-circuit making current =
file i03038
27
Question 9
Explain what AC reactance is, and how it differs from resistance despite being measured in the same
units (ohms). Then, calculate reactance values for the following components:
• 45 millihenry inductor at 400 Hz =
Ω
• 12 microfarad capacitor at 50 Hz =
Ω
• Brown-Red-Orange resistor at 1000 Hz =
• 1.5 henry inductor at 440 Hz =
Ω
Ω
After you have done this, comment on the amount of impedance exhibited by each of these components.
Suggestions for Socratic discussion
• One way to think of electrical resistance and electrical impedance in analogous terms is to liken then
to mechanical friction and mechanical inertia, respectively. Explain this association in terms of energy
transfer.
• Explain why the impedance of a real component differs from the impedance of an ideal component,
especially inductors.
• Will a series-connected inductor serve as a low-pass filter or a high-pass filter? Explain your answer.
• Explain how to build a low-pass filter circuit using a capacitor and a resistor.
file i03066
28
Question 10
Complex number arithmetic makes possible the analysis of AC circuits using (almost) the exact same
Laws that were learned for DC circuit analysis. The only bad part about this is that doing complex-number
arithmetic by hand can be very tedious. Some calculators, though, are able to add, subtract, multiply,
divide, and invert complex quantities as easy as they do scalar quantities, making this method of AC circuit
analysis relatively easy.
This question is really a series of practice problems in complex number arithmetic, the purpose being
to give you lots of practice using the complex number facilities of your calculator (or to give you a lot of
practice doing trigonometry calculations, if your calculator does not have the ability to manipulate complex
numbers!).
Addition and subtraction:
(5 + j6) + (2 − j1) =
(10 − j8) + (4 − j3) =
(−3 + j0) + (9 − j12) =
(3 + j5) − (0 − j9) =
(25 − j84) − (4 − j3) =
(−1500 + j40) + (299 − j128) =
(256 15o ) + (106 74o ) =
(10006 43o ) + (12006 − 20o ) =
(5226 71o ) − (856 30o ) =
(256 15o ) × (126 10o ) =
(16 25o ) × (5006 − 30o ) =
(5226 71o ) × (336 9o ) =
106 −80o
16 0o
256 120o
3.56 −55o
−666 67o
86 −42o
Multiplication and division:
=
(3 + j5) × (2 − j1) =
=
=
(10 − j8) × (4 − j3) =
(3+j4)
(12−j2)
=
1
(7506 −38o )
1
(10+j3)
=
Reciprocation:
1
(156 60o )
1
156
45o
=
1
+
=
1
926
1
12006
−25o
1
1
1106
−34o
+
1
806
19o
+
10
1
+
=
1
5746
1
23k6
21o
1
=
1
706
73o
=
1
89k6
−5o
+
1
15k6
33o
+
=
1
9.35k6
45
−67o
1
5126
34o
1
+
+
=
1
10k6
−81o
1
1
+
1k6
−25o
1
9426
+
−20
=
1
2.2k6
44o
Suggestions for Socratic discussion
• Your calculator’s manual will be an excellent reference for learning how to enter and interpret complex
numbers. Show where in the manual you were able to find instructions on entering complex numbers,
displaying them in different forms (e.g. polar vs. rectangular), and performing basic arithmetic
operations on complex numbers.
file i00846
29
Question 11
Three-phase motors and generators alike are manufactured in two basic forms: Wye (Y) and Delta (∆):
Mark in the above diagrams where the following electrical quantities would be measured (hint: each
coil shown in the diagram is called a phase winding, and each conductor connecting the motor or generator
to something else in the three-phase system is called a line):
• Phase voltage
• Line voltage
• Phase current
• Line current
In which circuit (Wye or Delta) are the phase and line currents equal? In which circuit (Wye or Delta)
are the phase and line voltages equal? Explain both answers, in terms that anyone with a basic knowledge
of electricity could understand (i.e. using the properties of series and parallel connections). Where phase
and line quantities are unequal, determine which is larger.
file i03258
30
Question 12
Suppose you need to design a three-phase electric heater to dissipate 15 kW of heat when powered by
480 VAC. Your options are to build a delta-connected heater array or a wye-connected heater array:
Rdelta
Rwye
Rwye
Rdelta
Rdelta
Rwye
Calculate the proper resistance value for each array, to achieve the desired heat output:
Rdelta =
Rwye =
Ω
Ω
file i01040
Question 13
A three-phase electric motor operating at a line voltage of 4160 volts AC (RMS) draws 27.5 amps of
current (RMS) through each of its lines. Calculate the amount of electrical power consumed by this motor.
Assuming the motor is 92% efficient and operating at a power factor of 1, calculate its mechanical output
power in the unit of horsepower.
file i01206
31
Question 14
Examine the primary and secondary connections on this three-phase transformer bank, and then
determine the line voltage to the customer, assuming 12.5 kV line voltage on the distribution power lines.
The schematic diagram shown in the grey box is typical for each of the three transformers:
po
we
r li
ne
insulator
crossarm
Fuse
Schematic diagram
7.2 kV
240/120 V
Fuse
Fuse
7.2 kV
7.2 kV
7.2 kV
240/120 V
240/120 V
240/120 V
Transformer
Transformer
Transformer
Power pole
file i01041
32
Low-voltage lines
to customer
Question 15
Three step-down transformers have their primary (high-voltage) terminals connected together in a “wye”
configuration so that the 12.5 kV line voltage energizes each primary winding with 7.2 kV. The secondary
terminals on each transformer have been left disconnected:
po
we
r li
ne
insulator
crossarm
Fuse
Schematic diagram
7.2 kV
240/120 V
Fuse
Fuse
7.2 kV
7.2 kV
7.2 kV
240/120 V
240/120 V
240/120 V
Transformer
Transformer
Transformer
L1
L2
L3
N
Power pole
Sketch proper wire connections to provide 120/208 VAC to the customer.
file i01042
33
Low-voltage lines
to customer
Question 16
A 15 kV three-phase alternator needs to have its windings connected properly to prepare it to send
power to a “bus” shared by other alternators in a power plant:
Three-phase alternator
Rotor
Disconnects
Circuit
breaker
Disconnects
. . . 15 kV generator bus
...
...
...
...
...
Each phase winding on the alternator is rated at 15 kV. The rotor winding is rated at 220 VDC. Sketch
all necessary connections to make this alternator work as intended.
file i01043
34
Question 17
Three-phase AC induction motors respond differently to the loss of one phase, depending on whether
they are internally wye- or delta-connected:
A
B
C
Open fault
Motor
Motor
Which of these two motor designs will fare better in the event of a phase loss such as the open fault in
phase C shown above, and why?
file i00967
35
Question 18
Convert the following rectangular-form complex numbers into polar form:
• 45 + i22 =
• 90 + i5 =
• −45 + i38 =
• 21 − i39 =
• −100 − i83 =
• −256 + i300 =
Also, perform the following arithmetic operations on these rectangular-form complex numbers:
• (50 + i22) + (−23 + i19) =
• (39 − i5) − (10 + i8) =
• (−8 + i7) × (2 + i1) =
• (9 − i2) ÷ (2 + i12) =
• (−4 − i20) × (−6 + i15) =
• (1200 + i8570) ÷ (−5400 + i1022) =
file i03115
Question 19
Convert the following polar-form complex numbers into rectangular form:
• 506 25o =
• 1706 82o =
• 116 165o =
• 756 299o =
• 316 190o =
• 61.56 −45o =
Also, perform the following arithmetic operations on these polar-form complex numbers:
• (346 10o ) × (186 − 20o ) =
• (56 30o ) ÷ (26 85o ) =
• (756 − 50o ) + (116 0o ) =
• (2506 17o ) − (816 − 40o ) =
• (0.00456 90o ) + (0.00126 − 110o ) =
• (93006 155o ) − (18106 25o ) =
file i03114
36
Question 20
Complex numbers are commonly used in AC circuit analysis to represent voltage, current, and impedance
quantities. A complex number is a quantity having both a “real” and an “imaginary” value, and may be
represented as a vector on a complex plane. For example, the following complex number has a “real” part
equal to +4 and an “imaginary” part equal to +j3 (also written as +i3):
+imaginary
+4
5
+j3
36.87o
-real
+real
-imaginary
Complex numbers may be written in terms of their real and imaginary parts, in which case we refer to
the notation as rectangular. The complex number in the above illustration is 4 + j3 in rectangular form.
Complex numbers may alternatively be written in terms of their magnitude and angle, in which case we refer
to the notation as polar. The complex number in the above illustration is 5 6 36.87o in polar form.
Your task is to build a computer spreadsheet program to convert from any complex number entered in
rectangular form into polar form, or vice-versa. A sample layout is presented here, where yellow shading
represents values entered by you, and blue shading represents values calculated by the computer. Two sets
of cells are shown, one for converting rectangular to polar and another for converting polar to rectangular:
1
1
2
Real
Imaginary
3
4
5
Magnitude
Angle
2
3
4
Magnitude
Angle
Real
5
37
Imaginary
When you are finished entering your spreadsheet’s formulae, test it by converting between the following
complex number formats:
• 56 − j23 =
• 105 6 20o =
• 15304 6 175o =
• −930 + j12944 =
Note: you are going to need a way to quickly convert between rectangular and polar forms of complex
numbers with some of the AC circuit calculations in this course!
An alternative to building a spreadsheet is to familiarize yourself with your scientific calculator’s complex
number functions, if it offers this functionality. If you have such a calculator, you may practice the following
calculations in lieu of building the spreadsheet:
• (−15 + j4) + (32 − j12) =
• (24 − j18) × (3 + j9) =
• (356 40o ) × (86 130o ) =
• (10 − j25) ÷ (196 31o ) =
• (436 80o ) + (356 − 15o ) =
file i03067
Question 21
Read and outline the “Circles, Sine Waves, and Cosine Waves” subsection of the “Phasors” section
of the “AC Electricity” chapter in your Lessons In Industrial Instrumentation textbook. Note the page
numbers where important illustrations, photographs, equations, tables, and other relevant details are found.
Prepare to thoughtfully discuss with your instructor and classmates the concepts and examples explored in
this reading.
file i03027
Question 22
Read and outline the “Phasor Expressions of Phase Shifts” subsection of the “Phasors” section of the
“AC Electricity” chapter in your Lessons In Industrial Instrumentation textbook. Note the page numbers
where important illustrations, photographs, equations, tables, and other relevant details are found. Prepare
to thoughtfully discuss with your instructor and classmates the concepts and examples explored in this
reading.
file i03028
Question 23
Read and outline the “Phasor Arithmetic” subsection of the “Phasors” section of the “AC Electricity”
chapter in your Lessons In Industrial Instrumentation textbook. Note the page numbers where important
illustrations, photographs, equations, tables, and other relevant details are found. Prepare to thoughtfully
discuss with your instructor and classmates the concepts and examples explored in this reading.
file i03043
38
Question 24
Read and outline the “Phasors and Circuit Measurements” subsection of the “Phasors” section of the
“AC Electricity” chapter in your Lessons In Industrial Instrumentation textbook. Note the page numbers
where important illustrations, photographs, equations, tables, and other relevant details are found. Prepare
to thoughtfully discuss with your instructor and classmates the concepts and examples explored in this
reading.
file i03029
Question 25
Read and outline the “Interconnected Generators” section of the “Electric Power Measurement and
Control” chapter in your Lessons In Industrial Instrumentation textbook. Note the page numbers where
important illustrations, photographs, equations, tables, and other relevant details are found. Prepare to
thoughtfully discuss with your instructor and classmates the concepts and examples explored in this reading.
file i03030
Question 26
Complete the following table of values for this circuit, expressing each quantity in both rectangular and
polar forms:
3.3 kΩ
525 V ∠ 0o
60 Hz
––
V (polar)
V (rect.)
I (polar)
I (rect.)
Z (polar)
Z (rect.)
2.7 H
R
L
Total
525 V 6 0o
525 + j0 V
Suggestions for Socratic discussion
Predict the effects on all voltages and currents in this circuit if the inductor fails open.
Predict the effects on all voltages and currents in this circuit if the inductor fails shorted.
Predict the effects on all voltages and currents in this circuit if the resistor fails open.
Predict the effects on all voltages and currents in this circuit if the resistor fails shorted.
Predict the effects on all voltages and currents in this circuit if the resistor gets replaced by a capacitor
with the same impedance magnitude.
• Predict the effects on all voltages and currents in this circuit if the inductor gets replaced by a capacitor
with the same impedance magnitude.
•
•
•
•
•
file i03048
39
Question 27
Complete the following table of values for this circuit, expressing each quantity in both rectangular and
polar forms:
600 V ∠ 0o
60 Hz
––
V (polar)
V (rect.)
I (polar)
I (rect.)
Z (polar)
Z (rect.)
10.6 µF
0.5 H
L
C
Total
600 V 6 0o
600 + j0 V
Suggestions for Socratic discussion
Predict the effects on all voltages and currents in this circuit if the inductor fails open.
Predict the effects on all voltages and currents in this circuit if the inductor fails shorted.
Predict the effects on all voltages and currents in this circuit if the capacitor fails open.
Predict the effects on all voltages and currents in this circuit if the capacitor fails shorted.
Predict the effects on all voltages and currents in this circuit if the capacitor gets replaced by a resistor
with the same impedance magnitude.
• Predict the effects on all voltages and currents in this circuit if the inductor gets replaced by a resistor
with the same impedance magnitude.
•
•
•
•
•
file i03044
40
Question 28
Calculate the amount of voltage between points A and B (VAB ) given the generator values shown:
A
B
479 VAC
∠ 35o
60 Hz
485 VAC
∠ 172o
60 Hz
State your answer both in symbolic form (e.g. ??? volts
showing the given generator voltages along with VAB .
6
?? degrees) as well as in a phasor diagram
Suggestions for Socratic discussion
• Would it be safe to connect points A and B together with the generator voltages as shown? Explain
why or why not.
• Is the calculated voltage for VAB equivalent to the voltage for VBA ? Why or why not?
file i03040
41
Question 29
Calculate the amount of current in each line of this balanced three-phase circuit. Capacitance and
resistance values are typical for each phase:
Three-phase generator
Vline = 2.4 kV @ 60 Hz
C
IC
B
IB
IA
15 Ω
N
A
(each)
30 µF
State your answers both in symbolic form (e.g. ??? volts
along with these generator voltage phasors:
6
?? degrees) as well as in a phasor diagram
VCN
VAN
VBN
Suggestions for Socratic discussion
• Predict how the phasor diagram of voltage and current would change if one of the capacitors failed open.
• Predict how the phasor diagram of voltage and current would change if one of the capacitors failed
shorted.
• Predict how the phasor diagram of voltage and current would change if one of the resistors failed open.
• Predict how the phasor diagram of voltage and current would change if one of the resistors failed shorted.
file i03041
42
Question 30
Calculate the amount of voltage between point A and ground (VA ) given the component values shown:
110 VAC
60 Hz
H1
H3
H2
H4
20:1 step-down
X1
A
X2
7.5 H
2.2 kΩ
1 µF
State your answer both in symbolic form (e.g. ??? volts 6 ?? degrees) as well as in a phasor diagram
showing the source voltage (its phase angle assumed to be zero degrees) and VA .
file i03049
43
Question 31
In this graph of two AC voltages, which one is leading and which one is lagging?
+5
+4
+3
+2
+1
V
0
-1
-2
-3
-4
-5
If the 4-volt (peak) sine wave is denoted in phasor notation as 4 V6 0o , how should the 3-volt (peak)
waveform be denoted? Express your answer in both polar and rectangular forms.
If the 4-volt (peak) sine wave is denoted in phasor notation as 4 V6 90o , how should the 3-volt (peak)
waveform be denoted? Express your answer in both polar and rectangular forms.
file i00839
Question 32
Draw the phasor 15 + i8 on a coordinate graph:
file i03117
44
Question 33
Draw the phasor 206 60o on a coordinate graph:
file i03116
Question 34
In this phasor diagram, determine which phasor is leading and which is lagging the other:
B
A
file i00840
45
Question 35
Calculate the operating current through each of the load resistances shown in this circuit (assuming
each three-phase load is balanced):
A
Vline = 13.8 kV B
C
16.67:1
16.67:1
16.67:1
R1
1240 Ω
R2
950 Ω
Also, calculate the power dissipated by each load.
file i02119
46
Question 36
An unbalanced wye-connected load receives power from a balanced 120/208 VAC source:
L1
1k5 Ω
120/208 VAC
balanced source
N
R1
0k8 Ω
2k3 Ω
R2
R3
L2
L3
Calculate the current through each of the three lines (L1, L2, and L3), as well as the current through
the neutral conductor:
• IL1 =
amps
• IL2 =
amps
• IL3 =
amps
• IN =
amps
file i01044
47
Question 37
A three-phase step-down transformer supplies 480 VAC to a pair of resistive loads. The secondary
winding is “corner-grounded” on the X2 leg:
Vline = 13.8 kV
Primary
Vline = 480 V
Secondary
H1
X1
X2
H2
H3
X3
H
G
J
K
M
L
N
Determine the following phase-to-ground voltages in this system while both loads are energized:
• VG =
volts
• VH =
volts
• VJ =
volts
• VK =
volts
• VL =
volts
• VM =
volts
• VN =
volts
Supposing the upper load has a total power dissipation of 8.4 kW and the lower load has a total power
dissipation of 3.9 kW, calculate the amount of current through line H2.
file i00966
48
Question 38
Calculate the total impedances (complete with phase angles) for each of the following inductor-resistor
circuits:
200 mH
0.5 H
290 Hz
470 Ω
100 Hz
1.5 kΩ
1H
100 Hz
0.5 H
0.2 H
470 Ω
1H
290 Hz
1.5 kΩ
file i01060
Question 39
Calculate the total impedances (complete with phase angles) for each of the following capacitor-resistor
circuits:
0.1 µF
3.3 µF
290 Hz
470 Ω
100 Hz
1.5 kΩ
0.22 µF
3.3 µF
100 Hz
0.1 µF
470 Ω
290 Hz
file i01072
49
0.22 µF
1.5 kΩ
Question 40
Is this circuit’s overall behavior capacitive or inductive? In other words, from the perspective of the AC
voltage source, does it “appear” as though a capacitor is being powered, or an inductor?
15 V
1.8 kHz
0.1 µF
85 mH
Now, suppose we take these same components and re-connect them in parallel rather than series. Does
this change the circuit’s overall “appearance” to the source? Does the source now “see” an equivalent
capacitor or an equivalent inductor? Explain your answer.
85 mH
15 V
1.8 kHz
0.1 µF
Suggestions for Socratic discussion
• Which component “dominates” the behavior of a series LC circuit, the one with the least reactance or
the one with the greatest reactance?
• Which component “dominates” the behavior of a parallel LC circuit, the one with the least reactance
or the one with the greatest reactance?
file i01076
Question 41
Read and outline the introduction and the “Potential Transformers” subsection of the “Electrical
Sensors” section of the “Electric Power Measurement and Control” chapter in your Lessons In Industrial
Instrumentation textbook. Note the page numbers where important illustrations, photographs, equations,
tables, and other relevant details are found. Prepare to thoughtfully discuss with your instructor and
classmates the concepts and examples explored in this reading.
file i01243
Question 42
Read and outline the “Current Transformers” subsection of the “Electrical Sensors” section of the
“Electric Power Measurement and Control” chapter in your Lessons In Industrial Instrumentation textbook.
Note the page numbers where important illustrations, photographs, equations, tables, and other relevant
details are found. Prepare to thoughtfully discuss with your instructor and classmates the concepts and
examples explored in this reading.
file i01244
50
Question 43
Read and outline the “Instrument Transformer Safety” subsection of the “Electrical Sensors” section
of the “Electric Power Measurement and Control” chapter in your Lessons In Industrial Instrumentation
textbook. Note the page numbers where important illustrations, photographs, equations, tables, and other
relevant details are found. Prepare to thoughtfully discuss with your instructor and classmates the concepts
and examples explored in this reading.
file i03026
Question 44
Read and outline the “Instrument Transformer Test Switches” subsection of the “Electrical Sensors”
section of the “Electric Power Measurement and Control” chapter in your Lessons In Industrial
Instrumentation textbook. Note the page numbers where important illustrations, photographs, equations,
tables, and other relevant details are found. Prepare to thoughtfully discuss with your instructor and
classmates the concepts and examples explored in this reading.
file i01246
Question 45
Explain how to isolate the protective relay from all PTs and all CTs prior to testing the relay:
C
B
A
X1
X2
X3
X4
X5
X1
X2
X3
X4
X5
X1
X2
X3
X4
X5
X5
X4
X3
X2
X1
X5
Protective relay
X4
X3
VA
VB
VC
IA
IB
IC
X2
Trip
X1
Power
X5
X4
X3
X2
X1
125 VDC
station
power
file i02883
51
Question 46
Read and outline the “Transformer Polarity” subsection of the “Electrical Sensors” section of the
“Electric Power Measurement and Control” chapter in your Lessons In Industrial Instrumentation textbook.
Note the page numbers where important illustrations, photographs, equations, tables, and other relevant
details are found. Prepare to thoughtfully discuss with your instructor and classmates the concepts and
examples explored in this reading.
file i03025
52
Question 47
Suppose a current transformer with a ratio of 400:5 sends its output signal to a protective relay and a
panel-mounted ammeter as shown in this schematic diagram:
400:5
283 amps
Power line conductor
Current
transformer
RCT
Rwire1
Protective
relay
Rrelay
•
•
•
•
•
•
Panel-mounted
ammeter
Rwire3
Rmeter
Rwire2
RCT = 0.3 Ω (this is the internal resistance of the CT’s secondary winding)
Rwire1 = 0.4 Ω
Rwire2 = 0.1 Ω
Rwire3 = 0.4 Ω
Rrelay = 2.5 Ω
Rmeter = 1.0 Ω
Calculate the following voltage drops in this current transformer circuit, from the given information:
• Vrelay =
• Vmeter =
volts
volts
• Total voltage dropped across all wires =
• Voltage output at CT terminals =
volts
volts
• Voltage generated by CT secondary winding (before any RCT losses) =
volts
Suggestions for Socratic discussion
• Explain why the two instruments (the relay and the meter) are connected in series with each other and
not in parallel.
• Predict the effects of wire 1 failing open in this circuit.
• Predict the effects of the power line conductor failing open in this circuit.
• Predict the effects of the protective relay failing shorted in this circuit.
• Predict the effects of the panel-mounted ammeter failing open in this circuit.
• Predict the effects of the panel-mounted ammeter failing shorted in this circuit.
file i02873
53
Question 48
Calculate VAB and VCD in this circuit, assuming both sources and transformers share a common ground
and that both transformers have 1:1 winding ratios:
A
C
240 V ∠ -37o
B
D
108 V ∠ 70o
Hint: since all transformers have a 1:1 turns ratio, the secondary voltage must be identical to the primary
voltage for each one. This means the phasor representing a transformer’s secondary winding voltage must be
exactly the same length and have exactly the same angle as the phasor representing that same transformer’s
primary voltage. Treat each phasor as a line segment you are free to move around so long as you do not alter
its length or direction, and you can see how they “stack up” onto each other according to how the windings
are electrically connected to form a complete phasor diagram.
Suggestions for Socratic discussion
•
•
•
•
Sketch the phasor for VBA .
Sketch the phasor for VDC .
Predict the effects of the upper transformer’s primary winding failing open on the phasor diagram.
Predict the effects of the lower transformer’s primary winding failing open on the phasor diagram.
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54
Question 49
Sketch phasor diagrams of both the input phase voltages (VA , VB , and VC ) and the output phase voltages
(VX , VY , and VZ ) for this Wye-Delta transformer bank powering a resistive load, assuming 1:1 transformer
turns ratios, an input line voltage of 2400 volts, an A-B-C phase sequence, and using phase A as the reference
voltage (0 degree phase angle with reference to ground):
X
Y
A
Vline = 2400 VAC
B
C
Z
Hint: since all transformers have a 1:1 turns ratio, the secondary voltage must be identical to the primary
voltage for each one. This means the phasor representing a transformer’s secondary winding voltage must be
exactly the same length and have exactly the same angle as the phasor representing that same transformer’s
primary voltage. Treat each phasor as a line segment you are free to move around so long as you do not alter
its length or direction, and you can see how they “stack up” onto each other according to how the windings
are electrically connected to form a complete phasor diagram.
Suggestions for Socratic discussion
• Identify two currents in this circuit that are guaranteed to be equal in value, even if the source and load
happened to be imbalanced.
• Identify two currents in this circuit that are unequal in value, and explain why one of them is larger
than the other.
• Identify two voltages in this circuit that are guaranteed to be equal in value, even if the source and load
happened to be imbalanced.
• Identify two voltages in this circuit that are unequal in value, and explain why one of them is larger
than the other.
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55
Question 50
This bank of pole-mounted power transformers steps 7.2 kVAC line power down to 120/208 VAC power
to service a small business:
po
we
r li
ne
V
W
U
insulator
crossarm
Fuse
Fuse
H1
H2
X2
Schematic diagram
4.16 kV
X1
H1
H2
X2
X1
Fuse
H1
X2
H2
X1
4.16 kV
4.16 kV
4.16 kV
120 V
120 V
120 V
120 V
H1
X2
L1
L2
L3
N
Power pole
X1
H2
Low-voltage lines
to customer
Given the following power line voltages (measured phase-to-ground), calculate the phase angles of the
specified secondary-side voltages:
• VU = 4160 V 6 0o
• VV = 4160 V 6 −120o
• VW = 4160 V 6 −240o
• VL1−N =
• VL2−N =
6
• VL3−N =
• VL1−L3 =
6
6
6
Suggestions for Socratic discussion
• Do these power transformers have additive or subtractive polarities? How can you tell?
• Identify the phase sequence (a.k.a. phase rotation) of this power system based on the given phase-toground power line voltage values.
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56
Question 51
Suppose you need to take a current measurement in a CT circuit, inserting an ammeter into the CT’s
secondary circuit to do so. The CT’s signal passes through a standard “shorting” test switch before going
to the panel instrument, and one pole of each two-pole CT switch has a “test jack” to facilitate current
measurement.
Explain how a “test jack” on a CT test switch works, and then outline a step-by-step procedure for
safely measuring current in the CT secondary circuit:
•
•
•
•
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57
Question 52
This wattmeter measures power on one phase of a three-phase power system by sensing both line voltage
and line current through instrument transformers. The nominal line voltage of this power system is 4160
volts AC, while the current may extend upwards of 180 amps AC under full-load conditions:
Three-phase power conductors
A
...
...
...
B
C
CT
200:5
Wattmeter
PT
Terminals
V
40:1
I
What would you have to do in order to check the calibration of this wattmeter? Specifically, devise a
step-by-step procedure that you could give to another technician telling them what they would have to do
in order to simulate precise amounts of electrical power to the wattmeter’s input, keeping safety in mind as
the first priority. Note: you are not allowed to shut power off in the three-phase system to do your test – it
must be done “live.”
The power of a balanced three-phase system is given by the following formula:
P =
√
3Vline Iline
Suggestions for Socratic discussion
• An important safety rule to apply when working with live circuit is the “one-hand rule.” Explain what
this rule is, and how it is applied to a scenario such as this.
• When loosening the screws on a terminal block to remove wires for the PT signal, should you remove
the wires from the left-hand side of the terminals (as shown in the diagram) or from the right-hand side,
or does this matter at all?
• The task of disconnecting a wattmeter from live instrument transformers presents significant hazard.
Devise a way to make this procedure safer, using special “test switches” installed on the signal wires
at the time of construction, so that a technician may simply throw the switches’ levers to isolate the
wattmeter instead of putting a screwdriver on “live” terminals and removing wires from terminal blocks.
• Suppose the PT’s output signal were 113.6 volts RMS, and the CT’s output signal were 2.9 amps RMS.
How much power does this represent flowing through the three-phase lines?
• Why are both instrument transformers’ secondary circuits grounded?
• Suppose the potential transformer has a reliability rating of 0.9995 and the current transformer has a
reliability rating of 0.9998. Calculate the probability that the wattmeter will receive good information
from which to calculate power.
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58
Question 53
A technician connects a DAQ (Data Acquisition) module to one phase of a 480 VAC three-phase electric
motor in order to measure and record that motor’s voltage and current simultaneously on a laptop computer.
The DAQ functions as a high-speed data recorder, allowing the computer to display and record a time-based
graph of motor voltage and motor current over time.
Knowing that the phase-to-phase voltage of approximately 480 volts and the line current of
approximately 25 amps will be far too great for the DAQ to directly measure, the technician uses instrument
transformers (a “PT” potential transformer and a “CT” current transformer) to step these voltages and
currents to more reasonable values:
CT
power conductor
100:5 ratio
AI0
PT
50:1 ratio
AI1
DAQ
±10 VDC
AI2
AI3
AI4
AI5
Computer
AI6
AI7
COM
USB
Three-phase 480 volt motor
COM
Unfortunately, as soon as the motor is energized, the DAQ disappears in a bright flash of light and cloud
of smoke. The destruction also propagated to the PC the DAQ was connected to (through the USB cable)!
What went wrong, and how should the technician correct his mistake? Assume we must use the same model
of DAQ unit having the same ± 10 volt input limits.
Suggestions for Socratic discussion
• What exactly does an instrument transformer do?
• Could this system be made to work with a differential-input DAQ? Why or why not?
• Suppose we were free to select a different DAQ for this application. What specifications would we be
looking for in the new DAQ to make it function properly in the circuit as shown?
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59
Question 54
Suppose the current through each of the ammeters is 2.81 amps, and the ratio of each current transformer
is 100:5. Calculate the horsepower output of this AC motor, assuming a power factor of 1 and an efficiency
of 88%:
Motor
Shaft
T1 T2 T3
Thermal overload
100:5
Contactor
Reset
Fuses
100:5
480 VAC
3-phase
100:5
Ammeters
P =
horsepower
file i01045
60
Question 55
Which component, the resistor or the capacitor, will drop more voltage in this circuit?
47n
725 Hz
5k1
Also, calculate the total impedance (Ztotal ) of this circuit, expressing it in both rectangular and polar
forms.
file i01039
Question 56
Calculate the voltage dropped across the inductor, the capacitor, and the 8-ohm speaker in this sound
system at the following frequencies, given a constant source voltage of 15 volts:
8Ω
2 mH
47 µF
8Ω
Amplifier
15 VAC
• f = 200 Hz
• f = 550 Hz
• f = 900 Hz
Regard the speaker as nothing more than an 8-ohm resistor.
Suggestions for Socratic discussion
• As part of an audio system, would this LC network tend to emphasize the bass, treble, or mid-range
tones?
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61
Question 57
Sketch phasor diagrams for both phase voltage and phase current in this balanced 3-phase power system:
Vline = 208 volts
Phase rotation = CBA
VC = 120 V ∠ 0o
A
B
C
Voltage phasor diagram
Current phasor diagram
35 Ω
35 Ω
35 Ω
Now suppose the load is removed from this system and a low-resistance fault appears between phases
B and C. Sketch phasor diagrams for both phase voltage and phase current, assuming the source generator
is “stiff” (i.e. its voltage does not sag appreciably even under heavy loads):
Vline = 208 volts
Phase rotation = CBA
VC = 120 V ∠ 0o
A
B
C
Voltage phasor diagram
Current phasor diagram
file i00833
62
Rfault = 0.25 Ω
Question 58
Calculate the amount of voltage between points A and B in this circuit, and also sketch a phasor diagram
showing how all the voltages relate to each other in this circuit:
22 kΩ
195 V ∠ 25
o
A
22 kΩ
B
220 V ∠ -40o
3:1 step-down
file i00834
Question 59
Question 60
Question 61
Read and outline the “Introduction to Protective Relaying” section of the “Electric Power Measurement
and Control” chapter in your Lessons In Industrial Instrumentation textbook. Note the page numbers
where important illustrations, photographs, equations, tables, and other relevant details are found. Prepare
to thoughtfully discuss with your instructor and classmates the concepts and examples explored in this
reading.
file i01247
Question 62
Read and outline the “ANSI/IEEE Function Number Codes” section of the “Electric Power
Measurement and Control” chapter in your Lessons In Industrial Instrumentation textbook. Note the page
numbers where important illustrations, photographs, equations, tables, and other relevant details are found.
Prepare to thoughtfully discuss with your instructor and classmates the concepts and examples explored in
this reading.
file i01250
Question 63
Read and outline the “Instantaneous and Time-Overcurrent (50/51) Protection” section of the “Electric
Power Measurement and Control” chapter in your Lessons In Industrial Instrumentation textbook. Note
the page numbers where important illustrations, photographs, equations, tables, and other relevant details
are found. Prepare to thoughtfully discuss with your instructor and classmates the concepts and examples
explored in this reading.
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63
Question 64
Examine an electromechanical time-overcurrent (51) relay, identifying the following:
•
•
•
•
•
•
•
•
•
•
Induction disk
Time dial
Tap connections (for pick-up coarse adjustment)
Seal-in unit
Connecting plug and “brush” contacts
Drag magnet
Target (indicator flag) unit
Instantaneous overcurrent unit (if present)
Terminal connections to connect the current transformer (confirm using your multimeter!)
Terminal connections for the trip contact (demonstrate using your multimeter!)
Be very careful when handling one of these relays! The induction disk shaft rests in two jeweled bearings,
and may be damaged if the unit is dropped or the disk forcibly turned. When you rotate the disk by hand,
please use only your fingertips, and touch the disk very lightly!
Partner with your classmates to drive current into the CT terminals of a time-overcurrent relay using a
relay test set or some other suitable source of adjustable alternating current. Apply slightly more current to
the relay than what the tap setting is set for, and measure the trip contact status using a multimeter. Ask
your instructor for assistance with the relay test set, as it is capable of generating significant AC voltage and
current values for input into protective relays.
Suggestions for Socratic discussion
• Demonstrate how setting the “time dial” to different positions affects the time required for the 51 relay
to trip. Is a small time dial number or a large time dial number needed to make the relay more sensitive
(i.e. trip sooner)?
• Suppose you were to remove the drag magnet from a 51 relay. How would the relay’s behavior be altered
as a result of this component loss?
• Suppose you were to remove the restraint spring from a 51 relay (the spiral spring responsible for
applying a restraining torque to the induction disk). How would the relay’s behavior be altered as a
result of this component loss?
64
file i01251
Question 65
The following is an electrical schematic diagram for a General Electric model IAC77 electromechanical
instantaneous/time-overcurrent protective relay:
GE model IAC77 50/51 overcurrent relay
51
Seal-in
contact
51
Seal-in
contact
Seal-in
coil
50
50
1
2
3
5
6
Circuit breaker
Fuse
52
52a
125 VDC
TC
Station
battery
Fuse
CT
Identify the following:
•
•
•
•
•
•
•
•
•
•
•
•
•
•
What type of symbol represents a coil of wire in this schematic
What type of symbol represents a relay contact in this schematic
What type of symbol represents a resistor in this schematic
What type of symbol represents a capacitor in this schematic
Where to connect the current transformer to the relay
How to make coarse adjustments of the pick-up value for the 51 (time-overcurrent) function
How to make fine adjustments of the pick-up value for the 51 (time-overcurrent) function
How to make adjustments of the pick-up value for the 50 (instantaneous overcurrent) function
Whether or not 50 and 51 pickup adjustments are interactive (i.e. adjusting one affects the adjustment
of the other)
The purpose of having a seal-in unit
How to wire the relay so it only functions as a “50” (instantaneous overcurrent) unit
How to wire the relay so it only functions as a “51” (time overcurrent) unit
How to wire the relay so it performs both “50” and a “51” protective functions
Why the circuit breaker has an auxiliary contact (52a) connected in series with the trip coil (note: this
contact opens and closes simultaneously with the breaker’s main power contacts, being operated by the
same mechanism)
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65
Question 66
The following is an electrical schematic diagram for a three-phase 50/51 overcurrent protective relay
circuit, where three overcurrent relays (one for each phase of the power circuit) trip a single breaker in the
event of an overcurrent fault. The power diagram on the left shows all the high-voltage components, while
the control diagram on the right shows the circuitry associated with the breaker’s trip coil:
Power diagram
Control diagram
51-1 SI
51-2 SI
51-3 SI
Fuse
51-1
51-1 SI
50-1
51-2
51-2 SI
50-2
51-3
51-3 SI
50-3
125 VDC
52
52a
Fuse
52 TC
51-1
51-2
51-3
50-1
50-2
50-3
Examine this schematic diagram, and then explain how the circuit breaker may be tripped by any one
of the three overcurrent relays. Also, identify at least one circuit fault in either the power diagram or the
control diagram that could prevent the circuit breaker from tripping when it needs to.
Finally, calculate the amount of voltage dropped by the instantaneous sensing coil of one of the relays
(coil 50-1, coil 50-2, or coil 50-3) when line current is 1300 amps at 60 Hz, assuming a 2000:5 CT ratio for
each line, and given a coil resistance of 31.35 milliohms and a coil inductance of 27.33 microhenrys:
Vcoil =
volts
Suggestions for Socratic discussion
• Explain the purpose of the circuit breaker’s 52a contact shown in the control diagram.
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66
Question 67
The following schematic diagram shows a Westinghouse model CO-11 overcurrent protective relay,
complete with time-overcurrent (“CO”), instantaneous overcurrent (“IIT”), and seal-in (“ICS”) elements.
The relay as shown has been removed from service:
Westinghouse model CO-11 overcurrent relay
ICS
CO
ICS
CO
IIT
IIT
1
2
3
4
5
6
7
8
9
10
Suppose you were asked to test this relay to ensure it performs both the “50” and the “51” protective
functions as designed. When in service, this relay is connected to a current transformer having a ratio of
400:5 amps, and it is supposed to trip the breaker if the power line current exceeds 950 amps (for any length
of time), or trip the breaker in 4.6 seconds if the power line current is at a value of 376 amps. Explain in detail
how you would bench-test this relay to ensure it is properly calibrated and functional for this application.
Suggestions for Socratic discussion
• Supposing you had no access to any precision protective relay calibration equipment, how could you build
a simple circuit to generate the precise amounts of AC current needed to simulate overload conditions?
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67
Question 68
Read selected portions of the “SEL-551 Relay” protective relay manual (document PM551-01, April
2011) and answer the following questions:
Identify three different ANSI/IEEE protective relay functions implemented by this one device. Hint:
the Settings Sheet section of the manual may be helpful in identifying its functions.
Figure 1.1 on page 1.2 shows some typical applications for the SEL-551 protective relay. Identify at
least two applications shown. Also, identify the direction of power flow in this single-line diagram.
A very useful feature of this relay is event reporting. This particular model provides a detailed report
on a 15-cycle time frame surrounding a trip event. An example of this is shown on page 7.12. Based on
the current data shown in this example, when did the fault condition occur, and on which phase of the
three-phase system did it occur?
The latter portion of the event report shown on page 7.13 shows the CT ratio for each phase being 120
(120:1, or 600:5) and the pickup value for the phase time-overcurrent being 6 amps. How many amps of line
current (RMS) does this translate to, for a pickup value? How many amps of line current (peak) does this
pickup value represent?
Suggestions for Socratic discussion
• Note which side of each power circuit breaker the CTs are located: on the line side or on the load side?
Explain the rationale behind this consistent placement of overcurrent protection CTs.
• What do you suppose a fast bus trip scheme is, as suggested in the single-line diagram of Figure 1.1?
• Some digital protective relays provide real-time phasor diagrams of line current for visual analysis of a
fault. Using data from the 15-cycle event report shown in this manual, describe what the live phasor
diagram of line currents would appear to do before, during, and after this particular fault event.
• Figure 7.3 on page 7.15 shows the method by which the SEL-551 relay calculates RMS values for current
based on instantaneous samples of each phase current (8 times per cycle), which is one sample every 45
degrees of phasor rotation. Explain how this method works.
• In the latter portion of the event report shown on page 7.13, a section called “SELogic Control
Equations” defines the variables able to initiate a trip. Figure 3.13 on page 3.17 shows a logic gate
diagram of the “Trip Logic” for this relay. Based on the information contained in the trip logic diagram
and in the event report’s summary of the SELogic equations, explain how trip conditions are defined
in this particular protective relay, and how the flexibility of SELogic allows a relay technician to do far
more with this than could be done with simple electromechanical relay technology.
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68
Question 69
An AC electric motor under load can be considered as a parallel combination of resistance and
inductance:
AC motor
240 VAC
60 Hz
Leq
Req
Calculate the current necessary to power this motor if the equivalent resistance and inductance is 20 Ω
and 238 mH, respectively.
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69
Question 70
An interesting technology dating back at least as far as the 1940’s, but which is still of interest today
is power line carrier: the ability to communicate information as well as electrical power over power line
conductors. Hard-wired electronic data communication consists of high-frequency, low voltage AC signals,
while electrical power is low-frequency, high-voltage AC. For rather obvious reasons, it is important to be
able to separate these two types of AC voltage quantities from entering the wrong equipment (especially the
high-voltage AC power from reaching sensitive electronic communications circuitry).
Here is a simplified diagram of a power-line carrier system:
"Line trap"
filters
Power generating
station
"Line trap"
filters
3-phase power lines
Transformer
secondaries
Substation /
distribution
Transformer
primaries
Coupling
capacitor
Coupling
capacitor
Transmitter
Receiver
The communications transmitter is shown in simplified form as an AC voltage source, while the receiver
is shown as a resistor. Though each of these components is much more complex than what is suggested by
these symbols, the purpose here is to show the transmitter as a source of high-frequency AC, and the receiver
as a load of high-frequency AC.
Trace the complete circuit for the high-frequency AC signal generated by the “Transmitter” in the
diagram. How many power line conductors are being used in this communications circuit? Explain how the
combination of “line trap” LC networks and “coupling” capacitors ensure the communications equipment
never becomes exposed to high-voltage electrical power carried by the power lines, and vice-versa.
file i01214
Question 71
Every protective relay or measuring device presents a burden to the instrument transformer(s) driving
signal into it. The greater a relay’s burden, the more power is demanded from the instrument transformer
and the less accurate the system will tend to be. For this reason, burden is a very important parameter to
consider when wiring a protective relay system.
The datasheet for a General Electric model CEB52 “distance” protective relay (ANSI/IEEE code 21)
shows the burden for its “polarizing coil” PT input to be 1540 − j162 ohms. Calculate the current through
this coil when the PT’s output signal is 103 volts 6 −6o .
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70
Question 72
Suppose a 51 (time-overcurrent) protective relay is used to provide protection for a large (3000
horsepower) electric motor. The motor runs on a line voltage of 4160 volts, and has a full-load efficiency of
88%. The relay obtains its line current data from a set of three 400:5 current transformers on the motor’s
T1, T2, and T3 leads.
Based on this information, identify the pick-up current value for this protective relay, in secondary CT
amps:
Ipickup =
Also, explain what other factor(s) will dictate the time dial setting and time-current curve type for this
51 relay to provide sufficient protection for the motor.
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71
Question 73
A programmable logic controller (PLC) may be used to command a high-voltage circuit breaker to trip
in the event of dangerous process conditions, such as the system shown here:
3-phase line
Programmable Logic Controller (PLC)
Power
supply
Circuit
breaker
120 VAC
power
TC
L1
52a
L2/N
Gnd
Processor
Output
0
1
2
3
Input
4
5
6
7
0
1
2
3
VAC 1
IN0
OUT0
IN1
OUT1
IN2
OUT2
IN3
OUT3
IN4
VAC 2
IN5
OUT4
IN6
OUT5
IN7
OUT6
COM
OUT7
COM
4
5
6
7
179 oF
Relay
4 feet
Key switch
33 PSI
DC trip
bus
3-phase load
Assume this process system is operating as it should (i.e. no abnormal conditions). Based on the status
LED indicators you see on the input card of the PLC, determine whether each of the process switches is
designed to trip on a low condition or a high condition. Then, determine what you would have to do to the
circuit to simulate a shutdown condition for each of the process switches (i.e. make the PLC “think” it sees
an abnormal condition, so that it will act to trip the breaker):
• Temperature switch: trips on low temperature or high temperature? How to simulate trip condition?
• Level switch: trips on low liquid level or high liquid level? How to simulate trip condition?
• Pressure switch: trips on low fluid pressure or high fluid pressure? How to simulate trip condition?
Suggestions for Socratic discussion
• Explain why the LED status indicators are so helpful for system troubleshooting in a PLC-controlled
system.
• Identify the purpose of the key switch in this circuit.
• Suppose you were asked to install a manual pushbutton “Emergency Trip” switch to trip the circuit
breaker. Where would you connect such a switch in this circuit?
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72
Question 74
A very important concept in overcurrent protection is something called coordination. This is where
overcurrent-protection devices (e.g. fuses, circuit breakers, reclosers, protective relays) closer to the power
source have trip thresholds greater than protection devices farther away from the source. The rationale
behind coordination is to trip the smallest portion of the power grid necessary to clear the fault.
Examine this single-line diagram of a single-bus substation where incoming power arrives through a
transmission line and exits to customer loads through four identical distribution feeder lines:
Transmission line
115 kV
13.8 kV
A
50 51
B
Distribution bus
50 51
50 51
50 51
50 51
C
D
E
F
Distribution
line
Distribution
line
Distribution
line
Distribution
line
Identify which of the protective relays should have the highest pickup value and/or longest tripping time
value, and which of the protective relays should have the lowest pickup/time values. Describe a “thought
experiment” whereby these different pickup values help clear a distribution line fault most effectively.
73
Now, consider the following modification to this substation, incorporating a protection strategy known
as fast bus trip scheme, also known as a reverse interlocking or zone interlocking scheme (shown in red):
Transmission line
115 kV
13.8 kV
A
50 51
B
Fast bus trip signal
Distribution bus
50 51
50 51
50 51
50 51
C
D
E
F
Distribution
line
Distribution
line
Distribution
line
Distribution
line
The purpose of a fast bus trip scheme is to detect and clear any faults on the substation bus by means
of overcurrent relays faster than they would be cleared by the incoming line relay’s regular action. The
“fast bus trip signal” informs breaker B’s relays whether or not high current is being sensed by any of the
distribution breaker relays. Explain how this protection scheme uses information sent to the bus relay from
the feeder relays to accomplish faster tripping. Again, describe a “thought experiment” that will illustrate
the effectiveness of this protection scheme.
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Question 75
Question 76
Question 77
Question 78
Question 79
Question 80
74
Question 81
This liquid level sensor circuit uses a plastic-coated metal rod as one “plate” of a capacitor, and the
metal vessel as the other “plate” of the capacitor:
R
Probe
A
High-frequency
AC voltage source
Dielectric
sheath
Metal vessel
(plastic)
Liquid
(conductive)
Sketch an equivalent circuit showing the level sensing probe as an ideal circuit element, and then
determine the following if the liquid level in the vessel happens to increase:
• Probe capacitance: (increase, decrease, or remain the same)
• Capacitive reactance: (increase, decrease, or remain the same)
• AC voltage between point A and ground: (increase, decrease, or remain the same)
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75
Question 82
Solve for all voltages and currents in this series LR circuit:
175 mH
15 V RMS
1 kHz
710 Ω
Also, calculate the phase shift between VR and Vsupply , as well as the phase shift between VL and Vsupply .
file i01034
76
Question 83
Sketch a phasor diagram for this transformer bank’s output voltages, and determine their phase rotation:
Vline = 13.8 kV
VA = 7.97 kV ∠ 15o
Rotation = ABC
A
B
C
H1
H2
H1
H2
H1
H2
20:1 ratios
X2
X1
X2
X1
X
Y
Z
file i00835
77
X2
X1
Question 84
A high-voltage circuit breaker is manually operated from a remote location using a pair of pushbutton
switches, connected to “trip” and “close” solenoid coils within the breaker:
3-phase line
(power in)
3-phase load
(power out)
SF6 gas pressure
switch
Circuit breaker
Trip
Close
52a
4
TC1
1
TC2
2
23
52a
5
24
25
52b
6
CC
22
3
26
125 VDC
station battery
27
Fuse
Fuse
28
29
30
This particular circuit breaker is gas-quenched by sulfur hexafluoride gas (SF6 ), which is normally
pressurized inside the circuit breaker to approximately 45 PSI for optimum electrical performance.
A low-pressure lockout switch is being installed on the circuit breaker to detect if the SF6 gas pressure
ever drops below 35 PSI. The purpose of this switch is to disable the breaker from either closing or tripping
if the gas pressure is abnormally low.
Your task is to modify the circuit shown above to include this pressure switch. The single-pole, doublethrow pressure switch is shown in the upper-right corner of the diagram, not yet connected to the 125 VDC
trip/close circuit.
file i02111
78
Question 85
The following diagrams document the overcurrent protection system for a feeder supplying three-phase
AC power to an industrial load:
Power diagram
Control diagram
51-1 SI
51-2 SI
51-3 SI
Fuse
51-1
51-1 SI
51-2
50-1
51-2 SI
50-2
51-3
51-3 SI
50-3
125 VDC
52
52a
Fuse
52 TC
51-1
51-2
51-3
50-1
50-2
50-3
Suppose one day the circuit breaker (52) trips for no apparent reason. None of the brightly-colored
“target” flags on the electromechanical protective relay are visible, as one would normally expect following
a relay trip event. Identify the likelihood of each specified fault for this system. Consider each fault one at
a time (i.e. no coincidental faults), determining whether or not each fault could independently account for
all measurements and symptoms in this circuit.
Fault
Dead DC station power supply
52/TC coil failed shorted
51-3/SI coil failed shorted
50-1 contact failed open
50-1 contact failed shorted
50-2 coil failed shorted
50-2 coil failed open
Possible
Impossible
Also, identify which side of the 52 circuit breaker should be the “line” (supply) and which side should
be the “load” in order for the 50/51 relay to provide maximum protection in this system.
file i01279
79
Question 86
Calculate the amount of current output to the ammeter by the current transformer (CT) under normal
load conditions, assuming a balanced three-phase source and a balanced three-phase load:
300:5
A
Ammeter
Vphase = 7.2 kV
65 Ω
65 Ω
C
65 Ω
B
Iammeter =
A
Now, re-calculate the ammeter’s current supposing a tree branch falls across lines A and C, causing a
low-resistance fault:
300:5
A
Ammeter
Vphase = 7.2 kV
65 Ω
Rfault = 10 Ω
C
Iammeter =
65 Ω
65 Ω
B
A
Hint: you will need to consider phase angles for the fault current calculation! Feel free to assume an
ABC phase rotation, where VA = 7200 V 6 0o and VB = 7200 V 6 − 120o and VC = 7200 V 6 120o .
file i02881
80
Question 87
Sketch wires connecting these multi-ratio CTs to the three ammeters, and also insert screws into the
shorting terminal blocks as appropriate, in order to provide a 200:5 CT ratio on each phase:
C
B
X1
X2
X3
X4
X5
X1
X2
X3
X4
X5
A
X1
X2
X3
X4
X5
Phase A ammeter
-
+
Phase B ammeter
-
+
Phase C ammeter
-
+
X5
X4
X3
X2
X1
X5
X4
X3
X2
X1
X5
X4
X3
X2
X1
Assume each of the multi-ratio CTs has the following number of wire turns between terminal pairs:
•
•
•
•
10 turns between X1 and X2
5 turns between X2 and X3
25 turns between X3 and X4
20 turns between X4 and X5
file i01029
81
Question 88
Examine this overcurrent protection system for a feeder, supplying three-phase power to a set of
industrial loads from a substation bus:
Bus
50-1 51-1
250:5
50-2 51-2
50-3 51-3
52
To compressor
motor starter
To pump
motor starter
To fan
motor starter
Feeder
Explain why 50/51 overcurrent protection is necessary at all, since each of the loads has its own set of
fuses to protect against overcurrent conditions.
Suppose the cable connecting phase 2 CT to the 50-2/51-2 relay fails shorted, such that the relay no
longer senses current through that phase. Will the other two overcurrent relays continue to provide adequate
protection? Explain why or why not, in detail.
file i02562
82
Question 89
Calculate all currents and voltages in this current transformer (CT) circuit:
300:5
180 A
0.25 Ω
Relay
2.3 Ω
Now, calculate all currents and voltages in this current transformer circuit, with two identical CTs
connected in series:
180 A
300:5
300:5
0.25 Ω
Relay
2.3 Ω
Finally, sketch the direction of current through each CT assuming the direction shown by the 180 amp
arrow at one particular instant in time.
file i02606
83
Question 90
Calculate the VGH in this circuit, expressing your answer in polar form. Assume an UVW phase rotation
with VU = 277 volts 6 -15o :
U
V
W
2.2 kΩ
5:1 ratio
G
VGH =
file i01195
84
H
Question 91
Lab Exercise – introduction
Your team’s task is to perform commissioning tests on one or more circuit breakers as well as commission
and test a protective relay for one protection zone within the lab’s miniature three-phase power grid. Your
instructor will assign the circuit breaker and protection zone for your team.
The following table of objectives show what you and your team must complete within the scheduled
time for this lab exercise. Note how some of these objectives are individual, while others are for the team as
a whole:
Objective completion table:
Performance objective
Team meeting
Verify phase rotation of a three-phase source
Commissioning tests and system inspection
Test e/m 50 (inst. overcurrent) relay
Test e/m 51 (time overcurrent) relay
“Stab” into a live CT circuit to measure current
Manually synchronize a generator with the grid
Configure digital relay per specification
Simulated fault and relay event report
Lab question: Wiring connections
Lab question: Commissioning
Lab question: Mental math
Lab question: Diagnostics
Lab clean-up
Grading
mastery
mastery
mastery
mastery
mastery
mastery
mastery
mastery
mastery
proportional
proportional
proportional
proportional
mastery
1
–
–
–
–
–
2
–
–
–
–
–
3
–
–
–
–
–
4
–
–
–
–
–
Team
––––
––––
––––
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
The only “proportional” scoring in this activity are the lab questions, which are answered by each student
individually. A listing of potential lab questions are shown at the end of this worksheet question. The lab
questions are intended to guide your labwork as much as they are intended to measure your comprehension,
and as such the instructor may ask these questions of your team day by day, rather than all at once (on a
single day).
It is essential that your team plans ahead what to accomplish each day. A short (10
minute) team meeting at the beginning of each lab session is a good way to do this, reviewing
what’s already been done, what’s left to do, and what assessments you should be ready for.
There is a lot of work involved with building, documenting, and troubleshooting these working
instrument systems!
As you and your team work on this system, you will invariably encounter problems. You should always
attempt to solve these problems as a team before requesting instructor assistance. If you still require
instructor assistance, write your team’s color on the lab whiteboard with a brief description of what you
need help on. The instructor will meet with each team in order they appear on the whiteboard to address
these problems.
85
Lab Exercise – team meeting
An important first step in completing this lab exercise is to meet with your instructor as a team
to locate the circuit breaker to be commissioned, as well as discuss safety concerns, team performance, and
specific roles for team members. If you would like to emphasize exposure to certain equipment (e.g. use
a particular type of control system, certain power tools), techniques (e.g. fabrication), or tasks to improve
your skill set, this is the time to make requests of your team so that your learning during this project will
be maximized.
Lab Exercise – phase rotation (sequence) testing
Once live three-phase power is available in the lab power grid, you will be required to verify its phase
rotation by connecting a suitable test instrument to it, either directly to the power lines (where applicable)
or through potential transformers pre-connected to the grid. If your station happens to be a generator, you
will need to verify its phase rotation before attempting to place it on-line (i.e. close the breaker to connect
it to the grid).
Suitable test equipment exists in the lab for you to measure phase rotation. A multi-channel oscilloscope
is one form of suitable test equipment, but others exist as well. Be sure to consult the manual before using
this equipment on the power system, as system voltages and currents are capable of damaging equipment if
incorrectly connected. A sample schematic shown here illustrates how you may build a three-phase voltage
divider resistor network to create a three-phase voltage divider for safely testing phase rotation in cases
where the line voltage could damage the test instrument’s inputs. This Wye-connected resistor network also
provides a “ground” reference if the power system lacks one:
To line "A"
Sec/Div
Volts/Div A
0.5 0.2 0.1
1
2
270 kΩ
5
A
B
2.5 µ
0.5 µ
100 m
0.1 µ
500 m
2m
1
2.5
DC Gnd AC
1 kΩ
50 µ
10 µ
25 m
5m
20
250 µ
5m
Position
10 m
10
270 kΩ
1m
50 m
20 m
off
0.025 µ
X-Y
Position
1 kΩ
A B Alt Chop Add
Triggering
To line "B"
1 kΩ
A
B
Alt
Line
Ext.
Volts/Div B
0.5 0.2 0.1
1
5
10 m
10
270 kΩ
50 m
20 m
2
20
5m
2m
Position
Invert
DC Gnd AC
Intensity
Focus Beam find
Off
Cal 1 V Gnd
Trace rot.
Norm
Auto
Single
Reset
Holdoff
Ext. input
AC
DC
Slope
To line "C"
ABC phase rotation shown
86
Level
LF Rej
HF Rej
You may construct your own phase rotation tester by building this simple circuit and using a voltmeter
to compare the voltage dropped by the two resistors:
Phase rotation CW
if VAX is larger
Phase rotation CCW
if VCX is larger
X
A
270 kΩ
1/4 W
C
270 kΩ
1/4 W
0.01 µF
("103" code)
Non-polarized
Note: capacitor’s peak voltage ≈ 25%
of the line RMS voltage (e.g. VAC)
Directions for use:
(1) Connect A, B, and C to 3-phase lines
(2) Leave X floating (not connected to power system)
(3) Measure VAX and VCX with an AC voltmeter
(4) If VCX > VAX then phase sequence is ABC
(5) If VAX > VCX then phase sequence is ACB
B
87
Lab Exercise – commissioning tests
Commissioning a circuit breaker and associated instrumentation involves the following tests, shown here
in table format to facilitate documentation of your measurements. You should print this table and write
all your test results in it, then leave this in the enclosure with the protective relay as a permanent record.
Note that a “quantitative” test is one where a numerical value must be recorded and assessed, whereas a
“qualitative” test is one that is simply pass/fail:
Test description
CT circuit wire connections secure (all phases)
(qualitative)
Perform this as the first CT test!
CT ratio check (all phases)
(quantitative)
CT polarity check (all phases)
(qualitative)
CT circuit total resistance
(quantitative) – ohmmeter
CT circuit insulation resistance
(quantitative) – insulation tester
Relay input burden (all phases)
(quantitative) – ohmmeter
CT circuit ground resistance (all phases)
(quantitative) – ohmmeter
CT test switch shorting function (all phases)
(qualitative)
Breaker trip circuit connections secure
(qualitative)
Perform this as the first 52/TC circuit test!
Breaker close circuit connections secure
(qualitative)
Perform this as the first 52/CC circuit test!
DC station supply voltage (unloaded)
DC station supply voltage (while tripping breaker)
(quantitative) – voltmeter
Breaker trip coil circuit loop resistance
(quantitative) – ohmmeter
Breaker close coil circuit loop resistance
(quantitative) – ohmmeter
Phase
Phase
Phase
Phase
Phase
Phase
Phase
Phase
Phase
Phase
Phase
Phase
Phase
Phase
Phase
Phase
Phase
Phase
Phase
Phase
Phase
Phase
Phase
Phase
Results
A=
B=
C=
A=
B=
C=
A=
B=
C=
A=
B=
C=
A=
B=
C=
A=
B=
C=
A=
B=
C=
A=
B=
C=
Ω
Ω
Ω
Ω
Ω
Ω
Ω
Ω
Ω
Ω
Ω
Ω
VDC =
VDC =
V
V
52/TC =
Ω
52/CC =
Ω
Note that some circuit breakers are equipped with multiple sets of current transformers, not just one
CT for each of the three phases. In such cases you must document the test results of each and every CT.
88
In order to accurately measure electrical resistance for certain commissioning tests (e.g. CT circuit total
resistance) where the expected value is quite low, you will need to compensate for the electrical resistance
of your meter’s test leads. Good-quality digital multimeters such as the Fluke 87 series provide a “Relative”
function whereby you can set the meter to measure resistance, connect the test leads together, and press
a button to make this the “zero” reference point for measurement. Be sure to do this for the appropriate
tests, re-checking the “zero” point before each new test.
Given the low-current nature of the lab’s miniature three-phase power grid, it is relatively easy to perform
primary injection testing of current transformers. This is where a relatively large amount of alternating
current is sent through the primary CT conductors, in order to test how accurately this current is registered
at the protective relay (i.e. realistically testing the CT ratio).
You may generate this injection current using a step-down transformer and a Variac for control, or you
may use the relay test set which contains both of these devices. Connect the AC source such that its current
flows through the regular power conductors and through the center of the CTs. Monitor current using a
suitable ammeter on the primary wiring and the current displayed by the digital relay in order to confirm
accurate measurement (within ± 5% of full-load current). Using the digital protective relay as an ammeter
during this test is recommended because this places the exact same amount of burden on the CT as it will
experience when the system is in operation. Connecting a second ammeter in series with the CT secondary
circuit places additional burden in that circuit which may very well affect the CT ratio!
89
Lab Exercise – electromechanical relay testing
Even though your protective relay scheme uses a digital relay, part of this lab project is testing a legacy
electromechanical relay such as the General Electric IAC series or Westinghouse CO series overcurrent
(50/51) relays.
Consult the manufacturer’s manuals on these relays for instructions on testing. You may wire your own
high-current AC source using step-down transformers and a Variac for control, or use a relay test set. Your
instructor will provide you with criteria for testing the relay. Assume the use of the same CTs (i.e. use those
same ratios) you are using in your digital relay protection scheme:
Instantaneous overcurrent (50) function:
Quantity
Pick-up current, primary amps
CT ratio
Pick-up current, secondary amps
Value
Who determines
Instructor
You research
You calculate
Value
Who determines
Instructor
Instructor
Time overcurrent (51) function:
Quantity
Pick-up current, secondary amps
Time dial setting
The instructor will verify your successful testing of both relay functions. The instantaneous (50) function
simply has one point to test, but the time (51) function requires multiple tests to verify against the given
trip-time curve.
90
Lab Exercise – live CT secondary current measurement
A practical but also potentially hazardous job function for relay technicians is to take live current
measurements on CT secondary circuits. Practical reasons include data logging and verification of relay
measurement accuracy without removing the relay from service. The hazards are simple to understand:
current transformers are capable of generating very high voltages if ever their secondary windings are opencircuited while the primary conductor is carrying current.
Special “test probes” are built to connect into “test jacks” on CT test switch assemblies for this purpose.
The test jack provides a means for a regular ammeter to be inserted into the CT secondary circuit without
ever breaking that circuit. Your Lessons In Industrial Instrumentation textbook describes test probes and
their safe usage.
Some legacy electromechanical protective relays such as the General Electric series used “paddle” plugs
to connect and disconnect the relays from outside devices such as CTs. These “paddles” could be removed
and replaced with special “test plugs” providing connection points for ammeters and other devices so that
these devices could connect in-line with the live relay.
In order to ensure your personal safety when using any of these devices to “stab into” a live CT circuit,
you must absolutely ensure you will not inadvertently open-circuit the secondary winding of a CT. This
means you must thoroughly test your plug/probe, leads, and ammeter before insertion into the test jacks.
A continuity test is all that is required, performed at the contacting terminals of the plug/probe to ensure
a complete circuit from one terminal through the ammeter and back out the other terminal.
Your instructor will observe your preparation and testing of a live CT circuit. Do not attempt to do
this without instructor supervision!
91
Lab Exercise – manually synchronize a generator with the grid
The lab’s miniature AC power grid is equipped with multiple generating stations, each of which must be
synchronized with the grid before closing its circuit breaker and placing it “on line”. Manual synchronization
entails bringing the generator up to speed and monitoring some form of differential voltage monitor indicating
the phase relationship between the generator’s output voltage and the power grid’s voltage. The circuit
breaker should only be closed when the generator’s speed is slightly greater than the power line’s frequency
and the phase shift is at a minimum.
The simplest form of differential voltage monitor is a set of “sync lamps” connected across the poles of
the open circuit breaker (or connected to PTs which have primary windings connected across the poles of
the breaker). The lamps will glow brightest when the generator and grid are 180o out of phase, and glow
dimmest (or go out completely) when the two are in-phase.
A more sophisticated differential voltage monitor suitable for manual synchronization is the
synchroscope, a special panel meter with a needle that can rotate without ever hitting a stop. Zero phase
shift is indicated by the needle pointing straight up, while 180o phase shift is indicated by the needle pointing
straight down.
If the generator and power grid are at different frequencies, the sync lamps will oscillate in brightness
at a frequency equal to the difference in generator and line frequencies. A synchroscope’s needle will rotate
at a speed equal to this difference frequency.
If the generator and power grid are at different voltage levels, the sync lamps will never fully go out, but
will merely become brighter and dimmer at the difference frequency. A synchroscope has no way of showing
differences in voltage level.
Once your generator is successfully synchronized with the grid and its circuit breaker closed, it becomes
electrically “locked” in phase with the rest of the grid. Attempting to speed it up or slow it down while
on-line merely places more or less load on the generator – it cannot actually speed up or slow down without
pulling the entire grid (and all the generators on it) to that new speed. Likewise, attempting to change the
output voltage by exciting the field winding more or less only changes the amount of reactive power the
generator produces – it cannot actually raise or lower grid voltage without pulling the entire grid (and all
the generators on it) to that new voltage level.
If something dramatic happens to pull your generator out of sync with the grid while its circuit breaker
is closed, very large currents will begin to flow in and out of your generator as it falls in and out of phase
with the grid. The generator will also experience very high mechanical torque at its shaft. The phenomenon
of falling out of phase with the grid is called “slipping a pole” and it can be catastrophic for large generators,
both electrically and mechanically. The protective relay(s) at each generating station should be set to trip
the generator off-line if this ever happens.
The act of manually synchronizing an AC generator to the grid helps one visualize the phase relationships
between a multiple rotating machines. Even if the section of the power grid your team has been assigned to
protect does not contain a generator, there is merit in learning how to synchronize AC generators.
92
Grid
Breaker contacts
Gen
Sync lamps
Grid
Breaker contacts
Gen
Synchroscope
93
Lab Exercise – digital relay settings
You will typically find a generic settings sheet for your digital relay in the manufacturer’s manual, or else
as a separate download from the relay manufacturer’s website. This settings sheet will have several cells or
blanks where you may hand-write the basic settings to be programmed into the protective relay. It is up to
you and your team to determine how to implement those general settings given the specific features provided
by your relay and the assigned protection zone within the power system. Your instructor will provide specific
settings or parameters as needed in order to make this objective unique to each student completing it.
Digital protective relays may often be configured via multiple means. For example, protective
relays manufactured by Schweitzer Engineering Laboratories (SEL) may be programmed through panel
pushbuttons, through ASCII serial data communication using a terminal emulator program such as
Hyperterminal on a personal computer, or through AcSELerator QuickSet SEL-5030 software on a
personal computer providing a point-and-click user interface. It matters little how you set the relay
parameters so long as they are all set correctly.
For the Schweitzer relays most of the important parameters may be set by any of the above means.
Some of the parameters, however (particularly the “Logic” parameters) may only be set via serial link, and
are not accessible through the front pushbutton panel.
94
Lab Exercise – simulated system fault and relay event report
After your system’s protective relay has been properly configured, it is ready to be tested on a simulated
fault. The simulation of a fault may be done with a relay test set (injecting secondary CT current signals
into the relay inputs), with a high-current AC source (injecting primary CT current signals into the installed
CTs), by placing a heavy load on the system (a suitable test for a generating station is to have it trip on the
inrush current of an induction motor during start-up), or by placing an actual fault into the power system
itself. Your team will work together with your instructor to devise a suitable test for the protection scheme
of your relay. If the test itself harbors any danger – as is in the cases of the primary injection or actual fault
tests – your instructor must be present to supervise the execution of that test.
It is also a fair test to place a fault on the power system that should not cause your team’s protective
function to trip, but which will cause some other protective function to activate. This tests the selectivity
of your protective function to ensure it only trips for faults within its protection zone while ignoring faults
lying outside of its protection zone.
For each fault, the team must show the event report generated by the digital relay and interpret the
data contained in that report. This event report will show the onset of the fault, the point in time at which
the protective relay “picks up” the fault, the point in time at which the relay asserts a trip command to the
circuit breaker(s), and the time at which the fault becomes cleared by the open breaker(s).
Event reports are accessed by connecting a personal computer to the digital relay through a
communications port. Protective relays manufactured by Schweitzer Engineering Laboratories (SEL)
show event reports via ASCII serial data communication using a terminal emulator program such as
Hyperterminal on a personal computer, or through AcSELerator QuickSet SEL-5030 software on a
personal computer.
95
Lab questions
• Wiring connections
• Determine correct wire connections between field components and a protective relay to create a working
protection circuit, based on diagrams of components with terminals labeled
•
•
•
•
•
•
•
Commissioning and Documentation
Explain how to test the turns ratio of a current transformer (CT)
Explain how to test the saturation point of a current transformer (CT)
Explain why current transformers can be so dangerous to work with
Identify the effects of changing the “time dial” setting on a time overcurrent (51) relay
Interpret the ratings on a current transformer (e.g. 0.6B1.8 or C600)
Explain what arc flash and arc blast are, and what causes these effects
• Mental math (no calculator allowed!)
• √
Calculate line and phase quantities (voltage, current) in a balanced three-phase circuit – Hint:
3 ≈ 1.75 = 74
• Diagnostics
• Determine whether or not a given diagnostic test will provide useful information, given a set of symptoms
exhibited by a failed system
• Identify at least two plausible faults given the results of a diagnostic test and a set of symptoms exhibited
by a failed system
• Determine whether or not a specified power system fault will cause a certain type of protective relay to
trip (i.e. matching the relay type to the protection needed to clear the fault)
• Propose a diagnostic test for troubleshooting a failed system and then explain the meanings of two
different test results
file i03020
96
Answers
Answer 1
Answer 2
Answer 3
Answer 4
Answer 5
Answer 6
Partial answer:
Fault on circuit breaker #5: we will need to trip breakers 1, 2, 3, 4, and 10. This will unfortunately
interrupt power to loads J, K, and L.
Answer 7
Answer 8
Answer 9
Resistance is to reactance in an AC electrical circuit as friction is to inertia in a mechanical system.
The former resists motion, while the latter resists changes in motion.
XL = 2πf L
XC =
XR = 0
1
2πf C
For a “pure” resistor
Impedance is the combination of resistance and reactance for any component or network.
97
Answer 10
Addition and subtraction:
(5 + j6) + (2 − j1) =
7 + j5
(10 − j8) + (4 − j3) =
14 − j11
(−3 + j0) + (9 − j12) =
6 − j12
(3 + j5) − (0 − j9) =
3 + j14
(25 − j84) − (4 − j3) =
21 − j81
(−1500 + j40) + (299 − j128) =
−1201 − j88
(256 15o ) + (106 74o ) =
31.356 30.87o
(10006 43o ) + (12006 − 20o ) =
1878.76 8.311o
(5226 71o ) − (856 30o ) =
461.236 77.94o
(256 15o ) × (126 10o ) =
3006 25o
(16 25o ) × (5006 − 30o ) =
5006 − 5o
(5226 71o ) × (336 9o ) =
172266 80o
106 −80o
=
16 0o
106 − 80o
256 120o
=
3.56 −55o
7.1426 175o
−666 67o
=
86 −42o
8.256 − 71o
(3 + j5) × (2 − j1) =
11 + j7
(10 − j8) × (4 − j3) =
16 − j62
(3+j4)
(12−j2)
=
0.1892 + j0.3649
1
=
(7506 −38o )
0.001336 38o
1
(10+j3)
Multiplication and division:
Reciprocation:
1
(156 60o )
0.06676
1
156
45o
=
− 60o
1
+
=
1
926
1
12006
−25o
14.066 36.74o
−34o
+
1
806
19o
29.896 2.513
o
1
+
=
1
5746
1
23k6
21o
425.76 37.23o
1
1
1106
73o
=
0.0917 − j0.0275
+
10
1
89k6
−5o
+
1
15k6
1
+
=
1
10k6
−81o
1
1
+
7.013k6 − 76.77o
1
=
1
706
−67o
33o
5.531k6 37.86
o
+
=
1
9.35k6
98
45
1
5126
34o
+
1k6
−25o
256.46 9.181
o
1
9426
+
−20
=
1
2.2k6
44o
Some Texas Instruments brand calculators such as the TI-84 offer an exponential key and imaginary (i)
key which allows you to enter numbers in complex exponential form (i.e. eiθ ). With the TI-84, for example,
the complex number 10 − j8 may be entered in either of the two following forms:
or
(10 - i8)
(10 - 8i)
The result may be displayed in either rectangular or polar forms according to the complex-number
display mode the TI-84 calculator has been set to. In rectangular mode the displayed result for 10 − j8 will
be 10 - 8i, whereas in polar mode the displayed result will be 12.806 e−38.66i . Note how the TI-84 uses
exponential notation for polar display, where the angle (−38.66 degrees, in this example) is an imaginary
power of e.
If you wish to enter a complex number in polar form on a TI-84, you must unfortunately express the
angle in units of radians (even though the calculator is able to display the result in degrees). For example,
to enter the number 256 15o into a TI-84 calculator, you must type:
25 ei15π/180
The fraction π/180 is the conversion factor from degrees to radians, since there are 2π radians to a full
circle, or π radians to every 180 degrees. Thus, writing 15π/180 multiplies the desired angle (15 degrees)
by the conversion factor π/180 to yield a power in radians. The obligatory i simply makes this power an
imaginary quantity, which is mathematically necessary with exponential notation for describing a complex
number. It should be noted that the order of entry for the power matters little. i15π/180 works just as well
as 15iπ/180 or 15π/180i.
A time-saving step some students find useful is to save the imaginary quantity iπ/180 to a memory
location in the TI-84 such as Z. That way, they can recall that imaginary factor from memory instead of
typing the whole thing by hand every time they wish to enter a polar-form complex number. Supposing the
memory location Z contains iπ/180, entering the number 256 15o becomes as simple as:
25 e15Z
or
25 eZ15
It should be understood that any memory location in your calculator is suitable for storing iπ/180, not
just Z. The TI-84 calculator even provides a Θ memory location (<Alpha>-<3>) that you may use and find
easy to remember because of its common association with angles. It should also be understood that this
imaginary quantity is not the same as i or j, which the calculator already provides a dedicated function for.
The imaginary quantity we’re storing in memory for the purpose of entering polar-notation angles contains
not only i but also the π/180 conversion factor necessary for translating your degree entry into radians.
Some calculators provide easier means of entering and displaying complex numbers in polar form. Both
the Texas Instruments TI-36X Pro and TI-89 offer an angle symbol (6 ) for this purpose, the TI-36X Pro
being a much less expensive and less complex calculator than the TI-89. Entering the number 25 6 15o into
one of these calculators is as easy as typing 25 6 15, and likewise the result will be displayed in this same
form when the calculator is set to “polar” complex mode.
99
Answer 11
Vline
Vline
Vphase
Ili
I line
Ili
I line
ne
V
as
I ph
ph
as
e
ne
e
e
has
Ip
e
I phas
s
ha
Vphase
Vphase
Vline
Vline
Vline
Iline
Iline
Vphase
Iphase
Vline
e
Ip
Vp
ha
s
e
Iphase
Wye configuration
• Iphase = Iline
• Vphase < Vline
Delta configuration
• Vphase = Vline
• Iphase < Iline
Answer 12
Perhaps the simplest approach to this problem is to calculate the power dissipation of each resistor inside
of each three-resistor array. Since power is a scalar quantity (i.e. it adds directly, not trigonometrically),
the 15 kW total heat output of each array means each resistor inside of each array must dissipate 5 kW of
power.
In the delta-connected heater, each resistor sees full line voltage (480 VAC), therefore the resistance
may be calculated as such:
R=
V2
4802
=
= 46.08 Ω
P
5000
In the wye-connected heater, each resistor sees √13 of the full line voltage (480 VAC), which is 277.1
VAC. Therefore the resistance may be calculated as such:
R=
277.12
V2
=
= 15.36 Ω
P
5000
Answer 13
Pelec = 198.146 kVA = 265.61 HP
Pmech = 244.36 HP
100
Answer 14
The transformer primary windings are connected in a Wye configuration, which means each primary
winding receives the 7.2 kV phase voltage. The secondary windings are connected in a Delta configuration,
making the secondary line voltage equal to 240 volts.
Primary
Secondary
7200 V
240 V
7200 V
240 V
240 V
7200 V
Answer 15
What we need here is a “wye” configuration on the secondary windings of the three transformers, using
the center-tap of each to get 120 VAC at each phase. The pictorial diagram shown here is one possible
solution, but not the only one:
po
we
r li
ne
insulator
crossarm
Fuse
Schematic diagram
7.2 kV
240/120 V
Fuse
Fuse
7.2 kV
7.2 kV
7.2 kV
240/120 V
240/120 V
240/120 V
Transformer
Transformer
Transformer
L1
L2
L3
N
Power pole
101
Low-voltage lines
to customer
Answer 16
This is one possible solution, but not the only one:
Three-phase alternator
220 VDC
Rotor
+
−
Disconnects
Circuit
breaker
Disconnects
. . . 15 kV generator bus
...
...
...
...
...
102
Answer 17
The delta-connected motor will fare better, because it will still generate a polyphase (truly rotating)
magnetic field, whereas the wye-connected motor will only generate an oscillating magnetic field. Also, the
voltage across each phase winding of the delta-connected motor will remain the same as the line voltage,
while the voltage across each phase winding of the wye-connected motor will decrease from what it was
previous to the fault.
If the motors’ mechanical loads are sufficiently light, both motors will continue to rotate. However, the
delta-connected motor will have a greater torque capacity in this phase-loss condition than the wye-connected
motor due to the fact that its rotating magnetic field still maintains a definite direction of rotation and also
that each of its phase windings receives the same (full) voltage as previously.
If these consequences are not clear for you to see, you might wish to apply the problem-solving technique
of adding quantitative values to the problem. Assign a line voltage (e.g. 480 VAC) to the incoming threephase power conductors A, B, and C. Then, analyze the voltages at each phase winding of each motor before
the fault versus after the fault. You may also calculate the phase angle for each of these winding voltages to
see that the delta-connected motor still has three 120o -shifted voltages powering it, while the wye-connected
motor only has one voltage (single phase) powering it.
Answer 18
• 45 + i22 = 50.096 26.05o
• 90 + i5 = 90.146 3.180o
• −45 + i38 = 58.906 139.8o
• 21 − i39 = 44.296 298.3o
• −100 − i83 = 130.06 219.7o
• −256 + i300 = 394.46 130.5o
• (50 + i22) + (−23 + i19) = 27 + i41
• (39 − i5) − (10 + i8) = 29 − i13
• (−8 + i7) × (2 + i1) = −23 + i6
• (9 − i2) ÷ (2 + i12) = −0.0405 − i0.7568
• (−4 − i20) × (−6 + i15) = 324 + i60
• (1200 + i8570) ÷ (−5400 + i1022) = 0.0754 − i1.573
103
Answer 19
• 506 25o = 45.32 + i21.13
• 1706 82o = 23.66 + i168.3
• 116 165o = −10.63 + i2.847
• 756 299o = 36.36 − i65.60
• 316 190o = −30.53 − i5.383
• 61.56 − 45o = 43.49 − i43.49
• (346 10o ) × (186 − 20o ) = 6126 − 10o
• (56 30o ) ÷ (26 85o ) = 2.56 − 55o
• (756 − 50o ) + (116 0o ) = 82.56 − 44.14o
• (2506 17o ) − (816 − 40o ) = 216.86 35.26o
• (0.00456 90o ) + (0.00126 − 110o ) = 0.0033976 96.94o
• (93006 155o ) − (18106 25o ) = 10554.96 162.5o
Answer 20
• 56 − j23 = 60.54 6
− 22.33o
• 105 6 20o = 98.67 + j35.91
• 15304 6 175o = −15245.8 + j1333.8
• −930 + j12944 = 12977.4 6 94.11o
Answer 21
Answer 22
Answer 23
Answer 24
Answer 25
Answer 26
Partial answer:
––
V (polar)
V (rect.)
I (polar)
I (rect.)
Z (polar)
Z (rect.)
R
501.68 V
6
L
−17.14o
45.61 + j147.87 V
1.018 kΩ
3.3 k + j0 Ω
104
6
90o
Total
525 V 6 0o
525 + j0 V
145.27 m − j44.81 mA
3.3 k + j1.018 kΩ
Answer 27
Partial answer:
––
V (polar)
V (rect.)
I (polar)
I (rect.)
Z (polar)
Z (rect.)
L
600 V 6 0o
600 + j0 V
C
600 V 6 0o
600 + j0 V
2.398 A 6 90o
0 − j3.183 A
188.5 Ω 6 90o
0 − j250.2 Ω
Answer 28
Partial answer:
VAB
VA
VB
Answer 29
Partial answer:
The magnitude (length) of each current phasor is 15.45 amps AC.
VCN
IA
VAN
IC
IB
VBN
105
Total
600 V 6 0o
600 + j0 V
0 − j0.785 A
763.9 Ω 6 90o
Answer 30
Partial answer:
VA = 8.588 V6 − 54.87o
Note how the voltage between point A and ground is actually larger than the transformer’s output
voltage of 5.5 volts!
Answer 31
The 4-volt (peak) waveform leads the 3-volt (peak) waveform. Conversely, the 3-volt waveform lags
behind the 4-volt waveform.
If the 4-volt waveform is denoted as 4 V
−90 , or 0 − j3 V.
o
If the 4-volt waveform is denoted as 4 V
should be denoted as 3 V 6 0o , or 3 + j0 V.
6
6
0o , then the 3-volt waveform should be denoted as 3 V
6
90o (0 + j4 V in rectangular form), then the 3-volt waveform
Answer 32
+i8
15
106
20
Answer 33
60o
Answer 34
In this diagram, phasor B is leading phasor A. By convention, phasors normally rotate in the counterclockwise direction. If you envision the two arrow-tips of these phasors racing around in a circle like two
race cars on a circular track, the one car that is ahead of the other is the one leading the race, while the one
behind is the one lagging.
107
Answer 35
In the direct-connected load, each resistor sees
each resistor current is equal to:
√1
3
of the 13.8 kV line voltage (7967.4 volts), therefore,
V
7967.4
=
= 6.425 amps
R
1240
Since each resistor sees 7967.4 volts and carries 6.425 amps, the power for each resistor will be:
I=
P = IV = (6.425)(7967.4) = 51.194 kW
The power for this load is simply the power of all resistors combined:
Ptotal = 153.58 kW
The three transformers have their primary windings connected in a Wye configuration, and their
secondary windings in a Delta configuration. Thus, each transformer primary sees 7967.4 volts, stepping it
down by a 16.67:1 ratio into 477.95 volts. The secondary windings, being Delta-connected, make this 477.95
volt value the line voltage for the load. The load is Delta-connected as well, and so each resistor in that load
sees 477.95 volts, giving a resistor current of:
477.95
V
=
= 0.5031 amps
R
950
Since each resistor sees 477.95 volts and carries 0.5031 amp, the power for each resistor will be:
I=
P = IV = (0.5031)(477.95) = 240.46 W
The power for this load is simply the power of all resistors combined:
Ptotal = 721.38 W
108
Answer 36
In a 4-wire system such as this, each phase of the load is guaranteed to see the proper (balanced) phase
voltage of 120 VAC. Thus, calculating each line current is the same as calculating each phase (resistor)
current as follows:
IL1 =
IL2 =
120
= 0.08 amps
1500
120
= 0.0522 amps
2300
120
= 0.15 amps
800
Neutral conductor current will be the phasor sum of these three phase currents:
IL3 =
IN = IL1 + IL2 + IL3
Of course, we must remember that each of these three currents is phase-shifted from one another by 120
degrees. Arbitrarily choosing IL1 as our zero-degree phase reference, and assuming an L1-L3-L2 rotation:
IN = 0.08 A 6 0o + 0.0522 A 6 120o + 0.15 A 6 240o
IN = 0.0873 A 6 256o
109
Answer 37
• VG = 0 volts
• VH = 480 volts
• VJ = volts
• VK = 480 volts
• VL = 0 volts
• VM = 480 volts
• VN = 480 volts
The phase-to-ground voltage at point J must be calculated trigonometrically:
480 VAC
G
H
27
7V
AC
AC
7V
J
27
12
277 VAC
AC
0V
0V
o
AC
0
48
48
30o
K
Each interior angle of the triangle GHK is 60o . Angle JGK is 30o . Angle GJK is 120o . Phasor JK’s
length may be calculated using the Law of Sines, where the ratio of side length to the sine of the opposite
angle is constant for any triangle:
A
B
=
sin a
sin b
VJK
480
=
sin 120
sin 30
480
VJK = sin 30
sin 120
480
VJK = 0.5
0.866
VJK = 277.13 volts
110
Total power in this system is 12.3 kW. The line current at the primary side of the transformer (assuming
no power losses in the transformer) may be calculated as follows:
Ptotal =
√
3(Iline )(Vline )
Ptotal
Iline = √
3(Vline )
Iline = √
12300
3(13800)
Iline = 0.5146 amps
The grounding of the secondary is irrelevant to calculations of current and power, because that ground
connection conducts no current at all and dissipates no power.
Answer 38
200 mH
0.5 H
290 Hz
470 Ω
100 Hz
1H
Ztotal = 2.652 kΩ ∠ 55.55o
Ztotal = 565.3 Ω ∠ 33.76o
100 Hz
0.5 H
1.5 kΩ
0.2 H
470 Ω
290 Hz
Ztotal = 261.2 Ω ∠ 56.24o
1H
Ztotal = 297.6 Ω ∠ 78.55o
111
1.5 kΩ
Answer 39
0.1 µF
3.3 µF
290 Hz
470 Ω
100 Hz
Ztotal = 673.4 Ω ∠ -45.74o
3.3 µF
100 Hz
1.5 kΩ
0.22 µF
Ztotal = 8.122 kΩ ∠ -79.36o
470 Ω
0.1 µF
0.22 µF
290 Hz
Ztotal = 336.6 Ω ∠ -44.26o
1.5 kΩ
Ztotal = 1.129 kΩ ∠ -41.17o
Answer 40
The first (series) circuit’s behavior is predominantly inductive, with 961.3 ohms of inductive reactance
overshadowing 884.2 ohms of capacitive reactance, for a total circuit impedance of 77.13 ohms 6 +90o (polar
form) or 0 + j77.13 ohms (rectangular form).
The second (parallel) circuit’s behavior is capacitive, with 1.131 millisiemens of capacitive susceptance
overshadowing 1.040 millisiemens of inductive susceptance, for a total circuit admittance of 90.74
microsiemens 6 +90o . This translates into a total circuit impedance of 11.02 kΩ 6 −90o , the negative
phase angle clearly indicating this to be a predominantly capacitive circuit.
Answer 41
Answer 42
Answer 43
Answer 44
Answer 45
Answer 46
Answer 47
112
Answer 48
Graphical (phasor diagram) solution:
VB
VB
VAB
VD
VCD
VA
113
VC
Answer 49
If “A” is the reference phasor and the sequence is A-B-C, it means phase B must lag 120 degrees behind
phase A, and phase C must lag 120 degrees behind phase B (same as leading phase A by 120 degrees). Thus:
VA = 1385.6 V6 0o
VB = 1385.6 V6 − 120o
Primary side phasor diagram
VC = 1385.6 V6 120o
Secondary side phasor diagram
(dots show transformer polarity)
(dots show transformer polarity)
VC
VYZ
VA
VZ
VZX
VY
VX
VXY
VB
Given the 1:1 transformer turns ratios, the Delta-connected line voltage must be the same as the Wyeconnected phase voltage (1385.6 VAC). Measuring VX , VY , and VZ with reference to ground means these
are phase voltages
√ to the 1385.6 volt line voltage, and therefore each of them must have a value of 800 volts
(1385.6 volts ÷ 3).
Judging by the secondary phasor diagram, VZ must have a phase angle of 90o because that phasor points
straight up. The other two secondary phasors are, of course, shifted 120o in either direction from each other,
which leads to the following results:
VX = 800 V6 − 30o
VY = 800 V6 − 150o
114
VZ = 800 V6 90o
Answer 50
Partial answer:
VW
VL3-N
V
L1
-L3
VU
VL1-N
VL2-N
VV
Answer 51
Remember that your personal safety depends on getting the procedure correct. You must thoroughly
understand the procedure and why it is necessary in order to keep yourself safe under all conditions!
• Connect an AC ammeter to a suitable test plug (matching the test jack).
• Use another meter to test continuity through the ammeter, taking measurements from the blades of the
test plug in order to check continuity of the test plug, test leads, and ammeter as one continuous circuit.
It is recommended you move and flex the test leads during this procedure to check for any intermittent
“open” faults.
• Open the knife switch where the test jack is located. Leave the shorting test switch in the closed position
so that current still passes through the switch and through the sensing instrument.
• Insert the test plug into the test jack and measure current.
Answer 52
The output of a PT is typically somewhere at or below 120 volts AC. The output of a CT is typically
at or below 5 amps AC. One of the things your procedure must address is how to accurately simulate these
voltage and current levels to the wattmeter!
1
of that (104 volts AC) to the
At the given line voltage of 4160 volts the 40:1 ratio PT should output 40
wattmeter’s voltage input terminals. At the maximum line current of 180 amps the 200:5 ratio CT should
5
output 200
of that (4.5 amps AC) to the wattmeter’s current input terminals.
115
Answer 53
There are problems with both the PT circuit and the CT circuit, although the more severe of the two
by far is the CT circuit.
Hint: from the DAQ’s perspective, the PT acts as an AC voltage source while the CT acts as an AC
current source. The DAQ itself acts like a voltmeter, having an extremely high input impedance (in the
millions of ohms).
Answer 54
With 100:5 ratios at each CT, the line current to this motor is twenty times the amount of current
through each ammeter:
100
= 56.2 amps
(2.81)
5
At a line voltage of 480 VAC and a line current of 56.2 amps, the total electrical power in this 3-phase
system may be calculated as follows:
√
Ptotal = ( 3)(Iline )(Vline )
√
Ptotal = ( 3)(56.2)(480) = 46.724 kW
At an efficiency of 88%, only 88% of this power becomes translated into mechanical horsepower. This
equates to 41.117 kW of mechanical power output at the motor shaft.
Since we know there are 746 watts to every horsepower, we may convert this kW figure into HP as
follows:
41117 W
1 HP
= 55.12 HP
1
746 W
Answer 55
The resistor will drop more voltage.
Ztotal (rectangular form) = 5100 Ω − j4671 Ω
Ztotal (polar form) = 6916 Ω
6
−42.5o
Answer 56
• f = 200 Hz ; VL = 1.750 V ; VC = 11.79 V ; Vspeaker = 5.572 V
• f = 550 Hz ; VL = 6.472 V ; VC = 5.766 V ; Vspeaker = 7.492 V
• f = 900 Hz ; VL = 9.590 V ; VC = 3.763 V ; Vspeaker = 6.783 V
This circuit is known as a midrange crossover in stereo system design.
116
Answer 57
Since we know resistors impart no phase shift between voltage and current, the phase angle of each
phase voltage remains preserved in the respective phase currents:
IA =
IB =
120 V6 120o
VA
=
= 3.43 A6 120o
RA
35 Ω6 0o
VB
120 V6 − 120o
=
= 3.43 A6 − 120o
RB
35 Ω6 0o
IC =
120 V6 0o
VC
=
= 3.43 A6 0o
RC
35 Ω6 0o
Vline = 208 volts
Phase rotation = CBA
VC = 120 V ∠ 0o
A
B
C
Voltage phasor diagram
Current phasor diagram
VA = 120 V ∠ +120o
35 Ω
IA = 3.43 A ∠ +120o
VC = 120 V ∠ 0o
IC = 3.43 A ∠ 0o
35 Ω
IB = 3.43 A ∠ -120o
VB = 120 V ∠ -120o
117
35 Ω
The situation with a line-to-line resistive fault is a bit different. First, the resistance in question sees full
line voltage (208 volts) not phase voltage (120 volts). Next is the fact that the phase angle of this voltage
is entirely different: being a phasor stretching between the B and C phasor end-points, VBC (red lead on B,
black lead on C) it has a phase angle of −150o .
Calculating phase current through conductor B is as simple as dividing VBC by the fault resistance of
0.25 Ω:
IB =
208 V6 − 150o
VBC
=
= 832 A6 − 150o
Rf ault
0.25 Ω6 0o
Calculating phase current through conductor C requires we view the fault voltage from that phase’s
perspective. VCB is pointed exactly opposite that of VBC and therefore has an angle of +30o rather than
−150o . Applying Ohm’s Law again:
IC =
208 V6 30o
VCB
= 832 A6 30o
=
Rf ault
0.25 Ω6 0o
Vline = 208 volts
Phase rotation = CBA
VC = 120 V ∠ 0o
A
B
C
Voltage phasor diagram
Rfault = 0.25 Ω
Current phasor diagram
VA = 120 V ∠ +120o
o
A
32
IC
VC = 120 V ∠ 0o
∠
0
+3
=8
o
V
08
lt
V fau
∠
0
-15
o
=2
∠
2A
0
-15
3
IB
=8
VB = 120 V ∠ -120
o
There is no phasor shown for conductor A because with no connection to that line IA = 0.
118
Answer 58
First, calculating the voltages between each test point and ground. VA is nothing more than the first
source’s voltage divided by 2 through the resistor network. VB is one-third of its source voltage, with an
additional 180o phase shift created by the reversed polarity of the secondary winding:
VA =
195 V6 25o
= 97.5 V6 25o
2
−(220 V6 − 40o )
= 73.33 V6 140o
3
Sketching both of these quantities on a phasor diagram, we can plot the voltage VAB by the distance
between the VA and VB phasor lines:
VB =
VAB = 144.7 V ∠ -2.35o
VB = 73.33 V ∠ 140o
VA = 97.5 V ∠ 25o
Voltage VAB is simply the difference between VA and VB :
VAB = VA − VB
VAB = (97.5 V6 25o ) − (73.33 V6 140o )
VAB = 144.7 V6 − 2.35o
Answer 59
Answer 60
Answer 61
119
Answer 62
Here is a list of some of the most common ANSI/IEEE function codes:
•
•
•
•
•
•
•
•
•
50
51
52
67
79
86
81
87
89
=
=
=
=
=
=
=
=
=
Instantaneous overcurrent protection
Time overcurrent protection
AC power circuit breaker
Directional overcurrent protection
Automatic reclose protection
Auxiliary/Lockout
Frequency protection
Differential protection
Line power disconnect
Answer 63
Answer 64
Your instructor will have some electromechanical relays for you to inspect.
Answer 65
Partial answer:
The pickup adjustments for the 50 function and the 51 function are non-interactive: adjusting one of
them does not affect the adjustment of the other.
The reason the breaker’s trip coil is wired in series with the normally-open 52a auxiliary contact is to
the trip circuit will not continue to (needlessly) draw current from the station battery power supply after
the breaker has already been tripped. Thus, the 52a contact unlatches the 51 relay’s “seal-in” circuit once
the breaker reaches the tripped position.
Answer 66
Answer 67
Partial answer:
To test the “50” (instantaneous overcurrent) function, apply 11.875 amps AC to terminals 3 and 8 (or
terminals 8 and 9) with an ohmmeter connected to terminals 2 and 10 to check for the IIT contact’s closure.
Of course, you would also need to re-test the relay at current values below 11.875 amps AC to verify that
the relay does not pick up at any lower current value.
To test the “51” (time overcurrent) function, apply 4.70 amps AC to terminals 8 and 9 with an ohmmeter
connected to terminals 1 and 10 to check for the CO contact’s closure after 4.6 seconds’ worth of time.
Answer 68
Answer 69
Isupply = 12.29 A
120
Answer 70
"Line trap"
filters
Power generating
station
"Line trap"
filters
3-phase power lines
Transformer
secondaries
Substation /
distribution
Transformer
primaries
Follow-up question #1: trace the path of line-frequency (50 Hz or 60 Hz) load current in this system,
identifying which component of the line trap filters (L or C) is more important to the passage of power to
the load. Remember that the line trap filters are tuned to resonate at the frequency of the communication
signal (50-150 kHz is typical).
Follow-up question #2: coupling capacitor units used in power line carrier systems are special-purpose,
high-voltage devices. One of the features of a standard coupling capacitor unit is a spark gap intended to
“clamp” overvoltages arising from lightning strikes and other transient events on the power line:
to power line
Coupling capacitor unit
Input
Spark
gap
121
Explain how such a spark gap is supposed to work, and why it functions as an over-voltage protection
device.
Answer 71
I=
I=
V
Z
103 V6 − 6o
1540 − j162 Ω
I = 66.52 mA6 0.0051o
Answer 72
The motor’s 3000 horsepower rating refers to its mechanical output, not its electrical input. The
electrical input power necessary at full load may be determined thusly:
Pin =
Pin =
Pout
Efficiency
3000 HP
= 3409.1 HP
0.88
This amount of electrical horsepower equates to 2.5432 megawatts (MW), given the conversion factor
of 746 watts per horsepower. Calculating line current for this three-phase motor:
√
P = Iline Vline 3
Iline =
Iline =
P
√
Vline 3
2.5432 MW
√ = 352.96 A
(4160 V) 3
5
times less to be exact:
The CT will output a proportionately lesser amount of current, 400
5
Isec = (Ipri )
400
5
= 4.412 A
Isec = (352.96 A)
400
Thus, the 51 relay will see 4.412 amps at each of its CT inputs when the motor is at full load. This
value of 4.412 amps must therefore be the pickup value for the relay’s time-overcurrent function, because
any current value larger than this is an overload and should result in the relay tripping the circuit breaker
at some point in time.
In order to determine the relay’s proper time dial setting and time-current curve, we must know the
damage curve for the motor: a time-current curve describing the limits of overload tolerable by the motor
before it sustains damage. The relay’s time-current curve must be chosen so as to trip the breaker before the
motor’s time-current limits are exceeded.
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Answer 73
The indicators for channels 3 and 6 are lit on the input card of this PLC. This tells us channels 3 and
6 are receiving power through their respective process switches, but channel 4 is not. Since we are told the
system is operating as it should (no abnormal conditions), we may assume the opposite state for each input
channel will initiate a trip. Thus:
• Temperature switch (channel 6) is currently closed, and opens with a high temperature.
• Level switch (channel 4) is currently open, and closes with a low level.
• Pressure switch (channel 3) is currently closed, and opens with a low pressure.
Since the temperature switch channel is de-energize to trip, you must open that circuit in order to force
the system to trip.
Since the level switch channel is energize to trip, you must jumper power to PLC input channel 4 in
order to force the system to trip.
Since the pressure switch channel is de-energize to trip, you must open that circuit in order to force the
system to trip.
Answer 74
Breaker B’s overcurrent relays must have the highest pickup values and/or longest time values, not only
because breaker B must typically bear a heavier load than any of the distribution line breakers (C through
F), but also because in the event of a fault on one distribution line we wish that line’s breaker to trip rather
than tripping breaker B which would shut off the entire bus (and all distribution lines with it).
The fast bus trip signal informs breaker B’s overcurrent relay if and when a likely fault occurs on any of
the distribution lines. In such a case, breaker B’s relay operates as normal with its longer-delayed trip (i.e.
longer than any of the distribution breaker relays, to give the relay on the faulted distribution time to trip
first).
If, however, the fault is within the substation bus and not along any of the distribution lines, breaker
B’s relay will sense high current while the relays for breakers C-F will not. The fast bus trip signal alerts
breaker B’s relay that none of the distribution lines are faulted, and thereby permits it to trip faster than it
otherwise would to clear the bus fault in the shortest possible amount of time. In other words, breaker B’s
relays are configured for two different settings: a first setting for conditions where a distribution line fault
exists and a second setting where no such fault exists. The second setting is configured for faster tripping
action than the first.
Answer 75
Answer 76
Answer 77
Answer 78
Answer 79
Answer 80
Answer 81
This is a graded question – no answers or hints given!
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Answer 82
This is a graded question – no answers or hints given!
Answer 83
This is a graded question – no answers or hints given!
Answer 84
This is a graded question – no answers or hints given!
Answer 85
This is a graded question – no answers or hints given!
Answer 86
This is a graded question – no answers or hints given!
Answer 87
This is a graded question – no answers or hints given!
Answer 88
This is a graded question – no answers or hints given!
Answer 89
This is a graded question – no answers or hints given!
Answer 90
This is a graded question – no answers or hints given!
Answer 91
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