Stacy Dunn
Rich East High School
Rich Township High School District 227
IIT Research Mentor: Dr. Alexander Flueck
This material is based upon work supported by the National Science
Foundation under grant No. EEC-0502174. Any opinions, findings, and
conclusions or recommendations expressed in this material are those of
the author(s) and do not necessarily reflect the views of the National
Science Foundation.
INTENDED AUDIENCE:
Honors Algebra (9th Grade)
Algebra 2 (11th Grade)
TIME REQUIREMENT
6 to 9 – 50 minute class periods, plus time for the pre and post test
PRIOR KNOWLEDGE REQUIRED:
1. Students need to be able to solve systems of equations.
2. Students need to be efficient with decimals or be able to use a
calculator to do calculations
OBJECTIVES
1.
Students will expand their current knowledge about what
engineers are and what they do.
2.
Students will apply systems of equations to electrical power
generating systems.
3.
Students will use problem solving to help design a power
system that is cost effective and reliable.
ILLINOIS LEARNING STANDARDS
Math Standards
7.C.5b Determine how changes in one measure may affect other
measures.
8.C.4b Apply algebraic properties and procedures with matrices,
vectors, functions and sequences using data found in
business, industry and consumer situations.
8.D.5 Formulate and solve nonlinear equations and systems
including problems involving inverse variation and
exponential and logarithmic growth and decay.
Science Standards
State Goal 11: Understand the processes of scientific inquiry and
technological design to investigate questions,
conduct experiments and solve problems.
State Goal 12: Understand the fundamental concepts, principles
and interconnections of the life, physical and
earth/space sciences.
13.B.4a
Compare and contrast scientific inquiry and
technological design as pure and applied
sciences.
TOPICS COVERED IN MODULE
•
What is engineering?
•
Types of Engineering
•
2003 Blackout in Northeastern United States
•
Brief overview of how electricity is transported
•
Brief overview of types of power plants
•
Power system modeling using equations
•
Use of PowerWorld Software
Activity #1 (Optional Motivational Activity)
WHAT IS ENGINEERING?
•
•
Students will brainstorm about what engineering is and
what it is not.
Students will also learn about different types of
engineering.
Activity #2
ENGINEERS FOR THE DAY!
•
Students will be engineers for the day. They will have to
use problem solving to make a truck distribution center
work.
A TASTE OF ACTIVITY #2
•
Turn to the Students Power System Demonstration
Diagram, this can be found in the Worksheets for
Mathicity Workshop on page 1.
Number of
Trucks
Produced:
6
Number of
Trucks
Needed:
Terminal
2
Terminal
3
Number of
Trucks
Produced:
6
Number of
Trucks
Needed:
14
2
Number of
Trucks
Produced:
8
Terminal
1
Number of
Trucks
Needed:
4
•
Turn to page 2 and we are going to repeat the same process but
now the roads between terminals 1 and 3 are shut down due to
construction. In emergency situations the trucking company
will allow 2 trucks on 50% of the roads between any 2 terminals.
Number of
Trucks
Produced:
6
Number of
Trucks
Needed:
Terminal
2
Terminal
3
Number of
Trucks
Produced:
6
Number of
Trucks
Needed:
14
2
Number of
Trucks
Produced:
8
Terminal
1
Number of
Trucks
Needed:
4
ACTIVITY 2 CONTINUED
•
Students would also do an example where a terminal is shut
down and they have to make the system work using the
emergency situation rules.
•
Turn to the Truck Problems Worksheets on pages
4 and 5 in your extra worksheets packet. Read the
directions and do the worksheets.
•
What happened with both examples?
•
It is impossible to make either of them work using the
rules provided.
•
Why are we working with trucks when the module is
about electricity, math, and engineering?
•
This activity teaches the basics of how a power system works
through an activity the students will not be intimidated by.
The connection is made in activity 3 and 4 later on in the
module.
Activity #3
WHAT ARE THE EFFECTS OF A BLACKOUT AND
WHAT DO ENGINEERS HAVE TO DO WITH IT?
•
Students will be introduced to the different types of
power plants and how electricity is transported.
•
Students will also learn about the 2003 Blackout in
the Northeastern United States.
•
Students will also learn about the United States Power
Grid. In the truck activity the terminals represented the
electrical substations, the roads represented the power
lines and the trucks represented the electricity. For our
purposes we will be working with systems that have 2
and 3 substations, but in reality our power grid is much
larger with thousands and thousands of substations
interconnected. The system is set up like this so that if
one power line or one generator goes down the rest of
the system can pick up the slack.
Activity #4
APPLYING SYSTEMS OF EQUATIONS
TO A POWER SYSTEM
•
This is the activity where students begin working with power
systems.
Turn to page 6 in the worksheet packet, Meeting Supply and
Demand Form A.
•
BUS 2
Load
300 MW
BUS 1
Generating
??? MW
75 MW
Generating
225 MW
Load
0 MW
•
Bus = substation (distribution center), Load = Demand, and
Generating = Supply
•
How much does bus 1 need to generate to meet the load on
the system?
•
•
Turn to page 7, Meeting Supply and Demand Form B, and
complete the worksheet.
Students will do these worksheets and then you will use
PowerWorld Software to check their answers in front of
the class so they can see all the different scenarios!
•
Check Form A Using PowerWorld Software
•
Check Form B Using PowerWorld Software
•
Now that the students have been introduced to power
systems and line loads we can apply math to them!
•
Turn to page 10, 2 Bus line loading exploration. This is
the worksheet that will be passed out to students. This
worksheet is inquiry based, so instead of showing the
students how to do it they will have to work through this
worksheet themselves.
•
In your group try and work through the worksheet!
1)
How much generation do we need at Bus 2 to meet the
demands of the system?
Total Load (Demand):
400 + 200 = 600
Load – Current MW being generated 600 – 200 = 400
Power System Equations
x1  0
500x2  gen2  load 2
2)
Solve for
x1 and x2
x 0
1
500 x  200  400
2
Line Flow Equations
Flow12  500( x1  x2 )
Flow 21  500( x2  x1)
2
x2 
5
x2 is less than x1, this tells us that the electricity is flowing
from bus 1 to bus 2. The power will always flow to the
bus with the lowest value for x.
3) Figure out the electrical flow across the power line, decide
whether the power line is overloaded or not.
Flow
21
Flow
12
checks electrical line load from bus 2 to bus 1.
checks electrical line load from bus 1 to bus 2.
Since we know that the electricity is going from bus 1 to bus 2
we will check Flow
12
Flow  500( x  x )
12
1 2
2
Flow  500(0  )
12
5
Flow  200 MW
12
•
In the diagram it tells us that the line load limit is 150
MW. This power line has too much power running
through it, it is overloaded. Once a power line is
overloaded the risk of it malfunctioning goes up.
•
After letting the students work on this for a while you will
eventually go over it with them to make sure they understand it.
There is a key in the full module that gives all the details we
talked about.
•
Now the students are ready to try one for themselves. There are
four different forms in the full module that you can use. They all
have line overloads. Once the students figure out that they have
line overloads they must redesign the system so that it is not
overloaded. Turn to page 51 in the full module.
Activity #5
DESIGNING A 3 BUS POWER SYSTEM COMPETITION
•
In this activity students will have to design a 3 bus
power system that is economical yet does not overload
any power lines. This will more than likely require your
students to design a few systems before they come up
with one that works.
•
In a 3 bus system you check the power lines through
the same process. The only difference is that you
need to use a system of equations to solve for the
variables. Other than that it is the same process.
•
Turn to page 15 and 16. Work on this in your groups.
For our purpose today you can ignore #7.
•
Most Efficient System Without Overloading Power
Lines
Activity #6
IS YOUR POWER SYSTEM DESIGN RELIABLE?
•
Students will learn about the reliability of a power
system.
•
Is the Most Cost Efficient Design a Reliable System if a
Power Line Goes Down?
•
After showing the students that the most cost effective
system is not reliable they will have to go back and
check the system they designed to see if it is reliable.
•
For extra credit I will let the students redesign their
power system to be cost efficient yet reliable if any one
of the power lines goes down.
The pictures used as backgrounds in this presentation are
photos taken by Darren Hester and have been used with
his permission. His pictures can be found at
www.pixelperfectdigital.com
www.designsbydarren.com
www.designpacks.com