Stacy DunnRich East High School

Rich Township High School District 227IIT 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.

OBJECTIVES1. 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.

INTENDED AUDIENCE: Honors Algebra (9th Grade) Algebra 2 (11th Grade)

TIME REQUIREMENT6 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

ILLINOIS LEARNING STANDARDSMath Standards7.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 StandardsState 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?

Activity #2ENGINEERS FOR THE DAY!

• Students will be engineers for the day. They will have to use problem solving to make a truck distribution center work.

• Students will brainstorm about what engineering is and what it is not. • Students will also learn about different types of engineering.

• Turn to the Students Power System Demonstration Diagram, this can be found in the Worksheets for Mathicity Workshop on page 1.

A TASTE OF ACTIVITY #2

Terminal 2

Terminal 3

Terminal 1

Number of Trucks

Produced: 6

Number of Trucks

Needed:

2

Number of Trucks

Produced: 6

Number of Trucks

Produced: 8

Number of Trucks

Needed:

14

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.

Terminal 2

Terminal 3

Terminal 1

Number of Trucks

Produced: 6

Number of Trucks

Needed:

2

Number of Trucks

Produced: 6

Number of Trucks

Produced: 8

Number of Trucks

Needed:

14

Number of Trucks

Needed:

4

• Turn to the Truck Problems Worksheets on pages 4 and 5 in your extra worksheets packet. Read the directions and do the worksheets.

• 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.

ACTIVITY 2 CONTINUED

• What happened with both examples?

• Why are we working with trucks when the module is about electricity, math, and engineering?

• It is impossible to make either of them work using the rules provided.

• 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 #4APPLYING 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 BUS 1Load Generating300 MW ??? MW

Generating Load 225 MW 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?

75 MW

• 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

• Turn to page 7, Meeting Supply and Demand Form B, and complete the worksheet.

• 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 = 600Load – Current MW being generated 600 – 200 = 400

x

x1 0

500 2 2 2

gen load

Flow

Flow12 500 1 2

21 500 2 1

( )

( )

x x

x x

Power System Equations Line Flow Equations

2) Solve for x x1 2 and

200

01500 4002

x

x

2

2

5x

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.

Flow12

Flow21 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 Flow12

Flow 500( )12 1 2x x 2

5Flow 500(0 )12

Flow 200 MW12

• 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.

• 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

• 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.

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.comwww.designsbydarren.com

www.designpacks.com