1/6

Final Project EE-431

Introduction

This project aims to determine your ability to apply the concepts and methods discussed in class

for a power system design problem. You can develop your own software in your language of

choice, and/or use the software tools utilized in the class (i.e. MATLAB) or you can follow the

procedure by hand calculations.

Objective

● To carry out the design of a power transmission system that runs through urban service

territories.

● To apply your knowledge from class in computing parameters for component models,

perform steady-state analysis.

● To build software scripts and use different software tools towards your design.

● To document your results, calculations, and source code (if applicable) in a report.

Design Project Statement and Data

Design Problem Statement

The design problem consists in expanding a transmission system to serve a 4-bus power system

shown in the map in Fig. 1 and to also determine if the existing transmission system needs to be

upgraded to handle an additional growth (40MW) in the existing load connected to the Bus 3. This

requires to redesign and build new transmission infrastructure, and to perform power flow analysis

studies using Newton-Raphson method.

Transmission System

The transmission system in Figure 1, below, contains both 161 kV transmission lines and

substations that go through urban service territories. The load at each of the buses is provided in

Table 1, and the parameters of the existing lines are shown in Table 2.

2/6

Figure 1. One-line Diagram of the 4-Bus Power System

Substations Buses and Loads

The buses shown in the diagram correspond not only to electrical buses, but to substations:

Buses 1-2 are substations at power sources (i.e. generation plants) at 161 kV.

○ Each power source is rated at 100 MVA, and should be represented by their

equivalent current sources with their reactances in per unit on a 100 MVA-

base as shown below.

Bus # Bus Name Reactance Capacity

1 Generator j0.25 100 MVA

2 Generator j0.20 100 MVA

● Buses 3-4 are urban load substations, assume a voltage magnitude of 1.0 per unit at

buses 3 and 4.

Bus # Load (MW) Load (MVAr)

3 100 25

4 150 50

Table 1. Loads at different buses

3/6

Transmission Lines

Parameters for Existing Lines

The parameters of the existing transmission lines representing by π model where series

reactances and shunt reactances expressed in per unit on a 100MVA base are provided in Table

2, below.

Bus # Bus # R (p.u) XL (p.u) XC (p.u)

1 2 0 0.25 -4

1 3 0 0.1 -4

1 4 0 0.4 -4

2 4 0 0.16 -4

3 4 0 0.2 -4

Table 2. Transmission Line Parameters

Design Phases Overview

The project is structured so that you conduct this project in 4 different phases, as follows:

1. In the first phase of the design, the only requirement is to convert the loads, generation

units, and transmission lines to the corresponding impedance parameters.

This phase consists of transforming all the data to per unit quantities, if not already in per

unit.

The remaining step of the design requires to consider the location of the equivalent current

source of power generators along with the given reactance per each generator.

2. The second phase consists in using the per-unit data of all system components to compute

both Ybus and Zbus.

3. The third phase consists in a power flow study of the system under different load growth

scenarios.

4. The final phase is to prepare a report describing obtained results based on this analysis.

Phase 1

In this phase you are asked to draw the existing system in per unit with all values making design

to serve the load and generation subject to the specifications and design tasks as described

below.

4/6

Design Tasks

a. Calculate per unit values of impedances of all the transmission lines using a suitable

software. You can make your own hand calculation, or use MATLAB. The resistance of

lines is ignored. The line reactances at rated voltage is provided in Table 2.

b. Each power source (generator) should be connected to the Bus 1 and Bus 2 with specified

reactance above.

c. Calculate all the per unit values of the loads on a 100 MVA base, with a voltage base of

161 kV (1 p.u.) as appropriate.

Create a table with all the parameters of the system in per unit.

Phase 2

This phase is a continuation of Phase 1 consists of building the Ybus and Zbus matrices.

Design Tasks

For the parameters determined in Phase 1, perform the following calculations.

d. Use the MATLAB Command other code to compute Ybus and Zbus. You can proceed

with hand calculations if you wish.

e. Compute the bus admittance matrix, Ybus and bus impedance matrix, Zbus with all the

parameters expressed in per unit on the common system base of 100 MVA.

Phase 3

This phase consists in performing different power flow studies for the system set up in the previous

phases. You will consider the following case studies:

● Case 1: Base case system with base loads as specified in Table 1.

● Case 2: Modified system with adding a 40 MW “Data Center” load connected to Bus 3.

Design Tasks

f. Perform power flow analysis based on Newton-Raphson method on Case 1 and verify the

design requirements listed below.

g. Modify the 4-bus power system to supply the new 40 MW load connected to Bus 3 and

repeat Newton-Raphson power flow analysis.

h. Summarize graphically (one plot for each Cases 1 and 2) the power flow results from the

two cases analyzed above, show the bus voltage magnitude and angle, active and

reactive powers.

i. Compare the MVA in the loads, the MVA used in the lines, and the MVA from the

generators in each case.

5/6

Design Criteria and Specifications

Criteria

When carrying out the design tasks above, you must meet the following design criteria:

● R1. Satisfactory system operation: all voltages should be in the range from 0.95 to 1.05

pu, with no overloaded lines.

● R2. Loads: from the power flow results, determine the total load in the system, the losses

across lines and total generation.

Phase 4

This final phase is about documentation of your obtained results considering the below guidelines:

A deadline for report submission is on December 11th, 2020 by 5:00 pm.

Report Requirements and Structure

Your report should be structured as described below.

1. Executive Summary: a maximum 1-2 page summary that includes the main information

of your project.

This should contain everything that I need to know to grade you without having to read

the whole report. Make this a “self contained” document.

Your summary should include at least the following:

a. Summarize the changes required (for example the capacity of transmission lines,

choosing lower or high capacity of cables, etc.) at each case in Phase 3 using a

table.

b. Contrast the analysis methods and results of Phase 3.

c. Use a minimum of 1 figure and a maximum of 2 figures to highlight your most

important finding.

2. Report Structure:

a. Title page

b. Table of contents.

c. System Description

i. A one-line diagram of the system showing the generators, bus, line, and

load connections. Explain your suggestion to achieve a better system

operation if you think there is a need for modifications by adding new 40MW

loads at Bus 3.

ii. Specifications of each line in the system: connection between buses,

voltage, series impedance and shunt capacitance reactance, and MVA and

current ratings.

6/6

d. Design Summary

i. Provide a summary of results from all other design phases here. You

should aim to summarize each phase with a short paragraph and preferably

through 1 or 2 figures. You might prefer that all other details (calculations,

tables, figures) for each design phase to be included in a dedicated

Appendix.

ii. Design Analysis:

1. Compare the analysis results of Case 1 and Case 2 in Phase 3.

2. Use a minimum of 1 figure and a maximum of 2 figures to highlight

your most important finding.

iii. Design Tools (if using software):

1. Software Documentation: Briefly explain, through a

flowchart/discussion, how you were able to do the analysis required

through different software routines or by using different

functions/software and reading data.

e. Conclusions: briefly discuss your findings. Keep this short, 1-2 paragraphs, 1

figure, and highlight your most important finding.

3. Other:

a. Number and title all figures.

b. Number and title all tables.

c. Document all changes made from the base case design in a dedicated Appendix,

be organized!

Final Remarks

Do your own work!

● This project serves as a way to measure your ability to apply the intended learning

outcomes. You must make sure during the course that you will be able to do the work

described here, and thus, you must do all the homework assignments to be able to have

the skills you need.

● This project may have not a unique solution, so there is likely possible way that you

can have the different solution as another student.

1/13

Final Project EE-431

Introduction

This project aims to determine your ability to apply the concepts and methods discussed in class

for a power system design problem. You can develop your own software in your language of

choice, and/or use the software tools utilized in the class (i.e. MATLAB).

Objective

● To carry out the design of a power transmission system that runs through both urban and

rural service territories.

● To apply your knowledge from class in computing parameters for component models,

perform steady-state analysis.

● To build software scripts and use different software tools towards your design.

● To document your results and source code in a report.

Design Project Statement and Data

Design Problem Statement

The design problem consists in expanding a transmission system to serve a new data center

called “Steel Mill” (indicated with a red square in the map in Fig. 1) and to also determine if the

existing transmission system needs to be upgraded to handle a 30% growth in the existing load.

This requires to design and build new transmission infrastructure, and to perform power flow

analysis studies.

Transmission System

The transmission system in Figure 1, below, contains both 161 kV and 69 kV transmission lines

and substations that go through both urban and rural service territories. Assume that all roads go

from North to South and East to West. The load at each of the buses is provided in Table 1, and

the parameters of the existing lines are shown in Table 2.

2/13

Figure 1. Eagle Power System One-line Diagram

3/13

Substations Buses and Loads

The buses shown in the diagram correspond not only to electrical buses, but to substations that

may contain transformers and other components as discussed next:

● Buses 1-3 are substations at power sources (i.e. generation plants) at 161 kV.

○ Each power source is rated at 490 MW, with a minimum volt ampere

reactive limit of -100 MVAr and a maximum limit of 250 MVAr.

● Buses 4-8 are urban load substations

● Buses 4-9 are rural load substations

Buses with loads under 30 MVA should be served at 69 kV and buses with loads over 50 MVA

should be served at 161 kV. Other buses can be served at either voltage, as discussed later.

Bus # Bus Name Load (MW) Load (MVAr)

1 Owl

2 Swift

3 Parrot

4 Lark 60 10

5 Jay 100 30

6 Raven 80 15

7 Wren 90 20

8 Robin 40 5

9 Siskin 10 5

10 Junco 15 10

11 Quail 75 15

12 Heron 40 15

13 Egret 30 10

14 Gull 35 10

15 Crow 10 0

Total: 585 145

Table 1. Loads at different buses

Transformers

There are 69 kV to 161 kV transformers with 60 MVA rating at the Siskin and Crow buses. Each

of the buses have 2 voltage levels. At Siskin, the high voltage side is labeled bus 9, while the low

voltage side is labeled bus 17. At Crow, the high voltage side is labeled bus 15, while the low

voltage side is labeled bus 16. The transformers have leakage reactance of 34.56Ω referred to

the 161 kV side.

4/13

To simplify the study, Tap changer setting for all transformers is 1.

Transmission Lines

Parameters for Existing Lines

The parameters of the existing transmission lines are provided in Table 2, below.

Bus # Bus # Bus Name Bus Name Miles Conductor R (Ohmns) X (Ohmns) BMVA

1 9 Owl 161 Siskin 161 24 Drake 3.085 17.47 3.629

1 11 Owl 161 Quail 161 36.7 Drake 4.718 26.7 5.55

1 14 Owl 161 Gull 161 28.2 Drake 3.629 20.53 4.264

2 11 Swift 161 Quail 161 21.5 Drake 2.774 15.66 3.251

2 12 Swift 161 Heron 161 20.3 Drake 2.618 14.78 3.07

2 14 Swift 161 Gull 161 24 Drake 3.085 17.47 3.629

3 6 Parrot 161 Raven 161 27.6 Drake 3.551 20.09 4.174

3 12 Parrot 161 Heron 161 27.6 Drake 3.551 20.09 4.174

3 15 Parrot 161 Crow 161 23.6 Drake 3.033 17.16 3.569

4 5 Lark 161 Jay 161 8.4 Dove 1.529 6.3 1.232

4 9 Lark 161 Siskin 161 18.8 Drake 2.411 13.69 2.843

5 6 Jay 161 Raven 161 10.8 Dove 1.97 8.09 1.584

5 7 Jay 161 Wren 161 6 Dove 1.089 4.48 0.88

5 8 Jay 161 Robin 161 10.9 Dove 1.996 8.17 1.599

7 15 Wren 161 Crow 161 14.6 Drake 1.866 10.63 2.208

8 12 Robin 161 Heron 161 9.8 Drake 1.27 7.13 1.482

5 11 Jay 161 Quail 161 19.5 Drake 2.514 14.18 2.949

10 13 Junco 69 Egret 69 14.3 Hawk 3.033 10.15 0.408

10 17 Junco 69 Siskin 69 16.2 Hawk 3.433 11.49 0.462

13 16 Egret 69 Crow 69 21.9 Hawk 4.642 15.54 0.624

BMVA: reactive volt-amperes generated by the total susceptance corresponding to line charging of the

transmission line at rated voltage.

Table 2. Transmission Line Parameters

5/13

The BMVA is determined as follows. The susceptance of the line as , consequently

the BMVA can be calculated from:

Conductor Data

● Conductor Types: For new lines that have to be built the only conductors available to

use are Partridge, Hawk, Dove, Drake and Cardinal, and their data is available in the

Appendix.

● Ampacity: the maximum current carrying capacity (or ampacity) of the allowable

conductors types listed above are: Partridge (475 A), Hawk (659 A), Dove (726 A),

Drake (907 A), Cardinal (996 A).

Design Phases Overview

The project is structured so that you conduct this project in 6 different phases, as follows:

1. In the first phase of the design, the only requirement is to choose the conductors for the

two voltage levels, and determine the corresponding impedance parameters of the lines

(series resistance and reactance, and one-half the total capacitance of susceptance,

0.5BC).

2. The following phase consists of transforming all the data to per unit quantities.

3. The third phase of the design requires to consider the location of the power generators

and to determine from data tables what the most adequate parameters to use are.

Tips: (MW, Mvar, Qmin, Qmax)

4. The fourth phase consists in using the per-unit data of all system components to compute

both Ybus and Zbus.

5. The fifth phase consists in a power flow study of the system under different load growth

scenarios.

6. The final phase is to prepare a report describing obtained results based on this analysis.

Phase 1

In this phase you are asked to upgrade the existing system making better design to serve the

load and generation subject to the following specifications and design tasks.

Design Tasks

a. Provide sufficient capacity in the transmission lines and transformers for a 30% growth of

the existing load.

b. The new “Steel Mill Data Center” will host a major IT operation for the new crucial

Infrastructure. This will be a critical load. It is estimated that the load will be 40 MW at unity

6/13

power factor, and will be located as shown in the map in Fig. 1. Design a suitable

transmission system to supply the load.

c. Transmission voltages of 161 kV or 69 kV can be used. Bundled conductors are not to be

used at these voltages.

d. Calculate impedances of all the new transmission lines using a suitable software. You can

make your own, or use MATLAB. The resistance of lines should be calculated at 50 deg.

C. The line capacitance in terms of the megavolt-amperes-reactive (MVAr) generated by

the total capacitance of susceptance at rated voltage is provided in Table 2. You need to

calculate these quantities for any new transmission line added.

e. Each power source (generator) should be connected to the rest of the system by at least

three 161 kV lines.

f. Do not oversize conductors without justification.

g. The maximum number of available transformers is four.

h. It is unlikely that you can justify using the same conductor size at both 161 kV and 69 kV.

Design Criteria and Specifications

In performing the above steps, you will need to verify that the transmission lines and transformers

have sufficient current carrying capacity (ampacity) at steady-state in this project. This can be

done accurately using power flow calculation programs, as done in the fifth phase. In this phase,

however, you should instead start by making an estimate.

To compute this estimate, you can take an intuitive approach. Because you are given the existing

voltages and loads at each bus, you can compute an estimate of the load currents. For simplicity,

assume that increasing the loads by 30% increases the currents proportionally. Once the current

of a particular bus has been determined, the next step is to figure out how much of this current is

supplied by each of the transmission lines to the bus. Of course, one could use the current divider

approach, however, this would require additional data and computations that are not possible at

this point.

In this phase, you can use the concept of “electrical distance”. The electrical distance is a

measure of the equivalent impedance between two nodes. When 2 buses are electrically close,

the equivalent impedance between them is low, and vice versa. While geographical closeness

and electrical closeness are mostly related, this is not always the case, as it depends on the value

of the impedances between two buses. For example, intuitively, bus 11 is connected to generator

bus 1 through a single line, whereas there are many other lines and equipment from bus 3 to

generator bus 11. So, you can expect that at bus 11 there is more current coming from bus 1 than

bus 3.

Hence, a simplified approach to quantify electrical closeness is to consider a particular

load bus and determine the impedance of all paths between the load bus and generator buses.

First, you can calculate the impedance for all possible transmission paths between bus 11 and

generator bus 1, which include pats (1-11), (1-14-2-11), (1-9-4-5-11), etc. Next, find the lowest

impedance path. In practice, some paths (those with many segments) can be ignored. If the result

is a low impedance, bus 11 is “close” to generator bus 1. Similarly, it is possible to find the lowest

impedance path from bus 11 to bus 2, and from bus 11 to bus 3. For simplicity, it can be assumed

that the currents to bus 11 only flow in the three lowest impedance paths and that they divide

7/13

according to the parallel current rule. Thus, the lower the path impedance, the greater the fraction

of the total current that flows in that path. This should provide results that would be reasonable,

at least qualitative.

Phase 2

This phase consists in transforming the data from the system designed in Phase 1 to per unit.

Design Tasks

For the system designed in Phase 1:

i. Calculate all the impedances on a 100 MVA base, with a voltage base of 161 kV or 69 kV

as appropriate.

j. The transformer reactance is 0.08 pu on the transformer base. You can ignore the

resistance or find the value in per unit by making your own assumptions.

Create a table with all the parameters of the system in per unit.

Phase 3

This phase consists in determining a location of the generators and parameters (MW, Mvar, Qmin,

Qmax) from data tables what the most adequate parameters to use in the system.

Design Tasks

The power system in Fig. 1 has three power generation plants located at Bus 1 (Owl), Bus 2

(Swift) and Bus 3 (Parrot). Assume that these three generators have a rating of 550 MVA each,

and recall that each of the generators is rated at 490 + j250 MVA.

k. Convert all machine parameters to a common system base of 100 MVA and the

appropriate voltages.

Phase 4

This phase is a continuation of Phases 3 and 4 and consists of building the Ybus and Zbus

matrices.

Design Tasks

For the parameters determined in Phases 3 and 4, perform the following calculations.

l. use the MATLAB Command other code to compute Ybus and Zbus.

m. Compute the Ybus and Zbus matrices with all the parameters expressed in per unit on the

common system base of 100 MVA.

8/13

Phase 5

This phase consists in performing different power flow studies for the system set up in the previous

phases. You will consider the following case studies:

● Case 1: Base case system with base loads and fixed tap transformers (tap setting 1)

● Case 2: Modified system with 40 MW “Steel Mill Data Center” load and base case loads

increased by 30% and fixed tap transformers.

Design Tasks

n. Use the software of your choice to perform power flow analysis on Case 1 and verify the

design requirements listed below.

o. Modify the transmission system to supply the new 40 MW load following the specifications

a-j in Phase 1.

○ Obtain the parameters of the lines as needed by the power flow program of your

choice, and provide a new table of data highlighting the new parameters used.

○ Use the software of your choice to perform power flow analysis on Case 2 and

verify the design requirements listed below.

p. Summarize graphically (one plot for the same variable for the two Cases) the power flow

results from the two cases analyzed above, show the bus voltage magnitude and angle,

active and reactive powers.

q. Determine the total power (P) loss in the system as a percentage of the total load for each

case. Compare the MVA in the loads, the MVA used in the lines and the transformers, and

the MVA from the generators in each case.

Design Criteria and Specifications

Criteria

When carrying out the design tasks above, you must meet the following design criteria:

● R1. Satisfactory system operation: all voltages should be in the range from 0.96 to 1.04

pu, with no overloaded lines or transformers.

● R2. Loads: from the power flow results, determine the total load in the system, the losses

and total generation.

● R3. Transformers: the transformer tap should be fixed at 1.00 (Tap 1 for both the 69 kV

and 161 kV) in the power flow for Case 1 and Case 2.

For Case 2, If any of the criteria above are violated you will need to modify your design at your

best effort and re-do the analysis until the modified system meets the criteria.

Specifications

The specifications below are to assist you in meeting the design criteria.

● S1. Generation:

○ Make Bus 1 (Owl) the slack/swing bus.

9/13

○ For the generation at Bus 2 (Swift) and at Bus 3 (Parrot) change the following at

both: Qmin - 100.00 MVA and Qmax 250.00 MVA, and Pmax at 430 MW.

○ In Cases 1, Pgen at each bus (2 and 3) should be 190 MW. In Case 2, change the

Pgen at each bus to more appropriate values. Since the voltage is usually highest

at generator buses, and since 1.04 is at the upper limit of acceptable voltages,

schedule the voltage on the three generators at or near 1.04 per unit.

● S2. Naming Conventions and Plotting: for each power flow you run, you must

summarize the results in graphical form (e.g. using bar plots) and in the title, you need to

specify the case as for Case 1, or for Case 2.

● S3. Check your data!: as you will have to modify either the one-line diagram or data files

for the power flow program, you need to be careful when modifying it. Be consistent with

naming conventions you will use as you make modifications to each case, use descriptive

names, and add comments to the source file or diagram. Spend time checking that you

are applying the correct changes to the files and that they are modifying the output as

expected. Also check that all the lines are connected to the correct buses. Typical issues

when doing these studies

Phase 6

This final phase is about documentation of your obtained results considering the below guidelines:

A deadline for report submission is on December 11th, 2020 by 5:00 pm.

Report Requirements and Structure

Your report should be structured as described below.

1. Executive Summary: a maximum 1-3 page summary that includes the main information

of your project.

This should contain everything that I need to know to grade you without having to read

the whole report. Make this a “self contained” document.

Your summary should include at least the following:

a. Total number of lines at each voltage level, total line at each voltage level.

b. The total number of transformers

c. Summarize the changes required at each phase using a table. Make a table that

has as either rows or columns the relevant phases (i.e. Phase 1, 3, and 4).

d. Contrast the analysis methods and results of Phase 1, 4, and 5.

e. Use a minimum of 1 figure and a maximum of 2 figures to highlight your most

important finding.

2. Report Structure:

a. Title page

b. Table of contents.

c. System Description

10/13

i. A one-line diagram of the system showing the bus, line, transformer, and

load connections. Don’t forget to include capacitor banks if they are needed

in based on your results in Phase 5. They should be as part of your

suggestion to achieve a better system operation.

ii. Specifications of each line in the system: connection between buses,

voltage, length, conductor size, series impedance and shunt capacitance

susceptance, and MVA and current ratings. For the new lines added to

supply the “Steel Mill Data Center”, show a sample impedance and

susceptance calculation. Summarize all remaining results from Phase 1 in

a dedicated Appendix.

d. Design Summary

i. Provide a summary of results from all other design phases here. You

should aim to summarize each phase with a short paragraph and preferably

through 1 or 2 figures. You might prefer that all other details (calculations,

tables, figures) for each design phase to be included in a dedicated

Appendix.

ii. Design Analysis:

1. Summarize the changes required at each phase using a table.

Make a table that has as either rows or columns the relevant phases

(i.e. Phase 1, 4, and 5).

2. Compare the analysis methods and results of Phase 1, 4, and 5.

3. Use a minimum of 1 figure and a maximum of 2 figures to highlight

your most important finding.

iii. Design Tools:

1. Software Documentation: Briefly explain, through a flowchart and

discussion, how you were able to do the analysis required through

different software routines or by using different functions/software

and reading data.

e. Conclusions: briefly discuss your findings. Keep this short, 1-2 paragraphs, 1

figure, and highlight your most important finding.

3. Other:

a. Number and title all figures.

b. Number and title all tables.

c. Document all changes made from the base case design in a dedicated Appendix,

be organized!

Final Remarks

Do your own work!

● This project serves as a way to measure your ability to apply the intended learning

outcomes. You must make sure during the course that you will be able to do the work

11/13

described here, and thus, you must do all the homework assignments to be able to have

the skills you need.

● This project may have not a unique solution, so there is likely possible way that you

can have the different solution as another student.

Appendix - Conductor Data for Transmission Lines

Figure 2. Bare Aluminum Conductors, Steel Reinforced (ACSR) Electrical Properties of Multilayer Sizes

12/13

Figure 3. Bare Aluminum Conductors, Steel Reinforced (ACSR) Electrical Properties of Multilayer Sizes

13/13

Figure 4. Bare Aluminum Conductors, Steel Reinforced (ACSR) Electrical Properties of Multilayer Sizes