ECE523: Symmetrical Components

Lecture 1

• Lecture 1 handwritten notes
• Course Syllabus
• Textbook information
• Hw 0: student background and objectives, Due Session 3, August 31
• Lecture 1 handout: Why use symmetrical components (PDF)

Lecture 2

• Lecture 2 handwritten notes
• Digital filter based phasor calculations (PDF)
• Digital filter based phasor calculations (Mathcad)
• Digital filter based phasor calculations (Zipped Mathcad Prime 2 format file)
• Digital filter based phasor calculations (Zipped Mathcad Prime 8 format file)
• Useful functions and Per Unit Example, for lecture 3 (PDF)
• Useful functions and Per Unit Example, for lecture 3 (Mathcad)
• Useful functions and Per Unit Example, for lecture 3 (Zipped Mathcad Prime 2 file)
• Useful functions and Per Unit Example, for lecture 3 (Zipped Mathcad Prime 8 file)

Lecture 3

• Lecture 3 handwritten notes
• Symmetrical Components Derivation for next time (PDF)
• Symmetrical Components Derivation for next time (Mathcad)
• Symmetrical Components Derivation for next time (Zipped Mathcad Prime file)

Reference reading

• Chapter 2 in Tleis book or Chapter 2 in Anderson book

Lecture 4

• Lecture 4 handwritten notes
• Link to paper: C.L. Fortescue, "Method of Symmetrical Coordinates Applied to the Solution of Polyphase Networks," Transactions AIEE, vol. 37, pp. 1027-1140, 1918.

Lecture 5

• Lecture 5 handwritten notes
• Phase A, B and C reference transforms and inverse transforms (PDF)
• Phase A, B and C reference transforms and inverse transforms (Mathcad)
• Phase A, B and C reference transforms and inverse transforms (Mathcad Prime)
• The textbook Hpnz transformation matrix vesrions A012 transformation matrix (PDF)
• The textbook Hpnz transformation matrix vesrions A012 transformation matrix (Mathcad)
• The textbook Hpnz transformation matrix vesrions A012 transformation matrix (Mathcad Prime)
• Symmetrical components modeling of balanced and unbalanced series impedances (PDF)
• Symmetrical components modeling of balanced and unbalanced series impedances (Mathcad)
• Symmetrical components modeling of balanced and unbalanced series impedances (Mathcad Prime)

Lecture 6

• Lecture 6 handwritten notes
• Neutral to ground voltage example from class (PDF)
• Neutral to ground voltage example from class (Mathcad)
• Neutral to ground voltage example from class (Mathcad Prime, zipped)
• Example from class implemented in ATPDraw, PSCAD/EMTDC and EMTP-RV (zip)

Lecture 7

• Lecture 7 handwritten notes
• Symmetrical component example in time domain updated (PDF)
• Symmetrical component example in time domain updated (Mathcad)
• Symmetrical component example in time domain updated (Mathcad Prime (zipped))
• Example from class implemented in ATPDraw (PSCAD/EMTDC and EMTP-RV to be added later (zip)
• Three phase fault analysis with circuit analysis and Zbus approaches updated (PDF)
• Three phase fault analysis with circuit analysis and Zbus approaches updated (Mathcad)
• Three phase fault analysis with circuit analysis and Zbus approaches updated (Mathcad Prime)

Reference Reading

• Shunt faults: Chapter 2 in Tleis book or Chapter 3 in Anderson book
• Bus impedance method for fault analysis: Chapter 7 in Tleis book or Chapter 11-12 in Anderson book

Lecture 8

• Lecture 8 handwritten notes
• Lecture 7 handouts updated to reflect changes shown in class

Lecture 9

• Lecture 9 handwritten notes
• Introduction to using Powerworld for fault analysis (PDF)
• Powerworld files for example case (zip)

Lecture 10

• Lecture 10 handwritten notes
• Examples of analyzing unbalanced faults using simple circuits approach (PDF)
• Examples of analyzing unbalanced faults using simple circuits approach (Mathcad)
• Examples of analyzing unbalanced faults using simple circuits approach (Mathcad Prime-zip)
• Examples of analyzing unbalanced faults using Zbus matrix method (PDF)
• Examples of analyzing unbalanced faults using Zbus matrix method (Mathcad)
• Examples of analyzing unbalanced faults using Zbus matrix method (Mathcad Prime-zipped)

Reference Material

• Online training on using Powerworld

Lecture 11

• Lecture 11 handwritten notes

Lecture 12

• Lecture 12 handwritten notes
• Homework 3 now due Lecture 14 (October 5)


• Powerworld files for example case (zip)
• Derivation of DLG sequence connections with fault resistance, for next lecture (PDF)

Lecture 13

• Lecture 13 handwritten notes

Lecture 14

• Lecture 14 handwritten notes
• Circuit based fault analysis with power sequence load flow (PDF)
• Circuit based fault analysis with power sequence load flow (Mathcad)
• Circuit based fault analysis with power sequence load flow (Mathcad Prime)
• Power flow example using Mathcad (PDF)
• Power flow example using Mathcad (Mathcad)
• Power flow example using Mathcad (Mathcad Prime)
• Faulted power system examples with power flow on the system (PDF)
• Faulted power system examples with power flow on the system (Mathcad)
• Faulted power system examples with power flow on the system (Mathcad Prime)

Lecture 15

• Lecture 15 handwritten notes
• Power flow case and fault cases with power flow implemented in Powerworld (zip)

Lecture 16

• Lecture 16 handwritten notes

Reference Material for Lectures 17 and 18

• Sections 2.3.7 and 2.3.8 in Tlies
• Section 7.6.4 in Tlies: series faults using Zbus approach
• Or part II of Chapter 3 in reference textbook by Anderson

Lecture 17

• Lecture 17 handwritten notes
• Series fault examples (PDF)
• Series fault examples (Mathcad)
• Series fault examples (Mathcad Prime)
• Sequence connection derivation for single phase series fault, (PDF)
• Sequence connection derivation for single phase series fault (Mathcad)
• Sequence connection derivation for single phase series fault (Mathcad Prime)
• Sequence connection derivation for two phase open series fault (PDF)
• Sequence connection derivation for two phase open series fault (Mathcad)
• Sequence connection derivation or two phase open series fault (Mathcad Prime)
• ATPDraw files for series fault examples from class handout
• PSCAD/EMTDC files for series fault examples from class handout
• EMTP-RV files for series fault examples from class handout

Lecture 18

• Lecture 18 handwritten notes
• Series fault cause without open phase (PDF)
• Series fault cause without open phase (Mathcad)
• Series fault cause without open phase (Mathcad Prime version 9 format (zipped))

Lecture 19

• Lecture 19 handwritten notes
• Analyzing series faults using Zbus method (PDF)
• Analyzing series faults using Zbus method (Mathcad)
• Analyzing series faults using Zbus method (Mathcad Prime)
• Brief overview of electromagnetic transient simulation (PDF)

Lecture 20

• Lecture 20 handwritten notes
• Simultaneous fault example (PDF)
• Simultaneous fault example (Mathcad)
• Simultaneous fault example (Mathcad Prime-zipped)
• ATPDraw files for simultaneous fault example from class handout

Reference Material

• Reference Material on Simultaneous faults: textbook by Anderson Chapter 9
• Reference Material on Simultaneous faults: textbook by Tleis (2nd edition) Sections 2.4 and 2.5
• D. Tziouvaras, "Analysis of Complex Power System Faults and Operating Conditions," Presented at 2009 Georgia Tech Protective Relaying Conference

Lecture 21

• Lecture 21 handwritten notes

Reference Material

1. References on detecting conductor breaks
• K. Dase, S. Harmukh,A. Chatterjee, "Detecting and Locating Broken Conductor Faults on High-Voltage Lines to Prevent Autoreclosing Onto Permanent Faults," 76th Annual Georgia Tech Protective Relay Conference, May 2023.
• K. Dase, J. Colwell, S. Pai, "Novel Methods for Detecting Conductor Breaks in Power Lines" 50th Western Protective Relay Conference, October 2023.
• Y. Gong, G. Juvekar, K. Dase, "Zero-Setting Broken Conductor Detection Method Using Local Measurements Only" 50th Western Protective Relay Conference, October 2023.
• W. O'Brien, E. Urden, K. Garg, D. Haes, B. Sridharan, "Catching Falling Conductors in Midair – Detecting and Tripping Broken Distribution Circuit Conductors at Protection Speeds" 50th Western Protective Relay Conference, October 2023.
2. References on transmission line and cable modeling
• Sequence pi models: section 3.5 of Tleis
• Calculting overhead line parameters: section 3.2 of Tleis
• Alternate reference for calculating overhead line parameters: Chapter 4 of Anderson

Lecture 22

• Lecture 22 handwritten notes
• Calculating series line constants for overhead lines-for lecture 23 (PDF)
• Calculating series line constants for overhead lines-for lecture 23 (Mathcad)
• Calculating series line constants for overhead lines-for lecture 23 (Mathcad Prime -zipped)

Lecture 23

• Lecture 23 handwritten notes
• Calculating conductor sag and modeling transposition (PDF)
• Calculating conductor sag and modeling transposition (Mathcad)
• Calculating conductor sag and modeling transposition (Mathcad Prime-zipped)

Lecture 24

• Lecture 24 handwritten notes

Reference Material

• Conductor data tables: P. Anderson, Analysis of Faulted Power Systems Appendex B, Tables B.4 to B.11
• conductor data tables: Glover, Sarma, Overbye (various versions), Power Systems AnalysisAppendix, Tables A.3 and A4

Lecture 25

• Lecture 25 handwritten notes

Reference Material

• Capacitance Calculations: Tlies Section 3.2
• Capacitance Calculations: Anderson Chapter 5

Lecture 26

• Lecture 26 handwritten notes
• Calculating sequence capacitances (PDF)
• Calculating sequence capacitances (Mathcad)
• Calculating sequence capacitances (Mathcad Prime)
• Calculating series impedance for mutually coupled lines (PDF)
• Calculating series impedance for mutually coupled lines (Mathcad)
• Calculating series impedance for mutually coupled lines (Mathcad Prime)
• Representing mutually coupled lines in Zbus method based fault analysis (PDF)
• Representing mutually coupled lines in Zbus method based fault analysis (Mathcad)
• Representing mutually coupled lines in Zbus method based fault analysis (Mathcad Prime)
• Inputting zero sequence mutual coupling data in Powerworld
• Powerworld cases illustrating results with representation of mutually coupled lines (zip)

Reference Material

• Calculation Mutually coupled line parameters: Tlies Section 3.2
• Calculation Mutually coupled line parameters: Anderson Sections 4.14-4.15
• Sequence representation of mutual coupling: Tlies section 3.4.3 and 3.5
• Adding mutually coupled lines in Ybus matrix: Anderson Chapter 11
• D. Tziouvaras, "Analysis of Complex Power System Faults and Operating Conditions," Presented at 2009 Georgia Tech Protective Relaying Conference

Lecture 27

• Lecture 27 handwritten notes

Reference Material

• Calculation of cable parameters, Tlies Section 3.3 and 3.4
• For next time
• Sections 5.6-5.9 in the Tleis
• Sections 6.11-6.13 in Anderson's Faulted Power Systems Book

Lecture 28

• Lecture 28 handwritten notes
• Generator grounding resistor, buswork and current transformers
• Synchronous machine models to include transient and sub-transient response of synchronous machines

For next lecture

• Derivation of steady-state equivalent circuit (PDF)
• Derivation of steady-state equivalent circuit (Mathcad)
• Derivation of steady-state equivalent circuit (Mathcad Prime)
• Derivation of equation to determine angle of q-axis plus several examples (PDF)
• Derivation of equation to determine angle of q-axis plus several examples (Mathcad)
• Derivation of equation to determine angle of q-axis plus several examples (Mathcad Prime)


• Examples comparing generator fault model with ATP simulation results (PDF)
• Examples comparing generator fault model with ATP simulation results (Mathcad)
• Examples comparing generator fault model with ATP simulation results (Mathcad Prime)
• Plot data from ATP case for import into Mathcad (zip)
• ATPdraw files for examples (zip)

Reference Material

• Sections 5.6-5.9 in the Tleis
• Sections 6.11-6.13 in Anderson's Faulted Power Systems Book
• For next time
• Chapter 6 in Tleis: specifically 6.11-6.22

Lecture 29

• Lecture 29 handwritten notes
• Instructions for important transient simulation output data into Mathcad from ECE 524 (PDF)
• Instructions for important transient simulation output data into Mathcad from ECE 524 (Mathcad)
• Instructions for important transient simulation output data into Mathcad from ECE 524 (Mathcad Prime)
• Transient simulation results to import into the L29import.mcd or L29import.mcdx files (zip)


• Induction machine phase open condition steady-state example (PDF)
• Induction machine phase open condition steady-state example (Mathcad)
• Induction machine phase open condition steady-state example (Mathcad Prime-zipped)

Reference Material for next time

• Autotransformer Equivalents: Section 4.2.5 of Tlies
• Autotransformer Equivalents: Section 7.5 of Anderson
• Grounding Transfomers: Section 4.2.6 of Tlies
• Grounding Transformers: Section 7.10 of Anderson
• Tap Changing Transformers and Phase shifting Transformers: Sections 4.2.8 and 4.3 of Tlies
• Tap Changing Transformers and Off nominal taps: Sections: 7.12 and 7.13 in Anderson

Lecture 30

• Lecture 30 handwritten notes
• Three winding transformer example (PDF)
• Three winding transformer example (Mathcad)
• Three winding transformer example (Mathcad Prime)
• Tap changer and phase angle regulator in the sequence domain (PDF)
• Tap changer and phase angle regulator in the sequence domain (Mathcad)
• Tap changer and phase angle regulator in the sequence domain (Mathcad Prime)
• Powerworld examples for tap changer and phase angle regulator in the sequence domain (zip)

Reference Material Inverter Based Generation

• Tleis, 2nd Edition, Section 6.2: voltage source converter overview
• Tleis, 2nd Edition, Sections 6.3-6-10: characteristics of IBR
• Tleis, 2nd Edition, Sections 6.11-6.16: fault characteristics and modeling of voltage source converters controlled in grid following mode.
• Tleis, 2nd Edition, Sections 6.17-6.22: fault characteristics and modeling of voltage source converters controlled in grid forming mode.


• Tleis, 2nd Edition, Section 2.6: Symmetrical components analysis for networks with a mix of voltage sources and current sources
• Tleis, 2nd Edition, Section 2.6: Symmetrical components analysis for networks with a mix of voltage sources and current sources
  
• Tleis, 2nd Edition, Sections 7.2 and 7.6: Ybus matrix approaches for large networks with mix of voltage and current sources.

Homework 1

• Homework 1 (PDF), due session 6 (Sept 7)
• Homework 1 (Mathcad), due session 6 (Sept 7)
• Homework 1 (Mathcad Prime), due session 6 (Sept 7)

Homework 2

• Homework 2 (PDF), due session 9 (Sept 19)
• Homework 2 (Mathcad), due session 9 (Sept 19)
• Homework 2 (Mathcad Prime), due session 9 (Sept 19)

Homework 3

• Homework 3 (PDF), now due Lecture 14 (October 5)
• Homework 3 (Mathcad), now due Lecture 14 (October 5)
• Homework 3 (Mathcad Prime), now due Lecture 14 (October 5)

Homework 4

• Homework 4 (PDF), due session 20 (Oct 26)
• Homework 4 (Mathcad), due session 20 (Oct 26)
• Homework 4 (Mathcad Prime), due session 20 (Oct 26)

Homework 5

• Homework 5 (PDF), Updated due session 28 (Nov 16)
• Homework 5 (Mathcad), Updated due session 28 (Nov 16)
• Homework 5 (Mathcad Prime), Updated due session 27 (Nov 28)

Homework 6

• Homework 6 (PDF), due session 30 (Dec 8)
• Homework 6 (Mathcad), due session 30 (Dec 8)
• Homework 6 (Mathcad Prime), due session 30 (Dec 8)