EE 581: Directed Study (Power System Analysis)

Instructor: Kevin Wedeward, office: Workman 221, phone: 835-5708, e-mail:, web-page:

Class Time/Place: TR 09:00am-10:15am in Workman 117

Office Hours: TWR 10:30am-12:00pm

Textbook: Either edition below will work for the course.

Prerequisites: Senior or graduate student status, and consent of instructor.

Description: EE 581 (Power System Analysis) is intended for advanced engineering students interested in learning the principles of power system behavior, and methods for computer-based modeling, simulation and analysis.


  1. Review of phasors, power and three-phase circuits - Chapter 2
  2. Transmission line parameters - Chapter 4
  3. Steady-state operation of transmission lines - Chapter 5
  4. Transformers and per-unit system - Chapter 3
  5. Power flow - Chapter 6
  6. Power distribution - Chapter 14
  7. Power system controls - Chapter 11
  8. Transient stability - Chapter 13
  9. Symmetrical components and unbalanced behavior - Chapter 8 and 9


Reading Assignments:


  1. Problems 2.3, 2.10, 2.30, 2.43, 2.52
  2. Problems 4.3, 4.5, 4.8, 4.14
  3. Problems 4.28 (0.25 Ohm/mi/phase), 4.32 (1.33x10^-11 F/m, j5x10^-6 S/km), 4.18 (1.34x10^-6 H/m, 0.506 Ohm/km), 4.39 (8.57x10^-12 F/m, j3.23x10^-6 S/km, 4.29x10^-12 kA/ Phase), 4.25 (Cardinal, 0.03 Ohm/mi, 0.52 Ohm/mi, 4040A), 4.44 (125x10^3 Ohm mi)
  4. Problems 3.4 (2300 V, 0.53+j0.4 Ohm, 53+j40 Ohm, 64 kW, 48 kVAR), 3.9 (243.8/_-4.67deg V, 2.54%)
  5. Problems 3.23 (G: j0.2, T1: j0.2, T2: j0.15, T3: j0.16, T4: j0.2, M: j0.25, L1: j0.1, L2: j0.54, Load: 0.95+j1.27), 3.28 (G1: j2, G2: j1, T1: j0.25, T2: j0.136, Line: 0.054+j0.217, M: can't say much other than 0.25puVA, 0.833puV)
  6. Problems 5.1 a) A=D=1 p.u., C=0 S, B=9.74/_60.8deg Ohms or 11.69/_60.8deg Ohms, b) VSLL=35.45 kV or 35.96 kV, c) VSLL=33.3 kV or 33.4kV; 5.9 a) A=D=0.99/_0.1deg p.u., B=51.1/_82.11deg Ohms, C=3.22e-4/_90.0deg S, VSLL=262 kV, %VR=21.2%, b) VSLL=236.6kV, %VR=9.43%, c) VSLL= 205.9kV, %VR=-5.6%; 5.16 (z=0.02+j0.335 Ohm/km, y=j4.807 uS/km) a) Zc=264.4/_-1.7deg Ohm, b) gamma*l=0.0113+j0.381 p.u., c) A=D=0.929/_0.258deg p.u., B=98.3/_86.7deg Ohm, C=1.405/_90.1deg mS; 5.24 Z'=5.673+j98.09 Ohm, Y'/2=6.37e-7+j7.294e-4 S, Z=6+j100.5 Ohm, Y/2=j7.211e-4 S, how much difference is there between these?
  7. Problems 5.31 a) beta=0.00126 rad/km, Zc=290.4 Ohm, v=2.994e5 km/s, lambda=4990 km, b) VsLN=356.5/_16.1deg kV, |VsLL|=617.5 kV, Is=902.3/_−17.9deg A, Ss3ph=800 + j539.7 MVA, %VR=32.9%; 5.32 a) 400kV, b) 1167 MW; 5.40 a) 2397.5 MW, b) Qr=-2358 MVAR delivered, pf = 0.713 lead
  8. Lectures 1 and 2 with homework from chapter 6.
  9. PDF file with details of problems 14.8 a) IOA=1.673 kA per phase, IFA=2.092 kA per phase, IFOA=2.719 kA per phase b) Ztran=0.2 pu c) Isc=20.91 kA/phase; 14.12 (answers in handout).

Programming Projects:

  1. Equivalent pi-model of transmission lines
    1. Line parameter calculator - Write a program to compute the resistance R (Ohm/km, Ohm/mi), inductance L (H/km, H/mi), capacitance C (F/km, F/mi), series impedance z = R + jwL (Ohm/km, Ohm/mi) and shunt admittance y = G + jwC (S/km, S/mi) all in per unit length of a three-phase, completely transposed transmission line. Inputs will be details of the geometry of the phases and bundles as well as characteristics of the conductors found in the ACSR table. Test your calculator on the lines in problems 4.18, 4.24, 4.25 and example 4.5.
    2. Equivalent pi circuit calculator - Write a program to compute the equivalent pi circuit (Z', Y'/2) for a transmission line. Inputs will be series impedance z, shunt admittance y, and length of the line.
    3. Per unit equivalent pi circuit calculator - Write a program to compute the per unit equivalent circuit (Z', Y'/2 in per unit) of a transmission line. Inputs will the the pi circuit series impedance Z' and shunt admittance Y'/2, three-phase base power Sbase3phi, and base line-to-line voltage VbaseLL.
    4. Line loadability calculator - Write a program to compute the practical line loadability PRprac and theoretical maximum power PRmax that can delivered by a transmission line to the receiving end, as well as the thermal limit PRtherm of the transmission line. Inputs will be line-to-line voltages at sending and receiving ends, series impedance Z', propagation constant gamma, angle across the line, approximate current-carrying capacity, power factor of the load, and number of conductors per bundle.
    5. Complete line calculator - Write a wrapper program to integrate the programs/functions above such that all the characteristics can be computed for a given transmission line with minimal inputs. Outputs should be z, y, Z', Y'/2, Z'pu, Y'/2pu, PRprac, PRmax, PRtherm.
  2. Admittance matrix builder and power-flow solver for power systems - due 05/09/2012
  3. Final design/analysis project - due 05/09/2012

Lectures/Topics and Presenters:

  1. Chapter 2 - Kevin (~2 lectures)
  2. Chapter 4 - Lucas (~5 lectures)
  3. Chapter 3 - Edward (~4 lectures)
  4. Chapter 5 - David
  5. Chapter 6 - Brian and Ian
  6. Chapter 14 - Charles