Sign up for a presentation slot. Deadline 11/30.

ECE 530: Analysis Techniques for Large-Scale Electric Systems

Fall 2020 [Go to Calendar & Materials] [Materials]

Richard Y. Zhang (ryz at illinois dot edu)
Office hours:
By appointment. Please email.
Section A:
Tue & Thu 2:00pm -- 3:20pm TR 2:00pm-3:20pm
Section ONL:
Tue & Thu 2:00pm -- 3:20pm TR 2:00pm-3:20pm
Piazza for class discussions.
Gradescope for homework and project (code: 92NP6K).
Compass2g for participation points.


Overview of power system analysis. Static power system models. Linear equations. Nonlinear equations. Linear and nonlinear least-squares. Exploiting sparsity. Dynamic power system models. Numerical integration.

Prerequisites. Circuit analysis. Linear algebra. Basic multivariate calculus. Some prior programing experience in MATLAB / Octave.

Texts. No required texts. I will be adding readings here as the course progresses. The following textbooks may be helpful.


Five homework assignments, roughly one every two weeks, worth 10% each. Release, submission, and grading through Gradescope.
We will simulate a conference paper submission to the IEEE Power & Energy Society General Meeting (PESGM), the premier conference on power systems research. Release, submission, and grading through Gradescope.
Your paper was selected as 1 of 60 best papers submitted to the conference! You will give a spotlight 8-minute presentation at one of our simulated PESGM Best Conference Papers Session.
The best presentation of each session, as decided by a panel of your peers, will receive a Best-of-the-Best Award worth 2% bonus.
Sign up for a presentation slot. Deadline 11/30.
0.5% for each endorsed question or answer or note, for up to 5% max.
1% in class and during project presentations, for up to 5% max.
10% bonus


Grading is on an absolute scale. You will be compared against the following performance standard, and not to other students.

A: 88% and up (A- 88-90%)
B: 78% to 88% (B+ 85-88%, B- 78-80%)
C: 67% to 78% (C+ 75-78%, C- 67-70%)
D: 55% to 67% (D+ 64-67%, D- 55-58%)

We reserve the right to adjust these numbers downward (in the students' favor) but guaranteed that they will not be raised.

Calendar & Course Materials [Back to top] [Top]

Future lecture schedules are tentative and are provided for your information only.

Tue 8/25
Topic 1: Overview of power system analysis.
Tue 8/25
[Video] [Slides] [Notes] Orientation & Logistics. What is the power system problem and why is it hard? Desire for reliability motivates interconnections.
Thu 8/27
[Video] [Notes] Desire for efficiency motivates AC. Power flow solves the coordination problem and unlocks economies of scale in both efficiency and reliability. The basic mechanics of operating a modern power system.
Tue 9/1
[Video] [Notes] Static analysis (power flow, voltage stability) and how they fit into existing operating practices. Maximizing efficiency: Planning vs scheduling vs real-time operations. Maximizing reliability: N-1 criterion.
Thu 9/3
[Video] [Notes] Optimization vs control vs analysis. Economic dispatch and unit commitment. Protection basics. Dynamic analysis (transient stability, small signal stability). Operating reserves.
Mon 9/7
Labor Day (all-campus holiday)
Tue 9/8
Topic 2: Power system models. Homework 1 out.
Tue 9/8
[Video] [Slides] [Notes] Review: Circuit analysis, inductors and capacitors, phasors, power circuits, three-phase power.
Thu 9/10
[Video] [Notes] Review: three-phase power, balanced sequence, per unit system.
Tue 9/15
[Video] [Notes] The complete power system static model. The bus admittance matrix and the idea of stamps.
Thu 9/17
[Video] [Notes] The simple power system dynamical model. Steady-state reduction to AC power flow. The linearized static model.
Mon 9/21
Topic 3: Linear equations. Homework 1 due. Homework 2 released.
Tue 9/22
[Video] [Notes] Review: Multivariate calculus. Linearized power flow equations and "DC" power flow.
Thu 9/24
[Video] [Notes] Complete "DC" power flow model: application, derivation, and underlying assumptions.
Tue 9/29
[Video] [Notes] Review: Linear algebra. Gaussian elimination and triangular factors.
Tue 10/6
[Video] [Notes] Derivation of the recursive LU formula. Operation count.
Thu 10/8
[Video] [Notes] Exploiting sparsity via case study: DC power flow.
Mon 10/12
Topic 4: Nonlinear equations. Homework 2 due. Homework 3 released. Project released.
Tue 10/13
[Video] [Notes] Newton-Raphson method for nonlinear equations. The power of quadratic convergence.
Thu 10/14
[Video] [Notes] Application of Newton-Raphson to AC power flow. Interpretation as a sequence of DC power flow. "Decoupled" and "Dishonest" power flow.
Tue 10/20
[Video] [Notes] Modern implementations of the AC power flow equations.
Thu 10/22
[Video] [Notes] Power flow Jacobian via complex matrix calculus. Linear least-squares. The normal equation.
Mon 10/26
Topic 5: Least-squares and nonlinear least-squares. Homework 3 due. Homework 4 released.
Tue 10/27
[Video] [Notes] Motivating least-squares for the power system. Linear least-squares is the "simplest" optimization problem. The idea of using linear least-squares to solve nonlinear least-squares.
Thu 10/29
[Video] [Notes] Making Gauss-Newton robust via backtracking line search.
Tue 11/3
Election Day (all-campus holiday)
Thu 11/5
[Video] [Notes] Relating nonlinear least-squares back to nonlinear equations.
Mon 11/9
Topic 6: Numerical integration. Homework 4 due. Homework 5 released.
Tue 11/10
[Video] [Notes] Wrap-up trust-region methods. Levenberg-Marquardt algorithm.
Thu 11/12
[Video] [Slides] ODE solvers. Implicit vs explicit methods. Accuracy vs stability vs cost trade-off. Circuit interpretations of forward and backward Euler.
Tue 11/17
[Video] [Notes] Swing equation. Separation of time-scales. Generator models.
Thu 11/19
[Video] [Notes] Transient stability formulation.
Sat 11/21 - Sun 11/29
Thanksgiving break
Tue 12/1
Course summary.
Thu 12/3
Presentation Session 1.
Tue 12/8
Presentation Session 2.
(c) 2020 R. Y. Zhang.