ECE 530: Analysis Techniques for Large-Scale Electric Systems

Fall 2022

Topics

Weeks 1-7: Static system analysis

• Static system modeling: motivation and canonical problems; the single-line per-unit phasor model with PV, PQ, slack buses; underlying assumptions and their real-world limitations
• Power flow and voltage stability analysis: the nonlinear and linearized power flow solutions; formulation via modified nodal analysis; solution of sparse linear equations; Newton-Raphson solution of nonlinear equations; continuation and homotopy methods
• State estimation and parameter estimation: formulation as nonlinear least-squares; Gauss-Newton solution of nonlinear least-squares; equivalence with power flow and Newton-Raphson; convergence guarantees
• Economic dispatch: formulation of optimal power flow problem and solution via KKT equations; Lagrange multipliers as the shadow price of electricity; connections to power flow and state estimation

Weeks 8-12: Dynamic system analysis

• Dynamic system modeling: motivation and canonical problems; basic synchronous generator models; time-scale decoupling of dynamic phenomena; modeling switching events
• Transient stability analysis: solution of differential-algebraic systems; handling of stiff differential equation systems; accuracy and numerical stability issues
• Small signal stability analysis: Modal analysis of large sparse systems; iterative computation of dominant eigenvalues and eigenvectors

Weeks 13-14: Special topics

• Special topics: formulation and solution of unit commitment as a mixed-integer linear program; convex relaxation approaches via semidefinite programming (SDP); exponential and geometric integration; Krylov subspace methods; model order reduction applications in power systems and electrical machines

Texts

We will aim to cover all chapters in Part II of Milano. The book is available in pdf form via SpringerLink with no purchase required. Crow is a good reference for the mathematical details, though we will also be covering the same details in our lecture notes.

• F. Milano, Power System Modelling and Scripting, Springer. PDF available at Springerlink.
• M. Crow, Computational Methods for Electric Power Systems, CRC press.

Prerequisites

Prior knowledge in power systems, circuit analysis, linear algebra, multivariate calculus. Programming experience in MATLAB and/or Python. The following texts will be helpful as backup references:

• D. Glover, M. Sarma, T. Overbye, Power System Analysis & Design, Cengage Learning.
• S. Boyd and L. Vandenberghe, Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares, Cambridge University Press. PDF available at Stanford.
• G. Strang, Introduction to Linear Algebra, Wellesley-Cambridge Press.

Evaluation

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