EE 521: Analysis of Power Systems and EE 523: Power System Stability and Control

Fall 2022 | Noel Schulz and Spring 2023 | Mani V. Venkatasubramanian

MATLAB implementations for the two courses at Washington State University, Pullman.

Power Flow Algorithms added:

• Newton Raphson Power Flow NRPF
• Decoupled NRPF
• Fast Decoupled NRPF
• Continuation Power Flow

Linear System Solving Algorithms added:

• LU Factorization

Textbook solved examples added:

• koth3: A 3 bus system from Kothari and Nagrath's Modern Power System Analysis.
• crow3: The 3 bus system in Example 5.9 from Mariesa L Crow's Computational Methods for Electric Power Systems.
• ieee11: Kundur's 2 Area 11 bus system as given in Example 12.6, Pg 813 of Power System Stability and Control by Prabha Kundur.

Data Strucutures and Algorithms Sparsified:

• YBus
• Jacobian J
• Computation of Mismatches $[\Delta P ;\Delta Q]$.
• sparmat and sparvec can convert matrices and vectors in compressed format (nrow, ncol, val) or (nIndex, val) into the sparse format [nnz, N]. All data structures are tables.

Stability and Control Scripts for the Kundur 4 Machine 2 Area System:

Model Type	Dynamic Initialization	Small Signal Stability Analysis	Transient Stability Analysis
Type 3 aka Classical Model	✅	✅	✅
Type 2 with AVR and Governor	✅	🟨	🟨
Type 1 with AVR and Governor	✅	✅	🔴

Legend:

Symbol	Remark
✅	Implemented and performing as expected
🟨	Implemented but NOT performing as expected
🔴	NOT implemented

Yet to implement:

• Sparse LU Factorization
• [OPTIONAL] Bus Changing (PV to PQ)
• [OPTIONAL] DC Power Flow

Caveats:

• Currently the NRPF algorithm does NOT support bus type conversion. This obviously affects convergence for bigger bus systems, but fortunately does not seem to affect the ieee14 and ieee30 bus systems.
• Currently it converges for the ieee14 and ieee30 bus systems, has trouble with ieee57 bus system for a couple of buses and blows up for the ieee118 bus system.
• $N$ bus systems with individual bus numbers $i$ outside the range of natural numbers from $[1, N]$ are currently NOT supported. The ieee300 bus system is one such system.