Lecture Methods of Electric power systems analysis - Lesson 9: Sparse systems, advanced power flow provide students with knowledge about Tinney scheme 2; coding Tinney 2; Tinney scheme 3; sparse forward substitution with a permutation vector; sparse vector methods; factorization paths; path table and path graph; computation with complex and blocked matrices; . | ECEN 615 Methods of Electric Power Systems Analysis Lecture 9 Sparse Systems Advanced Power Flow Prof. Tom Overbye Dept. of Electrical and Computer Engineering Texas A amp M University overbye@ Announcements Homework 3 should be done before the first exam but need not be turned in Start reading Chapter 7 the term reliability is now often used instead of security First exam is in class on Thursday Oct 1 Distance learning students do not need to take the exam during the class period Closed book notes. One by 11 inch notesheet and calculators allowed Last s years exam is available in Canvas 1 Tinney Scheme 2 The Tinney Scheme 2 usually combines adding the fills with the ordering in order to update the valence on-the- fly as the fills are added As before the nodes are chosen based on their valence but now the valence is the actual valence they have with the added lines fills This is also known as the Minimum Degree Algorithm MDA Ties are again broken using the lowest node number This method is quite effective for power systems and is highly recommended however it is certainly not guaranteed to result in the fewest fills . not optimal 2 Tinney Scheme 2 Example Consider the previous network 1 2 3 8 7 6 4 5 Nodes 1 2 3 are chosen as before. But once these nodes are eliminated the valence of 4 is 1 so it is chosen next. Then 5 with a new valence of 2 tied with 7 followed by 6 new valence of 2 7 then 8. 3 Coding Tinney 2 The following slides show how to code Tinney 2 for an n by n sparse matrix A First we setup linked lists grouping all the nodes by their original valence vcHead is a pointer vector If a node has no connections its incidence is 0 Theoretically mvValence should be n-1 but in practice a much smaller number can be used putting nodes with valence values above this into the vcHead mvValence is 4 Coding Tinney 2 cont. Setup a boolean vectors chosenNode to indicate which nodes are chosen and BSWR as a sparse working row .
