1. Western Electricity Coordinating Council
U of U Stress Metrics
Donald Davies
Western Electricity Coordinating Council

2. Western Electricity Coordinating Council
Criticality Metrics
Criticality – Measures how a line outage affects other lines
Rank of line x is the maximum flow through any other line in per unit of rating after the outage of line x
Degree of line x is the number of other lines that will have a flow above a per unit of rating threshold after the outage of line x
Western Electricity Coordinating Council

3. Vulnerability Metrics
Vulnerability – Measures how outage of other lines affects a line
Rank of line x is the maximum flow through line x in per unit of its rating for the outage of all other lines taken one at a time
Degree of line x is the number of outages of other lines after which line x is loaded above a threshold
Western Electricity Coordinating Council

4. DFAX (Line Outage Distribution Factor Matrix)
The DFAX matrix contains the partial derivatives of flows in lines with respect to outages in other lines. (Sometimes called Line Outage Distribution Factors)
A full loop WECC Case has a very large number of DFAX, ie square of the number of lines in the case. For 20,000 lines, that would be 400,000,000 elements.
Western Electricity Coordinating Council

5. Western Electricity Coordinating Council
DFAX continued
Study limited to the southwest to limit the number of matrix elements.
Western Electricity Coordinating Council

6. Western Electricity Coordinating Council
Metric Comparisons
Compared recent year 5 WECC operating cases, Heavy and light summer, heavy and light winter, high spring for the 4 metrics
Most stressed seasonal operating case – All 4 metrics indicate heavy summer case.
Least stressed seasonal operating case – All 4 metrics indicate light winter case
Heavy Spring has high stress, Heavy winter has medium stress, Light summer has low stress.
Western Electricity Coordinating Council

7. Vulnerability rank vs Demand
Vulnerability increases linearly with the log of demand. The slope of the increase changes at about 38,000 MW of Southwest Demand.
Western Electricity Coordinating Council

8. September 2011 Southwest Outage
Lines from Arizona to southern California had high criticality rank and degree
Low voltage system paralleling them had high vulnerability rank and degree
Western Electricity Coordinating Council