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

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

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

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

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

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

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

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