 | Vol 1., No. 8 July 12, 2023 Scott Clearwater, Gridmetrics, Inc.® s.clearwater-c@gridmetrics.io |
Imagine two piles of dirt. Then ask how much moving of dirt does it take to make the first pile of dirt exactly like the second pile of dirt? That is the idea behind the “earth-mover distance” also known as the Wasserstein-distance or Kantrovich-distance in one-dimension. Intuitively the more earth you have to move to make the piles the same the more they differed in the first place. This idea can be applied to the notion of energy equity for particular regions. In particular, consider the distribution of values for some energy resilience index for a region over some period of time (Fig. 1). We can compare this to the “perfect pile” where all the values of the index are at the maximum value of that index. In other words, the more earth that needs to be moved the more remedial work needs to be done on that region to bring it to a perfect pile. See Fig. 1 below which shows that the earth-moving distance for the left pile is greater than the right pile.
Fig. 1 Moving earth to make one distribution look like a perfect pile. Moving the left pile into the perfect pile takes more movement than for the right pile.
As a concrete example, using any of the PENS energy resilience indexes we can measure the earth-mover distance for a metro area. In this case the metro area’s index values will be spread out and we want to know how much “earth” it takes to move the distribution to the ideal one, the one that is a spike at the maximum value of the index. By ranking the metro areas by their earth-moving distance we can see which areas are most in need of some sort of remedial action to bring them more in line with the other areas and thus improve energy equity.
Table 1 shows the rank by earth-moving distance for twenty metro areas well-covered by Gridmetrics sensors during 2021-2022. The higher the rank the better, or the closer the distribution is to the ideal and therefore in less need of remediation. If one has been reading my previous blogs one will notice the same suspects in need of remedial action appear. The overall rank is based on the sum of the ranks of indexes used, the PENS [Outage, Reliability, Stability, Quality, Volatility ] Indexes.
| Rank | POI (Outages) | PRI (Reliability) | PSI (Stability) | PQI (Quality) | PVI (Volatility) | Overall (by Rank) |
| 1 | Las Vegas | Seattle | Portland | Portland | Houston | Portland |
| 2 | Phoenix | Portland | Atlanta | Las Vegas | Portland | Atlanta |
| 3 | Miami | Baltimore | Seattle | Seattle | Baltimore | Las Vegas |
| 4 | Chicago | Denver | San Francisco | Atlanta | Philadelphia | Seattle |
| 5 | Indianapolis | Atlanta | Sacramento | Houston | Las Vegas | Denver |
| 6 | Minneapolis | Pittsburgh | San Jose | Sacramento | Miami | Sacramento(tie1) |
| 7 | Sacramento | Minneapolis | Houston | Phoenix | Atlanta | Houston(tie1) |
| 8 | Philadelphia | Washington DC | Indianapolis | Miami | Washington DC | Miami |
| 9 | Denver | Miami | Denver | Minneapolis | San Jose | Philadelphia(tie2) |
| 10 | Baltimore | Philadelphia | Washington DC | San Jose | Seattle | Baltimore(tie2) |
| 11 | Atlanta | Las Vegas | Philadelphia | Denver | Denver | Washington DC |
| 12 | Washington DC | Houston | Detroit | Washington DC | Pittsburgh | Minneapolis(tie3) |
| 13 | Boston | Boston | Minneapolis | Pittsburgh | Sacramento | San Jose(tie3) |
| 14 | San Francisco | Sacramento | Las Vegas | San Francisco | Chicago | Phoenix(tie4) |
| 15 | San Jose | San Jose | Boston | Baltimore | San Francisco | Indianapolis(tie4) |
| 16 | Portland | Indianapolis | Chicago | Philadelphia | Detroit | Pittsburgh(tie4) |
| 17 | Pittsburgh | Chicago | Pittsburgh | Boston | Boston | San Francisco |
| 18 | Detroit | Phoenix | Baltimore | Indianapolis | Indianapolis | Chicago |
| 19 | Seattle | San Francisco | Phoenix | Detroit | Phoenix | Boston |
| 20 | Houston | Detroit | Miami | Chicago | Minneapolis | Detroit |
Note how some metros are quite good in some resilience metrics but poor in others. This is because the PENS resilience indexes, while there is some correlation between them, do in fact capture different dimensions of power resilience and in totality give a broader perspective of power resilience overall.
The point of this blog is that earth-mover distance along with various power resilience indexes can be used as a means to identify who needs the most grid improvement by resilience type and overall. While this blog looked at metro areas, it is just as easy to look at other regions such as counties, zip codes, and USNG 1km x 1km cells.
Learn more about Gridmetrics actionable power intelligence solutions.
