Site Selection Using PENS Power Resilience Indexes

Vol 1., No. 11 September 26, 2023   Scott Clearwater, Gridmetrics, Inc.® s.clearwater-c@gridmetrics.io

1. Introduction

Site selection is one of the most important tasks in setting up a new business location. One of the most important aspects of site selection, and one often taken for granted, is the access to reliable electrical power that is resilient across seasons and environmental events. Gridmetrics national-level suite of voltage sensors provides the best view into power resilience for site selection via its proprietary PENS Resilience Indexes.

The PENS Resilience Indexes have been described elsewhere[1]. Briefly, these indexes capture different aspects of historical voltage readings. Specifically, the indexes measure fraction of outage time (PENS Outage Index, POI), probability of voltage lying within a pre-defined range around a reference value (PENS Reliability Index, PRI), dispersion of voltages (PEN Stability Index, PSI), a non-linear function of deviation from a reference value (PENS Quality Index, PQI), and the fraction of voltage changes in a time period (PENS Volatility Index, PVI). While these measures have some correlation their overall comprehensiveness is able to tease out nuances in voltage behavior. For example, the stability index could be very high (meaning small magnitude of fluctuations), but the volatility index could be very high (meaning a lot of small voltage jitter).

2. Analysis

2.1 The Data

The data used in this analysis was from the more than 3 years of Gridmetrics data, May 2020 through July 2023. The index data was calculated on a daily basis and aggregated by month. Typically, about 280k sensors were involved overall. Twenty metro areas have high coverage by Gridmetrics sensors and these were used for comparative rankings of the regional indexes. These metro areas are: Atlanta, Baltimore, Boston, Chicago, Denver, Detroit, Houston, Indianapolis, Las Vegas, Miami, Minneapolis, Philadelphia, Phoenix, Pittsburgh, Portland, Sacramento, San Francisco, San Jose, Seattle,  and Washington DC. With the exception of Las Vegas all the metro areas were present in the entire sampling period.

Thirteen other areas were chosen as potential sites. The site areas were further divided into three polygonal areas denoted Small, Medium, and Large. With the exception of Area 9 all the test areas were present throughout the sampling period. All the potential site areas were included by some month in 2020. In general, any enclosed area can be used for such a site selection study as described here. For example, a circular area around a defined point or one or more USNG cells, or a polygon of arbitrary, but well-defined, shape. The caveat is that if there are too few sensors in the area then it could be more prone to anomalous events that might mask otherwise reasonable behavior. By the same token, it could be that the small number of sensors are truly representing anomalies in their area. The issue of the number of sensors is discussed in more detail below (c.f., § 2.7).

2.2 Weighting of Indexes

The table below summarized the results of the analysis. The final column gives the average ranking using all the indexes equally weighted. In general, any weighting could be used if a particular user wanted to emphasize or de-emphasize particular indexes and different weightings could significantly affect the overall PXI rank.

2.3 Relative Rankings versus Metro Areas

For some cities the Small, Medium, and Large had significant influence on the index ranking, namely the size of the sensor footprint significantly influenced the ranking. One interpretation of this observation is that the areas have different upstream substations. It could also mean that there are noticeable localized disturbances in these areas. Similarly, for cases where there is little difference in the indexes with size the substations are likely the same and local influences are negligible.

Table 1. Average Rankings of PENS Resilience Indexes versus 20 Metro Areas

Area	POI avg rank	PRI avg rank	PSI avg rank	PQI avg rank	PVI avg rank	PXI avg rank
Area 1 Small (22)	4.44	7.51	2.21	2.44	4.85	4.29
Area 1 Medium (179)	8.46	10.54	5.69	3.87	1.80	6.07
Area 1 Large (611)	11.18	5.54	2.74	2.92	1.41	4.76
Area 2 Small (0)	n/a	n/a	n/a	n/a	n/a	n/a
Area 2 Medium (28)	6.62	3.41	3.36	6.08	11.39	6.17
Area 2 Large (65)	8.62	3.31	3.72	7.56	4.77	5.60
Area 3 Small (5)	3.00	2.90	4.72	9.67	1.03	4.26
Area 3 Medium (49)	9.36	8.69	13.44	15.59	10.08	11.43
Area 3 Large (60)	7.54	4.67	12.00	13.28	3.97	8.29
Area 4 Small (5)	2.44	11.80	12.74	18.85	12.03	11.57
Area 4 Medium (47)	3.85	11.69	13.44	18.90	16.80	12.93
Area 4 Large (267)	5.05	15.31	15.72	20.49	12.74	13.86
Area 5 Small (1)	1.08	1.77	4.33	2.54	10.69	4.08
Area 5 Medium (14)	4.85	2.72	11.69	3.03	6.77	5.81
Area 5 Large (69)	5.85	5.69	14.90	6.31	8.62	8.27
Area 6 Small (228)	8.49	5.97	5.62	2.26	4.59	5.39
Area 6 Medium (615)	9.46	6.97	5.90	2.41	3.80	5.71
Area 6 Large (1471)	12.90	7.69	7.18	3.33	3.44	6.91
Area 7 Small (6)	1.49	2.69	1.97	2.64	1.00	1.96
Area 7 Medium (33)	5.82	2.49	2.59	1.49	2.67	3.01
Area 7 Large (175)	9.69	6.87	3.74	2.36	3.64	5.26
Area 8 Small (8)	2.00	3.56	8.62	3.23	5.03	4.49
Area 8 Medium (29)	5.23	2.85	10.77	4.03	8.05	6.19
Area 8 Large (346)	8.85	4.00	7.97	3.54	7.21	6.31
Area 9 Small (42)	7.80	5.92	7.74	4.13	7.82	6.68
Area 9 Medium (210)	10.33	10.77	8.39	4.05	4.74	7.66
Area 9 Large (560)	11.21	11.31	7.54	6.23	6.85	8.63
Area 10 Small (16)	2.56	8.25	9.83	3.44	13.69	7.56
Area 10 Medium (62)	5.22	9.19	11.56	5.25	17.11	9.67
Area 10 Large (166)	6.31	9.75	13.25	5.44	16.64	10.28
Area 11 Small (6)	1.62	1.85	2.46	2.26	19.77	5.59
Area 11 Medium (38)	3.05	3.77	6.62	9.33	15.05	7.56
Area 11 Large (135)	6.26	8.21	8.82	12.15	12.74	9.64
Area 12 Small (23)	4.82	14.46	6.69	13.51	19.10	11.72
Area 12 Medium (91)	8.72	16.90	9.23	16.15	18.21	13.84
Area 12, Large (231)	8.36	17.46	10.23	17.69	14.77	13.70
Area 13 Small (22)	9.28	3.56	5.26	3.80	1.03	4.59
Area 13 Medium (240)	16.05	7.28	9.21	10.36	7.03	9.99
Area 13 Large (704)	18.03	6.85	7.36	8.08	15.49	11.16

2.4 Ranking by Fraction of Time Greater than Median

Another way of ranking is to count the fraction of time that the index is above the median (with a higher rank, i.e., < 11 (or 10.5 for some of the 2020 data)) . This is shown in Table 2. Overall, the highest ranked areas, judging from rank with at least 10 sensors, were Area 1 (Small), Area 7(Medium), and Area 13(small). The worst areas are Area 12(Large), Area 4(Large), and Area 13(Large). Area 12 is near Detroit which is one of the worst metro areas and Area 4 is near Chicago, another of the worst metro areas.

Note the significant effect on enlarging the area for Area 13 which was both in the best (Small) and worst (Large) categories. Also, note the general tendency that the larger the area the worse the ranking tended to be, at least for the areas studied here.

Table 2. Fraction of time above the median

Areas	POI	PRI	PSI	PQI	PVI	PXI
Area 1 Small (22)	0.795	0.667	0.949	0.923	0.974	0.974
Area 1 Medium (179)	0.590	0.487	0.744	0.872	1.000	0.923
Area 1 Large (611)	0.385	0.795	1.000	0.923	1.000	0.974
Area 2 Small (0)	n/a	n/a	n/a	n/a	n/a	n/a
Area 2 Medium (28)	0.667	0.897	0.949	0.769	0.385	0.897
Area 2 Large (65)	0.564	0.923	0.949	0.718	1.000	1.000
Area 3 Small (5)	0.897	0.923	0.923	0.590	1.000	1.000
Area 3 Medium (49)	0.538	0.641	0.333	0.179	0.590	0.436
Area 3 Large (60)	0.641	0.769	0.462	0.282	1.000	0.795
Area 4 Small (5)	0.923	0.436	0.359	0.077	0.333	0.487
Area 4 Medium (47)	0.821	0.462	0.333	0.051	0.000	0.256
Area 4 Large (267)	0.821	0.231	0.128	0.000	0.282	0.128
Area 5 Small (1)	1.000	0.974	0.923	0.949	0.436	1.000
Area 5 Medium (14)	0.795	0.923	0.410	0.949	0.744	0.872
Area 5 Large (69)	0.769	0.821	0.179	0.795	0.769	0.769
Area 6 Small (228)	0.641	0.769	0.821	0.974	0.974	0.923
Area 6 Medium (615)	0.538	0.692	0.769	0.974	0.974	0.949
Area 6 Large (1471)	0.308	0.718	0.744	0.949	0.974	0.949
Area 7 Small (6)	0.974	0.949	0.949	0.923	1.000	1.000
Area 7 Medium (33)	0.718	0.974	0.897	1.000	1.000	1.000
Area 7 Large (175)	0.538	0.718	0.846	0.974	1.000	0.949
Area 8 Small (8)	0.949	0.872	0692	0.949	0.872	1.000
Area 8 Medium (29)	0.769	0.974	0.513	0.872	0.667	0.949
Area 8 Large (346)	0.590	0.923	0.769	0.949	0.846	0.872
Area 9 (42)	0.615	0.769	0.744	0.872	0.769	0.897
Area 9 (210)	0.487	0.513	0.641	0.897	0.974	0.872
Area 9 (560)	0.462	0.487	0.744	0.744	0.923	0.718
Area 10 Small (16)	0.889	0.667	0.611	0.944	0.222	0806
Area 10 Medium (62)	0.778	0.583	0.500	0.833	0.056	0.694
Area 10 Large (166)	0.778	0.500	0.333	0.833	0.083	0.583
Area 11 Small (6)	0.974	0.974	0.923	0.949	0.026	1.000
Area 11 Medium (38)	0.897	0.897	0.821	0.590	0.077	0.769
Area 11 Large (135)	0.744	0.641	0.615	0.308	0.282	0.692
Area 12 Small (23)	0.821	0.308	0.795	0.385	0.000	0.385
Area 12 Medium (91)	0.564	0.179	0.615	0.205	0.000	0.205
Area 12 Large (231)	0.615	0.128	0.487	0.128	0.000	0.179
Area 13 Small (22)	0.590	0.872	0.872	0.923	1.000	0.949
Area 13 Medium (240)	0.128	0.718	0.615	0.538	0.974	0.667
Area 13 Large (704)	0.000	0.718	0.769	0.718	0.000	0.462

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2.5 Sample Time Series of Index Ranks

Fig. 1 shows the three best areas and three worst areas based on PXI value rank. For the best areas the indexes tend to cluster near the top and for the worst areas the index values tend toward the bottom as one would expect.

2.6 Direct Area Rankings versus Metro Areas and Area-to-Area

Table 3 shows the overall PXI rank by area size and with respect to the metro areas and, separately, with respect to the other specific areas. The number in parentheses is the number of sensors involved. To look for consistent performers the cities should not move up or down too much based on the size of the area. For example, Area 7 and Area 1 on the highly-ranked side and Area 12 and Area 4 on the lower-ranked side. Overall, there was not much change in rankings going from the large metro area comparisons to the area comparisons.

Table 3. Ranks versus Metro and Areas by Size.

Rank	Rank vs Metros			Rank vs Areas
	Small	Medium	Large	Small	Medium	Large
1	Area 7(6)	Area 7(33)	Area 1(611)	Area 7(6)	Area 7(33)	Area 1(611)
2	Area 5(1)	Area 6(615)	Area 7(175)	Area 5(1)	Area 1(179)	Area 7(175)
3	Area 3(5)	Area 5(14)	Area 2(65)	Area 1(22)	Area 5(14)	Area 2(65)
4	Area 1(22)	Area 1(179)	Area 8(346)	Area 11(6)	Area 2 (28)	Area 6(1471)
5	Area 8(8)	Area 2 (28)	Area 6(1471)	Area 3(5)	Area 6(615)	Area 8(346)
6	Area 13(22)	Area 8(29)	Area 5(69)	Area 13(22)	Area 8(29)	Area 3(60)
7	Area 6 (228)	Area 11(38)	Area 3(60)	Area 8(8)	Area 9(210)	Area 5(69)
8	Area 11(6)	Area 9(210)	Area 9 (560)	Area 6(228)	Area 11(38)	Area 9 (560)
9	Newark, C(42)	Area 10(62)	Area 11(135)	Area 10(16)	Area 10(62)	Area 10(166)
10	Area 10(16)	Area 13(240)	Area 10(166)	Area 9(42)	Area 13(240)	Area 11(135)
11	Area 4 (5)	Area 3(49)	Area 13(704)	Area 4(5)	Area 3(49)	Area 13(704)
12	Area 12(23)	Area 4 (47)	Area 12(231)	Area 12(23)	Area 4 (47)	Area 4(267)
13	*	Area 12(91)	Area 4(267)	*	Area 12(91)	Area 12(231)

2.7 Affect of the Number of Sensors

Another issue affecting the overall power resilience is the number of sensors within an area. As seen in the tables above there are some of the “Small” areas that have less than ten sensors. Given the lack of knowledge of the actual power grid topology it could be that none of those sensors are on the same feeder line as the specific site location requested. This scenario is more likely with a smaller number of sensors, thus a higher number and density of sensors is preferred to more likely cover the area in question. By the same token it could be that the small number of sensors are on the same feeder line as the desired location making those sensors particularly effective in assessing power resilience versus a large number of less correlated sensors. In general, we desire correlated sensors that are on the same feeder line as the site in question. However, as mentioned above we have no knowledge of the actual grid topology and so the highly correlated sensors could completely miss the desired site.

The correlation between different index readings over an area can be calculated. This gives a way of determining the effective statistical sample size. A smaller number of sensors in a small area are more likely to be correlated index values, thus reducing the effective statistical number of sensors. A larger number of sensors over a larger area will have a lower correlation of index values, thus increasing the effective statistical number of sensors, but at the expense of washing out the power resilience index values for the area of interest. Using the correlations we can reduce the statistical error to a given level. However, even with this constraint on the statistical level, the systematic error of not knowing where the sensors actually are relative to the site grid topology eventually drives the overall uncertainty in the method.

Fortunately, given all the caveats about the number of sensors and their correlation with the desired site, observationally the area size is often a small effect for the best and worst rated areas meaning that one can be fairly confident in the index values for reasonably sized areas. We look into this size effect in more detail next.

Fig. 2 shows the number sensors(left) in the Small area versus the sum of absolute rank changes from the Small to the Medium and Large areas and the number of 1km x 1km USNG cells(right) in the Small area versus the same sum of absolute rank change. The smaller the sum of the absolute rank change the more stable the ranks are with respect to area size. With the exception of a few outliers most of the areas had rank changes of 3 or less even as the sensor count or number of USNG cells varied by up to an order of magnitude. Thus, even small areas have similar power resilience ranks as the area is scaled up by an order of magnitude in the number of sensors. For the outliers (Area 6, Area 5, Area 13, and Area 3), there is less confidence in the Small area being representative of the site area. This may be sufficient to reject these locations as potential sites because of their non-scaling of power resilience which gives doubt as to the actual level of power resilience. Again, this may be due to grid topology or local power usage or other environmental effects.

With power resilience scalability, while there is no guarantee that the smaller area is on the same feeder line as the site in question, it does add support for the small area being representative of the power resilience in the site area. Operationally, the scalability of power resilience can be used to determine a smallest size of a representative area. In other words, if the power resilience ranks are consistent over a wide range of areas, then the smallest area is likely representative of the power resilience in the desired area. This provides a good estimate of power resilience that can be obtained without grid knowledge.

3. Discussion

In this report we have given different means of ranking different potential corporate sites based on power resilience rankings versus twenty metro areas throughout the US as well as a site versus site comparison. A given user may prefer one over the others, but in general areas consistently ranking highly or lowly across different analyses gives confidence in their rank even without knowledge of the grid topology.

Limitations based on the number of sensors involved was deeply delved into as was user-specific weightings of the various indexes, both of which can significantly affect rankings. Overall, the methodology gives a comprehensive analysis of power resilience for site recommendation.

[1] https://gridmetrics.io/resources/

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