Discovering the Energy Story
Part 2: Multi-Load Characterization
August 8, 2016
Author:
Adriane Q. Wolfe
Principal and Founder
Quinn Energy, LLC
Copyright © 2016 Quinn Energy, LLC
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EXECUTIVE SUMMARY
Power distribution systems provide power to multiple loads at the same time. Because of
this, characterizing the relationships of multiple loads can be of more interest to system
operators and designers than characterizing an individual load. Of particular interest is
identifying and estimating the system peak, which drives capacity requirements.
This white paper is the second part of a series called Discovering the Energy Story. In
Part 1, methods for single-load power analysis were described and demonstrated using
an example residential load 1. This second paper looks at the multi-load power analysis of
a residential neighborhood. It applies approaches defined in Part 1 and expands to multiload specific characterization.
This paper includes load statistics and Coincident Load analysis for the thirty (30)
households in the neighborhood. Coincident Load represents the summation of individual
loads during the same instance in time. The average individual load levels are compared
to Coincident Load levels. Key metrics are assessed with an emphasis on the comparison
of Peak to Average Ratios.
The Peak to Average Ratio significantly decreased as the number of residences that were
summed in the Coincident Load increased. Peak to Average Ratio values were: 24 for
the individual residence average, 6 for the energy center average, and 3 for the entire
neighborhood. In Part 1, the Peak to Average Ratio for the example residence was 41.
The high variance in Peak to Average Ratio reflects a low Coincidence Factor for the
neighborhood residences of 0.2. The low Coincidence Factor and high individual
residence Peak to Average Ratios highlight how critical the selection and application of
load data is in characterizing a system node.
Keywords: multi-load, characterization, coincident load, power, residential, analytics
A.Q. Wolfe, “Discovering the Energy Story, Part 1: Load Characterization,” Quinn Energy, LLC, July 27 2016,
[Online] Available: http://www.quinnenergy.com/library
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1: INTRODUCTION
The electric grid is a web of interconnected energy sources and loads. Capacity
requirements are driven by the peak load at each node in a system. System operators
and designers are interested in identifying, predicting, and reducing power system
capacity requirements in order to reduce capital costs. To achieve these reductions, multiload characterization is required to go beyond single load analysis and address system
peaks.
In Part 1: Load Characterization of this white paper series, Discovering the Energy Story,
load characterization approaches for a single residence were described. This white paper
leverages some of the approaches described in Part 1 and provides an introduction to
methods that address analysis of multiple loads. A data set from a residential
neighborhood with thirty (30) households is characterized.
2. EXAMPLE DATA SOURCE
The example electric consumption data is from a neighborhood of energy efficient homes
located in Ithaca, NY. The example residence from Part 1 is located in the neighborhood
studied. Thirty-second interval data was collected over four weeks in February and March,
2016.
The homes were around 1300 square-feet and have an average of two to three
occupants. Their primary heat source and hot water source is a natural gas boiler located
in Energy Centers (EC) located outside the home. Power for the residences is delivered
via the four ECs. EC-1, EC-2, and EC-3 supply eight residences each and EC-4 supplies
six residences. The secondary heating source is electric. Cooking appliances are electric.
Washer and dryer are located outside the home.
3: LOAD STATISTICS
Develop individual load statistics before load aggregation.
Load characterization approaches detailed in Part 1 of this white paper series can be
applied to each load of a similar type. The results can be summarized using statistics to
describe the range of load characteristics. For demonstrative purposes, the load level
metrics approach was selected and applied to the thirty residences in the neighborhood
over the course of the four week study (Figure 1). These metrics highlight the load range
and frequency of the load levels. For the load level metrics the Peak Load is the
maximum, Near Peak Load is the 97.5th percentile, Average Load is the mean, Near Base
Load is the 2.5th percentile, and Base Load is the minimum of the load.
In Figure 1, the statistical representation of the data is in the form of a box plot. The line
inside the box represents the 50th percentile (i.e. median), the box represents the range
from the 75th percentile to the 25th percentile, the bar outside the box represents the non2|Page
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outlier data range outside the middle percentile range, and the red plus symbol (+)
represents outliers.
Figure 1: Load level statistics for thirty households.
The median and average values for each of the load level statistics are summarized in
Table 1. The average and median values are close to one another. The average Peak
Load is 6.5 kW. The average Peak to Average Ratio is 24. The high peak value relative
to the average is of concern because it could be used to justify high capacity
requirements.
Table 1: Load level statistics for thirty households.
Load Levels Statistics for 30 Households
Metric
Peak Load
Near Peak Load
Average Load
Near Base Load
Base Load
Peak to Average Ratio
Average Value
6.5 kW
1.7 kW
0.34 kW
0.12 kW
0.00 kW
24
Median Value
6.2 kW
1.7 kW
0.28 kW
0.09 kW
0.00 kW
25
4: COINCIDENT LOAD
From a systems perspective coincident load is key.
Individual loads often do not experience peaks at the same instance in time. Coincident
Load analysis addresses this time of use issue 2.
2
W.H. Kersting “Distribution System Modeling and Analysis 3rd Edition,” CRC Press, Jan. 24 2012.
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4.1: Coincident Load Metrics
The Coincident Load represents multiple loads at the same instance of time. The
Coincident Load is the summation of any n number of multiple loads at each time t
sampled.
𝑛𝑛
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿(𝑡𝑡) = � 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿(𝑡𝑡)𝑛𝑛
𝑖𝑖=1
The Peak Coincident Load is the maximum of the Coincident Load. This represents the
Peak Load that a given system node will experience.
𝑛𝑛
𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿(𝑡𝑡) = max( � 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿(𝑡𝑡)𝑛𝑛 )
𝑖𝑖=1
Peak Non-Coincident Load is the summation of the maximum of any n number of multiple
loads at any time. This represents the aggregation of each individual load maximum and
does not represent a load that the system node actually sees.
𝑛𝑛
𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿(𝑡𝑡) = � max(𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿(𝑡𝑡)𝑛𝑛 )
𝑖𝑖=1
Coincidence Factor is a common metric used to quantify the ratio between the Peak
Coincident Load and Peak Non-Coincident Loads. Coincidence Factors should be
calculated during the same time period and using the same sample rate.
𝑛𝑛
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 = 𝑚𝑚𝑚𝑚𝑚𝑚(𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿(𝑡𝑡))/ � max(𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿(𝑡𝑡)𝑛𝑛 )
𝑖𝑖=1
Diversity Factor is also used to characterize this relationship and is the inverse of
Coincidence Factor.
𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 =
1
𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝑐𝑐𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹
Coincidence metrics were calculated including the neighborhood data. The four-week
data for each of the thirty residences in the neighborhood was included (Table 2). While
the Non-Coincident Peak Load is 196.4 kW, the Coincident Peak Load is significantly less
at 40.6 kW. This highlights that adding up individual peak loads, without taking into
account timing, can result in drastically over estimated peak loads. This is particularly
evident when the Coincidence Factor is low.
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Table 2: Coincidence metrics using four weeks of residential data.
Neighborhood Coincidence Metrics
Metric
Non-Coincident Peak Load
Coincident Peak Load
Coincidence Factor
Diversity Factor
Neighborhood
196.4 kW
40.6 kW
0.2
4.8
4.2: Neighborhood Coincident Load
The Multi-Day Coincident Load for the aggregated thirty households in the neighborhood
is graphed with respect to the time of day in Figure 2. As described in Part 1: Load
Characterization, the multi-day analysis is including data over each day of the four-week
study to highlight the frequency that a load occurs during a given time of day. By
aggregating the residential loads, the overall effect of typical residential behavior
becomes more clear and peaks can be observed in the morning and evening.
Figure 2: Multi-day Coincident Load for the neighborhood with respect to the hour of the day.
The load level metrics and Load Duration Curve can be applied to a Coincident Load
similar to how it was applied to an individual load as shown in Figure 3.
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Figure 3: Load Duration Profile for Coincident Load of the neighborhood.
The load level metrics are summarized in Table 3. For the neighborhood, the Peak to
Average Ratio is 3, eight times lower than the average individual residence Peak to
Average Ratio of 24.
Table 3: Coincident Load Level Metrics for the neighborhood.
Coincident Load Level Metrics for Neighborhood
Metric
Residences
Peak Load
Near Peak Load
Average Load
Near Base Load
Base Load
Peak to Average Ratio
Neighborhood
30
40.6 kW
23.7 kW
13.3 kW
7.0 kW
4.8 kW
3
4.2: Energy Center Coincident Load
Each residence is fed power from an Energy Center (EC), from the perspective of power
systems each EC represents a load node. By calculating the Coincident Load per EC the
effective power requirement of the EC node can be determined. Similar to the total
neighborhood, the Multi-Day Coincident Load and the Load Duration Profile are provided
for EC-1 in Figure 4 and Figure 5 respectively.
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Figure 4: Multi-day Coincident Load for EC-1 with respect to the hour of the day.
Figure 5: Load Duration Profile for EC-1.
Table 4 summarizes the Coincident Load level metrics for each of the four Energy
Centers. The four EC have similar loads with some variance, the Peak to Average Ratios
range from 5 to 7 and their average is 6. This is two times greater than the Peak to
Average Ratio of the neighborhood and four times less than the ratio of the average of
the individual residences.
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Table 4: Coincident Load level metrics for the Energy Centers.
Energy Center Coincident Load
Metric
EC-1
Residences
Peak Load
Near Peak Load
Average Load
Near Base Load
Base Load
Peak to Average Ratio
8
19.0 kW
7.2 kW
3.7 kW
0.0 kW
0.0 kW
6
EC-2
EC-3
EC-4
8
16.2 kW
6.6 kW
2.7 kW
0.0 kW
0.0 kW
6
8
19.2 kW
9.7 kW
4.2 kW
1.3 kW
0.0 kW
5
6
17.5 kW
6.9 kW
2.4 kW
0.7 kW
0.0 kW
7
EC
Avg.
7.5
18.0 kW
7.6 kW
3.2 kW
0.5 kW
0.0 kW
6
5: RESULTS SUMMARY
Peak to Average Ratios are highly variant.
The Coincident Load metrics summarized in Table 1, Table 3, and Table 4 have a large
range of values. In order to provide a clearer comparison, the results are normalized by
the number of households in Table 5. This provides an average value per household. In
addition, the example residence data from Part 1 are also listed for comparison. In the
table, * notes non-zero values below the level of significant digits displayed in the table.
Table 5: Coincident Load level metrics per household.
Coincident Load Levels Metrics Per Household
Metric
Neighborhood
Average
Peak Load
1.4
Near Peak Load
0.8
Average Load
0.4
Near Base Load
0.2
Base Load
0.2
Peak to Average Ratio
3
EC
Average
2.4
1.0
0.4
0.*
0
6
Individual
Average
6.5 kW
1.7 kW
0.3 kW
0.1 kW
0.* kW
24
Individual
Example
6.2 kW
1.0 kW
0.2 kW
0.* kW
0.0 kW
41
As more households are aggregated the peaks even out and the average Peak Load
decreases drastically, which in turn reduces the Peak to Average Ratio. This is in line with
the neighborhood Coincidence Factor of 0.2. Considering Coincidence Factor and/or
conducting a Coincident Load analysis accurately can help to reduce capacity
requirements while maintaining confidence that Coincident Load can be met.
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6: CONCLUSIONS
Capacity constraint identification and mitigation requires Coincident Load analysis at the
node of interest. While individual load statistics summarize range and frequency of load,
they do not describe system level peaks when they have low Coincidence Factors.
The level and scope of load aggregation can drastically impact metric values. It is crucial
that the load data used to assess capacity constraints is appropriate to the physical
connectivity of the system and its loads. Accurate and meaningful results are highly
dependent on thoughtful load selection and statistical application. Each set of loads has
unique relationships that will be best represented via a range of approaches.
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