Identifying Errors in Service Transformer Connections

Abstract

Distribution system models play a critical role in the modern grid, driving distributed energy resource integration through hosting capacity analysis and providing insight into critical areas of interest such as grid resilience and stability. Thus, the ability to validate and improve existing distribution system models is also critical. This work presents a method for identifying service transformers which contain errors in specifying the customers connected to the low-voltage side of that transformer. Pairwise correlation coefficients of the smart meter voltage time series are used to detect when a customer is not in the transformer grouping that is specified in the model. The proposed method is demonstrated both on synthetic data as well as a real utility feeder, and it successfully identifies errors in the transformer labeling in both datasets.

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XXX-X-XXXX-XXXX-X/XX/$XX.00 ©20XX IEEE
Identifying Errors in Service Transformer
Connections
Logan Blakely, Matthew J. Reno
Electric Power Systems
Sandia National Laboratories
Albuquerque, NM, USA
lblakel@sandia.gov
Abstract—Distribution system models play a critical role in the
modern grid, driving distributed energy resource integration
through hosting capacity analysis and providing insight into
critical areas of interest such as grid resilience and stability. Thus,
the ability to validate and improve existing distribution system
models is also critical. This work presents a method for identifying
service transformers which contain errors in specifying the
customers connected to the low-voltage side of that transformer.
Pairwise correlation coefficients of the smart meter voltage time
series are used to detect when a customer is not in the transformer
grouping that is specified in the model. The proposed method is
demonstrated both on synthetic data as well as a real utility feeder,
and it successfully identifies errors in the transformer labeling in
both datasets.
Keywords—AMI, correlation coefficients, distribution system
modeling, transformer errors
I. INTRODUCTION
Utility models of the electric grid form the basis of the
simulations that inform control decisions, infrastructure
investment, hosting capacity analyses, and many other grid
applications. Historically, the utility models of the distribution
system have a larger quantity of errors compared to the
transmission system, [1], and this is especially true for the low-
voltage portion of the system. [2] provides an overview,
literature review, and several examples of the types of errors that
are often present in utility models of the distribution system.
These errors in the model are included in grid simulations
and propagate through to the results. For example, hosting
capacity analyses are critical for evaluating potential distributed
energy resources (DER) and reduced accuracy in those analyses
is an obstacle, [3]–[5]. The connections between customers, or
meters, and the low-voltage network is one area of utility models
that contains errors. Due to ongoing maintenance and record
keeping, the correct connection information may not be known
between a particular meter and a service transformer. This meter
to service transformer mapping error can affect the simulations
discussed earlier, but it also has a negative impact on equipment
usage. Both overloading transformers and not fully using the
potential of transformers are cases that would be avoided in an
optimal configuration. Thus, accurate specifications of which
service transformer each meter is connected to are necessary for
optimal infrastructure usage and accurate simulations.
This work leverages the recent availability of data from
advanced metering infrastructure (AMI), or smart meters; at the
end of 2018 ~60% of households in the United States were
equipped with smart meters and that number is projected to
continue rising [6]. The task within this work is to identify
customer to transformer mapping errors, specifically by flagging
transformers which contain meters specified in their low-voltage
network that are actually located under a different service
transformer. The proposed algorithm produces a list of
transformers which contain errors; this list can be used to
efficiently direct utility resources to correct those errors. The
primary contributions of this paper are as follows:
1) A method for identifying meter to transformer mapping
errors that does not inject new errors into the model.
2) A straightforward, easily-interpretable, data-driven
method for identifying meter to transformer mapping errors.
3) A significant reduction in required utility resources to
find/correct meter to transformer mapping errors by providing
a list of transformers to focus resources on.
II. RELATED WORK
This section provides an overview of related research in this
area. The use of correlation coefficients for this type of model
correction is well-documented in literature.
The work in [1] and [7] provides some of the foundational
work and inspiration for the proposed algorithm. The authors
used the voltage time series collected from AMI meters,
calculated a point-of-coupling (POC) voltage using the line
impedance and current, and calculated pairwise correlation
coefficients from the POC time series. The correlation
coefficients are then used both to identify customer to
transformer errors and identify the correct placement of those
customers, and both aspects must be successful for the method
to work. This work was field validated on a 700-customer feeder
in Vancouver, Canada.
[8] uses correlation coefficients combined with a two step
clustering process to solve the meter to transformer pairing
problem. First, customers are clustered spatially, either using
DBSCAN or using pre-existing knowledge about the feeder
laterals, and then customers are clustered using K-means with
correlation as a distance metric. The authors report 80%-90%
accuracy in their results. Given the importance of the
simulations using these models, better accuracy is desirable.
This material is based upon work supported by the U.S. Department of
Energy’s Office of Energy Efficiency and Renewable Energy (EERE) under
Solar Energy Technologies Office (SETO) Agreement Number 34226. Sandia
National Laboratories is a multimission laboratory managed and operated by
National Technology and Engineering Solutions of Sandia, LLC., a wholly
owned subsidiary of Honeywell International, Inc., for the U.S. Department of
Energy’s National Nuclear Security Administration under contract DE-
NA0003525. SAND2019-13628 C

[9] proposes a method based on linear regression for the
meter to transformer mapping task. The method uses the POC
approach, grouping pairs customers with the highest 𝑅2 fit value
from the linear regression in a hierarchical fashion, combining
paired customers into a POC until a complete tree is built. This
work was validated on a small dataset of 36 transformers.
[10] uses an approach based on calculating the POC voltage
for each customer labeled on a transformer and comparing the
resulting profiles for irregularities. The results in this work are
proof-of-concept examples. The authors note that this approach
could potentially be automated and be done hierarchically,
resulting in a tree structure, but that is left to future work.
In [11], the authors calculate a pairwise ‘concentration
matrix’, which is a type of correlation, and use that to build a
minimum spanning tree that represents the radial structure of the
distribution system. This work does not explicitly discuss meter
to transformer mapping, however the tree structure represents
similar knowledge. [12] uses phasor measurement unit (PMU)
data with the Chow-Liu algorithm for the topology estimation
problem. Utilization of this method requires access to PMU
data.
In [13] the authors use a two stage method for pairing
distribution transformers with the correct feeder label; they
separate the detection of an error from the correction step, as we
also propose to do in our method. The first stage flags
suspicious transformers based an 𝑅2 fit value from a linear
regression using voltage time series, and the second stage
corrects the pairing label.
One key consideration in all of these methods is the question
of whether the method potentially injects new error into the
model. The body of research discussed in this section does not
touch on this topic, and this may be a hinderance in applying
these methods in the field. A major advantage of the method
proposed in this paper is that it is incapable of adding additional
error to the utility model and only requires AMI voltage time
series data. For further experimental results from this work
comparing it with the proposed method to methods from [1], [9]
please see Section IV C.
III. METHODOLOGY
The proposed method leverages the concept that customers
connected to the same service transformer will have voltage time
series that are more correlated than two customers that are
connected to different transformers. This fact is well
demonstrated in the literature, both for customer to transformer
pairing research, as well as for customer phase identification [8],
[9], [14]. Pearson correlation coefficients were calculated
between the voltage time series of each pair of customers to
produce a pairwise correlation coefficient matrix. Pearson
correlation coefficients are used extensively in literature, both
for this type of application, referenced in Section II and for phase
identification applications. Although AMI meters may record
other information, only the voltage measurements are used in
this method. POC voltage could be explored as future work, but
the results shown here do not implement the POC technique
described above. This work focuses on the problem of flagging
service transformers that contain an incorrectly specified
customer (i.e. a customer that is actually in a different service
transformer grouping). Figure 1 shows a conceptual illustration
of the proposed method. There are four customers that are
specified as being connected in the low voltage network of a
single-phase transformer, and the table shows the pairwise
correlation coefficients of the voltage time series for this set of
customers. Customers 1-3 are highly correlated with each other,
while Customer 4 is not well correlated with any of the other
customers, suggesting that Customer 4 is in a different low
voltage network, connected to a different service transformer.
In this case, the transformer would be flagged for further
analysis by utility personnel. This method is currently designed
for single-phase customers, and the full set of customers is down
selected to include only single-phase customers as a pre-
processing step. The same algorithm could work for identifying
3-phase customers on the same transformers if voltage
measurements from all three phases (or average phase voltage)
is provided. Future work will investigate identifying
combinations of 3-phase and single-phase customers on the
same transformers. Another important distinction is that this
algorithm focuses on the set of customers assigned to a
transformer and not the mapping between that set and a physical
transformer.
Figure 1 - Conceptual example of the proposed method
Two other pre-processing steps are implemented prior to
beginning the transformer error flagging process. First, the
voltage time series are converted to per unit representation.
Second, the voltage time series are converted into a ‘voltage
difference’ representation. The difference is taken between
adjacent, time-consecutive measurements to produce the
transformed time series. The resulting time series are reduced
in length by one measurement and can now be interpreted as the
(per unit) voltage change between time steps. The efficacy of
these steps has been demonstrated in [8], [14].
Figure 2 shows a flowchart of the proposed methodology in
more detail. In Step 1, the pairwise correlation coefficient
matrix is calculated. This methodology uses a ‘window’
methodology to calculate the correlation coefficients, [8], [14].
A ‘window’ of available data, 4-days in this case, is selected,
any customers with missing data during this window are
removed, and the pairwise correlation coefficients are then

calculated for the remaining customers. This process is repeated
for subsequent windows until all available data has been
utilized. This approach has several advantages. First, it allows
a way to deal with datasets containing missing data; second, it
enables the algorithm to be more scalable in the case of large
datasets; and finally, it permits flexibility in the calculation of
the final pairwise correlation coefficient. In this algorithm, the
median of all pairwise values across the available windows is
used as the final correlation coefficient, but the window
approach allows for the choice to use the mean value, do outlier
detection before using the values, etc.
In Step 2, a group of customers specified as being on the
same transformer are selected, and the correlation coefficients
are analyzed. If any of the pairwise correlation coefficients are
below a previously determined threshold, then the transformer
is flagged for further analysis. Further discussion of the choice
of threshold can be found in the Results section. Steps 2 and 3
are repeated until all transformers on the feeder have been
analyzed. Note that using this methodology, transformers with
a single customer are omitted as this type of analysis cannot be
used on those transformers.
Figure 2 - Flowchart of the proposed methodology
IV. RESULTS
The proposed algorithm was tested on both a synthetic
dataset and a utility dataset. The bulk of the testing was
conducted on the synthetic dataset where the ground truth of
customers on a transformer is known, and realistic data concerns
can be controlled and understood. The algorithm was also
demonstrated in a proof-of-concept test on a real utility feeder.
A. Synthetic Data Results
1) Dataset
The synthetic dataset consists of one year of 1-minute
measurement interval AMI measurements for 1379 residential
customers and 581 service transformers. The average real
power was extracted from Pecan Street [15] to create load
profiles for the customers. OpenDSS [16] was then used with
EPRI’s Test circuit 5 [17] to calculate voltage time series. A
uniformly distributed range of power factors was used (0.79-
0.99), varied every 30 minutes. The data was then averaged to
15-minute intervals for use in this work. This dataset has also
been used in [14], [18], [19], and more details on the data
generation can be found in those references.
2) Experimental Results
A series of experiments were conducted to test the
robustness of the proposed algorithm under different data
conditions. The work in [18] details a selection of data
considerations of interest.
This work focuses on the number of customers which have
an incorrect transformer label and the amount of measurement
noise within the voltage measurements. The incorrect
transformer labels are injected by percentage of the customers,
thus 1% of customers mislabeled means that 13 of the 1369
customers were given incorrect transformer labels. In practice,
this is roughly equivalent to the number of transformers that
contain an error, until the percentage of customers mislabeled
becomes large. The voltage measurement noise was injected
into all customers uniformly at random up to a specified
maximum percentage. Thus, if the maximum percentage of
noise is 0.2% then for each measurement in the time series, a
value is selected uniformly at random from the range [-0.48,
+0.48] where 0.48 is 0.2% of 240V, the mean voltage.
There are two primary metrics of interest in these
experiments. The first is the number of transformers that should
have been flagged but were not flagged; those are referred to as
the ‘false negative’ transformers. Second, the number of
transformers which were incorrectly flagged; that group of
transformers is referred to as the ‘false positive’ transformers.
Ideally the set of false negative transformers and the set of false
positive transformers will both be empty sets.
The threshold for flagging a transformer based on the
correlation coefficients is the primary parameter that requires
selection in advance using this methodology. The following
figures demonstrate the sensitivity of that parameter on the false
negative and false positive results. Figure 3 shows the results
for 1% of customers mislabeled, without injecting any noise into
the dataset. The x-axis shows the value of the voltage
correlation coefficient threshold; for example, given a threshold
of 0.6, if there are pairwise correlation coefficients less than 0.6
in a group of customers labeled on a particular transformer, then
that transformer would be flagged. On the blue (left) y-axis is
the number of false positive transformers, and on the red (right)
y-axis is the number of false negative transformers. We can see
the tradeoff inherent in the choice of the threshold value: too
small of a value and the false negative rate increases, and too
large of a value and the false positive rate increases. There is a
range of acceptable values from ~0.5 to ~0.78 where both the
false negatives and false positives are 0 and the algorithm
achieves 100% accuracy in flagging transformers with incorrect
customers and does not flag any correct transformers.
The next figures demonstrate the sensitivity of the algorithm
to the quantity of customers that have incorrect transformer
labels and varying levels of measurement noise injected into the
voltage measurements. Figure 4 shows the results when a
maximum of 0.15% noise is injected into the dataset and the
quantity of customers which are given incorrect transformer
labels is varied. We can see that the range of acceptable
threshold values varies only slightly among the three
simulations. In fact, if the y-axis were given in percent instead
of number of transformers, the lines would be plotted nearly on
top of one another.

Figure 3 - Results using 1% of customers mislabeled without noise injection
Figure 4 - Results using 0.15% maximum noise with varying quantities of
mislabeled customers
Figure 5 shows the results using 10% of customers with
incorrect transformer labels with varying levels of injected
noise. Increasing the level of measurement noise shifts the plots
to the left, although note that in each case, there is still separation
where there are acceptable values for the threshold. This shift is
intuitive because the addition of measurement noise forces all
the correlation coefficient to be less correlated, but the
customers on different transformers remain less correlated than
customers on the same transformer. Work remains ongoing to
determine heuristics for setting the threshold in the presence of
an unknown quantity of noise within the data.
Figure 5 - Results using 10% of customers mislabeled with varying levels of
injected measurement noise
B. Utility Feeder Results
1) Dataset
The utility dataset used in this work is approximately 15
months of data, measured at 15-minute intervals, using the
averaging method, from the northeastern United States. This
dataset is also used in the [2], [14], and [2] gives examples of
the types of errors commonly found in distribution system
models. There are not ground truth labels for this dataset, thus
the following example is shown as a proof-of-concept that the
proposed method works given real data. In the absence of
ground truth labels, publicly available Google Street View
images can be used to validate certain algorithm predictions.
Further examples of this from the same dataset can be seen in
[2].
Figure 6 shows satellite imagery of two transformers and
four customers, and the original model shows that all four
customers are connected to the southern (bottom) transformer.
However, this transformer was flagged by the proposed
algorithm, and inspection of Google Street View imagery
confirms the configuration in Figure 7. Two customers are
connected to the south transformer and two are connected to the
north transformer. Table 1 shows the pairwise correlation
coefficients for this set of four customers, and the two groupings
of two can be clearly seen. Note that the correlation between
Customer 1 and Customer 2 is only 0.77, demonstrating that real
data can often contain factors that lower the correlation
coefficients even between customers on the same transformer.
The algorithm also correctly identified several other known
transformer labeling issues on this feeder that had been
previously identified in other work.
Figure 6 - Original utility labeling
Figure 7 - Actual labeling verified using Google Earth imagery

TABLE 1 – VOLTAGE CORRELATION COEFFICIENT MATRIX FOR THE
CUSTOMERS IN FIGURE 6
Cust #1
Cust #2
Cust #3
Cust #4
Cust #1
1
0.777
0.434
0.575
Cust #2
0.777
1
0.344
0.446
Cust #3
0.434
0.344
1
0.958
Cust #4
0.575
0.446
0.957
1
C. Comparison with Similar Algorithms
The proposed algorithm takes a similar approach to other
works in literature, particularly [1]. During initial work,
variations of the methods proposed in [1] (correlation
coefficients) and [9] (linear regression) were tested on our
synthetic dataset. We were able to show that the linear
regression methodology was not robust to the injected noise
perturbation and the correlation coefficient methodology was
not robust to increasing levels of mislabeled customers. Note
that some of the errors produced by these methods were
injecting new errors into the utility model. For the correlation
coefficient methodology, most errors were occurring in the
second stage of the process, assigning a customer known to
have a transformer labeling error to its correct transformer.
This fact inspired the direction taken in this work. Although
this work focused on flagging the error, this remains of great
use to utilities because the number of transformers to be
inspected is greatly constrained.
V. FUTURE WORK
There are several aspects of future work suggested by the
proposed method. The configuration of which customers
happen to be mislabeled is likely to have a role in the efficacy of
the algorithm; secondly, the assignment of noise to the voltage
time series is done in a random fashion, thus each simulation
would perform slightly differently. Further testing is also
required on other utility feeders to determine how the correlation
coefficients change under differing conditions. Finally,
although this work presents a novel method for identifying
customers labeled on incorrect transformers, in some sense it
solves an ‘abridged’ version of the complete customer to
transformer pairing problem. This work focuses on identifying
where the errors occur in the utility model, and work is ongoing
in correcting those errors, which is a much more challenging
problem.
VI. CONCLUSION
This work presents a methodology to identify service
transformers in distribution system models that have customers
which are not connected to the transformer group in which they
are labeled, leveraging the information provided by the
correlation coefficients between customers’ AMI voltage time
series. The proposed algorithm achieved 100% accuracy in
flagging on the synthetic dataset of 581 transformers, with
varying quantities of injected measurement noise and varying
percentages of mislabeled customers. It is possible to correctly
flag all incorrect transformers and avoid flagging any
transformers that have the correct grouping of customers. The
method was also tested as a proof of concept on a real utility
feeder and successfully flagged several of the known
transformer labeling errors within that feeder. This method
shows excellent promise in enabling utilities to intelligently
direct their personnel and resources towards transformers that
need further analysis.
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