# Low Voltage Customer Phase Identification Methods Based on Smart Meter Data

Alexander Hoogsteyn1, Marta Vanin12, Arpan Koirala12, Dirk Van Hertem12  1 KU
Leuven, Dept. of Electrical Engineering (ESAT), Kasteelpark Arenberg 10, 3001,
Heverlee, Belgium  2 EnergyVille, Thor Park 8310, 3600, Genk, Belgium

###### Abstract

The increased deployment of distributed energy generation and the integration
of new, large electric loads such as electric vehicles and heat pumps
challenge the correct and reliable operation of low voltage distribution
systems. To tackle potential problems, active management solutions are
proposed in the literature, which require distribution system models that
include the phase connectivity of all the consumers in the network. However,
information on the phase connectivity is in practice often unavailable. In
this work, several voltage and power measurement-based phase identification
methods from the literature are implemented. A consistent comparison of the
methods is made across different smart meter accuracy classes and smart meter
penetration levels using publicly available data. Furthermore, a novel method
is proposed that makes use of ensemble learning and that can combine data from
different measurement campaigns. The results indicate that generally better
results are obtained with voltage data compared to power data from smart
meters of the same accuracy class. If power data is available too, the novel
ensemble method can improve the accuracy of the phase identification obtained
from voltage data alone.

###### Index Terms:

clustering, ensemble learning, low voltage distribution system, phase
identification, smart meter

##  I Introduction

The shift to more distributed generation [1] and integration of new large
loads such as electric vehicles and heat pumps, can lead to various problems
in distribution systems (DS), such as increased imbalance and overvoltages.
Historically, imbalance was not considered a problem since DS were typically
underutilized and characterized by modest and unidirectional power flows. The
emergence of PV installations and larger loads implies more utilization and
unpredictability, which might push the DS state beyond the acceptable
operational limits.

To cope with the aforementioned issues, recent research on DS advocates for an
improved system exploitation and control, through the so-called Active DS
Management. Examples are optimal voltage control by means of tap changes [2]
or resilient restoration [3]. A distribution system operator (DSO) could also
preventively reconfigure the phase connection of its grid, such that a more
balanced configuration is obtained. For such applications, it is necessary to
identify the present phase connectivity.

Phase identification methods try to classify to which phase(s) a consumer is
connected, usually with the help of field measurements. Manual determination
of the phase labeling is often not viable because of the cost of this labour-
intensive approach, especially since the majority of the cables are
underground. Furthermore, cables are not color-coded. In literature, a wide
variety of data-driven approaches are proposed. In [4, 5], field measurement-
based methods are described that use communicating phasor measurement units
(PMU) between the consumer and the transformer. However, these devices are
quite expensive and unlikely to be widely available in DS in the near future,
especially at the low voltage levels. Smart meters, which are already being
rolled out, are a more realistic option, at least in the near future[6, 7, 8].
Developing practically applicable methods that rely on realistic assumptions
on available smart meter data is still an open research topic.

The remainder of the paper is structured as follows: In Section II, the
current literature on smart meter (SM) data based phase identification methods
is reviewed. In Section III, the mathematical formulation of the phase
identification methods used in the present work is given, including our novel
ensemble learning method. In Section IV, the performance of the different
methods is illustrated under a broad range of scenarios. Finally, conclusions
are drawn.

##  II Related work

Phase identification methods that use SM data can be categorized into 3 groups
based on whether they use:  a) mixed-integer programming (MIP) approaches
typically using power data,  b) machine learning, with voltage data (MLV), or
c) machine learning, with power data (MLP).  In [9, 10, 11, 12, 13], a MIP
approach is used to solve the phase identification problem. These
optimization-based implementations need measurements of the consumers’ demand
and the distribution transformer’s supply, and use the principle of
conservation of power to determine which consumer is connected to which phase.
The algorithm optimizes the allocation of the set of consumers to the three
phases by minimizing the difference between the total feeder demand and the
transformer supply. These MIP methods are inherently inferior at handling
missing data or incomplete datasets, and typically assume that all users have
a smart meter and there are no electricity thefts or similar phenomena [11].
MIP-based methods that require both voltage and power data have also been
proposed [12]. The authors propose a method which allocates the phases firstly
using voltage correlation, afterwards optimization techniques are used that is
initiated with the voltage-based solution and then iteratively solved.

To make these methods more rigorous, line losses should be modelled. However,
this requires knowledge of line impedance values, which are typically not
known in sufficient detail in low voltage networks. While [9, 12] do not
rigorously model the network physics, in [13], a MIP formulation is proposed
which explicitly adds linearized power flow equations as constraints.

In [14, 15, 16, 17, 18, 6, 19, 20, 21, 22, 23, 24, 25] MLV approaches are
proposed. The algorithm in [14, 15] uses the correlation between time-series
measurements of a customer’s voltage and the transformer voltage time series
of each phase to distinguish the phase connection. It relies on the principle
that consumers connected to the same phase will have similar voltage time
series and therefore have a higher Pearson correlation coefficient. The
advantage of using such machine learning methods is that they can deal with
incomplete data better, since they do not use the conservation of power. The
authors in [16] improve upon such an approach by leveraging the known topology
by accounting for the voltage drop corresponding to the distance between the
feeder and the consumer’s connection. In [17], the author uses other consumers
as reference instead of transformer measurements. This avoids the need to
collect transformer measurements which are often not available. Such an
approach does require data of a three-phase consumer. One problem MLV methods
face is that voltage variations are relatively small near the transformer.
Load correction is applied by [18] and [6] to mitigate this problem. In load
correction, power data is used in addition to the voltage data of a consumer
to estimate the voltage drop on the phase the consumer is connected to.

References [19, 20, 21] use K-means clustering, ref. [25] combines K-means
clustering and principal component analysis. Ref. [22, 23] use spectral
clustering (a variant of K-means) to group the voltage time-series
measurements in three clusters, based on their similarity. Each cluster
corresponds to one of the phases. This removes the need for a reference
voltage profile entirely. In [24, 26], a sliding window ensemble learning
method is used, which combines spectral clustering results using voltage data
of different days.

MLP methods were proposed in [27, 28, 29] that use concepts from ML such as
correlation. Such methods can cope with missing data and thus mitigate the
disadvantages of MIP methods while using power measurements. These
measurements are more often available than the voltage in a real-world setting
because they are needed for billing purposes. The approaches rely on the
principle that a consumers’ demand is more correlated to the supply of the
phase it is connected to. Consequently, the methods also need measurements of
the power supplied from each transformer’s phase. The advantages and
disadvantages of the categories of the discussed methods are summarized in
Table I.

Besides [30], research work that copes with the rigorous comparison of the
available phase identification techniques is currently scarce. This paper aims
to do such a comparison. The main contributions of this paper are:

  * •

Different existing techniques for phase identification in DS using SM data are
compared in a thorough and consistent manner. The comparisons are carried out
over different SM accuracy classes and data availability scenarios, on
multiple non-synthetic European feeders with different characteristics.

  * •

A novel algorithm for SM based phase-identification is proposed that makes use
of ensemble learning to combine results from voltage and power-based methods.
The ensemble method improves upon existing power-based techniques and
optionally takes voltage data into account to yield further improvements. To
the authors’ knowledge, it is the first ensemble learning algorithm that
combines results from voltage-based and power-based methods.

TABLE I: Advantages and disadvantages of phase identification methods. |  Advantages |  Disadvantages
---|---|---
MIP [9, 10, 11, 12, 13] |  • Can make use of existing optimization techniques • Load data more often available |  • Hard to cope with missing data • Need to model the losses to be accurate
MLV [14, 15, 16, 17, 18, 6, 19, 20, 21, 22, 23, 24] |  • Can cope with missing data • Can make use of existing machine-learning techniques |  • Voltage data often not available • Decreased performance for short feeders and close to the transformer
MLP [29, 27, 28] |  • Can cope with missing data • Load data more often available |  • Needs novel algorithms • Lower performance on feeders with a high amount of connections

##  III Problem formulation

Let $i$ be each of the $N$ customers in the radial low voltage distribution
network, and $j$ be one of the three phases: $j\in\\{a,b,c\\}$. Customer
voltage measurements $U$ are collected for the MLV method, and consumer $H$
and transformer $P$ power measurements for the MLP method. In the proposed
ensemble method, all of these can be used. All measurements are averages over
a period of time that depends on the meter resolution. Let $h_{t,i}$ and
$u_{i,t}$ represent the average power and voltage measurement of customer $i$
for the time period $t\in\\{1,\ldots,T\\}$. Finally, let $p_{t,j}$ be the
transformer power measurement for phase $j$, time $t$, such that:

$H=\left[\begin{array}[]{l l l l}h_{1,1}&\cdots&h_{1,N}\\\
\vdots&\ddots&\vdots\\\ h_{T,1}&\cdots&h_{T,N}\\\ \end{array}\right]$ (1)
$P=\left[\begin{array}[]{l l l l}p_{1,a}&p_{1,b}&p_{1,c}\\\
\vdots&\vdots&\vdots\\\ p_{T,a}&p_{T,b}&p_{T,c}\\\ \end{array}\right]$ (2)
$U=\left[\begin{array}[]{l l l l}u_{1,1}&\cdots&u_{1,N}\\\
\vdots&\ddots&\vdots\\\ u_{T,1}&\cdots&u_{T,N}\\\ \end{array}\right]$ (3)

Gaussian noise $E\sim\mathcal{N}(0,\,\sigma_{error}^{2})$ is added to $U$, $H$
and $P$ to simulate the accuracy classes of SM specified by the International
Electrotechnical Commission (IEC). 50 Monte Carlo runs are performed with
different noise samples, and the average obtained accuracies are reported. The
accuracy classes $0.1$, $0.2$, $0.5$, and $1.0$ state that the maximal
measurement error ($\delta_{class}$) needs to be below $\pm 0.1$, $\pm 0.2$,
$\pm 0.5$, or $\pm 1.0$ % of the nominal value of the meter (indicated as
$U_{n}$ or $P_{n}$). To mimic the requirement set by the IEC, which specifies
a maximal measurement error, we assume that the maximal error corresponds to 3
sigma of the chosen distribution, as such:

$\sigma_{error,U}=\frac{1}{3}\delta_{class}U_{n}$ (4)
$\sigma_{error,P}=\frac{1}{3}\delta_{class}{P_{n}}$ (5)

Two additional high accuracy classes, 0.2s and 0.5s, are considered. These
classes are especially more accurate in low loading conditions since the
maximum deviation of a measured value is defined as a fraction of the actual
loading and not as a fraction of the nominal rating (between 20% and 100% of
the nominal rating). This is useful for MLP methods, since power demand is
rarely close to the nominal value, unlike voltages. For these classes, the
standard deviation of the artificially added error is found as follows:

$\sigma_{error,P}=\begin{cases}\frac{1}{3}\delta_{class}\frac{p_{i,t}}{P_{base}}&p_{i,t}>0.2P_{n}\\\
\frac{1}{3}\delta_{class}\frac{0.2P_{n}}{P_{base}}&p_{i,t}\leq 0.2P_{n}\\\
\end{cases}\forall i,t.$ (6)

It is assumed that the user phase connectivity does not change over the
measurement collection time. This is a realistic assumption, as
reconfiguration actions are not performed often in low voltage networks, e.g.,
due to the lack of automatic switching devices. System operators can
reasonably schedule their operations such that the two activities do not
overlap in time.

###  III-A Voltage-based methods (MLV)

The first MLV method implemented is that of [14] (see Algorithm 1). The method
calculates the Pearson correlation (7) between the voltage time series
$U_{i}=[u_{1,i},u_{2,i},\ldots]$ of each consumer $i$ and a reference voltage
time series $U_{ref,j}$, which can be from a three-phase reference customer or
a transformer measurement. With $\mu(U_{i})$ the average voltage of $i$ and
$\sigma(U_{i})$ its standard deviation. Similarly, $\mu(U_{ref,j})$ the
average voltage of reference phase $j$ and $\sigma(U_{ref,j})$ its standard
deviation. Users are assigned to the reference phases with which they have the
highest correlation.

$\displaystyle\rho(U_{i},U_{ref,j})$
$\displaystyle=\frac{(U_{i}-\mu(U_{i}))(U_{ref,j}-\mu(U_{ref,j}))}{\sigma(U_{i})\sigma(U_{ref,j})}$
(7)
$\displaystyle=\frac{\sum^{T}_{t=1}(u_{t,i}-\mu(U_{i}))(u_{t,ref,j}-\mu(U_{ref,j}))}{\sigma(U_{i})\sigma(U_{ref,j})}$

Data: $U_{i}=[u_{1,i},\ldots,u_{T,i}]$ for all consumers $i$,

$U_{ref,j}=[u_{ref,1,j},\ldots,u_{ref,T,j}]$ for each phase $j$

for  _Each consumer $i\in\\{1,\ldots,N\\}$_ do

for  _Each phase $j\in\\{a,b,c\\}$_ do

Calculate $\rho(U_{i},U_{ref,j})$ using (7)

end for

Allocate $i$ with highest $\rho(U_{i},U_{ref,j})$ to phase $j$

end for

Algorithm 1 Pearson correlation [14].

Another MLV approach to voltage-based phase identification is K-means
clustering [19]. This aims to partition a data set in $k$ clusters by
allocating voltage time-series $U_{i}$ to a ‘mean profile’, also called
cluster center $C_{k}$. In this case there are 3 clusters, one for each phase.
The Euclidean distance between each data point and its cluster center is
minimized (8). This is obtained using an iterative process until the stopping
condition is met set by $\epsilon$, as described in Algorithm 2. Alternative
time-shift invariant distance metrics have been explored, such as dynamic time
warping. Such metrics can lead to better time-series clustering results [31],
but this was not the case in our examined numerical illustrations. The choice
to implement K-means method is based on literature considerations, as K-means
is by far and large the most widely employed clustering method for phase
identification. Other clustering approaches have been investigated, such as
hierarchical clustering and Gaussian mixture model, but their results are not
shown as they present no valuable difference to those of K-means. The
implementation of all methods explored in this work is available open
source111https://github.com/AlexanderHoogsteyn/PhaseIdentification.

$\underset{\ell_{1},\ldots,\ell_{k}}{\min}\sum_{j=1}^{k}\sum_{\mathbf{u}_{i}\in\ell_{j}}\lVert\mathbf{U}_{i}-\mathbf{C}_{j}\rVert^{2}_{2}$
(8)

Data: $U_{i}=[u_{1,i},\ldots,u_{T,i}]$ for all consumers $i$

Randomly initialize cluster centers $C_{j}$

while
_$\sum_{j=1}^{k}\sum_{\mathbf{U}_{i}\in\ell_{j}}||\mathbf{U}_{i}-\mathbf{C}_{j}||^{2}_{2}
>\epsilon$_ do

for  _Each consumer $i\in\\{1,\ldots,N\\}$_ do

for  _Each cluster $k\in\\{k_{1},k_{2},k_{3}\\}$_ do

Calculate distance to cluster center $d_{ik}\leftarrow||U_{i}-C_{k}||_{2}$

end for

Allocate consumer $i$ to $\ell_{k}$ with smallest $d_{ik}$

end for

for  _Each cluster $k\in\\{k_{1},k_{2},k_{3}\\}$_ do

Calculate mean
$M_{k}\leftarrow\frac{1}{|\ell_{k}|}\sum_{\mathbf{U}_{i}\in\ell_{k}}\mathbf{U}_{i}$

Set mean as new cluster center $C_{k}\leftarrow M_{k}$

end for

end while

Algorithm 2 K-means clustering [19].

###  III-B Power-based methods (MLP)

The power-based method proposed in [29] is implemented. This uses Pearson
correlation of the power measurements of each consumer and power measurements
of each phase of the distribution transformer (9). To provide accurate
results, some preprocessing of the power data is performed. Power variations
between two timesteps $\Delta h_{i}=h_{i,t+1}-h_{i,t}\;\;\forall t$ are
calculated. Secondly, salient components $SH_{i}$ are extracted. These are the
$m$ largest variations out of $T$ time samples. The corresponding salient
variations of the transformer on each phase $j$ is denoted $SP_{j}$. In [29],
salient components that exceed a threshold are selected, as opposed to
extracting the $m$ largest variations. However, the latter approach was found
to be more robust with our data set and was therefore chosen in favor of the
approach in [29]. The implemented method is summarized in Algorithm 3.

$\rho(SH_{i},SP_{j})=\frac{(SH_{i}-\mu(SH_{i}))(SP_{j}-\mu(SP_{j}))}{\sigma(SH_{i})\sigma(SP_{j})}$
(9)

In [29] a spectral analysis is also performed at the data preprocessing stage,
which filters out the low frequency variations in the power data. Calculating
(9) on high frequency variations alone improves the results in [29], but did
not have a significant impact in our numerical illustrations. As such,
spectral analysis is not discussed in this paper.

Data: $H_{i}=[h_{1,i},\ldots,h_{T,i}]$ for all consumers $i$

$P_{j}=[p_{1,j},\ldots,p_{T,j}]$ for each phase $j$

Sort consumer list $\ell$ according to highest
$MAV_{i}=\frac{1}{T}\sum_{t=1}^{T}|h_{i,t}|$ of each consumer $i$

for  _Each phase $j\in\\{a,b,c\\}$_ do

Calculate transformer power variations $\Delta
P_{j}=[p_{1,j}-p_{2,j},...,p_{T-1,j}-p_{T,j}]$

end for

for  _Each consumer $i\in\ell$_ do

Calculate power variations $\Delta
H_{i}=[h_{1,i}-h_{2,i},\ldots,,h_{T-1,i}-h_{T,i}]$

Select $m$ biggest variations $\Delta H_{i}$ and store as $SH_{i}$ Select
corresponding variations for $\Delta P_{j}$ for each $j\in\\{a,b,c\\}$ and
store as $SP_{i,j}$

for  _Each phase $j\in\\{a,b,c\\}$_ do

$c_{i,j}\leftarrow\rho(SH_{i},SP_{j})$ using (9)

end for

Allocate consumer $i$ to phase $j$ with highest $c_{i,j}$

Subtract power profile from transformer measurement $P_{j}\leftarrow
P_{j}-H_{i}$

end for

Algorithm 3 MLP [29]

In the MLP algorithm, the consumers with the highest variability in their
time-series measurement, according to the mean average variability (MAV) are
assigned to one of the transformer phases first. This is because consumers
with higher variability are more likely to be allocated to the correct phase,
since they contain more distinct changes in power, which might correspond to
turning on a big electrical appliance. Therefore, they tend to show higher
correlation with the transformer’s salient components.

###  III-C Ensemble methods

Two novel ensemble learning methods are proposed based on two common types of
ensembles: ‘bagging’ and ‘boosting’.

####  III-C1 Bagging ensemble method

In this method, different data sources are used with the same algorithm, and
the respective results are combined according to a chosen combination metric.
In a variety of other machine learning applications, such approach leads to
improved results [32]. Fig. 1 illustrates how such an approach could be
applied to phase identification. Voltage and power data can be separately
collected and used by different methods to obtain a phase identification
result. The results are then combined, e.g. by majority voting. A simple
variant of bagging ensemble is implemented in this work, as a reference to
compare the proposed boosting ensemble against. The implemented bagging
reference method uses the result from the voltage-based technique and if
voltage data is not available of a certain customer, it completes the phase
identification with the power-based technique. This approach, although simple,
leads to good results in the analyzed numerical illustrations.

Figure 1: Bagging ensemble with voltage and power data.

####  III-C2 Boosting ensemble method

In this method, a second model is trained using the data that are wrongly
classified by the first model. However, this requires labelled data and
therefore does not lend itself well to phase identification, as phase labels
that are not identified by the first method remain unavailable. Therefore, a
variant is implemented that does the phase identification partially using
voltage correlation. This technique is only applied to those consumers for
which this decision can be made with sufficient confidence.  A minimum
threshold $\rho_{threshold}$ is used on the voltage correlation. In our work
this threshold is set at $0.2*T$, with $T$ being the length of the time-
series. This was determined by inspecting the distribution of the obtained
voltage Pearson correlation coefficients. By setting the threshold at $0.2*T$,
there is a clear distinction between the highest correlating and second to
highest correlation phase, for most feeders. A more rigorous method to
determine the threshold or an alternative way to determine which method to use
could be the scope of future work. The threshold is dependent on the input
length $T$ to scale the threshold appropriately in the numerical illustration
where input length is varied. The full method is illustrated in Fig. 2.
Compared to the bagging ensemble method, the power-based step of the boosting
ensemble method is expected to perform better. This is because the demand of
the users which have their phase connectivity identified with sufficient
confidence by the voltage method, are subtracted from the transformer power
measurement. The MLP algorithm uses the residue to identify the remaining
users.

Figure 2: Boosting ensemble with voltage and power data.

Data: $U_{i}=[u_{1,i},\ldots,u_{T,i}]$ for all consumers $i$,

$H_{i}=[h_{1,i},\ldots,h_{T,i}]$ for all consumers $i$

$U_{ref,j}=[u_{ref,1,j},\ldots,u_{ref,T,j}]$ for each phase $j$

$P_{j}=[p_{1,j},\ldots,p_{T,j}]$ for each phase $j$

for  _Each consumer $i\in\\{1,\ldots,N\\}$_ do

for  _Each phase $j\in\\{a,b,c\\}$_ do

Calculate $\rho(U_{i},U_{ref,j})$ using (7)

end for

if  _max( $\rho(U_{i},U_{ref,j}),\forall$j$)>\rho_{threshold}$_ then

Allocate $i$ with highest $\rho(U_{i},U_{ref,j})$ to phase $j$

else

Use MLP method (Algorithm 3) to allocate customer $i$

end if

end for

Algorithm 4 Boosting ensemble

##  IV Numerical illustration

Three numerical illustrations have been analyzed to benchmark the different
methods. Realistic assumptions are made on the measurements, so that they
resemble those that are typically available to a DSO in a practical case.

###  IV-A Test feeders

A non-synthetic data set of a European DS is used [33], which contains real SM
power measurements and network topology information. From the 160 radial LV
feeders in this data set, six representative feeders are selected according to
the approach in [34], which clusters the feeders into groups with similar
features and then extracts one feeder from each cluster. The selected feeders’
properties are visualized in Figure 3 and summarized in Table II. In this
work, a radial LV distribution network is studied. In principle, nothing
prevents the application of the methods to meshed LV grids. In practice,
voltage-based results might be worse, as voltage variations might be less
evident on meshed networks. However, the meshed LV networks data is scarce,
and we do not perform this analysis for such network in the paper.

TABLE II: Features of the selected representative feeders. Case | Nb of | Yearly energy | Main path | Average path
---|---|---|---|---
| users | per user (kWh) | length (m) | impedance ($\Omega$)
A | 22 | 1852 | 878 | 0.206
B | 125 | 1894 | 245 | 0.117
C | 11 | 1802 | 102 | 0.0598
D | 20 | 4173 | 138 | 0.196
E | 45 | 2066 | 173 | 0.106
F | 74 | 1905 | 149 | 0.0914
Figure 3: Clusters and selected representative feeders from the non-synthetic
European DS [33].

###  IV-B Benchmarking existing phase identification methods

Figure 4: Accuracy for voltage based phase identification methods for all SM
classes in the six representative feeders.

In this numerical illustration, phase identification is performed with a
complete dataset, i.e., voltage and power measurements time-series of equal
time length, time resolution and accuracy are used. First, the deterministic
Pearson correlation method [14] and K-means clustering method [19] from the
literature are compared to each other and to a variant of the voltage-based
Pearson correlation which uses a three-phase customer as the reference instead
of the transformer [17]. The results for each representative feeder and
accuracy class are shown in Fig. 4. The accuracy on the y-axis shows the
fraction of the customers that were allocated to the correct phase by the
algorithm.

Fig. 4 shows that for the correlation approaches it is better to use the
transformer as a reference, rather than a three-phase customer. A possible
explanation for this is that customers that are on a feeder branch which is
different from that of the reference user, correlate worse to the reference
user’s voltage pattern. This could happen as voltage variations in a branch
are mainly influenced by the current through the branch sections, whereas the
transformer voltage variations account for the total feeder currents. As such,
the transformer voltage appears to be a good reference for all the feeders’
users.

In addition to the non-synthetic DS data [33], the methods are also applied to
a second dataset [35]. When applying the phase identification algorithms on
this dataset, a higher accuracy is obtained, similar that reported in [29].
The results are omitted here but this shows however, that the results of MLP
methods depend on the used data set, which is generally not the case for MLV
methods.

TABLE III: Obtained accuracy for all SM classes and methods, in average for the 6 cases. Best results for every SM class are highlighted. Bagging ensemble is omitted since results are identical to volt. Pearson. Method | 0.2s | 0.5s | 0.1 | 0.2 | 0.5 | 1.0
---|---|---|---|---|---|---
| (%) | (%) | (%) | (%) | (%) | (%)
volt. Pearson, transfo ref | 100 | 97.2 | 100 | 100 | 97.2 | 95.0
volt. Pearson, customer ref | 100 | 86.3 | 100 | 100 | 86.3 | 62.8
K-means clustering | 71.0 | 65.3 | 70.2 | 71.0 | 65.3 | 52.5
power Pearson | 97.2 | 93.3 | 79.8 | 62.3 | 44.0 | 39.1
boosting ensemble | 100 | 100 | 100 | 98.6 | 93.7 | 83.5

Figure 5: Accuracy of ensemble and power-based methods compared to voltage-
based methods for all SM classes in the six representative feeders. Bagging
ensemble results are identical to volt. Pearson.

In Figure 5 and Table III , the ensemble methods are compared with the
voltage-based method using the transformer reference and with power-based
algorithms. The comparison is made based on equal quality and quantity of
data. Voltage-based techniques outperform power-based techniques in almost all
cases and accuracy classes. The power-based technique outperforms the voltage-
based method in only one case, i.e., 0.5s class SM in case C. In this case,
the boosting ensemble method can identify that it cannot allocate consumers
using the voltage-based technique with high confidence. Instead, it correctly
allocates the remaining consumers with the power-based technique and obtains
an accuracy of 100%. The boosting ensemble uses the results of the power-based
technique even if (relatively) low accuracy meters such as 1.0 class are used.
Such low accuracy meters usually yield poor results when using a power-based
technique. This can be seen in case A and case C. The bagging ensemble is
omitted since it would yield the same results as the voltage-based method in
the case of complete data.

###  IV-C Impact of reduced voltage measurement points

As a second case, a numerical illustration is studied where voltage data for
20 days is only available for a limited number of consumers, while power data
is available for all consumers for 20 days. This could be the case in real-
life if power time-series are always available for billing purposes while
supplementary voltage data are collected for phase identification or other
grid-management applications. It could happen that only part of the consumers
allow for their voltage data to be shared with the DSO because of data
protection rules, or because they have newer generation SM.

In Fig. 6, the accuracy is shown in function of the fraction of consumers for
which 20 days of voltage data are collected. The SM accuracy class displayed
are 0.5s and 1.0. The accuracy obtained by the voltage-based method improves
linearly with the fraction of consumers with available data, and reaches 97.2%
in the case of 0.5s class SM and 95.0% in the case of a 1.0 class SM. The
power-based method is invariant to the change in voltage data collected and
therefore obtains higher accuracy than the voltage-based approach at low
levels of voltage data collected but worse at high levels. The boosting
ensemble can outperform the simple bagging approach when 0.5s class SM is
used, as shown in Fig. 6(a). However, when a 1.0 class SM is used, the
boosting method obtains worse results than the bagging ensemble, as can be
seen in Fig. 6(b). One possible reason for this is that the tuning of the
threshold was done based on the Pearson correlation distribution obtained
using a 0.5s class SM.

(a) Class 0.5s SM

(b) Class 1.0 SM

Figure 6: Influence of fraction of consumers for which 20 day voltage data is
collected on accuracy.

###  IV-D Impact of reduced voltage measurement length

In this numerical illustration, a situation is studied where power data is
available for 20 days, and supplementary voltage data is collected for a
limited duration from all customers. This could be the case in practice if the
network has a high SM penetration level, but the DSO wants to limit the amount
of supplementary voltage data to collect and store.

In Fig. 7, the obtained results are shown using 20 days of power data and
between 2 and 20 days of voltage data from a 0.5s class SM. This analysis
shows that the boosting ensemble can improve the average accuracy of the
studied feeders by 2.8%, compared to the voltage-based method. It can be
observed that with limited voltage data, the boosting ensemble still
overestimates the accuracy of the voltage method and, as a result, is
outperformed by the MLP. It can also be seen that the accuracy saturates with
increasing days of collected voltage data, especially in the case of the
boosting ensemble.

Figure 7: Accuracy for varying quantity of voltage data collected and 20 days
of power data (Class 0.5s SM).

The boosting approach only outperforms the voltage-based method when a 0.5s
class SM is used. In the case of a higher 0.2s class SM, the voltage-based
method already obtains 100% and in all lower class SM, the results of the
power-based method are low to start with, which makes it hard for the ensemble
methods to improve upon the voltage-based result.

###  IV-E Result Analysis

When benchmarking the existing methods, the voltage-based Pearson correlation
method showed better results compared to the use of K-means (see Figure 4). It
allocated all consumers correctly in most cases when a 0.1 class SM is used.
The best results are obtained for cases B and D, using a voltage-based
technique. Case B has the highest number of customers and case D mainly
consists of small and medium enterprises. It was expected from such feeders
that they show high voltage variation and therefore should be easier to
allocate. The power-based Pearson correlation method showed worse results than
the voltage-based methods. In contrast to the voltage-based techniques, the
method was not able to obtain a 100% accuracy in any case when using a
conventional non-‘s’ SM class when using 20 days of real smart meter data (see
Figure 5).

Ensemble methods can improve performance by leveraging the fact that some
consumers show more variation in their voltage while some have more
distinctive power variations. Furthermore, ensemble methods can be used to
combine different phase identification algorithms and/or different types of
data, including time-series measurements collected in different
campaigns/points in time.

In a scenario in which power and voltage data are available in equal quality
and quantity, the voltage-based method outperforms the power-based method in
all but one case. In such a scenario, the DSO would be recommended to use the
voltage-based approach. If there is missing voltage data, a bagging ensemble
can be used to identify the phase of the remaining customers using their power
data. The boosting approach only outperforms the simple bagging ensemble if
voltage-based methods obtain a lower accuracy then a power-based method, but
performs worse when using low class smart meters.

If supplementary voltage data is only available for a fraction of the
consumers in the network, a bagging ensemble improves the accuracy compared to
only using the available voltage data, especially when a low accuracy is
obtained with the power-based method (see Figure 6). The boosting ensemble
only outperforms the bagging ensemble in feeders where the power-based method
outperforms the voltage-based technique such that the boosting ensemble can
make use of the result of the power-based method. This is the case in the
studied network where the feeder in case C is better allocated with a power-
based method (when a 0.5s class SM is used).

In a scenario with a high roll-out of voltage-measurement capable smart
meters, a DSO is recommended to collect supplementary voltage data to use a
bagging ensemble only if he is confident that the power data could lead to a
decent phase identification. If not, it is best to use a bagging or voltage-
based method.

The boosting ensemble often allocates a customer using a power-based method
instead of a voltage-based method when the correlation threshold is not well
tuned. This shows the main challenge in combining power and voltage-based
techniques: it is not clear what accuracy the DSO can expect given a certain
scenario. Future work should address techniques to better understand which
factors influence the success of ensemble methods, allowing to draw better
decision-support guidelines.

##  V Conclusion

This paper investigated the performance of different state-of-the-art phase
identification methods and proposes an ensemble method. To the authors’
knowledge, it is the first ensemble method for phase identification that can
combine power and voltage data sets. This allows to leverage the advantages of
both power- and voltage-based machine learning methods. Furthermore, the two
data sets do not need to be collected synchronously, but can be shifted in
time. .

Our results show that for all accuracy classes the voltage Pearson correlation
methods performed better than K-means clustering. For correlation methods,
using transformer measurements as a reference leads to better results than
using a three-phase customer. For all but one accuracy class, the power-based
method is worse than the voltage-based method, for all analyzed feeders.
However, voltage measurements are not always available, whereas power-based
methods are more accessible, as the same data is used for billing purposes. In
general, feeders with fewer customers obtain higher accuracy than feeders with
many customers when using the power-based method. It is hard to predict the
accuracy of the power-based method a priori, because this varies considerably
depending on the type of feeder and the power profiles. However, in general,
if the SM accuracy class is high, the accuracy of the power method seems
acceptable.

In the future, additional ensemble methods could be proposed, which use
different algorithms from the literature and/or different data preprocessing.
Furthermore, the factors that influence the success of the different phase
identification methods could be further investigated. This would also help to
derive an improved metric or set of rules to assess a priori which phase
identification methods best suit different scenarios.

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