Contents Introduction
The expansion of sensors on the distribution system boosts the visibility of the distribution sector of the power grid which historically has low visibility and minimal data available for analysis. The penetration of advanced metering infrastructure (AMI) meters in the US reached 60% in 2018 [1] and the penetration continues to grow rapidly each year. Other types of sensors are also being installed at the distribution system level such as phasor measurement unit (PMU) devices, independently metered solar installations, electric vehicle (EV) metering, and smart relay devices. The wealth of sensors will only continue to grow as more internet-of-things (IoT) devices are incorporated into the power system [2]. Finding novel ways to leverage the newly available data from these sensors is a key task moving forward. These new capabilities are essential for grid modernization efforts, including the rapid interconnection of distributed energy resources (DERs), mitigating risks from increasing penetration of inverter-based resources, hosting capacity analysis, and efforts to increase resilience in the distribution system [3], [4], [5].
One of the key capabilities enabled by these sensors and newly available data is accurate distribution system model calibration. There are many well-documented problems that are common to distribution system models [6] and directly impact many of the grid modernization initiatives mentioned above. Examples of distribution system model calibration tasks include phase identification, topology detection, reconfiguration detection, customer-to-transformer mapping, and interconnection parameter estimation.
The method proposed in this paper focuses on leveraging all available data and sensors on the distribution system for the phase identification task, which is responsible for grouping customers by their service phase. This task is essential for detailed and accurate distribution system models and has a direct effect on the accuracy of the grid modernization tasks above, for example on hosting capacity analysis [7]. In addition to utilizing data produced by customer AMI meters, the proposed method also leverages any sensors that have been placed on the medium voltage network of the feeder. One example of this type of sensor is a distribution system relay, which also acts as a meter on the medium voltage lines in addition to its main objective of protecting grid assets. By taking advantage of multiple sensor types and a voltage correlation methodology, the proposed phase identification approach provides rapid, accurate results, and intuitive metrics for confidence in the algorithm phase predictions.
Related Works
Historically, the phase identification task has been solved using hardware-based methodologies. Types of hardware-based approaches include mobile PMU devices [8], [9], [10] and signal injection methods [11], [12], [13]. All of these methods have the advantage of high accuracy and being well-proven in practice. The disadvantages of this class of methods are the cost of the hardware itself and the cost of the man-hours required to install the hardware and subsequently carry out the phase identification task.
More recently there have been a number of algorithmic approaches for solving the phase identification problem. These are generally divided into power-based methods and voltage-based methods. The work in [14] provides a direct comparison between selected power-based methods and voltage-based methods. The authors concluded that the voltage-based methods have superior performance compared to the power-based methods tested; however, if a utility does not have access to AMI voltage data, then the power-based methods are a reasonable choice. The power-based phase identification methods are primarily load-summing approaches combined with optimization routines [15], [16], [17], leveraging the fact that all loads downstream of the substation should equal the load measured at the substation. There is also an event-based methodology that correlates high-profile events in the real power timeseries between customers and the substation [18]; these correspond to voltage spikes or dips that would be recorded by all customers on that phase.
The voltage-based methods rely on the fact that the voltage timeseries of customers on the same phase will be more correlated than customers serviced by different phases, although there are a variety of methodologies employed to leverage that fact. Work in [19] uses AMI voltage plus feeder topology information to formulate the task as a maximum marginal likelihood problem. Authors in [20] use voltage data as input to a spectral clustering ensemble that uses a co-association matrix for the final phase predictions. A constrained multi-tree approach is employed in [21] using correlation coefficients as a type of distance metric to build the tree structure. Authors in [22] propose a method for detecting changes in a customer’s phase as maintenance events or storm restoration alters phase connections from what is in the utility model. There are also a number of other clustering-based methods [23], [24], [25]. Finally, several approaches leverage correlations to ‘reference’ profiles to accomplish the phase identification task; these methods are the most similar to the method proposed here. One approach is to create an average representation of each of the three phases and compare that to each customer [26], [27]. One of the first uses of the reference profile approach compares each customer timeseries to the substation voltages [28], [29]. This can work reasonably well in simple feeders without voltage regulation in place. The method, referred to in the body of this paper as the Substation Method is used as a comparison method to the novel algorithm proposed in the following sections. Work in [30] first demonstrated that leveraging additional sensors on the medium voltage to act as reference profiles provides enhanced phase identification results, and provides a particular advantage when there are voltage regulators placed in the system.
The proposed algorithm leverages the sensors on the medium voltage lines in a similar way to the work described in [30] with some novel modifications to the algorithms. Although some of the methods mentioned above have demonstrated good performance, the inclusion of the additional data sources from sensors other than AMI meters provides an additional layer of information, performance, and confidence in the phase identification results. The contributions of this work include:
Implementation of a voting scheme for identifying phases
Leverages both AMI and sensors on the medium voltage of the distribution system to increase the accuracy and robustness of the phase predictions.
The experiment included robustness testing on a synthetic dataset under known conditions to ensure algorithm performance
Experiment included tests using four utility feeders with field-verified results. Demonstrates better phase identification performance compared to similar phase identification methods
Demonstrates the improvement of voltage estimation using QSTS methods after correcting customer phase labels
Methodology
A. Data Preparation
This methodology uses timeseries voltage data from single-phase AMI meters and additional sensors located on the medium voltage. Each additional sensor connected to three phase lines is assumed to have separate voltage measurements for each phase; thus, each AMI meter contributes one voltage timeseries and each sensor contributes three voltage timeseries to the analysis. The sensors could be any type of sensor placed on the medium voltage that records data at similar intervals and resolution to the AMI data. Prior to the steps shown in Figure 1, the voltage data is converted to a per-unit representation and then the difference between consecutive observations. Taking the difference transforms the timeseries from a per-unit magnitude timeseries into a per-unit change-in-voltage timeseries. This has previously been shown to be beneficial for voltage correlation methodologies [20], [30], [31]. Additionally, we assume that the phase labels for the sensor data are accurate before the application of this method. Any errors in the phase labeling of the sensors would significantly impact the results of this algorithm. As the customers are correlated directly to the sensor data streams and assigned phases using those labels, errors in the sensor phase labels would propagate directly to the predicted customer phases. Thus, the sensor phase labels must be verified in advance of applying the methodology proposed here. This is discussed further in Section IV.
Although a power injection at a particular bus (or customer) will have some impact on each of the phase lines A, B, and C, looking at the phase impedance and shunt admittance matrices informs the relative impact of the injection on each phase. The diagonal elements of the matrices, corresponding the phase of the power injection, will be significantly higher than the off-diagonal elements, corresponding to the other phases in the system. A more detailed description and analysis of these impacts can be found in [32]. This provides the basis for using voltage correlations for phase identification. Note that in the case where the power injections on each phase are extremely similar, voltage-based phase identification may not be possible.
B. Sensor-Based Phase Identification
Figure 1 shows a flowchart representation of the sensor-based phase identification methodology, and Algorithm 1 shows the pseudo-code for the method. In order to work with real data that often contains missing data, a window-based approach is used to calculate the correlation coefficients between the AMI timeseries and the sensor timeseries. This approach has been used successfully in [20] and [31]. In addition, using a windowed strategy leverages an ensemble in calculating the final correlation coefficients; Section V-C discusses the variability of single correlation instances, and the ensemble alleviates this effect.
Algorithm 1 Phase Identification Algorithm
For each customer
For each available window of data
For each
For a customer and a window and find the highest
Calculate the CC Separation Score,
If
Remove
Record
Calculate
Calculate
Vote on predicted phase
Calculate Window Voting Confidence Score,
Calculate Sensor Voting Confidence Score: in highest
Calculate
Find
For that
Calculate the CC Separation Score,
If
Exclude customer
In step 1, a window of data (4 days in this case, [20]) is selected, and any customers with missing data are discarded from consideration in that window. Thus, each window is a set of 4 days of contiguous voltage data from each customer. Pearson correlation coefficients are calculated between each customer and each sensor data stream (each sensor will have one data stream per phase). Equation 1 shows the Pearson Correlation Coefficient equation, where 
\begin{equation*} CC= \frac {\sum {({v1}_{i}-{v1}_{mean})}({v2}_{i}-{v2}_{mean})}{\sqrt { \sum {{({v1}_{i}-{v1}_{mean})}^{2}\sum {({v2}_{i}-{v2}_{mean})}^{2}}} } \tag{1}\end{equation*}
This work used the top 5 most correlated sensors for the voting, but this number would depend on the number of sensors available in the system. Selecting this number is discussed further in Section VII-C. The phase of the highest correlated data stream for the top correlated sensors is considered a vote for that phase for the customer in question. Using a voting approach, rather than taking only the highest correlated sensor (as is done in [30]), provides additional algorithm robustness under a variety of feeder conditions. In Step 5, the customer predictions are filtered based on a minimum window requirement per customer (see Section V-C for more details on that requirement) as well as filtering based on confidence scores (see Section III-C for more details on the confidence score metrics). Any customers with low confidence scores or too few windows available are considered to have low confidence in the predicted phase and should be either re-evaluated using more data or flagged for further post-processing investigation.
C. Confidence Metrics
Four confidence metrics were developed to evaluate the quality of the individual predictions for the phase of each customer. These metrics were originally defined in [30] and then adapted to this algorithm which uses a voting methodology for the phase assignment; additional details and examples can be found in that work. The four metrics are Correlation Coefficient Separation Score, Window Voting Score, Sensor Agreement Score, and Combined Confidence Score.
1) Correlation Coefficient Separation Score
The Correlation Coefficient Separation Score (CC Separation) considers the correlation coefficients between one customer and one sensor; this will consist of three values, one for each phase of the sensor. The difference is taken between the highest correlation coefficient and the next highest correlation coefficient, and this is defined as the CC Separation Score. Each customer will have a score with each sensor. Higher Separation Score values indicate a larger separation between the highest correlated phase on that sensor and the next highest correlated phase. This can be interpreted as having higher confidence in that phase prediction because the distance between the prediction (highest correlated phase) and the next is larger. Likewise, a low value indicates that more than one phase of the sensor was similarly correlated to the customer, and the results should be considered low confidence since only one phase should have a high correlation.
2) Correlation Coefficient Separation Filtering
The Correlation Coefficient Separation Filtering that occurs in Step 2 of Figure 1 leverages the CC Separation Score discussed in Section III-C1. If the CC Separation Score is low, then the correlation coefficients from that sensor are omitted from the window and not included in the mean calculated in Step 3. Effectively, this removes the correlation coefficients for sensors where more than one phase on that sensor is correlated with a customer. Those correlation coefficients are not helpful to incorporate into the final phase prediction. The correlation coefficients that are filtered in this manner, do not contribute to the final correlation coefficients, window voting, or sensor agreement; they are simply discarded for not containing useful information. One situation where this can occur is if a sensor is far away from the customer in question, especially if the sensor and the customer are separated by a voltage regulating device. Filtering those correlation coefficients before including them in the ensemble, eliminates the impact of sensor correlations that do not provide useful information. Setting the thresholds for this parameter is discussed in Section 5.4. One note about the correlation coefficients is that the magnitude of the coefficients themselves varies significantly depending on the particular dataset. For example, the CC are generally lower in the synthetic dataset compared to the utility datasets. For this reason, direct comparison or discussion of CC magnitudes is not used.
Figure 2 demonstrates the CC Separation Score and the filtering for a single customer with two different windows plotted, one which we believe predicts the phase correctly (circles, predicting Phase A) and one which we believe predicts the phase incorrectly (squares, predicting Phase C). The colors indicate the phases of each sensor data stream. Empty markers indicate that those correlation coefficients were filtered due to poor CC Separation. A good example of this is shown in the blue box. Looking at Sensor 14, the red and blue square markers overlap, indicating that Phase A and Phase C for that sensor were similarly correlated for that customer. For this reason, correlation coefficients from that sensor were filtered out in the window shown. The window plotted using the square markers has poor CC Separation Scores for nearly all sensors. The remaining sensors (Sensor 0 and Sensor 6) both predicted Phase C. However, for the window plotted with circles, twelve sensors remain after filtering and all predict Phase A for this customer.
Example of correlation coefficient separation for the same customer for two different time windows. Filtered correlation coefficients using a CC Separation Score filter of 0.06 are shown with empty markers; examples of poor correlation coefficient separation for the sensors can be seen inside the blue box.
3) Window Voting Score
The Window Voting Score considers each correlation coefficient calculated during steps 1 and 2 in Figure 1 separately. For each customer and each window, the top correlated sensor data streams are used to produce a ‘vote’ for the phase of the sensor data stream. The same sensor voting methodology used in Step 4 of Figure 1 is used here, just in a single window. The Window Voting Score is the percentage of windows that agree on the predicted phase. For example, in the case of 10 windows, if 9 windows had a predicted phase of B and 1 window had a predicted phase of C for a particular, then the Window Voting Score would be 90%. This score is used in Step 5, shown in Figure 1 as part of the final filtering step. An example of this is shown in the Results Section in Table 3, Customer/Row 7. This customer was filtered in Step 5 because of the Window Voting Score of 0.48; this means that only 48% of the included windows agreed on the predicted phase of this customer. Thus, the phase identification results are considered low confidence and it is flagged for further consideration.
4) Sensor Agreement Score
The Sensor Agreement Score considers the top correlated sensor data streams for each customer, and the score is the percentage of voting sensors (5 in this work) that agree on the predicted phase for that customer. This metric is calculated after the mean is taken in step 3 of Figure 1. For example, if there are 5 sensors included in the vote and, for a particular customer, the highest correlated data stream was Phase B for 4 sensors and Phase A for 1 sensor, then the Sensor Agreement Score for that customer would be 80%. This score is part of the filtering in Step 5 shown in Figure 1.
5) Combined Confidence Score
The Combined Confidence Score is a combination of the Window Voting Score and the Sensor agreement score. The decimal form of each is multiplied together to form a combined score. In the examples above the Window Voting Score of 90% (0.9) is multiplied with the Sensor Agreement Score of 80% (0.8) for a Combined Confidence Score of 0.72. If both scores are 100%, then the Combined Confidence Score will be 1.
These scores together provide an intuitive way to evaluate the quality of the predicted phase for each customer and discard predictions that should be treated as low-confidence predictions. Work shown below used 75% for the Sensor Agreement and Window Voting Score, individually. Low-confidence predictions can occur for a variety of reasons in real systems. One example which came up in this work is the case of a customer who was incorrectly included in the dataset for the feeder under consideration, when they were actually located on a different feeder. In this case, we would expect the confidence scores to be low because that customer will not be highly correlated with any sensor on the feeder.
Validation of Sensor Labels
The proposed algorithm relies on the accuracy of the phase labels of the sensors placed within the system; if the phase labels on the sensor data streams are incorrect, those errors will propagate directly to the phase identification results. In general, because there are only a few sensors and they are often incorporated into the Supervisory Control and Data Acquisition System (SCADA), there are usually fewer labeling errors. One way to double-check prior to running this phase identification algorithm is to determine if the sensor data streams for each phase are highly correlated with each other. This is done by calculating correlation coefficients between each sensor data stream and for each data stream take the highest correlated other sensor data streams as a vote, and if the vote matches the original label of that data stream then consider the label to be validated, [30].
Figure 3 shows an example of this; the correlations between Sensor 0– Phase B were plotted with all other sensor data streams. Sensor 0– Phase B is shown in the middle of the plot with other sensors around the circle and increasing correlation coefficients from the middle to the outer edge. The highest correlated data stream from every other sensor is Phase B, this is seen by the green line. An interesting note here is that it is also possible to see the impact of the voltage regulator in Feeder #1 (further described in Section VI). Sensor 0 is on the same side of the voltage regulator as Sensor 1, 6, 8, and 9; while Sensors 2, 3, substation, 4, 5, and 7 are on the opposite side of the voltage regulator.
Radar plot of correlation coefficients demonstrating an example of validating one of Sensor 0’s data streams on Feeder #1.
If discrepancies in phase labeling of the sensor data streams are discovered during this validation step, they must be resolved prior to running the phase identification algorithm. If a small number of the sensors appear to have incorrect phase labels, using the combined votes of the other sensors can be used to correct the labels prior to running the phase identification algorithm.
Synthetic Dataset Results
The sensor-based methodology is first demonstrated on a synthetic dataset where the ground truth is known, and any data quality issues can be tightly controlled. Actual real and reactive power profiles from anonymized utility AMI datasets with 1-minute resolutions were applied to the EPRI Ckt. 5 topology [33] and 10 sensors were placed throughout the feeder model. A yearlong quasi-static time-series (QSTS) simulation was performed in OpenDSS [34] using a 1-minute time step to generate the semi-synthetic voltage timeseries data for all sensors and AMI meters. The voltage data were then averaged down to 15-minute resolutions before being modified to include realistic data concerns. Overall, the baseline synthetic voltage dataset for this work includes 15-minute averaged timeseries data over a one-year period for 10 sensors, a substation, and 1379 customers.
A. Injecting Realistic Data Concerns into Synthetic Data
There are a number of different data issues that can occur in real data; please see [35] for a more detailed analysis of these issues. This work injects measurement noise, meter bias, and missing data in known quantities into the synthetic data to test algorithm robustness.
Normally distributed measurement noise was injected into both the AMI voltage data and the sensor voltage data with differing standard deviations for testing purposes. For each customer/sensor measurement, an additive noise quantity was pulled from the normal distribution specified by a mean of 1 (all voltages converted to per-unit representation as discussed in Section III-A), and the specified standard deviation was added to the measurement. For the baseline simulation, the standard deviation for the AMI data was chosen to be 0.07%. This value was chosen based on a meter testing report provided by one of our utility partners (not cited due to the proprietary nature of the report), where the demonstrated standard deviation on a set of metering tests on 0.5% class meters was 0.07%; this also ensures that 99% of the data (3 standard deviations) is within the upper bounds for the 0.2% meter class. The baseline for the injected measurement noise for the sensor voltage was chosen to be 0.04%. This value was based on the analysis of the utility sensor data discussed further in Section V. Each IntelliRupter Ⓡ sensor from that dataset records two data streams, one from each side of the device. This provides the ability to directly compare the two measurements (on the closed IntelliRupters Ⓡ in the middle of the feeder) and obtain an estimate of the measurement noise present in the sensors. Across all available sensors, this analysis showed a standard deviation of 0.04%.
Meter bias for the AMI and sensor data streams was chosen uniformly at random for each customer and sensor in the range +/−0.2% for the AMI meters and +/- 0.3% for the sensors. The proposed algorithm is not sensitive to the meter bias due to the transformation of the voltage into the difference representation discussed in Section III-A. The algorithm input is the change in per-unit voltage which eliminates any impact due to metering bias in the measurements.
Missing data is also injected uniformly at random for each customer data stream. A minimum and maximum missing interval (8 and 96 datapoints respectively) are supplied as well as a desired percentage of missing data. This missing data mimics the effects of communication failure and short outages in utility datasets. The proposed algorithm uses the ensemble approach in steps 1 and 2 in Figure 1 to deal with missing data in the voltage timeseries.
The injection of these real-world data issues enables the testing of algorithm robustness under known conditions and increases confidence in the algorithms’ ability to function under a variety of real-world conditions.
B. Baseline Results and Comparison with Substation Method
First, a baseline test was conducted by injecting a reasonable quantity of normally distributed noise into both the AMI voltage measurements and the sensor voltage measurements. The baseline noise injection was 0.07% standard deviation for AMI and 0.04% for the sensors as discussed above. The algorithm was able to identify the phases of the AMI meters with 100% accuracy. Figure 4 shows a histogram of the Correlation Coefficient Separation Score for the 1379 customers. This range of values for this score will vary depending on the dataset, thus determining a level of confidence for a particular customer based on this score must be done relative to the scores of the other customers in the dataset. The Combined Confidence Scores are shown in Figure 5; a large number of customers have a Combined Confidence Score of 1, meaning that both the Window Voting Score and the Sensor Agreement Score were 100%, and the majority of customers have scores above 0.95. This indicates a very high level of confidence in these phase predictions. In fact, on the synthetic data, the Sensor Agreement Score was 100%.
Histogram of correlation coefficient separation score for customers in the synthetic dataset.
A comparison was then made on the synthetic data between the proposed Sensor Method and the Substation Method from [28] and [29]. The Substation Method also achieved 100% accuracy on identify the phase of customers, and the CC Separation Scores were similar to what is seen in Figure 4 from the Sensor Method. Figure 6 shows a histogram of the Window Voting Confidence Score for the Sensor Method (blue) and the Substation Method (red), where it is clear that the Sensor Method had higher overall scores. In the case of the synthetic data, there is some advantage of the Sensor Method, but not an overwhelming one. In simple feeders, without voltage regulators and other complicating topology or data issues, the Substation Method may be sufficient for the phase identification task. However, there are many complicating factors in utility feeders, and there are two examples in Section VI where the Substation Method does not produce good results on utility data.
Combined histogram of window voting scores for the sensor method (blue) and the substation method (red).
C. Robustness Testing
Following the baseline testing, robustness testing with missing data and measurement noise was also performed. Missing data from 0.1% missing to 4% missing were tested, and the standard deviation of normally distributed noise from 0.01% to 0.4% was used for the noise sweep. The parameter sweeps for measurement noise and missing data were performed independently, and the CC Separation Scores were averaged across all customers for each parameter value. The results are shown in Figure 7 with the missing data sweep results shown in red and the measurement noise injection results shown in blue. There is a decline in the average CC Separation as the standard deviation of the injected noise increases. However, the CC Separation changes very little with the missing data sweep, even up to 4% of the data points missing. This is an intuitive result because the final correlation coefficient between each customer and each sensor data stream is the median of the correlation coefficients in the windows. As long as there is at least one window with a good quality correlation coefficient then the results should be similar. In practice, to guarantee that the median value is an accurate representation of the actual correlation, more than one value is required; this is discussed in detail in Section V-C which covers data requirements for the algorithm. In the synthetic data, the majority of the windows behave similarly, however, there is more variation in the behavior of the utility data windows.
Synthetic data robustness testing– CC Separation– missing data sweep shown in red, and measurement noise sweep shown in blue.
Figure 8 shows the same testing parameters with the Combined Confidence Scores plotted. Again, the score remains fairly consistent for the missing data sweep; if a window is missing due to missing data, it is not considered in either the correlation coefficient average or the Combined Confidence Score. There are simply fewer windows involved in the analysis. The Combined Confidence Score follows a similar, decreasing trend as the CC Separation Score as the measurement noise in the data increases.
Synthetic data robustness testing - Combined Confidence Scores– missing data sweep shown in red, and measurement noise sweep shown in blue.
Satellite image of a lateral in Feeder #4 that was identified to be incorrectly labeled as Phase B and actually connected to Phase A.
Both Figure 7 and Figure 8 indicate that the algorithm is robust to missing data, as long as there remains enough data for clear correlation coefficients. The amount of data required is discussed in Section VI-A in the context of the utility data results. In addition, these results show a gradual degradation of the CC Separation Score relative to the injected measurement noise. As discussed in Section 3.5, we consider a realistic baseline to be 0.04% standard deviation of noise for the sensor and 0.07% for the AMI data. At those values, the CC Separation Scores and Combined Confidence Scores remain very high
Utility Dataset Results
The methodology was also demonstrated on data from a utility in the southern United States. Results from four different feeders are shown below, as well as an analysis of the data requirements for the algorithm. Table 1 shows details and differences between the four feeders. Note that there is a range of lengths, substation regulator type, and number of per-phase regulators out in the feeder. Note that LTC regulators regulate all three phases together as a unit while the per-phase regulators regulate each phase independently of the others. The circuit configurations are shown in Figure 10 for Feeders #1 and #2 and in Figure 11 for Feeders #3 and #4. The substation is marked with a star, IntelliRupters Ⓡ with gold markers, and customers are colored by the utility phase labels. The medium voltage sensors for this utility are IntelliRupters Ⓡ that are recording voltage, real power, and reactive power data at a 15-minute resolution, equivalent to the AMI meters at the customer locations. IntelliRupters Ⓡ were used in this work because that is what the utility has installed; the proposed methodology will work with any type of sensor recording measurements at a similar resolution to the AMI meters. This work does not endorse any particular type of sensing device.
Circuit plot with heatmap of correlation coefficient separation score plotted by customer for Feeders 1 and 2.
Circuit plot with heatmap of correlation coefficient separation score plotted by customer for Feeders 3 and 4.
The data from this utility’s AMI meters are instantaneous measurements of voltage and cumulative measurements of real power at 15-minute intervals for approximately one year. Work in [36] suggests that average, rather than instantaneous, voltage measurements often work better in these types of algorithms. This conclusion was confirmed in our testing of this algorithm on this utility data. The correlation coefficient analysis was much more accurate using the 30-minute average data. Thus, for the two feeders discussed below, the additional pre-processing step of averaging the instantaneous 15-minute data to 30-minute data was added prior to the pre-processing steps discussed in Section III-A. In addition, for the simulated voltage results shown below, the voltage drop due to the secondary system and due to metering bias was corrected prior to calculating the results shown.
A. Phase Prediction Results for Four Feeders
The full results for all four feeders are shown in Table 2. Feeders 1– 4 had 6, 3, 5, and 77 customers respectively that were predicted to be on a different phase from the original utility labels. In each case, the majority of customers were predicted to have the same labels as in the utility model with a small number predicted to be incorrectly labeled. The omitted row shows the number of customers that were omitted from the analysis due to either having too much missing data or too much data being filtered due to poor correlations as discussed in Section III. For the omitted customers, both customers in Feeder #1 were due to the CC Separation Filtering. In Feeder #2, the omitted customers were all due to the CC Separation Filtering. In Feeder #3 the three omitted customers are all due to missing data. In Feeder #4, both omitted customers are due to missing data.
In Feeder #1, 6 high-confidence customers and 1 low confidence customer were identified as having different phase labels from the original utility model. Table 3 shows those results along with the confidence scores for those customers. One of the 7 (bottom row in Table 3) was eliminated from consideration due to low confidence scores in the Window Voting Score and the Combined Confidence Score. Only high confidence score customers should be used. This filtering step is critical for removing data that represents uncommon operations because there are many unique situations that occur in real data which may interfere with algorithm predictions and having the confidence scores per customer provides the ability to filter out unusual situations. The other 6 customers were investigated by the utility through field verification, and in each case, the algorithm phase predictions were proven to be correct. Notice the three columns for the confidence scores per customer, and the significant difference in magnitude between customers 1–6 and customer 7. Thus, all of the high-confidence predictions were proven to be accurate for Feeder #1.
Feeder #1 was used as an example to illustrate the confidence scores, but the utility did field verification of all four feeders for high confidence customers predicted to be different from the utility model, and in every case, the algorithm was shown to be 100% accurate.
In Table 2, notice the large number of customers (77) detected as being incorrectly labeled. Sixty-nine of those customers are on a single-phase lateral, which was incorrectly labeled in the utility’s GIS model. Figure 9 shows a satellite image of the lateral. This lateral was labeled as a Phase B lateral in the GIS system, but the algorithm predicted each of the customers was a Phase A customer. The utility field verified these results and determined that it is actually a Phase A lateral in the field.
These results on four utility feeders demonstrate the excellent performance of the proposed method. All of the predictions were either field-verified or eliminated (or flagged for further consideration) due to low-confidence predictions. The proposed method provides a way to algorithmically calibrate phase labels across utility feeders, and the intuitive confidence metrics enable the utility to act on the predictions with confidence that false-positive errors are not being introduced into the system.
B. Confidence Scores Analysis for Four Feeders
Inspecting the confidence scores produced by the algorithm for each of the four feeder cases leads to some general findings related to feeder characteristics. Figure 10 shows a circuit plot of Feeder #1 (blue) and Feeder #2 (black), fed off of the same substation (star), sensors are in yellow, and voltage regulators are light blue. The heatmap colors are the correlation coefficient separation score for each customer, where cooler colors indicate higher confidence. Figure 11 shows the same plot for Feeders #3 (blue) and #4 (black), again serviced by the same substation. Note that overall, the confidence scores are much higher in Figure 11 in both Feeder #3 and Feeder #4. We believe one reason for this is that the substation regulator for Feeders #3 and #4 (Figure 11) is a per-phase regulator while the regulator for Feeders #1 and #2 (Figure 10) is a load tap changer (LTC) regulator where all phases are regulated together. Per-phase voltage regulation would decrease the similarity of the voltage profiles, and the decreased cross correlation improves the ability to predict which phase each customer is on. Also, in both feeders shown in Figure 10, the confidence scores increase as the customers get farther away from the LTC regulator. Although there is a loose correlation in general with an increase in confidence scores farther away from the substation, it is especially key for substations with LTC regulators. Another thing to notice is that the confidence scores increase downstream of a mid-feeder per-phase regulator (blue diamond), as long as there are also sensors downstream of the regulator. This is especially apparent with the regulator in Feeder #1 in Figure 10 where we see a dramatic increase in confidence scores at the bottom part of the figure. The opposite case can be seen in Figure 11 in the bottom portion of Feeder #3. There are two regulators but no sensors downstream of them. Figure 12 shows a zoomed in view of that Section of Feeder #3. There is not a change in the overall magnitude of the confidence scores of those customers.
Zoomed in perspective of the bottom Section of Feeder #3 from Figure 10. The heatmap colors represent CC Separation scores; the scores do not change in magnitude downstream of the regulators (blue diamond) because there are no sensors downstream.
One interesting situation for phase identification occurs in the substation of Feeders #3 and #4, Figure 10. The sensor inside the substation is located upstream of the per-phase substation regulator. Thus, the data stream which is labeled as ‘substation’ is not useful (or at least minimally useful) for this type of phase identification method. This is because the measurement is functionally separated by the regulator from all customers served on that feeder. In this case, using the substation method for phase identification would not work at all, and either the sensor method proposed in this paper or some other distinct methodology, not leveraging the substation voltage, would be required. Without inspecting circuit diagrams for each feeder, it would be difficult to know this information in advance of running a phase identification algorithm.
The Combined Confidence Score distribution is shown in Figure 13 for Feeder #1 and Feeder #3. Compared to the scores on the synthetic dataset in Figure 5, these are lower overall with a larger spread. This indicates that the utility datasets are more challenging than the synthetic one. Again, notice that the Feeder #3 Combined Confidence Scores are overall higher than for Feeder #1, just as was seen in the Correlation Coefficient Separation scores plotted in Figure 10 and Figure 11.
C. Voltage Improvements After Phase Identification
To further demonstrate improvements due to correcting phase labels in the system, a yearlong quasi-static time series (QSTS) analysis at 15-minute resolution was conducted in OpenDSS on both versions of the model (i.e., with original phase labels and corrected phase labels); the QSTS analysis used the circuit model and AMI power to produce estimated AMI voltage. This estimated voltage was then directly compared to the actual measured AMI voltage recorded by the utility. The first QSTS simulation used the original circuit model provided by the utility, and the second used the model with the corrected phase labels shown for the six customers in Table 3. Figure 14 shows the improvement in voltage residuals averaged over the year for the six customers who had incorrect phase labels in the original utility model. The mean absolute error (MAE) for both the original phasing (blue) and Corrected phasing (green) was calculated by taking the difference between the measured voltage and the estimated voltage produced by OpenDSS at each time-step, and then calculating the average error over the year. In every case, there is an improvement in the MAE after correcting the phase labels; the improvements range from
MAE for the voltage difference between the measured and simulated voltage, showing the improvement in voltage error by correcting the phase labels in simulation.
D. Comparison Between Sensor Method and Substation Method on Utility Data
This Section demonstrates that the proposed method outperforms the substation method, using Feeder #1 as an example. Although the comparison between Substation Method and Sensor Method on the synthetic data indicated that under certain conditions the two methods both perform well, in the real world there are many situations where the Substation Method cannot perform well. One good example of this is in the presence of voltage regulators as there is in Feeder #1, see Figure 10. In that case, correlation coefficients between the downstream customers and the substation will not provide enough information for the phase identification task. Figure 15 shows the spread of correlation coefficients for the Sensor Method on Feeder #1. The ‘Labeled on Phase A’ box on the left contains all of the customers originally labeled on Phase A and their correlations to each of the sensor data streams A, B, and C. Since the majority of the original phase labels are accurate, we expect to see higher correlations in the boxplot for ‘Labeled on A’ with ‘Sensor A’, ‘Labeled on B’ with ‘Sensor B’, etc, and that is shown in Figure 15. That means that the phases are differentiable using the sensor correlations.
Boxplot showing the spread of correlation coefficients between customers and sensors, using the Sensor Method on Feeder #1.
Contrast that with Figure 16 that is the same type of figure, but for the Substation Method. In this case, the phases are not differentiable from one another. The substation method does not work for this feeder, the sensor method is essential.
Boxplot showing the spread of correlation coefficients between customers and the substation, using the Substation Method on Feeder #1. This shows the challenge of using correlation coefficients to substation voltage in the presence of voltage regulators.
Algorithm Parameter and Requirements Discussion
A. Data Requirements
There still remains the question of how much data is required for the algorithm to work correctly. The key issue with this question is the fact that there is some amount of ‘noise’ in the correlation coefficients for each window. This can be seen in Figure 2 and in Figure 13 in the Combined Confidence Score histograms. In fact, in the synthetic data case, the sensor agreement score is 100% for all customers, and the variation in Combined Confidence Score is driven entirely by the differences in Window Voting Score. This means that even in the controlled synthetic data case, there is some noise in the correlation coefficients, meaning that sometimes the highest correlated data stream does not correspond to the correct phase. For example, Figure 17 plots the correlation coefficients for a single customer located on Feeder #2, with all of the sensors in two different windows. This customer has a predicted phase label of Phase A, the Window Voting Score is 81% and the Sensor Agreement Score is 100%. Then, in total, 19% of windows have a different highest correlated phase than Phase A. Looking at Figure 17, in one window (circle markers), we believe the phase was predicted correctly, and in the other window (square markers), we believe the highest correlated phase to be incorrect. Note that only two sensors remain in that window after filtering using the CC Separation scores; this is also an indication that this particular window posed some difficulty. In both windows, sensors 12 and 13 were filtered due to the CC Separation filtering step. This provides a specific example of why the ensemble approach is important for this methodology; individual windows may not provide accurate correlation coefficients. The two remaining sensors (in the incorrect window, square markers), Sensor 0 and Sensor 6 both have fairly high CC Separation between the first and second highest correlated data streams, making it difficult to know that the results from this window are likely to be spurious, without seeing the results from the whole ensemble of multiple other windows. Although this is one particular example, there are similar problematic windows across all datasets that were tested in this work, both synthetic and utility datasets. This result clearly illustrates the need for an ensemble approach.
Correlation coefficients between one customer and the sensors in two different windows. The believed correct window is shown in circle markers and the believed incorrect window is shown in square markers. Sensor correlations that were eliminated due to CC Separation Filtering are not shown on the plot.
Based on testing with the utility datasets and the known (field-verified subset) of customers, we are recommending at least one month of data per customer as a minimum when using this methodology. In practice, with utility partners, three months is being used as a more cautious approach. On the four utility datasets used in Section VI, using one month (per customer) produced good results. However anecdotally, a utility partner mentioned that on some more difficult feeders, more data produces better results. In the utility datasets, using less data than one month per customer, began to produce additional flagged customers. Upon further investigation, those extra customers had similar behavior to the customer shown in Figure 17. Thus, we believe those results to be false positives. One month provides a reasonable set of windows for the ensemble, regardless of the window size chosen, and the ensemble protects against that type of spurious correlation. The absolute minimum data requirements are likely to vary between feeders; comparing Figure 10, Figure 11, and Figure 13, it appears that Feeders #3 and #4 are easier in the phase identification task, compared to Feeder #1 and #2 based on the fact that the confidence scores are higher overall. Requiring three months of data is a cautious recommendation based on the testing using the four utility feeders plus some additional windows as a buffer.
B. Parameter Tuning Analysis
There are two primary parameters that can be adjusted in this algorithm; these are the window size and the CC Separation filter parameter. Window size is simply the number of datapoints used for each correlation coefficient calculation in the ensemble in steps 1–2 in Figure 1. The CC Separation filter value is the value discussed in Section 3.4; higher values for this parameter will result in more values being excluded from consideration. The trade-offs associated with these parameters are discussed below. In addition, there is some discussion of utilizing the confidence scores for the purposes of filtering the algorithm results. Figure 18 shows the results of a parameter sweep of the window size (y-axis) and CC Separation filter threshold (x-axis) for Feeder #1 using one year of data. The heatmap values indicate the resulting (average) CC Separation using those parameters. The results are further filtered using the following constraints, the average Window Voting Score
Utility Feeder #1 parameter sweep results for window size (y-axis) and CC Separation filter threshold (x-axis). The heatmap values show the average CC Separation Scores and black squares represent parameters eliminated due to confidence scores or other criteria.
In choosing values for both parameters there are trade-offs. For the window size parameter, the main trade-off is that larger windows result in more customers being eliminated due to missing data (not meeting the minimum windows requirement). With the CC Separation filter threshold, there is also the missing customer issue. As more correlation coefficients are filtered, the minimum window requirement is also an issue. In addition, in Figure 18 we can see that the CC Separation Score increases as the CC Separation Filter Threshold value increases (lightening color left to right in the heatmap). This implies that for better generalizability a larger value of the CC Separation Filter Threshold should be chosen. For example, choosing a window size of 144 and a CC Separation Filter Threshold of 0.04– 0.07 might be reasonable choices. The results shown in the previous sections use a window size of 144 and a CC Separation Filter of 0.05.
While the results shown in Figure 18 demonstrate that the algorithm is not extremely sensitive to the choice of window size or CC Separation Filter Threshold, the following figures more rigorously demonstrate why a value of 0.05 was used for the CC Separation Filter Threshold in this work and why it may be generalizable as a starting value for the parameter. Figure 19 shows a sweep of the CC Separation Filter values on the x-axis and the median Window Voting Score across all customers on the y-axis. The dashed lines represent the synthetic dataset (blue), Feeder #3 (black), and Feeder #4 (purple) plotted as horizontal lines, using the median Window Voting Score without the CC Separation Filtering applied. For Feeder #1 (red) the median Window Voting Score increases as the CC Separation Filter Threshold increases until at 0.05 it is above the line for Feeder #4. Likewise for Feeder #2, there is a sharp increase in median Window Voting Scores with increasing CC Separation Filtering. At a value of 0.05 Feeder #4 has a median Window Voting Score of
Note from Table 1 that both Feeder #1 and #2 have LTC-type regulators while Feeder #3 and #4 have per-phase regulators. This makes sense that the overall scores are higher for Feeder #3 and #4 and why the CC Separation Filtering provides more benefit in the case of LTC regulators. Figure 20 demonstrates this benefit. Histograms for the Window Voting Score are shown in Figure 20 with the customers downstream of the voltage regulator plotted in blue and customers upstream of the regulator plotted in red. With the CC Separation Filter threshold set at 0.05 (right), notice that many of the customers in red have shifted to the right, increasing their Window Voting Score. This is a clear demonstration of the value of the CC Separation Filtering.
Histograms of feeder #1 window voting score with no CC separation filtering (left) and a threshold value of 0.05 (right). Notice the improvement in the Window Voting Scores with the CC Separation filtering.
The last parameter is the number of votes to include in the final phase prediction in Step 5 in Figure 1. This parameter should be set taking into consideration the total number of sensors on the feeder and any relevant feeder topology considerations. For example, in Feeder #1 discussed above, there are 10 total sensors, but there is also a voltage regulator placed in the feeder, thus the feeder is essentially divided into two segments. We would not expect sensors on the other side of a voltage regulator to give meaningful correlations to a customer. Thus 5 sensors were used for voting in Feeder #1 this work. The number of votes should be set with these considerations in mind, potentially using fewer votes if fewer sensors are available. However, using the CC Separation Filter will also help to eliminate the contribution from sensors that may not be providing useful information to the analysis.
C. Sensor Requirements Discussion
Finally, there is the question of the number and placement of the additional sensors on the medium voltage system. The requirements for sensor number and placement are heavily dependent on the feeder topology and specific data considerations, but there are some general guidelines and discussions that are possible. At a minimum, there needs to be at least one sensor per regulator ‘zone’. The specific placement appears to be less of a concern as long as all voltage regulation ‘zones’ are covered. That could include the substation, as long as the measurements are taken downstream of the substation voltage regulation equipment. This minimum configuration can be sufficient in easier feeder cases, as was seen in the synthetic dataset results in Section 4.2. However, in practice, more sensors are recommended. The ensemble nature of using multiple sensors to vote on the predicted phase is most robust when there is a larger number of sensors, for example, 5 votes were used for Feeder #1 which has 10 sensors available. In one case seen by a utility partner, for a particularly difficult feeder, adding data streams from two additional sensors proved necessary to produce quality results.
Conclusion
This work demonstrates a sensor-based phase identification method that leverages voltage data from customer AMI meters and medium-voltage sensors on the distribution system. The method is demonstrated on a synthetic dataset with testing for robustness in the presence of measurement noise, meter bias, and missing data, achieving 100% accuracy in those tests, as well as being demonstrated on four utility feeders. The utility field verified the high-confidence results on all feeders, confirming the algorithm’s predictions for incorrect phase labels to be 100% accurate in each case. In addition, it was demonstrated how correcting the phasing in the model improved the simulation accuracy and decreased the error between the simulated and measured voltages by 0.75 V on average over the year for the six customers that had their phasing corrected. The sensor-based algorithm was also compared with a substation-based algorithm and was shown to produce correlations with higher confidence and be more robust to complex circuit topologies that include voltage regulating devices. Taken together, these observations highlight the advantages of using the proposed algorithm prior to conducting QSTS simulations for distribution system planning and analysis purposes, even when just one month of data is available. Overall, the sensor-based method shows excellent promise in results, robustness to real data issues, and scalability in terms of data requirements.
ACKNOWLEDGMENT
The employee owns all rights, title, and interest in and to the article and is solely responsible for its contents. The U.S. Government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this article or allow others to do so, for U.S. Government purposes. The DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan https://www.energy.gov/downloads/doe-public-access-plan.