Investigation of Improved Distribution Load Allocation ...

IntroductionImportance of Improved Load ModelsSystem loads have a significant influence on system performance Consequently accurate modeling of system loads with distribution plan-ning tools is critical for effective system planning Increasing levels of distributed energy resources (DER) however also require planners to perform assessments beyond peak loading conditions For example host-ing capacity is often calculated assuming off-peak loading conditions inaccurate load models can result in under- or overestimating hosting capacity

The application and value of advanced metering infrastructure (AMI) and other measurement data to improve system models are the focus of this technical briefmdashin particular how increased visibility from these new data sources could be used to improve load allocation techniques This work is part of a continuing project in EPRIrsquos Distribution Operations and Planning program to advance methods for distribution load modeling

Brief Background on the Analyzed Data SetThe analyses documented in this technical brief are based on a single feeder derived from the data set described in Reference [1] The test feeder serves a total of 1898 customers off 614 service transformers The feeder load profilemdashthe total of the active power of all loads on the feedermdashover the measurement year is plotted in Figure 1 To emulate and test the application of historical data to represent future loading condi-tions the data surrounding the peak demand in July (775 MW) were often used in the analysis as the basis for load allocation models These models were then tested against the measurement for August peak load (733 MW) These two instances are indicated on the feederrsquos annual load profile shown in Figure 1

Figure 1 Measured annual load profile used in the analyses

Investigation of Improved Distribution Load Allocation Using Expanded System MonitoringTechnical Brief mdash Distribution Operations and Planning Power Delivery and Utilization

Report OutlineThe remainder of this report has two parts

1 The first part analyzes various load allocation methods in detail The accuracy of kWh load allocation is analyzed for kWh properties calcu-lated over different time periods The first part of the report also introduces a novel linear regressionndashbased load allocation method and compares its performance with kWh load allocation

2 The second part provides additional insights on diversity factor by comparing different diversity factor models to those estimated using AMI data

Load Allocation Methods with AMI DataBackgroundLoad allocation is commonly a precursor to load flow analysis and other distribution planning assessments Specifically load allocation is a model-ing technique used to distribute or ldquoallocaterdquo the total forecasted power typically at the feeder head to each of the downstream loads This was traditionally done in part because of limited customer measurement data as well as cost and inaccuracies associated with forecasting loads down-stream of the substation A more detailed introduction to load allocation and common load allocation methods can be found in Reference [1] An implementation of load allocation in distribution planning software OpenDSS is described in Reference [2] Results for commonly used kWh load allocation methods using different measurement data are presented in this section along with a novel linear regressionndashbased load allocation method

Load allocations are performed at the service transformer level As is cus-tomary for many utilities assigning the demand of large industrial cus-tomers is assumed to be done separately from the load allocations exam-ined here Distribution losses phase unbalance and other aspects that may influence load allocations are not discussed but may be addressed in the future

Traditionally feeder loads are allocated to represent expected peak condi-tions Depending on the system this may include both a winter and sum-mer peak When representing non-peak conditions some utilities may scale these allocations directly or may generate new allocation based on these conditions Nevertheless it is not well-understood how the allo-cated peak minimum or other system load conditions are best used to analyze other system load conditions Load diversity varies over time and

10217765

EPRI Technical Brief 2 November 2018

a load allocation from a single instance cannot be expected to perfectly represent feeder load diversity at another instance To illustrate trans-former loads during a feederrsquos July peak is compared to those for the August peak in Figure 2 Although an overall correlation exists across the loads during both system peaks the magnitudes of each individual load may vary significantly As a result the same load allocation factors cannot perfectly represent both time instances Recognizing this the subsequent analyses examine how well peak load allocation can be used to represent other feeder load conditions

Figure 2 Transformer load during the feeder peak load in July and a high feeder load time in August If the peak demand time and the high demand time had the same load diversity all the circles would be on the red line

Comparison of kWh Allocation Accuracy Using Sequential MeasurementskWh allocations assume that customers with high energy demand con-tribute more to the feeder load than customers with small energy demand Typically monthly customer billing datamdashalong with load surveysmdashwere used as the basis for determine kWh load allocation models The rollout of AMI provides the ability to examine customer peaks across the system as well as apply shorter time periods in the formulation of the kWh allocations

The distribution of calculated errors for kWh allocations using measure-ments representing different time periods (year month week and day) around the peak are provided in Figure 3 For context the errors com-puted when applying a kVA allocation method which is based on trans-former nameplate rating are also provided for this feeder Although the average error is zero for all allocation methods the breadth of the error distribution varies considerably among the allocation methods As was shown in Reference [1] the kVA allocation method does not perform as well as the kWh-based method doesmdashthe kVA allocation does not cap-ture the inherent diversity of loads and their relationship to the feeder peak Reducing the time period of kWh allocation from a year to a month (or less) reduces the allocation errors noticeably by considering the sea-sonal variations in load diversity However comparing results based on using a week or day of the peak load did not produce noticeable benefits compared to month-based kWh allocations This is somewhat surprising one would expect shorter time periods to better represent the time-based variations

Figure 3 Distributions of feeder peak load allocation errors (allocated minus the measured kW) Each boxplot represents the distribution of 598 transformers The median values are shown in a black line in the box 90 of values are within the box and 99 of the values are within the whiskers

Comparison of kWh Allocation Using Nonsequential Peak ValuesAs discussed the kWh properties of kWh allocation are typically calcu-lated over the peak load month or over a year Although using time peri-ods shorter than a month appears to provide little if any benefit the tem-poral granularity of the AMI measurements allows allocation methods to be based on a nonsequential set high feeder load times This approach has the potential to result in more accurate representation of the feeder load diversity during feeder high-load times

In this analysis the kWh properties were calculated using 24 or 168 hours of the highest feeder load times during the peak month The error results from these cases are compared in Figure 4 along with those for the peak month-based allocation As shown the errors are similar between differ-ent allocation methods This indicates that using nonsequential time periods may not provide notable benefit compared to sequential time periods around the peak load It should be noted that these findings are based on one year of load data taken from one feeder Different results may be obtained if load pattern variations among years andor feeders were considered

Figure 4 Distributions of peak load allocation errors (allocated minus measured kW) Each boxplot represents the distribution of 598 transformers The median values are shown in a black line in the box 90 of values fall within the box and 99 of the values fall within the whiskers

10217765


Novel Linear RegressionndashBased Load Allocation MethodA novel load allocation method that estimates a linear relationship between each customer load and the feeder load was also developed in this effort This load allocation method is referred to here as linear regres-sion (LR) load allocation

To provide context all load allocation methods are based on some assumption of how the customer loads contribute to the feeder load with the focus typically being on the feeder peak load (and sometimes mini-mum load) kVA allocation for example assumes that the kVA rating of the transformer correlates with the loadrsquos contribution to the total feeder load In kWh allocation a loadrsquos energy consumption is assumed to cor-relate with its contribution to the feeder peak demand These correlations and their limitations are discussed further in Reference [1]

The proposed LR allocation assumes no proxy correlation but estimates the best possible linear correlation with linear regression LR allocation has two phases

bull Phase 1 In this phase a linear relationship is estimated between each customerrsquos AMI load data and the feederrsquos supervisory control and data acquisition (SCADA) load data The resulting linear models can be stored for any future load allocation needs

bull Phase 2 In this phase a desired feeder head demand is allocated to the loads on the feeder leveraging the linear relationship estimated in the first phase Because the resulting feeder demand does not sum up to the measured demand the loads are scaled so that the feeder total load matches the measured value

The resulting linear models for a single customer using the LR allocation and kWh allocation are shown in Figure 5 In this case the linear models of kWh and LR allocation are similar Plotting result models over the measured data according to Figure 5 also demonstrates the inability of a deterministic linear model to fully represent the random coincidence between a loadrsquos demand with the feeder demand

Figure 5 Measured customer demand vs measured feeder demand (gray dots) The blue and red lines show the linear models of kWh allocation and LR allocation respectively Data from the peak load month are used to calculate kWh allocation properties and to estimate LR allocation linear models

Probabilistic load models would be necessary to fully account for the ran-domness of the individual loads but would require the application of probabilistic load flow methods to evaluate the system However because most planning studies focus on portions of the system that serve large numbers of customers and where the degree of loading variations is not as great these methods are generally not necessary

Alternatively when the focus of the planning assessment is on the feeder edges diversity factors could be used to adjust the allocated loads in a small localized area It is important to note that diversity factors which are discussed later cannot be simultaneously applied to all the feeder loads at the same timemdashit would result in higher overall feeder demand This is a well-known paradox of load modeling no single demand value is an accurate representation of a loadrsquos impact at all feeder levels Nonetheless correctly applied diversity factors could be used to scale local areas of the network of interest

The allocated share for each transformermdashthe transformer loading expressed as a percentage of the total feeder loadmdashis shown in Figure 6 using both methods These shares are essentially the slopes of the lines illustrated in Figure 5 for one customer Because the shares are similar for both allocation methods the allocation results are also expected to be similar As previously discussed the kWh allocation methodrsquos behavior depends considerably on the period over which the kWh properties are calculated Analogously LR allocation behavior also largely depends on the time periods used for calculating LR allocation linear models While using a full year of load data for the kWh and LR linear models provides a load allocation model that minimizes the model error across the year it does not provide a particularly accurate representation for any single load level On the other hand using load data from the peak load month (or shorter time periods) tends to result in better load allocation over high feeder load times

Figure 6 The allocated transformer shares of the feeder load for kWh and LR allocation methods The kWh properties of kWh allocation and the linear models of LR allocation are calculated based on peak load month data The maximum and average absolute differences between the shares of the two methods are 024 and 002 respectively

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Impact of Modeling Errors at Different Levels in the SystemBy their nature load allocation techniques generate system models that are more accurate for portions of the system serving large numbers of customers The main intent of these modeling practices is to better repre-sent the power flows expected on the primary three-phase elements by capturing potential load diversities As previously discussed however no demand value can fully represent the relationship between a loadrsquos ran-dom coincidence with the feeder demand Consequently it is important to investigate how the load allocation errors propagate for different levels of aggregated load

The expected change in model error with increasing levels of aggregated load is summarized in Figure 7 for both the kWh and LR allocation methods Specifically the figure shows the percent error distributions cal-culated based on random transformer groupings for a single transformer and increasing up to the full 598 transformers connected in the circuit Note that the distributions are similar for kWh and LR allocation meth-ods Therefore the two methodologies while providing different specific allocations provide similar results overall

In addition because of the randomness between the coincidence of a customer and feeder demands the percentage errors are high for small transformer group sizes However the percentage errors decrease rapidly with the transformer group size When the size of the group exceeds 50 transformers the percentage error is already less than 10 for almost all cases and nearer to 3 for the majority of cases (see Figure 7) There are two main reasons for the decreasing nature of errors First the percentage errors decrease because of an averaging effect in which independent ran-dom errors are summed Second the percentage errors decrease toward the feeder head where the demand is known However these findings do not rule out the potential of small groups of transformers experiencing much higher errors

Figure 7 Distribution of percentage errors of aggregated kWh and LR allocated loads ([aggregated allocated load minus aggregated measured load]aggregated allocated load x 100) with respect to transformer group sizes Both plots illustrate the error distributions for the feeder peak load time for 50000 random transformer groupings of each group size

To summarize neither allocation method can accurately represent the randomness of loads at the feeder edges but both allocation methods accurately represent aggregated feeder loads In general the higher the errors are at the level of individual allocated transformers the higher the aggregated errors Future work should evaluate the aggregation of errors against AMI data on diverse utility feeder models

Using Peak Load Allocation to Model Non-Peak Load DiversityTraditionally load allocation has focused on accurately representing feeder peak load conditions With the integration of DER it is becoming increasingly important to assess minimum load and other non-peak load planning scenarios Although a separate load allocation may be performed to represent the feeder demands at minimum load this is not always pos-sible because of data limitations and other factors As such those alloca-tions based on the peak demand and measurements may be employed in representing off-peak load diversity However it is not well-understood how applicable peak load allocation factors are to represent these other loading conditions

Figure 8 shows the mean absolute errors (MAE) of transformer loads allo-cated with LR kWh-month and kWh-168hr allocation methods with respect to the feeder load The MAE have been calculated separately for each allocation method and each feeder load level LR and kWh-month allocations were calculated using load data from the month of July The kWh-168hr allocation is calculated using measurements during the 168 hours with the highest feeder load

Figure 8 Mean absolute errors of transformer loads allocated with LR kWh-month and kWh-168hr methods for all feeder load levels LR allocation linear models and kWh-month allocation kWh properties are calculated with the feeder peak load month data

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The three allocation methods demonstrate similar errors At the lowest feeder loading periods the errors are shown to be relatively low for all the methods This can likely be attributed to overall low loading levels indi-cating that the allocation at these levels may not significantly impact over-all load flow results This is especially important when considering the analysis of these loading levels in performing hosting capacity studies Nonetheless customer loading levels may need to be considered further when performing analysis focused at the edges of the system

As expected the errors for all three allocation methods tend to increase with the feeder load At high feeder load levels the kWh-168hr allocation methodmdashwhich is based on the load data from the highest feeder load timesmdashoutperforms both kWh-month and LR allocation methods based on peak month data On the other hand at low to medium feeder load levels kWh-month and LR allocation methods outperform the kWh-168hr allocation method Similar performance was observed allocation methods based on high load data perform well at high load times alloca-tion methods based on longer periods of load data do a good job of rep-resenting loads over a wider range of feeder load levels but not particu-larly well at any one level

When examining Figure 8 it is apparent that the highest errors occur at feeder loading levels that are significantly lower than peak but not quite near the minimum ranges These errors are attributed to using a model based on the peak conditions to represent load diversity that may change seasonally in different ways than the peak demand In other words many transformers have seasonal patterns similar to the feeder total load but others may exhibit different seasonal patternsmdashas can be seen by compar-ing the profiles shown in Figure 9 for two example transformers with the feederrsquos profile given in Figure 1 These results indicate that it is impor-tant to properly account for seasonal load patterns when representing feeder load diversity over long periods

Figure 9 Load profiles of two sample service transformers the top differs greatly the bottom has a strong alignment with the feeder seasonal variations shown in Figure 1

Impact of Measurement InformationMeasurement sensors are being increasingly deployed across the distribu-tion system as part of new asset installationsmdashdistribution automation devices voltage regulating equipment DER and so on Although it is not possible to eliminate the load modeling errors because of the natural variability of the loads the visibility into the loading in other devices could be used to improve load allocation accuracymdashspecifically by shift-ing the measured or forecasted value to be allocated from the feeder head down into the system

To illustrate load allocation errors are shown in Figure 10 assuming dif-ferent locations for the ldquoknownrdquo value to be allocated to the downstream load The different lines represent the 90th percentile errors for feeder sections with 50ndash598 transformers downstream of a measurement sensor used for load allocation For example the purple line illustrates how the allocation errors aggregate on a feeder section with 300 service transform-ers downstream of a measurement sensor The errors grow quickly and peak with roughly half of the 300 transformers Then the errors decrease and become zero for the 300 transformers at the sensor location Note that a measurement device has only a small reduction in error for small transformer groups close to feeder edges However a measurement device can notably reduce the allocation errors close to the device itself In other words an additional sensor roughly midway on the feeder has almost halved the allocation error for groups of 250 service transformers Although the reduction in errors can be noticeable the reduction can be small compared to the errors associated with load forecasting and other planning decisions Future work should evaluate the value of feeder mea-surement sensors using feeder models and AMI data

Figure 10 The value of feeder sensors in reducing load allocation errors The lines show the errors for kWh-month allocated feeder peak load (aggregated allocated load minus aggregated measured load) under which 90 of 50000 random groupings of a given number of transformers reside The different lines represent the allocation errors for feeder sections with 50ndash598 transformers downstream of a measurement device used for the allocation

10217765


Load Diversity Factor AnalysisFinally a comparison was performed between diversity factor estimates traditionally performed by one utility with those calculated using AMI recordings

Introduction to Diversity Factor ConceptDiversity factor is a metric that represents how diverse the loads are within a customer group Diversity factor is defined as the ratio of the maximum noncoincident demand and the maximum diversified demand of a customer group

Diversity Factor =

Maximum noncoincident demand is the sum of the peak demands of all customers in the customer group Maximum diversified demand is the peak demand of the customer group Diversity factor is always 1 for a single customer but is always gt1 for groups of two or more customers Diversity factors depend on the customer group size and can vary largely from utility to utility and even from feeder to feeder According to Reference [3] diversity typically levels off to approximately 32 for groups of 70 or more customers According to Reference [4] diversity factors typically range from 2 to 3 but can be as high as 5

Diversity factors are commonly applied in distribution planning to esti-mate the maximum diversified demand of a customer group from the customer group maximum noncoincident demand

Max diversified demand =

When not available maximum noncoincident demand of a customer group can be estimated by multiplying the average peak demand of the customers in the group by the number of customers in the group

Maximum noncoincident demand asymp (customer type average peak demand)(customers in the group)

Maximum diversified demand is commonly applied for example for siz-ing transformers and other feeder elements

Applying diversity factors can be considered a bottom-up load modeling method in which downstream loads are used to estimate upstream distri-bution element load Opposite to this are top-down load modeling meth-ods such as load allocation in which an upstream known demand is allocated to downstream loads Diversity factor is typically applied to model the load diversity of small customer groups whereas load alloca-tion is typically applied to feeder-wide assessments

Diversity Factor ComparisonA comparison of the diversity factor models to those calculated based on AMI data is shown in Figure 11 The gray area in the Figure 11 illustrates the range of diversity factors that 90 of random customer groupings of each customer count have From the remaining random customer

groupings 5 had lower and 5 had higher diversity factors As illus-trated by the gray area there is no single diversity factor that perfectly describes the load diversity on the feeder Instead there is a range of pos-sible diversity factors for each customer group size

Figure 11 A textbook diversity factor example and a utility diversity factor model compared against the diversity factor distribution calculated from an AMI data set

The blue line in Figure 11 shows the diversity factors from an example in Reference [3] Compared to the diversity factor distribution of the AMI data the diversity factors from this example are too high for all customer group sizes Using overestimated diversity factors would result in under-estimating the maximum diversified demand of a customer group which can result in selecting distribution equipment with insufficiently small rating

The red line in Figure 11 shows the diversity factors used by the utility that provided the AMI data set These diversity factors closely follow the average diversity factors of the AMI data for groups of 1ndash15 customers For large customer groups the utility diversity factors tend to be conser-vatively low compared to the AMI data This may not be an issue because using underestimated diversity factors would result in overestimating maximum diversified demand which would result in conservatively over-sizing distribution equipment

Summary and Next StepsThis technical brief describes the application and value of advanced metering infrastructure and other measurement data to improve system modelsmdashparticularly load allocation techniques

Load allocations based on various sequential time periods as well as non-sequential high-demand points were examined It was observed that the use of sequential time periods shorter than a month as well as nonse-quential sets did not demonstrate marked improvements in load model-ing accuracy for the system peak beyond those using the kWh allocation based on the peak month Furthermore a novel allocation methodmdashrep-resenting the best possible linear model between each load and the total feeder loadmdashwas introduced This allocation method also showed similar performance to that of the kWh allocation based on the peak month data

Max noncoincident demandMax Diversified demand

Max noncoincident demandDiversity factor

10217765


Because the allocation methods are linear deterministic models they can-not accurately represent the randomness of the loading associated with few customers which is the case at the edges of the system However allocations were shown to provide reasonably accurate models during peak load for system assets typically the focus of distribution expansion planning studies The use of additional feeder measurements was shown to better capture load diversity However because of the modeling limita-tions they cannot reduce the allocation errors associated with the ran-domness see at the feeder edges

It is important to properly account for seasonal load patterns when repre-senting feeder load diversity over long periods of time Based on these comparisons kWh allocation using peak month data is the allocation method of choice achieving good performance at different feeder load levels and load aggregations without the additional complexity of LR allocation

Finally a comparison was performed between diversity factor estimates from a utility and those calculated using AMI recordings The utility esti-mates accurately reflected the average diversity factors calculated from an AMI data set but did not capture the highest or lowest diversity factors of any customer group size As a result distribution planners should be suf-ficiently conservative in applying diversity factors particularly to small customer groups that can exhibit very random load behavior

Future work will expand and apply the analysis considering multiple years of load data in addition to further evaluations using feeder models and AMI data Investigation into reactive power allocation and phase-specific active and reactive load allocation are also necessary Finally future work should analyze the distribution impact of load modeling errors Addressing these and other topics will be considered in subsequent phases of this project

References1 Enhanced Load Modeling for Distribution Planning Assessment of

Traditional Load Modeling Metrics and Load Allocation Methods Using AMI Data EPRI Palo Alto CA 2017 3002010995

2 R Dugan OpenDSS Documentation OpenDSS Load Allocation and State Estimation Algorithm 2008

3 W H Kersting Distribution system modeling and analysis Boca Raton CRC Press 2002

4 H L Willis Power distribution planning reference book 2nd ed New York M Dekker 2004

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10217765

3002013410 November 2018

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10217765


a load allocation from a single instance cannot be expected to perfectly represent feeder load diversity at another instance To illustrate trans-former loads during a feederrsquos July peak is compared to those for the August peak in Figure 2 Although an overall correlation exists across the loads during both system peaks the magnitudes of each individual load may vary significantly As a result the same load allocation factors cannot perfectly represent both time instances Recognizing this the subsequent analyses examine how well peak load allocation can be used to represent other feeder load conditions

Figure 2 Transformer load during the feeder peak load in July and a high feeder load time in August If the peak demand time and the high demand time had the same load diversity all the circles would be on the red line

Comparison of kWh Allocation Accuracy Using Sequential MeasurementskWh allocations assume that customers with high energy demand con-tribute more to the feeder load than customers with small energy demand Typically monthly customer billing datamdashalong with load surveysmdashwere used as the basis for determine kWh load allocation models The rollout of AMI provides the ability to examine customer peaks across the system as well as apply shorter time periods in the formulation of the kWh allocations

The distribution of calculated errors for kWh allocations using measure-ments representing different time periods (year month week and day) around the peak are provided in Figure 3 For context the errors com-puted when applying a kVA allocation method which is based on trans-former nameplate rating are also provided for this feeder Although the average error is zero for all allocation methods the breadth of the error distribution varies considerably among the allocation methods As was shown in Reference [1] the kVA allocation method does not perform as well as the kWh-based method doesmdashthe kVA allocation does not cap-ture the inherent diversity of loads and their relationship to the feeder peak Reducing the time period of kWh allocation from a year to a month (or less) reduces the allocation errors noticeably by considering the sea-sonal variations in load diversity However comparing results based on using a week or day of the peak load did not produce noticeable benefits compared to month-based kWh allocations This is somewhat surprising one would expect shorter time periods to better represent the time-based variations

Figure 3 Distributions of feeder peak load allocation errors (allocated minus the measured kW) Each boxplot represents the distribution of 598 transformers The median values are shown in a black line in the box 90 of values are within the box and 99 of the values are within the whiskers

Comparison of kWh Allocation Using Nonsequential Peak ValuesAs discussed the kWh properties of kWh allocation are typically calcu-lated over the peak load month or over a year Although using time peri-ods shorter than a month appears to provide little if any benefit the tem-poral granularity of the AMI measurements allows allocation methods to be based on a nonsequential set high feeder load times This approach has the potential to result in more accurate representation of the feeder load diversity during feeder high-load times

In this analysis the kWh properties were calculated using 24 or 168 hours of the highest feeder load times during the peak month The error results from these cases are compared in Figure 4 along with those for the peak month-based allocation As shown the errors are similar between differ-ent allocation methods This indicates that using nonsequential time periods may not provide notable benefit compared to sequential time periods around the peak load It should be noted that these findings are based on one year of load data taken from one feeder Different results may be obtained if load pattern variations among years andor feeders were considered

Figure 4 Distributions of peak load allocation errors (allocated minus measured kW) Each boxplot represents the distribution of 598 transformers The median values are shown in a black line in the box 90 of values fall within the box and 99 of the values fall within the whiskers

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