Investigation of Improved Distribution Load Allocation Using Expanded System Monitoring

Technical Brief — Distribution Operations and Planning; Power Delivery and Utilization

Report Outline Introduction The remainder of this report has two parts: Importance of Improved Load Models 1. The first part analyzes various load allocation methods in detail. The System loads have a significant influence on system performance. accuracy of kWh load allocation is analyzed for kWh properties calcu- Consequently, accurate modeling of system loads with distribution plan- lated over different time periods. The first part of the report also ning tools is critical for effective system planning. Increasing levels of introduces a novel linear regression–based load allocation method and distributed energy resources (DER), however, also require planners to compares its performance with kWh load allocation. perform assessments beyond peak loading conditions. For example, host- 2. The second part provides additional insights on diversity factor by ing capacity is often calculated assuming off-peak loading conditions; comparing different diversity factor models to those estimated using inaccurate load models can result in under- or overestimating hosting AMI data. capacity.

The application and value of advanced metering infrastructure (AMI) Load Allocation Methods with and other measurement data to improve system models are the focus of AMI Data this technical brief—in particular, how increased visibility from these new data sources could be used to improve load allocation techniques. This Background work is part of a continuing project, in EPRI’s Distribution Operations Load allocation is commonly a precursor to load flow analysis and other and Planning program, to advance methods for distribution load distribution planning assessments. Specifically, load allocation is a model- modeling. ing technique used to distribute or “allocate” 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 Brief Background on the Analyzed Data Set as well as cost and inaccuracies associated with forecasting loads down- The analyses documented in this technical brief are based on a single stream of the substation. A more detailed introduction to load allocation feeder derived from the data set described in Reference [1]. The test and common load allocation methods can be found in Reference [1]. An feeder serves a total of 1898 customers off 614 service transformers. The implementation of load allocation in distribution planning software feeder load profile—the total of the active power of all loads on the OpenDSS is described in Reference [2]. Results for commonly used kWh feeder—over the measurement year is plotted in Figure 1. To emulate and load allocation methods using different measurement data are presented test the application of historical data to represent future loading condi- in this section along with a novel linear regression–based load allocation tions, the data surrounding the peak demand in July (7.75 MW) were method. often used in the analysis as the basis for load allocation models. These models were then tested against the measurement for August peak load Load allocations are performed at the service transformer level. As is cus- (7.33 MW). These two instances are indicated on the feeder’s annual load tomary for many utilities, assigning the demand of large industrial cus- profile shown in Figure 1. tomers is assumed to be done separately from the load allocations examined 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 conditions. 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 allocated peak, minimum, or other system load conditions are best used to Figure 1. Measured annual load profile used in the analyses analyze other system load conditions. Load diversity varies over time, and 10217765 a load allocation from a single instance cannot be expected to perfectly represent feeder load diversity at another instance. To illustrate, transformer loads during a feeder’s 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 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 Values As discussed, the kWh properties of kWh allocation are typically calculated over the peak load month or over a year. Although using time periods shorter than a month appears to provide little if any benefit, the tem- Figure 2. Transformer load during the feeder peak load in July and a poral granularity of the AMI measurements allows allocation methods to high feeder load time in August. If the peak demand time and the high be based on a nonsequential set high feeder load times. This approach has demand time had the same load diversity, all the circles would be on the the potential to result in more accurate representation of the feeder load red line. diversity during feeder high-load times.

Comparison of kWh Allocation Accuracy Using In this analysis, the kWh properties were calculated using 24 or 168 hours Sequential Measurements of the highest feeder load times during the peak month. The error results kWh allocations assume that customers with high energy demand con- from these cases are compared in Figure 4 along with those for the peak tribute more to the feeder load than customers with small energy demand. month-based allocation. As shown, the errors are similar between differ- Typically, monthly customer billing data—along with load surveys— ent allocation methods. This indicates that using nonsequential time were used as the basis for determine kWh load allocation models. The periods may not provide notable benefit compared to sequential time rollout of AMI provides the ability to examine customer peaks across the periods around the peak load. It should be noted that these findings are system as well as apply shorter time periods in the formulation of the based on one year of load data taken from one feeder. Different results kWh allocations. may be obtained if load pattern variations among years and/or feeders were considered. The distribution of calculated errors for kWh allocations using measurements 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 transformer 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 does—the kVA allocation does not capture 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 seasonal variations in load diversity. However, comparing results based on Figure 4. Distributions of peak load allocation errors (allocated minus using a week or day of the peak load did not produce noticeable benefits measured kW). Each boxplot represents the distribution of 598 compared to month-based kWh allocations. This is somewhat surprising: 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 one would expect shorter time periods to better represent the time-based whiskers. variations.

EPRI Technical Brief 2 November 2018 10217765 Novel Linear Regression–Based Load Allocation Probabilistic load models would be necessary to fully account for the ran- Method domness of the individual loads but would require the application of A novel load allocation method that estimates a linear relationship probabilistic load flow methods to evaluate the system. However, because between each customer load and the feeder load was also developed in most planning studies focus on portions of the system that serve large this effort. This load allocation method is referred to here as linear regres- numbers of customers and where the degree of loading variations is not as sion (LR) load allocation. great, these methods are generally not necessary.

To provide context, all load allocation methods are based on some Alternatively, when the focus of the planning assessment is on the feeder assumption of how the customer loads contribute to the feeder load with edges, diversity factors could be used to adjust the allocated loads in a the focus typically being on the feeder peak load (and sometimes mini- small localized area. It is important to note that diversity factors, which mum load). kVA allocation, for example, assumes that the kVA rating of are discussed later, cannot be simultaneously applied to all the feeder the transformer correlates with the load’s contribution to the total feeder loads at the same time—it would result in higher overall feeder demand. load. In kWh allocation, a load’s energy consumption is assumed to cor- This is a well-known paradox of load modeling: no single demand value relate with its contribution to the feeder peak demand. These correlations is an accurate representation of a load’s impact at all feeder levels. and their limitations are discussed further in Reference [1]. Nonetheless, correctly applied, diversity factors could be used to scale local areas of the network of interest. The proposed LR allocation assumes no proxy correlation but estimates the best possible linear correlation with linear regression. LR allocation The allocated share for each transformer—the transformer loading has two phases: expressed as a percentage of the total feeder load—is shown in Figure 6 • Phase 1. In this phase, a linear relationship is estimated between each using both methods. These shares are essentially the slopes of the lines customer’s AMI load data and the feeder’s supervisory control and data illustrated in Figure 5 for one customer. Because the shares are similar for acquisition (SCADA) load data. The resulting linear models can be both allocation methods, the allocation results are also expected to be stored for any future load allocation needs. similar. As previously discussed, the kWh allocation method’s behavior depends considerably on the period over which the kWh properties are • Phase 2. In this phase, a desired feeder head demand is allocated to the calculated. Analogously, LR allocation behavior also largely depends on loads on the feeder, leveraging the linear relationship estimated in the the time periods used for calculating LR allocation linear models. While first phase. Because the resulting feeder demand does not sum up to the using a full year of load data for the kWh and LR linear models provides measured demand, the loads are scaled so that the feeder total load a load allocation model that minimizes the model error across the year, it matches the measured value. 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 The resulting linear models, for a single customer, using the LR allocation shorter time periods) tends to result in better load allocation over high and kWh allocation are shown in Figure 5. In this case, the linear models feeder load times. 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 load’s demand with the feeder demand.

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 0.24% and 0.02%, respectively. 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.

EPRI Technical Brief 3 November 2018 10217765 Impact of Modeling Errors at Different Levels in the System By 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 represent 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 load’s random 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 calculated, 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 methods. Therefore, the two methodologies, while providing different specific allocations, provide similar results overall. Figure 7. Distribution of percentage errors of aggregated kWh and LR In addition, because of the randomness between the coincidence of a allocated loads ([aggregated allocated load minus aggregated measured customer and feeder demands, the percentage errors are high for small load]/aggregated allocated load x 100%) with respect to transformer transformer group sizes. However, the percentage errors decrease rapidly group sizes. Both plots illustrate the error distributions for the feeder peak load time for 50,000 random transformer groupings of each group size. 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 Figure 8 shows the mean absolute errors (MAE) of transformer loads allo- two main reasons for the decreasing nature of errors. First, the percentage cated with LR, kWh-month, and kWh-168hr allocation methods with errors decrease because of an averaging effect in which independent ran- respect to the feeder load. The MAE have been calculated separately for dom errors are summed. Second, the percentage errors decrease toward each allocation method and each feeder load level. LR and kWh-month the feeder head where the demand is known. However, these findings do allocations were calculated using load data from the month of July. The not rule out the potential of small groups of transformers experiencing kWh-168hr allocation is calculated using measurements during the 168 much higher errors. hours with the highest feeder load.

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 Diversity Traditionally, load allocation has focused on accurately representing feeder peak load conditions. With the integration of DER, it is becoming Figure 8. Mean absolute errors of transformer loads allocated with LR, increasingly important to assess minimum load and other non-peak load kWh-month, and kWh-168hr methods for all feeder load levels. planning scenarios. Although a separate load allocation may be performed LR allocation linear models and kWh-month allocation kWh properties to represent the feeder demands at minimum load, this is not always pos- are calculated with the feeder peak load month data. sible because of data limitations and other factors. As such, those allocations 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.

EPRI Technical Brief 4 November 2018 10217765 The three allocation methods demonstrate similar errors. At the lowest Impact of Measurement Information feeder loading periods, the errors are shown to be relatively low for all the Measurement sensors are being increasingly deployed across the distribu- methods. This can likely be attributed to overall low loading levels, indi- tion system as part of new asset installations—distribution automation cating that the allocation at these levels may not significantly impact over- devices, voltage regulating equipment, DER, and so on. Although it is all load flow results. This is especially important when considering the not possible to eliminate the load modeling errors, because of the natural analysis of these loading levels in performing hosting capacity studies. variability of the loads, the visibility into the loading in other devices Nonetheless, customer loading levels may need to be considered further could be used to improve load allocation accuracy—specifically, by shift- when performing analysis focused at the edges of the system. ing the measured, or forecasted, value to be allocated from the feeder head down into 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 To illustrate, load allocation errors are shown in Figure 10, assuming dif- method—which is based on the load data from the highest feeder load ferent locations for the “known” value to be allocated to the downstream times—outperforms both kWh-month and LR allocation methods based load. The different lines represent the 90th percentile errors for feeder on peak month data. On the other hand, at low to medium feeder load sections with 50–598 transformers downstream of a measurement sensor levels, kWh-month and LR allocation methods outperform the kWh- used for load allocation. For example, the purple line illustrates how the 168hr allocation method. Similar performance was observed: allocation allocation errors aggregate on a feeder section with 300 service transform- methods based on high load data perform well at high load times; alloca- ers downstream of a measurement sensor. The errors grow quickly and tion methods based on longer periods of load data do a good job of rep- peak with roughly half of the 300 transformers. Then, the errors decrease resenting loads over a wider range of feeder load levels, but not particu- and become zero for the 300 transformers at the sensor location. Note larly well at any one level. that a measurement device has only a small reduction in error for small transformer groups close to feeder edges. However, a measurement device When examining Figure 8, it is apparent that the highest errors occur at can notably reduce the allocation errors close to the device itself. In other feeder loading levels that are significantly lower than peak but not quite words, an additional sensor roughly midway on the feeder has almost near the minimum ranges. These errors are attributed to using a model halved the allocation error for groups of 250 service transformers. based on the peak conditions to represent load diversity that may change Although the reduction in errors can be noticeable, the reduction can be seasonally in different ways than the peak demand. In other words, many small compared to the errors associated with load forecasting and other transformers have seasonal patterns similar to the feeder total load, but planning decisions. Future work should evaluate the value of feeder mea- others may exhibit different seasonal patterns—as can be seen by compar- surement sensors using feeder models and AMI data. ing the profiles shown in Figure 9 for two example transformers with the feeder’s profile given in Figure 1. These results indicate that it is important to properly account for seasonal load patterns when representing feeder load diversity over long periods.

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 50,000 random groupings of a given number of transformers reside. The different lines represent the allocation errors for feeder sections with 50–598 transformers downstream of a measurement device used for the allocation.

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.

EPRI Technical Brief 5 November 2018 10217765 groupings, 5% had lower and 5% had higher diversity factors. As illus- Load Diversity Factor Analysis trated by the gray area, there is no single diversity factor that perfectly Finally, a comparison was performed between diversity factor estimates describes the load diversity on the feeder. Instead, there is a range of pos- traditionally performed by one utility with those calculated using AMI sible diversity factors for each customer group size. recordings.

Introduction to Diversity Factor Concept Diversity 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 = Max. noncoincident demand Max. Diversified demand

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 Figure 11. A textbook diversity factor example and a utility diversity single customer but is always >1 for groups of two or more customers. factor model compared against the diversity factor distribution calculated Diversity factors depend on the customer group size and can vary largely from an AMI data set from utility to utility and even from feeder to feeder. According to The blue line in Figure 11 shows the diversity factors from an example in Reference [3], diversity typically levels off to approximately 3.2 for groups Reference [3]. Compared to the diversity factor distribution of the AMI of 70 or more customers. According to Reference [4], diversity factors data, the diversity factors from this example are too high for all customer typically range from 2 to 3 but can be as high as 5. group sizes. Using overestimated diversity factors would result in under- estimating the maximum diversified demand of a customer group, which Diversity factors are commonly applied in distribution planning to esti- can result in selecting distribution equipment with insufficiently small mate the maximum diversified demand of a customer group from the rating. customer group maximum noncoincident demand:

The red line in Figure 11 shows the diversity factors used by the utility Max. diversified demand = Max. noncoincident demand Diversity factor that provided the AMI data set. These diversity factors closely follow the average diversity factors of the AMI data for groups of 1–15 customers. When not available, maximum noncoincident demand of a customer For large customer groups, the utility diversity factors tend to be conser- group can be estimated by multiplying the average peak demand of the vatively low compared to the AMI data. This may not be an issue because customers in the group by the number of customers in the group: using underestimated diversity factors would result in overestimating Maximum noncoincident demand ≈ (customer type average peak demand)(#customers in maximum diversified demand, which would result in conservatively over- the group) sizing distribution equipment.

Maximum diversified demand is commonly applied, for example, for sizing transformers and other feeder elements. Summary and Next Steps Applying diversity factors can be considered a bottom-up load modeling This technical brief describes the application and value of advanced method in which downstream loads are used to estimate upstream distri- metering infrastructure and other measurement data to improve system bution element load. Opposite to this are top-down load modeling meth- models—particularly load allocation techniques. ods, such as load allocation, in which an upstream known demand is allocated to downstream loads. Diversity factor is typically applied to Load allocations based on various sequential time periods as well as non- model the load diversity of small customer groups, whereas load alloca- sequential high-demand points were examined. It was observed that the tion is typically applied to feeder-wide assessments. use of sequential time periods shorter than a month, as well as nonsequential sets, did not demonstrate marked improvements in load modeling accuracy for the system peak beyond those using the kWh allocation Diversity Factor Comparison based on the peak month. Furthermore, a novel allocation method—rep- A comparison of the diversity factor models to those calculated based on resenting the best possible linear model between each load and the total AMI data is shown in Figure 11. The gray area in the Figure 11 illustrates feeder load—was introduced. This allocation method also showed similar the range of diversity factors that 90% of random customer groupings of performance to that of the kWh allocation based on the peak month data. each customer count have. From the remaining random customer

EPRI Technical Brief 6 November 2018 10217765 Because the allocation methods are linear deterministic models, they can- DISCLAIMER OF WARRANTIES AND LIMITATION OF LIABILITIES not accurately represent the randomness of the loading associated with few customers, which is the case at the edges of the system. However, THIS DOCUMENT WAS PREPARED BY THE ORGANIZATION(S) allocations were shown to provide reasonably accurate models during NAMED BELOW AS AN ACCOUNT OF WORK SPONSORED OR peak load for system assets, typically the focus of distribution expansion COSPONSORED BY THE ELECTRIC POWER RESEARCH INSTITUTE, planning studies. The use of additional feeder measurements was shown INC. (EPRI). NEITHER EPRI, ANY MEMBER OF EPRI, ANY COSPON- to better capture load diversity. However, because of the modeling limita- SOR, THE ORGANIZATION(S) BELOW, NOR ANY PERSON ACTING tions, they cannot reduce the allocation errors associated with the ran- ON BEHALF OF ANY OF THEM: domness see at the feeder edges. (A) MAKES ANY WARRANTY OR REPRESENTATION WHATSOEVER, It is important to properly account for seasonal load patterns when repre- EXPRESS OR IMPLIED, (I) WITH RESPECT TO THE USE OF ANY INFOR- senting feeder load diversity over long periods of time. Based on these MATION, APPARATUS, METHOD, PROCESS, OR SIMILAR ITEM DIS- comparisons, kWh allocation using peak month data is the allocation method of choice, achieving good performance at different feeder load CLOSED IN THIS DOCUMENT, INCLUDING MERCHANTABILITY AND levels and load aggregations without the additional complexity of LR FITNESS FOR A PARTICULAR PURPOSE, OR (II) THAT SUCH USE DOES allocation. NOT INFRINGE ON OR INTERFERE WITH PRIVATELY OWNED RIGHTS, INCLUDING ANY PARTY’S INTELLECTUAL PROPERTY, OR (III) Finally, a comparison was performed between diversity factor estimates THAT THIS DOCUMENT IS SUITABLE TO ANY PARTICULAR USER’S from a utility and those calculated using AMI recordings. The utility esti- CIRCUMSTANCE; OR mates accurately reflected the average diversity factors calculated from an AMI data set but did not capture the highest or lowest diversity factors of (B) ASSUMES RESPONSIBILITY FOR ANY DAMAGES OR OTHER LIA- any customer group size. As a result, distribution planners should be suf- BILITY WHATSOEVER (INCLUDING ANY CONSEQUENTIAL DAM- ficiently conservative in applying diversity factors, particularly to small AGES, EVEN IF EPRI OR ANY EPRI REPRESENTATIVE HAS BEEN customer groups that can exhibit very random load behavior. ADVISED OF THE POSSIBILITY OF SUCH DAMAGES) RESULTING Future work will expand and apply the analysis considering multiple years FROM YOUR SELECTION OR USE OF THIS DOCUMENT OR ANY of load data in addition to further evaluations using feeder models and INFORMATION, APPARATUS, METHOD, PROCESS, OR SIMILAR ITEM AMI data. Investigation into reactive power allocation and phase-specific DISCLOSED IN THIS DOCUMENT. active and reactive load allocation are also necessary. Finally, future work should analyze the distribution impact of load modeling errors. Addressing REFERENCE HEREIN TO ANY SPECIFIC COMMERCIAL PRODUCT, these and other topics will be considered in subsequent phases of this PROCESS, OR SERVICE BY ITS TRADE NAME, TRADEMARK, MANU- project. FACTURER, OR OTHERWISE, DOES NOT NECESSARILY CONSTITUTE OR IMPLY ITS ENDORSEMENT, RECOMMENDATION, OR FAVORING References BY EPRI. 1. Enhanced Load Modeling for Distribution Planning: Assessment of THE ELECTRIC POWER RESEARCH INSTITUTE (EPRI) PREPARED THIS Traditional Load Modeling Metrics and Load Allocation Methods Using REPORT. AMI Data. EPRI, Palo Alto, CA: 2017. 3002010995. 2. R. Dugan, OpenDSS Documentation: OpenDSS Load Allocation and State Estimation Algorithm. 2008. This is an EPRI Technical Update report. A Technical Update report is 3. W. H. Kersting, Distribution system modeling and analysis. Boca intended as an informal report of continuing research, a meeting, or a topical study. It is not a final EPRI technical report. Raton: CRC Press, 2002. 4. H. L. Willis, Power distribution planning reference book, 2nd ed. New York: M. Dekker, 2004.

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