Analyzing the Energy Usage of a Community and the Benefits of Energy Storage

The architecture of the electric grid has three key components: generation, transmission, and distribution. The distribution grid is primarily responsible for supplying electricity to end consumers, which include industrial, commercial, and residential customers. While electricity is transmitted at high voltages through transmission lines, the distribution grid network uses a series of transformers to progressively step down the voltage and supply end-consumers with electricity at voltages of 110V (North America) or 230V (Europe and Asia). The distribution grid comprises sub-stations, feeders, and transformers that are responsible for supplying electricity to end consumers and can be viewed as a hierarchical network [6].

Such distribution edge transformers come in a range of capacities, varying from small 5-10 kilo-Volt-Ampere (kVA) pole-top transformers to larger 500, 1000 and 1500 kVA transformers. Note that transformer capacity is rated in kVA, which is the unit used for apparent power, i.e., the product of the root mean square (rms) of voltage and current in an AC power system. Small transformers may serve a small number of homes (e.g., two to four homes), while the larger ones serve apartment complexes or office buildings.

Electric utilities size edge transformers based on their expected load. However, typical capacity planning for transformers in the grid works differently from capacity planning in server farms and data centers, which is a well-studied problem [13, 34]. In particular, server capacities are computed based on their expected peak load, such that a server cannot service a peak load that exceeds its capacity, since they have a fixed computing capacity (based on their clock speed and bus bandwidth) that they cannot exceed. Transformer capacity is also sized based on its expected peak load, but a transformer is an analog device that can supply electricity that exceeds its rated capacity. Ultimately, the more power a transformer services, the more heat it generates. However, transformers have built-in safety mechanisms, specifically mineral oil, that can absorb some amount of excess heat generated from being over capacity. Thus, unlike servers, transformers are sized to operate over a wide range of their rated capacity, e.g., up to 1.25 of their rated capacity [27]. Even so, overloaded periods are undesirable as they reduce transformer efficiency (since the excess heat represents lost energy), and over time they can cause the insulating oil to evaporate. Once there is not enough oil to absorb the excess heat, it can melt the transformers coils and cause it to fail.

Moreover, overloaded transformers have a higher probability of experiencing outage. While we do not analyze outage information in this study as it is not available, prior studies have shown that overloading can be a good proxy for measuring grid reliability, and that preventing transformer overloading can reduce outages [39]. Thus, limiting the time periods (and magnitude) when the transformer load exceeds its rated capacity is important in reducing the negative impact on transformer lifetimes. For our analysis, we consider a transformer with a peak load between 0.9 to 1.25 its rated capacity to be highly utilized, a peak load between 1.25 to 1.5 to be overloaded and peak load exceeding 1.5 to be critically overloaded. Transformers with loads less than 0.9 are considered to have low to moderate utilization. We use the threshold of 1.25 of a transformer’s rated capacity to indicate overload because the rules for sizing overcurrent protection in transformers are that it should not exceed 125% of the primary current [1, 3, 52].

Utility companies have started deploying smart meter infrastructure in place of traditional electricity meters. Smart meters are electric meters capable of two-way communication, allow fine-grained metering of energy usage and can send send energy reports in real time – compared to traditional meters that are read manually. Some smart meters also have wireless reporting capabilities that enable outage notifications. In this work, we use smart meters to analyze electricity usage at fine granularity. The electricity meters used in our dataset monitor and report usage at a resolution of 5 minutes.

Grid-level energy storage, in the form of batteries, has emerged as a promising approach for various grid optimizations. Battery-based grid energy storage can be deployed at various points in the grid’s hierarchy—generation, transmission, or the distribution part of the grid network. Prior studies have shown that battery-based storage is especially appealing to handle the intermittency exhibited by renewable energy sources, such as solar and wind, by using storage to smooth out the fluctuations [8, 29]. Similarly, battery-based storage has been used for peak load shaving [40, 41].

Although the cost of battery-based energy storage remains high [32], prices are dropping more rapidly than expected even a few years ago, and commercial products and deployments are beginning to ramp up. At the same time, centralized grid-level large-scale battery storage systems capable of supplying a whole neighborhood have been shown to be a feasible alternative [55]. In this work, we consider the deployment of energy storage batteries at the grid level alongside distribution edge transformers to mitigate overloads caused by peak end user loads and enhance transfer lifetime—a use of batteries that has not seen much attention in the distribution network. Utilities are especially interested in using such application in the future as prices continue to fall.

The primary goal of our paper is to study the energy usage across an entire city at three spatial resolutions: at city-scale, at the level of distribution transformers, and at individual homes, and understand the distribution of peak energy demand experienced by distribution transformers, using real-world energy data. An additional goal is to understand whether emerging technologies, such as battery-based grid storage, can alleviate the overloads. Specifically, we seek to answer the following research questions.

The answers to these questions will vary from region to region, and clearly depend on the current state of the distribution grid in terms of its load over time, transformer capacities, and the resulting slack. In this paper, we use a city in the New England region of the United States and attempt to answer these questions for this city by conducting a city-wide data analysis. While the reliability of electric grids varies across regions around the world [21, 42], the distribution grid studied in this work is typical in many areas [28], and our high level insights are applicable in such regions.

Distribution Grid Dataset. Our dataset consists of electricity usage (load) data recorded by 14,849 smart meters that serve residential (13,458) and commercial (1,391) users in the city. These 14,849 meters are served by 1,270 distribution edge transformers. The dataset also includes a mapping of each meter to its edge transformer, and also includes a detailed specification of each transformer, including its rated capacity. The load data is recorded at a five minute granularity and spans from 2015 to 2019. The electric meters used to collect the data are advanced electronic meters which have the capability to be read remotely. All meter data is gathered using an automated meter reading system that allows meter readings to be sent directly to a central system via a secure communication network. Some meter readings contain spurious reads whose values are much higher than expected. In such cases, we limit the readings to the \(99.9^{th}\) percentile. Further, since there has been little seasonal variation during the whole duration of data availability, for this analysis, we use data from 2018 and 2019.

Since these edge transformers are low voltage transformers that are directly connected to end-customers, the load on each transformer can be computed by summing the load recorded by each meter connected to that transformer. Doing so yields highly detailed load information experienced by each distribution edge transformer over the two year period of the study. The availability of detailed load information for all 1,270 edge transformers in a city is a distinguishing feature of our study. Most prior work has considered simulation based studies to analyze transformer load data. In contrast, we study probability distribution of loads as well as the time of day/seasonal impacts that other studies did not consider using real world electric usage data.

Table 1 summarizes the key characteristics of our dataset discussed above. Figure 1(a) then depicts the diversity of transformer capacities in the distribution grids and the distribution of transformers across varying sizes. Note that, since the rated capacity is in apparent power as kVA, in our later analysis, we use the average power factor to convert it into kilowatts (kW) to make our results more intuitive. We use the equation below for the conversion.

Here, \(0 \le PF \le 1\) is the power factor. For our analysis, we use power factor of 0.9 and 0.95 for summer and winter, respectively, which represents the average power factor in these seasons.

Figure 1(a) shows that transformer capacities can vary from 5 kVA all the way to 1500 kVA. Most of the deployed transformers are ”small” and have a rated capacity of less than 150 kVA—a few transformers are large with a capacity of 500 kVA to 1500 kVA. Generally, the small transformers serve a small number of residential customers (e.g., two to four homes). The larger transformers serve apartment complexes, office buildings, other light commercial customers.

Figure 1(b) shows the distribution of meters connected to transformers of various sizes. We observe that the number of connected residential meters increases with the increase in transformer capacity. In contrast, fewer meters are connected to transformers that provide electricity to commercial buildings as they tend to consume higher energy. The median number of meters connected to these transformers ranges from 2 to 28.

Weather Data. In addition to electricity data, we also supplement our dataset with weather data for the city. We gathered weather data at one-hour granularity for the city from the Dark Sky API². Since temperature fluctuations are infrequent within the hour, this granularity for weather data is sufficient for our analyses.

In the sections that follow, we analyze this city-scale dataset to answer questions about aggregate usage: the distribution of energy usage across customers and the relationship of energy usage and weather. Later, we discuss the different types of customer segments that we observe in our dataset. Further, we study the impact of electricity usage on transformer overloading. Finally, we study the potential of storage at the home and transformer level to mitigate such overloading.

Next, we study the impact of outside temperature on the energy usage—both during winter and summer. Figures 3(a) and 3(b) plot the aggregate daily electricity demand over the course of a day along with the average daily temperature for winter and summer, respectively. Figure 3(a) shows a strong negative correlation of -0.8 between temperature and electricity usage in the winter—as the temperature falls, the electricity usage rises, due to increased heating costs from heating water, space heaters and homes with electric heaters.

Figure 3(b) shows a moderate positive correlation of 0.7 between temperature and electric usage in summer. Due to generally milder summers in the North England region, many homes do not have AC or run them infrequently, leading to a moderate (rather than high) correlation to outside temperature. The figure also shows that winter demand varies from 173 MWh to 369 MWh, while summer demand varies from 170 MWh to 440 MWh. In addition, the average absolute day-to-day change in the aggregate electricity demand is 5 MWh and 20.2 MWh in winter and summer, respectively.

Figure 4 compares average daily summer and winter usage to “extreme” weather days (e.g., hot summer day to an average summer day). Table 2 defines the criteria for “extreme” weather events. The scatter plots show the days selected using the criteria suggested in the table, whereas the bar chart show their average energy demand. Figure 4 shows demand can be 36% higher on a hot summer day than that on an average summer day—due to increased AC usage. The figure also shows 16.4% and 11.5% higher demand for cold winter days and during snowfall events over average winter days, respectively.

We first analyze the distribution of electricity usage across residential and commercial customers. Figure 5(a) depicts the histogram of average electricity usage for residential customers. The figure shows a mean power consumption of 0.8 kW and the distribution shows a long tail where the 99\({\rm {th}}\) percentile of the consumption is 4.6 times the mean. The mean consumption is lower than the average usage of 1.24 kW reported for a typical US household [2]. Figure 5(b) depicts the histogram of average electricity usage for commercial customers, and differs from residential consumption in a number of ways. First, the figure shows a mean power consumption of 1.4 kW, which is 1.75 times the residential mean consumption. This is because commercial customers typically have higher energy usage than residential ones driven by higher occupancy and energy for production needs. The figure also reveals that the highest consuming commercial buildings draw up to 20 kW, which is 14.3\(\times\) the average consumption. Figure 2(a) shows the aggregate energy demand of all customers for each hour of the day for the summer and winter seasons. In this study, the months with most days having an average daily temperature greater than 60°F are categorized as summer, whereas the rest are categorized as winter. We chose this threshold because the resulting summer and winter months coincide with summer and winter seasons in the North Eastern region of the United States, and included September in summer months because we observed a high number of days with an average temperature of 60°F or more. Thus, unless stated otherwise, winter days are defined as the days from Jan-Apr and Oct-Dec 2019, whereas summer days are defined as the period from May-Sep 2019.

Figures 6(a) and 6(b) are heat maps showing electric usage from two individual homes. Here, the energy consumption for each home has been normalized using Min-Max scaling. In Figure 6(a), the electricity usage pattern reveals clear peaks during morning and evening hours over the entire year with somewhat higher usage during summer evenings. Figure 6(b), on the other hand, reveals higher usage in winter months than summer months. Figure 6(b) also reveals higher usage during the morning (around 7AM) throughout the year—presumably due to the need for hot water for showers. Prior work that has analyzed daily energy trends also revealed morning and evening peaks [37]. However, these analyses lack seasonal patterns in the data as it is available across a shorter period of time.

Figure 6(b) depicts a home in which electricity is used to provide heat during the winter. The figure shows higher electricity demand in winter for electric heating and also shows higher morning and evening peaks. It also reveals higher usage for a few days in August—presumably due to higher cooling demand. Prior work that has analyzed seasonal energy consumption of residential customers also found higher energy usage during summer and winter months [30]. However, due to the coarse granularity of the data used, our analysis reveals these patterns at a much more granular scale.

Having examined the temporal and weather influence on energy use, we next study how different customers use energy on a day-to-day basis in their homes. For this analysis, we only cluster data from residential homes. Our hypothesis is that the energy usage within a home is largely determined by the daily routines and activities within a household, and depending on the characteristics of residents and their routines, different groups of customers will exhibit similar types of usage patterns. For example, homes, where everyone works during the day from 9AM-5PM, will have a different profile than a home with a retired person.

To validate this hypothesis, we perform customer segmentation analysis on the daily load profile of homes across the entire customer base. Since we are primarily interested in the pattern rather than the magnitude of the energy usage, we begin by normalizing the average daily load profile for each home between 0 and 1. We then use k-means clustering on these load profiles. k-means is a widely used clustering technique that takes a set of instances (individual homes) and their features (average energy consumption for each hour of the day) along with the desired number of clusters, k, as input. It uses an iterative approach to partition the data set into k groups such that the intra-cluster distance is small and inter-cluster distance is high. For this experiment, we used the sum of the squared distances between different load profiles. Typically, there exists statistical techniques to converge on the number of clusters such as Akaike Information Criterion(AIC) or Bayesian Information Criterion (BIC). However, these are generic model selection criteria and may not necessarily work well for all domains. Thus, we decided to employ visual model selection. By running k-means for different values of k, we found k = 8 to be the ideal choice for our dataset which did not result in any outlier clusters.

Figure 7 shows the eight clusters (customer segments) that resulted from our analysis. The lightly shaded lines are the profiles of each home present in that cluster and the bold line represents the centroid of the load pattern within each cluster. Broadly, there are four clusters that are bimodal with two peak usage periods of varying degrees and four clusters that are unimodal with a single peak usage period over the course of the day.

Table 3 summarizes the key characteristics of the customer segments within each cluster that include cluster type, peaks observed, the number of homes and their proportion in the dataset. As shown, around 7,216 homes (53.6% of total) exhibit bimodal usage (clusters a,b,c,d), 1,240 homes (9.2% of total) exhibit unimodal daytime peak usage (cluster e), 2,291 homes (17.0% of total) exhibit unimodal evening peak usage (cluster f), while 2,711 homes (20.1% of total) exhibit “nocturnal” usage (clusters g,h).

Figures 7(a)–7(d) depict the four bimodal clusters. Figures 7(a) and 7(b) are homes with a small morning peak and a more prominent evening peak. These homes usually correspond to homes with working/school routine. Figure 7(c) is the opposite with a greater morning peak and a less prominent evening peak. Figure 7(d) depicts households with large morning and evening peaks. The nature of these peaks reflect appliance usage with homes at different times of day. For example, a taller morning peak reveals greater appliance use in the morning (e.g., use of laundry machines), while those with taller evening peaks reveal homes where more of these activities are performed in the evenings. Figure 7(d) depicts a more uniform distribution of activities in the morning and evenings. These represent homes that are occupied during the day.

Figures 7(e)–7(h) depict four clusters with unimodal usage characterized by a single peak. Figure 7(e) depicts households where energy usage peaks in mid-day—presumably due to occupancy during daytime hours. Figure 7(f) depicts homes where peak usage occurring during evenings, with different peaks reflecting when daily chores are performed. Figures 7(g) and 7(h) represents nocturnal homes where the off-peak period occurs in the late morning or mid-afternoon and peak usage occurs during night hours. Presumably, these homes represent occupants who come home late at night.

Prior work that has studied segmentation based on energy usage also revealed similar unimodal and bimodal peaking profiles, with households that exhibit an evening peak accounting for the largest group of customers [31]. However, as with most other prior studies, the data used in this prior work is less granular (\(\gt 10\times\)) than the data used in this work, and this enables segmentation at a much finer scale.

Next, we analyze the peak power consumption recorded by each meter. We define peak power as the maximum power recorded by a smart meter at any time during the year. The recorded power in the data contains a few instances of unusually high values, which we attribute to spurious meter readings. Therefore, to compute the peak, we take the the 99.9th percentile reading across all data to eliminate these spurious reads which may affect peak analysis.

Figures 8(a) and 8(b) depict the cumulative distribution function of peak power drawn by residential and commercial meters during the year, respectively. Figure 8(a) shows that the median peak power across residential meters is 5.4 kW. In comparison, this is approximately 7.7\(\times\) the average usage depicted in Figure 5(a). The figure also shows that some meters draw up to \(\approx\)88 kW at some point in time during the year, while the 95\({\rm {th}}\) percentile is 10.4 kW. On the other hand, Figure 8(b) shows that the median peak power across commercial meters is 3.5 kW, which is 5\(\times\) the average usage depicted in Figure 5(b). The figure also shows that the 95\({\rm {th}}\) percentile is 20.0 kW, which is 2\(\times\) the highest peak observed in 95% of all residential meters.

To examine the extremity of peak usage from the average usage, we compute the peak-to-average ratio for each home during the year. Figure 8(c) plots the distribution of this ratio. The median peak-to-average ratio is 6.9, indicating that the peak usage is approximately 7\(\times\) the average usage. Similar to the peak usage, this distribution also depicts a long tail, with some homes experiencing as high as 40\(\times\) the average power consumption. As we will see later in Section 6.2, the peak-to-average ratio experiences a smoothing effect at the transformer level, i.e., when multiple meters are combined into one transformer, their respective peaks occur at different times, and this leads to a lower aggregate peak at the transformer level.

We begin with an analysis of the monthly and daily loads seen by the 1,270 edge transformers across the city. Figure 9 depicts the monthly load experienced by a representative transformer over the year 2019. The figure illustrates the seasonal variation in the load, and is characterized by two peak demand periods—winter and summer. The winter peak occurs due to increased use of electric heaters during the winter, while the summer load coincides with the increased use of air conditioning on hot summer days. Although the winter peak is slightly higher than the summer one, the summer peak has a greater impact on transformer efficiency and lifetimes. Prior studies have shown that a high ambient temperature can have an adverse impact on transformer lifetimes [19, 51], as a high ambient temperature contributes to the effect of overloading by further heating up (and evaporating) the insulation oil, which protects transformers from overheating. On the other hand, spring and fall seasons see lower peak loads, have cooler temperatures and transformers have more slack, and as a result, they are less vulnerable during these periods.

Next, we analyze the daily load profile of edge transformers to identify the most common types of transformers based on their load profile. For this analysis, we clustered the average daily profile of all transformers using k-Means clustering. Since the transformers are of different sizes, we normalize the daily load profile of each transformer to a range between 0 and 1 (e.g., using MinMaxScaler in scikit-learn), and then perform clustering. Figure 10 depicts the five clusters that emerge when using k-means with k = 5. After running k-means with multiple values of k, we selected k = 5 since 5 was the highest value of k that yielded clusters that were qualitatively different, and also did not yield an outlier cluster with few transformers. The bold line depicts the centroid of the clusters, while the lightly shaded gray lines show the energy profiles of all the transformers in the cluster. A summary of the clusters with the type, peak period, number of transformers and their respective proportion is shown in Table 4.

The five clusters reveal interesting patterns. For example, Figures 10(a) and 10(b) depict transformers that exhibit daytime peaks, while Figures 10(c), 10(d) and 10(e) depict transformers that exhibit evening peaks. The captions depict the number and percentage of transformers in each cluster. We hypothesize that the transformers exhibiting daytime peaks, in Figures 10(a) and 10(b), serve office buildings that have a 9 am to 5 pm workday, or businesses, such as retail stores, that have 9 am to 9 pm work hours. These transformers have a low load during the late evening and nighttime hours.

The clusters shown in Figures 10(c), 10(d), and 10(e) all exhibit evening peaks and also exhibit a nontrivial amount of nighttime usage—we hypothesize that these are large residential customers with different daily routines. The cluster in Figure 10(c) shows transformers that see a low load during the day—these are likely users who are away from home (i.e., working) during the day and at home in the evening and night. Figures 10(d) and 10(e) show residential customers with evening peaks, but also a non-trivial amount of daytime and nighttime usage. These are likely to be families where someone is at home during the day, where the increased evening activities result in an evening peak—these two clusters 10(d) and 10(e) also account for a large fraction of the transformers, 39.6%, and 43.9%, respectively.

Comparing transformer clusters (Figure 10) with home clusters (depicted in Figure 7) makes some interesting observations. First, the number of transformer clusters is lower than the number of home clusters depicted in Figure 7. This fewer number of distinct clusters is brought about by energy loads from multiple homes being aggregated at each transformer. This leads to a smoothing effect on the load observed at the transformer level, as well as merging some clusters into others. Second, predominant patterns in usage data at the individual building level, e.g., unimodal and bimodal daily usage, persist even at the transformer level. These patterns also contain the highest number of transformers in the dataset. This is due to the localization of transformer installations, where multiple homes that have the same characteristics, e.g., residential neighborhood, are connected to the same distribution transformer. Lastly, similar to the home profile analysis, a high number of transformers also exhibit high daytime usage, with only a small number of transformers exhibiting higher usage at night time (4.9%).

Next, we analyze the peak load experienced by transformers throughout the year. The availability of high granularity energy usage data at the transformer level (5 minutes) enables us to study peak distribution at a fine temporal scale, and this is a distinguishing feature of this work. We define the peak as the maximum power drawn at any point during the year, i.e., we take the max of the 5-minute granularity power profile of each transformer. Before summing up smart meter data to create a transformer profile, we take the \(99.9^{th}\) percentile of meter readings to eliminate spurious reads which may affect the peak analysis of transformer loads. Using Equation (1), we compute the rated capacity of transformers in kW and then compute the utilization by normalizing the load observed at the transformer with its rated capacity.

We then group the transformers into four categories, explained in Section 2.1 and depicted in Table 5: low-to-moderate, highly utilized, overloaded, and critically overloaded. As noted in Section 2.1, we use the threshold of 125% of a transformer’s rated capacity to indicate overload because the rules for sizing overcurrent protection in transformers are that it should not exceed 125% of the primary current [1, 3, 52]. Figure 11(a) depicts the peak load distribution of the transformer across the whole city, while Table 5 shows the number and percentage of transformers that fall in each category. Since transformers have a typical lifetime of 20-30 years, one would expect careful sizing, such that the peak load is well below the rated capacity. However, as shown in Table 5 and Figure 11(b), only 60.6% of the transformers service a peak load of less than 90% utilization over the course of the year. Around 26% of the transformers are heavily utilized and service a peak load of up to 125% of their rated capacity. Note that this implies that the transformer operated at or above its rated capacity for at least part of the time over the year. Around 7.2% of the transformers are overloaded and see a peak load that exceeds 125% utilization, while an additional 6.4% of the transformers are critically overloaded with the peak load exceeding 150%. As explained earlier, it is not “abnormal” for a transformer to exceed 100% utilization for short periods, since they have mineral oils to insulate them from overheating, although sustained overloads for long periods are dangerous. Therefore, we next analyze the duration of the overloads experienced by the edge transformers.

We consider only the transformers that are in the overloaded and the critically overloaded groups and compute the number hours over the year for which they service a load exceeding 125% of their rated capacity, and also compute the maximum “session duration” over which the transformer is continuously overloaded. Figure 12(a) plots the total number of hours for which transformers are overloaded or critically overloaded during the year. The figure shows that the overload distribution is long-tailed—the majority are overloaded for 162 hours over a year, while a few see overloads of as many as 1,000 - 3,000 hours. Figure 12(b) analyzes each continuous period that experiences an overload, and plots the longest continuous duration for which a transformer was overloaded. The figure, plotted on a log scale, shows the median duration of overload was 45 minutes, while some transformers see a sustained overload of 143 hours.

Next, we analyze the extremity of peak loads from regular demand. To do so, we compute the peak-to-average ratio of a transformer’s peak load from the average load during the year. Figure 11(c) shows the distribution of the peak-to-average across all transformers in the dataset. The median peak-to-average ratio is 3.9, indicating that peak loads are approximately 4 times the average. Compared to individual homes, the median peak-to-average ratio is lower than that of individual homes (the median peak-to-average ratio for homes is 6.9 as shown in Figure 8(c)). This indicates some kind of statistical smoothing which is brought about by peaks occurring at different times at the home level. Because peaks at the home level do not directly coincide, a smoothing effect is experienced at the aggregate peak causing transformer peaks to be lower than that of individual customers.

For this analysis, we consider different storage penetration levels across homes and understand the impact of storage on the peak demand seen by homes and the transformers they are connected to. While prior work has studied other aspects of storage deployed at the home level such as coordinated charging and discharging of distributed energy resources [11], in this work, we focus on the effect of energy storage on energy demand at a home, transformer peak and overloading.

To model energy storage at the home level, we use the following battery specifications. We assume that a battery with a capacity of 13.5 kWh, a peak output capability of 7 kW, and a continuous discharge rate of 5 kW is installed at each home. These specifications follow a popular home battery configuration that is in production today. Therefore, for each day, we assume that a home’s energy demand can be shaved by up to 8 kWh (discharging a battery to zero capacity reduces the battery’s lifetime, so we assume a maximum discharge of 8 kWh per day). We then shave off the top 8 kWh for each home during the year and generate a new synthetic energy load. We then experiment with different levels of battery penetration across homes in the grid e.g. 10%, 20%, 30%, 40%, 50%. We define penetration as the number of homes in the grid that have an installed battery. For each penetration level, we select the percentage of homes from the grid at random and assume that a battery is present. We then compute the resulting transformer loads using the shaved load in homes that have a battery and the original load for homes that do not have a battery. We repeat each experiment for 20 runs with a different random selection of homes to ensure our results have tight confidence intervals.

Figure 13(a) shows a sample home with the top 8.0 kWh shaved off the total demand of 115.4 kWh during a particular day. The figure shows that load shaving occurs during instances of peak usage. On the other hand, Figure 13(b) depicts the results of varying the battery penetration level from 0% (no batteries at all) to 50%. The figure shows that with only 10% of homes in the grid having a battery, the number of overloaded transformers can be reduced by up to 30%, while the number of heavily utilized transformers can be reduced by up to 16.6%. The figure also shows that increasing the battery penetration to 50% can reduce the number of overloaded and heavily utilized transformers by up to 74% and 60%, respectively.

Next, we consider the impact of deploying energy storage in the distribution grid, rather than in individual homes. We assume that batteries are installed by the utility next to distribution transformers. Prior work has shown that deploying storage at the transformer level can reduce distribution costs by up to 3.75%, and this makes it a viable option for curtailing costs [35].

We begin by addressing the problem of storage sizing, i.e., quantifying the amount of energy storage that is required to mitigate overload at each transformer, and then analyze the impact of installing such storage on peak shaving. Installing energy storage at the transformer level can alleviate transformer overloading by absorbing peak loads thereby increasing transformer lifetime. This in turn can become a key cost saving strategy for utility companies. For example, the cost of replacing a single distribution transformer can vary from $7,000 [49], while the cost of replacing larger transformers, e.g., a 100 MVA rated transformer, may cost >$2 million [47]. Comparatively, the cost of a small lithium-ion battery system can be as low as $3,000 [18], which presents considerable savings for the utility. However, since transformers in the distribution grid vary in size, they will need different size batteries to achieve a certain level of load reduction. To calculate the energy storage capacity required per transformer, we propose a simple peak-shaving algorithm that clips the maximum contiguous peak above a given threshold. Specifically, for each transformer, our algorithm scans over its load and computes the contiguous period when the load exceeds the threshold. Our algorithm then computes energy storage capacity by computing the energy above the threshold across the periods, and selects the maximum. Our premise is that the energy storage that can flatten the maximum contiguous peak can also provide energy to flatten the smaller peaks experienced at other periods.

Figure 14(a) shows that energy storage capacity can vary between 1 kWh and 532 kWh. We note that the 90\({\rm {th}}\) percentile of energy storage is 50 kWh, which indicates that even a small battery size can dramatically reduce the risk of failures in transformers. In particular, 85% of overloaded and critically overloaded transformers can benefit from an energy storage capacity of 20 kWh or less installed per transformer. Since the battery capacity is a function of the size of the transformer capacity, we plot the distribution of battery size against transformer size. Figure 14(b) shows the median energy storage capacity increases with increases in transformer capacity, with the highest capacity required occurring at 112.5kVA. We hypothesize that such transformers are connected to a large number of homes such as an apartment building. The larger energy storage capacity can be attributed to the higher number of homes that such transformers serve.

We then analyze the effect of adding storage as a function of transformer sizing. We define battery scale factor as a 1:1 ratio to a transformer’s kVA rating, i.e., for each kVA, what effect would adding 1 kWh of storage to the transformer have on the transformer’s overload status. Figure 14(c) shows the result of adding storage using this factor. By adding a 0.1 factor of storage, we are able to reduce the number of heavily utilized and overloaded transformers by up to 45% and 39%, respectively.

Lastly, we evaluate the impact of deploying grid-level storage under budgetary constraints. Typically, utility companies have limited budgets for grid upgrades, and it is important to ensure that the limited resources are utilized in a manner that maximizes the gains made in the grid. To model budgetary constraints, we assume that utility companies are limited in the total amount of storage they can deploy across the grid, i.e., in kWh. Next, since transformer replacement cost is directly proportional to the size of the transformer, we assume that deploying storage at a transformer with a higher transmission rating adds more value than deploying at one with a lower transmission rating. This is because decreasing the lifetime of larger transformer incurs a higher replacement cost than a smaller one. However, since the amount of storage that can be deployed is finite, this introduces a tradeoff between the number of transformers at which storage is deployed and the net value gained from such deployment. For instance, is it more beneficial to deploy storage at many small transformers vs one large transformer?

Formally, this problem of distributing finite storage across transformers of different sizes can be formulated as the classic knapsack problem in combinatorial optimization. Here, the amount of storage required by each transformer is the weight, the transformer kVA rating is the profit value, and the budget limit is the capacity. We implement this formulation using our dataset and analyze the tradeoff between number of transformers at which storage is deployed and the overall net gain. Figure 15 depicts the results of this analysis. The figure shows that at lower budgets, the net value gained increases super-linearly as the storage budget increases. However, at higher budgets, the net value gained increases sub-linearly with an increase in storage budget. This is mainly because larger transformers are mostly selected at higher budget allocations. Lastly, the figure shows that deploying \(\approx\)25% of the total storage required to eliminate transformer overloading in the grid results in the best net value tradeoff.