Nonintrusive disaggregation of residential air-conditioning loads from sub-hourly smart meter data

Energy and Buildings 81 (2014) 316–325

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Nonintrusive disaggregation of residential air-conditioning loads from sub-hourly smart meter data Krystian X. Perez a,c , Wesley J. Cole a,c , Joshua D. Rhodes b,c , Abigail Ondeck a,c , Michael Webber b,c,d , Michael Baldea a,c,e , Thomas F. Edgar a,c,d,∗ a

McKetta Department of Chemical Engineering, The University of Texas at Austin, Austin, TX 78712, United States Department of Civil, Architectural & Environmental Engineering, The University of Texas, Austin, TX 78712, United States c Department of Mechanical Engineering, The University of Texas, Austin, TX 78712, United States d Energy Institute, The University of Texas, Austin, TX 78712, United States e Institute for Computational Engineering and Sciences, The University of Texas, Austin, TX 78712, United States b

a r t i c l e

i n f o

Article history: Received 2 December 2013 Received in revised form 19 June 2014 Accepted 21 June 2014 Available online 28 June 2014 Keywords: Nonintrusive load monitoring Disaggregation Residential energy Air conditioning Smart meter

a b s t r a c t The installation of smart meters has provided an opportunity to better analyze residential energy consumption and energy-related behaviors. Air-conditioning (A/C) use can be determined through nonintrusive load monitoring, which separates A/C cooling energy consumption from whole-house energy data. In this paper, a disaggregation technique is described and executed on 1-min smart meter data from 88 houses in Austin, TX, USA, from July 2012 through June 2013. Nineteen houses were sub-metered to validate the accuracy of the disaggregation technique. The R2 value between the predicted and actual A/C energy use for the 19 houses was 0.90. The algorithm was then applied to all houses. On average, daily energy use from A/C increased by 25 ± 11 kWh between a mild temperature day of 15.5 ◦ C (60 ◦ F) and a hotter day of 31.5 ◦ C (89 ◦ F), with an 11 kWh increase just during peak hours (14:00–20:00). Average time operated, number of cycles, and A/C fraction of energy were found to increase linearly with outdoor temperature up to 25 ◦ C (77 ◦ F); a plateau was detected at higher temperatures. The accuracy of A/C disaggregation on 5-min data was found to be comparable to 1-min data. However, 15-min data did not yield accurate results due to insufficient granularity. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Approximately 40% of power consumption within the United States is due to buildings, a substantial share of which is due to heating, ventilation and air conditioning (HVAC) [1]. Residential use accounts for approximately one half of building energy use. The load placed on the grid by residential consumers is highly variable and strongly influenced by weather and human activity patterns. For warm climates, such as the southern United States, residential electricity use peaks in the later afternoon hours (16:00–19:00) during summer months, reaching values over five times higher than spring day mornings [2]. The combined effect on the grid causes substantial increases in power demand (see Fig. 1 [3]). Meeting such fluctuations in demand is challenging for grid operators and requires excess capacity from generation facilities to be available.

∗ Corresponding author at: McKetta Department of Chemical Engineering, The University of Texas at Austin, Austin, TX 78712, United States. Tel.: +1 512 471 3080. E-mail address: [email protected] (T.F. Edgar). http://dx.doi.org/10.1016/j.enbuild.2014.06.031 0378-7788/© 2014 Elsevier B.V. All rights reserved.

Reducing the high variability in residential energy use can increase the uniformity of energy demand on the grid (“leveling the load”), which reduces reliance on less-efficient peaking plants. Achieving this goal requires an increased understanding of how residential air-conditioning (A/C) usage for individual houses and entire neighborhoods are affected by external factors. Dynamic or sub-hourly A/C residential energy use problems remain understudied, partly because the cost to obtain detailed measurements is high. For example, it has been a challenge to obtain some general statistics such as daily A/C runtime or daily number of cooling cycles. While a single house does not have an appreciable effect on the grid, entire neighborhoods, or large groups of houses in aggregate have a significant impact. An improved understanding of the effect of external temperatures on residential energy consumption will create more accurate predictions of energy use and better dynamic residential models. Improved models will establish a reliable means to evaluate the effectiveness of thermal storage, district cooling and other large-scale approaches for leveling peak loads [4–8]. This analysis seeks to fill this knowledge gap through the use of newly available smart meter data.

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Table 1 Mueller houses’ basic characteristics [24].

Fig. 1. System-wide energy demand and day-ahead settlement point prices from the Electric Reliability Council of Texas (ERCOT) for June 25, 2012 shows great variability throughout the day [3]. Peak electricity is the most expensive.

Smart meters allow the derivation of valuable information about residential A/C energy use through non-intrusive load monitoring (NILM). However, most meters report solely the whole-house energy use every 15 min. This information is useful in demandresponse systems for energy providers; however, most residential loads (including HVAC systems) cycle or operate at much higher frequencies, and their operation and individual energy use can be difficult to estimate from such data. Sub-metering specific circuits such as the A/C is expensive. NILM mitigates this problem by employing algorithms to extract the A/C usage from the wholehouse measurements provided by the smart meter. The NILM method was first described by Hart in 1970 [9]. Hart proposed that an edge-detection algorithm be applied to energy profiles at 1-s time intervals. The algorithm would then segment the profile into periods in which the power is steady (the input does not vary by more than a specified tolerance) and periods in which it is changing. The changes in power were clustered so that “on” and “off” clusters match in relative magnitude. Appliances were then identified using a priori knowledge from direct or indirect measurements. Iterations of this concept by other researchers follow a similar pattern by first developing a library of signatures to identify appliances, through either direct measurements or the application of edge detection [10–17]. Other NILM techniques have been implemented in many ways, including the added use of voltage and current values to better define electronic signatures [18–22]. Then, using various mathematical techniques, changes in power consumption are paired to appliances. A review on NILM techniques was recently published by Zeifman et al. [23], so interested readers are directed there for more information. The technique used in this paper is different from previous methods in that it is only concerned with the A/C use. One of the challenges in Hart’s method is that it used clustering to match changes in power of on and off events, which required previous knowledge of devices to accurately pair behaviors to devices. By focusing exclusively on A/C energy, this new technique can be accurately tuned for any house to separate just A/C energy use. Rather than pair on and off power events, this technique uses edge detection and k-means clustering to find key parameters on A/C behavior. The parameters are then used to identify A/C on and off events. The purpose of this research is twofold: (1) to develop an algorithm to disaggregate A/C energy use from sub-hourly whole-house energy data and (2) to derive A/C usage information for a residential neighborhood. Because mass installation of smart meters has not occurred until recently, the application of NILM to multiple houses has not been evaluated. The Pecan Street Research Institute has provided unique access to sensors that collect data at 1-min intervals, which is granular enough to implement disaggregation [24].

Audit field

Average

Median

St. Dev.

Year built Number of levels Conditioned area (m2 ) A/C capacity (kW) A/C efficiency (EER) A/C age HVAC duct R-value Duct leakage (%)

2008 1.7 192.5 10.6 10.6 2008 6.8 15.5

2008 2 192.1 10.6 11 2008 6 15

0.7 0.5 50.0 2.8 1.4 0.7 1 3.8

Since A/C is a dominate feature in the energy profile at 1-min intervals, the on/off events of an A/C unit can be detected. A statistical analysis evaluates the accuracy of utilizing a general disaggregation algorithm by comparing actual vs. estimated A/C use. The algorithm is then applied to a larger dataset of homes in order to estimate A/C usage information for a residential neighborhood. At the close of the paper, the disaggregation technique is used to perform an analysis on the cost of air conditioning under various rate structures. This cost analysis is only possible using a disaggregated data set, demonstrating the value of the disaggregation technique presented in this work. 2. Methods 2.1. Data Total energy usage was taken from 88 single-family houses in the Mueller neighborhood in Austin, TX from July 2012 to June 2013. Each house had been metered with an eGauge power monitor that reported whole-house power consumption in watts on 1-min time intervals [24]. Of the 88 houses, 19 had been sub-metered with an additional meter to directly measure power used for the A/C system during the full year. The Mueller neighborhood consists mostly of newer (since 2007), green-built houses and has a large amount of new technology penetration, such as rooftop photovoltaic panels and plug-in vehicles. The houses were equipped with electric A/C cooling units and natural gas heating systems. A/C energy will refer to electricity use used to cool the houses. Table 1 gives results from an advanced energy audit performed by Pecan Street and contains information on general housing characteristics. The statistics (average and standard deviation) refer to the neighborhood containing the evaluated houses. The data set included some errors, such as missing data (17 days total), mislabeled timestamps, meter error reporting constant values (5 days total) and extreme outliers (7 points), which were removed from the evaluated data set prior to analysis. 2.2. Disaggregation outline This paper uses a non-intrusive load monitoring technique to disaggregate the A/C cooling energy consumption from the 1-min whole-house energy consumption data. In this technique, the magnitude of change in load that signals the A/C turning on or off is found, which is then used to identify on and off events of A/C use. A typical example of daily 1-min data can be found in Fig. 2 for a house that had the A/C sub-metered. A decision flowchart for the disaggregation process is seen in Fig. 3. The algorithm functions as an edge-detection algorithm, which has been used in other disaggregation techniques [9]. First, energy use data for each house was separated by day from midnight to midnight. The difference in energy between Ei = Ei+1 − Ei

(1)

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Fig. 2. Example of whole-house data with sub-metered A/C cooling for a single day. Power is reported in kW where power use is the calculated average across 1-min time intervals. The A/C energy consumption can be readily separated from the rest of the energy use because the cycling of the A/C system dominates the profile.

each time step (Ei ) was calculated and stored as seen in Eq. (1) where Ei is the change of energy between time i (the current time step) and i + 1. The value of i in the study was 1 min unless otherwise stated. If the HVAC system begins in the “off” state, Ei is compared to Eon , which is the minimum energy change to signal an “on” event. If the difference in energy was large enough to signal that the A/C unit turned on (Ei ≥ Eon ) and the energy at time i + 1 was greater than a lower limit (Ei+1 ≥ lon ), then the time stamp was stored as the system turning on. The sum of the change in energy value at time step i with the average of the E values before and after the signal was also stored (Ei + ((Ei−1 + Ei+1 )/2)). The Ei value represents the amount of energy increased due to the A/C system turning on. The average of the E value before and after the time step was added for events where the system ramped on

between time steps. Otherwise the algorithm would underestimate energy because of the offset. The stored value incorporated power consumed by the airhandling unit (the blower fan and controls). The algorithm stepped forward in time until Ei was less than the condition for the “off” signal (Ei < Eoff ) and Ei+1 was smaller than the upper limit (Ei+1 ≤ loff ), meaning the decrease in the energy consumption was strong enough to indicate that the system turned off and the total energy was below the lower limit threshold. Then the algorithm would step forward in time until another on signal was found. The decision process was repeated until the end of each day. The total estimated A/C energy consumption was calculated by multiplying the total duration of time during which the A/C unit was on with the average of the A/C energy values over a day. Therefore the power required by the A/C was assumed to be constant whenever the A/C was on. In reality, the amount of energy consumed by the A/C slightly fluctuates throughout the day as a result of inefficiencies due to changes in outside temperature [25]. Power draw will increase at higher temperatures, such as the afternoon, when the COP decreases. The averaged value was used because it is resistant to noise that would otherwise decrease the estimated value. However, as a result the resulting estimated energy value may be lower than if there was a correction factor dependent on outdoor temperature that adjusted for a changing COP. In Austin, during early morning hours and warm weather the dominant feature in the energy profile is the sporadic cycling of the A/C unit. The premise of the algorithm is that during months where A/C is used (and most likely the dominant consumer), there is a time during the day when the A/C load is a dominant feature in the electricity load. That time period can be used in the algorithm as a training period to determine key parameters, such as the magnitude of A/C spikes that indicate that the A/C unit has turned on (Eon ). The parameters derived from this training period are then applied to the rest of the data in order to identify and extract information about the A/C energy usage. The following sections describe how the parameters were derived. 2.3. Disaggregation parameters

Fig. 3. Decision flowchart to demonstrate how A/C cycles are determined and stored. Ei is the change in energy at time step i. Eon and Eoff are the changes in magnitude large enough to indicate the system has turned on or off. lon and loff are limits on how much power is used by the A/C system.

In Austin, the early morning period electricity profile for the houses was dominated by the A/C load. Thus the algorithm training period was defined as midnight to 6:00 a.m. for each day in the training period. The first six hours were chosen as the training period because the A/C unit was the primary feature in the energy profile as it is typically operated by a thermostat that does not require constant human interaction. During later hours of the day, the signal of other appliances can interfere with the signal indicating the A/C turning on. Note that this training period is unique to warm climates such as Austin where temperatures during early morning periods still require the use of the A/C. Were this algorithm to be extended to other climates, a different training period would be required. The timing of the training period is not important—what matters is that the A/C is the dominant load during the training period. The Ei for the training period was separated into three clusters using the k-means clustering algorithm (see Fig. 4), which partitions the data according to the squared Euclidean distance between points, where each point is the change in energy usage (Ei ). The resulting clusters revealed “on” (strongly positive E), “neutral” (E vacillating around zero) and “off” clusters (strongly negative E). The minimum of the “on” cluster (Eon ) and maximum of the “off” cluster (Eoff ) were stored from the first two weeks of the data set (starting July 2012). Only one day is needed as the training set to determine Eon and Eoff , so long as the A/C operates during that period. However, we used the first six hours each day for 2 weeks in July as the training period to ensure that there was not atypical behavior (such as vacation)

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Fig. 4. Example of clustering E from training period for one day. The E clusters show the on/off behavior of the A/C unit through positive, neutral and negative E clusters. The magnitude of the signal parameters (Eon and Eoff ) are determined using this training period because the A/C dominates changes in energy use.

that would inhibit the training. The medians of the Eon and Eoff across the two weeks were used as signal strength parameters to determine if the difference in energy indicated an on or off switch. Fig. 5 shows the on and off values for the 14 days with the final Eon and Eoff values. In addition to the signal size parameters, two constraints were derived for both the “on” and “off” switch. On days when multiple appliances are running throughout the day, non-A/C loads can reach the same order magnitude as the A/C unit. These appliances can lead to false detection of “on” and “off” events. Two boundary conditions, one for both the on and off switch, serve to separate changes in load due to other appliances from those from the A/C unit. The first is a lower limit for the on signal (lon ). The parameter lon described the minimum total energy that was required to signal that the A/C usage did in fact turn on. In order to signal an “on” switch, first the system had to be “off”. A variable s kept track of whether the system was on or off [1,0]. Then, the energy use at i + 1 (Ei+1 ) needed to be above this boundary such that Ei+1 ≥ lon

(2)

Ei ≥ Eon

(3)

where lon is the lower limit of the energy consumption necessary to signal an “on” switch and Eon is the minimum change in Ei to signal an “on” switch.

Fig. 5. Stored Eon and Eoff values for the first two weeks in July. Values were determined from clustering E and taking the minimum of the on cluster and the maximum of the off cluster.

319

Fig. 6. Energy profile with on/off limits plotted. In order to give an on signal, the Ei needed to be greater than Eon and the Ei+1 had to be above lon (the long dashed line.) In order to give an off signal, the Ei of the step change needed to be below Eoff and Ei+1 had to be below loff (the short dashed line.).

Similarly an upper limit was found for the “off” switch (loff ). In order to signal a switch “off”, first the system needed to be “on.” Ei+1 needed to be below this boundary and Ei was less than Eoff Ei+1 ≤ loff

(4)

Ei ≤ Eoff

(5)

Both boundaries prevent noise from other appliances from signaling an A/C “on” or “off” event. The limit lon was taken from the total energy usage data by taking the maximum energy value within the first six hours starting at midnight, during which the A/C unit dominates the energy profile and regularly cycles. Half that value was used for loff (i.e. loff = (1/2)lon ). The averages across the training period were the values used for the rest of the year. Fig. 6 shows the boundaries imposed on a typical day. By default, the algorithm assumed that the system started off at the beginning of the day’s data. In some cases, however, the A/C was already on at the beginning of the day. Two additional conditions were given at the beginning and end of the day. If the energy consumption was higher than the “lower bound on” at minute zero, the A/C was considered to be in the “on” state. If the unit was on at the end of the day without an “off” signal, an artificial “off” signal was given at i = 1440 so that the energy could be accurately summed. An example of a typical day where the energy was disaggregated can be seen in Fig. 7. Because the average energy consumption of the A/C was applied to the entire day, differences due to efficiency are not reflected in the estimated energy as seen by the difference between the estimated and measured A/C value at 2 p.m. in Fig. 7.

Fig. 7. Sample day of disaggregated energy for a house. Measured A/C energy denotes the values given from the sub-circuited eGauge on the A/C system. Estimated A/C is the disaggregated energy.

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K.X. Perez et al. / Energy and Buildings 81 (2014) 316–325 Table 2 House ID for sub-metered houses. R2 value is that given from the fit of the data to the parity plot. The CV(RMSE) values (in %) are also given.

Fig. 8. Overall energy for house B during relevant time period. The residual plot indicates that the disaggregation algorithm accurately predicts actual A/C energy.

3. Results and discussion 3.1. Validation from sub-metered houses First, 19 houses were used to validate the technique and then all 88 houses were used for analyzing A/C consumption. The 19 houses that had the A/C sub-metered were used as a benchmark to evaluate the accuracy of the algorithm. The estimated daily A/C energy consumption was compared with the measured daily energy consumption. Fig. 8 shows the estimated values of the disaggregation technique compared with the measured values reported by the submeter for one house. The estimated energy aligns very closely with the actual total energy throughout the evaluated time period of May through October. The parity plot shows that the estimated values follow the parity line closely. During the rest of the year, the algorithm was less accurate because other loads in the profile appear similar to the A/C. Thus the algorithm detected false events and would overestimate A/C energy. The algorithm does not differentiate changes in energy due to the A/C or other appliances if they are the same magnitude. Therefore, when A/C is not a dominant load the load is still perceived as A/C. The degree to which the estimated A/C energy is different from the measured energy depends on how many loads mimic the A/C. Generally speaking, most A/C units in this study consumed about 2.5 kW of power when on. It appears that only high loads such as an electric dryer are of the same size. In the case of a highly efficient unit that drew substantially less power, such as 1 kW, the algorithm likely would not successfully discriminate between that and other similarly sized loads. For some houses, accuracy in estimated A/C use during winter months was the same as summer and for others the difference was substantial. Therefore only cooling months were taken into consideration. The limitation to this algorithm is that it is specific to A/C loads during cooling months. It should be noted that the key parameters such as Eon were derived from training time in July 2012, but were still applicable and accurate during summer 2013 indicating that the model may not need to be retrained frequently. Because the A/C power is not a function of behavioral considerations (e.g., plug loads, thermostat set point changes), the parameters should continue to be valid until the air conditioning unit is changed. Were this technique to be extended farther in the future, there might be larger differences between estimated and actual values. May through October was chosen for the Austin area because air-conditioning units being in use during a significant portion of the day; furthermore, this time period overlaps with summer time as defined by the Electric Reliability Council of Texas (ERCOT).

House ID

R2

CV(RMSE)

House ID

R2

CV(RMSE)

A B C D E F G H I J

0.92 0.99 0.95 0.95 0.97 0.95 0.99 0.93 0.87 0.99

22.4% 7.2% 16.3% 13.1% 10.5% 17.4% 7.5% 25.3% 25.8% 9.5%

K L M N O P Q R S

0.74 0.96 0.92 0.82 0.98 0.69 0.97 0.95 0.97

64.6% 22.9% 30.6% 30.3% 12.4% 44.1% 14.2% 15.2% 8.9%

Observing all the houses that had the A/C sub-metered, a parity plot of May through October of estimated A/C energy consumption vs. measured A/C energy consumption exhibited high R2 (coefficient of determination) values and relatively low CV(RMSE) (coefficient of variation of the root mean square error) values as shown in Table 2. R2 is used to describe the variation in the linear relationship between measured and modeled A/C use while the CV-RMSE is used to quantify variation of residuals (the differences between predicted values and observed values.) ASHRAE Guideline 14 adopted CV-RMSE to evaluate prediction uncertainty of energy inverse models, which would also include the energy disaggregation model presented in this work [26]. According to the standard, “typically models are declared to be calibrated if they produce . . .CV(RMSE)s within ±30% when using hourly data.” House N, while having a high R2 also had a regular electric vehicle charging load that resembled an A/C unit turning on for a sustained time. Thus the algorithm effectively tracked the variation in A/C consumption, but consistently over-estimated the amount of A/C energy. We note that house P also had lower values of these goodness of fit matrices. A closer inspection of the data showed low A/C use during morning hours and thus a poor training period to identify A/C loads. However, houses with low A/C use in the morning could be screened prior to disaggregation. Overall the results on the sub-metered houses indicate that the disaggregation technique accurately differentiates the A/C energy from the overall energy profile. On average for the 19 houses, the total estimated A/C energy value differed from the measured value by less than 14% (2.1 kWh) of the measured energy consumption. The algorithm was then applied to all 88 houses including those of which had not been sub-metered. A/C energy consumption was then compared against cooling degree days (CDDs). CDD is a metric for the cooling that will be required in a given day and is used extensively in the building HVAC industry. A cooling degree day is defined as CDD = Tday 015.5 ◦ C

(6)

where Tday is the average temperature of the day. The cooling degree days were obtained from Austin-Bergstrom International Airport (Weather Station KAUS), which is approximately 8 miles from the location of the metered houses. 3.2. A/C energy trends Fig. 9 shows the total daily energy and A/C energy consumption vs. CDD summed for all the houses. As would be expected, both total energy and A/C energy increase with increasing temperature. The relative changes in A/C energy and other energy consumption have different slopes as the temperature ranges from mild to hot days. The magnitude of change between the extremes in CDD shows that the total A/C consumption for the 88 houses increased from around 1500 to 4500 kWh. Of that, half of the increase was due to A/C. The

K.X. Perez et al. / Energy and Buildings 81 (2014) 316–325

Fig. 9. Daily disaggregated total, A/C, and base-load energy summed for all the houses in the study vs. CDD. Each point represents the summation of all the houses on one day. Between extremes in temperature A/C increases by a factor of 8, while overall energy triples. Points were taken between May and October.

increased A/C energy use comes from A/C units that need to run for longer times throughout the day. The final reason for the baseline energy doubling could be due to additional sources of cooling, such as fans, or by increased presence at house by occupants due during hot weather. On average, A/C energy use for houses in the study increased by 25 kWh in total between the mild and hot extremes, 67% of the total energy increase. A closer inspection of just A/C energy during peak hours (14:00–20:00 as defined by Austin Energy, the local municipally-owned electric utility) shows most houses each increase by roughly 11 kWh, ten times as much as during a mild day. Of the overall change in energy use due to hotter weather, almost 31% can be attributed to the increased A/C use during just peak hours. Fig. 10 displays the total A/C energy used just during peak hours vs. maximum daily temperature. The values derived are the average across all the houses. There appears to be a threshold at approximately 25 ◦ C (77 ◦ F) after which the energy consumption increases fairly linearly with respect to maximum outdoor temperature. The energy use actually increases by an order of magnitude, which is substantial, especially if an entire neighborhood follows suit. An important result of disaggregating 88 houses is found in Fig. 11, which shows average power consumption and standard deviation vs. cooling degree days. Overall and A/C energy use increase linearly with increasing CDD. A significant point to notice is the increasing trend in standard deviation. As power consumption increases, the spread of energy behaviors and consumption

321

Fig. 11. Plot of average total and A/C power consumption and standard deviation vs. cooling degree day for all 88 houses.

increases linearly. During hotter weather, there is a larger spread in consumption, which may be due to differences in thermostat set points, house size and occupant schedules. When building a neighborhood or city model, a sufficient sample size must be considered in order capture this spreading behavior appropriately. The fraction of A/C energy from total energy vs. CDD is displayed in Fig. 12. A boxplot was chosen to display the spread of the data. In a boxplot, the median of the data is represented by the solid line inside the box and the edges extend to encompass 50% of the data surrounding the median. The whiskers spread to 1.5 of the quartile ranges with outliers represented by the small markers. The distribution of the data can be seen in the relative spread of each boxplot. The graph shows that as CDD increases, the fraction of energy dedicated to the A/C also increases. The fractional increase is largest for cooling degree days between 3 and 10 ◦ C, then the fraction appears to level out. This could be due to the saturation of some A/C units always on during the hottest periods. The average fraction across summer months (June–August) was 47% and 40% for the entire evaluation period (May–October). The number of cycles in the day is one predictor of wear and tear of an A/C system. Excessive cycling can cause deterioration on the A/C system and can be an indicator of an oversized A/C unit. Excessive cycling could also signify that the thermostat does not correctly represent the temperature in the house, such as when a thermostat is placed directly under a cooling vent. The number of cycles throughout the day is modestly affected by temperature. As temperature increases, so will the average number of cycles (see Fig. 13). It was found that the number of cycles a house experiences is on average 32 cycles/day during the entire time period and 37 cycles/day for the summer months (see Table 3). Fig. 14 shows the total time that the A/C unit was on with CDD on the x-axis and the total time on the y-axis (in hours). The spread of the data across the houses is fairly large with some houses with their A/C on during a significant portion of the day even during milder days. That spread might indicate a house with someone who works from house or low temperature thermostat setting. Similar distributions of run times have been seen in other publication [27,28]. Regardless, with increasing CDD the total time that A/C Table 3 Summary of overall analysis. Average total time A/C on, number of cycles and A/C fraction of energy for all houses given for just summer months and then the total evaluated time.

Fig. 10. Mean total A/C energy during peak hours (14:00–20:00) vs. maximum daily temperature. Each point represents the average A/C energy consumption for all the houses during one day. The A/C power increases from 1 kWh to 11 kWh between the two extremes in temperature.

Metric

June–August

Total time A/C on Number of cycles A/C fraction of energy

9.5 37 47%

May–October 7.4 32 40%

Unit Hours Cycles/day –

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Fig. 12. A box plot showing the fraction of total energy that is A/C energy vs. CDD. The increasing fraction with increasing CDD shows a positive correlation up to about CDD = 14.

Fig. 13. A box plot showing the number of cycles vs. CDD. Number of A/C cycles increase with CDD before leveling out.

Fig. 14. A box plot showing the total A/C runtime vs. CDD. Runtime increases linearly with CDD until leveling out.

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Fig. 15. Comparison of sample times on the ability of the algorithm to estimate A/C power consumption for a single day. The top plot uses a 1-min sample time, the middle plot uses 5-min sample time, and the bottom plot uses 15-min sample time. As sample time increases, it becomes more difficult to disaggregate the A/C load.

unit is on also increases. That being said, there appears to be a limit reached where the time on does not linearly increase. This limit could come from limitations to the air conditioner unit for safety or to prevent excessive wear on the system. Properly sized residential A/C units are only designed to meet ∼96% of summer cooling hour demand, which may explain the plateau [29]. The main difference between mild days and hot days was a substantial increase in the duration of time the system was on during the late morning and early afternoon. The A/C unit needed to operate most of the day to maintain the thermostat temperature. The average time spent on during summer months (June–August) was 9.5 h. Across the entire time period (May–October) it was 7.4 h. 3.3. Various sampling times In this analysis, the data set considered energy use measured in 1-min time intervals. However, most utilities have smart meters that report energy usage in 15-min time intervals. As energy use data becomes coarser, it becomes more difficult to identify and separate individual loads (see Fig. 15). A brief analysis evaluated the sampling time to which A/C loads can still be reliably disaggregated. Fig. 15 is a comparison of the energy profile for 1, 5 and 15-min data. Five-minute data is visibly coarser than the 1-min data, but still retains a degree of granularity that makes it possible to recognize which peaks are the A/C. The 15-min data is even coarser, making it difficult to even visibly distinguish A/C peaks from the base load. For 5-min data, it may still be possible to count the number of cycles if the cycle times are shorter than 5 min. In the 15-min profile it was extremely difficult to accurately measure cycle numbers. The 5-min data does have advantages. For example, taking the average across 5 min, anomalies, such as random spikes, would not be seen in the profile. Lower frequency data have lower hardware storage requirements but this savings comes at the cost of granularity as highlighted below. Fig. 16 describes the error differences between 1, 5 and 15min data. The disaggregation technique was scaled to match 5 and 15-min data in terms of the training period. The techniques then followed the same algorithm to cluster changes in energy to define the parameters that indicate on and off events. They then stepped through the algorithm just like in the 1-min technique. The resulting R2 and absolute error values were found and then compared with the 1-min technique as seen in Fig. 16. Overall, both 1 and 5-min data had very high R2 values while the 15-min data had significantly lower values. A similar trend was found in the absolute error. Although for some houses, the 5-min data had a smaller absolute error. In the 1-min data scheme, sometimes a very busy energy profile made it hard to distinguish A/C events from other

Fig. 16. Comparison of R2 and absolute error values for 1, 5 and 15-min data.

appliances, especially if a system ramped on between sampling times. The 5-min profile smoothed out the profile to remove most hard to distinguish events. On days with low A/C usage, the 5min profile is especially accurate because of this smoothing effect. Depending on the required amount of detail, 5-min time intervals can be accurate enough to make control decisions while reducing the amount of data stored. It also gives a fairly accurate overall picture of energy use. Fifteen-minute data does not have high enough resolution to discriminate between A/C and non-A/C events. When considering the benefit vs. cost of storing smart grid data, utilities should consider flexibility in new installations so that the benefits of more discrete data can be fully explored. 3.4. Cost analysis Disaggregation is a powerful tool to perform unique analyses of smart meter data. As an example, a cost comparison of A/C energy is conducted on two rating structures using disaggregated data. With HVAC a major part of the residential electricity sector especially during the summer months, the energy charge for using the A/C is likewise a large portion of the electric bill and of importance to the homeowners. Austin Energy, the electricity provider for the 88 houses in the study, offers two rate schedules for residential users: monthly and time-of-use (TOU). The Monthly rate has different tiers of energy use and charges a flat rate per kWh per level and bills through an inverted block rates. The second option, timeof-use, monitors the electricity use and charges the customer for electricity based on the time period (off-, mid- and on-peak hours) and the amount of electricity used that month [30] (Fig. 17). For the 88 houses in the study, the A/C electricity costs were calculated for both rate schedules. To calculate the electricity price for the monthly rate, the total monthly electricity use was charged according to the inverted block rate to find the total electricity bill. The A/C percentage of total house electricity was applied to the total monthly electricity cost to establish the cost for A/C electricity use only. For the TOU rate, the minute data for A/C electricity use was summed into hourly data, broken into weekday or weekend, and

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lowered if participants were actually engaged in a TOU pricing program. On average, the time-of-use and monthly rates that Austin Energy charges the residential customers are similar for each month except June, where the average difference is approximately $28.00 per user. During the other months, the TOU price was one average $5.00 higher than the monthly rate. Because the standard deviations between the two values overlap in range, we cannot conclude that there is a significant different in total price. 4. Conclusions

Fig. 17. Electricity costs for the 88 houses in the study and the average using two different rate schedules: monthly [on the left] and time-of-use [on the right].

then off-peak, mid-peak, and on-peak time periods. Using the rate levels determined by the total amount of electricity used by a house per month, the off-peak, mid-peak, and on-peak rates were applied to the hourly A/C electricity data, giving the cost to run the A/C unit per month. For both pricing structures, the houses followed similar electricity cost trends based on the month of the year, with the hotter months costing the customer up to 5 times more than the cooler months due to both increased A/C use and increased electricity prices. For both price structures, there is a large spread of total electricity costs during summer months. TOU pricing did not appear to have a much larger spread during months when peak demand becomes a larger issue. It appears the TOU pricing structure allows most homes to naturally (i.e. these houses are not currently billed according to TOU pricing) have comparable prices to monthly pricing (see Fig. 18.) The TOU pricing totals may be significantly

This paper has shown that a generic NILM algorithm was able to accurately disaggregate A/C usage from total energy profiles. The average R2 value of measured vs. estimated A/C energy values for 19 sub-metered houses was 0.90 with an average CV(RMSE) of 25.4. This technique requires a training period in which the A/C is the dominant load, but once the parameters have been estimated, they will likely remain valid until the A/C unit undergoes significant change. The validated algorithm was then applied to 88 houses in an Austin, TX neighborhood. On average, it was found that daily energy use from A/C for individual houses increased by 25 ± 11 kWh (a factor of 8) between a mild temperature day of 15.5 ◦ C (60 ◦ F) and a hotter day of 31.5 ◦ C (89 ◦ F), 11 of which were just during peak hours (14:00–20:00). The average time the A/C unit operated per day during the months for which A/C use is a prevalent feature in the energy profile (May–October in Austin) was 7.4 h. Similarly the average number of cycles per day was 32. The fraction of energy attributed to the A/C from total energy during these months was on average 40%. Average time operated, number of cycles, and A/C fraction of energy are reported and were all found to increase linearly with increasing outdoor temperature up to 25 ◦ C (77 ◦ F) and then they began to level off. An analysis of Monthly vs. TOU pricing for A/C energy costs did not reveal significant differences. A comparison between 1, 5 and 15-min sampling times revealed the accuracy of 5-min data in disaggregating A/C loads to be comparable to 1-min data. However, 15-min data did not yield accurate results due to insufficient granularity of data. 5. Future work Storing data for daily energy usage in 1-min time intervals can be expensive and difficult, especially for thousands of houses in a city. The disaggregation technique was optimized to function for 1-min data, but most energy use data are stored in averaged 15min intervals. Future work includes evaluating what granularity would allow the disaggregation technique to remain accurate while minimizing the amount of information stored. Disaggregated A/C energy loads make it possible to build semiempirical models of house energy use. One future avenue for residential energy management research is to develop simple, efficient and realistic models of individual houses that can then be used to describe energy use of an entire neighborhood. The neighborhood model can provide the generic framework to describe the dynamics of a neighborhood in response to ambient temperature. Ultimately, the model can be used to investigate the use of energy storage and capital cost/energy efficiency trade-offs for an entire residential community, providing insights into the economic feasibility of using energy storage to “flatten” energy demand. Acknowledgements

Fig. 18. Comparison of Austin Energy’s TOU and monthly pricing structures using an average over all 88 houses in the study. Bars represent the ±std. deviation.

This work was supported by the Pecan Street Research Institute (a 501(c)3 nonprofit public-private partnership in Austin, TX), the

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