Free Article: TETC - Human Behavior Aware Energy Management in Residential Cyber-Physical Systems

Baris Aksanli Department of Electrical and Computer Engineering, San Diego State University, San Diego, CA Tajana Simunic Rosing Department of Computer Science and Engineering, University of California, San Diego, CA

Abstract

Technological advancements, such as smart appliances, have enabled residential buildings to become a true Cyber-Physical System (CPS), where the devices correspond to the physical system and the smart computation and control mechanisms define the cyber part. An important aspect of these residential cyber-physical systems is their large portion of the overall energy consumption in the electric grid. Researchers have proposed several methods to address the issue, targeting to reduce both the consumption and the cost associated with it, either individually or simultaneously. These methods include using renewable energy sources, energy storage devices, efficient control methods to maximize the benefits of these resources, and smart appliance rescheduling. However, a residential CPS, different than a common CPS, has a lot of direct human interaction within the system. Although the previous residential energy management methods are effective, they do not consider the inherent and dominant human factor. This paper develops a human-behavior-centric smart appliance rescheduling method for a residential neighborhood. We first show an accurate representation of the relationship between the activities of the household members and the power demand of the house. We use this model to efficiently generate several power profiles based on different household characteristics. Then, we formally model how flexible users are when rescheduling appliances. In contrast to previous studies, our work is able to capture the intrinsic human behavior related decisions and actions when automating the residential energy consumption. Our results show 16 percent energy savings and 22 percent reduction in peak power relative to the case without appliance rescheduling while accurately representing and meeting human-related constraints. We also demonstrate that ignoring human preferences can lead to up to more than 90 percent violation of user deadlines.

I. Introduction

Cyber-Physical Systems (CPS) define environments where the devices (physical part) are highly integrated with the control and computation units (cyber part) . These systems are traditionally leveraged in large-scale industrial and autonomous domains . However, with the recent advancements in technology, we are now able to see many more application domains for CPS. Examples include medical applications smart grid applications vehicular applications etc. To provide support for more applications, most CPS environments expand their domains with additional devices and thus it becomes inevitable to interact with humans. Recent studies recognize this connection between humans and the CPS domains as “human-in-the-loop CPS (HilCPS)” . Analyzing the human factor in CPS domains may provide many additional useful insights (such as real-time medical information ), but also result in several important interdisciplinary challenges. In this paper, we focus on residential CPS environments. With recent technological advancements, such as smart appliances, appliance control, etc., residential buildings have become a true CPS. Furthermore, these systems have a lot of interactions between the humans and the physical devices, making them a HilCPS . An important aspect of these HilCPS environments is their high energy portion of the overall energy consumption in the US, accounting for around 35 percent of the overall consumption . The recent technological advancements, such as smart metering, widespread sensor deployment, smart appliances, etc., and increasing awareness across people have enabled both industry and researchers to better study the residential energy consumption. These studies mostly target heating, air conditioning and ventilation (HVAC) units, appliances, and electric vehicles (EVs). This is because these electrical devices form a big portion of the overall residential demand and can be controlled either manually by the users or automatically with new technologies. These residential energy management studies show that it is possible to obtain significant savings by cleverly adjusting the power demand, and these savings can easily add up to correspond millions of dollars savings. Despite the effectiveness of the residential energy solutions, there are several issues to be resolved to attain meaningful results, such as scalability and human factor. The main cause of these issues is the underlying human factor in residential buildings, which makes it more difficult to formally model and eventually predict the power demand. This factor in turn, affects the validity of a solution across hundreds of potentially different power demand profiles. Another issue with the human factor is related to their willingness to adjust their behavior in cooperation with the energy management solutions. Unlike larger scale commercial and industrial buildings, where automation is widely available, residential buildings highly require explicit participation of the household members. Also, even if complete automation is possible for residential units, there are still human habit/behavior based satisfaction factors. If these requirements are not clearly met, the households may not participate in energy/power savings programs, and thus, the potential benefits to be obtained by residential energy/power savings methods may not be achieved. In order to include this aspect in their models, previous studies generally make high-level assumptions to account for user willingness, such as allowing a 6-hour or 12-hour horizon for rescheduling the appliances, etc. –. However, this aspect might differ across different households, mostly depending on the household members, i.e., number of people living in a house, age, gender, employment status, etc. In this paper, we present a new smart appliance scheduling-based energy management solution for residential neighborhoods, where we explicitly model the human factor. Figure 1 shows the main workflow of this paper, where we adopt a computational approach (workload and quality of service modeling, resource (energy) scheduling) to manage residential energy based on user behavior constraints, forming a HilCPS environment. We first present a user-behavior model to estimate the energy consumption of a house. Our model is based on detailed activity sequences of household members and the connections between these activities and appliances. We use two publicly available data sets, American Time Use Survey (ATUS) and Residential Energy Consumption Survey (RECS) to account for user activity and appliance usage habits. We compare our model against real house traces from Pecan Street database . The power profiles we generate follow the trends in real traces, e.g., matching the peak demand times and frequencies. We show the importance of this with a case study, where we evaluate voltage deviation in a neighborhood, where voltage deviation is used as a measure to quantify the potential endangering situations in the electrical circuit.

Figure 1. Computation-oriented workflow for user behavior-aware residential energy management.

Next, we model user willingness by formally modeling the flexibility of the residential buildings when using different appliances. This is another point where we explore the HilCPS aspect of residential buildings. Based on this flexibility, we can assign reasonable deadlines to different appliance usage instances for different households. To obtain the flexibility values, we analyze historical data available from Pecan Street database . We process the data representing hundreds of houses using different types of appliances. Specifically, we focus on appliance start times in houses with different inhabitant characteristics. Based on the distribution of these start times in a single day; we attribute different interval lengths as reschedule horizons. We use information theory when analyzing the cumulative distribution functions of different appliances in terms of their starting times. During this process, the entropy value of a cumulative distribution function tells us how flexible a house is when using a specific appliance, e.g., no flexibility, 1h-6h flexibility, etc. With these deadline values, we can treat the appliance usage instances as automatic jobs that can be scheduled to use the energy resource and remove the explicit assumptions about users. Lastly, we create multiple optimization problems to cleverly schedule the appliance instances in a residential neighborhood. This third part completes our energy management solution by actually solving when the jobs (appliance instances) should be scheduled to run, completing our computation-oriented HilCPS modeling. Our idea here is analogous to job/resource scheduling in data centers or cloud systems . We use multiple objective goals to first show that objectives with single goals might end up creating significant inefficiencies when considering the system as a whole. We first create solutions to two well-known objective functions, i.e., minimizing the total neighborhood electricity cost and minimizing the total peak power consumption of the neighborhood. We show the minimizing only for electricity cost increases the peak power in the neighborhood while optimizing for peak power may not always result in lower electricity cost. Finally, we create a solution for the problem that still tries to minimize the electricity cost while maintaining a peak power budget. Our framework is able to achieve 16 percent energy savings and 22 percent peak power reduction in a neighborhood, compared to the case where there is no appliance rescheduling. We also show that if human choices are not accurately represented, up to more than 90 percent of the deadlines that represent human flexibility deadlines, can be violated. This demonstrates the importance of modeling the habits of individuals. Lastly, we present a sensitivity analysis showing how sensitive our framework is under different prediction error assumptions.

II. Related Work

There have been many studies on Cyber-physical systems (CPS) and how they can be used for different applications. These systems, which have highly coupled device and computational parts, have been used extensively in industrial automation . Recently, with the technological advancements and the rise of the Internet of Things there have been even more application domains for CPS, e.g., smart, pervasive living communities smart grid medical devices smart transportation agriculture etc. Recently, researchers have also focused on analyzing the interactions between the CPS environments and the humans . This is mostly because the number of devices has been constantly increasing (reasons include IoT, availability of technology, reduced cost, etc.) and thus, there is a higher chance for people to interact with these devices during their daily routines. Schirner et al. specifically define a term, “human-in-the-loop CPS (HilCPS)”, to represent the CPS with increased human factor. Example HilCPS domains include health applications, residential applications, etc. Residential HilCPS applications include user behavior modeling that estimates appliance and plug-load energy consumption based on different behavior footprints. Previous studies construct models based on historical activities – using commonly available activity data sets such as ATUS data. They group the activities into meaningful clusters and create user categories based on people's age, gender, employment status, and the number of other household members. Other studies use similar survey data from France UK and Spain . These studies also use machine learning methods such as Markov chains neural networks, Bayesian networks, and decision trees to determine the activity chains, i.e., which activity is more likely to follow another. Using these data sets, previous studies determine which activities are related to appliances either manually or by using another data set (RECS ). After this linking, they estimate the starting time of appliances (such as washer, dryer, dishwasher) and the operating conditions of bigger units (e.g., refrigerator, HVAC, lighting, etc.). The house energy consumption is then simply aggregation of all the individual appliances and plug load units. By disaggregating the total energy consumption, previous studies can apply different mechanisms (such as appliance rescheduling, controlling HVAC and lighting parameters, etc.) to participate in demand response programs ultimately to save energy and electricity cost . There are also the widely-used residential energy databases, REDD and Smart* that show the disaggregated energy consumption of several houses over a couple of months. To get detailed user behavior models, the researchers use the disaggregated appliance consumption to deduce the user behavior or occupancy . Here, the main disadvantage is that there is no real information in the data set on what the users were actually doing and thus it has to be guessed. Although previous studies show significant savings with clever energy management, none of them formally model the human factor, thus, their large-scale savings estimates do not represent a mid-sized to large neighborhood where there are various types of households with different energy usage behavior. This paper fills this gap by explicitly creating the bridge between a residential energy solution (smart appliance scheduling) and human behavior by modeling a residential building as a HilCPS. In our HilCPS, the physical devices are the appliances, the cyber part is the smart appliance control mechanisms and humans constantly interact with these devices during their daily routines.

III. User Behavior Modeling

This section develops a graph-based model to represent the chain of user activities. Our main goal is to probabilistically capture the time-series nature of user behavior.

A. Activity Graph Definition

User activities are the main events in a house that trigger energy consumption. We define user activity as a set of actions associated with one or multiple appliances over a time period. For example, cooking is an activity that includes all actions between getting into the kitchen and cleaning the dishes. During this activity, the user might use several appliances such as refrigerator, oven, microwave, etc. The exact set of appliances associated with an activity changes among different activity instances. All activities have a duration associated with them. The day of a person is divided into discrete activity blocks. The next step is determining the chain of activities for a user. We model the next activity for a given one probabilistically, which depends on a similar set of variables as described earlier. Using this information, we build activity graphs, where the nodes are the activity blocks (with inner graphs as actions for a specific activity) and the edges are the activity transitions. The graph is designed to be cyclic with sleeping activity as the reference node. This is based on the assumption that the activity “sleeping” happens every day and enables us to use it as a reference point connecting multiple days. An example of a formally constructed activity graph is shown in Figure 2 and the details can be found in our previous study .

Figure 2. Activity graph structure.

B. Activity Graph Construction

This section shows how we calculate the activity graph parameters. There is a separate graph for each individual, thus we estimate the parameters separately for different classes of people. To meet our classification needs, we use ATUS data . It has more than 10,000 participants from different parts of the society and includes their detailed activity information, which corresponds to the actions/activities in our graphs. ATUS does not have any details about appliance usages. We use another data set, RECS which surveys more than 110 million households and has statistics regarding the families, the types and numbers of appliances used, and how frequently they use the appliances. We get the family and appliance statistics from RECS and connect them with the individual activity data from ATUS. These parameters include the set of activities and actions, their durations and finally the action/activity transition probabilities. We show how we calculate these values in our previous work and include examples in Tables 1 (list of activities and actions), 2 (action durations for user groups) and 3 (appliance triggering probabilities given an action).

TABLE 1. List of activities, actions and appliances.

TABLE 2. Average action duration values.

TABLE 3. Example appliance triggering probabilities.

Finally, we combine the activity graphs of individuals in the same house. We construct families based on ATUS and RECS family statistics and activity graphs of family individuals. We add up their graphs if they are mutually exclusive or solve conflicting appliance events as explained in more detail in our previous study .

IV. User Flexibility Modeling

The previous section shows how we create the “workload” for the residential buildings, where the workload determines when the appliance instances occur. This section shows how we determine the deadline of each job and how user behavior affects the deadline strictness. We define flexibility of each household when using an appliances in terms of the willingness to shift the usage of those appliances. To understand the effects of user behavior on appliance usage flexibility, we leverage historical power data. We start our analysis with the disaggregated house energy profiles from the Pecan Street database . We gather a year's worth of data, between 01-01-2014 and 01-01-2015. However, this database is not fully complete, i.e., not every house has data for all the appliances. Thus, the number of houses with available data for each appliance is different. The granularity of the consumption data is 15 minutes. Then, we partition the appliance list into two disjoint sets: frequency based versus continuous appliances . The former has specific start/end times for an appliance usage instance whereas the latter has a continuous power consumption profile. The former set has dishwasher, clothes washer, dryer, pool pump, electric car, oven and microwave. The latter has the rest (such as refrigerator and HVAC). For appliance rescheduling purposes, we focus on the first set of appliances as they have explicit start times. For each appliance in the frequency-based appliance set and each house, we extract the appliance start times. We divide the day (24h) into 15-minute chunks and then count the number of appliance instances that start in each chunk over the entire year. We convert these counts into a cumulative probability density function (CDF). Our intuition is that the shapes of the CDF curves present useful information about how each house uses a specific appliance. For example, sharp jumps in a CDF mean that the residents use their appliance around specific times and would be less willing for shifting their usage. In contrast, the houses with smoother profiles would be more open to alter their original appliance usage schedule, as their usage times are more uniformly distributed across a day. This way, we can formally build a model to understand how users could respond to appliance reschedules, and place confidence intervals for appliance start times, which can translate into deadlines. Next, we assign values to different CDF curve shapes, i.e., a function that translates a CDF curve into a numerical value. To achieve this, we use a well-known concept: (Shannon) entropy. Entropy is a measure of unpredictability of information content . In our case, when the appliance start times accumulate around certain intervals, the CDF curve has sharp jumps and becomes more predictable. Thus, the amount of information CDF curve carries is low and this translates into low entropy. In contrast, a smoother CDF means that the appliance start time is less predictable and thus it has a high entropy value. In Figure 3, we first show how different CDF profiles for each appliance in the frequency-based appliances set correspond to different entropy values. In the graphs, the x -axis correspond to the time chunks in day and y -axis show the probability values for the CDFs. Although each graph shows CDFs for a different appliance, the shapes of those CDFs show great similarity if they have similar entropy values.

Figure 3. CDF versus entropy relationship for appliances (electric car, dishwasher, microwave, oven).

The main conclusion is that lower entropy corresponds to a stricter appliance usage profile. Figure 4 shows how the entropy values for different appliances vary across the houses. In these graphs, the y -axis shows the entropy values and the x -axis shows the corresponding house numbers for entropy values. These graphs show how many of households are flexible versus strict when using different appliances.

Figure 4. Entropy values versus number of houses for different appliances (car, dishwasher, microwave, oven).

We then apply clustering to determine disjoint sets of houses based on entropy values. The main goal of this process is to understand which entropy values translate into similar user flexibility values. We use the k-NN algorithm with

k = 5

and observe that the cluster centroids gather around integer values. Since the observed entropy values are between 0 and 5, we form the clusters as presented in Table 4. This table ultimately shows the distribution of houses that fall into different flexibility categories.

TABLE 4. House Counts and percentages for different flexibility categories for different appliances.

The last step is to assign flexibility intervals around appliance start times based on the entropy value observed for the given appliance. In our framework, these flexibility intervals correspond to job deadlines that reflect the user behavior. The CDFs with entropy values smaller than 1 exhibit sharp jumps; hence present no opportunity for rescheduling. This flexibility increases with higher entropy, giving rescheduling opportunities within from 1h to 12h. Table 5 summarizes the user flexibility in terms of entropy intervals, which are valid for all the reschedulable appliances. These intervals are one sided, i.e., if the flexibility interval is

Δ t

hours and the original start time is

t_{1}

, then the appliance start time can be selected from

[t_{1}, t_{1} + Δ t]

. This decision entirely depends on system design choices. We use a one-sided flexibility interval because our scheduling applications are all online. If our framework is used for offline scheduling where the appliance start times are known ahead of the time, then the flexibility interval can be modeled as two-sided.

TABLE 5. Appliance flexibility versus entropy values.

V. Human Behavior-Aware Scheduling

The main goal of this section is to demonstrate the applicability of our framework on a well-known residential energy management mechanism: appliance rescheduling –. We formally show our framework manages appliance rescheduling decisions and preserve its formal construct to model the user behavior and flexibility. The schedulers are based on optimizing different quantities such as electricity cost, peak power etc. Each scheduler can shift the jobs (appliance instances) based on job deadlines (based on user flexibility), electricity price (assuming time-of-use pricing) and a preset peak power threshold. Throughout the section, we assume that the future arrival times of the jobs are not available, i.e., we only know the current state of the system. Since the schedulers give the best decisions in the current interval, the schedule is heuristic and can be suboptimal. Implementing optimal schedulers is out of our scope, instead, we provide a proof-of-concept demonstration of appliance rescheduling using our framework.

A. Scheduler Minimizing the Energy Cost

This scheduler minimizes the total electricity cost of a neighborhood. We assume that no appliance instance can be canceled to save energy. Thus, the total energy consumption stays the same and cost minimization has to be achieved by exploiting electricity price differences. We assume a time of use (ToU) pricing scheme. If there are additional constraints on how the energy should be allocated across houses (e.g., peak power limits, etc.), energy becomes a shared resource across the houses. But in this section, no such constraint exists, i.e., houses do not need to coordinate. Thus, we disaggregate the energy consumption in appliance level, preserving the semantic dependencies, such as using the dryer after the washer. Equation (1) shows the start time of an appliance based on electricity prices and user flexibility,

\begin{matrix} (1) & t_{n e w} = \arg min_{t} {\sum_{i = t}^{t + t_{a}} P_{a} (i) * c (i) | t_{o r i g} \leq t \leq t + Δ t_{a}}, \end{matrix}

where

t_{o r i g}

and

t_{n e w}

are the original and newly determined appliance start times,

t_{a}

is the appliance operation duration,

Δ t_{a}

is the appliance flexibility in hours,

P_{a} (i)

is the power consumption of the appliance in interval

i

and

c (i)

is the electricity cost in interval

i

. We further simplify (1) with the assumption that

P_{a} (i) = P_{a}

in all time intervals where the appliance a is in operation. This assumption is used by many previous studies . Then, (1) becomes:

\begin{matrix} (2) & t_{n e w} = \underset{t}{\arg min} {\sum_{i = t}^{t + t_{a}} c (i) | t_{o r i g} \leq t \leq t + Δ t_{a}} . \end{matrix}

Equation (2) finds the sub-interval in the flexibility region of an appliance with the lowest electricity cost. Our formulation assumes that future electricity prices are available, which holds for most of the utilities since they make their ToU prices available ahead of time. If this is not the case, we can apply prediction methods to estimate the future prices –.

B. Scheduler Minimizing the Peak Power

The peak power costs are calculated over a billing period (e.g., a month). Hence, we apply peak power minimization over the entire billing period. We assume that we do not know the exact arrival times of the jobs. Our online scheduler finds the best possible starting time of a job as it arrives. We solve a constrained resource-scheduling problem where the resource is energy. The best (lowest peak power) schedule is only possible when the job arrivals over the entire period are known. Even with this assumption, the solutions are NP-Hard (power allocation to sensor units data center power allocation in the power grid virtual machine power allocation in data centers ). Our online approach uses a preset threshold to minimize the peak power, as previously used in . The advantage of our framework is that we can put appliances into a context in which we can apply existing peak power shaving methods. This is achieved by representing appliance instances as jobs with deadlines that require power as resource. Once this representation is used, we can apply previous power capping mechanisms, such as in our previous work to stay under a power threshold. Algorithm 1 in Figure 5 presents an overview of solution. When an appliance instance arrives at time

t

, we first check if running this appliance at time

t

creates a peak power violation. If there is no violation, the job is scheduled to run at time

t

. If there is a potential violation, we calculate the duration of the violation,

v i o l a t i o n T i m e

. The idea is to find a job that can be shifted for at least

v i o l a t i o n T i m e

. To find this job, we use an adaptation of the EDF (earliest deadline first) scheduler. Since we cannot stop the jobs that are already running, we list the jobs that are scheduled for future use. We sort these jobs based on their deadlines and choose the one that has the latest deadline and at least

v i o l a t i o n T i m e

flexibility. The goal here is to minimize the probability of missing a job deadline.

Figure 5. Peak power-aware appliance rescheduling algorithm.

This scheduler cannot guarantee if a peak power threshold is maintained over the entire period because we do not know future job arrivals. If there is a potential peak power violation on a job arrival and we cannot reschedule any of the jobs, we have two options: 1) we cannot meet the current peak power threshold and should update the threshold to a higher value or let this instance violate the threshold, 2) relax the deadlines of some jobs to create more opportunities for job rescheduling. The solution depends on the system design and the choices of the users, i.e., if they are willing to relax their appliance usage times or to pay additional cost for increased peak power.

C. Scheduler with Combined Optimization

This case considers both a peak power threshold and the electricity cost. Similar to the previous version, we present an online solution. Figure 6 shows the steps of the scheduling approach. First, we find the duration for which the peak power threshold is violated,

δ

. Then, we sort the on-hold appliances with respect to their deadlines. We make a table that shows the price change when shifting each on-hold appliance by

k δ

duration, where

k

is a positive integer. The fifth step of Figure 6 depicts this table. The upper limit of

k

depends on the appliance instance with the furthest deadline away. Also, not all the entries in the table are feasible, thus some table cells can be annotated with “not applicable”, as in the figure. This applicability depends on: 1) the job deadline and 2) if the shift solves the peak power violation. Sometimes, the shift might be feasible in terms of job deadline but may not solve the peak power violation. This has been demonstrated in Figure 6, i.e., the incoming job can actually be shifted for

δ

duration but this shift does not reduce the system peak power. At the end, we choose the minimum of the price changes across the values in the table (discarding the “not applicable” ones). This process is also shown in Algorithm 2 in Figure 7.

Figure 6. Combined optimization with respect to electricity prices and peak power limit.

Figure 7. Peak power-aware and cost-aware rescheduling algorithm.

Due to the problem nature, there may not be any feasible shift. In this case, there are possible directions: 1) the schedule runs as it is and the peak power is violated and 2) one of the deadlines of the on-hold appliances is “relaxed”. If the system does not tolerate any user discomfort, we can use the first solution. If the peak power is more important, some appliance deadlines can be sacrificed. In this case, another problem is to find the appliance instance whose deadline requirement can be dropped. To solve this, we follow an approach with minimum number of deadline misses. The current version of the feasibility table consists only of “not applicable” values since we cannot find a valid schedule. Assume that the last column of the table corresponds to

x δ

shift duration. We extend the table by one (i.e.,

(x + 1) δ

) until there is a valid entry. After one or more valid entries, we choose the minimum one and schedule the shift accordingly.

VI. Evaluation

This section presents our methodology for the experimental setup, the results of the scheduling methods, and demonstrates the capabilities of our framework to manage residential energy. We also show that not modeling human behavior may lead to the violation of several human constraints and may result in misleading conclusions about the savings.

A. Methodology

We first demonstrate workload creation, i.e., the jobs. We model a neighborhood with 100 houses with different family types. The family types include single adults, couples without and with 1 or 2 children. The percentage breakdown of the families is taken from our previous work . The appliance power consumption values, shown in Table 6, are from Home Appliance Energy Use data from General Electric . We use power traces from Pecan Street database to 1) evaluate and verify our workload generation model and 2) model appliance usage flexibility based on historical user behavior (create job deadlines for workloads).

TABLE 6. Appliance power consumption values [44].

We use data from CAISO for ToU electricity prices shown in Figure 8. Some appliances (such as electric cars and pool pumps) do not exist commonly in the current neighborhoods and their power consumption rate is higher than usual appliances. Thus, we create multiple cases to analyze results with and without them.

Figure 8. ToU electricity price over a sample day.

B. Validation of Power Profiles

We compare our generated traces against real profiles obtained from Pecan Street Database . Profiles are generated for 5 days to observe the daily changes. We match the time frames of the traces to the time frames of the generated traces. We select 5 consecutive days for each family type, randomly between 01-01-2014 and 06-01-2014 from the database. It is difficult to directly compare the exact values in generated versus real power traces since 1) the data we build with our model do not have direct correspondence with Pecan Street database, 2) ATUS and RECS data span the entire country, whereas Pecan Street has data only from certain states, 3) the appliance power ratings from General Electric and Pecan Street do not match. Although the exact values may not match, our model still accurately finds the peak demand times for both individual houses and a neighborhood with several houses. We scale the appliance ratings based on the peak values observed in generated versus real traces and show that our model is more accurate with the correct appliance ratings. Figure 9 shows the total power of a neighborhood with 50 houses. Comparing the real (straight) and generated (dotted) traces, we see that our model matches the times of peak spikes, but not the exact values due to 1) different appliance power ratings and 2) various small plug loads not included in our model as we either could not associate any user activity with them or did not find any usage data for them in ATUS and RECS data sets. We scale values based on the maximum observed in generated versus real traces and add an offset to account for the various plug loads. We show this new trace with the dashed line in Figure 9. The scaled trace matches the peak times and obtains 38 percent absolute mean error, with min 0.25 percent error, i.e., our model is more accurate once appliance values closely match the original appliances used. We also compute the correlation coefficient between generated and real traces. This coefficient is 0.45 for the neighborhood with original generated traces and 0.62 with scaled generated traces. Our values have strong correlation with real traces for aggregate consumption, by correctly detecting the power spikes.

Figure 9. Total power consumption comparison.

We use this profile to study voltage deviation. Deviation values elevate with increased total consumption thus, it is imperative to correctly estimate both the times and the magnitude of the spikes. We use the grid simulator in to compute the deviation values. We get the physical circuit as a subset from one of EPRI's openly released test circuits . Figure 10 shows the maximum deviations for both real and generated (scaled) traces. The deviation values show significant correlation with the spikes in Figure 9. Our traces match these high deviation events (captures 5/5), which generally occur during the evenings. During these events, we get little or no error in voltage deviation.

Figure 10. Voltage deviation comparison.

C. Electricity Cost Minimization

We apply appliance rescheduling in 100 houses over a month period to obtain the monthly savings and peak power statistics. We create four different cases for analyzing the cost savings, with the availability of EV and pool pump. Table 7 shows the total energy cost of 100 houses for four cases. The first row shows the cost if there is no flexibility, i.e., none of the appliances can be rescheduled. The second row shows the results with the appliance flexibility and the third one shows the savings using appliance rescheduling. The results show that when EVs are present the savings are the highest. This is because EVs create a large demand compared to the other loads. Although pool pumps also have large demand, their duty cyclic behavior decreases the their flexibility and reduces the opportunities to reschedule.

TABLE 7. Main results for electricity cost minimization.

Table 7 shows the savings with the observed flexibility distribution across the houses. To observe upper and lower bounds for the saving percentages, we analyze the edge cases where each house has the same flexibility level. Table 8 demonstrates that if the flexibility intervals are not properly modeled, i.e., small flexibility intervals, then the savings can be lower as much as 3x. We also see that additional flexibility (entropy > 4) does not bring more savings.

TABLE 8. Edge case analysis for the savings percentages.

Although this problem setup minimizes the electricity cost, since the appliances simultaneously search for cheaper electricity price intervals, the peak power increases. Table 9 shows that the peak demand increase due to electricity-price aware rescheduling can be as high as 22 percent, which can have significant negative effects for the electricity providers.

TABLE 9. Peak power statistics when minimizing the cost.

D. Peak Power Minimization

We summarize the results of this analysis using the same main metrics as the previous case. Instead of having a fixed peak power threshold, we report the results for the best (lowest) peak power threshold for which we can guarantee job scheduling without any deadline misses. Table 10 shows the electricity cost savings when minimizing for the peak power. Similar to the previous case, the results show that when EVs are present together the savings are the highest. But we cannot obtain the best savings since rescheduling does not consider the cost. This becomes more obvious in the last two cases (no EV present). The savings become negative, i.e., the framework sacrifices savings completely to reduce the peak power.

TABLE 10. Cost savings when minimizing peak power.

Table 11 shows the peak power demands of the same analysis. We observe that the peak power can be reduced, by up to 25.6 percent. One important observation is that peak power reduction is higher when EVs are not present. This is because the power demand of each job corresponds to a higher percentage when there are not any EVs.

TABLE 11. Peak power statistics minimizing peak power.

E. Combined Optimization

This part shows the results of the combined optimization. Tables 12 and 13 summarize the main results. We observe that the cost savings are somewhere between the values observed in cost-only and peak power-only minimization cases. The same observation holds for the peak power results as well. The values observed in these tables are achieved without any peak power limit violation or job deadline misses. Thus, we can see that as we relax some of these constraints, the numbers will converge to values previously observed. For example, if we allow higher peak power levels, the peak power savings will reduce and the cost savings will increase, and eventually these numbers will converge to the ones observed in Tables 7 and 9.

TABLE 12. Cost savings for combined optimization.

TABLE 13. Peak power statistics for combined optimization.

F. Satisfaction of User Behavior Based Deadlines

In this section, we show the significance of meeting human-behavior based constraints, i.e., the job deadlines corresponding to the user flexibility values. The main comparison points here are the case where each house is assumed to have the same, fixed flexibility for all the reschedulable appliances –. Previous studies use fixed deadlines either because of lack of individual user data or in order to provide a larger-scale simulation . Some other studies determine these deadlines stochastically, but these random processes cannot effectively crate the flexibility distribution present across individual households. Our results indicate that these assumptions can lead to several violations of user behavior-based deadlines, and thus potentially reduce the user participation in automatic residential energy management programs along with the benefits coming with it. Figure 11 quantifies the number of missed deadlines if user behavior constraints are assumed to be fixed across all the houses in a neighborhood. The x -axis demonstrates the changing fixed deadline, ranging from 1 hour to 12 hours, whereas y -axis shows the percentage of missed deadlines for the individual appliances. Each line represents a different appliance. The idea here is that if the fixed deadline is larger than the flexibility of a given house (determined by the entropy value), there will potentially be deadline misses for that house. We observe that appliances cluster mainly into 2 classes. The first set is the oven and microwave, where the percentage of missed deadlines is already high even with 1-hour deadline. This is because these appliances do not have large flexibility across the users. Also, we see that the percentage of missed deadlines can go up to 98 percent (oven with 12 hour fixed deadline). The other set consists of dishwasher, washer, dryer and EV, where the percentages of missed deadlines are under 30 percent if the fixed deadline is less than 12 hours, for which the percentage values increase over 60 percent, up to 83 percent. This is because these appliances present good flexibility up to 12 hours.

Figure 11. Satisfaction of user behavior based deadlines.

G. Sensitivity to Flexibility Prediction Error

In the previous optimization cases, we schedule different appliance instances based on the user deadlines provided by our user flexibility framework. Our optimization algorithms assume that the entire user flexibility interval for each appliance can be used for appliance rescheduling purposes. In other words, we assume that flexibility prediction have no errors. In this section, we re-analyze the performance of our user flexibility framework in the presence of prediction errors. Since we do not have access to the actual flexibility intervals of individuals from Pecan Street Database, we cannot calculate the actual prediction error. Thus, we conduct multiple experiments where we assume that user flexibility calculation contains some error, which varies from 10 to 100 percent averaged across the houses in the neighborhood. Figure 12 demonstrates the average user deadline violations in terms of minutes with different prediction error assumptions. For brevity, we include results from only the first optimization case. The other cases provide similar results. In this figure, the x -axis shows the gradually increasing prediction error assumption, whereas the y -axis illustrates the average user deadline violations in terms of minutes. Similar to the previous figure, each line represents a different appliance. We include only dishwasher, washer, dryer and EV because of their relatively wider flexibility intervals. For each appliance, we report, on average, how long we could violate a user flexibility deadline with our appliance rescheduling if our flexibility prediction has X percent error (where

X = 10, \dots, 100

). We observe that the maximum violation can be as high as 2 hours (with 100 percent error), for relatively less critical appliances such as washer, dishwasher. For a more critical appliance, such as EV, the error is limited to 65 min. With a more optimistic assumption (around 10-20 percent error), the maximum violation is only 40 minutes.

Figure 12. Sensitivity to error shown in terms of deadline violation (minutes).

VII. Conclusion

Residential energy accounts for a significant portion of the overall energy in the power grid. Researchers have proposed efficient energy management methods for this domain, but these methods do not accurately represent the human behavior that intrinsically affects the residential energy consumption. In this paper, we first present a framework to create residential power profiles based on household properties, e.g., number of people, gender of people, etc. Then, we formally define user flexibility for different appliances using information theory. This flexibility definition is based on historical appliance usage and thus accurately represents how willing a user would be when changing the starting time of an appliance. We finally present scheduling frameworks to demonstrate the applicability of our human behavior-based model. We separately analyze well-known scheduling goals such as minimizing the electricity cost, minimizing the peak power, etc. Our results indicate that our model is effectively handling the appliance rescheduling (or energy allocation problem), achieving 16 percent energy savings and 22 percent reduction in peak power relative to the case without appliance rescheduling. Also, we compare our model with other studies, which assume fixed deadlines for every user when scheduling energy consumption. Without modeling user behavior constraints, the percentage of missed appliance deadlines can be as high as 83 percent (for more flexible appliances like washer) or 98 percent (for less flexible appliances like oven). Failing to represent user preferences when scheduling residential energy might have severe consequences, such as decreased user participation in energy savings programs or inaccurate estimation of energy flexibility in a neighborhood for demand response programs.

Acknowledgments

This paper is submitted to the Special Issue in Cyber-Physical Social Systems: Integrating Human into Computing. This work was supported in part by TerraSwarm, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA; and ARPA-E Network Optimized Distributed Energy Systems (NODES) DE-FOA-0001289.

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BARIS AKSANLI received the two BS degrees in computer engineering and mathematics from Bogazici University, Turkey, the MS and PhD degrees in computer science from UCSD. He is currently an assistant professor in the Electrical and Computer Engineering Department, San Diego State University. Previously, he was a postdoctoral researcher in the Computer Science and Engineering Department, University of California, San Diego (UCSD). His research interests include energy efficient cyber physical systems, human behavior modeling for the Internet of Things, big data for energy efficient large-scale systems. He won the Internet2 IDEA Award with his work in Lawrence Berkeley National Laboratory and Spontaneous Recognition Award from Intel. He is a member of the IEEE. TAJANA SIMUNIC ROSING is a professor, a holder of the Fratamico Endowed chair, and a director of System Energy Efficiency Lab at UCSD. She is currently heading the effort in SmartCities as a part of DARPA and industry funded TerraSwarm center. During 2009-2012 she led the energy efficient datacenters theme as a part of the MuSyC center. Her research interests are energy efficient computing, embedded and distributed systems. Prior to this she was a full time researcher at HP Labs while being leading research part-time at Stanford University. She finished her PhD in 2001 at Stanford University, concurrently with finishing her Masters in Engineering Management. Her PhD topic was Dynamic Management of Power Consumption. Prior to pursuing the PhD, she worked as a Senior Design Engineer at Altera Corporation. She is a member of the IEEE.