Conference Paper

NREL/CP-550-47685

August 2010

Tool for Generating Realistic 

Residential Hot Water Event 

Schedules

Preprint

Bob Hendron and Jay Burch

National Renewable Energy Laboratory

Greg Barker

Mountain Energy Partnership

Presented at SimBuild 2010

New York, New York

August 15–19, 2010
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TOOL FOR GENERATING REALISTIC RESIDENTIAL HOT WATER 

EVENT SCHEDULES

Robert Hendron1

, Jay Burch1, and Greg Barker2

1

National Renewable Energy Laboratory, Golden, CO 2

Mountain Energy Partnership, Boulder, CO

 

 

The installed energy savings for advanced residential 

hot water systems can depend greatly on detailed 

occupant use patterns. Quantifying these patterns is

essential for analyzing measures such as tankless water 

heaters, solar hot water systems with demand-side heat 

exchangers, distribution system improvements, and 

recirculation loops. This paper describes the 

development of an advanced spreadsheet tool that can

generate a series of year-long hot water event 

schedules consistent with realistic probability 

distributions of start time, duration and flow rate 

variability, clustering, fixture assignment, vacation 

periods, and seasonality. This paper also presents the 

application of the hot water event schedules in the 

context of an integral-collector-storage solar water 

heating system in a moderate climate. 

ABSTRACT

Energy savings for certain residential building 

technologies depends greatly on occupant behavior.

Simulating realistic occupant behavior is a major 

challenge, because of wide variations in how 

households use hot water, lighting, appliances, and 

miscellaneous electric loads. Even an individual 

household has highly variable behavior from day to 

day, introducing a random component to the problem.

Domestic hot water (DHW) use is a particularly 

important issue, because occupant use patterns can 

significantly affect the energy savings achieved by 

advanced hot water systems that are common in highperformance homes. 

INTRODUCTION

For example, gas tankless water heaters do not fire at 

low flow rates (usually less than 0.5 gpm), and when 

used with solar preheat, may not fire even at higher 

flow rates when the entering water is above 80°–90°F

(Hendron et al. 2009). Tankless water heater efficiency 

is also influenced by thermal mass effects in the 

burner, which in turn are strongly affected by the time 

between hot water events. 

Hot water distribution system measures such as pipe 

insulation, home run plumbing, and demand-controlled 

recirculation loops are affected by the time between 

draws and which fixtures produce the draw for each 

event (Klein 2004). High- and low-use households can 

have very different energy savings potentials. These 

effects were quantified in a study by the National 

Renewable Energy Laboratory (NREL) and Davis 

Energy Group (Hendron et al. 2009).

Other more advanced systems are also heavily 

influenced by hot water use patterns. The energy saved 

by a solar hot water system with a demand-side heat 

exchanger is affected by the flow rate in the heat 

exchanger and the overall volume of hot water use

(Davidson et al. 2002). Wastewater heat recovery 

depends on the flow rate and duration of each event.

Hot water tank and solar integrated collector storage 

(ICS) sizing considerations may include an analysis of 

the realistic peak hourly demand for hot water that 

randomly occurs over a year because of event 

clustering. The cost effectiveness of an ICS system is 

also strongly affected if a household uses a high or low 

volume of hot water each day. 

Several hot water studies have developed hot water 

event schedules for use in energy simulations or hot 

water system testing, including average hourly use 

profiles, typical flow rates and durations, and day-today variability (DOE 1998, Burch et al. 1993, 

Christensen et al. 2000). However, many of these 

studies neglect realistic event clustering, seasonality, 

fixture use, and variable flow rates, all of which can 

signficantly affect the annual energy savings for 

advanced hot water systems. Even when those details 

were included, they were often addressed in a fairly 

simplistic manner. One recent approach used the 

German tool DHWCalc (Jordan and Vajen 2001) to 

generate annual hot water event schedules, but event 

durations were fixed and event clustering could only be 

approximated (Hendron and Burch 2007). 

This paper describes the development of a spreadsheet 

tool that generates random event profiles based on 

realistic probability distributions for hot water event 

duration, flow rate, clustering, individual fixture use, 

and time between events. It also includes realistic 

simulation of vacation periods, weekend/weekday 

1
effects, geographic location, and seasonality. The 

assumptions about the profiles were derived from a 

variety of sources, primarily two residential water use 

studies conducted by Aquacraft (Aquacraft 2008, 

Mayer and DeOreo 1999). One of these studies 

included 1200 houses, but measured total water use

only. The other study was a smaller 20-house study

that disaggregated hot and cold water events.

Cluster Start Times

TECHNICAL APPROACH

The start time for each cluster of events in each of the 

five major end-use categories (sink, shower, bath, 

clothes washer, dishwasher) is determined by using a 

“dartboard” approach, where the number of darts 

represents a predetermined set of clusters (which will 

be explained in the Event Clustering section of this 

paper). The dartboard has 8,760 sections representing 

the hours of the year. Sections of the dartboard may be 

larger or smaller, depending on the probability that a 

cluster of events will begin during that hour. Each hour 

is assigned a probability based on the average hourly

profiles defined in the Building America (BA) 

Research Benchmark (Hendron and Engebrecht 2010), 

resulting in a cumulative probability of 1.0 over the 

course of a year. An example probability distribution

for shower use on a typical day is shown in Figure 1. 

Figure 1 Probability distribution for shower use 

Adjustments to the probabilities are made to reflect

differences between weekdays and weekends, and 

seasonal differences for each month. These 

adjustments were derived from the 1200-house

Aquacraft study (Mayer and DeOreo 1999). Three 

vacation periods (totaling 14 days) with no hot water 

use were also added, and the probabilities for the 

remaining days were increased accordingly. Typical 

vacation periods were estimated based on a published 

travel study (TIA 2008) combined with engineering 

judgment. These probability adjustments are 

summarized in Table 1. The monthly adjustments were 

eventually abandoned because the data indicated that

the differences were much smaller than the statistical 

errors for all five end uses (see Figure 2 for an 

example). 

Table 1 Adjustments to hourly probability distribution

Probability 

Multipliers: Sink Shwr Bath CW DW

Weekend 1.15 1.05 1.05 1.26 1.04

Weekday 0.94 0.98 0.98 0.90 0.98

Vacation (May 26-28, 

Aug 12-18, Dec 22-25) 0 0 0 0 0 

Not Vacation 1.04 1.04 1.04 1.04 1.04

January 0.97 0.99 0.75 1.01 1.05

February 0.95 1.03 1.15 0.94 0.97

March 1.03 1.02 1.27 1.01 1.03

April 1.00 1.00 1.33 0.98 1.00

May 0.98 1.01 0.95 0.94 0.95

June 1.06 1.02 1.12 1.05 0.96

July 1.03 1.00 1.12 0.94 0.97

August 1.04 0.96 1.04 1.03 0.99

September 1.03 1.02 1.02 0.99 0.90

October 0.94 0.99 0.66 1.01 1.10

November 0.99 0.98 1.02 1.03 1.09

December 0.98 0.99 0.92 1.03 1.07

 

Figure 2 Seasonality of clothes washer use

The uniform random number generator in Microsoft 

Excel is used to assign the specific hour during which 

each cluster begins. Another random number is used to 

assign the minute and second for the start time, using a 

simple uniform probability distribution. 

Event Clustering

Hot water events in actual households tend to occur in 

clusters for four end-use categories: sinks, showers, 

dishwashers, and clothes washers. Bath events tend to 

be isolated. Clothes washers have two levels of 

clustering. A load usually has several hot water draws 

associated with the various cycles (primarily wash and 

rinse), depending on occupant choices. In addition, 

several loads often occur over the course of a few 

hours. Dishwashers are similar in terms of multiple hot 

water draws per cycle, but loads are rarely clustered.

0.00

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0.14

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Probability

Hour of Day

0

0.5

1

1.5

2

2.5

3

3.5

4

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Seasonality of Normalized CW Use

Hot and Cold Combined

Normalized Daily CW Volume

Sample Size (1000s)

2
Clustering across end uses was not factored into the 

approach described in this study.

A simple hierarchical clustering analysis (Norusis

2006) was performed on the data from the 20-house 

Aquacraft study to quantify the following 

characteristics for each end-use category:

• Likelihood of a specific number of events in 

each cluster (between 1 and 10)

• Average time between events within a cluster 

(two levels for clothes washers)

• Upper limit for time between consecutive 

events classified within the same cluster

The results of the cluster analysis of hot water events

are shown in Table 2. 

Table 2 Results of hierarchical cluster analysis

Characteristics Sink Shwr Bath CW DW

Average Daily Volume 

(gal/day, hot and cold) 25 28 7 15 5 

Average Daily Events 

(events/day) 32.9 1.7 0.3 2.2 2.4

Annual Events 

(events/year) 12007 611 109 788 858

Maximum Time Between 

Events in Cluster (min) 15 60 60 60

Average Time Between 

Events in Cluster (min) 1.93 30.5 9.78

Average Events per Cluster 1.90 1.24 1.00 1.96 4.89

Number of Clusters per 

Year 6319 493 109 402 176

Maximum Time Between 

Events in Load (min) 30

Maximum Time Between 

Loads in Cluster (min) 240

Number of Loads per 

Cluster 1.40

Average Number of Events 

per Load 1.40

Average Time Between 

Events in Load (min) 4.97

Average Time Between 

Loads in Cluster (min) 74.27 

Derived from AWWA 1200 house total water study 

Derived from AWWA 20 house hot water study 

Derived from Benchmark

Engineering Judgment

The average number of events per year for each enduse category is determined by dividing the annual hot 

water volume from the BA Research Benchmark 

(about 60 gallons/day, depending on geographic 

location and number of occupants) by the average 

event volume from the Aquacraft studies (see section 

on Event Characteristics). The number of clusters per 

year is calculated by dividing the number of events per 

year by the average number of events per cluster. As 

clusters are assigned start times, a random number is 

used to determine the number of events associated with 

that cluster. As a result, the annual number of clusters 

is locked in, while the annual number of events can 

vary slightly depending on random effects. Time 

between events within a cluster is held constant.

Event Characteristics

Once the hot water events are assigned a start time, the 

specific flow rate and duration are calculated. Again, 

the Aquacraft data were used to characterize the range 

of flow rates and durations that occur in typical houses.

Flow rate and duration are treated as independent 

variables, because the Aquacraft data suggested a very 

weak negative correlation between them. For sinks and 

clothes washers, the smaller 20-house Aquacraft study 

of hot water events was used to remove the effect of 

cold water sink draws and cold rinse cycles. Variability 

was calculated as a percentage of the average duration 

or flow rate in each household, resulting in normalized 

values for standard deviation. As a result, the 

variability within households, rather than variability 

across households, determined the probability 

distributions used in our approach. The resulting event 

characteristics are summarized in Table 3.

The probability distributions for flow rate were 

approximately normal for all end uses, but were more 

diverse for duration. Sink duration was approximated 

by an exponential decay. Probability distributions for 

shower and dishwasher event duration were 

approximately log-normal; the draw duration for bath 

events was normal. Because clothes washer event 

durations were erratic, a discrete probability 

distribution was used. The probability distribution 

selected for showers is compared to the actual 

distribution from the Aquacraft study in Figure 3. 

Table 3 Flow rate and duration characteristics

Characteristics Sink Shwr Bath CW DW 

Average Duration 

(min) 0.62 7.81 5.65 3.05 1.53

Standard Deviation

for Duration (min) 0.67 3.52 2.09 1.62 0.41

Probability 

Distribution for 

Duration 

ExponentialLogNormal Normal DiscreteLogNormal

Average Flow Rate 

(gpm)* 1.14 2.25 4.40 2.20 1.39

Standard Deviation 

for Flow Rate 

(gpm)* 0.61 0.68 1.17 0.62 0.20

Probability 

Distribution for 

Flow Rate Normal Normal Normal Normal Normal

Average Event 

Volume (gal)* 0.76 16.73 23.45 6.95 2.13

* Hot and cold water combined for sinks, showers, baths 

Derived from AWWA 1200-house total water study 

Derived from AWWA 20-house hot water study 

3
Figure 3 Curve fit of a perfect lognormal distribution 

to measured data for shower duration

The Excel random number generator is used to 

determine the specific flow rate and duration of each 

event. Equations 1-3 describe the calculation of event 

characteristics for normal, log-normal, and exponential 

probability distributions, based on a random number 

uniformly distributed between 0 and 1. The calculation 

for the discrete probability distribution used for clothes 

washer is not representable in equation form, but is 

straightforward to apply. For normal distributions, 

negative flow rates are possible, in which case the flow 

rate is changed to an inconsequential 0.05 gpm.

ln( ) ln 21)( 1 sin(ln 2 )2 2

22

2

XxX

lognorm eY

π μ

σ

μσ

μ  −×



 



 + +

+ = (1)

Where: Y = random variable with a log-normal distribution

X1 and X2 are two uniform random numbers 

between 0 and 1

μ = mean of lognormal distribution 

σ = standard deviation of lognormal distribution

sin( )ln(2)2 Ynorm += πσμ X1 − X2 (2)

Where: Y = random variable with a normal distribution

μ = mean of normal distribution

σ = standard deviation of normal distribution

Y X )ln( exp = μ (3)

Where: Y = random variable with an exponential 

distribution 

X = a uniform random number between 0 and 1

μ = mean of exponential distribution 

Fixture Assignment

We assumed that a typical house has four sinks, two 

showers, two bathtubs, a single dishwasher, and a 

single clothes washer. The user of the tool can easily 

modify these assumptions through postprocessing. A 

simple probability was assigned to the fixtures in each 

end-use category, as shown in Table 4. Because the 

authors could not identify reliable references for these 

probabilities, we used the results from a study of seven 

houses by Kempton (1986), four houses monitored by 

NREL, and engineering judgment. Each event is

randomly assigned to a specific fixture based on these 

probabilities. As a result, event clusters often cut 

across multiple fixtures.

Table 4 Probabilities that an event occurs at a specific 

fixture

Probability 

Distributions: Sink Shwr Bath CW DW

Kitchen Sink, Master 

Bath Shower/Tub, 

Primary DW or CW 0.70 0.75 0.75 1.00 1.00

Master Bath Sink, 

2nd Bathroom 

Shower/Tub 0.10 0.25 0.25 

3rd Bathroom Sink 0.10 

4th Bathroom Sink 0.10

Statistical Checks

The use of random numbers in our methodology 

creates the potential for results that significantly 

deviate from expected values. To ensure the final event 

schedules are reasonably consistent with the 

probability distributions that were used to generate 

them, we added a series of statistical checks. The most 

important checks are summarized in Table 5. If any of 

the statistical metrics fall outside the specified limits, 

the event schedules are regenerated using a new set of 

random numbers. This process is repeated until all 

statistical criteria are met.

 

Table 5 Key statistical checks to ensure consistency 

between output and input parameters

Statistical Metric Criterion*

Average Flow Rate and Duration (sinks) <3% 

Average Flow Rate and Duration (showers, DW, CW) <5% 

Average Flow Rate and Duration (baths) <10% 

Standard Deviation of Flow Rate and Duration (sinks) <10%

Standard Deviation of Flow Rate and Duration 

(showers, DW, CW) <15%

Standard Deviation of Flow Rate and Duration (baths) <25%

Weekend/Weekday Ratio of Daily Volume (sinks, 

showers, DW, CW) <30%

Weekend/Weekday Ratio of Daily Volume (baths) <50% 

Average Daily Volume (individual end uses) <5% 

Average Daily Volume (total) <3% 

Hourly Profile (4-hour increments) <10%

* Difference between output value and input value

0

500

1000

1500

2000

2500

3000

0.10.20.30.40.50.60.70.8

0.9

1

1.11.21.31.41.51.61.71.81.9

2

2.12.22.32.4

2.5

Frequency

Normalized Duration

Shower Normalized Duration Histogram

Aquacraft Histogram

Perfect Lognormal

4
Postprocessing

Once the event schedules for each end use comply with

the statistical checks, the five separate schedules are 

combined into a single annual hot water schedule with 

four values: start time, duration, flow rate, and fixture.

Adjustments are made to the start time and duration of 

each event based on the desired time step. Flow rate is 

also adjusted to keep the event volume fixed. The user 

is cautioned that flow rates can become very unrealistic 

when the time step exceeds 1 minute, and the resulting 

events will not provide accurate results if the system 

being analyzed is sensitive to flow rate, as would be 

the case with a tankless water heater or wastewater 

heat recovery system. Additional adjustments are made 

to the flow rates to reflect differences in mains water 

temperature in different climates. The BA Benchmark 

mains water temperature approximation was used for 

this purpose (Burch and Christensen 2007). 

A simple user interface was added to the spreadsheet 

tool to enable researchers to generate hot water events 

tailored to their own needs. The user interface allows 

the user to select the geographic location, number of 

bedrooms (surrogate for daily hot water use), and 

desired time step for the model that will be used to 

analyze the hot water system. Users can also choose 

whether the events are specified as hot water only or 

the total of hot and cold water for mixed events such as 

sinks and showers. 

A partial hot water event schedule for a four-bedroom 

house in St. Louis, Missouri, is provided graphically in 

Figure 4, and in numerical format in Table 6. The timestep is 6 seconds, and the flow rates are expressed as 

the total of hot and cold water for mixed end uses. 

Note the cluster of three sink events beginning at 6:11 

AM, and the cluster of clothes washer events within a 

single load beginning at 10:48 AM.

RESULTS

Figure 4 Example series of hot water events

Table 6 Example hot water event schedule for a fourbedroom house in St. Louis

Start Time

Duration 

(sec) 

Flow Rate 

(Hot & 

Cold) (gpm) Start Time

7/2 12:59:18 AM 6 1.698 Sink 2

7/2 3:22:36 AM 36 1.238 Kitchen Sink

7/2 6:11:36 AM 48 0.645 Kitchen Sink

7/2 6:13:36 AM 6 0.022 Sink 2

7/2 6:15:30 AM 24 0.92 Sink 2

7/2 6:19:42 AM 54 1.296 Sink 3

7/2 8:38:30 AM 732 2.462 Shower 2

7/2 9:01:30 AM 6 0.199 Kitchen Sink

7/2 9:50:48 AM 18 0.528 Kitchen Sink

7/2 9:52:42 AM 90 0.049 Kitchen Sink

7/2 10:20:00 AM 30 1.852 Sink 3

7/2 10:21:54 AM 12 0.871 Kitchen Sink

7/2 10:23:48 AM 12 0.673 Kitchen Sink

7/2 10:25:48 AM 96 0.105 Kitchen Sink

7/2 10:26:42 AM 6 0.107 Kitchen Sink

7/2 10:27:42 AM 42 1.794 Kitchen Sink

7/2 10:48:12 AM 210 2.304 CW

7/2 10:53:12 AM 174 2.188 CW

7/2 10:58:12 AM 48 2.619 CW

7/2 11:03:12 AM 180 2.392 CW

For sinks, the average distribution of events throughout 

the day is very consistent with the underlying 

probability distribution, as shown in Figure 5. For end

uses that have fewer total events, such as baths, 

random effects cause the actual distribution of events 

to deviate from the probability distribution, as shown 

in Figure 6. 

 

Figure 5 Comparison of outputs to inputs for sink 

events

0

0.5

1

1.5

2

2.5

3

12 AM 1 AM 2 AM 3 AM 4 AM 5 AM 6 AM 7 AM 8 AM 9 AM 10 AM 11 AM 12 PM

Flow Rate (gal/min)

Sink

Shower

Bath

CW

DW

0.00

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0

50

100

150

200

250

300

350

400

450

500

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Annual Event Frequency

Fraction of Daily Usage

Hour of Day

Sink Time of Day Check

Event Frequency

Benchmark Profile

5
Figure 6 Comparison of outputs to inputs for bath 

events

One application of the hot water event generator was to 

examine the energy savings for an integral-collectorstorage (ICS) solar water heating system in

Sacramento, California, as a function of occupant hot 

water use profile. A schematic of the system is shown 

in Figure 7, and the key specifications are listed in 

Table 7. The primary goal was to determine the 

difference between the energy savings on average for a 

cross-section of representative occupant behaviors 

compared to a single “average” household, which

could affect optimal design choices for solar hot water 

systems when applied on a community scale. 

EXAMPLE APPLICATION

The hot water event generator was used to develop a 

representative set of 12 hot water use patterns (3 levels 

of hot water use and 4 hourly profiles). Each use 

pattern represented a “bin” of households based on the 

Aquacraft 1200-house study. The definition of each bin 

and its summary characteristics are shown in Table 8.

Example hourly profiles for medium use households 

are shown in Figure 8. These bin characteristics 

defined the constraints and probability distributions 

imposed on the hot water event generation tool.

Figure 7 Schematic of solar ICS system analyzed using 

alternative DHW event schedules

Table 7 Specifications of solar hot water system used 

for analyzing alternative DHW event schedules

Collectors

Working Fluid Water

Total Area 32 ft2

Volume 49 gal 

Slope 18 degrees 

Azimuth -18 degrees

Optical Gain Coefficient [FR(τα)] 0.5279 

Thermal Loss Coefficient (FRUL) 0.6818 Btu/h·ft2·°F 

Environment Temperature 68°F

Pipe Length, indoor, supply/return 10 ft

Pipe Length, outdoor, supply/return 20 ft

Auxiliary Storage Tank

Volume 40 gal 

Height 4.5 ft

R-value 10 h·ft2·°F/Btu 

Environment Temperature 68°F

Heating Element Capacity 15,353 Btu/h

Setpoint 120°F

Table 8 Hot water use pattern “bin” definitions 

Bin Categories 

Bin 

# 

Volume 

(All EndUses) Shower 

Occupants at 

Home During 

the Day

Daily 

Use 

(gal)

% in 

Bin 

1 Low Morning At Home 27 10%

2 Low Morning Not at Home 28 6%

3 Low Evening At Home 26 7%

4 Low Evening Not at Home 28 3%

5 Medium Morning At Home 61 25%

6 Medium Morning Not at Home 63 10%

7 Medium Evening At Home 60 12%

8 Medium Evening Not at Home 63 3%

9 High Morning At Home 112 14%

10 High Morning Not at Home 117 4%

11 High Evening At Home 115 6%

12 High Evening Not at Home 119 2%

Avg - - - 66 100%

Figure 8 Hourly profiles for medium use households

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2

4

6

8

10

12

14

16

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Fraction of Daily Usage

Annual Event Frequency

Hour of Day

Bath Time of Day Check

Event Frequency

Benchmark Profile

Mains Water

To DHW Load

Integral Collector/Storage

Auxilliary Tank

= Tempering Valve

0

0.02

0.04

0.06

0.08

0.1

0.12

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Fraction of Daily Use

Hour of Day

Bin 5

Bin 6

Bin 7

Bin 8

6
The resulting event schedules were used as inputs to a 

TRNSYS model of the ICS system with a simulation 

time step of 6 minutes. In this case, relatively large 

time steps were acceptable because ICS systems are 

insensitive to flow rate and time between events. 

Random daily variations in hot water volume and timeof-use are more important drivers of ICS performance. 

The model predicted the annual energy savings 

associated with each of the 12 use patterns, along with 

the “average” use pattern. The combined “bin average” 

energy savings was calculated based on the average of 

all bins, weighted using the percentage of the 

population each bin represents. The model was also 

used to analyze whether using a simple repeated daily 

use pattern provides as much accuracy as the more 

complex annual use pattern, and whether including 

vacation periods in the simulation makes a significant 

difference. The results for all cases are shown in Figure 

9. The energy savings were normalized within each 

series (1-4, 5-8, 9-12) based on the daily volume of the 

first bin in the series (1, 5, or 9), in order to illustrate 

the effects of different hourly profiles. 

Figure 9 Energy savings for an ICS system using alternative DHW use patterns

The analysis of very high (120 gal/day) and very low 

(20 gal/day) households compared to a nominal 60 

gal/day household demonstrates the nonlinearity of 

energy savings for an ICS systems. An increase in hot 

water use of 60 gal/day adds about 1.4 MBtu of 

additional energy savings; a smaller 40 gal/day 

decrease results in a much larger 2.7 MBtu loss in 

energy savings. The relationship between hot water use

and energy savings is shown in Figure 10. 

Figure 10 Non-linearity of energy savings relative to 

daily volume

The bin assignments, including the alternate profiles 

within each volume grouping, had a significant effect 

on annual energy savings. This suggests that for ICS 

systems in moderate climates, analyzing a variety of 

hourly profiles provides valuable information about the 

range of energy savings that different households 

might achieve, depending on their hot water use 

patterns. Based on the simulations, the weighted 

average energy savings of all 12 bins is estimated to be 

about 6% less than that for a single average household. 

This improvement in accuracy is significant, but may 

not be worth the additional effort when other sources 

of modeling error are considered.

A small decrease in energy savings can be observed 

when 14 vacation days with no hot water use are 

included in the analysis, while holding the total annual 

hot water use constant. This can be explained by the 

fact that when hot water is not being used, the collector 

gets very hot, and energy losses increase accordingly. 

Also, the assumption of no day-to-day variation results 

in an overstatement of energy savings because highand low-use days do not average out over the long run. 

Our analysis indicates that the inclusion of day-to-day 

Bin 1, no daily variation, no 

vacation

Bin 1, no daily variation, 2 

weeks vacation

Bin 1Bin 2Bin 3Bin 4

Bin 5, no daily variation, no 

vacation

Bin 5, no daily variation, 2 

weeks vacation

Bin 5Bin 6Bin 7Bin 8

Bin 9, no daily variation, no 

vacation

Bin 9, no daily variation, 2 

weeks vacation

Bin 9

Bin 10

Bin 11

Bin 12

20 gpd60 gpd

120 gpd

Average Profile

Weighted average of 12 bins

0

1

2

3

4

5

6

7

8

(Million Btu/year)

0

1

2

3

4

5

6

7

0

20406080

100120140

Savings (MBtu/year)

Average Daily Volume (gal)

7
variations in hot water use, including vacation days, 

provides much more realistic estimates of annual 

energy savings. Impacts on other hot water systems 

and other climates will be examined in future studies.

The tool described in this paper enables analysts to 

more accurately predict energy savings for a variety of 

hot water measures that are sensitive to specific draw 

patterns. This improvement in accuracy was quantified 

for a simulation of an ICS hot water system in 

Sacramento, California, and shown to be significant. 

Using a large database of actual use patterns, combined 

with advanced statistical methods, the authors were 

able to generate more realistic draw profiles than were

developed in past studies. The tool includes a userfriendly interface to enable analysts to generate a 

variety of use profiles tailored to specific applications. 

The tool is posted on the Building America website 

(www1.eere.energy.gov/buildings/building_america/pe

rf_analysis.html). 

CONCLUSION

The authors express their appreciation to Terry Logee, 

Ed Pollock, and George James of the U.S. Department 

of Energy Building America Program for their

leadership and financial support of this project. We 

would also like to thank Ren Anderson, Christina 

Haley, and Mark Eastment of NREL, Ed Hancock of 

Mountain Energy Partnership, and Peter DeOreo of 

Aquacraft for their ideas and assistance with the 

development of this methodology.

ACKNOWLEDGMENTS

CW Clothes washer

NOMENCLATURE

DW Dishwasher

X, X1, X2 Uniform random numbers between 0 and 1

Y Random variable 

μ Mean of statistical distribution 

σ Standard deviation of statistical distribution 

Aquacraft. 2008. “Hot & Cold Water Data from EPA 

Retrofit Studies – EBMUD & Seattle.” Boulder, 

CO: Aquacraft, Inc. 

REFERENCES

Burch, J., Christensen, C. 2007. “Towards 

Development of an Algorithm for Mains Water 

Temperature.” Proceedings of the 2007 ASES 

Annual Conference, Cleveland, OH.

Burch, J., Wood, B., Huggins, J., Thornton, J. 1993. 

“Simulation-based Ratings for Solar Hot Water 

Systems,” ASES Conference Proceedings 1993, 

American Solar Energy Society, Boulder, CO.

Christensen, C., Barker, G., Thornton, J. 2000. 

Parametric Study of Thermal Performance of 

Integral Collector Storage Solar Water Heaters. 

NREL Report CP-550-28043. Golden, CO: NREL. 

J.H. Davidson, S.C. Mantell, F.A. Kulacki, W. Liu, and 

Wu, C. 2002. “Mechanical and Thermal 

Performance of Polymer Heat Exchangers for 

Solar Hot Water,” Heat Transfer 2002, 

Proceedings of the 12th International Heat 

Transfer Conference, pp. 357-362.

Hendron, R., Burch, J. 2007. “Development of 

Standardized Domestic Hot Water Event 

Schedules for Residential Buildings.” Paper No. 

ES2007-36104. Proceedings of the 2007 ASME 

Energy Sustainability Conference (ES2007), 27-30 

June 2007, Long Beach, California. New York, 

NY: American Society of Mechanical Engineers. 

Hendron, R., Burch, J., Hoeschele, M., Rainer, L.

2009. “Potential for Energy Savings Through 

Residential Hot Water Distribution System 

Improvements.” Paper No. ES2009-90307.

Proceedings of the 3rd International Conference on 

Energy Sustainability, July 19-23, 2009, San 

Francisco, CA. New York, NY: ASME.

Hendron, R., Engebrecht, C. 2010. Building America 

Research Benchmark Definition: Updated 

December 2009. NREL Report No. TP-550-

47246. Golden, CO: NREL.

Hendron, R., Fang, X., Burch, J., Hancock, E., Barker, 

G. 2009. Building America Field Test & Analysis 

Report: Coastal Habitats, Hilton Head, SC (Draft – 

July 31, 2009). Golden, CO: NREL.

Jordan, U., Vajen, K. 2001. “Realistic Domestic HotWater Profiles in Different Time Scales.” 

Marburg, Germany: Universität Marburg.

Kempton, W. 1986. Residential Hot Water: A 

Behaviorally-Driven System. Energy Vol. 13, No. 

1, pp. 107-114. Great Britain. 

Klein, G. 2004. “Hot Water Distribution Systems: Part 

2,” Plumbing Systems and Design, May/June 2004

Mayer, P., DeOreo, W. 1999. “Residential End Uses of 

Water,” Prepared for the American Water Works 

Association, Boulder, CO: Aquacraft, Inc.

Norusis, M. 2006. SPSS 15.0 Statistical Procedures 

Companion. Chicago, IL: SPSS. 

Travel Industry Association (TIA). 2007. Data from 

TravelscopeDIRECTIONS Survey. 

http://www.tia.org/researchpubs/marketing_progra

ms_US_travel_overview.html. 

U.S. Department of Energy (DOE). 1998. “Code of 

Federal Regulations Title 10, Energy, Part 430 

Subpart B, App. E -- Uniform Test Method for 

Measuring the Energy Consumption of Water 

Heaters,” Washington, DC.

8
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Tool for Generating Realistic Residential Hot Water Event 

Schedules: Preprint

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B. Hendron, J. Burch, and G. Barker

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14. ABSTRACT (Maximum 200 Words)

The installed energy savings for advanced residential hot water systems can depend greatly on detailed occupant 

use patterns. Quantifying these patterns is essential for analyzing measures such as tankless water heaters, solar 

hot water systems with demand-side heat exchangers, distribution system improvements, and recirculation loops. 

This paper describes the development of an advanced spreadsheet tool that can generate a series of year-long hot 

water event schedules consistent with realistic probability distributions of start time, duration and flow rate variability, 

clustering, fixture assignment, vacation periods, and seasonality. This paper also presents the application of the hot 

water event schedules in the context of an integral-collector-storage solar water heating system in a moderate 

climate. 

15. SUBJECT TERMS

residential hot water; occupant use; recirculation loop; demand-side heat exchanger

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