Development of an Accurate Feed-Forward Temperature

Development of an Accurate Feed-Forward Temperature
2008
Development of an
Accurate FeedForward Temperature
Control Tankless
Water Heater
Cooperative Agreement Number:
DE-FC26-05NT42327
Final report to the National Energy Technology Laboratory of the United States
Department of Energy.
DE-FC26-05NT42327 Final Report:
David P. Yuill
Solutions, Inc.
Development of an Accurate Feed-Forward Temperature Control Tankless Building
Water Heater
11/17/2008
i
Acknowledgement: This material is based upon work supported by the Department of Energy under
Award Number DE-FC26-05NT42327.
Disclaimer:
This report was prepared as an account of work sponsored by an agency of the United States
Government. Neither the United States Government nor any agency thereof, nor any of their
employees, nor any of their contractors, subcontractors, nor their employees, make any warranty,
express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or
usefulness of any information, apparatus, product, or process disclosed, or represents that its use would
not infringe privately owned rights. Reference herein to any specific commercial product, process, or
service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply
its endorsement, recommendation, or favoring by the United States Government or any agency,
contractor, or subcontractor thereof. The views and opinions of authors expressed herein do not
necessarily state or reflect those of the United States Government or any agency thereof.
DE-FC26-05NT42327 Final Report: Development of an Accurate Feed-Forward Temperature Control Tankless Water Heater
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Executive Summary
The following document is the final report for DE-FC26-05NT42327: Development of an Accurate FeedForward Temperature Control Tankless Water Heater. This work was carried out under a cooperative
agreement from the Department of Energy’s National Energy Technology Laboratory, with additional
funding from Keltech, Inc.
The objective of the project was to improve the temperature control performance of an electric tankless
water heater (TWH). The reason for doing this is to minimize or eliminate one of the barriers to wider
adoption of the TWH. TWH use less energy than typical (storage) water heaters because of the
elimination of standby losses, so wider adoption will lead to reduced energy consumption.
The project was carried out by Building Solutions, Inc. (BSI), a small business based in Omaha, Nebraska.
BSI partnered with Keltech, Inc., a manufacturer of electric tankless water heaters based in Delton,
Michigan. Additional work was carried out by the University of Nebraska and Mike Coward.
A background study revealed several advantages and disadvantages to TWH. Besides using less energy
than storage heaters, TWH provide an endless supply of hot water, have a longer life, use less floor
space, can be used at point-of-use, and are suitable as boosters to enable alternative water heating
technologies, such as solar or heat-pump water heaters. Their disadvantages are their higher cost, large
instantaneous power requirement, and poor temperature control.
A test method was developed to quantify performance under a representative range of disturbances to
flow rate and inlet temperature. A device capable of conducting this test was designed and built. Some
heaters currently on the market were tested, and were found to perform quite poorly.
A new controller was designed using model predictive control (MPC). This control method required an
accurate dynamic model to be created and required significant tuning to the controller before good
control was achieved. The MPC design was then implemented on a prototype heater that was being
developed simultaneously with the controller development. (The prototype’s geometry and
components are based on a currently marketed heater, but several improvements have been made.)
The MPC’s temperature control performance was a vast improvement over the existing controller.
With a benchmark for superior control performance established, five additional control methods were
tested. One problem with MPC control is that it was found to be extremely difficult to implement in a
TWH, so that it is unlikely to be widely adopted by manufacturers. Therefore the five additional control
methods were selected based on their simplicity; each could be implemented by a typical manufacturer.
DE-FC26-05NT42327 Final Report: Development of an Accurate Feed-Forward Temperature Control Tankless Water Heater
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It was found that one of these methods performed as well as MPC, or even better under many
circumstances. This method uses a Feedback-Compensated Feed-Forward algorithm that was
developed for this project. Due to its simplicity and excellent performance this method was selected as
the controller of choice.
A final higher-capacity prototype heater that uses Feedback-Compensated Feed-Forward control was
constructed. This prototype has many improvements over the currently marketed heaters:





excellent control
a modular design that allows for different capacity heaters to be built easily
built-in fault detection and diagnosis
a secondary remote user-interface
a TRIAC switching algorithm that will minimize “flicker factor”
The design and engineering of this prototype unit will allow it to be built without an increase in cost,
compared with the currently marketed heater. A design rendering of the new product is shown below.
It will be launched with a new marketing campaign by Keltech in early 2009.
DE-FC26-05NT42327 Final Report: Development of an Accurate Feed-Forward Temperature Control Tankless Water Heater
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Table of Contents
Executive Summary....................................................................................................................................... ii
List of Figures ............................................................................................................................................... vi
List of Tables ............................................................................................................................................... vii
1. Introduction .............................................................................................................................................. 1
1.1 Rationale for a focus on electric resistance heaters ........................................................................... 1
1.2 Background Study ............................................................................................................................... 2
1.2.1 Conclusions of the background study .......................................................................................... 3
1.3 Project Objectives and Scope.............................................................................................................. 5
1.4 Project Team ....................................................................................................................................... 5
2. Measurement of TWH Temperature Control Performance ..................................................................... 7
2.1 Requirements of test method ............................................................................................................. 7
2.2 Resulting Test Method ........................................................................................................................ 7
2.3 Testing System .................................................................................................................................... 9
2.3.1 Hydronic System .......................................................................................................................... 9
2.3.2 Data Acquisition System ............................................................................................................ 12
2.4 Testing Heaters ................................................................................................................................. 16
2.4.1 Test Results ................................................................................................................................ 17
2.5 Temperature Control Performance Rating ....................................................................................... 19
3. Development of an Improved Controller ................................................................................................ 20
3.1 Technical description of development of MPC for a prototype heater............................................ 20
3.1.1 Development of a Thermal Model ............................................................................................. 21
3.1.2 State Space Formulation ............................................................................................................ 25
3.1.3 Complete Model of the Tankless Water Heater Assembly ........................................................ 26
3.1.4 Model Validation and Parameter Estimation ............................................................................ 27
3.1.5 Development Environment ........................................................................................................ 31
3.1.6 Performance comparison of MPC and existing controller ......................................................... 33
3.2 Assessment of alternative control techniques ................................................................................. 36
3.2.1 Control Approaches ................................................................................................................... 37
3.3 Hardware Development .................................................................................................................... 40
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3.3.1 Heat Exchanger .......................................................................................................................... 41
3.3.2 Microcontrollers......................................................................................................................... 42
3.3.3 Sensors ....................................................................................................................................... 44
3.3.4 Packaging ................................................................................................................................... 45
4. Project Administration ............................................................................................................................ 47
4.1 Budget ............................................................................................................................................... 47
4.1.1 Differences between proposed and actual expenditures.......................................................... 47
4.2 Schedule ............................................................................................................................................ 48
5. Final Results ............................................................................................................................................ 50
5.1 Product .............................................................................................................................................. 50
5.2 Objectives and outcomes.................................................................................................................. 50
5.3 Technology Transfer.......................................................................................................................... 52
5.3.1 Papers......................................................................................................................................... 52
5.3.2 Presentations ............................................................................................................................. 52
5.4 Future work ....................................................................................................................................... 53
5.4.1 Refinement of the test method to a standard method of test .................................................. 53
5.4.2 Peak power issues ...................................................................................................................... 53
5.4.3 Gas TWH control performance .................................................................................................. 54
6. References Cited .................................................................................................................................... 55
DE-FC26-05NT42327 Final Report: Development of an Accurate Feed-Forward Temperature Control Tankless Water Heater
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List of Figures
Figure 1. Schematic diagram of testing system ........................................................................................... 9
Figure 2: Photo of water carrying portion of test system .......................................................................... 12
Figure 3: LabVIEW Data Acquisition Interface ........................................................................................... 13
Figure 4: Temperature sensor in-situ calibration ...................................................................................... 14
Figure 5: Thermocouple transient response tests ..................................................................................... 15
Figure 6: Flow sensor accuracy test ........................................................................................................... 16
Figure 7: Temperature response of a TWH to a step change in flow rate ................................................. 17
Figure 8: Temperature response of another TWH to a step change in flow rate ...................................... 18
Figure 9: Zoning of a single TWH heating chamber ................................................................................... 22
Figure 10: Section through an individual heating chamber ....................................................................... 22
Figure 11: Zoning of heating chamber relative to heater element and ambient ...................................... 23
Figure 12: RC network for construction element ...................................................................................... 24
Figure 13: Block model of prototype TWH ................................................................................................ 26
Figure 14: Block model of individual heater chamber ............................................................................... 27
Figure 15: Initial parameter estimation result for training data set .......................................................... 28
Figure 16: Initial estimated model response and measured result of inlet temperature fluctuation........ 29
Figure 17: Hankel singular value decomposition showing relative energy per state ................................ 30
Figure 18: Bode diagram comparing full-order with reduced-order model .............................................. 31
Figure 19: Software and hardware setup for rapid controller prototyping and development ................. 32
Figure 20: Development platform.............................................................................................................. 33
Figure 21: MPC controller performance on test 6 - a cold start with 12 L/min flow ................................. 35
Figure 22: MPC and PID performance comparisons .................................................................................. 36
Figure 23: Simulink block diagram of Feedback Compensated Feed Forward Controller ......................... 40
Figure 24: Schematic design of electrical system ...................................................................................... 41
Figure 25: Preliminary prototype heat exchanger ..................................................................................... 42
Figure 26: Main board prototype............................................................................................................... 43
Figure 27: Remote board ........................................................................................................................... 44
Figure 28: Comparison of production and laboratory flow sensors .......................................................... 45
Figure 29: Heater packaging design ........................................................................................................... 46
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List of Tables
Table 1:
Table 2:
Table 3.
Table 4:
Table 5:
Table 6:
Table 7:
Table 8:
Table 9:
Project Objectives and success criteria .......................................................................................... 5
Members of the project team ........................................................................................................ 5
Test set for an 18 kW heater .......................................................................................................... 8
ISE results for existing controller and MPC controller ................................................................. 34
Summary of ISE results for performance test of seven control approaches ............................... 38
Total approved budget proposed................................................................................................. 47
Actual expenditures ..................................................................................................................... 47
Objectives and outcomes ............................................................................................................. 50
ISE results for final (production model) 30 kW TWH ................................................................... 51
DE-FC26-05NT42327 Final Report: Development of an Accurate Feed-Forward Temperature Control Tankless Water Heater
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1. Introduction
Water heating in homes in the US consumes 1.68 quads (1015 Btu) of primary energy annually.1 Most
homes have a tank-type heater, in which water is heated and stored in a tank for later usage. The tanks
continually lose heat to the environment, and these losses - referred to as “standby losses” – can be
significant. A tankless water heater (TWH) – sometimes referred to as a “demand” or “instantaneous”
water heater – doesn’t store heated water in a tank. Instead it heats water as it is being used. This
virtually eliminates the standby losses associated with tank-type heaters. Despite this benefit, only 1%
of houses in the US2 employ TWH as their primary water heating system.
As with most technologies, TWH have both benefits and drawbacks when compared with the status quo
technology. One important drawback is that it is difficult to control the outlet temperature in TWH.
This is because the flow rate in a domestic water heating system can change very quickly (such as when
an end use is started or stopped) and the system dynamics are inherently non-linear. The purpose of
this project is to improve the temperature control of an electric TWH that is currently manufactured and
sold in the US, by applying advanced control methods. The rationale is that addressing an important
barrier to adoption of TWH will encourage consumers to adopt this energy-saving technology in greater
numbers. In the US about 39% of water heaters use electric resistance heat and 54% use natural gas [US
DOE 2001]. However, the focus of this project is specifically electric TWH.
This report describes the final results of this project. As requested by our sponsor, it does not describe
the paths to success or related work previously conducted, and mentions only briefly some of the
background work conducted. A review of some of the scientific literature reviewed during this project is
included in a paper that presents some findings from this project [Henze et al. 2009].
1.1 Rationale for a focus on electric resistance heaters
There are several reasons for the specific focus on electric TWH. One is that the current market for
electric resistance heaters is large despite the higher energy costs associated with electricity. Another is
that the likelihood of combustion always being a better option than electricity is low. Alternate energy
sources such as solar, wind or nuclear can produce electricity, but cannot produce natural gas. Finally,
because electric water heaters don’t require a flue they are often easier to install in point-of-use
1
Source: Energy Information Administration, 2001 Residential Energy Consumption Survey: Household Energy
Consumption and Expenditures Tables.
2
According to the tables in footnote 1, out of 111.1 million homes, 1.3 million use tankless water heaters.
DE-FC26-05NT42327 Final Report: Development of an Accurate Feed-Forward Temperature Control Tankless Water Heater
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applications, where the benefits of reducing piping losses may overcome any disadvantages associated
with electricity compared to gas.
The efficiency of electric resistance heating cannot be improved. Thus, the current project is not
intended to improve the energy efficiency of the TWH; it is to improve the temperature control
performance. The most successful energy conservation projects don’t necessarily improve equipment
efficiency. Rather, they increase adoption by the public. That is the goal of this project: to eliminate
one of the barriers to widespread adoption of an existing technology that uses less energy than the
status quo.
One of the most successful energy conservation product development projects in recent times is the
development of the compact fluorescent light bulb. However, fluorescent lighting, which is far more
energy efficient than incandescent lighting (typical efficacy above 75 lumens/watt compared to around
15 lumens/watt for incandescent), was available for many years before this project. Homeowners
would not adopt this technology despite the vast increases in efficiency (and attendant reductions in
cooling load). They didn’t want to change their fixtures. The compact fluorescent that was developed
was less efficacious than the tubular fluorescent lights at the time, but it has saved a tremendous
amount of energy by increasing adoption rates. The current project is intended to work in a similar
fashion.
1.2 Background Study
A comprehensive review of the work previously conducted in the areas related to temperature control
was conducted. There are four main reasons for this review: a) to avoid unnecessary duplication of
prior work; b) to gain insight into development methods, successful and unsuccessful; c) for guidance on
areas that are important to this research, but beyond the scope of this project (such as human
perception of temperature variation in showers); d) to discover whether an acceptable solution already
exists but isn’t being used. Six categories of sources were searched for relevant literature.
1.
2.
3.
4.
Manufacturers’ data from marketing materials, websites, and personal discussion
Codes and Standards from the US and other countries
Patents from the US Patent and Trade Office.
Scientific articles from a broad range of journals covering areas such as control theory and
application, HVAC, thermal sciences, ergonomics, computing, and human physiology.
5. Articles from broad market technical publications such as Popular Science, Heating Piping and
Air Conditioning (HPAC), Consumer Reports, and Homebuilder magazine.
6. Reports to governmental agencies, such as Department of Energy, California Energy
Commission, and the National Institute of Standards and Technology.
DE-FC26-05NT42327 Final Report: Development of an Accurate Feed-Forward Temperature Control Tankless Water Heater
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The information gathered from these sources was reviewed, assessed, and pertinent parts were
summarized. (A side note: a great deal of inaccuracy and misperception about TWH was found,
particularly in the manufacturers’ data, patents, and broad market articles. Technical literature on TWH
is unusual in this regard, possibly a result of the immaturity of the TWH market).
1.2.1 Conclusions of the background study
There are six main benefits to TWH. These are:
1. Standby savings – this is the energy lost to the environment when the heater is not being used,
as compared with a tank-type water heater. The DOE’s Office of Energy Efficiency and
Renewable Energy (EERE) estimates standby losses to be 8 – 34% of the total water heating
energy for storage water heaters, depending on water usage patterns and tank insulation.
2. Size – tankless water heaters take up very little space, and can be hung on a wall. For homes
with a high cost-per-area ratio ($/ft²) this can be a significant factor, often more significant than
the higher first cost of the TWH. Furthermore, the smaller size allows point-of-use tankless
water heaters to be used in applications that wouldn’t allow a tank, such as under a sink.
3. Durability – the most common cause of water heater replacement – tank failure – doesn’t occur
in TWH, so they tend to last much longer: 20 years, versus 13 years for tank-type heaters.
4. Continuous Hot Water Supply – the TWH can be used at capacity for multiple events in series,
such as multiple morning showers, without a decrease in supplied temperature.
5. Distributions Savings – this is normally overlooked and wasn’t discussed anywhere in the
literature, but is significant. “Distribution loss” refers to the heat lost by hot water in the pipes
that distribute it through a home or building. These losses are significant, typically 10 – 20% and
up to 50% of water heating energy [ASHRAE 2007, Hiller 2005], and they can be reduced with
tankless water heaters. This reduction is brought about by reducing the supply temperature,
and mixing less cold water at the point of use.
In a tank-type heater reducing the supply temperature reduces the capacity of the water heater,
but this is not the case with TWH. Another reason that tank-type heaters are kept at higher
temperatures is to reduce growth rate of legionella bacteria in the tank [ASHRAE 2007]. Since
TWH do not store hot water they do not have this problem to the same extent as tank-type
heaters. Achieving these supply-temperature-related savings requires very good temperature
control.
6. Special Applications – many emerging technologies can produce heated water far more
sustainably than current technologies, but are not widely adopted because of first cost or
reliability. These technologies can be enabled by integrating them with TWH boosters. Current
DE-FC26-05NT42327 Final Report: Development of an Accurate Feed-Forward Temperature Control Tankless Water Heater
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examples include solar water heaters and heat pump water heaters. However, booster
applications require very good temperature control.
There are three main drawbacks to TWH that keep them from being more widely adopted by US
consumers. These are:
1. Large power requirement – since the water must be heated very quickly, a great deal of power
must be added to the flow stream. For a whole house application, 30 kW or more may be
needed. This requires larger electrical equipment than is commonly used in US homes. Some
electric utilities have expressed concern over the potential for higher peak loads on
neighborhood transformers. However, electric TWH can be an excellent application of a load
limiting device, in which a current transformer can be placed on the service entrance and the
TWH power reduced if the total load nears capacity. We conceived of this idea during this
project, but found that it has already been patented by a TWH manufacturer. Furthermore, a
study by Johnson and Clark [2006] shows that the peak load of a small number of TWHequipped homes is identical to tank-equipped homes because of load diversity. These issues are
discussed further in section 5.4.2.
2. Higher first cost – a TWH is typically about $700 more to purchase than a tank-type heater.
Also, the additional power capacity may bring about higher installation costs. However, it seems
likely that this is a result of an immature market. If TWH were produced in the same quantity as
storage heaters it seems likely that their smaller size would cause them to be similarly priced,
since they require much less material, are easier to ship and store, and can be carried into a
house by one installer.
3. Difficult to control – the poor temperature control of existing TWH in the market is one of the
factors that slows the adoption rate. Real estate developers know that a comfort issue is likely
cause a homebuyer to complain, whereas higher energy consumption is not. In European and
Asian markets, users are less sensitive to sacrifices in comfort and accept greater temperature
swings in their shower water [Herrmann et al. 1994, Ohnaka et al. 1994, Rohles and Konz 1982].
This has allowed fairly high adoption rates, but until control is improved, American consumers
are unlikely to adopt TWH in large scale.
One of the difficulties of control is that there are no currently existing standards, guidelines or
methods to describe the control performance of TWH and rate it. This leaves developers
without guidance when trying to improve control. For example, is it better to have a 10°
overshoot for 1 second, or a 5° overshoot for two seconds? Is it better to have a short term
overshoot or a long term offset error? Furthermore, few developers are able to measure and
characterize performance, and this means that it is difficult for them to improve performance
because any changes they make may or may not improve control.
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1.3 Project Objectives and Scope
The objective of this project is to develop an improved controller for an existing electric TWH. This
controller should give superior temperature control performance without imposing a significant cost
premium. Based on the discussion of drawback # 3 in section 1.2.1, it is also necessary to develop a
method by which to test and rate the temperature control performance of TWH. Finally, for the work in
this project to be useful, the controller must be adopted into a product that is manufacturable for sale
to the US public, and the work must be described and made available to the public so that other
manufacturers and developers can take advantage of it.
These objectives and criteria for evaluating successful completion of them are summarized in Table 1
below.
Table 1: Project Objectives and success criteria
Objective
Develop a test method
Develop a rating system
Develop an improved TWH controller
Include controller in manufacturable prototype
Impose minimal cost premium
Disseminate results
Criterion for success
Ability to quantify control performance
Ability to meaningfully quantify better performance
A working controller that improves control
A prototype that is ready for mass production
Increase overall cost by < 5%
Published papers or public presentation
1.4 Project Team
The project team was made up of several highly motivated individuals with a keen interest in the
success of this project. The members of this team are shown below in Table 2.
Table 2: Members of the project team
Department of Energy
Project Manager:
Paul Giles
Building Solutions, Inc.
Principal Investigator:
Project Manager and Co-PI:
Research Scientist:
Grenville Yuill
David Yuill
Andrew Coward
Subcontractors
Keltech, Inc.:
University of Nebraska:
Consultant:
Ken Lutz
Gregor Henze
Mike Coward
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Building Solutions, Inc. (BSI) is a small business based in Omaha, Nebraska, who specialize in engineering
and scientific research of heating, ventilation and air-conditioning related topics, with a special focus on
energy conservation. The company was formed in 2003 and is headed by David Yuill. Dr. Grenville Yuill
is a part-time employee of BSI and was the principal investigator in the project’s proposal. Near the
outset of the project he accepted an upper-level administration job at the University of Nebraska, the
demands of which prevented him from contributing significant effort to the current project. Therefore,
David Yuill took over the role of principal investigator.
For this project Building Solutions, Inc. partnered with Keltech, Inc., a manufacturer of electric tankless
water heaters. Keltech was founded in 1987 by Ken Lutz, and now produces over 80 models of TWH for
many different applications: residential, commercial, industrial (process water heating), safety shower,
emergency eyewash, aircraft and non-water fluid heating. Their standard heaters range in size from 5 to
144 kW. They specialize in highly durable, carefully constructed water heaters made with the fewest
possible imported parts, and in customized heater designs for special applications. They have four
current patents on their TWH technology and several more patents in process. Keltech has 15
employees at its factory in Delton, Michigan.
Some of the controls modeling and algorithm development was subcontracted to Dr. Gregor P. Henze,
PE, an associate professor at the University of Nebraska’s Architectural Engineering Program.
Some of the microcontroller prototype development work was subcontracted to Michael Coward, cofounder of Continuous Computing, a multinational computer hardware and software producer
headquartered in San Diego, California.
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2. Measurement of TWH Temperature Control Performance
As described above, a method of measuring and assessing temperature control performance in electric
TWH is needed, but doesn’t exist in the literature. Such a method was required for this project, so a
method was developed and a testing system was built to conduct the tests. There were many
substantial refinements to the test method and to the testing system, based on our experience testing
commercially available electric TWH. Only the final method, test system, and rating system are
presented here.
2.1 Requirements of test method
Repeatable – The test method must be repeatable, not only by us but by other researchers or
developers. This is a basic requirement of any valid scientific study. It should be possible for results to
be duplicated so that others can verify their accuracy. Ideally, it should be possible for the test method
to be used by developers and manufacturers so that they may benefit from this work. This will
contribute to improvement of temperature control throughout the industry – a central goal of this
project.
Applicable – The test method must measure the type of performance that is applicable to human
comfort. Therefore, measurement accuracy levels finer than those that humans can detect in showers
are unnecessary. Similarly, test conditions that do not occur in residential service water heating
applications are also unnecessary.
Inclusive – The test method must be “as simple as possible, but not simpler” (to quote Albert Einstein).
The goal, therefore, is to use the minimum number of tests that still manage to fully capture the myriad
different types of control performance shortcomings that would affect residential users.
Understandable – Results gathered from early versions of the test (prior to refinements that
significantly condensed the test procedure) contained a huge number of data of many categories.
Comparing these results for two different TWH controllers was difficult or impossible. Therefore, the
test method must contain a way to distill the important control performance features into a compact
form, for easy comparison of different TWH controllers.
2.2 Resulting Test Method
The final test method consists of 11 separate tests for a given heater. Each of these tests involves a step
change to either flow rate or inlet temperature. During the flow rate change the heater is raising the
water temperature by 30°C. There are seven step changes to flow rate: increases and decreases of
DE-FC26-05NT42327 Final Report: Development of an Accurate Feed-Forward Temperature Control Tankless Water Heater
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various magnitudes. These flow rates are selected based upon the heater’s power capacity. The
maximum flow rate used in the test should not require more than 90% of the heater’s power when
raising the water by 30°C. This is calculated with a steady-state energy balance (a simplified First Law of
Thermodynamics statement):
𝑄 = 𝑚 ∙ 𝑐𝑝 ∙ Δ𝑇
where Q is the heater power (kW), 𝑚 is mass flow rate of water (kg/s), cp is the specific heat of water
(4.18 kJ/kg-K), and T is the temperature rise (30°C, or 30 K).
For the 18 kW heater that was used as a development prototype in this project, the flow rate can be
determined by rearranging the equation above and substituting values:
𝑚=
0.9 × 18 𝑘𝑊
𝑘𝐽
4.18
∙ 30 °𝐶
𝑘𝑔 ∙ °𝐶
= 0.13
𝑘𝑔
𝑜𝑟 8 𝐿/𝑚𝑖𝑛
𝑠
This means that the flow rate basis is 8 L/min, and all test flow rates are ¼, ½ or ¾ of this value.
Besides the seven step changes to flow rate there are also four step changes to inlet water temperature.
These step changes have fixed magnitude of 5°C and 15°C in both increasing and decreasing
temperatures. During these tests, the flow rate is kept constant at ½ of the basis flow rate, as
determined above.
The resulting test set for an 18 kW heater is summarized in Table 3 below.
Table 3. Test set for an 18 kW heater
Flow Rate [L/min]
Test #
1
2
3
4
5
6
7
8
9
10
11
Initial
2
8
4
8
0
0
0
Final
8
2
8
4
2
4
8
Temperature Step
[°C]
5
-5
15
-15
Total
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2.3 Testing System
A device was constructed and modified until it was able to successfully carry out the tests required in
the test method. This device controls the flow and inlet water temperature very steadily and accurately,
using a complex system of valves, and allows for very crisp step changes to these parameters. It has a
data acquisition system that accurately senses: temperature at four locations; water flow rate; and
electrical power used by the TWH. These quantities are logged at high frequency and can be monitored
in real time by the operator. Each of the sensors in this system was calibrated (NIST traceable) by the
manufacturers, and the calibration was verified when the sensor was installed in the test system.
2.3.1 Hydronic System
The hydronic system is shown schematically in Figure 1 below. A discussion follows that is intended to
describe the system sufficiently so that other researchers or developers may use it to construct their
own testing system with minimal effort.
Figure 1. Schematic diagram of testing system
a. Starting from the upper left of Figure 1 the water enters from the domestic cold water (DCW)
and hot water (DHW) lines, which are connected to city water. The DHW line is connected to a
tank-type water heater with 60°C (140°F) water in it. A thermo-regulating valve mixes cold and
hot water and the first temperature sensor, T1, senses this mixed water temperature. The
purpose of this mixing is to maintain the nominal hot water at constant temperature (slightly
below 60°C).
b. From this point the hot water enters a diverting valve where it is either mixed with cold water
(upwards) or dumped (downwards). The purpose of dumping is that the flow rate through the
hot water supply piping must be constant because of inevitable heat loss (if the hot water was
not dumped, it would cool off in the pipe upstream of the thermostatic valve prior to the start
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of the test). Similarly, the cold water is also either mixed or bypassed. Both cold and hot water
lines are insulated.
c. The bypass side of the diverting valve, where the dumped water passes, has a rough-grade flow
sensor and a needle valve on it. The valve is used to balance the system so that the pressure
loss through the test system is the same as the pressure loss through the bypass line. This helps
protect the system from pressure fluctuations, which could affect temperature in an unbalanced
system. The flow sensor indicates whether the valve is succeeding in balancing the system.
d. The two diverting valves, shown in the figure with a pair of small curved arrows beside them,
mix the hot and cold water together, and it enters the test heater at the point marked “T2” on
Figure 1 (T2 is temperature sensor 2). Care must be taken to ensure sufficient flow disturbance
in this section so that stratification does not occur. Stratification can damage the accuracy of
the temperature measurement at T2.
e. After passing through the test heater the temperature is measured by T3. Significant
stratification is also possible here, but it is important to measure the outlet temperature as close
to the outlet as possible. Again, care must be taken in selection of the location for the outlet
temperature sensor. Also, if the temperature sensor is very thin (which is necessary in order to
have a short thermal time constant) and not well supported, it may oscillate in the flow stream’s
turbulence, and in doing so make thermal contact with the pipe walls for brief periods. This will
affect results, but may go unnoticed.
f.
A pressure reducing valve reduces the pressure that the flow control valves downstream will
experience. This prevents fluctuations in the supply water pressure (city water) from affecting
the flow rate (whereas the discussion of a balanced system, above, addresses pressure
fluctuation effects on inlet temperature).
g. Next, a laboratory-grade turbine flow sensor supplies high frequency flow measurements to the
data acquisition system. This sensor must be selected to be able to accurately measure hot
water. It is located downstream of the heater because flow sensors typically require a long
undisturbed inlet and exit condition (i.e. no fittings or bends nearby). A long length of pipe
upstream would lose heat to the environment, whereas downstream this heat loss doesn’t
affect any measurements.
h. A fourth temperature sensor, T4, is located downstream of the flow sensor. This was used for
informal experiments to determine piping effects on heat loss and damping of temperature
fluctuations, but is not required for typical control performance testing.
i.
Finally, four sets of valves are piped in parallel. Each set consists of a needle valve and a ball
valve connected in series. These valves control the flow rate. They allow step changes to be
DE-FC26-05NT42327 Final Report: Development of an Accurate Feed-Forward Temperature Control Tankless Water Heater
10
imposed on the system, from one controlled flow rate to another. To illustrate the rationale
behind these four sets of pipes, an example is used.
Consider a step from 4 L/min to 8 L/min. To prepare for this step, open ball valve 1 (others
closed) and adjust needle valve 1 until 8 L/min is attained. Then close ball valve 1 and open ball
valve 2. Adjust needle valve 2 until 4 L/min is attained. Now, start the test, gathering data until
the system is stable with 4 L/min of flow. Once the system is stable, simultaneously close ball
valve 2 while opening ball valve 1. This provides the desired step, with the instant of the switch
being defined as t = 0.
The fourth (rightmost) set of valves in Figure 1 has an actuated valve. This valve was calibrated
with the data acquisition system so that accurate and repeatable ramp changes to flow rate
could be achieved. However, our experience testing and analyzing multiple heaters suggests
that the ramp changes are not necessary; they do not increase the ability to characterize good
control appreciably. Furthermore, they do not mimic typical conditions in a residential hot
water system as well as step changes.
The use of actuators for the ball valves was considered. It was concluded that a technician can
provide a reliable and sufficiently crisp step (rapid simultaneous opening and closing of valves),
and that automation of this process would not reduce technician time for a set of tests.
Therefore, automated valves are not recommended.
j.
Finally, downstream of these valve sets the system drains into a large pipe that is open to air
pressure.
Copper pipe (nominal ½”) is used for most of the system. Although rubber and synthetic hose have
lower overall heat conductivity, they have higher thermal mass for a given length, compared with
copper (because the specific heat of copper is much lower). Thus there is a trade-off between steady
and transient response associated with the choice of hose or pipe.
A photograph of the hydronic portion of the test system is shown in Figure 2. In the photo a
commercially available TWH (with its cover removed) is mounted on the upper part for testing. This
system is mounted on a wheeled lightweight frame.
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Figure 2: Photo of water carrying portion of test system
2.3.2 Data Acquisition System
The data acquisition system (DAQ) consists of a software human interface, a hardware interface and
several sensors.
2.3.2.1 Software interface
LabVIEW software and an SCC signal conditioner (both produced by National Instruments) were used to
collect and store data. A LabVIEW interface was developed, as shown in Figure 3. Four temperatures
are shown in real time (thermometer-style, with digital readouts below them), a flow sensor, and
electric power. These values are also plotted on a sub-screen in real-time. The use of such real-time
monitoring is highly recommended because it illuminates many kinds of problems that naturally occur in
such testing, and because it allows the technician to know when steady-state has been reached, so the
test can be started.
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In the upper right of the figure a box encloses the actuated valve, discussed in point i. of 2.3.1, above.
Start Flow, End Flow and ramp time can be entered, then started by clicking “start”. Clicking “Manual”
causes the dial on the left, or the digital entry field below it, to control the flow through this valve.
Finally, “Record” and “New File” buttons (left, middle) cause the measured data to be recorded in the
current file or a new file.
Figure 3: LabVIEW Data Acquisition Interface
2.3.2.2 Sensors
Temperature sensors must be chosen carefully because they must be accurate, but also have rapid
response (a low thermal time constant), because of the rapidity and importance of temperature changes
in TWH testing.
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Thermocouples – Omega TMTSS-020U-6
Stated Accuracy: ± 0.6° F
Measured Repeatability: ± 0.1° F comparison between 4 thermocouples, ± 0.02° F self-comparison
Measurement frequency: 4 Hz
A field check of the temperature sensors’ accuracy was conducted after they were interfaced with the
DAQ. The four thermocouples were immersed in hot water that was continuously stirred. The probes’
tips were in close proximity to each other, and were held against the bottom of the stainless steel pot.
The four thermocouples were measured sequentially, and a total of 200 readings (50 for each
thermocouple) were taken at several different temperatures. Figure 4 shows the error of each
thermocouple (defined as the deviation of the reading from the thermocouple to the average of the
thermocouples) at the temperatures tested.
Error (deg C)
T (thermocouple) - T (Average of all thermocouples)
1.00
Thermo 1
0.80
Thermo 2
Thermo 3
0.60
Thermo 4
0.40
0.20
0.00
-0.20
-0.40
-0.60
-0.80
-1.00
0
10
20
30
40
50
60
70
80
90
Temperature (deg C)
Figure 4: Temperature sensor in-situ calibration
The small magnitude of the errors (less than 0.1°C) at the temperatures encountered in this experiment
suggests good confidence in the thermocouple measurements.
A reference to compare the thermocouples to was not readily available. However, the test apparatus
needs to measure temperature differences rather than absolute temperature. Therefore, even if the
mean temperature measurement was inaccurate, the TWH performance measurement would be
accurate.
The transient behavior of the thermocouples was checked to verify an adequately fast response. A
thermocouple at thermal equilibrium with the surrounding air was quickly immersed in hot water. This
was repeated several times. The results are shown in Figure 3. The three lines are from different tests.
The change in temperature – over 50° C – occurs entirely within a 0.2 second period, and all significant
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change is within a 0.1 second period. (The immersion time is not at t = 0; it is unknown and must be
inferred from each of the measurements.)
80
70
Temperature (deg C)
60
50
40
30
20
10
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Time (sec)
Figure 5: Thermocouple transient response tests
The response shown is adequately rapid to accurately capture the water temperature fluctuations.
Flow Sensor – Appleton GR-EFHC Series
Stated Accuracy: ± 0.5%
Stated Repeatability: ± 0.02%
Measurement frequency: 20 Hz (with accumulation time-averaging)
The flow sensor was tested in-situ. The totalized flow read by the flow meter was multiplied by nominal
density and compared to the mass of water collected during the test. This test was repeated at various
flow rates, concentrating on the flow rates outside of the linear range of the turbine meter.
The scale that weighed the water had a resolution of 0.05 kg and an accuracy of ± 0.11 kg at our 15 kg
sample size, i.e. about 0.7%. Figure 6 shows the results of the test.
Power Sensor – Omega OM10 Watt Meter
The power sensor is not required for testing in general. In the current project it was required for
development and for diagnosis.
Specified Accuracy: ± 0.2%
Measurement frequency: 20 Hz (with accumulation time-averaging)
The field accuracy of the watt meter was not checked. None of the reported results required a high
level of power accuracy.
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30.00%
25.00%
Percent error
20.00%
15.00%
10.00%
5.00%
0.00%
-5.00%
0
5
10
15
20
25
Flow rate (L/min)
Figure 6: Flow sensor accuracy test
The plotted data are the measured error, defined as the variation between the measured aggregate of
the flow through the turbine meter, and the sample in the bucket. The vertical line indicates 1.89 L/min
(0.5 GPM), which is the typical minimum flow rate for heating in TWH.
The clear repeatable pattern that emerges in the low flow range indicates a bias error that can be
corrected for. Therefore we conducted a regression analysis of the data using an exponential fit curve
(this curve is suggested by the physical phenomenon and appears to fit well). In the range of our testing
(0.5 gpm and above) the maximum deviation recorded between the measured data and the correction
curve is less than 0.5%.
These data show that the flow sensor that was used is certainly adequate throughout the range of our
tests.
2.4 Testing Heaters
Heaters from three manufacturers were purchased and tested. These heaters each had a capacity in the
range of 18 kW. Two are manufactured in the USA, and one in Europe.
There were several purposes for testing these heaters.
1. To illustrate the kinds of control problems that a control performance test needs to sense and
characterize
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2. To provide the first quantitative data that support the anecdotal evidence that TWH control
poorly
3. To understand the control approaches used by different manufacturers (by inverse modeling).
The TWH industry is very non-standardized with respect to control approaches.
4. To see what level of performance had to be exceeded by the controller developed in this
project.
These heaters were tested with an exhaustive set of tests, 60 in total, to ensure that the tests would
capture all of the different possibilities for control performance problems. Data are collected for 60
seconds for each test, giving roughly 2900 data per test, or 14,000 data per heater. Experimentation has
shown that the majority of disturbances have settled within a 60 second time period.
2.4.1 Test Results
For each test these data are plotted, as shown in Figure 7. This figure depicts the response to a flow
rate step from 2.8 L/min to 7.6 L/min. This heater begins to ramp up its power (red line) for about 8
seconds, then continues this ramp up far more slowly for the duration of the test, as the outlet
temperature continues to stay below setpoint. This behavior is a classic response from a PID
(proportional-integral-derivative) controller. The outlet temperature (green) dips from 50°C (the steadystate temperature prior to the flow rate change) down to a minimum of 36°C at t = 7 seconds, then
slowly rebounds, but experiences a constant offset error of about 4°C. This plot shows temperature
control that would cause a severe discomfort event to a user in a shower.
60
20
18
50
16
12
30
10
8
Flow (L/min)
Power (kW)
Temperature (deg C)
14
40
20
6
10
Inlet TWH
Outlet TWH
4
Flow
2
Power
0
0
-10
0
10
20
30
40
50
60
70
Time (seconds)
Figure 7: Temperature response of a TWH to a step change in flow rate
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Another example, from a different heater is shown below in Figure 8. This controller appears to use PIDbased control that has been modified with a complex algorithm that causes the power to fluctuate
rapidly. The control here is better than for the heater in Figure 7, but a significant constant-offset error
still results – about 3°C. Furthermore, the rapid power fluctuations may cause shorter heater element
life, and “flicker factor”, a situation in which lights in the home flicker because of the voltage
fluctuations associated with varying such a large load so rapidly.
60
20
18
50
16
12
30
10
8
Flow (L/min)
Power (kW)
Temperature (deg C)
14
40
20
6
Inlet TWH
Outlet TWH
10
Flow
Power
4
2
0
0
-10
0
10
20
30
40
50
60
70
Time (seconds)
Figure 8: Temperature response of another TWH to a step change in flow rate
The battery of tests on the three heaters showed control problems in each one; the research team
deems the control performance of all three heaters to be unacceptable. The maximum deviation
(undershoot or overshoot) in each of the heaters:
TWH 1: 11°C (20°F)
TWH 2: 11°C (20°F)
TWH 3: 26°C (47°F)
The deviations shown above are not brief; they occur over a sufficient time period that the damping
effect of the distribution piping is not likely to ameliorate the problem before the off-temperature water
reaches the end user.
The purposes of this testing, described above in section 2.4, were met. A conclusion can be drawn that
the current state-of-the-art in TWH temperature control performance is very poor. Based on an analysis
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of the results of this testing a revised test method that requires only 11 tests was developed, as shown
in Table 3 on page 8.
2.4.1.1 Special Case: Cold start tests
Cold start tests are ones in which the flow rate steps up from zero to some value. In all other tests the
system has reached a steady state before a test is started, i.e. before a step change is imposed.
However, for the cold start tests the entire system would need to reach room temperature, including
the water supply lines. Then the water temperature would not be steady as it entered the heater; the
volume of water in the supply pipe would provide a plug of room temperature water, which is not
normally at the supply water temperature.
To overcome this problem cold start cases are conducted with the full flow rate provided before the
start of the test, but with no power delivered. At t = 0 the power is provided to the TWH. This gives an
identical result to a perfect step-up in flow with water at constant temperature.
2.5 Temperature Control Performance Rating
Due to the difficulty of describing the control performance, a rating system was developed. This system
was developed with the intent of accurately matching the comfort requirement of a user in a shower –
the most stringent and most important temperature control requirement in a residential setting – while
still being simple and concise.
The control performance is rated based on the integral of the square of the error (ISE) over the 60second test period.
60
𝑒 2 𝑑𝑡
𝐼𝑆𝐸 =
𝑡=0
The ISE algorithm was selected because it more strongly penalizes larger magnitude errors and
minimizes the weighting of smaller errors, which is similar to human perception of water temperature.
For example, temperature swings less than +0.3°C or -0.2°C are typically not detected by humans in
showers [Herrmann 1994], and therefore should not be penalized significantly.
The ISE calculation can be easily performed numerically in a spreadsheet program.
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3. Development of an Improved Controller
The objective for this phase of the project was to use advanced control methodology to develop a
controller that gives a TWH better control performance than any currently on the market. Advanced
control methodologies include adaptive control, robust control, expert systems, fuzzy logic, artificial
neural networks, and model predictive control [Burns 2001].
Model predictive control (MPC) was selected as the appropriate advanced control methodology for the
TWH application. It was anticipated that MPC has capabilities that exceed the control needs of the
TWH, but since the price of microcontrollers has become so low in recent years, the excess capability
has little or no effect on the hardware cost of the controls. By exceeding the control needs, the MPC
controller developed in this project was intended to show how good control could be in a practical
application; to provide a benchmark against which other control approaches could be compared.
An important factor in selecting a control approach is consideration of unusual applications; in
particular, the use of the electric TWH as a booster for alternative heating approaches such as solar or
heat pump water heaters. The heater must be able to deliver good control with very low or very high T
conditions, and possibly rapid changes to inlet temperature. One previously considered advanced
control approach for TWH – adaptive fuzzy control – assumed fairly constant inlet water temperature
[Haissig & Woessner 2000].
One important drawback of MPC is that it requires a high level of sophistication and a significant effort
to develop. In particular an accurate model of the transient heat transfer must be developed. As with
any model, this model must be validated and tuned, if necessary. This means that an accurate
measurement device, such as the test system described in section 2.3, is required. Since the model is
used as the basis of the control decisions, any flaw or inaccuracy in the model tends to compound the
error in the temperature output.
3.1 Technical description of development of MPC for a prototype heater
An 18 kW prototype heater was selected as the development platform. This is smaller than a typical
whole-house heater; the rationale is that after developing MPC control for one heater, modifying it for a
different sized heater requires relatively little effort.
The subject TWH has three chambers of 3.2 cm diameter copper pipe connected in series through
headers. Each chamber contains a 6 kW tubular heater, consisting of a nickel-chromium resistance wire
element, surrounded by powdered magnesium oxide insulation, wrapped in an austenitic nickel-based
alloy sheath. Each tubular heater is controlled by a TRIAC. The heat input can modulate in a quasiDE-FC26-05NT42327 Final Report: Development of an Accurate Feed-Forward Temperature Control Tankless Water Heater
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continuous (resolution of 0.8% of full scale) range from 0 to 18 kW. The total volume of water in the
heating chambers and headers is approximately 0.4 L.
Accurate temperature control of TWH is only possible when accounting for the dynamic thermal
response of TWH to variations in water flow rate, inlet water temperature, setpoint changes, and other
unmeasured disturbances. Conventional feedback control cannot account for the plant dynamics in an
anticipatory fashion, nor does it allow for the inclusion of constraints, such as a maximum allowable
overshoot error (for scald protection). MPC, however, does have these capabilities.
An overview of the methodology for the MPC controller development follows:
a. TWH Modeling and Validation: A dynamic model of the TWH was created and tuned,
accounting for the thermal mass of the components of the tubular heater and heat
exchange with the environment, in addition to the thermal energy required to heat the
water flow. We developed lumped-parameter thermal models of the TWH and validated
these models using experimental data from dynamic tests conducted with the testing
system described in section 2.3. Matlab software and its block-based dynamic systems
analysis front end, Simulink, were used for modeling.
b. Development of a model predictive controller for tankless water heaters: The Simulink
framework is extended with MPC Toolbox – an add-on module specifically for development
of model predictive control. Rapid control prototyping is accomplished with a further addon, Real Time Workshop, which automatically generates and compiles source code from the
Simulink block models to create real-time software applications on a variety of systems. The
complete system allows automatic code generation tailored for a variety of target
platforms, a rapid and direct path from system design to implementation and provides a
graphical user interface with open architecture. Finally, a hardware target platform, xPC
Target, which allows for controller evaluation in the laboratory setting, was used. xPC
Target causes a target computer that is connected to the TWH to emulate the performance
of any of several available microprocessor families, to test how well a candidate
microprocessor will handle the processing requirements of the final application.
c. MPC controller evaluation: The performance of the MPC controller is fine-tuned by
minimizing the integral squared error (ISE) discussed in section 2.5 over the 11-test
evaluation set shown in Table 3.
3.1.1 Development of a Thermal Model
The dynamic thermal model is broken into the two dominant components: the water contained in the
heater chamber and the heating element. The thermal mass of the wetted heating chamber
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components does not play a significant role in the dynamic response of the system, and is lumped with
the water.
3.1.1.1 Heater Chamber Water Content
For problems involving control system design, a quasi-steady-state approach fails to capture the
dynamics that describe the heat transfer problem, so the TWH system must be described dynamically.
The simplest approach is the stirred tank methodology which is, in effect, a lumped parameter method
for the TWH system. Here, each of the three heater chambers of the prototype TWH is modeled as a
series of inter-connected zones such that the thermal properties of each zone can be assumed to be
uniform: the outlet water temperature is equal to the zone temperature for each zone. This is an
acceptable approximation so long as a sufficient number of zones is used. A third-order approach
provides acceptable accuracy for most heat exchanger components. On this basis, we split each of the
three heating chambers into three equally-sized series-connected subsystems (with index ‘i’ referring to
the inlet condition and index ‘o’ to the outlet condition) as shown in Figure 9:
Figure 9: Zoning of a single TWH heating chamber
The water is modeled as flow through an annulus bounded by the cylindrical heating chamber shell on
the exterior, and the sheath of the tubular heater on the interior. There are actually several passes of
the tubular heater because of its hairpin configuration, but for the purpose of modeling the heat
transfer all of the heater elements were assumed to be concentrically located around the center line of
the heater chamber, as illustrated in Figure 10.
Figure 10: Section through an individual heating chamber
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This assumption allows us to sketch a modified zoning schematic for one chamber of the TWH as shown
in Figure 11.
Figure 11: Zoning of heating chamber relative to heater element and ambient
Given the stirred tank philosophy, the mean water temperature is replaced with the zone water
temperature. This leads to three energy balances for each chamber. The change of internal energy of
each zone is due to a) water flow into and out of the zone, b) convective heat transfer from the surface
of the sheath to the water and c) convective heat transfer from the water to the outer heater chamber
body. Conduction resistance in the chamber body (the outer shell in Figure 10) is considered negligible,
and the chamber body is considered to be adiabatic. The three energy balances are expressed:
dT
T T
T T
dU A
 Vch cpw wA  3Vch cpw (Twi  TwA )  sA wA  bA wA
dt
dt
Rvs
Rvb
dT
T T
T T
dU B
 Vch cpw wB  3Vch cpw (TwA  TwB )  sB wB  bB wB
dt
dt
Rvs
Rvb
dU C
dT
T T
T T
 Vch cpw wC  3Vch cpw (TwB  TwC )  sC wC  bC wC
dt
dt
Rvs
Rvb
or
dTwA
V
T T
T T
 3 ch (Twi  TwA )  sA wA  bA wA
dt
Vch
Vch cpw Rvs Vch cpw Rvb
dTwB
V
T T
T T
 3 ch (TwA  TwB )  sB wB  bB wB
dt
Vch
Vch cpw Rvs Vch cpw Rvb
dTwC
V
T T
T T
 3 ch (TwB  TwC )  sC wC  bC wC
dt
Vch
Vch cpw Rvs Vch cpw Rvb
Here, U is the internal energy [J], Vch the total chamber volume [m3], cpw the specific heat of water
[J/kgK],  the density of water [kg/m3], 𝑉is the volumetric flow rate through the chamber [m³/s], Rvs is
the convective heat transfer resistance in [K/W] from the surface of the sheath to the water, and Rvb is
the convective heat transfer resistance in [K/W] from the water to the surface of the chamber body. The
appearance of overall values for these parameters accounts for the scaling value of 3 in each of the
water energy terms in the above. TsA, TsB, TsC, are the sheath surface temperatures in zones A, B, and C,
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while TwA, TwB, and TwC are the water temperatures in zones A, B, and C. TbA, TbB, TbC, are the chamber
body temperatures in zones A, B, and C.
3.1.1.2 Thermal Model of Heater Elements
Within each heating chamber zone (A, B, or C), modeling is simplified by assuming that the heat transfer
is symmetrical about the central heater chamber axis, which leaves a one-dimensional problem (in
cylindrical coordinates) to be solved in each heating chamber zone, i.e., heat flow from the tubular
heater to the water and from the water to the ambient in a direction perpendicular to the direction of
water flow.
One can visualize the problem of transient heat transfer through an opaque multilayer construction
element as an equivalent electric RC circuit using a lumped parameter modeling approach:
Figure 12: RC network for construction element
This will represent a heater chamber subcomponent of multiple layers using four capacitors,
Ci , Cins , Cs , Cb , four resistors, Rdi , Rdo , Rvs , Rvb , and a heat source Q s [W] at the core of the tubular heater.
The heat source term is multiplied with a heat input efficiency  to account for the fact that not all of
the heat delivered to the TWH ends up in the water stream; i.e., some it is lost to the environment. Ci
[J/K] is the thermal capacitance of the heater element (wire), Rdi [K/W] is the thermal resistance through
the annular inner shell of insulation, Cins [J/K] is the thermal capacity of the insulation, Rdo [K/W] the
thermal resistance through the annular outer shell of the insulation and the sheath, Cs [J/K] is the
thermal capacity of the sheath, Rvs [K/W] is the convective resistance between the sheath and the water,
Rvb [K/W] is the convective resistance between the water and the heating chamber body. This model is a
fourth-order linear time invariant system with eight parameters (4R4C). As can be seen by the units, all
relevant areas must be accounted for.
Based on the total sheath area As [m2] and the convective heat transfer coefficient hs [W/m2K], we can
determine the convective heat transfer resistance Rvs [K/W]
Rvs 
1
hs As
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The conduction heat transfer resistance Rdi or Rdo [K/W] through the insulation and sheath may be
determined from
Rd 
r
1
ln o
2 L ri
where L [m] is the heating chamber length,  [W/mK] the thermal conductivity and ro [m] and ri [m] the
outer and inner radii of layer j.
3.1.2 State Space Formulation
dT
Now, using notation T 
, this thermal network is described by the following energy balances about
dt
the surface and inside temperature nodes when substitutions for Ci , Cins , Cs , Cb are made:
CbTb  (Tw  Tb ) / Rvb
CsTs  (Tw  Ts ) / Rvs  (Tins  Ts ) / Rdo
CinsTins  (Ts  Tins ) / Rdo  (Ti  Tins ) / Rdi
C T  (T  T ) / R  Q
i i
ins
i
di
s
Rearranging:
T  Tb
Tb  w
Cb Rvb
T T T T
Ts  w s  ins s
Cs Rvs
Cs Rdo
T T
T T
Tins  s ins  i ins
Cins Rdo Cins Rdi
T  T Q
Ti  ins i  s
Ci Rdi
Ci
The outputs, Tb , Ts , Tins , Ti , are defined as the state variables; Tb , Ts , Tins , Ti are the time rate changes of the
state variables; Tw , Qs are the input variables and Rvs , Rvb , Rdo , Rdi , Cb , Cs , Cins , Ci , are parameters. We can
express these equations in matrix-variable or state space notation:
x  Ax  Bu
y  Cx  Du
in which x is a vector of state derivatives; x and u are vectors of state and input variables; y is a vector of
output variables and A, B, C, D are matrices of parameters. Specifically:
DE-FC26-05NT42327 Final Report: Development of an Accurate Feed-Forward Temperature Control Tankless Water Heater
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1

 C R
 b vb


 Tb 
 0
  
 Ts   

Tins 
 0
  

 Ti 


 0


 1

C R

 b vb
T   1
 1
1 
1


0  b  

Cs Rdo
  Ts   Cs Rvs
 Cs Rvs Cs Rdo 


 1
1
1 
1  Tins   0
  



Cins Rdo
 Cins Rdo Cins Rdi  Cins Rdi   Ti  

1
1 
 0
0


Ci Rdi
Ci Rdi 
0
 y1  1
y  
 2   0
 y3  0
  
 y4   0
0
0
1
0
0
0
0
1
0
0  Tb  0
 
0  Ts  0


0  Tins  0
   
1   Ti  0
0
0
0
0

Ci





 Tw 
 Q s 





0
0  Tw 

0  Q s 

0
Next, we would prefer to formulate the coupled differential equations for the water content of the
heater chamber in state space notation as well. However, the volumetric flow rate that will appear in
state matrix A is variable, and thus we cannot adopt the state space notation. Part of the problem is
nonlinear because two variables (flow and a dependent temperature) appear as a product. Therefore
we numerically solved the overall TWH model, using an assembly of state space submodels and the
numerical integration of differential equations.
3.1.3 Complete Model of the Tankless Water Heater Assembly
The complete model is shown below in Figure 13 and Figure 14 as a block model. The inputs are flow
rate (Vdot), inlet temperature (Twi) and input power (Qdots). The output is outlet temperature (Two).
Figure 13: Block model of prototype TWH
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Figure 14: Block model of individual heater chamber
3.1.4 Model Validation and Parameter Estimation
To validate the model a test environment was set up in which the behavior of the new dynamic model
can be simulated and compared with measured data from the physical prototype. The model validation
is conducted in a three-step process consisting of parameter initialization, coarse parameter estimation
of highly uncertain parameters, and finally fine parameter estimation of all model parameters. The
parameter estimation is conducted within Simulink by calling the TWH model repeatedly, and examining
outputs using a nonlinear least squares regression algorithm, until the predicted model response
adequately mirrors the measured data.
3.1.4.1 Determination of Initial Parameter Values
Initially, the thermal capacitances Ci, Cins, Cs, and Cb and the conduction resistances Rdi and Rdo are
calculated based on the available measured and manufacturer’s data.
3.1.4.2 Loosely Bounded Parameter Estimation of Convection Resistances and Volume
Since the convection resistances Rvs and Rvb change significantly with flow, a parameter estimation
algorithm based on nonlinear least squares minimization was developed to find appropriate parameter
value estimates. The TWH water volume V, transport delay td, and efficiency  were included in the
parameter estimation. Reasonable initial values for the parameters to be estimated were derived from
DE-FC26-05NT42327 Final Report: Development of an Accurate Feed-Forward Temperature Control Tankless Water Heater
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shorter 1-minute measurements taken on the TWH prototype. These initial values are passed to the
system identification routine and solutions are sought within two orders of magnitude of the initial
values. Long measurements with a high degree of variance in the driving values were chosen to ensure
that a wide range of flow rates would be seen in the system identification process. The top of Figure 15
shows experimental data from the test bed compared to simulated data. The TWH is being controlled
by a PID controller and is subjected to flow rate changes, shown in the lower portion of the figure. A
long lead-in is followed by a ramp-up, a long settling period, a ramp down, and finally a long settling
period. The predicted TWH outlet temperature (gray dashed line) matches the measured value (black
line) already within a very narrow band of about 0.1 Kelvin.
Figure 15: Initial parameter estimation result for training data set
This model also generalizes quite well to changes in inlet temperature, as can be seen in Figure 16. A
long lead-in is followed by inlet temperature steps-up and a step-down. Again, the model accuracy is so
high that it is difficult to distinguish between the predicted response and the measured response. This
figure also shows the classical oscillations of an unstable feedback controller.
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Figure 16: Initial estimated model response and measured result of inlet temperature fluctuation
3.1.4.3 Tightly Bounded Parameter Estimation of All Model Parameters
The five estimated parameters Rvs, Rvb, Vch transport delay td, and heat input efficiency  are now taken
as initial guesses for the next step. The parameter estimation process is finalized by including all eleven
model parameters (4 capacitances, 4 resistances, 1 chamber volume, 1 transport delay, and 1 heat input
efficiency) and allowing a refined system identification process to search in a narrow range of 20%
around the six initial R and C values as well as the five remaining parameter values identified in the
previous parameter estimation step. The final parameter values are within -18% and +10% of the initial
values, with the objective function value decreasing by 4.6%. Obviously, the second estimation step
achieved only minor improvements. Visual inspection confirms that only slight improvements in model
match could be attained by tuning all nine model parameters around their calculated and initially
estimated values.
3.1.4.4 Model Reduction
The linearized models are saved as state-space models with three inputs, one output and 45 states, as
there are three chambers each having 15 states (three slices per chamber with 5 integrators associated
with 5 temperatures). It is likely that not all of these states are essential, so model reduction could
allow for efficient hardware implementation. The given in this report use the full model order, but an
analysis showed to what degree model reduction could be employed so that constrained memory and
computational performance of embedded controllers would not pose a problem.
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In order to determine the relative amount of energy per state, a Hankel singular value decomposition of
the high-flow model revealed that only the first six of the 45 states significantly contribute to the
input/output behavior of the TWH, as can be seen in Figure 17. Consequently, a sixth-order
approximation is created in which only the first six states are retained using a reduced-order
approximation of the linear time invariant (LTI) system.
Figure 17: Hankel singular value decomposition showing relative energy per state
To assess the error introduced through the model reduction, the Bode diagram in Figure 18 shows the
original 45th-order model in solid lines and the reduced 6th-order model in dashed lines. The
magnitude portion reveals that the magnitude of both models in all three input variables drops by 40-60
dB for excitations up 1 Hz, indicating that the tankless water heater is a slow dynamic system. The point
at which the reduced-order model deviates from the original model occurs when the magnitude of the
full-order model response has become negligible (-50 dB and less). The phase portion of the Bode
diagram also shows that both models are basically in phase for the relevant portion of the forcing
frequency (< 1 Hz). In summary, a reduced-order model would be perfectly appropriate for use in a
MPC-based TWH controller.
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Figure 18: Bode diagram comparing full-order with reduced-order model
With the model completed and validated with experimental results, it was then implemented into a
MPC control algorithm.
3.1.5 Development Environment
The overall model predictive controller design is supported by a commercial tool chain that enables
rapid prototyping of the desired accurate TWH controller. The development environment consists of the
following elements employed sequentially:
a) The TWH model development is conducted in Simulink, while the parameter estimation
and subsequent validation is achieved with an associated optimization routine in
Matlab.
b) Simulink is extended by a toolbox for the design of model predictive controllers (MPC
Toolbox 2007). The MPC design entails creating linearized plant models at one or
several water flow rates. Because of the nonlinearity caused by the variation in TWH
water flow rate, a high-flow and a low-flow plant model are created. The measured
flow rate triggers which model the MPC controller uses, in what is called a bumpless
transfer design.
c) Once the MPC has been tuned in simulation, rapid control prototyping is accomplished
with the help of a further extension for Simulink that automatically generates, packages,
DE-FC26-05NT42327 Final Report: Development of an Accurate Feed-Forward Temperature Control Tankless Water Heater
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and compiles source code from the block models to create real-time software
applications on a variety of systems (Real-Time Workshop 2007). This extension
provides automatic code generation tailored to a variety of target platforms, a rapid and
direct path from system design to implementation, and a simple graphical user interface
with an open architecture.
d) Finally, a target platform, xPC Target 2007, was used for microcontroller evaluation. The
target platform is a solution for prototyping, testing, and deploying real-time systems
using standard personal computer (PC) hardware. It is an environment that uses a
target PC, separate from a host PC, for running real-time applications. In this
environment, one uses a desktop computer as a host PC with the above mentioned
tools to create a model using blocks. After creating the model, one can run simulations
in nonreal time. The executable code is downloaded from the host PC to the target PC
running the hardware target real-time kernel. After downloading the executable code,
one can run and test the target TWH control application in real time in the laboratory
setting. The interaction of these tools is shown in Figure 19, below.
Host Computer
Dynamic Model
of Tankless
Water Heater
Model Predictive
Control Toolbox
Target Computer
Real Time
Workshop
Toolbox
Water Heater
xPC Target
Control Algorithm
Configuration
Figure 19: Software and hardware setup for rapid controller prototyping and development
e) The same tool chain could be used to develop production code for embedded microcontrollers selected for the large-scale production of the accurately controlled TWH.
Part of the reason this approach was chosen was to provide a streamlined path to
production, with rapid modifications for different physical heater configurations.
This development environment has been put assembled to allow for rapid accommodation of changes
to hardware and software that are inevitable in a project of this nature. Each element is modular, so
that it may be switched out easily. In Figure 20 the system is shown testing a particular control and heat
exchanger combination. The heat exchanger is bolted to the water carrying system (3 parallel tubes,
upper right), but the TRIACs controlling the power to the heating elements are located on a separate
panel with the fusing, to the left of the heat exchanger. A different heat exchanger can be substituted
very easily. The target computer is black; the host computer is located behind the monitor and
keyboard.
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Figure 20: Development platform
3.1.6 Performance comparison of MPC and existing controller
The physical TWH was subjected to the 11 test series described in Table 3 while being controlled by the
existing PID controller, and while being controlled by the MPC controller. The ISE criterion was
evaluated for each of these tests, with the results shown in Table 4 below. Table 4(a) shows the results
of flow rate step changes, and Table 4(b) shows the results of inlet water temperature step changes.
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Table 4: ISE results for existing controller and MPC controller
(a)
Flow rate (L/min)
Test # Initial
Final
1
2
8
2
8
2
3
4
8
4
8
4
5
0
2
6
0
4
7
0
8
(b)
ISE (K²s)
Existing MPC
2271
184
5038 2544
748
99
1229
219
8607 7568
5159 4956
5146 3695
T inlet
Test # Step (K)
8
+5
9
-5
10
+15
11
-15
ISE (K²s)
Existing MPC
53
25
64
26
510
114
511
150
The table shows that the MPC controller substantially reduces the error for this TWH in most of the 11
tests. In other tests the MPC performs only slightly better than the original PID controller, such as Test #
6. In this test, and Tests 5 and 7, the flow rate is initially 0, and the heater is at room temperature.
There is a significant time lag before hot water flows from the heater because of the thermal
capacitance of the water and heater. Unheated water initially is purged from the heater, and combined
with the time lag this gives a large error, regardless of the control technique. This is illustrated in Figure
21, which shows the MPC controller’s result to Test 7. (This plot is from a later prototype with a nominal
30 kW capacity, for which no PID controller ever existed. The results in Table 4 are a comparison of PID
and MPC control for the same 18 kW heater, which gives a more meaningful comparison than for two
different heaters. The flow step for Test 6 in the larger heater is scaled accordingly, with a final flow
rate of 12 L/min, instead of 6 L/min.)
At t = 0 the controller gives full power (red line) and continues full power until shortly before the
temperature (green line) reaches setpoint. This is the best possible action – it brings the temperature
up as rapidly as is physically possible. After this it gives a small overshoot then remains at setpoint.
However, the ISE is still high because it is heavily dominated by the shaded region on the plot. Thus, the
controller is very close to the theoretical optimal performance.
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60
40
35
50
30
40
25
30
20
15
20
10
Inlet
Outlet
Flow
Power
10
Flow (L/min)
Power (kW)
Temperature (°C)
Setpoint
5
0
0
-10
10
30
Time (seconds)
50
70
Figure 21: MPC controller performance on test 6 - a cold start with 12 L/min flow
Returning to the comparison of PID and MPC control for the same 18 kW heater, Table 4 shows that in
Test # 6 the PID performs almost as well as the MPC controller. The reason for this is that this PID
controller was tuned at 4 L/min – the final flow rate in this test – so it performs quite well at this flow
rate. This suggests that a gain-scheduled controller based on a flow rate input (i.e. one that used a
different set of PID values for several different flow rates) might perform quite well.
The logged temperatures and power for Test # 3 and Test # 4 are shown in Figure 22. In these tests the
TWH is subjected to flow rate steps from 4 to 8 L/min, and from 8 to 4 L/min. In Test # 3 both
controllers experience an initial undershoot after t = 0, where the flow rate step change occurs. This is
caused by the same physical constraint described in Figure 21: water cannot be heated instantly. The
lower part of the plot shows that the MPC controller immediately gives full power for several seconds –
again, the best control action available – and this limits the undershoot to its theoretical minimum;
about 3°C. The PID controller slowly ramps up power in response to the error, but has an undershoot of
about 8°C. Furthermore, the PID controller gives a constant offset error of almost -2°C.
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Figure 22: MPC and PID performance comparisons
In Test # 4, shown on the right side of the figure, the flow rate is stepped from 8 to 4 L/min. A
temperature overshoot is unavoidable because of thermal energy stored in the heater. The MPC
controller rapidly cuts power to zero, to minimize the overshoot. The resulting overshoot is less than
3°C, while the PID controller gives an overshoot of over 10°C. If this overshoot occurred at the end use
(such as a shower supplied by a point-of-use water heater) it would be not only uncomfortable, but
dangerous. The seriousness of this overshoot is reflected in the ISE value associated with this test –
1229 K²/s for the PID controller, compared with 219 K²/s for the MPC controller.
The MPC controller in both plots exhibits similar oscillation to what is expected in PID control. There are
two possible explanations for this. The first is that the discretization of linearized flow regimes is too
coarse (only two are used: low flow and high flow). A second is that there exists a tradeoff between
performance and robustness, just as with PID control, and we opted for performance. Additional work
would likely improve the performance of the MPC controller, if necessary.
The MPC controller was found to have a lower maximum error and a lower steady state offset for each
of the 11 tests.
3.2 Assessment of alternative control techniques
The development of the MPC controller described in the previous section can be seen as a benchmark.
It is the best control for the TWH application that can be achieved practically. An analysis of the
theoretical best control would be of little use; just as a model that has not been validated
experimentally is of little use.
Besides the control performance results of the MPC controller, two important insights were gained:
DE-FC26-05NT42327 Final Report: Development of an Accurate Feed-Forward Temperature Control Tankless Water Heater
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1) Control for the TWH application is less straightforward than one might assume. Unknown
disturbances are more significant and numerous than was anticipated.
2) Development of an MPC controller is far more difficult than was anticipated.
The sponsors of this project have emphasized that a successful outcome is an application that is brought
to the marketplace. Implicit in this message is that the results of this project are better if they can be
exploited by many (or all) manufacturers of TWH than if only one manufacturer adopts them. Having
developed an MPC controller our assessment is that few, if any, TWH manufacturers have the necessary
expertise or development capital to develop MPC control for their own heaters, or to contract the work
out. Therefore, our next step was to use the MPC result as a benchmark and to assess several simpler
control methodologies to compare them with MPC. One approach, described below, turned out to
provide excellent control – comparable, and in some cases better than MPC – with a far simpler
algorithm. The algorithm is one that most, or all, TWH manufacturers are likely to be able to implement.
This work was beyond the scope of the Cooperative Agreement from DOE, but obviously it leverages the
overall success of the project vastly.
3.2.1 Control Approaches
Seven control approaches were investigated, including the previously discussed MPC and the existing
controller. These approaches are
1.
The original (off the shelf) controller of Keltech, used in their Acutemp product line. This
controller uses PID feedback control tuned with Keltech’s own approach.
2.
PID feedback control, tuned to the Chien-Hrones-Reswick tuning rules, and tuned at a flow
rate at the midpoint of the flow range.
3.
PID feedback control as in 2, but gain-scheduled (tuned to a low flow and to a high flow,
with a bumpless transfer between the two sets of PID values.
4.
PID feedback control, tuned optimally. The optimization minimized the ISE. This controller
was also gain-scheduled to two flow rates, as in controller 3.
5.
Simple Feed-forward
6.
Feedback-Compensated Feed-forward with optimal feedback compensation. In this
approach the control action is calculated by combining the feed-forward value with a PID
correction value. The feedback compensation was tuned to minimize the ISE.
7.
Model Predictive Control
The seven control approaches were tested on the 18 kW heating unit that has been the subject of most
of the work described above. The development system, shown in Figure 19, was used for each
DE-FC26-05NT42327 Final Report: Development of an Accurate Feed-Forward Temperature Control Tankless Water Heater
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controller. This allowed each new controller to be programmed into the host computer – often with as
little as 4 or 5 lines of code – then downloaded onto the target computer, which behaves as a virtual
microcontroller. Without having the development platform in place this assessment would have been
more time-consuming: each controller would need to be programmed to a microcontroller, which
would then be wired into the controller chassis of the TWH to connect it with the inputs (temperature
and flow sensors) and outputs (TRIAC signal).
Each controller was then tested while it controlled the physical heater during the 11-test performance
protocol, described in Table 3. The results of this testing are summarized below, in Table 5. The control
approaches are numbered as above (in columns) and the tests are numbered as in Table 3 (in rows).
The highlighted values are the lowest (best) ISE score for each test.
Table 5: Summary of ISE results for performance test of seven control approaches
1
Flow Rate (L/min)
Test # Initial
Final
1
2
8
2
8
2
3
4
8
4
8
4
5
0
2
6
0
4
7
0
8
8
9
10
11
TempStep (°C)
5
-5
15
-15
Sum:
Keltech
2271
5038
748
1229
8607
5159
5146
Control Option
3
4
CHR PID
Opt PID
CHR PID bumpless bumpless
1536
270
475
6295
1018
1390
756
753
552
1370
1469
1479
17090
7552
8943
6418
6345
6451
5455
5689
5230
2
5
FF
237
1076
95
351
11502
8275
5602
6
FB comp
FF
170
843
68
180
7656
6288
5600
7
MPC
184
2544
99
219
7568
4956
3695
53
64
510
511
101
71
477
483
76
79
1060
1141
211
181
1164
1042
16
6.7
21
13
17
6.5
18
19
25
26
114
150
29336
40050
25452
27117
27194
20865
19580
At the bottom of the table the results for each heater are summed for the 11-test set. MPC does have
the lowest sum, even though it is the best performer in only two tests. These two tests are flow rate
increases from 0 to 4 or 0 to 8 L/min – a “cold start” situation, such as turning on a shower while no
other hot water devices are being used. In these cases the MPC has sufficient pseudo-intelligence to
give full power immediately until it anticipates that an overshoot would occur in the future then backs
off the power to avoid this overshoot.
However, for a cold start scenario in a typical house, a quantity of cold water is expected because the
pipes must be purged with hot water (and the copper pipe heated) before hot water arrives at the end
use. Therefore these tests should be considered less important than others that might involve a user
already in a water stream when a flow change happens.
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The conclusion from these results is that the Feedback-Compensated Feed-Forward control is the best
approach. This is a surprising result, but it is serendipitous because this approach is so much simpler
than MPC.
Some other notes or observations about Table 5:
1.
There is a minimum ISE in each case, based on physical constraints (i.e. a zero score is
physically impossible). In many cases where there are multiple best performers in the same
range, they are all very near this minimum.
2.
The Keltech heater performs much better than the CHR-tuned PID. This is essentially the
best performance that can possibly be achieved with PID only. (Cases 3 and 4 have
scheduling, wherein there are essentially two different PID controllers that are tuned at
different flow rates (high and low), with a bumpless transition program between the two.
This cannot be implemented by a simple PID controller, and requires a flow sensor.)
3.
Step changes in inlet temperature are more easily handled by all controllers because the
temperature is sensed upstream of the heat; in the time it takes the water to pass through
the heater many control actions can be taken.
3.2.1.1 Feedback Compensated Feed-Forward Control
In light of the superior performance of control approach 6 – Feedback-Compensated Feed-Forward
(FBCFF), the specifics of this approach will be explained in greater detail.
FBCFF requires a compensation scheme to be developed. This controller starts with a simple feedforward calculation (the First Law of Thermodynamics: q = m Cp T where q is the rate that heat that
must be added, m is the mass flow rate, Cp is specific heat, and T is the difference between inlet and
desired water temperatures). To compensate for dynamics (non-steady-state conditions), variations in
voltage, and error in the flow sensor, a PID feedback loop is added.
The feed-forward and feedback terms are added to give the total control output. We developed a
system for combining these control approaches, although it is likely that this system or other systems
exist in the literature. Our system is shown schematically in Figure 23.
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Gain
flow rate (lps)2
PID
FF Power 1
Controller
Sp
Disturbance Step
-K40
SETPOINT
-KCp water
SP Switch
FF Power
W to kW
Saturation 1
Vdot
Twi
Twi
Disturbance Step
Two
Twi Switch
Qdots
Med Flow Model
20
Twi
Scope
1/60
flow rate (lps)
Vdot
Disturbance Step
Vdot Switch
6
Constant Vdot
Figure 23: Simulink block diagram of Feedback Compensated Feed Forward Controller
Since the sensitivity of the controller will increase as flow increases, the feedback component is
multiplied by the flow rate. We have optimized the tuning parameters of the feedback portion to give
the minimum combined ISE value.
3.3 Hardware Development
Keltech’s existing heater used analog controls, and since it used feedback control only, it had no inlet
temperature sensor and no flow rate sensor. Thus, the hardware had to be changed significantly to
accommodate the improved control approach.
The final design of the electrical system is shown schematically in Figure 24.
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SAFETY GND / EARTH
Green
Terminal
Block
220V AC INPUT
Red
Terminal
Block
220V AC INPUT
GND
LUG
Water Outlet
POWER BOARD
Terminal
Block Black
Outlet
RTD
Heater
Water Flow
Remote 1
Remote 2
MT2
Outlet RTD
MT1
Inlet RTD
MT2
Flow
Sensor
MT2
4 conductor cable
MT2
REMOTE #2
+12V Power
GND
TX
RX
MT1
Gate
MAIN CONTROL BOARD
4 conductor cable
Heater
MT1
Gate
TRIAC Gates
AC In 1
MT1
Gate
REMOTE #1
+12V Power
GND
TX
RX
TRIACs
AC In 2
Gate
Black
AC
White
Heater
Heater
Inlet
RTD
Flow
Meter
+5V Power
GND
Flow Sensor
Water Inlet
3 conductor cable
Figure 24: Schematic design of electrical system
3.3.1 Heat Exchanger
Since the control performance is affected by the heat exchanger (volume of water in tubes, thermal
mass of system, convection and mixing conditions caused by flow configuration, etc.) a holistic approach
needed to be taken in developing the improved prototype. Furthermore, a secondary goal of this
project is to develop an improved-control TWH without imposing a significant cost premium, so the heat
exchanger design was modified during the project. A preliminary prototype is shown in Figure 25 with
labels.
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Figure 25: Preliminary prototype heat exchanger
The flow is in a serpentine configuration. Cast bronze headers in the preliminary prototype were costly
and added thermal mass to the system. Also, they were not scalable. The final prototype has a modular
design so that any number of passes can be connected (each with a 7.5 kW heater). It is not shown here
because of proprietary technology belonging to Keltech.
Part of the rationale behind developing a modular design came from the DOE Peer Review of this
project. The reviewers felt it was important that the application of the results of this project be
available for booster heaters for solar and heat pump water heaters. The booster’s power requirements
can vary significantly, suggesting that a modular design would best address this requirement.
Another issue stemming from the peer review was that this project’s results should be ready to apply to
point-of-use water heaters, because they have the potential to save a great deal of energy. The reason
is that distribution losses are significant, wasting typically at least 10-20%, and often 50% of total water
heating energy [ASHRAE 2007; Baskin et al. 2004; Hiller 2005]. These losses apply whether the water
heating system is high efficiency, solar, heat pump, condensing gas combustion, etc. However, these
losses are not present (or are minimal) with point-of-use heaters. In most cases electric resistance is the
only practical alternative for point-of-use heaters. In light of this, we continually made sure that the
approach for this project will apply to point-of-use heating, including the use of a modular design.
3.3.2 Microcontrollers
Two separate, but communicating controllers are used in the final product: the main board and the
remote board(s).
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3.3.2.1 Main Board
The system shown in Figure 24 has a “Main Board”, which contains the microcontroller that runs the
control program, receives input from the sensors, sends output signals to the TRIACs, and communicates
with the remote boards. The remote board prototype that was developed is shown in Figure 26 below.
The printed circuit board (PCB) is labeled with the various inputs and outputs. A temperature unit
switch (to display °C or °F) is configurable by the assembler (not user). Some resistors and LEDs on the
right were being used for testing when the photo was taken.
Figure 26: Main board prototype
This main board connects via a serial communication connector (on the left) to the remote board(s).
The microprocessor can be programmed by connecting to a computer via the 6 pin ISP connection at the
bottom center of the photograph.
3.3.2.2 Remote board
One or two remote boards connect to the main board. The remote boards contain the user interface.
One is normally located on the unit’s cover. The second optional remote board can be located in a
bathroom, kitchen, or some central location. This second board can be wired or wireless. The
prototype remote board is shown below, in Figure 27. The front has labels silkscreened on it to
correspond with the button switches that will be put there: Flow Rate, Inlet Temp, Outlet Temp, Up,
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and Down. The latter two are used to change the outlet temperature setpoint. The first three control
which quantity is shown on the display. If no button is depressed, the display shows the temperature
setpoint.
Figure 27: Remote board
3.3.3 Sensors
Inlet and outlet temperature are measured using RTDs. These sensors are unchanged from the currently
existing heater (except that there are two instead of one).
Flow rate is more challenging to measure, for several reasons. Flow sensors can be very expensive
depending on the sensor type and desired accuracy. They must be able to handle water with varying
impurities and often carrying sediment without losing accuracy over time. They must give signals quite
rapidly. The final selection for a flow sensor is a Hall-effect turbine sensor. This sensor is custom
manufactured to have additional magnets to give higher frequency signals.
The accuracy of this production sensor was compared with our laboratory-grade sensor. The production
sensor gives periodic pulse signals to indicate flow rate. The main board has signal conditioning
algorithms programmed into it to interpret the periodic pulse signals being received and translate them
into a flow rate. Figure 28 shows the comparison of the two sensors; the production sensor behaves
extremely well, showing excellent repeatability even in the low flow range (below its specified range).
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50
45
y = 9.568x - 0.331
R2 = 0.9997
40
Frequency (Hz)
35
30
25
20
15
10
5
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Flow (gpm)
Figure 28: Comparison of production and laboratory flow sensors
3.3.4 Packaging
The new heaters have been repackaged because of the changes to all of their components. The design
of the new packaging is complete, and an electronic rendering is shown below in Figure 29, with cover
and without cover. The new design accommodates the flow sensor’s requirement of a straight length of
pipe, uses a small loop of unheated water to cool electronic components, and supports the new modular
header design. The prototype model has a 30 kW capacity, which is sufficient for whole-house water
heating for a large portion of houses in the US.
An unusual feature of the unit’s design is that it uses internal fusing for overcurrent projection, rather
than using the circuit breakers in the electrical panel. If the unit was not internally fused the heating
elements would need to be on individual 30 Amp breakers. Using multiple breakers would typically
increase the installation cost, whereas using internal fusing increases the manufacturing cost. Keltech’s
belief is that the option with the lowest cost for the consumer – combined cost of installation and
manufacture – is the best choice, hence their decision to internally fuse. This is rare or perhaps unique
in the electric TWH currently on the market.
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Figure 29: Heater packaging design
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4. Project Administration
4.1 Budget
The project was completed within the budget allocated by the cooperative agreement. No additional
funding was requested. A breakdown of how the budget was allocated by category in the cooperative
agreement is shown below in Table 6. The actual expenditures for the project are shown in Table 7.
Table 6: Total approved budget proposed
a. Personnel
b. Fringe Benefits
c. Travel
d. Equipment
e. Supplies
f. Contractual
g. Construction
h. Other
i. Total Direct Charges
j. Indirect Charges
k. TOTALS
Federal
Non-Federal
137361
2039
0
0
8050
98
12124
0
986
14
53590
87399
212111
152470
364581
89550
2264
91814
Total
139400
0
8148
12124
1000
140989
0
0
301661
154734
456395
Table 7: Actual expenditures
a. Personnel
b. Fringe Benefits
c. Travel
d. Equipment
e. Supplies
f. Contractual
g. Construction
h. Other
i. Total Direct Charges
j. Indirect Charges
k. TOTALS
Federal Non-Federal
149043
0
0
0
4429
0
15248
0
3442
0
29183
152788
201345
163236
364581
152788
2202
154990
Total
149043
0
4429
15248
3442
181971
354133
165438
519571
4.1.1 Differences between proposed and actual expenditures
The approved budget in the cooperative agreement included non-federal cost sharing of 20% of the
total project cost. During the project additional opportunities for improvement presented themselves,
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and Keltech became increasingly committed to the project. These opportunities increased the scope of
work for Keltech and for BSI.
Keltech increased their effort in the project from $87k to $153k – a 75% increase. This brought their
total cost sharing portion to 30%. It also illustrates their commitment to the goals of this project.
BSI was constrained by a finite budget so we made several adjustments to complete the original tasks
and the additional opportunities within the approved total budgeted amount of $365k. For example, we
found that during the execution of the project tasks we had developed sufficient in-house expertise that
some of the work intended to be subcontracted could be completed in-house. Since our rates are quite
low, this reduced the cost of these portions of the work. Thus the personnel costs, line a, increased and
the federal portion of contractual costs, line f, decreased. In addition, our subcontractors, Dr. Gregor
Henze and Mike Coward, kindly agreed to substantial increases in scope without increasing their fees.
4.2 Schedule
This project was originally planned to be completed in a two-year period, from 07/01/05 to 6/30/07, but
a no-cost extension of an additional year was required, with the project ending 6/30/08. There were
numerous unexpected setbacks in the project that required additional time, but these are present in
almost every research project and to some extent they had been budgeted for. The most significant
delays were caused by the following
1. No existing method of test for tankless water heater control performance. We had anticipated
that a literature review would reveal some reference to an approach to measure temperature
control in TWH or in a similar application. We planned adapt this reference to be used in a
temperature control method of test for TWH, but none was discovered so we had to fully
develop the method of test and apparatus to conduct it.
2. Modified approach to controller testing and development platform. At the suggestion of
subcontractor Dr. Gregor Henze the rapid prototype development platform was built. This
improved the quality of the final product because it allowed rapid assessment of different
approaches combined with different microcontroller hardware. However it took a great deal
more effort that the original plan, which was to develop the control entirely in the simulation
environment, subcontract the selection and programming of a microcontroller, and install the
microprocessor into the prototype heater. The rapid prototype development encountered
problems in software compatibility and with software bugs. It stalled the project for six months
before it worked for the first time. However, once it worked it was used to test hundreds of
possibilities whereas the original plan would have allowed only a few to be tested.
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3. Health problems with manufacturing partner. Ken Lutz, founder and chief technical engineer at
Keltech suffered a serious heart problem and was away from work for three months, before
returning to work for only a few hours per week. Mr. Lutz is our main contact at Keltech, and is
responsible for all new product development there. Although we continued to work on the
project while he recuperated we weren’t able to proceed at a full pace because some decisions
needed to be made by the manufacturer who will be using the results in his product for many
years.
4. Other increases to scope. There were several opportunities that presented themselves, as
mentioned above, that could greatly increase the usefulness of the project’s results. These also
tend to increase the scope of work. One example is the testing of additional control approaches
besides MPC. This had not been planned but it turned out to produce some of the most
powerful results of the project, because it showed that a simpler alternative control method can
provide results comparable to the highly complex MPC. Such increases to scope increased the
time required to complete the project.
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5. Final Results
5.1 Product
The central result of this project is a new Keltech heater that will be marketed starting in spring of 2009.
This heater is shown in Figure 29. It will be the premier electric TWH, with the best control performance
of any consumer TWH available, robust components, compact size and sold in the mid-market price
range.
5.2 Objectives and outcomes
This project was very successful in achieving its goals and in providing unanticipated positive outcomes.
Table 1 gave a list of criteria for success. Table 8 compares these criteria with the actual outcomes of
the project. A brief discussion of these criteria and the outcomes follows the table.
Table 8: Objectives and outcomes
Objective
Develop a test method
Develop a rating system
Develop an improved TWH
controller
Include controller in
manufacturable prototype
Impose minimal cost premium
Disseminate results
Criterion for success
Ability to quantify control
performance
Ability to meaningfully quantify better
performance
A working controller that improves
control
A prototype that is ready for mass
production
Increase overall cost by < 5%
Published papers or public
presentations
Outcome
A MOT was developed and refined
Developed a system using the ISE
criterion for 11-test set
New controller gives far better control
and other benefits
Done. Prototype heater was also
improved
Cost was not increased at all
Multiple papers and presentations
The development of a test method may be one of the most important results of this project. The reason
is that the test method can help usher in better temperature control throughout the industry by helping
manufacturers assess their control performance, know where improvements are needed, and quantify
the improvement (or damage) caused by changes to their approach. Furthermore, if the method of test
and rating system developed in this project lead to a rating standard for consumers, this will encourage
all TWH manufacturers to improve control. Once good control is standard in TWH, a significant barrier
to widespread adoption will have been removed.
Goals
Outcomes
1 Improve control for Keltech heater
Big improvement
2 Develop method to quantify control
Developed and refined
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The controller developed in this project uses the Feedback-Compensated Feed-Forward control
algorithm described earlier. Its control performance is vastly improved, as was shown in Table 5. The
results in Table 4 are for the 18 kW development model, but the final production model is a 30 kW
model. The ISE results of this unit are given in Table 9 below. Unfortunately, ISE results by themselves
do not give a very good comparison for different sized heaters. For example, a larger heater holds a
larger volume of water, typically, and will produce a larger plug of cool water before the heated water
enters the supply pipe. The cold start tests (5-7) will, therefore, give higher ISE values for larger heaters.
A system could be devised to normalize across sizes to give reasonable comparisons. This is discussed
further under “Future Work”. Regardless, the results below indicate excellent temperature control.
Table 9: ISE results for final (production model) 30 kW TWH
Flow Rate [L/min]
Test #
1
2
3
4
5
6
7
Initial
3
12
6
12
0
0
0
8
9
10
11
Step
[°C]
5
-5
15
-15
Final
12
3
12
6
3
6
12
Total
ISE
[K²-s]
247
680
117
152
12221
6274
4653
ISE
K²-s
13
14
83
50
24504
An additional successful outcome for the project is the finding that the Feedback-Compensated FeedForward control approach can provide superior control. This approach is simple enough for most
manufacturers to use, so it is likely to be adopted by many manufacturers once the results of this
project are disseminated through the technology transfer activities described later in this report.
The new controller gives additional benefits besides improved control:
1. Several fault detection and diagnosis routines have been programmed into the controller to
increase safety and ease repair. The specifics of these routines are considered proprietary by
Keltech.
2. The TRIAC control uses a proprietary routine that was devised to spread the electric load evenly
over time to avoid “flicker factor” – the flickering of lights caused by rapid variations in system
voltage, which is a common problem in electric TWH (or other large switched electric loads).
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3. The controller has been configured to allow two user-interfaces, so that a remote secondary
user interface may be placed in a location near an end-use, such as in a bathroom.
We had assumed that the cost would increase for the improved controller. However, through careful
design and component selection the cost of the production line of heaters is roughly the same as the
previous generation, which used analog controls, and may be slightly less when bulk pricing of
components is finalized.
The dissemination of results is discussed under “Technology Transfer”, below.
5.3 Technology Transfer
5.3.1 Papers
A paper [Henze 2009] on the results of this project will be published in HVAC&R Research on January 2,
2009. This paper discusses the use of Model Predictive Control for TWH.
A second paper is in progress and will be submitted in January. This paper describes the alternative
control approaches tested in this project, and the results of the tests.
A third paper will describe the development of a method of test for temperature control of TWH, and
the design of the test system. This paper is not yet in progress.
A fourth paper is planned; an engineering overview of TWH technology. This is intended for a broader
but still technical audience, such as ASHRAE Journal, Engineered Systems, etc.
5.3.2 Presentations
“Improving Temperature Control in Electric Tankless Water Heaters,” Seminar at ASHRAE in Dallas,
Winter 2007 by Gren Yuill
“A Method of Test for Tankless Water Heater Temperature Control Performance,” Seminar at ASHRAE in
Dallas, Winter 2007 by David Yuill
“A Comparison of Advanced Control Methods for a Thermal Process,” seminar to be proposed by David
Yuill for ASHRAE Annual meeting, Louisville, KY, 2009.
“Applying Model Predictive Control,” seminar to be proposed by Gregor Henze for ASHRAE Annual
meeting, Louisville, KY, 2009.
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5.4 Future work
Several ideas for future work that would benefit the US have presented themselves during the execution
of this project.
5.4.1 Refinement of the test method to a standard method of test
This would include a weighting system to give the ISE scores for each test different weights, depending
on how important each test is to the comfort and safety of users. Then, the weighted scores should be
combined in such a way that a simpler single number, or perhaps alpha-number rating could be
expressed for laypersons (particularly consumers). It would also include a way to scale the overall
scores for different sized heaters so that the same rating system could be used regardless of the heater
size.
Finally, it would be prudent to conduct some temperature control performance tests on gas-fired
tankless water heaters. All of the performance testing conducted so far has been for electric heaters.
Gas TWH may present some unanticipated artifact of control that should be taken into account before
the rating system is developed. The method of test and rating system should cover all TWH regardless
of energy source, so that consumers can make fair comparisons.
The publication of a standard and rating system would encourage and allow manufacturers to improve
control of their heaters. This, in turn, would help foster the adoption of TWH in the USA. ASHRAE has
members that are interested in developing this standard when the necessary work is complete. The
method of test also may be used by the Energy Star program as a rating criterion.
5.4.2 Peak power issues
Two issues related to peak electrical power usage suggest further work.
5.4.2.1 Development of a current transformer load-shedding device
One significant barrier to adoption of electric TWH is the large power requirement. The power drawn by
a TWH is often greater than all other electric appliances combined. It means that larger electrical panels
and conductors are required. During this project we conceived of an idea to include with the TWH a
current transformer (CT) that would send a signal to the TWH controller. The CT would monitor wholehouse power and when the signal got to a maximum value (such as 190 Amps for a 200 Amp panel) the
TWH would attenuate its power to avoid exceeding the maximum.
The effect would be that during the rare occasion when, for example, the air-conditioning is running,
electric stove is in use, electric dryer is running, and two simultaneous showers are being taken, the
water in the showers would get cooler until the air-conditioning cycled off or one shower stopped, etc.
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The TWH is an excellent candidate for load shedding because it can be attenuated and because it is a
large user that would likely be able to reduce power sufficiently with a single piece of equipment.
We began to proceed with development of this product, but a patent search showed that a TWH
manufacturer has already patented such a device. Regardless of intellectual property rights, it would be
useful for this product to be available in the marketplace, particularly if it can be used for multiple
manufacturers’ TWH.
5.4.2.2 Utility Peak Power Concerns
We have met with representatives from some large electrical utilities during this project who have
voiced concerns over widespread adoption of TWH. Their fear is that transformers will be overloaded
by high demand during the morning peak (when many homeowners are showering). Even if the
transformer’s peak capacity is not exceeded, coming near to this capacity frequently reduces the life of
the transformer.
A study by Johnson and Clark (2006) showed that it requires very little diversity for TWH to give the
same peak load profile as storage heaters. Their study monitored one house that switched between
electric storage and TWH heater on a weekly basis for several months. They superimposed the
instantaneous power data from multiple days to simulate multiple homes on a single day. This would
likely give a less diverse profile than if multiple homes were monitored, because the morning routine in
a single home is likely to repeat more exactly (showering at the same time every day). It would be
useful to conduct a similar study to Johnson and Clark’s but with a larger number of houses and more
rigorous measurement approach. The results would allow utilities to assess potential benefits and costs
of widespread TWH adoption, and to consider solutions to any anticipated problems.
5.4.3 Gas TWH control performance
Anecdotal evidence suggests that some gas TWH experience similar control problems to electric TWH.
Measurement of a small number of gas TWH would show the extent of the control difficulty. If similar
control problems exist in gas TWH as in electric TWH the results of the current project could be adapted
to apply to gas TWH, which constitute a larger portion of the market than electric. This would leverage
the successes of the current project to reach a broader market.
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6. References Cited
ASHRAE, 2007. HVAC Applications Handbook. Chapter 49.
Baskin, E., R. Wendt, R. Lenarduzzi, and K. A. Woodbury, 2004. Numerical Evaluation of Alternative
Residential Hot Water Distribution Systems. ASHRAE Transactions, Vol. 110 Issue 2, pp. 671-681.
Haissig, C.M., and M. Woessner, 2000. An Adaptive Fuzzy Algorithm for Domestic Hot Water
Temperature Control of a Combi-Boiler. HVAC&R Research, 6(2): 117-134.
Herrmann, C., V. Candas, A. Hoeft, and I. Garreaude, 1994. Humans Under Showers: Thermal Sensitivity,
Thermoneutral Sensations, and Comfort Estimates. Physiology & Behavior, Vol. 56, No. 5, pp. 10031008.
Henze, G.P., D.P. Yuill, and A.H. Coward, 2009. Development of a Model Predictive Controller for
Tankless Water Heaters. HVAC&R Research, Vol. 15, No. 1.
Hiller, C.C., 2005. Comparing water heater vs. hot water distribution system energy losses. ASHRAE
Transactions 111(2): 407-417.
Johnson, R.K., and C.A. Clark, 2006. Field Evaluation of Two Demand Electric Water Heaters. ASHRAE
Transactions, 112(1): 426-435.
Maciejowski, J. M., 2002. Predictive Control with Constraints. Pearson Education POD.
Ohnaka, T., Y. Tochihara and Y. Watanabe, 1994. The effects of variation in body temperature on the
preferred water temperature and flow rate during showering. Ergonomics, 37(3): 541-6.
Rohles, F.H. and S.A. Konz, 1982. Showering behavior: Implications for water and energy conservation.
ASHRAE Transactions, 88(1): 1063-1072.
U.S. Department of Energy, 2001. A Look at Residential Energy Consumption in 2001. Energy
Information Administration.
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