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NBS BUILDING SCIENCE SERIES 150

Low-Voltage

Room Thermostat

Performance

U.S. DEPARTMENT OF COMMERCE • NATIONAL BUREAU OF STANDARDS
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act of Congress on March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology

and facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau's technical work is per- formed by the National Measurement Laboratory, the National Engineering Laboratory, and

the Institute for Computer Sciences and Technology.

THE NATIONAL MEASUREMENT LABORATORY provides the national system of

physical and chemical and materials measurement; coordinates the system with measurement

systems of other nations and furnishes essential services leading to accurate and uniform

physical and chemical measurement throughout the Nation's scientific community, industry,

and commerce; conducts materials research leading to improved methods of measurement,

standards, and data on the properties of materials needed by industry, commerce, educational

institutions, and Government; provides advisory and research services to other Government

agencies; develops, produces, and distributes Standard Reference Materials; and provides

calibration services. The Laboratory consists of the following centers:

Absolute Physical Quantities'^ — Radiation Research — Chemical Physics —

Analytical Chemistry — Materials Science

THE NATIONAL ENGINEERING LABORATORY provides technology and technical ser- vices to the public and private sectors to address national needs and to solve national problems; conducts research in engineering and applied science in support of these efforts; builds and maintains competence in the necessary disciplines required to carry out this research and technical service; develops engineering data and measurement capabilities;

provides engineering measurement traceability services; develops test methods and proposes

engineering standards and code changes; develops and proposes new engineering practices;

and develops and improves mechanisms to transfer results of its research to the ultimate user. The Laboratory consists of the following centers:

Applied Mathematics — Electronics and Electrical Engineering^ — Manufacturing

Engineering — Building Technology — Fire Research — Chemical Engineering^

THE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts

research and provides scientific and technical services to aid Federal agencies in the selection,

acquisition, application, and use of computer technology to improve effectiveness and

economy in Government operations in accordance with Public Law 89-306 (40 U.S.C. 759), relevant Executive Orders, and other directives; carries out this mission by managing the Federal Information Processing Standards Program, developing Federal ADP standards

guidelines, and managing Federal participation in ADP voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal agencies; and

provides the technical foundation for computer-related policies of the Federal Government.

The Institute consists of the following centers:

Programming Science and Technology — Computer Systems Engineering.

'Headquarters and Laboratories at Gaithersburg, MD, unless otherwise noted; mailing address Washington, DC 20234. ^Some divisions within the center are located at Boulder, CO 80303.
NBS BUILDING SCIENCE SERIES 150

Low-Voltage Room

Thermostat Performance

MAY 1 7 no :

' : -

James Y. Kao

George Sushinsky

David A. Didion

Center for Building Technology

National Engineering Laboratory

National Bureau of Standards

Washington, DC 20234

E.J. Mastascusa

and

Bucknell University

Lewisburg, PA 17837

Joseph Chi HCP Systems

Rockville, MD 20850

Sponsored by the

Office of Building Research and Development

U.S. Department of Energy

and the

Civil Engineering Laboratory

U.S. Naval Construction Battalion Center

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Director

Issued April 1983
Library of Congress Catalog Card Number: 83-600505

National Bureau of Standards Building Science Series 150

Natl. Bur. Stand. (U.S.), Bldg. Sci. Ser. 150, 46 pages (Apr. 1983)

CODEN: BSSNBV

U.S. GOVERNMENT PRINTING OFFICE WASHINGTON: 1983

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402

Price $4.75

(Add 25 percent for other than U.S. mailing)
ABSTRACT

To predict performance of low voltage electric thermostats in a dynamic

building system, a computer model representing two types of thermal feedback, was developed. Unlike the information obtained from existing test standards,

this model allows thermostat performance to be determined under any load con- ditions. As input to the model, the basic parameters of thermostat performance were first identified and then determined experimentally in a controlled

laboratory facility. The experimental results from the tests were used as input parameters for the simulation model. Based upon the results from the

simulation model and test results on four commercially-available thermostats, a switch-feedback model computer simulation is recommended for studying lowvoltage room thermostat performance.

Key words: room temperature control; temperature controller; thermostat

evaluation; thermostat modeling; thermostat test; two-position

control

iii

TABLE OF CONTENTS

Page

ABSTRACT iii

1. INTRODUCTION 1

2. MECHANICAL THERMOSTATS AND THERMOSTAT MODELS 2 2.1 MECHA1>JICAL THERMOSTAT PHYSICAL DESCRIPTION 2 2.2 CONCEPTUAL MODELS OF MECHANICAL THERMOSTAT PERFORMANCE 2 2.2.1 Bimetal Feedback Model 4

2.2.2 Switch Feedback. Model 6

3. EXPERIMENTAL FACILITIES AND GENERAL TEST PROCEDURES 8

3.1 RATIONALE FOR EXPERIMENTAL EVALUATION 8

3.2 TEST CHAMBER 10

3.3 MEASUREMENT AND CONTROL SYSTEM 13

3.3.1 Digital Ramp Generator 13

3.3.2 Test Logic Unit 13

3.3.3 Temperature Sensing Circuit 15

3.3.4 Proportional Controller 15

3.4 GENERAL TEST PROCEDURES 15

4. RESPONSE EQUATIONS AND MEASUREMENT METHODS FOR OBTAINING THE

VALUES OF THE FOUR THERMOSTAT PARAMETERS 17

4.1 THERMOSTAT COMPONENT RESPONSE ANALYSIS 17

4.2 EQUATIONS REPRESENTING THERMOSTAT RESPONSE 17

4.3 MEASUREMENT METHODS 21

5. COMPUTER MODELING 27

6. RESULTS AND DISCUSSION c 28

7. CONCLUSION 32

REFERENCES 33

APPENDIX A. NEMA STANDARD FOR TESTING THERMOSTAT PERFORMANCE A-1

APPENDIX B. PROGRAM FOR SIMULATING THERMOSTAT PERFORMANCE B-1

V
LIST OF FIGURES

Page

Figure 1. Bimetal feedback model of a thermostat 3

Figure 2. Switch feedback, model of a thermostat 3

Figure 3. Conceptual representation of sensing element

temperature distribution at steady state of a switch

feedback model 7

Figure 4. Air and sensor temperature relationship, and switch

positions to element temperature 9

Figure 5. The thermostat test system 11

Figure 6. Thermostat test chamber 12

Figure 7. Digital ramp generator 14

Figure 8. Sensor response to a slow ramp temperature change 18

Figure 9. Air and sensor temperature under ramp test 23

LIST OF TABLES

Table 1. Nomenclature for Variables Used in Thermostat Models 5

Table 2. Parameter Test Results 28

Table 3. Comparison of Thermostat No. 1 Performance, Experimental

vs. Simulation, Using Different Anticipator Constants

in the Bimetal Feedback Model 29

Table A. Comparison of Thermostat Performance, Experimental vs. Simulations, Thermostat No. 1 30

Table 5. Comparison of Thermostat Performance, Experimental vs. Simulations, Thermostat No. 2 30

Table 6. Comparison of Thermostat Performance, Experimental vs. Simulations, Thermostat No. 3 31

Table 7. Comparison of Thermostat Performance, Experimental vs. Simulations, Thermostat No. A 31

vi
1. INTRODUCTION

Almost all heating and cooling systems installed in residential houses and

small buildings use "on-off" type mechanical thermostats for temperature regulation. The thermostat, an important part of a closed control loop, acts

within a dynamic system created by characteristics of the heating and cooling

plant, the overall thermal characteristics of the building and the load changes — both internal and external — to regulate the space temperature. Although

each component in the loop influences the temperature level and the energy

consumption of the building, as well as occupant comfort, it is particularly

important that the behavior of the themostat be understood and analyzed. To

simulate and predict the performance of the thermostat within a dynamic system

requires a thermostat model that is compatible with dynamic models of the whole

system (plant, building, and load).

The present mechanical thermostat test standard adopted by the National

Electrical Manufacturer's Association (NEMA) [1 & 2]* determines thermostat

performance in an oversimplified dynamic environment. This standard assumes a certain fixed relationship between the heating/cooling plant performance,

building thermal characteristics, and weather variations in which only three

load conditions can be assessed. The NEMA test standard can measure thermostat

performance within fixed constraints, but the results of the NEMA tests cannot

be used to make detailed time—history predictions of the thermostat interactions within a more complex and realistic environment. The need exists for a dynamic, physically oriented model to predict thermostat performance within a complex, dynamic building system.

This report identifies four parameters necessary for predicting thermostat

performance and uses a combination of experimental data and mathematical equations to calculate values of the parameters. These values are used as con- stants in a computer program which simulates thermostat performance, as represented by two different conceptual models, as a function of time and dynamic

variations in the building system. The simulation results predicted from the

two conceptual models are compared with experimental data for four thermostats.

One conceptual model, the switch-feedback, model, is shown to be in closest

agreement with the observed test results.

Numbers in brackets indicate references cited at the end of the report.
2. MECHANICAL THERMOSTATS AND THERMOSTAT MODELS

2.1 MECHANICAL THERMOSTAT PHYSICAL DESCRIPTION

The thermostats covered by the NEMA standards can be described as wall-mounted,

low-voltage room thermostats that control the heating and cooling of a structure. All of these thermostats contain certain functional components including

a temperature sensing element, an on-off signalling and switching mechanism,

and a protective case. Most thermostats also include an anticipating element

(anticipator) which produces local heating of the sensor to increase the system

cycling rate, resulting in reduced space temperature variation, as well as improved thermostat and system performance.

The actual construction of mechanical thermostats varies depending on manufacturer and model. Generally, for cooling applications, most thermostats

have anticipators closely coupled with the sensing elements, with the heat

transfer from the anticipators to the sensing elements occurring mostly by

conduction. Thus, the anticipator can act directly on the thermostat switch

without much delay from the sensor. However, significant differences in thermostat construction occur for the heating mode. These differences require two

different conceptual models for representation — a switch feedback model and

a bimetal feedback model. Some thermostats rely more on conduction heat transfer to transmit heat from the anticipator to the sensor and others depend more

on convective heat transfer from the anticipator to the sensor. The parameters

needed to define these models will be discussed in the next section.

2.2 CONCEPTUAL MODELS OF MECHANICAL THERMOSTAT PERFORMANCE

The basic thermostat with secondary feedback consists of a two-position switch,

a temperature sensor (usually a bimetal strip or coil), and an anticipating

element as described previously. Two conceptual models of the dynamic performance of such thermostats have been used in simulations of residential heating

systems [3, 4, 5, 6]. These models are presented schematically in figures 1

and 2

.

Development of a workable computer simulation for each conceptual model

requires physical (experimental) determination of four basic thermostat parameters. Two parameters can be used to describe the performance of the basic

thermostat components including the sensor, and switching-signalling mechanism.

They are:

• Tgen — the sensing element thermal time constant and, • Ts;^(j — the thermostat switch differential

The sensing element time constant, Tggm is related to the time required for

the thermostat sensing element to reach the temperature of the surrounding air

and may be approximated by a first order response [5]. The switch differential,

Tswd» relates the difference in the switch on or off temperatures, due to switch

design and construction.

2
DTant, ss

Figure 1. Bimetal feedback model of a thermostat

Tida— 1

1

'0

0 rswd

DTant.ss STant +1

Figure 2. Switch feedback model of a thermostat

3
The addition of the anticipating element — usually a small resistive heater — adds the additional two parameters to be considered in the modeling of

thermostat performance, namely:

• T^nt — anticipating element thermal time constant and, • DT^j^j-^gg — the steady-state anticipator temperature rise.

These parameters are somewhat misnamed in that each is a measure of the

anticipator's effect on the sensing and switching element and not singly concerned with the anticipator. All of these parameters are listed and identified

in table 1 along with the nomenclature for other variables that will be used

throughout this report.

In these models, the ambient air influences the thermostat temperature through

a time constant which accounts for the thermal dynamics associated with the

thermal capacitance of the sensor. For heating, when the sensor temperature

^sen' (i^ot the air temperature) rises above Tq + Tg^^j, the thermostat switches

OFF, and the output of the switch block, lOF, is taken as "0". When the sensor temperature falls below the set point, Tq , the thermostat comes ON, calling

for heat, and the output, lOF, goes to "1". The effect of the anticipator

is accounted for with a second time-constant block. The second time constant

is attributed to the thermal dynamics of the anticipator and sensor.

2.2.1 Bimetal Feedback Model

The thermostat model shown in figure 1, identified as the bimetal feedback model,

has been previously used at NBS in control loop analysis of heating and cooling

in residences and small building models. In this model the ambient air (T-^^g)

influences the sensor temperature (Tgg^) through the sensor time constant

(Tggjj). The anticipator, characterized by a second time constant (13^) temperature rise (DT^j^t gg), also acts through the sensor time constant to produce

the localized heating effect on the sensor. The latter two parameters in this

model are defined as those of the air surrounding the sensor.

In the bimetal feedback model, the only way to affect the sensor temperature,

Tggn» is through the sensor time constant, Xggn* This places a fundamental

restriction on the value of the anticipator time constant. In particular, with

a typical sensor time constant around 15 minutes, and an effective anticipator

temperature rise of 4 or 5 degrees, simulations and calculations both show that

the anticipator time constant must be short in order to result in reasonable

cycle rates.

The state equations of the sensor and anticipator for this model are:

*^^sen 1 -Tp^ = (Tida DTant " ^gen) > and sen dDTant 1

^ ' ant

4
Table 1. Nomenclature for Variables Used in Thermostat Models

lOF Variable describing thermostat state, 1 when ON, 0 when OFF

^opd Thermostat operating differential

T^sen Sensor temperature

Tida Room air temperature

Tq Thermostat set point

(Does not necessarily coincide with indication on thermostat)

^swd switch differential of the mechanical switch

''•sen Thermal time constant of the sensor

"^ant Thermal time constant associated with the anticipator (see text)

^"^ant Temperature rise effect of sensor when the anticipator is ON (see

text)

DTg^nt ss Steady-state temperature rise effect of sensor when the anticipator

is on (see text)

t Time

FR Falling temperature ramp rate

RR Rising temperature ramp rate

s The Laplace operator

5
2.2.2 Switch Feedback Model

The block diagram of this model is shown in figure 2. As in the bimetal

feedback model, the ambient air (T^da) influences the sensor temperature (Tggj^)

through the sensor time constant (Tggj^). However, in this model, the anticipator parameters Xant ^^'^ ^^ant defined as the effect of the anticipator on the sensor itself, not to the air surrounding the sensor. The anticipator con- tribution is added directly to the sensor without acting through the time lag

induced by the sensor time constant. Thus, the time required to make the

thermostat switch is much shortened.

In the switch feedback model, the temperature distribution along the sensor at

equilibrium (steady state) would be different for the two excitations. For

the ambient air, a uniform distribution would prevail. For the anticipator a non-uniform distribution would be found. The sketch in figure 3 is a rough

version of what might be found with an anticipator tightly coupled only to the

center support of a coiled spring sensing element.

The state equations of the sensor and anticipator for switch feedback are: ~— ^^ida ~ ^sen,l)»

sen

(lOF X DTant.ss " ^T^anO ^ and

''^ant

'^sen,2 = '^sen,l ^'^ant

In the next sections, a description of the experiments to obtain the values of

the four parameters will be given. The experimental parameter values were then

used in a computer simulation. At the same time the response of several

thermostats to known changes in test chamber conditions were measured. Finally,

the output from the simulation models were compared with experimental results

to determine which conceptual model best predicts thermostat performance in a total system.

dT sen,l _ dt

dDTant _ dt

6
SUPPORT FREE

POST EMD

DISTANCE ALONG SENSOR ELEMENT

Figure 3. Conceptual representation of sensing element temperature

distribution at steady state of a switch feedback model

7
3. EXPERIMENTAL FACILITIES AND GENERAL TEST PROCEDURES

3.1 RATIONALE FOR EXPERIMENTAL EVALUATION

The performance characteristics of thermostats may be assessed by experimental

methods. As mentioned earlier, NEMA has a simplified test standard [2]. That

standard provides some operating characteristics which are used generally to

describe thermostat performance. Three important operating characteristics

are listed below with NEMA's definitions.

• Operating differential — the difference between cut-in and cut-out

points as measured at the thermostat under specified operating

conditions.

• Cycle time — the time which elapses between successive cut-in points.

• Droop — the deviation in the cut-in point which results from a change

in the duty cycle, heating load or cooling load.

To assess the operation and performance of a thermostat under dynamic plant and

building conditions, as opposed to certain fixed plant and building characteristics such as those used in the NEMA test method, computer model simulation is

necessary. This simulation requires the determination of the values of:

• Tg^jj = thermostat switch differential,

• Tggj^ = thermostat time constant,

• a,nt ~ anticipator time constant, and

• ^Tant,ss ~ anticipator temperature rise at steady state.

In addition to these four design parameters, the thermostat set point, an operating parameter, must also be known.

Direct measurement of the temperature of the thermostat sensor and anticipator

is difficult, if not impossible. However, if the thermostat is placed in a temperature controlled test chamber, an output process that can readily be

observed is the thermostat transition from OFF to ON, and ON to OFF, following

a step or ramp change in the air temperature of the chamber.

The transition points from ON to OFF and OFF to ON define characteristic

temperature points for each thermostat. Given a thermostat with a switch

point of Tq as defined by the OFF to ON transition temperature, the ON to OFF

transition will occur at a sensor temperature of Tq + '^s\id where Tg^^j defines

the switch differential of the thermostat under test. Figure 4 is a diagram

of the response of a themnostat to a ramped input for a given switch differential and element time constant. In this representation, the thermostat "controls" the input ramp direction and reacts to the ensuing change in temperature.

This is similar to events occurring in an actual thermostat installation.

8
TIME, t

a. Air and sensor temperature relationship

ON

OFF

CO

Tswd

SENSOR TEMPERATURE

b. Switch positions to element temperature

Figure 4, Air and sensor temperature relationship, and switch positions

to element temperature

9
Measurements of the chamber air temperature and the time between thermostat

transitions are used to obtain the thermostat parameters by using some of the

equations presented later in the thermostat responses section (4.3).

A block diagram of the complete experimental test system, as constructed, is

shown in figure 5. The system is composed of several sub-units, each of which

is discussed individually.

3.2 TEST CHAMBER

All thermostat tests were conducted in a NEMA type test chamber as shown in

figure 6. This chamber contained:

• The theirmostat under test;

• A controllable air supply with provision for controlling air

velocity and air temperature at the thermostat;

• Provision for measurement of air flow with a hot-wire anemometer,

• Several sets of copper-constantan thermocouples, and an associated

ice bath reference.

Air circulated downward in the test chamber and was returned through the

recirculation duct where electric heating wire was placed for chamber air

temperature control. The entire test box was housed in a 10' x 10' x 9'

(3.05 m X 3.05 m x 2.74 m) high environmental room which was controlled at

lower temperature than the test chamber to provide cooling necessary for the

test box during temperature ramp down tests. The speed of the circulation fan

was adjustable by varying the supply electric voltage through an adjustable

autotransf ormer. A manual damper located in the circulation duct was also used

to adjust the air velocity of the test chamber in conjunction with the autotransformer. The air velocity at the thermostat was checked and maintained

manually. The variance in air velocity within the horizontal and vertical

planes 1 to 4 inches (2.54 x 10"^ to 10.16 x 10"^ m) in front of the center

of the thermostat was within + 6 ft/min (3.05 x 10"^ m/s) during the experiment.

The velocity at 1" (2.54 x 10"^ m) in front of the center of the thermostat was

30 ft/min (1.52 x 10"^ m/s) and the variance in velocity at this point was within + 3 ft/min (1.52 x 10"^ m/s) during a 5-minute duration. A hot-wire

anemometer was used to check the air velocity at the beginning and the end of

each test. The thermostat mounting panel was suspended in the chamber on shock

cords to minimize the interference of the thermostat by outside disturbances.

The primary difference between this chamber and that of the NEMA standard was

the lack of a cooling coil in this chamber, which limited step-down temperature

input capability. The high capacity electric heating wire gave satisfactory

step up chamber temperature changes, however.

10
1^
Wooden box with 2" thick

rigid insulation

Figure 6. Thermostat test chamber

12
3.3 MEASUREMENT AND CONTROL SYSTEM

The chamber temperature measurement and control system consisted of a digital

ramp (temperature) generator, a test logic unit, a temperature sensor, and a proportional controller. The system was capable of;

• Generating all appropriate test signals, including ramps at any desired

rate, and step ups of any reasonable size;

• Generating an electrical indication of the air temperature applied to

the thermostat;

• Using the test input and electrical temperature indication to control

the air temperature applied to the thermostat;

• Recording the control signal and the measured temperature;

• Operating with the anticipator on or off, as required; and

• Providing a means for thermostat control of the applied air temperature.

3.3.1 Digital Ramp Generator

The digital ramp generator produced an increasing or decreasing binary count

that was converted to a discretely stepped ramp in a D/A convertor. The digital

ramp generator consisted of:

• A pulse generator with provision for controlling the frequency output;

• Logic to provide the necessary control signals for an up/down counter,

• One-shot multivibrators to provide very short count signals to

minimize noise problems in the counter;

• A ten bit binary counter built from three four-bit counter chips, and

• A D/A converter block, to convert the counter ouput to an analog signal.

In operation, the output of the counter went to the D/A converter which drove

an operational amplifier. The converter and amplifier were calibrated so that

each count corresponded to .01°F for .01 volt. For example, a ten volt signal

resulted in a change of ten degrees.

Figure 7 shows the general signal flow in the digital ramp generator.

3.3.2 Test Logic Unit

The primary function of the test logic unit was to provide an up/down binary

signal for the counter, based on the thermostat ON or OFF state, and to provide

a varying load for the anticipator, or provision for disabling the anticipator

If desired.

13
Figure 7. Digital ramp generator

14
The test logic unit served as an interface between the thermostat and the rest

of the circuitry while electrically isolating the thermostat. A 24 volt transformer, which served as an isolation transformer, provided 24 volts to drive

the anticipator. The anticipator current could be varied from zero to one ampere.

When the thermostat contacts were closed, a 24 volt signal appeared across a rectifier-type detector. This signal produced a Em: voltage to drive an optical

isolator which produced a logic level output of one when the thermostat was ON

(about 3 volts) and zero when OFF (less than one volt).

3.3.3 Temperature Sensing Circuit

The temperature sensing circuit consisted of a thermopile comprised of eight

junctions and an ice-bath reference. It provided an output signal indicating

the air temperature in the test chamber. An instrumentation amplifier and an operational amplifier were used to amplify the thermopile output. Zero and

gain adjustments were provided to produce a 0 volt output at 70°F and a 10 volt

output at 80°F under normal operation. Voltage output was monitored on a digital voltmeter and recorded on a strip chart recorder. The measurements of

chamber temperature were monitored using a thermopile of four junctions

connected to a temperature indicator.

3.3.4 Proportional Controller

A proportional controller provided proportional, derivative, and integral (PID)

control of the wire wound electric heater in the test chamber. The controller

was used to amplify an input signal consisting of the algebraic difference

between the ramp generator control signal and the temperature sensing circuit

ouput voltage. During the test program, the controller provided heat input

rates corresponding to 0.062°F per hour, which gave essentially constant

ambient temperature.

3.4 GENERAL TEST PROCEDURES

Experimental tests were set up and conducted under conditions prescribed by the

NEMA test procedures to the extent possible. These procedures included the

specification of the test chamber, thermostat installation, anticipator setting,

thermostat duty cycles, and corresponding temperature input ramp rates. Duty

cycles of 20, 50, and 80 percent were used in tests requiring slow ramps where

the corresponding temperature ramp rates were (+8/'-2) °F/h, (+6/-6)°F/h, and

(+2/-8)°F/h. Measurements and calculations were made of the thermostat operating differential (Tqp^) , cycle rate, and droop, as well as the thermostat parameters as discussed previously. Part 4 of the NEMA Standard, "Testing and

Performance," [2] is included for reference in appendix A.

Before the start of any test, a settling period was provided to allow the

thermostat system to come to an equilibrium. For stepped temperature ramp or anticipator input tests, this settling period consisted of application of a constant temperature input (+0.062 °F/h) for a time period not less than four

estimated sensor time constants, usually 1 1/2 to 2 hours. For the slow ramp

15
tests, a quasi-steady state was assumed to exist when successive high and low

switch points were free of transient drift, i.e., successive readings differed

by less than 0.1°F.

All temperature measurements were taken in degrees Fahrenheit, since this

temperature scale is used exclusively for home thermostats in the United States.

16
4. RESPONSE EQUATIONS AND MEASUREMENT METHODS FOR OBTAINING THE VALUES OF

THE FOUR THERMOSTAT PARAMETERS

4 . 1 THERMOSTAT COMPONENT RESPONSE ANALYSIS

A series of measurements of thermostat component response was used to calculate

the values for the thermostat parameters noted earlier. These measurements

involved different combinations of test chamber conditions and thermostat

operating characteristics.

The input to a thermostat in an actual installation can never be exactly

specified. However, simple excitations, such as step and fixed-rate ramp temperature changes, can be used in a laboratory to observe the response of the

thermostat. The observed thermostat responses to these excitations, then, may

be used to calculate values for the various parameters discussed in the previous

section.

All of the mathematical models of thermostat response contain exponential terms

with time constants for either the sensor or the anticipator. If the time of

the tests are held long, it may be assumed that all such exponential terras have decayed to insignificance. Therefore, asymptotic, steady-state forms

will be discussed for all responses.

In this report, the terms "slow ramp" denotes those ramps in which transients

decay to insignificance. For a "very slow ramp" the term "RR Tgen" also significant. With a "very slow ramp," however, the entire thermostat is at the same temperature as the air and changes slowly. With a "slow ramp," the

thermostat comes to a uniform temperature, but a small temperature difference

exists between the air and the sensing element depending on the ramp rate and

the time constant of the sensor. This is shown in figure 8.

4.2 EQUATIONS REPRSENTING THERMOSTAT RESPONSE

A series of equations representing the sensor temperature as a function of

various combinations of simple excitations and anticipator activator were developed. The following are mathematical representations of some of the possible sensor responses subjected to a step or ramp temperature change of the

space air with the anticipator either disabled or activated. The sketches in

the following paragraphs depict the possible temperature variations of the

space air and the sensor. Temperature is shown on the ordinate and time is

shown on the abscissa. In all cases, the thermostat and the space air are in

equilibrium at t=0, with this initial temperature represented as Ti(ia>0' "^ida.l

is the space air temperature after the step jump. Other notations are as shown

in table 1

.

17
AIR TEMP.

SENSOR TEMP.

TIME

Figure 8. Sensor response to a slow ramp temperature change

a. Sensor temperature (Tggj^) as a function of a step up of space air temperature, with the anticipator disabled (both models)

Tida.l AIR TEMP.

/

/

i Tida,0

SENSOR TEMP

TIME

''^sen^'^^ " "^ida.O ^"^ida.l

Asymptotic at large t:

Tsen(t) = Tida.l

-t/-

Tida.0)(l18
b. Sensor temperature with space air temperature constant and anticipator

activated, (bimetal feedback model)

c

.

2g

ANTICIPATOR TEMP.

[AIR AROUND SENSOR)

/

/X/

y

SENSOR TEMP.

sen ^

TIME

ant

ant - T (e

-t/T sen -t/i

- e ant

)] sen Asymptotic at large t:

Tsen^t) = Tida 0 + DT^nt.ss

Sensor temperature with space air temperature constant, and the anticipator

activated, (switch feedback model)

/ \SENSOR TEMP.

TIME

'^sen^^^ = T.^a,0 + ^^ant.ss ^^"^

Asymptotic at large t:

Tsen(t) = Tida.O + I>Tant,ss

19

-t/T

ant
d. Sensor temperature after a rising ramp of space air temperature, with the

anticipator disabled (both models)

TIME

-t/T

sen>

e.

= Tida.O + - CRR)^sen(l-^

Asymptotic at large t:

Tsen(t) = Tida.O + (RR)^ - (RR)Tsen

Sensor temperature after a rising ramp of space air temperature, with

anticipator activated (bimetal feedback model)

it:

TIME

-t/x

= Ti^a.O + - KRR)T3en-DTant,ssl(l-^

^^ant,ss ''^ant ^^"^/'^sen _ ^~^^'^ant^

ant ~ "^sen

Asymptotic at large t:

Tsen(t) = Tida.O + (RR)t: - l(RR) Tgen " DTant,ss]

20
f. Sensor temperature after a rising ramp of space air temperature, with

anticipator activated (switch feedback model)

Asymptotic at large t:

Tsen(t) = Tida,0 + (RR)t " [(RR) Tgen " DTant.ssi

Values for the constants, Tg^d* "i^sen* DT^nt ss "^ant^ given in these

equations, are be determined sequentially. Experimental results are used to

calculate Tg^^j* This value is then combined with experimental data to calculate Tggjj, and so forth. The experimental procedure is described in section

4.3.

4.3 MEASUREMENT METHODS

Values of the four constants, Tg^^* ^T^nt ss "^ant* were determined by

inserting experimentally obtained data into a sequential series of thermostat

response equations. It should be noted that some parameters may be determined by more than one method. The measurement procedure and response equation

is described for each constant in turn.

a. Measuring Switch Differential Tg^^^j and Set-Temperature Tq—Very Slow Ramp

Method

The switch differential and set-temperature may be measured using very slow

ramps with the anticipator disabled. For a very slow ramp, all transient (time

constant) effects are negligible in the steady state, and the temperature lag,

(RR)Tsen» due to ramp rate (RR) and sensor time constant (tge^) is insignificant. If this condition can be achieved, then a quasi-steady state exists, and

it can safely be assumed that the sensing element of the thermostat is at the same temperature as the test chamber air. Under these conditions, a reasonable

way to measure set temperature and switch differential is as follows:

21
Set the anticipator resistance to zero.

• Turn the thermostat ON and set at a temperature not too far below the

expected value of Tq + Tg^^j.

• Slowly ramp the chamber temperature up until the thermostat switches

from ON to OFF. The chamber temperature at which this occurs is very

close to Tq + Tg^^jj.

• Ramp down until the thermostat switches back ON. The chamber

temperature at which this occurs is close to the set-temperature Tq.

While this method for measuring set point and switch differential seems reasonably direct, some precautions should be observed. It is assumed that

the applied ramp is very slow, so that all transients die out, and the lag

(RR) Tggn is negligible. If the time-constant is expected to be approximately

a quarter of an hour, then for a 0.1°F error, the ramp rate must be less than

0.4°F/hr. If sufficient care is not taken, then ramp rate can lead to an excessively long test, especially if the set point is not well known.

b. Measuring Sensor Time-Constant Tqq^ — Step Temperature Method

Once the set-temperature and switch differential have been determined, it is

possible to measure the sensor time constant by applying a step to the chamber

temperature while the anticipator is disabled. In this situation, the procedure

for measuring the sensor time constant is:

• Bring the system to steady state by applying a constant chamber

temperature, Ti^a^o* To achieve steady state, the thermostat input

must be held at this value for a time that permits all transients to

decay, usually at least four time constants. Since the time constant

is being measured, some reasonable estimate must be used.

• Step up the chamber temperature to a new value, T^jj^ i* The response

to this step is shown in paragraph 4.2a.

• Record the elapsed time t until the thermostat switches from ON to OFF,

or when the sensor temperature reaches Tq + T^sMd*

o From the sensor response equation of paragraph 3.1a, solve for the sensor time constant.

Tsen = - t/(£n [Ii^AJL\Jl-^\ ) ^ida,l ^ida,0

c. Measuring Switch Differential Tg^^^j, Set-Temperature Tq and Sensor Time

Constant Tg^n — Slow Ramp Method

An alternate method for determining switch differential, set temperature, and sensor time constant is to disable the anticipator and conduct two ramp tests

at different ramp rates. Figure 9 shows the test chamber air and sensor

temperatures as a function of the ramp tests, once they have stabilized.

22
Tsen.O < ^^^.^^

Tida.O

TIME

Figure 9. Air and sensor temperature under ramp test

While the chamber air temperature is ramping up, the sensor temperature at the

switching off point can be determined by (similar to the response shown in

paragraph 4.2.d):

-t/x

T = T <a sen I J. ^sen,l ^sen,0 ^ ^ '^ida.O (1-e ^^^sen)

+ (RR)t - (RR)Tg3^ (1-e ^'^''sen)

Similarly for ramping down, the sensor temperature at the switching on point is;

T = T «a ^'''^sen . rr, n-p ^''^senx

^sen,0 ^sen,l ® ^ ^ida,l ®

^

-til

+ (RR)t + (RR)Tsgn (1-e s^^)

Substracting one equation from the other and using the relations

'^sen,l ~ ^sen,0 ~ ^swd»

Tida,l " Tida,0 = '^o^d^ and

Tida.l = Tida,0 + (IiR>t

we have

(1+e"^^''^^^) = Tg^^ (1+e"''^''^^") + 2 (RR)t_„ (1-e"^^''^^^) ^opd sen

23
The same equation may be used for two ramp tests. If the subscripts f and s denote the representation of the faster and slower ramps and using Ef for

"^f'^sen and E„ for ~^^'^sen, we have

Topd,f U+Ef) = Tswd (1+Ef) + 2(RR)f Tgen d'Ef)

and

Topd.s (1+Es) = Tgwd (1+Es) + 2(RR)s T^en d'Ef)

Solving for the sensor parameters:

_ 1 (T sen

opd,f - ^opd,s) ^l-^^f> ^l^^s)

2 (RR)f(l-Ef)(l+Eg)-(RR)g(l+Ef)(l-Eg)

T

_ ^opd,f(^)s^l-^Ef)(l-E3) - T^pd,s^RR)f^l-Ef)(l+E3)

swd (RR)f(l+Ef)(l-Eg) - (RR)g(l-Ef)(l+Eg)

Since the time constant of the sensor appears exponentially on the right hand

side, these two equations are impossible to solve analytically. However, they

may be used iteratively to obtain the parameter values.

If a thermostat has a very small time constant and relatively large switch

differential, the transient effect of the sensor fades before the switch

changes. Then these two equations become

T — T

_ _1 opd,f opd,s

T swd

2 (RR)f - (RR),

^ Topd,f<RR>s - Topd,s^^>f

(RR)f - (RR)g

and the set-temperature is

To = Tida,0 + RR^send. Measuring Steady State Anticipator Temperature Rise DT^nt ss — Slow Ramp

Method

The steady state temperature rise of the thermostat sensor due to the

anticipator, DT^j^j- gg, can be determined from the asymptotic solutions to the

sensor response given in paragraphs 4.2e and 4.2f using a slow ramp. The

procedure consists of initially bringing the thermostat system into a steady

state equilibrium condition at Tj^^a 0* This temperature should be low enough

that the switch will not turn on before the sensor transient dies out. With

the air and sensor in equilibrium, a slow ramp temperature input is applied

and the anticipator is turned on. The asymptotic sensor response is

Tsen = Tida,0 + - (RR)Tsen + DTant,ss

24
At the thermostat ON to OFF switch point,

Tsen = To + Tgwd '^±da,0 "•" (RR)t = ^i^a.t

therefore

^^ant.ss ~ Tq + T^swd ^±da,t (^^^^^sen.

where Tj^(ja,t ^i'^ temperature at the switch point.

e. Measuring Anticipator Time Constant t^j^j- by Activating the Anticipator

The anticipator time constant T^^t determined by activating the

anticipator after the sensor and the test chamber air are in equilibrium. So

that the anticipator heat will turn the thermostat switch from ON to OFF, the

chamber air temperature should be kept higher than the thermostat cut-out

temperature, minus the steady state anticipator temperature rise. In equation

form, it is represented by

Tida,0 + '^s\id ~ '^TantjSS*

The elapsed time from ON to OFF is recorded.

From paragraph 4.2b the sensor temperature at switch OFF point for the bimetal

feedback model can be represented by:

Tsen = + T3^d = T^^^^y + ^^^nt.ss

+ "^ant ^g"^/'^sen _ ^'^/'^ant^

^ant ~ ''^sen Although the values of Tq, Tg^^j, T^^^ g* ^'^ant ss> ^> ^^'^ "^sen are all known

from previous tests, T^^t "'^y difficult to determine, since the anticipator

and sensor temperature history curves do not converge before the sensor is ON

(see sketch of sensor and anticipator temperatures in paragraph 4.2b). Because

of the relatively high thermal diffusivity of air and because most thermostat

anticipators have very small thermal mass resistant heaters, the anticipator

time constant of the bimetal feedback model should be very short. Test results

by McBride indicate that the anticipator time constant is almost instantaneous

[5]. If this assumption is acceptable, then x^^t vanishes from the sensor response equation and the equation becomes

To + Tg^d = Tida,0 + DTant,ss ^^"^

Then, this equation may be used to check the assumption of t^j^t = 0.

For the switch feedback model, the sensor temperature at the switch off point

as given in paragraph 4.2c is

25
^^ant ,ss

All variables on the right hand side are known and the anticipator time constant

may be calculated.

26
5. COMPUTER MODELING

The values calculated by solving the equations given in section A were used in

a computer simulation of thermostat performance. This program simulated thermostat performance based on the two conceptual models discussed in section 2.

The program uses the experimental results for the parameters identified in pre

vious sections and user assigned rates of building air temperature change

during heating plant ON and OFF periods to calculate the space temperature

variations. Using the space temperature variations, one can readily calculate

the thermostat operating characteristics such as operating differential, cycling rate and droop. Although any user assigned rates of air temperature chang

can be easily used in the program, this segment of the program may be replaced

with a set of more realistic building and plant sub-programs to simulate perfo mance of the thermostat-plant-building system. The listing of this program is

given in appendix B.

The computer program was used to calculate the output of the two conceptual

models of thermostat performance using NEMA ramp rates. NEMA ramp rates are 2 6, and 8°F/hr., with both positive and negative slopes controlled by the thermostat states. The results of the simulation model, which were then compared

with the NEMA test results, are presented in section 6.

27
6. RESULTS AND DISCUSSION

Four thermostats (numbers 1-4) were tested in the laboratory using the

procedures discussed in section 4.3. Thermostat number 1 was a clock thermostat. Thermostats 2 and 4 had single loop anticipator wires. Thermostats 1 and 3 had wound anticipator wires. Thermostats 2 and 3 had combination heating

and cooling mercury-bulb switches and the other two thermostats had individual

heating and cooling switches. The values obtained for the basic parameters for

each thermostat during the tests, as well as other related data are reported in

table 2. The sensor time constants, switch differentials, and set temperatures

were determined by using the method described in paragraph C of section 4.3.

Table 2. Parameter Test Results

Thermostat Number 1 2 3 4

Sensor time constant, Tgg^* 15.00 19.13 17.25 21.75

in minutes

Switch differential, tg^,^, 1.5 1.7 1.2 1.4

in °F

Anticipator steady-state 5.2 5.5 7.0 7.6

temperature rise, DT^nt ss» in °F

Anticipator time constant 11.2 10.8 11.6 12.6

for switch feedback model,

"^ant' minutes

Anticipator current setting, 0.65 0.58 0.65 0.48

in amps

Set temperature, Tq , in 75.6 73.9 75.5 75.3

°F

The adjustable anticipators of the thermostats were set approximately in the

middle portion of the range between the highest and lowest setting. The

measured current data are reported in table 2. The thermostats were set to

a nominal temperature of 75°F.

Tests were conducted to measure the thermostat operating performance according

to NEMA test procedures. The NEMA test procedures require that the test chamber temperature rise and fall at 6°F/hr to obtain the thermostat cycling rate

at 50 percent building load. As discussed in paragraph 4.3e, the anticipator

time constant should be very short for the bimetal feedback model. Several

computer runs for thermostat No. 1 were made with different anticipator timeconstant values to compare the calculated thermostat operating performance with

the experimental data. Table 3 indicates that with a very short anticipator

time constant it ant ~ minute), the simulated performance was closest to the

28
experimental results. Therefore, the assumption of a very small anticipator

time constant for the bimetal feedback model is valid.

Table 3. Comparison of Thermostat No. 1 Performance, Experimental vs. Simulation, Using Different Anticipator Constants in the

Bimetal Feedback Model

NEMA Test Simulation

^ant* minute

Maximum Temperature, °F

Minimum Temperature, °F

Operating Differential, °F

Rise/Fall Periods, Minute

74.0

73.5

0.5

5/5

0.1

74.1

73.3

0.8

8/8

1 74.1

73.2

1.0

11/11

2

74.4

73.0

1.4

14/15

4

74.5

72.9

1.6

16/16

10

74.9

72.6

2.3

23/23

Tables 4 to 7 compare thermostat performance obtained by the NEMA test

procedures with the computer simulation results for both conceptual models.

During the simulations, the anticipator time constant was assumed to be 0.1

minute for the bimetal feedback model. The use of 0.1 minute as the anticipator

time constant in the bimetal feedback model simulation greatly increased the

number of integration steps, resulting in longer computing time than for the

switch feedback model simulation. Generally, the results from the switch feedback model were in closer agreement with the experimental results than were the

results from the bimetal feedback model.

It should be noted, however, that part of the difference between the simulation

and the NEMA test data resulted from experimental and computational errors in

developing the thermostat parameters since the parameter values were determined

by sequential tests and calculations. Errors in early tests and calculations

thus were entered into succeeding calculations. In addition, temperature mea- surement errors, undecayed transient errors, and steady-state differences

between the sensor and test chambers air temperature during range tests also

occurred. As a result, the simulation cycle rates, which are the inverses of

the rise/f all periods given in tables 4 through 7, were generally much smaller

than those for the NEMA test reuslts. Although all simulations represented

more than eight hours of thermostat operation, not all iterations reached

stable conditions, depending on the assumed initial input data for the sensor,

air, and anticipator temperatures. Nevertheless, the maximum and minimum

temperature of most of the simulations were within 0.3°F of the corresponding

test data.

29
Table 4. Comparison of Thermostat Performance, Experimental vs. Simulations, Thermostat No. 1

Ramp Rate NEMA Bimetal Feedback Switch Feedback

°F/hr Test Model Model

Maximum Temp. , °F 74.0 74.1 74.1

Minimum Temp. , °F 73.5 73.3 73.4

Operating Dif f ., °F 0.5 0.8 0.7

Rise/Fall Periods, min. 5/5 8/8 7/7

Maximum Temp. , °F 75.2 75.6 75.6

Minimum Temp. , °F +8/-2 74.8 74.9 75.0

Rise/Fall Periods, min. 3/12 6/22 5/17

Maximum Temp. , °F 72.6 72.6 72.5

Minimum Temp. , °F +2/-8 72.1 71.9 71.9

Rise/Fall Periods, min. 12/3 22/7 20/5

Droop, °F 2 6 1 3.0 3.1

Table 5. Comparison of Thermostat Performance, Experimental vs. Simulations, Thermostat No. 2

Ramp Rate NEMA Bimetal Feedback Switch Feedback

°F/hr Test Model Model

Maximum Temp. , °F 72.1 72.6 72.4

Minimum Temp. , °F +6/-6 71.5 71.4 71.6

Operating Dif f ., °F 0.6 1.2 0.8

Rise/Fall Periods, min. 6/6 12/12 8/8

Maximum Temp. , °F 73.9 74.1 73.9

Minimum Temp. , °F +8/ -2 73.4 73.1 73.2

Rise/Fall Periods, min. 4/16 9/30 5/20

Maximum Temp. , °F 70.6 70.9 70.7

Minimum Temp. , °F +2/-8 70.1 69.9 70.1

Rise/Fall Periods, min. 15/14 30/8 20/5

Droop, °F 3.3 3.2 3.1

30
Table 6. Comparison of Thermostat Performance, Experimental vs. Simulations, Thermostat No. 3

Ramp Rate NEMA Bimetal Feedback Switch Feedback.

°F/hr Test Model Model

Maximum Temp. °F 73.0 72.9 72.9

Minimum Temp. , °F +6/-6 72.5 72.3 72.4

Operating Dif f ., °F 0.5 0.6 0.5

Rise/Fall Periods, min. 4/4 6/6 15/15

Maximum Temp. , °F 75.0 74.9 74.9

Minimum Temp. , °F +8/-2 74.4 74.4 74.5

Rise/Fall Periods, min. 3/10 5/14 3/12

Maximum Temp. , °F 70.3 70.8 70.7

Minimum Temp. , °F +2/-8 70.0 70.3 70.3

Rise/Fall Periods, min. 9/3 15/5 12/3

Droop, °F 4.4 4.1 4.2

Table 7. Comparison of Thermostat Performance, Experimental vs. Simulations, Thermostat No. 4

Ramp Rate NEMA Bimetal Feedback. Switch Feedback

°F/hr Test Model Model

Maximum Temp., °F 72.2 72.6 72.5

Minimum Temp. , °F +6/-6 71.6 71.8 71.9

Operating Diff ., °F 0.6 0.8 0.6

Rise/Fall Periods, min. 5.5/5.5 9/18 6/6

Maximum Temp. , "F 74.2 74.8 74.6

Minimum Temp. , °F +8/-2 73.8 74.1 74.2

Rise/Fall Periods, min. 3/13 6/20 3/12

Maximum Temp. , "F 69.5 70.3 70.2

Minimum Temp. , °F +2/-8 69.0 69.6 69.8

Rise/Fall Periods, min. 12/4 20/6 12/3

Droop, "F 4.8 4.5 4.4

31
7. CONCLUSION

In this paper, four parameters of thermostat operation were identified. Test

procedures for obtaining these parameters were developed using both experimental

data and mathematical calculations. In addition, a computer program was developed to simulate two different types of thermostat operation. As input,

this program used the four parameters to simulate thermostat performance. The

performance of four mechanical thermostats was also determined using the NEMA

test procedure. The simulation results for the switch feedback model were in

better agreement with the experimental test data than were the results from the

bimetal feedback model. In addition, because the anticipator time constant can

be determined experimentally and shorter computing time is required for

simulation, the switch feedback model is recommended over the bimetal feedback

model for use in low-voltage room thermostat studies. It also provides some clues to the probable operational characteristics of thermostats within a dynamic system. Thus, the switch feedback model, in which the anticipator

works directly upon the sensor, is seen as a better model of actual performance

than the bimetal feedback model. This model may then be combined with heating

plant and building models to predict dynamic building thermal performance.

The authors wish to acknowledge Mr. Lih Chern for his assistance in editing

and running the computer programs of the models.

32
8. REFERENCES

1. Boldt, N.A., A New NEMA Standard for Room Thermostat Test Equipment , IEEE

Transactions on Industry Applications, Vol. IA-10, No. 6, November/December

,

1974.

2. Low-Voltage Room Thermostat, National Electrical Manufacturers Association

Standards Publication No. DC3-1978; Washington, D.C., 1978.

3. Kaya, A., Analytical Techniques for Controller Design, ASHRAE Journal , April 1976.

4. Anderson, V.R. , Tobias, J.R., Comfort Control for Central Electric Heating

Systems, IEEE Transactions on Industry Applications , Vol. IA-10, No. 6,

November/December 1974.

5. McBride, M.F., Dynamic Modeling of System Transients by Computer Simulations

for Prediction of Residential Energy Consumptions, Ph.D. Thesis, The Ohio

State University, 1979.

6. Roots, W.K. , Nightingale, J.M., Two Position Discontinuous Temperature Control

in Electric Space Heating and Cooling Processes: Part I - The Control System,

IEEE Transactions of Application and Industry , January 1964.

33
I
APPENDIX A. NEMA STANDARD FOR TESTING THERMOSTAT PERFORi-IANCE

Pub. No. DC3

Part 4, Page 1

Part 4

TESTING AND PERFORMANCE

DC 3-4.01 DIELECTRIC TESTS

Thermostats shall be capable of withstanding for 1 minute without breakdown

the application of a 50/60-hertz alternating potential of 500 volts applied

between uninsulated low-voltage live-metal parts of opposite polarity (with

contacts closed) and between uninsulated low-voltage live-metal parts and the

enclosure and grounded dead-metal parts.

As an alternate, the dielectric test on thermostats may be conducted for

1 second with a 50/60 hertz test voltage of 600 volts.

NEI-IA Standard 3-8-1978

DC 3-4.02 ENDURANCE

Thermostats shall be capable of thermally operating at the maximum rated

electrical load for at least 100,000 cycles at a rate of not more than 4 cycles

per minute.

NEMA Standard 7-19-1972

DC 3-4.03 ENVIRONMENTAL TESTS

A. General Conditions

All environmental tests shall be conducted in accordance with the equipment

and operating instructions described in Part 7.

All tests shall be conducted with the air velocity through the test chamber

set at 0.15 m/s (30 feet per minute) in the downward direction.

All tests shall be conducted with the scale setting at a point between 21°C

(70°F) and 27°C (80°F). A different setting may be used if required to com- plete the performance tests within the range of the test equipment.

All tests on anticipating-type thermostats shall be conducted with anticipators in place and connected. Where more than one choice of anticipation

is supplied, the manufacturer's instructions for electrical load under test

shall be followed.

1. Thermostats having adjustable anticipators shall be set at the midpoint

of the anticipator range and tested with current represented by the

setting.

A-1
2. Theraostats with fixed-series anticipators shall be tested at the

midpoint of the manufacturer's specified anticipator rating.

3. Thermostats having fixed-parallel-voltage-type anticipators shall be

tested at their current and voltage rating.

All tests on nonanticipating-type thermostats shall be conducted at the

manufacturer's specified rating.

All tests on thermostats which have heat-generating elements shall be

conducted with those elements energized as they would be in normal operation.

B. Differential Test

The differential tests shall be conducted with the test equipment set for

uniform rates of temperature change of 3.3°C (6°F) per hour. Tests shall be

conducted at 50 percent duty cycle.

The thermostat under test shall be connected so that it determines the

direction on the temperature change during the cycle.

Tne operating differential shall be recorded.

C. Cycle Rate Test

The cycle rate test shall be conducted at 20, 50 and 80 percent duty cycle

and recorded.

The thermostat under test shall determine the direction of temperature change

during the cycle with the rate change set as follows:

Percent

Duty

Rate of Change, °K/Hour(F)

Heating Thermostat Cooling Thermostat

Rise Fall Rise Fall

20 4.4(8) 1.1(2) 1.1(2) 4.4(8)

50 3.3(6) 3.3(6) 3.3(6) 3.3(6)

80 1.1(2) 4.4(8) 4.4(8) 1.1(2)

The thermostat shall be allowed to cycle until it has stabilized to a uniform

rate.

A-2
D. Droop Test (Heating and Cooling)

The effective operating droop value shall be recorded as the average

temperature difference between the cut-in points at the 20 percent and

80 percent duty cycles as determined from the cycle rate test.

NEMA Standard 3-8-1978

E. Test Data Forms

The test data may be presented in one or both of the following forms:

1. Test Data Form—See Fig. 4.1.

2. Test Data Curves—The curves shown on Fig, 4.2 are typical effective droop and cycle rate curves which graphically represent the test

results tabulated on the test data form shown in Fig. 4.1. A curve can

be shown for each electrical load tested.

Authorized Engineering Information 3-8-1978

Electrical Load

Volts Amperes

Operating Differential

Heating Cooling

Effective Operating

Droop Value °C(°F)

20% to 80% Duty Cycle

Cycle Rate

Heating or Cooling

Fig. 4.1

Test Data Form

A-3
Pub. No. DC 3

Part 4, Page 3

100 DUTY CYCLE—PERCENT

Fig. 4.2

Test Data Curves

A-4
APPENDIX B. PROGRAM FOR SIMULATING THERMOSTAT PERFORMANCE

C

C PROGRAM FOR SIMULATION OF THERMOSTAT

C DIMENSION X(10)

C

C THE ARRAYtX. CONTAINS THE "STATES* OF THE SYSTEM.

C COMMON TSEN.TSUDrTZEROf T ANT »DT ANTS

COMMON lOF

COMMON RRtFR

1111 FORMAT (' INPUT THE THERMOSTAT PARAMETERS.')

URITE (6fllll)

1112 FORMAT (' USE E10.4 FORMAT.')

URITE (6flll2)

1113 FORMAT (' TSEN TSWD TZERO TANT DTANTSS')

WRITE (6»1113)

1001 FORMAT (BE10.4)

READ (5»1001) TSEN»TSWD.TZEROf TANTf DTANTS

URITE <6rl002) TSEN»TSUD»TZEROf TANT.DTANTS

1115 FORMAT (' INPUT THE TWO RAMP RATES (DEGF/HR).')

DT=TANT/5.0

IF(DT.GT. 1 .0) DT=1.0

TSTEP=1 .0/DT+O. 00001

ISTEP=IFIX(TSTEP)

WRITE (6flll5)

READ (5»1001) RRiFR

WRITE (6fl002) RRrFR

RR=RR/60.

FR = FR/60.

1120 FORMAT (' NOW INPUT DATA FOR THE DIGITAL SIMULATION.')

WRITE (6»1120)

1002 FORMAT (1X»9E12.6)

URITE (6.1002) DT

1122 FORMAT (' INPUT THE NUMBER OF INTEGRATION STEPS.')

WRITE (6.1122)

1123 FORMAT (' USE 13 FORMAT.')

WRITE (6.1123)

1003 FORMAT (1015)

READ (5.1003) ITER

WRITE (6.1003) ITER

1124 FORMAT (' INPUT THE NUMBER OF SIMULATION STATES.')

WRITE (6.1124)

WRITE (6.1123)

READ (5.1003) N WRITE (6.1003) N 1125 FORMAT (' INPUT THE STARTING VALUE OF THE STATES.')

WRITE (6.1125)

READ (5.1001) (X(I). 1=1. N)

URITE (6.1002) (X(I). 1=1. N)

1130 FORMAT (IHl.' TIME AND STATES')

URITE (6.1130)

T = 0.

lOF = 1 WRITE (6.1002) T.(X(I). 1=1. N)

DO 100 I = LITER

CALL EULER (X.T.DT.N)

I1=I/ISTEP

III=II*ISTEP

IF(I.NE.III) GOTO 100

WRITE (6.1002) T.(X(J). J^l.N)

100 CONTINUE

STOP

END

B-1
SUBROUTINE XDOT (X»XD»T»N)

COMMON TSENf TSWD>TZERQ»TANT»DTANTS

COMMON lOF

COMMON RRfFR

DIMENSION X(10). XD(IO)

C *»«»«««»«««»«««»*»«»«»»««»««»»»»»««»«««»»«»»««««

cC THERMOSTAT MODEL ( BIMETAL FEEDBACK ) C

C X(l) • SENSOR TEMPERATURE

C X(2) * ANTICIPATOR TEMPERATURE

C lOF s 1 WHEN 0N> ' 0 WHEN OFF.

C

C %tttttttttttt%ttt%ttttttttt%t%%tttttttttttt*%t%*

TIDA = X<3)

XD(1) « -(X(1)/TSEN) + (TIDA + X(2))/TSEN

XD(2) = -(X(2)/TANT) + ( DTANTS»IOF/TANT

>

C

C PROGRAM SEGMENT FOR THE NONLINEAR FUNCTION

C IF (T .EQ. 0. ) lOF * 1 IF (lOF .EQ. 1) TSW = T2ER0 + TSWD

IF (lOF .EQ. 0) TSy = T2ER0

IF(X<1) .GE. TSU> lOF = 0

IF(X(1) .LE. TSW) lOF = 1 C

C END OF THERMOSTAT MODEL SEGMENT

C

C

C ttttttt*t%%tt%t*tt%tttttt%%tt*tttttttttttttttt*t

C

C NEMA BOX SEGMENT

CC

C DEFINE PARAMETERS

CC RR IS THE RISING RAMP RATE

C FR IS THE FALLING RAMP RATE

C XD(3) = FR (RR-FR)*IOF

RETURN

END

C

C

c SUBROUTINE EULER (XrT>DTfN>

C

C EULER DOES EULER INTEGRATION OF DIFFERENTIAL EQUATIONS

C DIMENSION X<10>> XD(10>

CALL XDOT(X»XD»T»N)

DO 100 I=lfN

X(I) = X(I) + XD(I)«DT

100 CONTINUE

T = T + DT

RETURN

END

E0F:123

o:>

B-2
SUBROUTINE EULER (XfTtDTrN)

C

C EULER DOES EULER INTEGRATION OF DIFFERENTIAL EQUATIONS

C DIMENSION X(10)f XD(IO)

CALL XDOTCXf XDfTfN)

DO 100 I=1>N

X(I ) = X(I) + XD(I)«DT

100 CONTINUE

T = T + DT

RETURN

END

C

C

C SUBROUTINE XDOT (XfXDfTtN)

COMMON TSENf TSUD»TZERO»TANTf DTANTS

COMMON lOF

COMMON RRfFR

DIMENSION X(10)» XD(IO)

C «»««««»*»»»<»»»» »X« ««»»«« «»»!!»»«»««»«»»»«

C

C THERMOSTAT MODEL ( SWITCH FEEDBACK ) C

C X(l) = SENSOR TEMPERATURE

C X(2) = ANTICIPATOR TEMPERATURE

C lOF = 1 UHEN 0N> = 0 WHEN OFF*

C

C t*t**tt**tt*ttt*ttttt*tt**tt$ttt*t*ttttt*ttt*tt*

TEMSEN = X(l) + X(2)

C

C PROGRAM SEGMENT FOR THE NONLINEAR FUNCTION

C

IF (T .EO. 0.) lOF = 1 IF (lOF .EQ. 1) TSW = TZERO + TSWD

IF (lOF .EQ. 0) TSy = TZERO

IF(TEMSEN .GE. TSW) lOF = 0

IFCTEMSEN .LE. TSU) lOF =1

TIDA = X(3)

XD(1) = -(X(1)/TSEN) + (TIDA/TSEN)

XD(2) * -(X<2)/TANT) + <DTANTS*IOF/TANT)

C

C END OF THERMOSTAT MODEL SEGMENT

CC

C *tttt*t*t*t***ttttt*t*ttt*ttttt**t*t**tttttt*tt*

c

C NEMA BOX SEGMENT

C

C

C DEFINE PARAMETERS

C

C RR IS THE RISING RAMP RATE

C FR IS THE FALLING RAMP RATE

C XD(3) = FR + (RR-FR)tlOF

RETURN

END

E0F:124

o:>

B-3
NBS-n4A (REV. 2-8C) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBS BSS 150

2. Performing Organ. Report No, 3. Publication Date April 1983

4. TITLE AND SUBTITLE

Low-Voltage Room Thermostat Performance

5. AUTHOR(S)

James Y. Kao , George Sushinsky , David A. Didion , E. J. Mastascusa, and Joseph Chi

6. PE RFORMING ORGANIZATION (If joint or other thon NBS. see /n struct/on sj

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City. State. ZIP)

Office of Building Research and Development, U. S. Department of Energy, and

Civil Engineering Laboratory, U. S. Naval Construction Battalion Center

10. SUPPLEMENTARY NOTES

Librairy of Congress Catalog Card Number: 83-600505

I I Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual sun)mary of most si gnificant infomation. if document includes a significant

bi bliography or literature survey, mention it here)

To predict performance of low voltage electric thermostats in a dynamic

building system, a computer model representing two types of thermal feedback

was developed. Unlike the information obtained from existing test standards,

this model allows thermostat performance to be determined under any load con- ditions. As input to the model, the basic parameters of thermostat performance

were first identified and then determined experimentally in a controlled

laboratory facility. The experimental results from the tests were used as input parameters for the simulation model. Based upon the results from the

simulation model and test results on four commercially-available thermostats, a switch-feedback model computer simulation Is recommended for studying low^

voltage room thermostat performance.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons) room temperature control; temperature controller; thermostat evaluation;

thermostat modeling; thermostat test; two-position control..

13. AVAILABILITY

Unlimited

I I For Official Distribution. Do Not Release to NTIS

Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C,

20402.

Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

46

15. Price

$4.75

USCOMM-DC 6043-P80

US. GOVERNMENT PRINTING OFFICE ; 1983 O—380-997 (888)
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