1.0 Summary

This report summarizes the experimental results from 30 field tests in 23 Central Florida homes during the Summer of 1990. Detailed thermostat measurements were made at each site for a one to three day period. The purpose of this study was to determine how thermostats operate in actual buildings. This knowledge is necessary to understand the part load performance of air conditioners (ACs).

1.1 Background

While a great deal is known about how ACs and buildings perform separately, very little is known about how they perform together. The interactions between the building and AC are typically controlled by a thermostat. The thermostat senses the space temperature and turns the AC ON and OFF to maintain the required setpoint. Thermostat operation is complex because it depends on thermostat characteristics (e.g., switch deadband, sensing element time constants, anticipator) as well as building characteristics (thermal mass, etc.).

The purpose of this study was to measure thermostat/AC/building performance in several residences. This measured data provided insight into how thermostats really operate. Understanding thermostat performance is necessary to
quantify the part load performance of AC systems.

1.2 Experimental Approach

A portable apparatus was developed which could be temporarily installed in a home. The apparatus included a Campbell 21XL datalogger, temperature and humidity sensors, and a thermostat status sensor. The datalogger sensed and recorded time, temperature and humidity each time the thermostat turned ON or OFF. Measured quantities were averaged and summed as required.

For each test site, the experimental apparatus was placed near (and connected to) the thermostat. It remained at each site for one to three days collecting and storing data. The test was repeated a total of 30 times at 23 different sites.

1.3 Results and Discussion

General Characteristics of the Homes

In addition to detailed thermostat data, average temperatures and humidities were recorded for each test period along with general information about each site. Table 1-1 lists some general information about the tested homes.

Generally, the characteristics of the test sites were typical of the results measured or assumed in other studies (Cummings 1990).

Cycling Rates

One of the primary interests of this study was to measure the cycling rate. The cycling rate (N) is defined as one over the time required to complete an ON and OFF cycle. While the concept of runtime fraction, or duty cycle, is widely understood, cycling rate is a more difficult concept. If AC unit is running 50% of the time, this indicates nothing about how often the AC unit turns ON and OFF. The AC unit could be ON for 60 minutes and OFF for 60 minutes (0.5 cycles/hour), or it could be ON for 10 minutes and OFF for 10 minutes (3 cycles/hour). Cycling rate is important because it indicates how often the AC unit starts and stops. Since losses occur each time an AC starts, part load performance depends on the cycling rate.

Cycling rate (N) is related to the runtime fraction (X) by the following equation:

N = 4 Nmax X(1-X)

The development and basis of this equation is discussed in Section 3 and Appendix A. The constant Nmax is defined as the maximum cycle rate, which occurs when the runtime fraction is 50% (X=0.5). The constant Nmax fully defines cyclic behavior of a system at all conditions.

Equation (1-1) was curve-fit to the measured data for each test site to determine the constant Nmax. Figure 1-1 is a histogram of the values of Nmax determined for each site. The average value was 2.5 cycles/hour with a minimum and maximum of 0.15 and 4.07, respectively. The average is lower than the nominal value of 3.125 cycles/hour implicitly assumed in the SEER rating procedure.

There was a fair amount of variation in Nmax from site to site. One of the goals of this study was to statistically analyze the dependence of Nmax on other system parameters. Several factors were analyzed including: temperature droop, thermostat deadband, AC sizing, house age, average runtime, and temperature setpoint. Only two of the parameters were correlated to Nmax at statistically significant levels (i.e., with T-ratios greater than 2): temperature droop and thermostat deadband. While these parameters were statistically significant, they explained only 41% of the variability of Nmax.

Another goal of this study was to determine if building construction (frame vs. block) had any impact on cycling rate. It was postulated that block houses would have more thermal mass, which would decrease cycling rate. Of the 23 test sites, only six were frame construction; therefore, a statistical analysis was not feasible. However, a qualitative evaluation of the houses indicated no discernable differences between frame and block construction.

Figure 1-1 Histogram of Maximum Cycle Rate (Nmax) Measured at All Sites

Temperature Variation

The variation of temperature with runtime fraction (X), commonly referred to as droop, was also of interest in this study. Temperature droop is a commonly recognized occurrence in thermostats with anticipators. The average slope of temperature versus runtime (X) measured in this study was 2.1°F/X. The three electronic thermostats included in this study were observed to have negative droop; this was expected since electronic thermostats have no anticipating circuit.

Humidity Variation

The variation of relative humidity (RH) with X was also analyzed. Since RH is not directly controlled by the thermostat, the variation of RH with X was not highly correlated. Weather effects and other factors tended to overwhelm the impact of the thermostat on RH. The only consistent trend was that RH was always lower when the AC turned OFF than when it turned ON.

1.4 Application of Results

The results of this study improve our understanding of part load losses, which depend on Nmax. Using the part load function developed in this study, part load losses increase by 4.2% per each unit increase in Nmax (assuming a time constant of 80 seconds for the AC unit). Based on the measured values of Nmax, the energy use attributable to part load losses ranged from 0% to 18%, with an average of 11%, in the tested houses.

1.5 Conclusions and Recommendations

The following conclusions and recommendations are made from this study:

2.0 Introduction

This report summarizes the experimental results from 30 field tests conducted in 23 homes during the Summer of 1990. For each test, detailed measurements of thermostat performance as well as indoor temperatures and humidities were measured over a one to three day period. The purpose of this study was to quantify how thermostats perform in actual buildings. This knowledge is necessary to understand the interactions of the building and air conditioner (AC) under part load conditions.

2.1 Background

While a great deal is known about the performance of ACs and buildings separately, very little is known about how they perform together. The interaction between the building and the AC is typically controlled by a thermostat. The thermostat senses air (and wall) temperature to determine when the AC unit should cycle ON and OFF to maintain the required setpoint. The thermostat itself is a complex device which includes a sensing element, a switch and an "anticipating" circuit. Building and furniture mass as well as transient characteristics of the AC system further increase system complexity.

Thermostat performance is important because it affects the part load performance of an AC. Generally, the fraction of time an AC unit operates (i.e., the runtime fraction) is directly proportional to the load. While the runtime fraction gives an indication of the amount of time an AC unit runs, it does not indicate how often the AC system cycles ON and OFF. For instance, if an AC system runs 50% of the time at a certain load condition, what is the cycling rate? The AC could be ON for 1 hour and OFF for 1 hour, or it could be ON for 10 minutes and OFF for 10 minutes. The cycling rate is what determines the part load performance since losses occur each time an AC system starts up. In summary, the cycling rate of the overall building/thermostat/AC system is important in determining part load performance of an AC.

2.2 Previous Studies

Several studies have modeled thermostat, building, and AC system performance including Henderson (1991), Nguyen and Goldschmidt (1983), Lamb and Tree (1981), McBride (1979) and Nelson (1974). These studies have generally shown that the thermostat is the most important factor in determining cycling rate. The anticipator size and deadband of the thermostat are the dominant factors, though the thermal mass of the building and the furniture also play an important role.

While a great deal of effort has gone into simulating thermostat performance, only a few studies have measured the actual performance of thermostats in the field (see Appendix D). Parken et al. (1985) measured cycling rates at three sites as part of the verification process for DOE's Seasonal Energy Efficiency Ratio (SEER) test procedure. Miller and Jaster (1985) measured the cycling rate of a several heat pumps in the heating mode. Goldschmidt et al. (1980) measured the cycling rates of an AC in a mobile home with and without furniture and showed how the cycling rate changed.

Generally, these limited studies all found the maximum cycling rates to vary widely in the 1 to 3 cycles/hour range. This contrasts with the value of 3.125 cycles/hour implicitly assumed in the SEER test procedure (ARI 1984).

2.3 Purpose of Study

The purpose of the current study was to measure thermostat performance in several Florida homes. This experimental data was necessary to verify the findings and assumptions of previous simulation and experimental studies. The approach used was to develop a portable data logger system to accurately and quickly measure the performance at multiple sites. With data available from multiple sites, a statistical approach to analyzing thermostat performance could be taken.

Additionally, temperature and humidity were measured for each site to determine the average values, as well as their variation with AC operation.

2.4 Overview of This Report

This report is organized into the following sections: Section 1 is a summary, Section 2 is an introduction, Section 3 discusses the theory and operation of thermostats, Section 4 discusses the experimental procedure and equipment used, Section 5 presents and discusses the experimental results, Section 6 presents an application of this cycling rate data, and section 7 lists the references. The Appendices include a derivation of the commonly used thermostat cycling equation (Appendix A), a listing of the datalogger program (Appendix B), a complete listing of the experimental results for each site (Appendix C), a listing of measured parameters from previous studies (Appendix D), and a derivation of a part load equation (Appendix E).

3.0 Thermostats: Theory and Operation

This section discusses the theory and operation of thermostats in cooling applications. First, basic thermostat operation is discussed, along with the different types and configurations of thermostats which are available. Next, the mathematical theory and concepts necessary to quantify thermostat performance are developed. These concepts are used to quantify system performance in the following sections.

3.1 Basic Thermostat Operation

The basic function of the thermostat is to sense space temperature and switch the air conditioner (AC) ON and OFF to maintain the desired temperature setpoint. In this process, the thermostat interacts with the building and AC system. The dynamic characteristics of the building, AC system, and the thermostat all affect how the combined system reacts.

There are two primary types of thermostats used in cooling (and heating) applications today: 1) the conventional, bimetallic thermostat, and 2) the electronic, or programmable, thermostat. While both of these perform same basic function -- controlling the AC system to maintain a temperature setpoint -- their dynamic response differs. The characteristics of each thermostat is discussed below.

A Conventional Thermostat consists of a liquid mercury switch attached to a helical bimetal element. The air temperature is sensed by a bimetallic element which rotates as temperature increases (or decreases). The mercury switch, which is attached to the bimetal element, also rotates and switches the AC system ON and OFF. Another component common to this type of thermostat is the anticipator. The anticipator is a resistive heating element (e.g., a resistor) which artificially heats the bimetal element when the AC unit is OFF (for cooling). This forces the AC system to turn ON sooner than if the anticipator were not present. In effect, it "anticipates" when the turn-on temperature is about to be reached. The purpose of the anticipator is to improve comfort by reducing temperature swings in the space.

With an anticipator present, comfort is improved, but at the cost of increasing cycle rate of the AC system. The increased cycle rate increases the number of time the equipment starts, which decreases the overall efficiency of an AC system.

Conventional bimetallic thermostats are the most common type of thermostat used today.

An Electronic Thermostat consists of a temperature sensor interfaced to electronic logic which activates a relay. This type of thermostat differs form conventional thermostats in a couple of ways. First, the response of the temperature sensor in an electronic thermostat is much faster than the bimetal element in a conventional thermostat. This affects how the thermostat reacts to changes in space conditions. Second, electronic thermostats typically do not have an anticipator. Therefore, the only means to control the cycling rate is to change the deadband. Typically, the deadband (the difference between the turn-ON and turn-OFF temperature) is field adjustable. The deadband must be large enough to minimize AC system cycling, yet not so large as to cause excessive swings in air temperature.

3.2 Thermostat Theory and Performance: Cycling

To understand how thermostats perform, a few terms must first be defined. Figure 3-1 shows how the space temperature varies as the thermostat turns the AC ON and OFF for one complete cycle.

Figure 3-1 The Impact of AC Status on Space Temperature

A common feature of all thermostats is a deadband (ΔTspt), or temperature difference, between the temperature at which the AC unit cycles ON (Ton) and OFF (Toff). Typically the setpoint (Tspt) is taken as the mid-point between these temperatures.

The time to complete one cycle of operation is defined as:

tcycle = ton + toff

ton is the time the AC unit was ON and toff is the time the AC unit was OFF, as shown in Figure 3-1.

The runtime fraction (X), which indicates the fraction of time the AC unit runs, is defined as:

X = ton/tcyle = ton/(ton + toff)

Another useful term useful for describing system performance is the cycle rate (N), which is defined as:

N = 1/tcycle = 1/(ton + toff)

The performance of a thermostat in a building is commonly thought to be described by:

N = 4NmaxX(1-X)

This equation is used in the NEMA standard (1990) to quantify performance of wall-mounted, low voltage thermostats. The advantage of equation (3-4) is that the cyclic behavior of a thermostat is quantified by one constant (Nmax). Nmax is physically defined as the maximum cycling rate, which occurs when the AC unit runs 50% of the time (X=0.5).

Equation (3-4) has also been used by others (Parken et al. 1985) to describe system cycling performance. They found that their field data conformed to this model very well. A discussion of the physical basis for equation (3-4) is given in Appendix A.

An algebraically equivalent form of equation (3-4) is:

ton = ton,min/(1-X)

Equation (3-5) comes from algebraically recombining equations (3-1) through (3-4).

This equation has been used by Goldschmidt et. al. (1980) and Miller and Jaster (1985) to model field data. The constant in this equation (ton,min) is physically defined as the minimum ON time -- which occurs when the runtime fraction (X) is zero.

Since equations (3-4) and (3-5) are algebraically equivalent, their constants can be related:

ton,min = 60/4Nmax

The factor of 60 is included in the numerator of equation (3-6) assuming units are minutes for ton,min and cycles/hour for Nmax. This equation is useful for relating data from different researchers who may have used either equation (3-4) or (3-5).

Miller and Jaster (1985) developed an alternate form of equation (3-5) that they suggested for heat pumps and air conditioners:

ton = gamma(1+ alpha X)/(1-X)

They stated that the extra constant (αlpha) was added to account for the dependence of cooling (or heating) capacity on outdoor temperature. Since runtime fraction (X) also depends on outdoor temperature, the cooling (or heating) capacity is a function of X; thus, the constant (αlpha) is required. Their data from field tests of three heat pumps in the heating mode confirmed the need for this extra term.

3.3 Thermostat Theory and Performance: Droop

Another important aspect of thermostat performance is droop: the variation of space temperature with runtime fraction (X). Droop typically occurs because of the anticipator. The artificial heating from the anticipator causes the AC unit to turn ON sooner than if it were not present. The anticipator's effect is only realized when the AC unit is OFF, therefore the average temperature depends on X.

Simulation studies by Henderson (1991), Lamb and Tree (1981) and Nguyen and Goldschmidt (1983) have all demonstrated how the anticipator effects droop. For cooling, the net result is an increase in space temperature with increasing runtime fraction (X). When no anticipator is present, the opposite trend was observed: space temperature decreased with increasing runtime fraction.

In the NEMA Standard (1990), droop is defined as the change in average air temperature from X=0.2 to X=0.8. In this study, droop is defined as the slope of temperature versus runtime.

Tavg = co + doX

Or, as the constant do in equation (3-8), where Tavg and X are defined over the same interval. In this study, Tavg and X are determined over each on/off cycle (tcycle).

4.0 Experimental Setup

This section describes the experimental method used to collect the data presented in this report. First, the apparatus used to collect the data is described. Next, the techniques used to reduce and analyze data are presented. Finally, the experimental protocol used for each house is explained.

4.1 Experimental Apparatus

The goal of this study was to collect detailed cycling, temperature, and humidity data in several houses in an efficient manner. To meet these goals an apparatus was developed which: 1) was portable and easy to install and 2) could collect and store the required data.

A Campbell 21XL was selected as the datalogger in this study because it could be programmed to log data on an event (such as a switch closure). The datalogger was installed in a covered box with a 5 ft. pole attached to it's side. Temperature and humidity sensors were mounted at the top of this pole to sense space conditions. In addition, two wires extended from the top of the pole, which were attached to the thermostat terminals to sense thermostat status (i.e., ON or OFF). The AC status signal was input to the Campbell to determine when the thermostat turned ON and OFF. The apparatus was placed near the thermostat in each house as shown in Figure 4-1.

Figure 4-1 Placement of Experimental Apparatus Near Thermostat

Instrumentation

The datalogger and instrumentation are shown schematically in Figure 4-2. The measured quantities for this study were temperature, relative humidity, and AC runtime status.

Figure 4-2 Schematic of Datalogger and Instrumentation

Temperature was measured with an unshielded type-T thermocouple (TC). The TC was mounted at the top of the pole as shown in Figure 4-1. The top of the pole, which was approximately 5 ft. above the floor, could typically be located within 1 to 2 feet of the thermostat location.

Relative Humidity was measured with a TCS 1200-HB humidity sensor (±1% accuracy). The humidity sensor was also mounted at the top of the pole as shown in Figure 4-1. The 4-20mA output of this sensor was converted to a voltage at the data logger, where it was read.

AC Status was determined by measuring the voltage between the R and Y terminals on the thermostat. Two wires from the experimental apparatus were attached to these thermostat terminals in each house. When the AC unit is OFF, the voltage between R and Y is approximately 24 VAC, since the switch (e.g., either a liquid mercury bulb or a relay) is open. When the AC unit is ON, the switch closes and the voltage between these terminals is nearly zero.

A DC power supply was used to convert 24 VAC at the thermostat to 1 VDC as shown in Figure 4-2. The 1 VDC output signal was easily measured by the datalogger as a status signal. The DC power supply was designed to have a high input impedance (100,000 ohms) so that it would not impact the low impedance anticipator circuit (approximately 0.5 ohms).

Since thermostat switches often have a finite resistance, the voltage drop across the switch did not always go to zero. In electronic thermostats, this voltage drop across the switch was sometimes found to be as high as 1.5 VAC with the AC ON. Therefore, the threshold between ON and OFF was selected to be 0.1 VDC at the datalogger (or 2.4 VAC at the thermostat).

Programming the Campbell for the Required Data

Because detailed thermostat data were required, the data collection requirements for this study were slightly different than for other studies. Instead of collecting and storing data on a regular interval (e.g., 5 minutes), data had to be collected every time the AC unit switched ON and OFF. Therefore, the Campbell had to be programmed to collect and store times, temperatures, and humidities each time the AC status changed. It also had to average data over periods of indefinite length.

The datalogger monitored the status of the AC unit every ten seconds. If the AC status changed the required data was collected, averaged if necessary, and stored. Table 4-1 shows the data which was logged each time the AC status changed. The Campbell program used to collect this data is listed in Appendix B.

4.2 Data Collection and Reduction

After each house was tested, the apparatus was taken to FSEC where the stored data was down-loaded for analysis. The raw data listed in Table 4-1 was reduced to final form by a FORTRAN program. The AC status flag was used determine whether the data in each scan was for an ON or an OFF cycle. Then for each complete ON/OFF cycle, the data listed in Table 4-2 were calculated. See section 3 for definitions of the variables listed in Table 4-2.

Calculating Averages

In Table 4-2, the average T and RH over each complete ON/OFF cycle were calculated by time-weighing the average values for each scan (see note in Table 4-2). In the same fashion the averages over larger intervals were also calculated. This technique was used to determine the average T and RH for the entire test period in each house.

Hourly Runtime Profiles

The hourly runtime fraction was also calculated with an additional FORTRAN program. The average 24 hour profile for the house was also calculated. See Appendix C, plot 4.

4.3 Experimental Protocol

Each time a house was tested, the experimental protocol listed below was used:

1) The experimental apparatus was placed near the thermostat, the thermostat status wires were attached, and the unit was plugged into an AC outlet (to charge the Campbell's internal battery).

2) The occupants were asked questions about their house, including: floor area, number of occupants, house age, house type, etc. The name plate information was also taken off of the AC unit as well as the thermostat. Any abnormalities in the house, AC unit or thermostat were noted.

3) The experimental apparatus was left in the house for 1 to 3 days to log data automatically.

4) After 1 to 3 days, the apparatus was removed from the house and taken back to FSEC were the data was down loaded to an IBM-compatible PC. The apparatus was reset for the next test site.

5.0 Results and Discussion

This section presents the experimental data measured in this study. First, a summary of the general characteristics for all the monitored houses is presented. Second, measured cycling rates, dead bands, and droop are presented. Finally, the interdependence of cycling rate with other system parameters is analyzed.

5.1 General Description of Monitored Houses

Several houses were monitored for this study using the experimental apparatus and protocol described in section 4. 30 separate tests were conducted in 23 different houses and apartments in Brevard County. The detailed results for all 30 of the tests are given in Appendix C, along with a summary table.

Table 5-1 summarizes the general characteristics of the monitored homes. Histograms of these values are also shown in Figures 5-1 through 5-5.

In general, the houses monitored in this study had characteristics typical of Florida homes. The temperature set point and the average relative humidity were both similar to results found in other studies in Central Florida (Cummings 1990). The size and age of the homes were also typical. It is interesting to note that the age of homes was either newer than 10 years, or older than 20 years -- a trend roughly corresponding to the activity level at Kennedy Space Center.

AC equipment sizing seems to follow the "one ton per 500 ft2 of floor area" rule of thumb. New houses, which typically had higher insulation levels, tended towards the 600 to 700 ft2/ton range.

Several houses were tested multiple times. Typically the house was retested to determine the direct impact of a change (e.g. adding a new thermostat). These cases are discussed in section 5.8.

The tested homes are listed in Table 5-2. The type of construction (block, frame, apartment), type of thermostat (conventional or electronic) and date of test are listed, along with an ID letter. The ID letter is used to identify the houses on scatter plots presented later in this section.

Figure 5-1 Histogram of Average Space Temperature

Figure 5-2 Histogram of Average Space Relative Humidity

Figure 5-3 Histogram of Floor Area

Figure 5-4 Histogram of AC Sizing (Floor Area per AC Unit Size)

Figure 5-5 Histogram of House Age

5.2 Thermostat Cycling Rate: Nmax

For each test, equation (5-1) (the same as eqn. (3-4)) was curve-fit to the measured data to determine the constant Nmax. Figure 5-6 shows the measured data from one test (Rudd, C) along with the resulting fit to the equation. Each measured point corresponded to the X and N calculated for one complete ON/OFF cycle (see section 4.3). The Nmax which resulted in the best fit for this test was 1.75 and the standard deviation of the measured data from the curve was 0.14.

N = 4NmaxX(1-X)

As discussed in section 3, the constant Nmax corresponds to the maximum value of the cycling rate function. The curve-fit of measured data to determine Nmax was repeated for each test. The measured data and resulting curve-fit are shown for each test in Appendix C (see Plot 1).

Figure 5-7 shows a histogram of the curve-fit values of Nmax for all tests. The average Nmax for all tests was 2.48 cycles/hour. The standard deviation, minimum and maximum were 0.96, 0.15 and 4.07 respectively. The ratio of the standard deviation of the curve-fit (σ) to Nmax gives a good indication of how well equation (5-1) fits the measured data. Figure 5-8 is a histogram of this ratio (100σ/Nmax) from all tests. Typically the ratio of the standard deviation of the measured data from the curve (σ) to Nmax was smaller than 10%, indicating that equation (3-4) fits the measured data well and accurately represents cycling rate performance.

Figure 5-6 Thermostat Cycling Equation Fit to Measured Data (Rudd, C)

Figure 5-7 Histogram of Maximum Cycling Rate (Nmax)

Figure 5-8 Relative Error of Curve-Fits for Nmax

5.3 Thermostat Cycling Rate: ton,min

Equation (5-2) (which is the same as equation (3-5)) is an alternate form of the cycling rate equation which finds the ON time (ton) as a function of X.

ton = ton,min/1-X

As discussed in section 3, this equation is algebraically equivalent to (5-1) (and the constant ton,min is related to Nmax).

Miller and Jaster (1985) suggested adding the term alphaX to account for the dependence of AC capacity on outdoor temperature (see section 3 and Appendix A).

ton = gamma(1 + alphaX)/1-X

Note when alpha is zero, the constants ton,min and gamma are equivalent.

Figure 5-9 shows equations (5-2) and (5-3) curve-fit to the measured data for one test (Rudd, C). Since both functions go to infinity as X approaches 1, only data points for X less than 0.9 were used in the curve-fits. The standard deviation of the data points from the curve-fits were 0.96 and 0.85 for equations (5-2) and (5-3) respectively.

Figure 5-9 Curve-Fit of Equations (5-2) and (5-3) to Measured Data (Rudd, C)

Figure 5-10 Comparing Standard Deviation of Fits for eqns. (5-2) and (5-3)

This indicates that equation (5-3), which includes an extra parameter α, fits the measured data slightly better than equation (5-2). The curve-fit of equations (5-2) and (5-3) to the measured data was repeated for each test (see Appendix C, Plot 2). Figure 5-10 compares the standard deviations of the curve-fits of equations (5-2) and (5-3) for each test. Most data points fall on or below the dashed line representing equal error, indicating that equation (5-3) fits the data better than equation (5-2).

The average value for α was 0.14, with the minimum and maximum ranging from -0.25 to 0.7. As discussed in Appendix A, positive values of α skew the cycling equation (5-1) to the left while negative values skew it to the right.

In summary, the addition of the α term in equation (5-3) improves the degree of fit, but at the cost of increased complexity. In many cases it is questionable if the increased complexity is warranted.

Besides cycling rate, other important aspects of a thermostat's performance are deadband and droop. The thermostat deadband (ΔTspt) is the difference between the temperatures at which the thermostat turns ON and OFF (see section 3). Droop is the variation of the average temperature with the runtime fraction (X). More specifically, it is defined as the slope of average temperature with X (do in equation (3-8)).

Figure 5-11 shows the deadband (ΔTspt) as well as Ton, Toff and Tavg versus the runtime fraction (X) for one of the test cases (Rudd, C). The deadband, though slightly scattered, was not a function of X. The average deadband (ΔTspt) for this thermostat was higher than typical, at about 4°F.

The middle plot in Figure 5-11 shows the turn-ON and turn-OFF temperatures versus X (Ton and Toff). Both Ton and Toff were fit to a linear function. The slope for both of these lines was about 6°F, indicating that the anticipator in this thermostat had a strong effect.

The bottom plot in Figure 5-11 shows the average temperature versus X (for a complete ON/OFF cycle, as defined in section 4). The slope of the line curve-fit to the data is defined as droop in this study. For this test site the droop (do) was 2.9°F.

The analysis in Figure 5-11 was repeated for all the test sites (see Appendix C, plot 3). Figure 5-12 is the histogram of the temperature deadband (ΔTspt) calculated for each test and Figure 5-13 is the histogram of the droop (do). The average, standard deviation, minimum and maximum for deadband and droop are also given in Table 5-3.

Figure 5-11 Deadband (ΔTspt) and Ton, Toff, and Tavg
versus Runtime Fraction (X) (Rudd, C)

Figure 5-12 Histogram of Measured Deadband (ΔTspt)

Figure 5-13 Histogram of Droop (do)

The measured deadbands varied substantially from 0.8°F to 6.7°F. However, most were in the 2°F to 3°F range which have typically been observed in other studies (see Appendix D). The size of the deadband has been shown to effect the cycling rate by Henderson (1991) as well as others. This impact of deadband on cycling rate is further analyzed in a following section.

Both positive and negative values of droop were measured in the 30 tests. The 4 negative values for droop corresponded to 3 electronic, programmable thermostats and as well as an older thermostat which apparently had no anticipator (or a very weak one). The simulation study by Henderson (1991) also observed "negative droop" when an anticipator was not used. Typical values of droop with an anticipator present were in the 2°F to 4°F range. Droop is the primary indicator of anticipator strength (i.e., heating rate). The relationship between droop and cycling rate is discussed further in a following section.

5.5 Relative Humidity Deadband and Droop

In addition to temperature, the variation of relative humidity with X was also measured. Figure 5-14 shows the RH deadband (ΔRHspt), as well as RHon, RHoff, RHavg versus X for one of the test sites (Rudd, C). For this particular site, the RH deadband was typically 3% RH, but with a fair degree of scatter. The average RH also decreased slightly with increased X, indicating that the space RH depended on how often the AC operated. This analysis was repeated for each test site (see Appendix C, plot 6).

Figure 5-15 is a histogram of the RH deadband (ΔRHspt) for all the test sites. The RH deadband was positive for all the test sites, indicating that the RH was always lower after the AC unit turned OFF. In psychrometric terms, this implied that the SHR line of the cooling process was always steeper than the RH contours on the psychrometric chart.

One test site had a very large RH deadband of 7.3%. This test site (Dutton, O) was the only one which operated in the CONSTANT fan mode. The average humidity at this site was also the highest measured in this study, at 70% RH. This result reinforced the findings of Khattar et al. (1985) that the CONSTANT fan mode greatly reduces AC latent capacity and increases indoor humidity levels.

Figure 5-16 is a histogram of the slope of RH with runtime fraction (RH droop). In general, the RH droop was negative, indicating that the average RH was lower when the AC ran more often. However, several sites exhibited the opposite trend. The large variation of droop was largely attributed to weather effects. While temperature is being directly controlled, RH is only controlled indirectly. Therefore, the variation of outdoor humidity across the test period could impact the indoor humidity more than the runtime fraction.

In general, the RH trends with X showed a more scatter than the temperature trends. This was true because the thermostat/AC unit does directly control RH. Therefore, variations in weather during each test period tended to overwhelm the other measured effects.

Figure 5-14 RH Deadband and RHon, RHoff, and RHavg
versus Runtime Fraction (X) (Rudd, C)

Figure 5-15 Histogram of RH Deadband (RHon - RHoff)

Figure 5-16 Histogram of RH Droop (slope versus X)

5.6 Statistical Analysis of Cycling Rate (Nmax)

One of the major purposes of this study was to determine which system parameters affect the maximum cycling rate Nmax. Figures 5-17 through 5-22 show how Nmax varies with deadband (ΔTspt), droop (ao), average space temperature, average runtime fraction (Xavg), house age, and relative AC sizing (ft2/ton) respectively. Each point on these scatter plots is identified by an ID letter/number, which corresponds to the IDs listed in Table 5-2. The correlations of the system parameters to Nmax are summarized in Table 5-4.

Figure 5-17 shows how Nmax varies with deadband (ΔTspt). As expected from theory (see Appendix A), cycle rate is inversely proportional to deadband. The house with the highest deadband (Vieira1, Q) was also the site with the lowest observed cycling rate. Even though there is a substantial amount of scatter, Table 5-4 shows that the correlation between Nmax and ΔTspt was significant (i.e., T-ratio much greater than 2).

Figure 5-18 shows how Nmax varies with temperature droop (do). As discussed previously, the amount of droop is determined by the strength of the anticipator. Again, in spite of the scatter, the strength of the anticipator (or droop) was highly correlated to Nmax. The T-ratio relating droop (do) to Nmax was 3.5, indicating high confidence level in the trend.

Figure 5-19 shows Nmax versus the average space temperature. As expected, there was no measurable dependence of Nmax on the average temperature set point (the T-ratio for space temperature is listed in Table 5-4).

Figure 5-20 shows Nmax versus the average runtime fraction (Xavg) for each site. As for space temperature, no statistically significant trend of Nmax with Xavg could be discerned. This implies that the measured value of Nmax was not dependent on the load on the building or the size of the AC unit.

Figure 5-17 Scatter Plot of Nmax Versus Thermostat Deadband (ΔTspt)



Figure 5-18 Scatter Plot of Nmax Versus Temperature Droop (do)

Figure 5-19 Scatter Plot of Nmax Versus Average Space Temperature

Figure 5-20 Scatter Plot of Nmax Versus Average Runtime Fraction (Xavg)

Figure 5-21 Scatter Plot of Nmax Versus House Age

Figure 5-22 Scatter Plot of Nmax Versus AC Unit Sizing (ft2/ton)

Figure 5-21 shows Nmax versus house age. This trend was also not statistically significant. However, one interesting factor about this plot is the degree of scatter on Nmax for the newer versus the older houses. New houses, especially when a conventional thermostat is used, exhibit much less scatter than older houses. This seems to confirm the findings suggested by previous studies (McBride 1979) that modern thermostats with anticipators tend to dominate cycling rate and reduce the impact of other system parameters.

Figure 5-22 shows Nmax versus the relative sizing of the AC unit (ft2 floor area per ton of AC). As expected, no statistical trend of Nmax with AC sizing could be discerned (see Table 5-4). The relative sizing of the AC, which is also related to the average runtime (Xavg), had no impact on the cycling characteristics of the thermostat/building/AC system. While AC sizing does effect the value of X, it does not change the constant Nmax in the cycling equation.

In summary, only two parameters, deadband (ΔTspt) and droop (do) were statistically significant. While they were significant to a high level of confidence, the degree of fit was poor. A multi-variable, linear regression of Nmax to these two parameters resulted in:

The R2 indicates that the curve-fit explains only 41% of the total variation in Nmax, which leaves more than half of the variation of Nmax unexplained.

5.7 Other Factors Related to Thermostat Performance

It was suspected that several characteristics of the building, AC unit and thermostat would also qualitatively affect thermostat performance. Some of these are discussed below.

Block vs. Frame.

Initially, one goal of this study was to determine if the type of building construction (frame versus block) could be determined to have an impact on cycling rate (Nmax). The premise was that block houses have more thermal mass, which should decrease the cycling rate. Figure 5-23 shows the same data as Figure 5-18, except each point has been labeled to indicate the type of building construction (F - Frame, B - Block, or A - Apartment).

Figure 5-23 The Effect of Construction (Block, Frame, or Apartment) on Nmax

Only 6 of the 30 tests were frame construction, so a statistical analysis of the differences was not possible. However, qualitative examination of the data indicates that building construction has no noticeable impact on Nmax; the frame houses (F) are equally distributed with the block houses (B). Similarly, Apartments (A) showed no specific trend.

Thermostat Location.

Another important characteristic which effects thermostat performance is location. Thermostat manufacturers always recommend that thermostats be located on an inside wall where they are never exposed to direct sun. However, several houses had thermostats installed on both outdoor and garage walls, which are typically warmer than indoor walls. Figure 5-24 shows the same data as 5-18 but with each point labelled according to thermostat location (I - Indoor, O - Outdoor, or G - Garage). Again, no discernable trend was observed. Though the house with the highest cycle rate had the thermostat located on the garage wall (G), so did the house with the lowest cycling rate.

Figure 5-24 The Effect of Thermostat Location on Nmax

5.8 Multiple Tests in the Same House

At several of the sites, multiple tests were run to test the impact of a system characteristic. Some of these special cases are discussed below.

Changing Thermostats. At the Vieira residence, an electronic thermostat was installed for the first test conducted at the site (VIEIRA1, ID=Q). This thermostat had an extremely wide deadband (6.7°F) which resulted in a very low cycling rate (0.15 cycles/hr). After this test, the thermostat was replaced with a conventional unit and site was retested (VIEIRA2, ID=R). This conventional thermostat decreased the deadband and increased the cycle rate to the values shown in Table 5-5.

Thermostat Covers.

All thermostats come with a decorative cover which hides the internal workings of the thermostat. In addition to being decorative, this cover also effects the rate of heat transfer to the bimetallic element. Table 5-6 compares the measured performance of thermostat with and without the cover at the Cummings residence. In this case, removing the cover increased the cycle rate (Nmax) from 1.16 to 1.52.

Temperature Setpoint.

The impact of temperature setpoint was also analyzed at the Cummings residence. Table 5-7 compares thermostat performance at two different setpoints in the same house. Note that for this specific site, lowering the setpoint increased the temperature swing (or deadband) and reduced the effective droop. Both of these effects can be explained by the time response (i.e., time constant) of the bimetallic sensing element. Consistent with the statistical analysis of all the tests in section 5.6, the temperature set point had only a small impact on Nmax.

Changing AC Units.

At the Raustad residence, the test was repeated when the old AC unit was replaced with a new, high-efficiency AC system of approximately the same size. The same thermostat was used for both systems. Table 5-8 compares the thermostat performance at this site before and after the new AC was installed. Surprisingly, the deadband and droop on the thermostat change substantially which in turn increased the cycling rate for the new unit. Upon further investigation, it was determined that some of this difference may have been due to occupant behavior. For the first test (RAUSTAD1), the occupants were using an oscillating fan which may have affected the thermostat. This was not true for the second test (RAUSTAD2).

Another factor which may have played a role was the close proximity of the thermostat to a supply duct. The new AC may have delivered colder air which hit the thermostat and affected the cycling rate.

While it was not the case for the system tested here, in general changing the AC unit should have no impact on thermostat performance.

5.9 Daily Runtime Profiles

From the collected thermostat cycling information, it was possible to construct a profile of the average AC runtime for each hour over the test period. Figure 5-25 shows a typical runtime profile which was constructed from the measured cycling data. (Rudd, C) In the top plot, the profiles for each day of the test period are shown, labeled as A, B, C for the first, second and third day. In the bottom plot, the composite runtime profile is developed by averaging the runtimes for each hour over the test period. The runtime profiles developed for each test site are shown in Appendix C (plot 4).

These runtime profiles give an indication of the average hourly power demand profiles at each site.

Figure 5-25 Composite Hourly Runtime Profiles
Constructed from Cycling Data (Rudd, C)

5.10 Summary of Results

Section 5 has presented the measured results for this study. The following conclusions can be drawn from these results:

- The homes tested in this study were typical of homes in Brevard County. The average temperatures and humidities were 78°F and 56% RH for the 30 tests, and the average home size was 1500 ft2.

- The average cycling rate (Nmax) for the 30 field tests was 2.5 cycles/hour, with a high and a low of 4.1 and 0.15 respectively. While the average was in line with the value of 3.125 cycles/hour implicitly assumed in the SEER test procedure, there was a great deal of scatter in the measured values of Nmax. A statistical analysis of the test sites revealed that thermostat deadband (ΔTspt) and anticipator strength had the largest impact on Nmax. While these two thermostat parameters were statistically significant, they explained less than half of the total variation of Nmax. The source of this unexplained variation could not be determined from this study.

- A statistical analysis the of alternative cycling equation (5-3) proposed by Miller and Jaster (1985) indicated that it fit the measured data slightly better than the conventional cycling equation (5-2). Because the alternate equation is only slightly better, it is recommended that the simpler, conventional equation (5-1 or 5-2) still be used.

- A positive value of thermostat droop was observed in almost all the conventional thermostats tested. Electronic thermostats were all observed to have negative droop. These findings were consistent with simulation results from Henderson (1991). The average slope of temperature with runtime was 2.1°F/X.

- A qualitative examination of building construction (block versus frame) and thermostat location (garage versus interior wall) indicated no discernable affect on cycling rate. However, the sample size was inadequate to draw definitive, statistically-based conclusions.

- A repeat test at one house (Vieira) indicated the dramatic impact the thermostat can have on cycling rate. For the first test, an electronic thermostat was used which had an extremely wide deadband of 6.7°F. The value of Nmax measured at this site was 0.15 cycles/hour. For the second test, the original thermostat was removed and replaced with a conventional thermostat. The cycle rate for this case increased dramatically to 1.74 cycles/hour.

6.0 Applications

This section briefly describes how the data collected in this study can be used. A equation for determining part load performance as a function of Nmax is developed and used to estimate the impact of Nmax on cycling losses.

6.1 Developing a Part Load Function

The part load efficiency of an air conditioner (AC) is a function of several parameters: the amount of time the AC operates, the number of times the AC turns ON and OFF, and the transient characteristics of the AC.

Equation (6-1) determines the degradation of efficiency at part load for an AC considering all the factors listed above.

PLFi+1 = 1 - 4τNmax(1-CLF/PLFi)[1-e(-1/4τNmax(1-CLF/PLFi))]

The derivation of this equation is given in Appendix E. Note that the only assumptions used to derive this equation were: 1) that capacity is first order at start-up (equation E-4), and 2) that the cycling rate equation (E-2 or 1-1) is representative of thermostat performance.

Iterations are required to solve equation (6-1) since PLF occurs on both sides of the equation. Initially, PLF0 is assumed to be 1, which is used to find PLF1. Iterations proceed until PLFi+1 converges to PLFi.

Figure 6-1 shows how PLF varies with CLF when Nmax equals 1 through 4 cycles/hr, with the AC time constant (τ) equal to 80 seconds. Increasing Nmax decreases the part load factor (PLF) at a given value of CLF. The part load curve from the SEER test procedure, with the default CD=0.25, has also been included in the on the plot as a reference (ARI 1984). Note that the Nmax = 3 curve closely corresponds to this curve. This is not surprising since a value of 3.125 of Nmax is implicit in the conditions specified in the SEER cyclic test.

Figure 6-1 Equation (6-1) Plotted with Nmax = 1,2,3,4

6.2 The Impact of Nmax on Cycling Losses

Table 6-1 compares the part load performance with Nmax at 1,2,3,4 at 50% load (CLF=0.5). 50% load is used as the seasonal average in the SEER procedure to find part load efficiency.

Nmax has a substantial impact on the part load performance. When Nmax is 2.5, the average value measured in this study, it is expected that cycling losses would account for approximately 11% of total energy use.

7.0 References

ARI. 1984. "Unitary Air-Conditioning and Air-Source Heat Pump Equipment," 1984 Standard for Air-Conditioning & Refrigeration Institute, ARI Standard 210/240-84.

Cummings, J.B. 1990. "Infiltration Rates, Relative Humidity, and Latent Loads in Florida Homes." ASHRAE Seminar 01 - Winter Meeting.

Goldschmidt, V.W., Hart, G.H., and Reiner, R.C. 1980. "A Note on the Transient Performance and Degradation Coefficient of a Field Tested Heat Pump -- Cooling and Heating Mode," ASHRAE Trans., 86(2), No. 2610, pp.368-375.

Goldschmidt, V.W. 1981. "Effects of Cyclic Response of Residential Air Conditioners on Seasonal Performance," ASHRAE Trans., 87(2), CI-81-6 No. 2, p. 757-770.

Hart, G.H. and Goldschmitt, V.W. 1980. "Field Measurements of a Mobile Home Unitary Heat Pump (In the heating Mode)" ASHRAE Trans., 86(2), pp. 347-367.

Henderson, H.I. 1991. "Simulating Combined Thermostat, Air Conditioner, and Building Performancein a House", To be Presented at the 1992 ASHRAE Winter Meeting, FSEC-PF-224, July.

Khattar, M.K., Ramanan, N., Swami, M. 1985. "Fan Cycling Effects on Air Conditioner Moisture Removal Performance in Warm, Humid Climates," Florida Solar Energy, Center, FSEC-PF-75-85.

Lamb , G., and Tree, D.R. 1981. "Seasonal Performance of Air Conditioners -- An Analysis of the DOE Test Procedures: The Thermostat and Measurement Errors," Energy Conservation, U.S. Department of Energy, Division of Industrial Energy Conservation Report No. 2, DOE/CS/23337-2, Jan.

McBride , M.F. 1979. "Measurement of Residential Thermostat Dynamics for Predicting Transient Performance," ASHRAE Trans., 85(1) PH-79-7A, No. 3, pp. 684-694.

Miller , R.S., and Jaster, H. 1985. Performance of Air-Source Heat Pumps, Project 1495-1 Final Report, EPRI EM-4226, Nov.

Murphy , W.E., and Goldschmidt, V.W. 1979. "The Degradation Coefficient of a Field-Tested Self-Contained 3-Ton Air Conditioner," ASHRAE Trans., 85(2), No. 2554, pp. 396-405.

Nelson , L.W. 1974. "Predicting Control Performance of Residential Heating Systems with an Analog Computer," IEEE Transactions of Industry Applications, Vol. IA-10, No. 6, November/December, pp.731-740.

NEMA. 1990. "Residential Controls -- Electric Wall-Mounted Room Thermostats," NEMA Standards Publication No. DC 3, National Electrical Manufacturers Association, Washington, DC.

Nguyen , H.V., and Goldschmidt, V. 1983. "Modeling of a Residential Thermostat and the Duty Cycle of a Compressor-Driven HVAC System," ASHRAE Trans., 89(2A), No. 2783, pp. 361-372.

Parken, W.H., Didion, D.A., Wojciechowshi, P.H., and Chern, L. 1985. "Field Performance of Three Residential Heat Pumps in the Cooling Mode," NBSIR 85-3107, report by National Bureau of Standards, sponsored by U.S. Department of Energy for U.S. Department of Commerce, March.