Fault detection and diagnostics for commercial coolers and freezers.
In general, HVAC&R systems are not well maintained (Proctor and Downey 1995; Cowan 2004; Li and Braun 2006) because of the relatively high cost of service and low cost of energy. Recently, there has been a growing interest in the development of automated fault detection and diagnostics (FDD) for HVAC&R equipment. For vapor-compression cooling equipment, most of the methods presented in the literature (Grimmelius et al. 1995; Stylianou and Lau 1996; Rossi and Braun 1997) utilize differences between measurements and model predictions (residuals) of state variables to perform FDD. Although these methods have good performance for individual faults (Breuker and Braun 1998; Li and Braun 2003), they do not handle multiple-simultaneous faults. In addition, these methods require measurements over a wide range of conditions for training reference models, the development of which can be time consuming and cost prohibitive.
Recently, a diagnostic method was developed that handles multiple-simultaneous faults (Li and Braun 2007a) through the use of decoupling features (Li and Braun 2007b). Decoupling features are parameters that are uniquely influenced by individual faults and are insensitive to variations in ambient conditions. For example, air mass flow rate through the condenser is a feature that is strongly influenced by the level of fouling and condenser fan problems but is nearly independent of other faults that can occur for an air-conditioning system that incorporates fixed-speed fans.
In developing decoupling features, it is important to utilize low-cost sensors, such as temperature sensors (see Table 4 for a summary of the temperature measurements required to perform the diagnostics presented in this paper). These low-cost measurements are used in simple models as virtual sensors to infer other system measurements. For example, as described by Li and Braun (2007b), condenser airflow can be estimated using an energy balance with air-side and refrigerant-side measurements. For this energy balance, the refrigerant flow is estimated using a compressor map as a virtual sensor. Furthermore, virtual evaporating and condensing pressure sensors utilize surface-mounted temperature measurements at locations where saturated conditions exist and property relations to estimate saturation pressures.
The virtual and physical measurements are used to determine the decoupling features for diagnostic purposes. When a decoupling feature deviates significantly from its normal value, a fault is indicated (e.g., low condenser airflow for fouling or fan problems).
The decoupling-based FDD method was originally developed for air-conditioning (AC) systems. Although the vapor-compression equipment used for commercial refrigerators and freezers is very similar to that used for air conditioning, operation occurs over a different range of temperatures and the systems utilize different refrigerants. In addition, commercial refrigeration equipment typically utilizes liquid-line receivers that are not generally employed for air conditioners.
In this paper, the decoupling-based FDD method was applied to equipment used in small-scale walk-in coolers and freezers. Faults were artificially introduced in the laboratory, and the performance of the diagnostic method was evaluated.
WALK-IN COOLER AND FREEZER EXPERIMENTS
Walk-in cooler and freezer units were tested within psychrometric chambers to allow control of the condenser air inlet conditions. Figure 1 shows a cooler unit and walk-in cabinet. The walk-in cooler and freezer experiments utilized the same refrigerated space but employed different refrigeration equipment. The cooler system utilized R-22 as the refrigerant, whereas the freezer unit employed R-404A. Both systems were equipped with a thermal expansion valve (TXV) and a liquid-line receiver. The receiver provides a volume for liquid refrigerant to collect after it exits the condenser. This volume keeps the refrigerant exiting the condenser in a saturated liquid state during operation, unless the unit is overcharged to the point where the receiver is completely filled with liquid refrigerant. When the receiver is full, then additional charge added to the system will back up in the condenser and lead to subcooling of the refrigerant exiting the condenser under steady operating conditions. The liquid-line receiver is shown in Figure 2.
[FIGURE 1 OMITTED]
[FIGURE 2 OMITTED]
Figure 3 shows a schematic of the refrigerant cycle depicting the methods used for simulating faults and the measurements taken. Table 1 provides the list of faults along with a description of the fault simulation approaches. Refrigerant undercharge, refrigerant overcharge, liquid-line restriction, compressor valve leakage, condenser fouling, and evaporator fouling were considered. A leaky compressor valve allows high-pressure refrigerant to flow back to the low-pressure side of the system, which lowers the volumetric efficiency of the compressor and lowers the mass flow rate of the system. To simulate a leaky compressor valve, a bypass line with a flow control valve was added around the compressor that can be opened to allow refrigerant to flow from the high-pressure side of the system to the low-pressure side. Heat exchanger fouling in vapor-compression equipment can be characterized as a decrease in airflow across the coils. Previous work (Pak et al. 2005; Yang et al. 2007) has demonstrated that the primary effect of air-side heat exchanger fouling is an increased pressure drop leading to a reduced airflow rate. Fouling was simulated for both the condenser and evaporator by connecting fan speed controllers to control the airflow rates across the heat exchangers. During operation, a vapor-compression system can experience clogging of the filter dryer, which restricts the flow through the liquid line. In a system with a fixed-orifice expansion device, a liquid-line restriction can lead to a reduced mass flow rate. The walk-in cooler tested uses a TXV, which can compensate for the pressure drop incurred for moderate restrictions and keep the refrigerant flow rate relatively constant. For severe restrictions, the TXV will saturate, opening fully, and act like a fixed orifice. A flow control valve was added to the liquid line, which was partially closed to simulate this fault.
[FIGURE 3 OMITTED]
Table 1. Fault Simulation Methods Fault Type Simulation Method Compressor valve leakage Partially open bypass valve Condenser fouling Slow compressor fan using installed speed controller Evaporator fouling Slow evaporator fan using installed speed controller Liquid-line restriction Partially close liquid-line restriction valve Refrigerant undercharge Purposely undercharge the system Refrigerant overcharge Purposely overcharge the system
The instrumentation depicted in Figure 3 includes condenser inlet and outlet air temperatures ([T.sub.cai] and [T.sub.cao]) and evaporator inlet and outlet air temperatures ([T.sub.eai] and [T.sub.eao]) that were measured using thermocouple grids. Refrigerant pressures and temperatures were measured at the inlets and outlets of all components to accurately determine the refrigerant states. To understand where the two-phase regions in both the condenser and evaporator are located, eight thermocouples were soldered to the return bends of both the condenser ([T.sub.cond, 1-8]) and the evaporator ([T.sub.evap, 1-8]) and insulated from the surrounding air to obtain an indication of the refrigerant temperatures inside the tubes. Compressor power and refrigerant mass flow rate were also measured in order to determine system cooling capacity and efficiency.
Table 2 provides a description of the test matrix employed for the cooler. For the cooler, each individual fault was simulated at three different ambient conditions ([T.sub.cai]). Five fault levels were tested and characterized by percent of nominal cooling capacity. The nominal cooling capacity was determined in the unfaulted condition or 0th fault level test. Fault levels were chosen so that the degradation in cooling capacity would occur in even increments with the maximum degradation depending on the fault type. The compressor valve leakage and liquid-line restriction faults degraded cooling capacity by more than 50%. Undercharging the system degraded capacity by around 20%. Slowing the heat exchanger fans over the test range degraded the capacity by only 10%. Overcharging the refrigerant had very little effect because of the presence of a receiver. Four combinations of multiple faults were tested for the cooler. For these tests, the system was undercharged by 50%, and four other faults were applied to the system, all at maximum fault levels defined by the single-fault tests.
Table 2. Single- and Multiple-Fault Test Matrix for the Walk-In Cooler Fault Ambient Fault Capacity Tests Temperatures Levels Degradation Compressor valve leakage 55[degrees]F, 0-5 0%-55% 18 75[degrees]F, 95[degrees]F Liquid-line restriction 55[degrees]F, 0-5 0%-55% 18 75[degrees]F, 95[degrees]F Condenser fouling 55[degrees]F, 0-5 0%-9% 18 75[degrees]F, 95[degrees]F Evaporator fouling 55[degrees]F, 0-5 0%-10% 18 75[degrees]F, 95[degrees]F Low refrigerant charge 55[degrees]F, 0-5 0%-20% 18 75[degrees]F, 95[degrees]F High refrigerant charge 55[degrees]F, 0-5 0%-4% 18 75[degrees]F, 95[degrees]F Low charge, evaporator 75[degrees]F 5 20% 1 fouling Low charge, condenser 75[degrees]F 5 20% 1 fouling Low charge, compressor valve 75[degrees]F 5 15% 1 leakage Low charge, liquid-line 75[degrees]F 5 40% 1 restriction
Based on knowledge gained during testing of the walk-in cooler, a smaller test matrix was employed for the freezer; it is described in Table 3. Only one ambient condition was tested. The overcharging tests on the cooler showed that a liquid-line receiver prevents overcharging from being a fault that affects the performance of the system. Therefore, no overcharging tests were performed on the freezer. Multiple fault tests were run on the freezer combining evaporator fouling with the other four faults. One of the concerns with a freezer is ice accumulation and distinguishing it from evaporator fouling. To gather data on this phenomenon, an ice accumulation test was performed.
Table 3. Single- and Multiple-Fault Test Matrix for the Walk-In Freezer Fault Ambient Fault Capacity Tests Temperatures Levels Degradation No fault 55[degrees]F, 0 n/a 3 75[degrees]F, 95[degrees]F Compressor valve leakage 75[degrees]F 0-5 0%-10% 6 Liquid-line restriction 75[degrees]F 0-5 0%-60% 6 Condenser fouling 75[degrees]F 0-5 0%-2% 6 Evaporator fouling 75[degrees]F 0-5 0%-8% 6 Low refrigerant charge 75[degrees]F 0-5 0%-22% 6 Ice accumulation 75[degrees]F n/a n/a 1 Evaporator fouling, 75[degrees]F 5 20% 1 compressor valve leak Evaporator fouling, condenser 75[degrees]F 5 4% 1 fouling Evaporator fouling, 75[degrees]F 5 25% 1 liquid-line restriction Evaporator fouling, system 75[degrees]F 5 5% 1 undercharge
Except for the ice accumulation test, all of the data were obtained at steady-state conditions. Heaters were controlled within the cooled spaced in order to add the necessary load to achieve steady-state indoor conditions of 37.4[degrees]F. Data were collected and averaged over 10- to 15-minute intervals with the unit operating at a steady-state condition.
Compressor Valve Leakage
Compressor valve leakage is meant to include any fault within the compressor that leads to a loss in volumetric efficiency and refrigerant flow rate. As this fault develops, the volumetric efficiency of the compressor decreases. This decreases the refrigerant mass flow rate, which in turn decreases the discharge enthalpy. In order to detect this type of fault, a simple model is used to estimate the nominal discharge temperature ([T.sub.dis]) from the compressor. This expected value is then compared to the measured [T.sub.dis]. The normal discharge enthalpy is calculated as
[h.sub.dis, normal] = [h.sub.suc] + [[[W.sub.comp] - [Q.sub.loss]]/[m.sub.ref]], (1)
where [h.sub.suc] is suction enthalpy, [m.sub.ref] is refrigerant mass flow rate, [W.sub.comp] is compressor power, and [Q.sub.loss] is compressor heat loss. The suction pressure is determined using a virtual pressure sensor (described in the next section), and suction temperature is measured so [h.sub.suc] can be calculated. [W.sub.comp] and [m.sub.ref] are calculated using a compressor map and [Q.sub.loss] is estimated using a simple model as described later. The normal discharge temperature is determined using property relations with [h.sub.dis,normal] and the condensing pressure ([P.sub.c]) as inputs. Compressor maps are readily available from compressor manufacturers.
The discharge temperature residual is calculated as the difference between the measured and normal discharge temperatures as
[T.sub.dis, residual] = [T.sub.dis, measured] - [T.sub.dis, normal]. (2)
This residual is used as the fault feature for loss in compressor volumetric efficiency.
The refrigerant mass flow rate and compressor power used to determine this fault feature would normally be obtained using a compressor map available from the manufacturer. The compressor power consumption is insensitive to the compressor valve leakage fault. However, the compressor map is not accurate for estimating refrigerant flow rate with this fault. To handle this situation, Li (2004) proposed a refrigerant mass flow virtual sensor that is based on a compressor energy balance and described as
[m.sub.ref] = [[[W.sub.comp] - [Q.sub.loss]]/[[h.sub.dis] - [h.sub.suc]]]. (3)
Both the walk-in cooler and walk-in freezer use a constant-speed fan to force ambient air across the condenser. When fouling develops, the air side of the condensing coils becomes dirty and/or blocked by debris. This reduces the airflow over the coil, which increases the condensing pressure of the refrigerant and wears down the compressor at a greater rate while decreasing the cooling capacity and coefficient of performance (COP).
Li and Braun (2007b) used the air volumetric flow rate across the condenser coil as the feature to detect this fault. Airflow measurements are expensive and difficult to implement by a technician in the field, so a virtual sensor was developed for estimating the airflow rate. Using an energy balance on the condenser, the volumetric airflow rate can be estimated as
[V.sub.ca][approximately equal to][[[v.sub.ca][m.sub.ref]([h.sub.dis]([P.sub.c'][T.sub.dis]) - [h.sub.ll]([P.sub.c'][T.sub.ll]))]/[[c.sub.p,ca]([T.sub.cao] - [T.sub.cai])]], (4)
where [V.sub.ca] is the condenser air volumetric flow rate, [V.sub.ca] is the condenser air specific volume, [m.sub.ref] is the refrigerant mass flow rate, [h.sub.ll] is the liquid-line enthalpy, [T.sub.ll] is the liquid-line temperature, and [c.sub.p,ca] is the specific heat of the condenser air.
Since the change in temperature of the air across the condenser is relatively small, it is reasonable to assume that [V.sub.ca] and [c.sub.p,ca] are constant across the coils and can be calculated using the inlet conditions. Equation 4 is an approximation because it is assumed that there are no refrigerant pressure drops across the condenser and liquid line so that [P.sub.c] is equal to the pressure in the liquid line ([P.sub.ll]).
The primary effect of evaporator fouling is a reduction in airflow rate. For many air conditioners, this fault would generally be caused by fouling of an evaporator air filter. However, the walk-in cooler contains no filter, so evaporator fouling would occur due to deposits on the evaporator coil and through ice buildup. It could also occur, but to a lesser degree, by food products blocking the evaporator air inlets inside the cooler.
The reduction in airflow rate is used as the feature for this fault. A virtual sensor for evaporator airflow rate was presented by Li and Braun (2007b) as
[V.sub.ea][approximately equal to][[[v.sub.ea][m.sub.ref]([h.sub.suc]([P.sub.e],[T.sub.suc]) - [h.sub.ll]([P.sub.c],[T.sub.ll]))]/[[h.sub.eai]([T.sub.eai],[[PHI].sub.eai]) - [h.sub.eao]([T.sub.eao],[[PHI].sub.eao])]], (5)
where [V.sub.ea] is the evaporator air volumetric flow rate, [v.sub.ea] is the evaporator air specific volume, [P.sub.e] is the evaporation pressure, [h.sub.eai] is the evaporator air inlet enthalpy, [[PHI].sub.eai] is the evaporator air inlet relative humidity, [h.sub.eao] is the evaporator air outlet enthalpy, and [[PHI].sub.eao] is the evaporator air outlet relative humidity. The use of [h.sub.ll] in Equation 5 implies that the expansion process is isenthalpic.
For a cooler or freezer application, the air is very dry and it is not necessary to measure humidity. The air enthalpy difference can be evaluated based on measurements of temperature only and ideal gas behavior with constant specific heat.
Most commercial vapor-compression equipment uses a filter dryer in the liquid line to absorb water dissolved in the refrigerant and to filter out dirt. Over time, these devices can become saturated with water and dirt, which creates a large pressure drop.
In a typical air-conditioning system, there is usually about 15[degrees]F of subcooling at the condenser exit. This makes it difficult to use a temperature drop across the filter dryer ([DELTA][T.sub.ll]) as a fault indicator, because it would require a large pressure drop to get the refrigerant to change phase and generate a large enough [DELTA][T.sub.ll] for detection. However, for systems with a liquid-line receiver, the refrigerant at the condenser exit is a saturated liquid. Therefore, it requires a very small pressure drop in the liquid line to get the refrigerant to change phase. For detection of a liquid-line restriction, using two temperature measurements across the filter dryer should be adequate since a change in temperature can be directly correlated to pressure drop.
Undercharge and overcharge of a vapor-compression system usually occurs during service of the system. Refrigerant leakage is another fault that fits into this category because in doing fault detection, leakage is detected in the same manner as system undercharge. During fault diagnosis, they can be separated because the refrigerant leakage will become more severe over time while the system undercharge will remain constant. In this analysis, refrigerant leakage and system undercharge will be classified together as system undercharge.
Li (2004) suggested that a good measure of system charge would be the difference between the suction line superheat and the liquid-line subcooling, defined as
[DELTA][T.sub.[sh - sc]] = [T.sub.sh] - [T.sub.sc], (6)
where superheat and subcooling are defined as
[T.sub.sh] = [T.sub.suc] - [T.sub.e] and (7)
[T.sub.sc] = [T.sub.c] - [T.sub.cond, out]. (8)
Values of [T.sub.sh] and [T.sub.sc] for normal refrigerant charge levels will vary to some extent based on the ambient temperatures. To include the effects of driving conditions, Li and Braun (2007b) developed a new charge feature described as
[DELTA][T.sub.[sh - sc]] = [k.sub.sc, sh]([T.sub.sh] - [T.sub.sh, normal]) - ([T.sub.sc] - [T.sub.sc, normal]), (9)
where [k.sub.sc,sh] is the ratio of subcooling change to superheat change with the ambient temperatures and [T.sub.sh,normal] and [T.sub.sc,normal] are values of superheat and subcooling degree for the normal refrigerant charge at a rating condition. For air-conditioning equipment, the feature in Equation 9 is sensitive to refrigerant charge but is relatively insensitive to ambient conditions and other faults. The rating condition for Equation 9 is somewhat arbitrary and could be chosen as the standard rating condition for the air-conditioning unit.
Liquid-line receivers cause the refrigerant in the liquid line to be saturated, so the difference between the normal and measured subcooling is approximately zero, even with changing operating conditions at full charge. Furthermore, the use of a TXV causes the superheat to be relatively constant. Therefore, as charge is removed or added, the feature defined by Equation 9 should not change until the receiver becomes either completely empty or completely full. When the system is undercharged to the point where the receiver is empty, there should be two-phase refrigerant in the liquid line. This will cause the TXV to fully open and lose control of the superheat. Undercharging the system further should cause superheat to increase while subcooling should remain approximately equal to zero. At the other extreme, when the receiver is completely full, refrigerant will back up in the condenser and additional charge will cause an increase in the condenser subcooling. However, the superheat should remain relatively constant for overcharging. Since superheat only changes for low-refrigerant charge and subcooling only varies for severe overcharging, the simple feature of Equation 6 was chosen for characterizing these faults. However, practically it is not necessary to consider refrigerant overcharging for the walk-in cooler and freezer because both systems had to be charged to at least 200% of nominal charge before the receiver completely filled. Below this level of refrigerant charge there was essentially no impact on system performance.
EVALUATION OF VIRTUAL SENSORS
A virtual pressure sensor uses a thermocouple mounted to a return bend of the condenser or evaporator to infer the high-side or low-side pressure. In both the walk-in cooler and walk-in freezer experiments, eight thermocouples were soldered to the return bends of both the condenser and the evaporator and insulated from the ambient air using two layers of foam tape. The thermocouples at the inlet to the evaporator and on the fifth return bend of the condenser were selected to calculate evaporating and condensing pressures because these positions had two-phase refrigerant for all conditions. The calculated pressures were then compared to the averages of the measured inlet and outlet pressures for each heat exchanger.
Figures 4 and 5 compare measured and virtual evaporating and condensing pressures for the walk-in cooler for all of the test conditions. Uncertainty bars for the virtual pressures are included along with lines that represent an error of [+ or -]5%. The differences between virtual and actual pressure outputs were within the uncertainty of the actual pressure sensors except for one evaporating pressure that had a difference of about 10%. This operating point corresponded to a liquid-line restriction for the highest fault level at an ambient temperature of 75[degrees]F. Very similar results were obtained for the freezer. It should be noted that there is small bias in the results of Figure 5 in that the virtual condensing pressure is always lower than the actual pressure measurement. The most logical explanation for the bias is that the virtual pressure measurement is based on the use of a surface temperature measurement, which is always lower than the refrigerant temperature.
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[FIGURE 5 OMITTED]
Refrigerant Mass Flow
Figure 6 compares mass flow rate from the compressor map to measured mass flow rate for all of the experiments performed on the walk-in cooler. The mass flow was calculated using virtual pressure sensors as inputs and a correction for superheat. The large uncertainties in the estimated mass flow rates are primarily due to uncertainties in the evaporating pressure estimates. Overall the predictions agree well with measured mass flow rates. The root mean square (RMS) errors were 1.06 [lb.sub.m]/h for all of the data. Somewhat worse results were obtained for the freezer.
[FIGURE 6 OMITTED]
A compressor energy balance is used to determine refrigerant mass flow rate instead of the compressor map when the compressor is known to be faulted. Figure 7 compares measured mass flow rates with flow rates determined from a compressor energy balance for all of the data points. The terms in the energy balance were evaluated using measured suction and discharge temperatures with virtual measurements for pressures and power consumption. The accuracy of this approach is considerably worse than that of the compressor map (RMS error of 3.63 [lb.sub.m]/h versus 1.06 [lb.sub.m]/h for the compressor map approach). However, it is adequate for estimating mass flow rate for conditions where the performance of the compressor is known to have degraded.
[FIGURE 7 OMITTED]
Compressor Power Based on a Compressor Map
Compressor power is estimated using a compressor map available from the manufacturer. The map power was calculated using virtual pressure inputs to simulate the implementation of the diagnostic method. The compressor map power was evaluated without correcting for superheat, as recommended by Shen (2006). Figure 8 compares the compressor map power to the measured compressor power for all of the experiments performed on the cooler. The uncertainty in the compressor map is primarily due to uncertainties in the virtual pressure measurements. The RMS error for the compressor map is 22.2 W. Comparisons for the compressor used in the freezer were somewhat worse. However, the accuracy of these maps is adequate for use in estimating discharge temperatures to perform compressor fault diagnoses.
[FIGURE 8 OMITTED]
Compressor Heat Loss
It is necessary to estimate compressor heat loss for use in an energy balance for determining the normal compressor discharge temperature. For small hermetic compressors, heat loss typically is between 20% and 75% of the input power consumption. Data collected from the experiments was used to develop a simple correlation for heat loss. The heat loss is a function of the ambient temperature and the compressor shell temperature. However, the instrumentation setup did not include any shell temperature measurements, so a pseudo-shell temperature was defined as
[T.sub.shell][approximately equal to][[[T.sub.dis] + [T.sub.suc]]/2]. (10)
A heat loss factor was estimated from measurements and correlated with the temperature difference between the shell and ambient temperatures. The heat loss factor ([[alpha].sub.loss]) is the ratio of the compressor heat loss to the electrical input and was estimated from measurements using an energy balance on the compressor according to
[[alpha].sub.loss] = 1 - [[[m.sub.ref]([h.sub.dis] - [h.sub.suc])]/[w.sub.comp]]. (11)
The measurements included everything necessary to evaluate the heat loss factor, including discharge temperature and pressure, suction temperature and pressure, refrigerant mass flow rate, and compressor power. However, these measurements would generally not be available; therefore, virtual measurements of pressures and power consumption and mass flow rate from compressor maps were used to determine the heat loss factor.
The heat loss factor for the walk-in cooler is plotted as a function of the difference between the shell temperature ([T.sub.shell]) and the ambient temperature ([T.sub.amb]) in Figure 9. The heat loss rate ranged from about 46% to 56% of the compressor input power. The data points in Figure 9 include relatively large error bars associated with the heat loss estimates. A best-fit linear relationship was determined from the data and used for estimating heat loss as a function of temperature difference. A linear relationship was chosen for simplicity and because one would expect a linear relationship with temperature difference. For the freezer, the heat loss factors were much lower (between about 10% and 20%) because of the significantly lower suction pressures and temperatures. Furthermore, there was a little more scatter in the data. However, a linear relationship also provided a reasonable fit to the data.
[FIGURE 9 OMITTED]
FAULT FEATURE CHARACTERISTICS
In this section, individual fault features are presented as a function of percent capacity degradation associated with different individual faults. The cooling capacity of the 0th fault level was taken as a baseline value for determining percent capacity degradation. Cooling capacity degradation was chosen as a general indicator of the severity of fault because it is more sensitive to fault level than efficiency degradation. Furthermore, for refrigeration equipment, lost cooling capacity could mean the loss of valuable refrigerated or frozen product, which is more important than lost efficiency.
The cooling capacity was determined using a refrigerant flow measurement, and enthalpies were determined with inlet and outlet refrigerant temperatures and pressures. Average uncertainties in capacities for the refrigerator and the freezer were 7.1% and 7.4%, respectively. As capacity is reduced with increasing fault severity, the absolute value of the uncertainty remains relatively constant, causing the percent uncertainty to increase. Although these uncertainties may seem high, cooling capacity measurements were not used to detect faults. They were only used to provide a common way to indicate the level of each fault.
In this section, only sample results that highlight particular performance characteristics and problems are presented. The fault features were calculated for two cases: 1) using all of the measured data and 2) using virtual sensors wherever possible. Table 4 summarizes the measurements used in calculating the fault features when using all real sensors and when employing the virtual sensors presented in this paper. The left-hand column is a list of all sensors required if all real sensors (and no virtual sensors) were used in performing the diagnostics. The right-hand column is a list of temperature sensors required if virtual sensors were used.
Table 4. Measurements for Estimating Diagnostic Features with Real and Virtual Sensors (See Figure 3 for Nomenclature) Measurements Required When Using All Measurements Required When Using Real Sensors Virtual Sensors [T.sub.dis], [degrees]F [T.sub.dis], [degrees]F [T.sub.cond,out], [degrees]F [T.sub.cond,out'] [degrees]F [T.sub.ll1], [degrees]F [T.sub.ll1], [degrees]F [T.sub.ll2], [degrees]F [T.sub.ll2], [degrees]F [T.sub.exp,in], [degrees]F [T.sub.exp,in], [degrees]F [T.sup.evap,in], [degrees]F [T.sub.evap,in], [degrees]F [T.sup.evap,out], [degrees]F [T.sub.evap,out], [degrees]F [T.sub.suc], [degrees]F [T.sub.suc], [degrees]F [T.sub.eao], [degrees]F [T.sub.eao], [degrees]F [T.sub.eat], [degrees]F [T.sub.eai], [degrees]F [T.sub.cao], [degrees]F [T.sub.cao], [degrees]F [T.sub.cai], [degrees]F [T.sub.cai], [degrees]F [T.sub.cond,5], [degrees]F [T.sub.cond,5], [degrees]F [P.sub.dis], psia -- [P.sub.cond,out], psia -- [P.sub.evap,in], psia -- [P.sub.suc], psia -- [m.sub.ref], l[b.sub.m]/h -- [W.sub.comp],W --
Compressor Valve Leakage
Figures 10 and 11 show the effect of capacity degradation due to compressor valve leakage on discharge temperature residuals for the walk-in cooler and freezer. This fault feature increases with fault level for both systems with either real or virtual sensors. However, the discharge residual is much less sensitive to capacity degradation for the cooler than for the freezer. The small dependence of discharge temperature residual on capacity degradation for compressor valve leakage fault with the cooler is problematic because this feature also depends on condenser fouling, as shown in the next section. This effect may be due to an inadequate heat loss model for the compressor. The compressor heat loss is much more significant for the cooler application than for the freezer application because of higher suction pressures and temperatures. Therefore, errors in this model have a more significant effect on the discharge temperature for the cooler.
[FIGURE 10 OMITTED]
[FIGURE 11 OMITTED]
The compressor valve leakage fault also caused the feature for low refrigerant charge to increase at high fault levels for the walk-in cooler, as demonstrated in Figure 12. As the compressor flow is reduced, the TXV must open to maintain the target superheat. At severe fault levels, the TXV saturates open and the superheat increases. This could potentially lead to a false alarm for low charge for capacity degradations greater than about 40%. However, this may not be a problem, because the compressor fault would normally be identified at lower fault levels before the charge feature is affected. Furthermore, false alarms could be avoided for individual faults because the diagnostic feature for compressor valve leakage would take precedence. In other words, if the compressor temperature discharge feature exceeded a threshold for this fault, then the refrigerant charge feature would be ignored. However, under some circumstances it may not be possible to remotely diagnose both low refrigerant charge and compressor valve leakage if they are simultaneously present. In this case, a technician might need to visit the unit and use a sight glass to determine whether the refrigerant charge is low prior to deciding whether to replace the filter dryer.
[FIGURE 12 OMITTED]
The virtual condenser airflow rate determined with virtual sensors was also found to have some dependence on the compressor valve leakage fault. However, this feature increased with fault level, which would not lead to a false alarm.
Figure 13 shows the impact of the condenser fouling fault level on the virtual condenser aiflow rate. This feature is very sensitive to the condenser fault and decreases by a factor of two for about a 5% degradation in cooling capacity. This feature was also effective in characterizing condenser fouling for the freezer.
[FIGURE 13 OMITTED]
For the cooler, the discharge temperature residual also increased with condenser fouling level (shown in Figure 14). This will lead to a false alarm for a compressor valve leakage fault in the presence of condenser fouling. The discharge temperature residual did not have the same level of dependence on condenser fouling for the freezer. Therefore, this behavior may be due to an inadequate heat loss model for the compressor. As previously mentioned, the compressor heat loss is much more significant for the cooler application than for the freezer application because of higher suction pressures and temperatures.
[FIGURE 14 OMITTED]
Figure 15 shows the impact of evaporator fouling on the virtual evaporator airflow rate. The results are very similar to those for condenser fouling. This feature is very sensitive to fouling and decreases by a factor of two for less than a 5% degradation in capacity. Very similar results were obtained for the freezer. Furthermore, this feature was insensitive to other faults and would not trigger any false alarms.
[FIGURE 15 OMITTED]
One of the issues for the walk-in freezer was the ability to distinguish between evaporator fouling and ice accumulation on the heat exchanger prior to a defrost cycle. To characterize the ice buildup, an ice accumulation test was run. First, the freezer was allowed to reach its normal steady-state operating conditions. Then, a pot of boiling water was placed inside the freezer on a heater to promote the accumulation of ice. When a steady state was achieved again, data was collected for about 9600 seconds. Over time, the temperature difference across the evaporator ([DELTA][T.sub.ea]) increased as ice built up on the heat exchanger. As a result, the virtual evaporator airflow rate decreased over time, as shown in Figure 16, and is a good indicator of the buildup of frost. Although not shown in this figure, the virtual evaporator airflow feature returned to a value of about 1200 cfm after a defrost cycle.
[FIGURE 16 OMITTED]
Evaporator fouling and ice accumulation could easily be distinguished within a fault detection system. After a defrost cycle and when steady-state conditions are achieved, the evaporator aiflow rate should return to a normal, unfaulted value. If the evaporator were fouled, then a defrost cycle would not return the virtual evaporator airflow indicator to normal and a fault could be flagged.
In fact, the virtual evaporator airflow feature could be used as part of a smart defrosting scheme to determine the need for defrosting. A threshold could be determined that balances the trade-offs between improved cycle efficiency and defrost energy. This could lead to reduced defrost cycles for situations where the evaporator is not exposed to significant moisture (e.g., infrequent door openings) and increased defrost cycles for cases with high indoor box moisture levels.
Figure 17 shows the effect of capacity degradation due to liquid-line restriction on the liquid-line temperature difference for the cooler. This fault feature increases significantly with fault level for all three ambient conditions. However, the impact is less at lower ambient temperatures due to a lower pressure ratio for the system. For the same fault level, the pressure drop across the restriction is larger for higher ambient temperatures, which increases the temperature drop across the restriction. Very similar results were obtained for the freezer.
[FIGURE 17 OMITTED]
The liquid-line restriction also caused the feature for low refrigerant charge to increase for the walk-in freezer, as demonstrated in Figure 18. Again, this occurs because of an interaction with the TXV. As the refrigerant flow is reduced with a liquid-line restriction, the TXV must open to maintain the target superheat. At a sufficient fault level, the TXV saturates open and the superheat increases. Although the refrigerant charge feature is sensitive to liquid-line restriction, false alarms can be avoided for individual faults because the diagnostic feature for liquid-line restriction would take precedence. In other words, if the liquid-line feature exceeded a threshold for this fault, then the refrigerant charge feature would be ignored. However, it may not be possible to remotely diagnose both low refrigerant charge and a liquid-line restriction if they are simultaneously present. In this case, a technician would need to visit the unit and use a sight glass to determine whether the refrigerant charge is low.
[FIGURE 18 OMITTED]
A liquid-line restriction did not cause changes in other fault features that would lead to false alarms.
Figure 19 shows the effect of refrigerant charge level on capacity degradation for the walk-in cooler. Overcharging the system had very little effect on performance because of the liquid-line receiver. Very high charge levels had a small impact at low ambient temperatures at the point where the receiver became full of refrigerant. Reduced charge did have an impact on cooling capacity once the charge was less than about 80% of the nominal charge. At this point, the liquid-line receiver was empty and the TXV saturated at a fully open position. This led to an increasing superheat and fault feature with decreasing charge, as demonstrated in Figure 20. Similar results were obtained for the freezer.
[FIGURE 19 OMITTED]
[FIGURE 20 OMITTED]
Low or high refrigerant charge did not have a significant effect on other fault features and would not lead to false alarms. Although it is not possible to detect system overcharging for these systems, this is not a problem because overcharging does not impact system performance.
Li (2004) defined a normalized fault indicator as
[IND.sub.faultname] = [[f[v.sub.current]]/[f[v.sub.predefined]]], (12)
where [IND.sub.faultname] is the fault indicator for a specific fault, f[v.sub.current] is the current fault feature value, and f[v.sub.predefined] is the predefined fault feature value.
For this study, the f[v.sub.predefined] was chosen as the feature value that represented a 10% cooling capacity loss. All of the thresholds for [IND.sub.faultname] were then set to be 0.5, which represents a 5% capacity loss. Tables 5 and 6 show the f[v.sub.predefined] and fault thresholds set for the walk-in cooler and freezer, respectively. The compressor valve leakage fault thresholds are extremely different between the cooler and freezer because of different impacts on cooling capacity.
Table 5. Fault Thresholds and Predefined Fault Feature Values for the Walk-In Cooler Compressor Condenser Fault Valve Leak Fouling Feature [DELTA] [DELTA][V.sub.ca] [T.sub.dis] F[v.sub.predefined] 1.5[degrees]F -652 [ft.sup.3]/min Threshold 0.5 0.5 Evaporator Liquid-Line Fault Fouling Restriction Feature [DELTA][V.sub.ea] [DELTA][T.sub.ll] F[v.sub.predefined] -594 4.7[degrees]F [ft.sup.3]/min Threshold 0.5 0.5 System Fault Undercharge Feature [DELTA][T.sub.sh-sc] F[v.sub.predefined] 4.7[degrees]F Threshold 0.5 Table 6. Fault Thresholds and Predefined Fault Feature Values for the Walk-In Freezer Compressor Condenser Fault Valve Leak Fouling Feature [DELTA] [DELTA][V.sub.ca] [T.sub.dis] F[v.sub.predefined] 41.7[degrees]F -600 [ft.sup.3]/min Threshold 0.5 0.5 Evaporator Liquid-Line Fault Fouling Restriction Feature [DELTA][V.sub.ea] [DELTA][T.sub.ll] F[v.sub.predefined] -700 2.2[degrees]F [ft.sup.3]/min Threshold 0.5 0.5 System Fault Undercharge Feature [DELTA][T.sub.sh-sc] F[v.sub.predefined] 4.2[degrees]F Threshold 0.5
Fault features determined using data from the experiments were used along with the fault thresholds to determine the levels at which faults could be detected and to identify false alarms. Virtual sensors were used for this evaluation to represent actual implementation of the decoupled diagnostic method. Tables 7 and 8 give results for fault detection sensitivity. For the single-fault tests on both the walk-in cooler and walk-in freezer there were no missed faults. The diagnostic method was able to detect compressor valve leak, condenser fouling, and liquid-line restriction at the first fault level implemented on the cooler. Liquid-line restriction was detected at the first level on the freezer as well.
Table 7. Fault Levels Where the Algorithm Could First Diagnose Individual Faults for the Walk-In Cooler Ambient Degraded Fault Temperature Fault Level Capacity Compressor valve leak 55[degrees]F First 21.0% Compressor valve leak 75[degrees]F First 16.0% Compressor valve leak 95[degrees]F First 17.5% Condenser fouling 55[degrees]F First 1.2% Condenser fouling 75[degrees]F First 1.2% Condenser fouling 95[degrees]F First 2.6% Evaporator fouling 55[degrees]F Second 1.9% Evaporator fouling 75[degrees]F Third 5.2% Evaporator fouling 95[degrees]F Third 6.1% Liquid-line restriction 55[degrees]F First 19.4% Liquid-line restriction 75[degrees]F First 7.5% Liquid-line restriction 95[degrees]F First 8.5% System undercharge 55[degrees]F Fourth 7.9% System undercharge 75[degrees]F Third 10.5% System undercharge 95[degrees]F Third 6.1% Table 8. Fault Levels Where the Algorithm Could First Diagnose the Individual Faults for the Walk-In Freezer Ambient Fault Degraded Fault Temperature Level Capacity Compressor valve leak 75[degrees]F Third 3.5% Evaporator fouling 75[degrees]F Third 3.0% Liquid-line restriction 75[degrees]F First 22.5% System undercharge 75[degrees]F Fourth 11.9%
Although the diagnostic method did not miss any faults, in some cases two faults were identified when only a single fault was present. Table 9 shows the implemented faults and fault levels that resulted in secondary fault indications. As previously described, both compressor valve leakage and liquid-line restriction can influence the feature used to determine low refrigerant charge if they are severe enough to cause the TXV to saturate in a fully open position. For the compressor valve leakage fault with the cooler, this occurred at a significantly higher fault level (third level in Table 9) than necessary to detect the compressor valve leakage fault (first level in Table 7) and would not be a problem. However, the fault indicators for both liquid-line restriction and low refrigerant charge fault exceeded their thresholds at the lowest level of liquid-line restriction. If it were only necessary to diagnose a single fault, then this would not be a problem because the indicator for liquid-line restriction would take precedence since it is independent of other faults. However, the method can't reliably diagnosis combinations of liquid-line restriction/low refrigerant charge or compressor valve leakage/low refrigerant charge. In order to eliminate low refrigerant charge as a possible fault in situations where these fault combinations are indicated, it would be necessary to visit the site and observe the refrigerant level using a receiver sight glass.
Table 9. Implemented Faults Causing Secondary Fault Indications System Implemented First Fault Level Falsely Indicated Fault Fault Indicating Secondary Fault Cooler Compressor valve Third System undercharge leak Cooler Condenser First Compressor valve leak fouling Cooler Liquid-line First System undercharge restriction Freezer Liquid-line First System undercharge restriction
Table 9 also shows a secondary fault indication for compressor valve leakage when condenser fouling was implemented. Both faults were indicated at the lowest level of condenser fouling, so the condenser fouling indicator would take precedence because its feature is independent of all faults. As previously discussed, it is believed that diagnosis of a compressor valve leakage for this case is due to inaccuracies in the estimate of the normal compressor discharge temperature due to an inadequate heat loss model.
Besides the secondary fault indications, there were no false alarms encountered for either the cooler or freezer at any of the fault levels.
Diagnostic performance was also examined for the multiple fault tests described in Tables 2 and 3. For these tests, the method applied to the cooler yielded no false alarms. Also, the method could correctly diagnosis low refrigerant charge combined with either condenser or evaporator fouling. However, as expected, the method could not detect combinations of refrigerant undercharge with either a liquid-line restriction or compressor valve leakage. For the freezer, the diagnostic method correctly detected evaporator fouling combined with either compressor valve leakage or refrigerant undercharge. However, the method detected refrigerant undercharge in addition to evaporator fouling and liquid-line restriction when those two faults were implemented.
In general, the decoupling features developed for compressor valve leakage, condenser fouling, evaporator fouling, liquid-line restriction faults, and refrigerant charge should work well for diagnostics applied to vapor-compression systems used in walk-in coolers and freezers. However, it was found that the refrigerant charge feature is not completely decoupled from liquid-line restriction and compressor valve leakage faults at high-fault levels. Systems that utilize a liquid-line receiver and TXV are insensitive to charge until the system becomes starved and the TXV saturates open. A saturated TXV leads to an increase in superheat, which is used to indicate low refrigerant charge. However, the TXV can also be saturated open when refrigerant flow is reduced significantly due to a high level of compressor valve leakage or a severe liquid-line restriction.
Although the refrigerant charge feature is sensitive to liquid-line restriction and compressor valve leakage faults, false alarms can be avoided for individual faults because the diagnostic features for these other faults work well and would identify the appropriate fault in the absence of low charge. However, it is not possible to identify multiple fault combinations of low refrigerant charge and either compressor valve leakage or liquid-line restriction. Furthermore, it is not possible to determine overcharging of refrigerant with this feature, unless the charge is severely overcharged to the point where the receiver is full. For systems with liquid-line receivers and TXVs, it may make sense to employ a low-cost level sensor in the receiver. The normal charge level could be correlated with operating conditions and used to decouple charge from other faults.
There is also a need to develop a better model for estimating heat loss in order to improve estimates of the normal compressor discharge temperature under all conditions. This should eliminate an indication of compressor valve leakage when condenser fouling is present.
Evaporating frosting tests were also implemented, and the evaporator fouling feature was found to be a reliable indicator. This feature could be used as part of a smart defrosting scheme to determine the need for defrosting. A threshold could be determined that balances trade-offs between improved cycle efficiency and defrost energy. This could lead to reduced defrost cycles for situations where the evaporator is not exposed to significant moisture (e.g., infrequent door openings) and increased defrost cycles for cases with high indoor box moisture levels.
This work was supported by the U.S. Department of Energy. We appreciate the donation of equipment provided by Manitowoc, Inc., and coordinated by Daryl Erbs.
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Student Member ASHRAE
James E. Braun, PhD
Received December 29, 2007; accepted April 16, 2008
Adam Wichman is a reactor engineer at PSEG Nuclear LLC, Hancock's Bridge, NJ. James E. Braun is a professor in the School of Mechanical Engineering, Purdue University, West Lafayette, IN.