Journal of Engineering, Design and Technology Prediction of coefficient of performance and simulation design of an air-source heat pump water heater Stephen Loh Tangwe, Michael Simon, Edson Leroy Meyer,
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Received 30 June 2016 Accepted 2 February 2017
Prediction of coefficient of performance and simulation design of an air-source heat pump water heater Stephen Loh Tangwe, Michael Simon and Edson Leroy Meyer Fort Hare Institute of Technology, University of Fort Hare, Alice, South Africa
Abstract Purpose – The purpose of this study was to build and develop mathematical models correlating ambient conditions and electrical energy to the coefficient of performance (COP) of an air-source heat pump (ASHP) water heater. This study also aimed to design a simulation application to compute the COP under different heating up scenarios, and to calculate the mean significant difference under the specified scenarios by using a statistical method.
Design/methodology/approach – A data acquisition system was designed with respect to the required sensors and data loggers on the basis of the experimental setup. The two critical scenarios (with hot water draws and without hot water draws) during the heating up cycles were analyzed. Both mathematical models and the simulation application were developed using the analyzed data.
Findings – The predictors showed a direct linear relationship to the COP under the no successive hot water draws scenario, while they exhibited a linear relationship with a negative gradient to the COP under the simultaneous draws scenario. Both scenarios showed the ambient conditions to be the primary factor, and the weight of importance of the contribution to the COP was five times more in the scenario of simultaneous hot water draws than in the other scenario. The average COP of the ASHP water heater was better during a heating cycle with simultaneous hot water draws but demonstrated no mean significant difference from the other scenario.
Research limitations/implications – There was a need to include other prediction parameters such as air speed, difference in condenser temperature and difference in compressor temperature, which could help improve model accuracy. However, these were excluded because of insufficient funding for the purchase of additional temperature sensors and an air speed transducer.
Practical implications – The research was conducted in a normal middle-income family home, and all the results were obtained from the collected data from the data acquisition system. Moreover, the experiment was very feasible because the conduction of the study did not interfere with the activities of the house, as occupants were able to carry out their activities as usual.
Social implications – This paper attempts to justify the system efficiency under different heating up scenarios. Based on the mathematical model, the performance of the system could be determined all year round and the payback period could be easily evaluated. Finally, from the study, homeowners could see the value of the efficiency of the technology, as they could easily compute its performance on the basis of the ambient conditions at their location. Originality/value – This is the first research on the mathematical modeling of the COP of an ASHP water
heater using ambient conditions and electrical energy as the predictors and by using surface fitting
Journal of Engineering, Design and Technology Vol. 15 No. 3, 2017 pp. 378-394 © Emerald Publishing Limited 1726-0531 DOI 10.1108/JEDT-06-2016-0042
The authors are grateful for and wish to acknowledge the financial support from the Department of Science and Technology, National Research Funding, Eskom and the University of Fort Hare, which enabled them to purchase the research equipment for this study.
multi-linear regression. Further, the novelty is the design of the simulation application for a Simulink environment to compute the performance from real-time data.
Keywords Mathematical models, Air source heat pump (ASHP), Coefficient of performance (COP), Data acquisition system (DAS), Simulation application, Vapour compression refrigeration cycle (VCRC)
Coefficient of performance
Paper type Research paper
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Nomenclature E P t n Q c m Tin Tout l AT RH COPcal COPmod d0 d1 d2
= total electrical energy consumption in kWh = average power consumption in kW, every 5 min = time interval of 5 min = number of successive 5-min intervals in a heating up cycle = total thermal energy gained in kWh = specific heat capacity of water in kJ(kgk)1 = mass of water in kg every 5 min = ASHP inlet water temperature in °C = ASHP outlet water temperature in °C = average of the product of the ambient temperature and relative humidity in (°C.%) = average ambient temperature in °C every 5 min = average relative humidity in per cent every 5 min = average calculated coefficient of performance = average modeled coefficient of performance = forcing constant = electrical energy scaling constant in (kWh)1 = product of ambient temperature and relative humidity scaling constant in (°C.%)1
List of abbreviations t RH AT Vdo Pa Pm E Q COP
= time taken = average relative humidity = average ambient temperature = volume of hot water drawn from the storage tank = average power consumption during a heating up cycle = maximum power consumption during a heating up cycle = electrical energy consumed during a heating up cycle = thermal energy gained by stored water in the storage tank = average coefficient of performance
1. Introduction An air-source heat pump (ASHP) water heater is an efficient and renewable energy device for sanitary hot water production (Morrison et al., 2004). The coefficient of performance (COP) of an ASHP water heater can range from 2 to 4 and depends on the component design of the system, ambient weather conditions, duct space and the speed of the cold and dehumidified expelling air (Levins, 1982; Bodzin, 1997). The excellent efficiency for an ASHP water heater can be attributed to its performance characteristics known as COP (De Swardt and Meyer, 2001). The optimal COP of an ASHP water heater can be achieved by an efficient installation of the system (Douglas, 2008). The system COP can also be enhanced by
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the use of a primary refrigerant of an excellent thermo-physical property (Hashimoto, 2006; Maruyama, 2008). A salient and better understanding of the refrigeration cycle of a heat pump water heater was presented by Ashdown et al. (2004) and Sinha and Dysakar (2008). It is crucial to note that extensive research has been conducted on the simulation and mathematical modeling of the performance of heat pump water heaters. More elaborately, the performance of a heat pump water heater was simulated using the TRYSYN simulation software package (Kline, 2000). However, note that a TRYSYN simulation cannot effectively model the performance of an ASHP water heater because of the complexity of the metal fins embodying the evaporator. Furthermore, an analytical mathematical model was presented to predict the COP of a solar-assisted heat pump water heater in correlation to temperature (Itoe et al., 1999). A quantitative method can be used for computing the COP of an ASHP water heater on the basis of the quantity of electrical energy consumed by the ASHP system and the thermal energy gained by the stored water (Tangwe et al., 2013). Precisely, Tangwe et al. (2013) developed and built a surface fitting multiple linear regression model to predict the performance of a domestic split-type ASHP water heater under the first-hour heating rating, standby losses and heating cycles as a result of hot water being drawn (Tangwe et al., 2013). The residential ASHP water heater technology is fast gaining maturity in the market and can be classified into two categories, namely, the split and the integrated type. The major focus of this study was to develop and build a linear surface fitting model of the COP of an ASHP water heater (split-type heater consisting of a SIRAC ASHP with a 1.2-kW power input and a 200-L kwikot high-pressure geyser with its 4-kW element disabled) (SIRAC Southern Africa, 2010; www.montanaplumbers.co.za, Montana Plumbers, 2012). The COP of the ASHP water heater under both the mentioned scenarios was mathematically modeled using the derived multiple linear regression models correlating the predictors and the response (E, l and COP) (Coleman and Li, 1996). The Simulink environment of MATLAB was used for developing the architectural algorithm of the simulation application (Chapoutot and Martel, 2008). The heating up cycles in both scenarios were compared using the one-way analysis of variance (ANOVA) test (Hogg and Ledolter, 1987) as well as the simulation linear model plots. In addition, a multiple comparison procedure test was performed to verify the existence of a significant difference in the average COP for the two critical heating up scenarios (Hochberg and Tamhane, 1987). 2. Materials and methods The equipment, transducers, sensors and data logger listed in Table I were used in the study.
Materials
Table I. Materials used in the study
1.2-kW input SIRAC ASHP unit 200-L high-pressure kwikot geyser T-VER E50B2 power and energy meter T-minol 130 flow meter 12-bit S-TMB temperature sensor 12-bit S-THB ambient temperature and relative humidity sensor S-UCC electronic input pulse adapter S-UCD electronic input pulse adapter U30-NRC HOBO data logger
Quantity 1 1 1 2 3 1 3 2 1
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2.1 Description of the components of the experimental setup The ASHP water heater consisted of an ASHP unit retrofitting a 200-L geyser (its 4-kW element disabled), as illustrated in Figure 1. The temperature sensors were installed in the ASHP inlet and outlet pipes and measured the temperature of the water flowing in and exiting the ASHP unit. A temperature sensor was also installed on the hot water pipe of the geyser delivering hot water to the building. The T-minol 130 flow meters were connected to the ASHP inlet pipe and the geyser outlet pipe, and measured the volume of water heated by the ASHP unit and the volume of hot water draws into the building. Each of the flow meter measurements was recorded by the data logger via a connecting cable integrated with an S-UCD electronic input pulse adapter. The flow meter measurements were stored in counts, and 1 count represented 3.7854 L. The T-VER E50B2 power and energy meter was installed to measure the active energy in watt hours (Wh), the reactive energy in reactive voltage ampere hours (VARh) and the current capacity in ampere hours (Ah). These three measurements were stored into the data logger by using the three S-UCC electronic input pulse adapters. In the data logger, all these measurements were stored as pulses, and the data logger was configured such that 1 Wh and 1 VARh were equal to 1 pulse, while 100 Ah was equal to 1 pulse. The ambient temperature and relative humidity sensor measured the ambient temperature and relative humidity, and these data were also stored in the data logger. The ambient temperature and relative humidity sensor was protected by a solar radiation shield. All the temperature sensors and the ambient temperature and relative humidity sensor were integrated with the S-UCC electronic input pulse adapter attached to the connecting cables. These electronic input pulse adapters converted the analog sensing signals to digital in a bid to eliminate the interference of noise. All the sensors and the transducers were accommodated by the U30-NRC 15 channel data logger (www.onsetcomp.com, ONSET, 2013). The U30-NRC data logger was configured to log data at 1-min intervals. Figure 2 shows the designed and built DAS deployed in the performance monitoring. Figure 3 shows a detailed installation of the ASHP unit used for the study. The study was conducted in a middle-income family residence (two adults and a child) in Fort Beaufort, Eastern Cape Province, South Africa, from January to May 2014.
Coefficient of performance
381
Figure 1. Schematic representation of a typical split-type ASHP water heater
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Figure 2. Data acquisition system designed and built for the study
Figure 3. Detailed ASHP unit installation
3. Calculation and theory The total electrical energy consumed during a heating up cycle is given by equation (1): E5
n X
Pi t
(1)
i51
The total thermal energy gained by the hot water in the storage tank is given by equation (2):
Q¼
n X
cmi ðTout Tin Þi
(2)
i¼1
Coefficient of performance
The parameter l (average of the product of the ambient temperature and relative humidity) is given by equation (3):
l ¼ ðATÞi ðRHÞi
(3)
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The ASHP water heater calculated the COP as the ratio of the useful output thermal energy gained (Q) by the heated water and the input electrical energy consumed (E). Equation (4) shows the calculation of the COP for an ASHP water heater: COPcal ¼
Q E
(4)
The linear surface fitting model of the COP correlating E and l is given by equation (5). The parameters E and l are the predictors: COPmod ¼ d 0 þ d 1 E þ d 2 l
(5)
4. Results and discussion The performance of the domestic split-type ASHP water heater was monitored from January 1 to May 30, 2014. The results were critically analyzed under two scenarios: where the heating up cycle was simultaneously conducted with hot water drawn from the storage tank into the building, and where the heating up cycle occurred without any hot water draws. 4.1 Heating up cycle with simultaneous hot water draws from storage tank into the building This scenario occurred due to long duration of hot water drawn off and stored water in the tank was forced to attain lowered temperature below the threshold of the hot water set point differential. This resulted in the triggering of the ASHP unit while the hot water was continuously drawn. Table II shows some typical results achieved during the five months of the performance monitoring of the ASHP water heater under the scenario where hot water was simultaneously drawn during the heating up cycles. It can be delineated from Table II that a huge amount of hot water draws resulted in an increase in the duration of the heating up cycle. Furthermore, it can be depicted that an increase in the average ambient temperature and in the average relative humidity could lead to an increase in the COP of the ASHP water heater. The maximum average COP of the
t (h)
RH (%)
AT (°C)
Vdo (L)
Pa (kW)
Pm (kW)
E (kWh)
Q (kWh)
1.08 0.75 0.50 0.58 0.83
55.9 60.2 63.7 64.3 72.1
30.8 26.7 31.3 28.6 24.6
114 27 11 42 45
1.36 1.24 1.33 1.35 1.26
1.60 1.57 1.64 1.63 1.60
1.59 0.93 0.67 0.79 1.05
3.92 1.88 1.53 2.01 2.51
COP
Table II.
2.47 Important results 2.02 achieved during the 2.67 heating up cycles 2.52 2.40 with hot water draws
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ASHP water heater was associated with the highest average power consumption (Tangwe et al., 2014). The ambient temperature and relative humidity impacted the magnitude of the average power consumption, which also depended on the volume of hot water drawn during the vapour compression refrigeration cycle (VCRC) of the ASHP water heater. The average power consumption for a specific VCRC was always lower than the maximum power because of the variability in the water load that was heated up and the water temperatures in and out of the ASHP unit, measured throughout the entire heating up duration.
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4.2 Heating up cycle without simultaneous hot water draws from the tank into the building This scenario occurred because of transient hot water drawing that could lower the stored water temperature in the tank but not exceed the hot water set point differential, and then, coupled with the standby losses over time finally resulted into the heating up cycle. Alternatively, the whole contribution could be from the standby losses in situations where there was no hot water drawn from the storage tank of the ASHP water heater on consecutive days. This resulted in the running of the ASHP unit. Table III shows some typical results achieved during the five months of the performance monitoring of the ASHP water heater under the scenario without a successive hot water drawing from the storage tank during the heating up cycles. It can be deduced from Table III without any loss of generality that the average power consumption during the heating up cycle under no successive hot water draws was lower than in the scenario of simultaneous hot water draws. In spite of the difference in the heating up cycle’s duration in both the scenarios, the one-way ANOVA showed no significant difference. The mean heating up cycle duration was 0.748 h and 0.55 h for the scenario with simultaneous hot water draws and the scenario without successive hot water draws, respectively. In the scenario of whereby heating up cycle was occurring without simultaneous hot water drawn off from the storage tank of the ASHP water heater. Most significantly, with reference to Table III, it was revealed that the longer the heating up cycle was, the lower was the COP achieved as a result of the possibility of a huge amount of hot water draws that resulted in the initiation of the VCRC. Further, the water in the storage tank was at a much lower temperature with respect to the hot water set point temperature (55°C). 4.3 Mathematical model of the heating up cycle with simultaneous hot water draws from the tank The data set of more than 100 values of the predictors (E and l ) and their corresponding responses (COP) in the five months of the monitoring period was used for developing and building the multiple linear surface regression model. The modeled equation is given as equation (5), and Table IV shows the scaling constants and the forcing constant of the derived mathematical model under the heating up cycles.
Table III. Important results recorded during the heating up cycles without hot water draws
t (h)
RH (%)
AT (°C)
Vdo (L)
Pa (kW)
Pm (kW)
E (kWh)
Q (kWh)
COP
0.50 0.58 0.58 0.42 0.67
47.8 80.9 88.1 54.5 74.9
31.1 23.0 22.2 30.5 24.6
0 0 0 0 0
1.43 1.39 1.29 1.51 1.45
1.62 1.56 1.57 1.64 1.54
0.71 0.81 0.75 0.63 0.97
1.91 1.70 1.58 1.60 2.15
2.68 2.14 2.10 2.54 2.20
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From the modeled equation and the scaling constants presented in Table IV, it can be inferred that the increases in l and E resulted in an increase in the COP. The determination coefficient between the calculated COP and the modeled COP was 0.962 and the p-value was 0.927. This justifies that there was minimal deviation and a significant correlation between the calculated and the predicted COP. Table IV also shows that for a constant electrical energy consumed, an increase in the value of the product of the average ambient temperature and relative humidity was associated with an increase in the COP with a constant slope of 0.0018/°C per cent. Figure 4 shows the plot of the sample data set points over the range of the calculated COP and the surface fitting modeled with l , E and COP on the x, y and z axis, respectively. Figure 4 also illustrates that for a constant l , an increase in the electrical energy consumed by the ASHP water heater was associated with a corresponding increase in the COP of the ASHP water heater with a constant gradient of 0.31/kWh. The reliefF statistical test is an algorithm used for ranking predictors according to their weight of importance to the response using regression analysis (Robnik-Sikonja and Kononenko, 2003). It is imperative to point out that the weight ranking ranged between 1 and 1. A specific predictor can be termed as a primary factor to an output if the weighted value for the predictor was positive. Similarly, the predictor would be referred to as a secondary factor, if the value was negative. By using the reliefF algorithm for the simultaneous hot water draws scenario, it was shown that the predictor E was a secondary factor and the ranking by the weight of contribution to the COP was 0.145, while the predictor l was a primary factor with a rank of 0.068 by the weight of importance to the COP. The reliefF algorithm revealed that the predictor l although ranked by the weight of importance to the COP as the primary factor, it did not contribute significantly to the COP of the ASHP water heater. It should be emphasized that the volume of water heated by the ASHP unit and the hot water set point temperature are the
Predictors Product of AT and RH Electrical energy Forcing constant
Symbol
Scaling constant
l E ...
0.0018 0.310 1.072
Output COP
Coefficient of performance
385
Table IV. Mathematical model scaling constants in the simultaneous draws scenario
Figure 4. Data set points and the modeled surface plot for simultaneous draws scenario
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Table V. Mathematical model scaling and forcing constants in the no draw scenario
Figure 5. Data set points and modeled surface plot for no draw scenario
other primary factors with a significant contribution to the COP. In general, an increase in the volume of water heated by the ASHP unit and with a lower hot water set point temperature can lead to a significant increase in the COP of the ASHP water heater. 4.4 Mathematical model of the heating up cycle without simultaneous hot water draws The data set constituting of more than 70 values of the predictors (E and l ) and the corresponding output (COP) in the five months of the monitoring period was used for developing and building the multiple linear surface regression model. The modeled equation is given as equation (5), and Table V shows the scaling constants and the forcing constant of the derived mathematical model. From the modeled equation scaling constants shown in Table V, it can be visualized that increases in l and E resulted in a decrease in the COP of the ASHP water heater. The determination coefficient between the calculated COP and the modeled COP was 0.952, and the p-value was 0.932. This also confirmed that there was marginal deviation and a very strong correlation between the calculated COP and the modeled COP. Figure 5 shows the plot of the sample data set points over the calculated range of the COP and the surface fitting modeled with l , E and COP on the x, y and z axis, respectively. From Figure 5, it is clear that for constant l , an increase in the value of the electrical energy was associated with a decrease in the COP of the ASHP water heater with a constant slope of 0.277/kWh. Furthermore, for constant electrical energy consumption, a decrease in the values of l would result in an increase in the COP with a constant gradient of 0.0013/°C per cent. The reliefF algorithm also showed that l was a primary factor, while E was a secondary factor; their ranking by weight of contribution to the COP was 0.350 and 0.014, respectively. Predictors
Symbol
Product of AT and RH Electrical energy Forcing constant
l E ...
Scaling constant 0.0013 0.277 4.823
Output COP
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4.5 Simulation linear model plots for the heating up cycle with simultaneous hot water draws The simulation linear model plots are multi-dimensional plots used for modeling the variation of a specific predictor with the output in any given surface fitting multiple regression model while the other predictors are held constant. The simulation linear model plots can be used for up to 13 predictors. In this study, the simulation linear plots were used for visualizing the variation of the ambient conditions (l ) with the COP for constant electrical energy consumption, and the changes in the electrical energy (E) with the COP while the ambient conditions were maintained constant. Figure 6 shows the simulation linear model plots for the hot water drawn scenario. The positive slope of both the plots indicated that an increase in both predictors resulted in an increase in the COP. The green lines on both plots show the linear relationship between the predictors and the COP, and both the red broken lines define the 95 per cent confidence bound. The slopes of the COP and the ambient conditions and the COP and electrical energy were 0.0018/°C per cent and 0.310/ kWh, as determined from the derived mathematical model. The simulation linear model plots can also be used for predicting the COP over a range of a specific predictor while the other predictor was held constant.
Coefficient of performance
387
4.6 Simulation linear model plots for the heating up cycles without any hot water draws Figure 7 shows that under the scenario wherein no hot water was successively drawn into the building during the heating up cycles, the COP decreases as ambient conditions change and the electrical energy consumption increases. This is in agreement with the scaling coefficient obtained from the derived mathematical model. The calculated slopes for the COP with respect to the ambient conditions (l ) and the electrical energy consumed were 0.0012/ °C per cent and 0.278/kWh. 4.7 Simulation application design to model the ASHP water heater performance The COP of the ASHP water heater was simulated in the Simulink environment by using the developed and built mathematical models. Figure 8 shows a schematic representation of the architectural algorithm of the designed simulation application.
Figure 6. Simulation linear model plots for the hot water drawn scenario
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Figure 7. Simulation linear model plots for the no successive draws scenario
Figure 8. Simulation application of an ASHP water heater performance
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The derived mathematical models for both the COP with simultaneous hot water draws and the COP without concurrent hot water draws were embedded into a system block represented by the full photograph of an ASHP water heater in Figure 8. All the predictors were loaded into the respective source blocks (sequence interpolate blocks), while the desired output was displayed in the sink blocks represented by a scope block contained in the Simulink libraries. Both responses were combined with the help of a multiplexer. By setting the respective gain block to 1, the performance of that particular scenario could be monitored. However, if the gain block was set to 0, by default, the particular scenario would display a COP of 0 for all the observations. The simulation was configured to start at the observation denoted by 1 and stop at the observation denoted by n (where n corresponded to the last observation), as the analyzed data inputted into the source blocks of the simulation corresponded to a finite, discrete number of observations. Figures 9 and 10 illustrate the modeled COP in the case of simultaneous hot water draws and without successive hot water draws during the heating up cycles, generated from the data in Tables VI and VII, respectively. The difference between the modeled COP and the calculated COP in both the scenarios showed a deviation of 65 percent. Figure 9 illustrates the modeled COP (red line plot) and the observations using the Table VI (a scenario with simultaneous hot water draws) data set; this plot was generated from the scope block after running the simulation in the Simulink environment. The COP associated with no successive hot water draws (yellow line plot) was set to 0 by default.
Coefficient of performance
389
Figure 9. Modeled COP based on observations from Table VI (scenario with simultaneous draws)
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Figure 10. Modeled COP based on observations from Table VII (scenario without successive draws)
Table VI. Observed and simulation-predicted COP under simultaneous draws condition
Observations
Table VII. Observed and simulation-predicted COP under no successive draws condition
Observations
1 2 3 4 5
1 2 3 4 5
E (kWh)
l = Product of (AT and RH)/°C%
Simulated-predicted COP
Measured COP
1.59 0.93 0.67 0.79 1.05
1,721.72 1,607.34 1,993.81 1,838.98 1,773.66
2.52 2.10 2.72 2.48 2.45
2.47 2.02 2.67 2.52 2.40
E (kWh)
l = Product of AT and RH)/°C%
Simulated-predicted COP
Measured COP
0.71 0.81 0.75 0.63 0.97
1,486.58 1,860.70 1,955.82 1,662.25 1,842.54
2.69 2.18 2.07 2.48 2.16
2.68 2.14 2.10 2.54 2.20
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Figure 10 shows the modeled COP (yellow line plot) in the scenario wherein no successive hot water draws occurred throughout the heating up cycles and the observations obtained from Table VII. The modeled COP was generated from the scope block after running the simulation. The presented simulated plots of the COP mimicked the calculated COP and, hence, justified the agreement between the simulated COP results and the calculated COP. 4.8 Comparing the COP of the different scenarios using one-way ANOVA test The average COP of the ASHP water heater in the respective heating up cycle scenarios was compared using the one-way ANOVA test. The one-way ANOVA algorithm uses a linear regression analysis and treats the data set as a normal distribution (Hochberg and Tamhane, 1987). Based on the one-way ANOVA test, although the heating up scenario with no successive hot water draws had a maximum average COP of 2.68 as opposed to the maximum average COP of 2.67 for the heating up scenario with simultaneous hot water draws, the latter exhibited a better mean COP. Figure 11 shows ANOVA plots in which there exist no outliers in the data sets of the different heating up scenarios. The mean COP of the heating up scenario with no successive draws and with simultaneous draws was 2.332 and 2.416, respectively. The result showed that the average COP of the ASHP water heater during the simultaneous hot water draws scenario was slightly higher than that in the scenario with no successive hot water draws. The p-value of the one-way ANOVA test was 0.6124, and based on the null hypothesis, there was no mean significant difference in the COP in the two heating up scenarios. Note that for a comparison analysis of two or more variable parameters using the one-way ANOVA test, if the p-value is less than 0.5 and very close to 0, then there exists no mean difference. Further, if the p-value is greater than 0.5 and very close to 1, then there exists a mean difference.
Coefficient of performance
391
4.9 Comparing the COP of the different scenarios using multiple comparison simulation The results obtained from the one-way ANOVA plots of the COP were further analyzed using a multiple comparison procedure to test for a mean significant
Figure 11. One-way analysis of variance plots of the two heating up scenarios
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difference in the COP under the two distinct operation scenarios. A simulation plot of the multiple comparisons between the COP of the ASHP water heater under the two heating up scenarios is shown in Figure 12. The horizontal lines show the range of the COP, while the marked circle on the line indicates the mean COP, and if the lines overlap, there exists no mean significant difference. The COP range with no successive hot water draws (yellow line plot) and that with simultaneous hot water draws (red line plot) in Figure 12 show no mean significant difference, as they do overlap. The mean difference in the average COP for the two scenarios was 0.084. The difference in the average actual COP and the 95 per cent confidence level average COP for the hot water draws scenario was 0.283. The difference in the average actual COP and the 95 per cent confidence level average COP for the no draw scenario was 0.451. Hence, as there exists the value 0 in between this interval (0.283, 0.451), there is no significant difference in the mean COP for both the scenarios.
5. Conclusion It is worth concluding that modeling the COP of an ASHP water heater with the aid of a simulation application can give insight into the performance, as it can be automated and visualized from a user-friendly environment. An increase in both the electrical energy consumed and the product of the ambient temperature and the relative humidity, which were considered to be the predictors, can often result in a decrease in the COP during the no successive hot water draws heating up cycles. However, such increases in these predictors’ parameters give rise to an increase in the COP during the simultaneous hot water draws heating up cycles. Furthermore, although in both the scenarios, the ambient conditions were a primary factor, the weight of importance of the contribution of this predictor to the COP was five times more in the scenario of simultaneous hot water draws. The ASHP water heater average COP was much better during a heating cycle with simultaneous hot water draws but demonstrated no mean significant difference when compared to the heating up scenario with no successive hot water draws.
Figure 12. Simulation plot of a multiple comparison of the means of the COP
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References Ashdown, B.G., Bjornstad, D.J., Boudrean, G., Laspsa, M.V. and Schernayder, S. (2004), “Heat pump water heater technology: experiences of residential consumers and utilities”, Technical Report, Oak Ridge National Laboratory, Oak Ridge. Bodzin, S. (1997), “Air-to-water heat pumps for the home”, available at: www.homeenergy.org/show/ article/nav/hotwater/page/8/id/1315 (accessed July/August 1997). Chapoutot, A. and Martel, M. (2008), “Static analysis of Simulink programs (short paper)”, ModelDriven High-Level Programming of Embedded Systems. Coleman, T.F. and Li, Y. (1996), “A reflective newton method for minimizing a quadratic function subject to bounds on some of the variables”, SIAM Journal on Optimization, Vol. 6 No. 4, pp. 1040-1058. De Swardt, C. and Meyer, J.P. (2001), “The performance of a municipality water reticulation groundsource reversible heat pump system compared to an air-source system”, South Africa’s 10th International Air Conditioning, Refrigeration and Ventilation Congress, Gallagher Estate, Midrand, 8-11 March, p. 7. Douglas, J. (2008), “Demonstrations encourage wider use of efficient technologies”, EPRI Journal, Vol. 4, pp. 15-17. Hashimoto, K. (2006), “Technology and market development of heat pump water heaters (ECO CUTE) in Japan”, IEA Heat pump Centre Newsletter, Vol. 24 No. 3. Hochberg, Y. and Tamhane, A.C. (1987), Multiple Comparison Procedures, John Wiley & Sons, Hoboken, NJ. Hogg, R.V. and Ledolter, J. (1987), Engineering Statistics, MacMillan, New York, NY. Itoe, S., Miura, N. and Wang, K. (1999), “Performance of heat pump using direct expansion solar collector”, Solar Energy, Vol. 65, pp. 189-195. Kline, S.A. (2000), “TRNSYS 15 a transient system simulation program”, University of Wisconsin Solar Energy. Levins, W.P. (1982), “Estimated seasonal performance of a heat pump water heater including effects of climatic and in-house location”, Technical Report, Oak Ridge National Laboratory, Oak Ridge, TN, USA. Maruyama, T. (2008), “Eco-cute- carbon dioxide heat pump water heater in Japan”, 2008 ACEEE Water Heating Forum, Sacramento. CA, 1-3 June. Montana Plumbers (2012), available at: www.montanaplumbers.co.za/montana-plumbers-price-list/ kwikot-200-litre-geyser Morrison, G.L., Anderson, T. and Behnia, M. (2004), “Seasonal performance rating of heat pump water heaters”, Solar Energy, Vol. 76, pp. 147-152. ONSET (2013), “HOBO data loggers and products”, available at: www.onsetcomp.com Robnik-Sikonja, M. and Kononenko, I. (2003), “Theoretical and empirical analysis of ReliefF and RReliefF”, Machine Learning, Vol. 53 Nos 1/2, pp. 23-69. Sinha, S.K. and Dysakar, A. (2008), “United States patent application heat liquid heater”, available at: http//appl.ft1.uspto.gov/netacgi/nph-parser SIRAC Southern Africa (2010), “Sales and technical training manual”, available at: www.sirac.co.za Tangwe, S., Simon, M. and Meyer, E. (2013), “Computational approach to evaluate performance of split type residential air source heat pump water heater at different operational state”, 12th International Conference on Sustainable Energy Technology, 26-29 August. Tangwe, S., Simon, M. and Meyer, E. (2014), “Mathematical modelling and simulation application to visualize the performance of retrofit heat pump water heater under first hour heating rating”, Renewable Energy Journal, Vol. 72, pp. 203-211.
Coefficient of performance
393
JEDT 15,3
Further reading Tangwe, S., Simon, M., and Meyer, E. (2016), “Experimental investigation to quantify the benefits of residential air source heat pump water heater in South Africa”,presented at the 5th International Conference on Applied Energy, 1-4 July.
About the authors
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Stephen Loh Tangwe holds a BEng (Hons) degree and an MEng degree in Electrical Engineering from AIU, Honolulu, Hawaii. He is an IEE graduate student and an IEE Power and Energy Society member. At present, he is a graduate student member of the South African Institute of Electrical Engineers and an ad-hoc Eskom M&V engineer with the UFH team. He is also an energy efficiency PhD research candidate with the Fort Hare Institute of Technology and a MATLAB application engineer. He is also a member of SAEE and WSSET. He has published papers in many peer-reviewed journals accredited nationally and internationally. Stephen Loh Tangwe is the corresponding author and can be contacted at:
[email protected] Michael Simon holds a PhD degree in Physics from the University of Fort Hare. He is presently the University of Fort Hare Energy Manager and Head of the Energy Efficiency Group at the Fort Hare Institute of Technology. He is also a certified Eskom M&V professional and the team leader of the Eskom M & V UFH team. He is a photovoltaic and energy efficiency specialist. Edson Leroy Meyer holds a PhD degree in Physics from the Nelson Mandela University, Port Elizabeth. He is presently Director of the Fort Hare Institute of Technology. He is also a certified Eskom M&V professional and the Eskom chair in the Southern region. He is a renewable energy consultant and a seasonal author and reviewer in accredited peer-reviewed journals.
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