energy efficient geyser

ENERGY EFFICIENT GEYSER RSM Thomas, X Xia and JF Zhang University of Pretoria, Pretoria, South Africa ABSTRACT It is observed that the thermostat reading of the geyser is not an indication of the outlet hot water temperature. This paper aims at computing the outlet hot water temperature by the information of the thermostat reading of the geyser. Control based on the outlet water temperature would improve the energy efficiency of a geyser, whose switching is based on the thermostat temperature. Unnecessary switching caused by the thermostat can therefore be avoided. 1.

Various control efforts have been discussed in [1]-[12] to control the hot water load in order to reduce the national system load peak. The disadvantages of these various efforts are as follows: • •

INTRODUCTION

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According to [1], approximately 40% of the domestic energy consumption is caused by geysers. The need to improve the efficiency of existing geysers arises due to the increasing energy demand. When an amount hot water is extracted from the geyser, the same amount of cold water enters the geyser. According to [2], the cold water that enters the geyser mixes immediately with the remaining hot water to reach a stable temperature. It is supposed that the thermostat reading of the geyser gives the exact reading of this stable temperature and is used in the energy management problems of geysers. The above hypothesis does not consider the position of the thermostat and the stratification phenomenon. Stratification is a non-linear process where cold water that enters the geyser remains at the bottom because it is denser than hot water [2]. The thermostat reading can therefore not be used as the average temperature of the water in the geyser since the thermostat is located near the bottom of the geyser. In [2]-[5], the effect of stratification has not been considered. With the incorporation of the effects of stratification in the model, a more optimal controller can be developed. A zonal approach has been used to develop a model that describes the effects of thermal stratification in a geyser [13], but this model is too complicated for control purposes due to the numerous zones. In [2]-[5], the flow rate must be known in order to determine the outlet water temperature. This would require the user to define the exact flow rate at the specific times of usage. A real-time application is therefore not possible with this approach. Any deviation from the defined parameters would result in ineffective control. Control based on the developed model is therefore not based on assumptions of the flow rate or the output of a flow meter. It does not require the user to define the exact flow rate required during the required periods.

•

Centralized control is inefficient in terms of the user’s comfort needs. Decentralized control is based on the thermostat reading assuming that the thermostat reading gives the temperature of the outlet water temperature. Modifications to the structure of the geyser at homes are required. Examples of modifications are the installation of flow meters, temperature sensors at the outlet pipe and the installation of an inlet tract block to block the entry of cold water until a low-volume set-point is reached. The effect of stratification has not been considered in [1]-[12]. Kenjo provides a stratification model that is too complicated for control purposes.

Control based on the predicted upper temperature of the geyser enables the elimination of the abovementioned disadvantages. The only input to the system is the user requirements and the thermostat reading. Only two zones and a variable of the volume of hot water in the geyser are required for the application of the model and therefore reduces the complications in applying a suitable control system. The developed model captures the stratification effect efficiently, estimates the outlet water temperature accurately and is simple for controller design. This paper’s main contribution is to display the results of control based on the output of the developed model The layout of the paper is as follows. In Section 2, the development of geyser model is described. Section 3 displays the accuracy of the model. Section 4 discusses the differences between the current control system where control variable is the raw thermostat temperature and the proposed control system where the control variable is the output of the developed model. The last section is the concluding remarks. 2.

CONCEPT OF MODEL

In the computation of the hot water temperature, it is assumed that the hot water temperature of any point inside the geyser is irrelevant with its horizontal position and is determined only by its vertical position.

The following test-setup was used to study the effect of the heating element, flow rate and stratification at the different regions of the geyser.

Figure 2 demonstrates the behaviour of the water temperature in the various regions of the geyser while the following activities where done. • The geyser was heated until sensor 3 reached 50ºC as shown in section A of the graph. • An amount of 40 of hot water is extracted from the geyser. The effect of the extraction can be seen in section B. • The geyser was left for 8 hours where no extractions were made.

Figure 1: Placement of the various sensors. The effect of the heating element, flow rate and stratification are incorporated in the model. The structure of the geyser was considered in the modelling of the geyser. The inlet pipe of all geysers is at the bottom of the geyser and the outlet pipe is at the top of the geyser. The geyser has a spreader at the inlet pipe, which forces the cold water that flows into it to the bottom of the geyser. The implications of the general structure of the geyser are as follows. • The water that is extracted from the geyser is at the temperature of the water in the upper region of the geyser. • The cold water that enters the geyser, when hot water is extracted, fills the geyser from the bottom of the geyser. The element of the geyser is positioned at the centre of the geyser. Table 1 describes the position of each thermostat pocket on the geyser and the corresponding volume of water that the geyser holds below the specified position. Table 1: The volume of water below the corresponding thermostat pocket. Position 1 Position 2 Position 3 Position 4 Position 5

Volume ( ) 5 20 50 80 95

Thermostats of standard geysers are placed in position 3. The thermostat was placed in thermostat pocket 6 during all experiments for safety reasons. The temperature displayed by sensor 3 is considered to be the temperature of the lower region of the geyser. The temperature displayed by sensor 5 is considered to be the temperature of the upper region of the geyser.

Figure 2: The temperature change at the different positions in the geyser The effect of the heating element is illustrated in region A of figure 2. The rate of heating in the different regions in the geyser is not equal. The upper region heats at a rate of 45Û&KRXUDQGWKHORZHUUHJLRQKHDWVDWDUDWHRIÛ&KRXU when the geyser is heated from an initial temperature of 23Û&'XULQJWKHKHDWLQJSURFHVVWKHVHQVRULQSRVLWLRQ is not affected at all. This shows that a minimum of 20 RI water remains at the initial temperature. The assumption that a geyser with a capacity of 100 FDQSURYLGH RI hot water is therefore not valid. The position of the heating element therefore plays an important role in the amount of water that is heated in the geyser. The effect of flow rate is illustrated in region B of figure 2. It is evident that the effect of extracting a certain amount is dependant on the rising of the boundary between the cold and hot water in the geyser. Since the cold water that enters the geyser rises from the bottom of the geyser to the top, sensor 3 drops to the inlet water temperature, while sensor 5 drops by 10Û&. The difference in sensitivity to flow rate between the two points is due to the sensor position relative to the distance between the respective sensor and the boundary between the cold and hot water in the geyser. This is illustrated in figure 2.

Figure 3: The two zones of geyser and the placement of the sensors. The temperature at the sensor positions decreases until the indicated boundary reaches the position of the sensor. Once the boundary exceeds the sensor position, the temperature remains at the cold-water temperature. The ratio between the volume of water above the sensor position and the total volume of hot water, which is dependant on flow rate, is indicative of the effect of flow rate at the various positions. The effect of standby losses is illustrated in the region C of figure 2. Standby losses consist of air losses and the effect of stratification. The drop in temperature is due to the mixing of the cold water that enters the geyser with the remaining hot water. The realization that the geyser contains more than 20 RI FROG ZDWHU DIWHU LW LV KHDWHG implies that the effect of stratification is present even when the geyser is fully heated. From experimental results, it has been studied that the temperature of the lower region in the geyser rises and the temperature of the upper region decreases as a result of mixing. The temperature difference between the upper and lower regions of the geyser results in an energy transfer by motion within the water to reach equilibrium, due to convection. 3.

Figure 5: The extraction of 5 .


RESULTS

The following figures show the comparison between the computed upper temperature and the measured upper temperature. In each scenario, the geyser was heated, an amount of hot water was extracted and the geyser was left for at least eight hours.



range. The improvement in the stratification curve obtained from the model is evident in the results obtained from the experiment The effect of flow rate was evaluated by extracting 20 DW different flow rates. The results of the test are as follows. Table 3: The accuracy of model for various flow rates Flow rate( /minute) 5 10 17


Minimum Accuracy of upper temperature(%) 91.72 93.98 94.4

Mean Accuracy (%)

Volume extracted detection

94.37 97.05 97.96

21.95 20.69 17.81

It is observed that the volume extraction detected by the model is most accurate when the flow rate is 10 PLQXWH At slower flow rates, the volume detected is larger than the actual volume that is extracted. At larger flow rates, the volume detected is smaller than the actual volume that is extracted. 4.

Figure 9: The extraction of 50 . The accuracy of the model outputs shown in figures 4 to 9 are presented in table 2.

CONTROLLER

A rule-based controller is implemented where the control variable is varied between the upper temperature and the lower temperature. The first controller switches the geyser off when the thermostat reading reaches 50ºC and switches on when the thermostat reading drops below 50ºC. This represents the normal operation of the geyser. The second controller calculates the upper temperature of the geyser using the thermostat reading and switches the geyser based on the upper temperature. The usage profile of water applied to both control systems after the desired set point of 50ºC is reached is shown in figure 10.

Table 2: The accuracy of the model outputs Amount of Minimum extraction accuracy ( ) of Tu (%) 0 93.8 5 89.25 10 92.2 20 91.72 40 84.68 50 82.87 Average: 89.09

Mean accuracy of Tu (%) 98.49 97.57 95.96 94.37 97.72 95.53 Average: 96.61

Volume extraction Detected ( ) 1 4.5 10.86 21.95 35.14 54.09

Figure 10: The water usage during the implementation of both controllers. Control based on the thermostat action is depicted in figure 11.

Since the lower temperature is an input to the system, inaccuracies due to the imprecise prediction of the lower temperature are avoided. From the results, it can be concluded that the mass of water extracted from the geyser can effectively be predicted with the inclusion of a sensitivity factor. The minimum accuracy of the upper temperature is computed to be 89.09%. The model is therefore within a 85% accuracy

Figure 11: The effect of a controller when the lower temperature is the control variable.

Control based on the upper temperature of the geyser is depicted in figure 12.

Figure 12: The effect of a controller when the upper temperature is the control variable. The following table shows a comparison between the temperature of the upper region of the geyser for the different controllers. The period during which hot water is required is displayed in the table. Denote the method of thermostat control by TC and optimal control by OC. Table 4: Temperature comparison Time 19:00 19:02 19:04 19:06 19:08 19:10 19:12 19:14 19:16 19:18 19:20 19:22 19:24 19:26 19:28 19:30 19:32 19:34 19:36 19:38 19:40 19:42 19:44 19:46

TC (ºC) 67.5677 67.4456 67.2014 67.6898 68.4224 69.3992 70.376 71.3528 72.3296 73.4285 74.4053 75.0158 75.0158 74.6495 74.5274 75.0158 75.7484 76.481 77.2136 78.0683 78.5567 77.9462 70.376 40.4615

OC (ºC) 49.9853 50.1074 49.9853 49.8632 49.7411 49.7411 49.4969 49.3748 49.3748 49.2527 49.1306 49.0085 49.0085 46.8107 46.4444 45.7118 45.7118 46.6886 47.9096 49.2527 50.5958 51.5726 49.4969 33.3797

Table 4 shows that TC has a considerably higher upper temperature than the required temperature of 50ºC throughout the control period. The upper temperature reaches 67ºC when the thermostat reading reaches 50ºC. This is due to the difference in the rate of heating in the

upper region and the lower region. Figure 11 illustrates that the collection of 10 RIZDWHUFDXVHVDVLJQLILFDQWGURS in the thermostat temperature, but an insignificant drop in the upper temperature of the geyser. Since the thermostat temperature dropped below 50ºC, the element is activated till the thermostat temperature reaches 50ºC. The activation of the element causes the upper temperature to rise from 67.2ºC to 75ºC, which is unnecessary. The controller based on the calculated upper temperature is heated until the upper region is 50ºC. The thermostat reading is only 31ºC when the control variable reaches 50ºC. The element of the geyser is activated 34 minutes less than when the control variable is the thermostat reading. The extraction of 10 GRHV QRW FDXVH DQ\ activation of the heating element since the upper temperature had not dropped sufficiently. The reheating period of 17 minutes, as illustrated in figure 11 is eliminated by using the model output, the upper temperature as the control variable. The reaction of the first controller, illustrated in figure 11, to the second extraction of 10 LV VLPLODU WR Whe first extraction of 10 7KH WHPSHUDWXUH RI WKH XSSHU UHJLRQ unnecessarily rises from 75ºC to 78.5ºC due to control based on the thermostat reading. The second extraction of 10 FDXVHV D VLJQLILFDQW GURS LQ WKH XSSHU WHPSHUDWXUH LQ the scenario illustrated in figure 12. The heating element is therefore activated until the upper temperature reaches 50ºC. The temperature difference between the required temperature and the actual outlet water temperature for thermostat control varies between 17ºC and 28ºC. The temperature difference between the required temperature and the actual outlet water temperature for TC varies between 17ºC and 28ºC. The temperature difference between the required temperature and the actual outlet water temperature for OC is within the range of 5ºC. For the extraction of 60 RIZDWHUERWKFRQWUROOHUVUHDFWLQ the same way. The temperatures of the control variables drop very fast for both scenarios. The controllers are not able compensate fast enough for large extractions since the element rating is limited to 3kW. The temperature of OC is relatively stable in comparison to TC. To summarize, OC consumes less electricity and causes a lower aggregated desired temperature deviation than the TC method as expected. The cost of electricity and the aggregated desired temperature deviation is evaluated by means of (1) and (2). The cost of electricity is calculated in (1). J e = ∑ tft0 Pp(t )u (t ) ,

(1)

where P is the element rating of the geyser, p(t) is the cost of electricity as a function of the time of day, u(t) is the switching input, t 0 is the initial time and t f is the final time.

The aggregated desired temperature deviation is calculated by (2). 2

tf

L = ∑ (Tu (t ) − F (t )) ,

(2)

t0

where Tu (t ) is the actual temperature of the outlet water at time t, F (t ) is the desired temperature at time t, t0 is the initial time and t f is the final time. The cost of electricity is assumed to be 50c/KWh. Table 5: A comparison between the cost and the aggregated desired temperature deviation level of TC (currently used) and OC. Cost(R) Aggregated desired temperature deviation

TC 2.70 28207.41

OC 1.24 1239.68

It is evident from figure 11 and figure 12 that the variation in the control variable makes a significant difference in the period that the element is switched on. The geyser controlled by the lower temperature of the geyser is on for approximately one hour longer than the geyser controlled by the upper temperature. The cost of TC is therefore much greater than the cost of OC. Since the temperature of the lower region drops very quickly in response to small extractions of water, the heating element is activated regularly in TC. The unnecessary switching of the standard geyser causes the upper temperature of the geyser to rise significantly, although it is unnecessary. The aggregated desired temperature deviation is accelerated due to this. 5.

CONCLUSION

The efficiency of a controller depends on the accuracy of the model it is implemented on. Since the temperature of the upper region of the geyser is not directly accessible, the development of a suitable model to estimate the upper temperature using the thermostat reading was done. A control system based on the model developed can easily be implemented on standard geysers. The structure of the geyser need not be modified for the implementation of the control system. Controlling the geyser with the upper temperature is able to minimise the cost and discomfort caused to the user. 6. REFERENCES [1] Beute, N.: “Domestic utilisation of electrical grid energy in South Africa” Ph.D. Dissertation, Department of Electrical and Electronic Engineering, Potchefstroom University of CHE, Vaal Triangle Campus, May 1991. [2] Calmeyer, J.E. and Delport, G.J.: “The modeling and control of hot water consumption in residential hostels” Africon, Vol 2, 1999, pp.825-830. [3] Zhang, J. and Xia, X.: “Best switching time of

hot water cylinder-switched optimal control approach” Africon, 2007 [4] Delport, G.J., van Harmelen, G.: “ Multilevel expert-modelling for the evaluation of hot water load management opportunities in South Africa” IEEE transactions on power systems, Vol. 14, No. 4, 1999, pp.1306-1311. [5] Rautenbach, B. and Lane, I.E.: “The multiobjective controller: A novel approach to domestic hot water load control” IEEE transactions on power systems, 4, 1996, pp.1832-1837. [6] Beute, N.: “Domestic utilisation of electrical grid energy in South Africa” Ph.D. Dissertation, Department of Electrical and Electronic Engineering, Potchefstroom University of CHE, Vaal Triangle Campus, May 1991. [7] Neihrir, M.H, LaMeres, B.J. and Gerez, V.: “A customer-interative electric water heater demand-side management strategy using fuzzy logic” IEEE Power Engineering Society 1999 Winter Meetings, Vol.1, 31 Jan-4 Feb 1999, pp. 433-436. [8] Haissaig, C.: “Adaptive fuzzy temperature control for hydronic heating systems” Proceedings of the 1999 IEEE International Conference on Control Applications, Hawaii, USA, August 22-27, 1999, pp. 582-588. [9] Lemmer, E.F. and Delport, G.J.: “The influence of a variable volume water heater on the domestic load profile” IEEE transactions on energy conversion, Vol. 14, 4, 1999, pp.1558- 1563. [10] Gustavson, M.W., Baylor, J.S. and Epstein, G.: "Direct Water Heater Load Control - Estimating Program Effectiveness Using an Engineering Model" IEEE Transactions on Power Systems, Vol. 8, No. 1, January 1993, pp.137-143. [11] Kenneth, R.: “A Model-based Control Laboratory Experiment” IEEE Proceedings of the American Control Conference June 4-6, 2003 [12] Grobler, L.J.: “Measurement and verification methodology of a residential load management. Potchefstroom” Department of Mechanical Engineering, North-West University, 2000. [13] Kenjo, L., Inard, C., Caccavelli, D.: “Experimental and numerical study of thermal stratification in a mantle tank of a solar domestic hot water system.” Applied thermal engineering, Vol. 27, 11-12, 2007, 1986-1995. Principal Author: Rinu Thomas holds a BEng degree in Electronic Engineering from the University of Pretoria. At present she is employed by ESKOM.

Co-author: Xiaohua Xia obtained his Ph.D. degree at Beijing University of Aeronautics and Astronautics,Beijing, China, in 1989. He is a Senior IEEE member, served as the South African IEEE Section/Control Chapter Chair. He also serves for IFAC as the vice-chair of the Technical Committee of Non-linear Systems. He has been an Associate Editor of Automatica, IEEE Transactions on Circuits and Systems II, and the Specialist Editor (Control) of the SAIEE Africa Research Journal. He is supported as a leading scientist by the National Research Foundation of South Africa, and elected a fellow of the South African Academy of Engineering. Co-author: Jiangfeng Zhang obtained his B.Sc. and Ph.D. in computational mathematics from Xi’ an Jiaotong University, China, in July 1995 and December 1999, respectively. He is now a research fellow in the University of Pretoria, South Africa. Presenter: The paper is presented by Rinu Thomas.