- Email: [email protected]
A simple peak shifting DSM (demand-side management) strategy for residential water heaters
Energy 62 (2013) 435e440
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
A simple peak shifting DSM (demand-side management) strategy for residential water heaters ur Atikol Ug Department of Mechanical Engineering, Eastern Mediterranean University, via Mersin 10, Gazimagusa, N. Cyprus, Turkey
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 July 2013 Received in revised form 18 September 2013 Accepted 23 September 2013 Available online 11 October 2013
In many developing countries due to lack of infrastructure the utilities experience difficulties in monitoring their customers’ demand or time of use of electricity and hence it is very difficult to apply DSM (demand-side management) programs for peak shifting. In several of these countries the residential EWHs (electric water heaters) are usually responsible for the evening peak. The general attitude of people is to turn them on just before they need hot water and statistics have shown that this takes place in the evening hours constituting the evening peak. The present work reviews the experimental findings about the static and dynamic cooling behavior of hot water in storage tanks and discusses the possible timer programs to avoid the peak hours. It is deduced from the experiments that even when the hot water is kept standing in a tank for 12 h after the initial withdrawal of 64.2 L, it would be possible to have warm water at temperatures above 40 C in the top 15% of the tank to utilize. If the DSM programs are carefully designed it would be possible to set the timers to operate the EWHs for once or twice a day to meet the daily demand of households. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Cyclic load control Demand-side management Developing countries Electrical water heater Peak shifting
1. Introduction In USA and many European Countries the customers benefit from the TOU (time of use) tariff and the DR (demand reduction) if they use the electricity at off-peak hours. Reducing the peak by such applications is favored by the utilities as this would lead to avoided costs of installing new power units. It is possible to meter both the TOU and the monthly peak demand which are both penalized if they cause the peak to increase. In developing countries demand meters are rarely found and the commonly used analog meters are not capable of measuring the energy used during off-peak hours; hence it is not easy to apply a TOU tariff effortlessly either. In Cyprus, in some houses, storage heaters that basically consisted of electric resistant heaters embedded in concrete blocks were used for benefiting from the off-peak night tariff, however, in these houses a separate analog meter was used with an additional electric wiring installed specifically for this heater. Nowadays this practice is abandoned due to its difficulties in implementation. In many industrial countries direct control of electric appliances (such as storage-type EWHs (electric water heaters), air conditioners and swimming pool pumps) have been commonly practiced
E-mail addresses: [email protected], [email protected]. 0360-5442/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.energy.2013.09.052
for peak shaving the demand curve [1e5]. The appliances are turned off in groups for short periods of time during the peak hours. The typical cycling periods for air conditioners and water heaters are 15 min and 6 h respectively [4]. Bzura [1] studied the use of a VHF-FM radio communication system to control the heating elements of 100 residential customers in Rhode Island. Vaiciunas [2] introduced a fully integrated SCADA and load management system to control customer water-heater load in Ontario, Canada. A digital switch connected to each water heater operated by a radio signal sent from the remote transmitter controller. LaMeres et al. [3] presented a fuzzy-logic based variable power control of the EWHs. The fuzzy controller can be loaded on a microprocessor chip and installed on the water heater. Based on the status of the water temperature, maximum and minimum water temperatures desired and distribution level power demand, fuzzy controller determines the fraction of the maximum allowable power that the water heater should consume. Ericson [4] studied the impact of direct load control of residential water heaters in Norway on the peak load. The size of the tank was 200 L while the power of the heating element was 2 kW. It was discovered that the average consumption reduction per household was approximately 0.5 kWh/h during disconnection. The energy storage capacity of EWHs provides favorable opportunities for longer periods of cyclic load control. It would be desired by the utilities to have the EWHs turned on continuously,
436
U. Atikol / Energy 62 (2013) 435e440
Eout , Xout, Tout
controlled with a thermostat to operate with water temperature below a set maximum value. This would give the utilities flexibility in choosing the time for disconnecting them in a cycle to reduce the peak demand. In many developing countries where electricity is considered as a “luxurious” form of energy, the EWHs are usually turned on for a few hours prior to their use. In North Cyprus, it is common to turn on the EWHs once a day and consume the daily required hot water from this production. This makes cyclic load control of EWHs difficult to apply. In order to devise DSM (demandside management) programs in this respect, it is of interest to investigate the feasibility of using this one-time prepared hot water for all hot water requirements in one day. The aim of the present work is to define more clearly this behavior which is recognizable in many developing countries and explore the possibility of applying a timer-controlled DSM program for reducing the peak demand induced by EWHs.
Outlet
V, E st, X st
j th layer
.
z
Tin,V
Inlet 2. Defining a daily pattern for hot water preparation In many developing country households, the EWHs are turned on just before they are used. Peak shifting can be achieved if their connection times can be known or handled carefully in a purposedesigned DSM program. Papakostas et al. [6] monitored hot water consumption in Greece and reported that families consumed between 25 and 35 L per day per person and on average the consumption patterns of daily use indicated a peaking between 19:00 and 22:00 h. Meyer et al. [7], who studied the hot water consumption in South African traditional houses, discovered that hot water consumption increases 70% from summer to winter, and people in the more developed communities consume approximately 10 times more hot water than people in the less developed communities. It is also evident from their work that both in summer and winter the consumption of hot water peaks two times in a day; at 7:00 in the morning and between 17:00 and 23:00 h in the evening. Prado et al. [8] stated that in Brazil a major part of the energy consumption in the residential sector was attributed to water heating. In their investigation of hourly shower demands they found out that the peak times are in the evening, starting at approximately 17:00 and continuing until almost midnight. Atikol et al. [9] also obtained similar patterns of residential hot water use in N. Cyprus. In their study they identified a small morning peak between 7:00 and 11:00 and a much larger evening peak developing between 17:00 and 22:00.
Fig. 2. Performance parameters and the storage tank (volume V ¼ 121 L, height H ¼ 700 mm, thickness of thermal insulation ¼ 35 mm).
It is evident from the literature that the EWHs are mostly turned on between 17:00 and 22:00 which forms the basis of the simple model displayed in Fig. 1. After the preparation of hot water there is a period that continues until almost midnight during which it is consumed, mostly by taking showers. The EWHs are not usually used after midnight and the remaining hot water stays in the tank until at least morning, when a secondary need of hot water consumption may come up. The period after midnight until the morning can be referred to as standing time, ts. This definition of standing time agrees well with the definition made by Atikol et al. [10] who referred to this period as the interval between the initial and the final use of hot water. They investigated the effect of standing time on the performance of EWHs. Turkish standards [11] indicate that for a comfortable shower, 50 L of water at 40 C is required. In our model, it is assumed that all the useful hot water is consumed during the second use period, such that the hot water temperature drops below 40 C. The period during which the hot water cannot be used comfortably is referred to as “unused period”. The hot water usage practice described here will form the basis of the timer control strategies which will be developed in the following sections.
70
MW Load of EWHs
60 50 The water temperature is After the first use of the below 40oC. In this period EWHs the remaining hot the EWHs will not be in water will stay in the tank service. until it is used again. This A need of using the hot period is referred to as water from the tank may "standing time". arise again. It is assumed that the hot water is consumed until the water temperature drops to 40oC.
40 30 20 10 0 0
2
4
6
8
10
12
14
16
18
20
22
24
Hours Fig. 1. A simple representative model for daily usage pattern of EWHs generated by approximately 60,000 residents as observed in Ref. [9].
U. Atikol / Energy 62 (2013) 435e440
3. A review of the experimental findings on the cooling of hot water in vertical cylindrical tanks
1 static cooling, t =10 h [13] dynamic cooling, 5 L/min [12]
t = 900s
z/H
Experiments carried out by investigators in Refs. [10,12e14] can be useful in the analysis of hot water availability after the cooling periods under different conditions. Fig. 2 represents the EWH used in the experiments by Atikol et al., details of which are given in Refs. [10,12]. The cylindrical tank has a height of 700 mm and an internal diameter of 470 mm with an electric immersion heater mounted vertically at the bottom. The tank is produced from a 2 mm-thick galvanized steel sheet and thermally insulated with a 35 mm fiberglass on all sides. Fernandez-Seara et al. performed experiments for both static [13] and dynamic modes [14] using a similar cylindrical tank having a storage capacity of 150 L. The static mode refers to the thermal behavior in the tank when there is no charging/discharging taking place. The tank had a height and diameter of 870 mm and 480 mm respectively. The equations used in Refs. [10,12] and in other literature [13e16] are given in Table 1. Transient temperature distributions for both the static mode [13] and while the hot water is discharged from the tank [12] are shown in Fig. 3. Initially a sharp temperature gradient exists at the bottom of the tank mainly due to the non-uniform heating of the vertical heating element at the bottom of the tank. It is evident from Ref. [13] that in the static cooling mode, the initial temperature distribution retreats by approximately 5 C in 10 h within all layers except at the bottom parts of the tank, meaning that in cases where the consumers do not use the hot water for a few hours immediately after the heating period, the performance of the EWHs will be hardly affected. However, in the case of charging/discharging taking place at 5 L/min, a region of steep temperature gradient, separating the cold and hot portions of water, known as ‘thermocline’ forms. The shape of the thermocline remains almost unchanged but gradually moves upwards while the water flow through the tank continues. The cooling behavior of the hot water was also investigated between an initial consumption and a second use [10,12], which was coined as “standing time” [10]. It is observed in these studies that if the hot water draw-off is stopped and a standing period is elapsed, the thermocline deteriorates due to mixing of hot and cold water masses, leading to temperature drop at the top of the tank (Fig. 4). The effects of standing time on the availability of useful hot water for different volumes of initial uses were examined thoroughly in Ref. [12]. It was assumed that 21.4 L of hot water, extracted at 80 C, can be used to prepare 50 L of warm water by mixing it with the cold water at approximately 10 C, was sufficient to take a shower. Therefore, the tests were carried out for 21.4, 42.8 and 64.2 L pre-extracted hot water and standing times of 12 and 20 h. Fig. 4 displays the temperature distributions in the tank for each case. The second discharging was performed until the water temperature dropped below 40 C. It was observed that as the amount of pre-extracted hot
437
0.5
d) ischarge (64.2 L d
2.8 L t = 600s (4 t = 300s
d) discharge
) ischarged (21.4 L d
0 0
0.5
1
Dimensionless temperature, T* Fig. 3. Transient temperature distributions in the storage tank while the hot water is drawn off at 5 L/min. as reported by Atikol et al. in Ref. [12]. The dashed line shows the transient temperature distribution if the tank is left unused for 10 h immediately after heating the water [13].
water and the standing time were increased the hot water availability was reduced. When the discharging process is restarted (referred to as the 2nd use period in the present work), the availability of hot water is inevitably limited due to decreasing hot water temperature. Table 2 shows the impact of standing time on the draw-off temperature and the volume of water available at that temperature for 21.4 L, 42.8 L and 64.2 L of pre-drawn hot water at 80 C. The authors indicated that the worst case was when 64.2 L of hot water (equivalent to what is required by three persons to take a shower) was drawn off initially and the discharging was started again after 20 h [12]. Atikol et al. [10] also investigated the case where one person takes the first shower and then the rest of the hot water is consumed all at once (until Tout is less than 40 C) after standing periods of 4, 8, 16 and 24 h. The results indicated that, as the standing time before the next draw-off was increased, the thermocline separating the hot upper fluid and the cold bottom fluid weakened, completely dying out after a standing time of 24 h. For a family of four, the maximum standing time, after the first person had taken a shower, was determined to be 8 h. 4. Exergy destruction during hot water consumption Not only the quantity of energy, but also its quality ought to be taken into account during the assessment of any thermodynamic process. The work potential of energy, which is known as exergy, indicates the quality of energy. It is important to minimize the exergy destruction in a process, so that the energy is used at its best quality. In all EWHs heat losses take place due to mixing of hot and
Table 1 Performance parameters used in the literature. Definition Energy contained in water leaving the storage tank Initial energy stored in the tank (j represents each of the horizontal layers) Exergy contained in water leaving the storage tank Initial exergy stored in the tank (j represents each of the horizontal layers) Discharging energy efficiency Discharging exergy efficiency Dimensionless temperature of water in the tank Stratification number (indicates the rate of decay of thermal stratification, where J represents the total number of layers)
Energy and exergy equations Rt
_ p ðTout ðtÞ T Þdt Eout ðtÞ ¼ 0 rVC in P35 Est ðt ¼ 0Þ ¼ j ¼ 1 ðrVCp Þj ðTj Tin Þ Rt _ Xout ðtÞ ¼ 0 ðrVÞ out ½ðhout h0 Þ T0 ðsout s0 Þdt P35 Xst ðt ¼ 0Þ ¼ j ¼ 1 fðrVÞj ½ðuj u0Þ Þ T0 ðsj s0 Þg
hI ¼ Eout ðtÞ=Est ðt ¼ 0Þ hII ¼ Xout ðtÞ=Xst ðt ¼ 0Þ
T * ¼ ðT ðz; t Þ Tin Þ=ðTmax Tin Þ R ¼ ðvT=vzÞt =ðvT=vzÞt¼0 where vT=vz ¼ f1=ðN 1Þg
PJ1 j¼1
vT=vz
Eqn. no.
References
(1)
[10,12,14,15]
(2)
[10,12e15]
(3)
[14]
(4)
[14]
(5) (6) (7)
[10,12,14,15] [14] [10,12,14,15]
(8)
[13e16]
438
U. Atikol / Energy 62 (2013) 435e440 Table 2 Dimensionless temperature at the outlet before the beginning of 2nd draw-off. (Experiment was conducted with Tin ¼ 10 C and Tmax ¼ 80 C [12]).
1
z/H
t s = 20 h
0.5
ts = 12 h
First draw-off (L)
ts (h)
T* before the beginning of 2nd draw-off
Constant temperature discharge available by volume (%)
Tout > 40 C?
21.4
12 20 12 20 12 20
0.7 0.56 0.58 0.45 0.5 0.36
40 33 25 23 15 10
Yes Yes Yes Yes Yes No
42.8 64.2
-drawn 21.4 L pre
0 0
0.5
Dimensionless temperature, T*
1
(a)
1
Xdes ðtÞ ¼ Xst ðt ¼ 0Þ Xout ðtÞ
t s = 20 h
z/ H
0.5
-drawn 42.8 L pre
* Xdes ðtÞ ¼
0 0
0.5
Dimensionless temperature, T*
1
(b)
1
t s = 20 h
(9)
where Xst (t ¼ 0) is the exergy initially stored in the tank and Xout (t) is the exergy contained in the water leaving the tank. The dimensionless form of exergy destruction at any time during the discharging can be expressed as follows:
t s = 12 h
z /H
Exergy stored and exergy discharged out of the tank can be calculated by using Eqns. (3 and 4). Exergy destruction at any time during the discharging of hot water can be evaluated from:
ts = 12 h -drawn 64.2 L pre
0.5
Xst ðt ¼ 0Þ Xout ðtÞ Xst ðt ¼ 0Þ
(10)
Fig. 5 displays the dimensionless exergy destruction, expressed in percentage of stored exergy, for the experimental discharging conditions presented in Refs. [10,12]. Linear trend lines are fitted through the available data for initial discharging volumes of 21.4 L, 42.8 L and 64.2 L. The vertical axis represents the total exergy loss that takes place during the first discharging period, the standing time and the final discharging period, which continues until the water temperature at the outlet of the tank drops down to 40 C. If the hot water is discharged continuously (that is to say, ts ¼ 0), the exergy destroyed will be approximately 7.5% which is the minimum possible amongst all the options. As the standing time between the two periods of usage is increased the exergy loss is also increased. The exergy destruction can be reduced if the amount of hot water used during the first discharge is increased. In other words, it is better for a family to use as much hot water as possible immediately after the hot water is prepared. 5. Discussion of timer-setting strategies for load shifting
0 0
0.5
Dimensionless temperature, T*
1
(c) Fig. 4. Temperature profiles in the tank after standing times of 12 and 20 h for predrawn hot water of (a) 21.4 L, (b) 42.8 L and (c) 64.2 L [12].
cold layers and through the walls of the storage tanks. These losses constitute the undesired irreversibilities or exergy destruction during the charging/discharging periods and standing time. Although Rosen et al. [17] discussed the exergy methods for analyzing the discharging from thermal energy storage systems; they have not considered the case of intermittent discharging. In this section it is aimed to present the total exergy losses covering the periods of first discharge, standing period and the final discharge.
The proposed DSM program relies on timer switches that can be pre-programmed to turn on (or turn off) the EWHs at any time (or times) of the day and at the same time guarantee hot water availability for domestic use. It is recommended that the hot water usage pattern of each household is examined before a timer program is suggested for them. The most conservative way to program the timers would be to set them off only during the peak hours (17:00e21:00) and let the consumers decide when they prefer to turn them on outside these hours. This is possible if the timer switches and the heater switches are connected in series. However, it would be necessary to ask the consumers to make sure they prepare hot water at least a few hours before the peak hours if they need to use them during the peak hours or just after that period. What would be challenging is to prepare hot water at 80 C only once in a day and use this water throughout the day without requiring any extra preparation of hot water. This depends greatly on the times of hot water requirement during a typical day. In North Cyprus, residential customers usually consume hot
U. Atikol / Energy 62 (2013) 435e440 45
439
Hot water demand First draw-off = 21.4 L [10]
40
First draw-off = 42.8 L [12]
35
First draw-off = 64.2 L [12]
Before peak hours?
30
Yes
25
Not elligible to participate in DSM program
No
20 15
Hot water requirement during peak hrs (17:00 - 21:00)
10 5
Hot water requirement after peak hrs for the period:
0 0
2
4
6
8
10
12
14
16
18
20
22
24
Fig. 5. Total dimensionless exergy destruction including the periods of initial and secondary discharging together with standing times ranging between 0 and 24 h. Initially drawn volumes were 21.4 L (one person using hot water), 42.8 L (two consecutive uses) and 64.2 L (three consecutive uses). The ‘unused period’ during which the water temperature drops below 40 C is excluded.
water from the EWHs for taking showers as a great majority of them use washing machines for washing clothes and dishes. The washing machines have their own heating arrangements to prepare hot water. Therefore it is essential to examine at what times residents in each household are taking showers on typical days before using the experimental findings described in the previous sections to propose timer settings for them. The general behavior of occupants, modeled in Section 2 and presented in Fig. 1, indicated that the EWHs are turned on mostly in the evenings and some times in the mornings. Fig. 6 summarizes some possibilities that can be utilized in a DSM program in order to achieve peak shifting and also make sure that hot water is available for taking shower next morning. If the hot water requirements are during or just after the peak hours (17:00e 21:00), it would be necessary to turn on the EWHs before the peak hours (15:00e17:00) generating a peak shifting to pre-peak hours. It is evident from Table 2 that, in the worst case, there will be warm water at temperatures above 40 C in the top 15% of the tank available after 12 h standing time even in the case of 3 persons taking showers in succession initially. On the other hand there is the possibility that some consumers may require to use the showers after 23:00 or later. In that case it would be more fitting to turn on the EWHs between 21:00 and 23:00 h, avoiding the peak time and also securing more hot water for morning needs. A straightforward cost estimation of this DSM strategy can be made by noting that analog and digital timers for water heaters can be purchased from the market in N. Cyprus at an approximate cost of $22 USD and the labor cost for installing them can be assumed to be $20 USD. Previous experience in N. Cyprus reveals that a new reciprocating engine power generation unit of 17-MW capacity costs approximately $12,000,000-USD. In order to defer the purchase of such a power plant an equivalent number of water heaters with 3-kW ratings must be turned off at peak hours. This will be possible with 5667 properly selected water heaters which are normally turned on during the peak hours. If a rebate of $200 USD, which is highly conservative, is given to those households who participate in this program the total cost of the program for each household would be $242 USD. For 5667 houses, the program would cost $1,371,414-USD. The avoided cost of deferring the need of a new power plant would be estimated to be $10, 628,586-USD.
21:00 - 23:00
EWH turned on before peak hrs (15:00 - 17:00)
Peak shifting
EWH turned on before peak hrs (15:00 - 17:00)
Peak shifting
23:00 onwards
EWH turned on after peak hrs (21:00 - 23:00)
Peak shifting
Fig. 6. Simplified timer-setting strategies for different times of hot water requirement on typical days to be applied in a DSM program.
6. Conclusion Utilities always prefer to operate their power units at full load in order to obtain the maximum efficiency from them. However, this depends very much on the hourly demand profile for each day in a year. In order to modify the demand curve, DSM strategies can be applied. One of the most powerful strategies is to control the times of connections of the water heaters. In non-industrialized countries this could be a very effective way of shifting the load from peak hours to off-peak hours. Additionally, by controlling the connection times of the EWHs instead of the disconnection times, the utilities will have more control over the hourly load curve. By this way it is possible to calculate more precisely how many MWs of those participating in the DSM program are connected at any given time period. Although load management of residential water heaters by using timer switches is not a new idea [9,18], it is the cheapest and simplest choice, suitable for places where the infrastructure and technical expertise are not favorable for the more advanced options. Moreover, the majority of the consumers in such countries prefer to switch their water heaters on, only for a few hours, just before they need the hot water. The present study investigates the practicability of utilizing timers to suit these conditions. It is found that if the DSM programs are carefully designed for each household it would be possible to set the timers to operate the EWHs for once or twice a day to provide enough hot water meeting the daily demand. If the EWH in a household is turned on between 21:00 and 23:00 h and three persons take showers consecutively, then they can be assured that next morning there will be enough hot water for at least one more shower. For other hot water consumption routines the utilities may need to plan different settings
440
U. Atikol / Energy 62 (2013) 435e440
for the timer switches. It is anticipated that there would be a high motivation in opting for this DSM strategy as the estimated cost of the program is extremely low compared to the cost of the deferred power unit. In some Mediterranean countries such as Cyprus, Greece and in southern parts of Turkey the majority of the hot water tanks are coupled with solar collectors and they are located on the roofs of the houses exposed to outdoor conditions. Therefore it would be advisable to include strengthening of the thermal insulation around the tanks as a part of the designed DSM programs.
References [1] Bzura JJ. Radio control of water heaters in Rhode Island. IEEE Trans Power Syst 1989;4(1):26e9. [2] Vaiciunas D. Load management and SCADA get into hot water. Transm Distrib World 1997;49(6):63e9. [3] LaMeres BJ, Nehrir MH, Gerez V. Controlling the average residential electric water heater power demand using fuzzy logic. Electr Power Syst Res 1999;52: 267e71. [4] Ericson T. Direct control of residential water heaters. Energy Policy 2009;37: 3502e12. [5] Heffner CH. Innovative approaches to verifying demand response of water load control. IEEE Trans Power Deliv 2006;21(1):388e97. [6] Papakostas KT, Papageorgiou NE, Sotiropoulos BA. Residential hot water use patterns in Greece. Sol Energy 1995;54(6):369e74.
[7] Meyer JP, Tshimankinda M. Domestic hot water consumption by developing communities in South African traditional houses. Energy 1996;21(12):1101e 6. [8] Prado RTA, Gonçalves OM. Water heating through electric shower and energy demand. Energy Build 1998;29:77e82. [9] Atikol U, Dagbasi M, Güven H. Identification of residential end-use loads for demand-side planning in northern Cyprus. Energy 1999;24(3):231e8. [10] Atikol U, Aldabbagh LBY, Sezai I. Effect of standing time after usage on the performance of storage-type domestic electrical water-heaters. J Energy Inst 2006;79(1):53e8. [11] ISISAN-series 147. Sanitary plumbing systems. Istanbul; 1997 [in Turkish]. [12] Atikol U, Aldabbagh LBY, Sezai I. The hot water availability and the discharging efficiency of a storage-type domestic water-heater. In: Proceedings of the 2nd International Exergy, Energy and Environment Symposium (IEEES2), Kos-Greece 3e7 July 2005. [13] Fernandez-Seara J, Uhia FJ, Sieres J. Experimental analysis of a domestic electric hot water storage tank. Part I: static mode of operation. Appl Therm Eng 2007;27:129e36. [14] Fernandez-Seara J, Uhia FJ, Sieres J. Experimental analysis of a domestic electric hot water storage tank. Part II: dynamic mode of operation. Appl Therm Eng 2007;27:137e44. [15] Sezai I, Aldabbagh LBY, Atikol U, Hacisevki H. Performance improvement by using dual heaters in a storage-type domestic water heater. Appl Energy 2005;81:291e305. [16] Shyu RJ, Hsieh CK. Unsteady natural convection in enclosures with stratified medium. J Sol Energy Eng 1987:109e27. [17] Rosen MA, Dincer I. Exergy methods for assessing and comparing thermal storage systems. Int J Energy Res 2003;27:415e30. [18] Banerjee R. Load management in the Indian power sector using US experience. Energy 1998;23(11):961e72.
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
A simple peak shifting DSM (demand-side management) strategy for residential water heaters ur Atikol Ug Department of Mechanical Engineering, Eastern Mediterranean University, via Mersin 10, Gazimagusa, N. Cyprus, Turkey
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 July 2013 Received in revised form 18 September 2013 Accepted 23 September 2013 Available online 11 October 2013
In many developing countries due to lack of infrastructure the utilities experience difficulties in monitoring their customers’ demand or time of use of electricity and hence it is very difficult to apply DSM (demand-side management) programs for peak shifting. In several of these countries the residential EWHs (electric water heaters) are usually responsible for the evening peak. The general attitude of people is to turn them on just before they need hot water and statistics have shown that this takes place in the evening hours constituting the evening peak. The present work reviews the experimental findings about the static and dynamic cooling behavior of hot water in storage tanks and discusses the possible timer programs to avoid the peak hours. It is deduced from the experiments that even when the hot water is kept standing in a tank for 12 h after the initial withdrawal of 64.2 L, it would be possible to have warm water at temperatures above 40 C in the top 15% of the tank to utilize. If the DSM programs are carefully designed it would be possible to set the timers to operate the EWHs for once or twice a day to meet the daily demand of households. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Cyclic load control Demand-side management Developing countries Electrical water heater Peak shifting
1. Introduction In USA and many European Countries the customers benefit from the TOU (time of use) tariff and the DR (demand reduction) if they use the electricity at off-peak hours. Reducing the peak by such applications is favored by the utilities as this would lead to avoided costs of installing new power units. It is possible to meter both the TOU and the monthly peak demand which are both penalized if they cause the peak to increase. In developing countries demand meters are rarely found and the commonly used analog meters are not capable of measuring the energy used during off-peak hours; hence it is not easy to apply a TOU tariff effortlessly either. In Cyprus, in some houses, storage heaters that basically consisted of electric resistant heaters embedded in concrete blocks were used for benefiting from the off-peak night tariff, however, in these houses a separate analog meter was used with an additional electric wiring installed specifically for this heater. Nowadays this practice is abandoned due to its difficulties in implementation. In many industrial countries direct control of electric appliances (such as storage-type EWHs (electric water heaters), air conditioners and swimming pool pumps) have been commonly practiced
E-mail addresses: [email protected], [email protected]. 0360-5442/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.energy.2013.09.052
for peak shaving the demand curve [1e5]. The appliances are turned off in groups for short periods of time during the peak hours. The typical cycling periods for air conditioners and water heaters are 15 min and 6 h respectively [4]. Bzura [1] studied the use of a VHF-FM radio communication system to control the heating elements of 100 residential customers in Rhode Island. Vaiciunas [2] introduced a fully integrated SCADA and load management system to control customer water-heater load in Ontario, Canada. A digital switch connected to each water heater operated by a radio signal sent from the remote transmitter controller. LaMeres et al. [3] presented a fuzzy-logic based variable power control of the EWHs. The fuzzy controller can be loaded on a microprocessor chip and installed on the water heater. Based on the status of the water temperature, maximum and minimum water temperatures desired and distribution level power demand, fuzzy controller determines the fraction of the maximum allowable power that the water heater should consume. Ericson [4] studied the impact of direct load control of residential water heaters in Norway on the peak load. The size of the tank was 200 L while the power of the heating element was 2 kW. It was discovered that the average consumption reduction per household was approximately 0.5 kWh/h during disconnection. The energy storage capacity of EWHs provides favorable opportunities for longer periods of cyclic load control. It would be desired by the utilities to have the EWHs turned on continuously,
436
U. Atikol / Energy 62 (2013) 435e440
Eout , Xout, Tout
controlled with a thermostat to operate with water temperature below a set maximum value. This would give the utilities flexibility in choosing the time for disconnecting them in a cycle to reduce the peak demand. In many developing countries where electricity is considered as a “luxurious” form of energy, the EWHs are usually turned on for a few hours prior to their use. In North Cyprus, it is common to turn on the EWHs once a day and consume the daily required hot water from this production. This makes cyclic load control of EWHs difficult to apply. In order to devise DSM (demandside management) programs in this respect, it is of interest to investigate the feasibility of using this one-time prepared hot water for all hot water requirements in one day. The aim of the present work is to define more clearly this behavior which is recognizable in many developing countries and explore the possibility of applying a timer-controlled DSM program for reducing the peak demand induced by EWHs.
Outlet
V, E st, X st
j th layer
.
z
Tin,V
Inlet 2. Defining a daily pattern for hot water preparation In many developing country households, the EWHs are turned on just before they are used. Peak shifting can be achieved if their connection times can be known or handled carefully in a purposedesigned DSM program. Papakostas et al. [6] monitored hot water consumption in Greece and reported that families consumed between 25 and 35 L per day per person and on average the consumption patterns of daily use indicated a peaking between 19:00 and 22:00 h. Meyer et al. [7], who studied the hot water consumption in South African traditional houses, discovered that hot water consumption increases 70% from summer to winter, and people in the more developed communities consume approximately 10 times more hot water than people in the less developed communities. It is also evident from their work that both in summer and winter the consumption of hot water peaks two times in a day; at 7:00 in the morning and between 17:00 and 23:00 h in the evening. Prado et al. [8] stated that in Brazil a major part of the energy consumption in the residential sector was attributed to water heating. In their investigation of hourly shower demands they found out that the peak times are in the evening, starting at approximately 17:00 and continuing until almost midnight. Atikol et al. [9] also obtained similar patterns of residential hot water use in N. Cyprus. In their study they identified a small morning peak between 7:00 and 11:00 and a much larger evening peak developing between 17:00 and 22:00.
Fig. 2. Performance parameters and the storage tank (volume V ¼ 121 L, height H ¼ 700 mm, thickness of thermal insulation ¼ 35 mm).
It is evident from the literature that the EWHs are mostly turned on between 17:00 and 22:00 which forms the basis of the simple model displayed in Fig. 1. After the preparation of hot water there is a period that continues until almost midnight during which it is consumed, mostly by taking showers. The EWHs are not usually used after midnight and the remaining hot water stays in the tank until at least morning, when a secondary need of hot water consumption may come up. The period after midnight until the morning can be referred to as standing time, ts. This definition of standing time agrees well with the definition made by Atikol et al. [10] who referred to this period as the interval between the initial and the final use of hot water. They investigated the effect of standing time on the performance of EWHs. Turkish standards [11] indicate that for a comfortable shower, 50 L of water at 40 C is required. In our model, it is assumed that all the useful hot water is consumed during the second use period, such that the hot water temperature drops below 40 C. The period during which the hot water cannot be used comfortably is referred to as “unused period”. The hot water usage practice described here will form the basis of the timer control strategies which will be developed in the following sections.
70
MW Load of EWHs
60 50 The water temperature is After the first use of the below 40oC. In this period EWHs the remaining hot the EWHs will not be in water will stay in the tank service. until it is used again. This A need of using the hot period is referred to as water from the tank may "standing time". arise again. It is assumed that the hot water is consumed until the water temperature drops to 40oC.
40 30 20 10 0 0
2
4
6
8
10
12
14
16
18
20
22
24
Hours Fig. 1. A simple representative model for daily usage pattern of EWHs generated by approximately 60,000 residents as observed in Ref. [9].
U. Atikol / Energy 62 (2013) 435e440
3. A review of the experimental findings on the cooling of hot water in vertical cylindrical tanks
1 static cooling, t =10 h [13] dynamic cooling, 5 L/min [12]
t = 900s
z/H
Experiments carried out by investigators in Refs. [10,12e14] can be useful in the analysis of hot water availability after the cooling periods under different conditions. Fig. 2 represents the EWH used in the experiments by Atikol et al., details of which are given in Refs. [10,12]. The cylindrical tank has a height of 700 mm and an internal diameter of 470 mm with an electric immersion heater mounted vertically at the bottom. The tank is produced from a 2 mm-thick galvanized steel sheet and thermally insulated with a 35 mm fiberglass on all sides. Fernandez-Seara et al. performed experiments for both static [13] and dynamic modes [14] using a similar cylindrical tank having a storage capacity of 150 L. The static mode refers to the thermal behavior in the tank when there is no charging/discharging taking place. The tank had a height and diameter of 870 mm and 480 mm respectively. The equations used in Refs. [10,12] and in other literature [13e16] are given in Table 1. Transient temperature distributions for both the static mode [13] and while the hot water is discharged from the tank [12] are shown in Fig. 3. Initially a sharp temperature gradient exists at the bottom of the tank mainly due to the non-uniform heating of the vertical heating element at the bottom of the tank. It is evident from Ref. [13] that in the static cooling mode, the initial temperature distribution retreats by approximately 5 C in 10 h within all layers except at the bottom parts of the tank, meaning that in cases where the consumers do not use the hot water for a few hours immediately after the heating period, the performance of the EWHs will be hardly affected. However, in the case of charging/discharging taking place at 5 L/min, a region of steep temperature gradient, separating the cold and hot portions of water, known as ‘thermocline’ forms. The shape of the thermocline remains almost unchanged but gradually moves upwards while the water flow through the tank continues. The cooling behavior of the hot water was also investigated between an initial consumption and a second use [10,12], which was coined as “standing time” [10]. It is observed in these studies that if the hot water draw-off is stopped and a standing period is elapsed, the thermocline deteriorates due to mixing of hot and cold water masses, leading to temperature drop at the top of the tank (Fig. 4). The effects of standing time on the availability of useful hot water for different volumes of initial uses were examined thoroughly in Ref. [12]. It was assumed that 21.4 L of hot water, extracted at 80 C, can be used to prepare 50 L of warm water by mixing it with the cold water at approximately 10 C, was sufficient to take a shower. Therefore, the tests were carried out for 21.4, 42.8 and 64.2 L pre-extracted hot water and standing times of 12 and 20 h. Fig. 4 displays the temperature distributions in the tank for each case. The second discharging was performed until the water temperature dropped below 40 C. It was observed that as the amount of pre-extracted hot
437
0.5
d) ischarge (64.2 L d
2.8 L t = 600s (4 t = 300s
d) discharge
) ischarged (21.4 L d
0 0
0.5
1
Dimensionless temperature, T* Fig. 3. Transient temperature distributions in the storage tank while the hot water is drawn off at 5 L/min. as reported by Atikol et al. in Ref. [12]. The dashed line shows the transient temperature distribution if the tank is left unused for 10 h immediately after heating the water [13].
water and the standing time were increased the hot water availability was reduced. When the discharging process is restarted (referred to as the 2nd use period in the present work), the availability of hot water is inevitably limited due to decreasing hot water temperature. Table 2 shows the impact of standing time on the draw-off temperature and the volume of water available at that temperature for 21.4 L, 42.8 L and 64.2 L of pre-drawn hot water at 80 C. The authors indicated that the worst case was when 64.2 L of hot water (equivalent to what is required by three persons to take a shower) was drawn off initially and the discharging was started again after 20 h [12]. Atikol et al. [10] also investigated the case where one person takes the first shower and then the rest of the hot water is consumed all at once (until Tout is less than 40 C) after standing periods of 4, 8, 16 and 24 h. The results indicated that, as the standing time before the next draw-off was increased, the thermocline separating the hot upper fluid and the cold bottom fluid weakened, completely dying out after a standing time of 24 h. For a family of four, the maximum standing time, after the first person had taken a shower, was determined to be 8 h. 4. Exergy destruction during hot water consumption Not only the quantity of energy, but also its quality ought to be taken into account during the assessment of any thermodynamic process. The work potential of energy, which is known as exergy, indicates the quality of energy. It is important to minimize the exergy destruction in a process, so that the energy is used at its best quality. In all EWHs heat losses take place due to mixing of hot and
Table 1 Performance parameters used in the literature. Definition Energy contained in water leaving the storage tank Initial energy stored in the tank (j represents each of the horizontal layers) Exergy contained in water leaving the storage tank Initial exergy stored in the tank (j represents each of the horizontal layers) Discharging energy efficiency Discharging exergy efficiency Dimensionless temperature of water in the tank Stratification number (indicates the rate of decay of thermal stratification, where J represents the total number of layers)
Energy and exergy equations Rt
_ p ðTout ðtÞ T Þdt Eout ðtÞ ¼ 0 rVC in P35 Est ðt ¼ 0Þ ¼ j ¼ 1 ðrVCp Þj ðTj Tin Þ Rt _ Xout ðtÞ ¼ 0 ðrVÞ out ½ðhout h0 Þ T0 ðsout s0 Þdt P35 Xst ðt ¼ 0Þ ¼ j ¼ 1 fðrVÞj ½ðuj u0Þ Þ T0 ðsj s0 Þg
hI ¼ Eout ðtÞ=Est ðt ¼ 0Þ hII ¼ Xout ðtÞ=Xst ðt ¼ 0Þ
T * ¼ ðT ðz; t Þ Tin Þ=ðTmax Tin Þ R ¼ ðvT=vzÞt =ðvT=vzÞt¼0 where vT=vz ¼ f1=ðN 1Þg
PJ1 j¼1
vT=vz
Eqn. no.
References
(1)
[10,12,14,15]
(2)
[10,12e15]
(3)
[14]
(4)
[14]
(5) (6) (7)
[10,12,14,15] [14] [10,12,14,15]
(8)
[13e16]
438
U. Atikol / Energy 62 (2013) 435e440 Table 2 Dimensionless temperature at the outlet before the beginning of 2nd draw-off. (Experiment was conducted with Tin ¼ 10 C and Tmax ¼ 80 C [12]).
1
z/H
t s = 20 h
0.5
ts = 12 h
First draw-off (L)
ts (h)
T* before the beginning of 2nd draw-off
Constant temperature discharge available by volume (%)
Tout > 40 C?
21.4
12 20 12 20 12 20
0.7 0.56 0.58 0.45 0.5 0.36
40 33 25 23 15 10
Yes Yes Yes Yes Yes No
42.8 64.2
-drawn 21.4 L pre
0 0
0.5
Dimensionless temperature, T*
1
(a)
1
Xdes ðtÞ ¼ Xst ðt ¼ 0Þ Xout ðtÞ
t s = 20 h
z/ H
0.5
-drawn 42.8 L pre
* Xdes ðtÞ ¼
0 0
0.5
Dimensionless temperature, T*
1
(b)
1
t s = 20 h
(9)
where Xst (t ¼ 0) is the exergy initially stored in the tank and Xout (t) is the exergy contained in the water leaving the tank. The dimensionless form of exergy destruction at any time during the discharging can be expressed as follows:
t s = 12 h
z /H
Exergy stored and exergy discharged out of the tank can be calculated by using Eqns. (3 and 4). Exergy destruction at any time during the discharging of hot water can be evaluated from:
ts = 12 h -drawn 64.2 L pre
0.5
Xst ðt ¼ 0Þ Xout ðtÞ Xst ðt ¼ 0Þ
(10)
Fig. 5 displays the dimensionless exergy destruction, expressed in percentage of stored exergy, for the experimental discharging conditions presented in Refs. [10,12]. Linear trend lines are fitted through the available data for initial discharging volumes of 21.4 L, 42.8 L and 64.2 L. The vertical axis represents the total exergy loss that takes place during the first discharging period, the standing time and the final discharging period, which continues until the water temperature at the outlet of the tank drops down to 40 C. If the hot water is discharged continuously (that is to say, ts ¼ 0), the exergy destroyed will be approximately 7.5% which is the minimum possible amongst all the options. As the standing time between the two periods of usage is increased the exergy loss is also increased. The exergy destruction can be reduced if the amount of hot water used during the first discharge is increased. In other words, it is better for a family to use as much hot water as possible immediately after the hot water is prepared. 5. Discussion of timer-setting strategies for load shifting
0 0
0.5
Dimensionless temperature, T*
1
(c) Fig. 4. Temperature profiles in the tank after standing times of 12 and 20 h for predrawn hot water of (a) 21.4 L, (b) 42.8 L and (c) 64.2 L [12].
cold layers and through the walls of the storage tanks. These losses constitute the undesired irreversibilities or exergy destruction during the charging/discharging periods and standing time. Although Rosen et al. [17] discussed the exergy methods for analyzing the discharging from thermal energy storage systems; they have not considered the case of intermittent discharging. In this section it is aimed to present the total exergy losses covering the periods of first discharge, standing period and the final discharge.
The proposed DSM program relies on timer switches that can be pre-programmed to turn on (or turn off) the EWHs at any time (or times) of the day and at the same time guarantee hot water availability for domestic use. It is recommended that the hot water usage pattern of each household is examined before a timer program is suggested for them. The most conservative way to program the timers would be to set them off only during the peak hours (17:00e21:00) and let the consumers decide when they prefer to turn them on outside these hours. This is possible if the timer switches and the heater switches are connected in series. However, it would be necessary to ask the consumers to make sure they prepare hot water at least a few hours before the peak hours if they need to use them during the peak hours or just after that period. What would be challenging is to prepare hot water at 80 C only once in a day and use this water throughout the day without requiring any extra preparation of hot water. This depends greatly on the times of hot water requirement during a typical day. In North Cyprus, residential customers usually consume hot
U. Atikol / Energy 62 (2013) 435e440 45
439
Hot water demand First draw-off = 21.4 L [10]
40
First draw-off = 42.8 L [12]
35
First draw-off = 64.2 L [12]
Before peak hours?
30
Yes
25
Not elligible to participate in DSM program
No
20 15
Hot water requirement during peak hrs (17:00 - 21:00)
10 5
Hot water requirement after peak hrs for the period:
0 0
2
4
6
8
10
12
14
16
18
20
22
24
Fig. 5. Total dimensionless exergy destruction including the periods of initial and secondary discharging together with standing times ranging between 0 and 24 h. Initially drawn volumes were 21.4 L (one person using hot water), 42.8 L (two consecutive uses) and 64.2 L (three consecutive uses). The ‘unused period’ during which the water temperature drops below 40 C is excluded.
water from the EWHs for taking showers as a great majority of them use washing machines for washing clothes and dishes. The washing machines have their own heating arrangements to prepare hot water. Therefore it is essential to examine at what times residents in each household are taking showers on typical days before using the experimental findings described in the previous sections to propose timer settings for them. The general behavior of occupants, modeled in Section 2 and presented in Fig. 1, indicated that the EWHs are turned on mostly in the evenings and some times in the mornings. Fig. 6 summarizes some possibilities that can be utilized in a DSM program in order to achieve peak shifting and also make sure that hot water is available for taking shower next morning. If the hot water requirements are during or just after the peak hours (17:00e 21:00), it would be necessary to turn on the EWHs before the peak hours (15:00e17:00) generating a peak shifting to pre-peak hours. It is evident from Table 2 that, in the worst case, there will be warm water at temperatures above 40 C in the top 15% of the tank available after 12 h standing time even in the case of 3 persons taking showers in succession initially. On the other hand there is the possibility that some consumers may require to use the showers after 23:00 or later. In that case it would be more fitting to turn on the EWHs between 21:00 and 23:00 h, avoiding the peak time and also securing more hot water for morning needs. A straightforward cost estimation of this DSM strategy can be made by noting that analog and digital timers for water heaters can be purchased from the market in N. Cyprus at an approximate cost of $22 USD and the labor cost for installing them can be assumed to be $20 USD. Previous experience in N. Cyprus reveals that a new reciprocating engine power generation unit of 17-MW capacity costs approximately $12,000,000-USD. In order to defer the purchase of such a power plant an equivalent number of water heaters with 3-kW ratings must be turned off at peak hours. This will be possible with 5667 properly selected water heaters which are normally turned on during the peak hours. If a rebate of $200 USD, which is highly conservative, is given to those households who participate in this program the total cost of the program for each household would be $242 USD. For 5667 houses, the program would cost $1,371,414-USD. The avoided cost of deferring the need of a new power plant would be estimated to be $10, 628,586-USD.
21:00 - 23:00
EWH turned on before peak hrs (15:00 - 17:00)
Peak shifting
EWH turned on before peak hrs (15:00 - 17:00)
Peak shifting
23:00 onwards
EWH turned on after peak hrs (21:00 - 23:00)
Peak shifting
Fig. 6. Simplified timer-setting strategies for different times of hot water requirement on typical days to be applied in a DSM program.
6. Conclusion Utilities always prefer to operate their power units at full load in order to obtain the maximum efficiency from them. However, this depends very much on the hourly demand profile for each day in a year. In order to modify the demand curve, DSM strategies can be applied. One of the most powerful strategies is to control the times of connections of the water heaters. In non-industrialized countries this could be a very effective way of shifting the load from peak hours to off-peak hours. Additionally, by controlling the connection times of the EWHs instead of the disconnection times, the utilities will have more control over the hourly load curve. By this way it is possible to calculate more precisely how many MWs of those participating in the DSM program are connected at any given time period. Although load management of residential water heaters by using timer switches is not a new idea [9,18], it is the cheapest and simplest choice, suitable for places where the infrastructure and technical expertise are not favorable for the more advanced options. Moreover, the majority of the consumers in such countries prefer to switch their water heaters on, only for a few hours, just before they need the hot water. The present study investigates the practicability of utilizing timers to suit these conditions. It is found that if the DSM programs are carefully designed for each household it would be possible to set the timers to operate the EWHs for once or twice a day to provide enough hot water meeting the daily demand. If the EWH in a household is turned on between 21:00 and 23:00 h and three persons take showers consecutively, then they can be assured that next morning there will be enough hot water for at least one more shower. For other hot water consumption routines the utilities may need to plan different settings
440
U. Atikol / Energy 62 (2013) 435e440
for the timer switches. It is anticipated that there would be a high motivation in opting for this DSM strategy as the estimated cost of the program is extremely low compared to the cost of the deferred power unit. In some Mediterranean countries such as Cyprus, Greece and in southern parts of Turkey the majority of the hot water tanks are coupled with solar collectors and they are located on the roofs of the houses exposed to outdoor conditions. Therefore it would be advisable to include strengthening of the thermal insulation around the tanks as a part of the designed DSM programs.
References [1] Bzura JJ. Radio control of water heaters in Rhode Island. IEEE Trans Power Syst 1989;4(1):26e9. [2] Vaiciunas D. Load management and SCADA get into hot water. Transm Distrib World 1997;49(6):63e9. [3] LaMeres BJ, Nehrir MH, Gerez V. Controlling the average residential electric water heater power demand using fuzzy logic. Electr Power Syst Res 1999;52: 267e71. [4] Ericson T. Direct control of residential water heaters. Energy Policy 2009;37: 3502e12. [5] Heffner CH. Innovative approaches to verifying demand response of water load control. IEEE Trans Power Deliv 2006;21(1):388e97. [6] Papakostas KT, Papageorgiou NE, Sotiropoulos BA. Residential hot water use patterns in Greece. Sol Energy 1995;54(6):369e74.
[7] Meyer JP, Tshimankinda M. Domestic hot water consumption by developing communities in South African traditional houses. Energy 1996;21(12):1101e 6. [8] Prado RTA, Gonçalves OM. Water heating through electric shower and energy demand. Energy Build 1998;29:77e82. [9] Atikol U, Dagbasi M, Güven H. Identification of residential end-use loads for demand-side planning in northern Cyprus. Energy 1999;24(3):231e8. [10] Atikol U, Aldabbagh LBY, Sezai I. Effect of standing time after usage on the performance of storage-type domestic electrical water-heaters. J Energy Inst 2006;79(1):53e8. [11] ISISAN-series 147. Sanitary plumbing systems. Istanbul; 1997 [in Turkish]. [12] Atikol U, Aldabbagh LBY, Sezai I. The hot water availability and the discharging efficiency of a storage-type domestic water-heater. In: Proceedings of the 2nd International Exergy, Energy and Environment Symposium (IEEES2), Kos-Greece 3e7 July 2005. [13] Fernandez-Seara J, Uhia FJ, Sieres J. Experimental analysis of a domestic electric hot water storage tank. Part I: static mode of operation. Appl Therm Eng 2007;27:129e36. [14] Fernandez-Seara J, Uhia FJ, Sieres J. Experimental analysis of a domestic electric hot water storage tank. Part II: dynamic mode of operation. Appl Therm Eng 2007;27:137e44. [15] Sezai I, Aldabbagh LBY, Atikol U, Hacisevki H. Performance improvement by using dual heaters in a storage-type domestic water heater. Appl Energy 2005;81:291e305. [16] Shyu RJ, Hsieh CK. Unsteady natural convection in enclosures with stratified medium. J Sol Energy Eng 1987:109e27. [17] Rosen MA, Dincer I. Exergy methods for assessing and comparing thermal storage systems. Int J Energy Res 2003;27:415e30. [18] Banerjee R. Load management in the Indian power sector using US experience. Energy 1998;23(11):961e72.