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Improved differential control for solar heating systems
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Solar Energy 86 (2012) 3489–3498 www.elsevier.com/locate/solener
Improved differential control for solar heating systems R. Kicsiny a,⇑, I. Farkas b b
a Department of Mathematics, Szent Istva´n University, Go¨do¨ll}o, Hungary Department of Physics and Process Control, Szent Istva´n University, Go¨do¨ll}o, Hungary
Received 22 July 2011; received in revised form 3 May 2012; accepted 6 August 2012 Available online 24 August 2012 Communicated by: Associate Editor C. Estrada-Gasca
Abstract One possibility to exploit solar energy better is the efficiency enhancement of the control of solar thermal heating systems. In this paper an improved differential control and the generally used ordinary differential control operating with fixed switch-on and switchoff temperature differences are compared in different efficiency viewpoints. The comparison is based on measured data of a particular system at the Szent Istva´n University, Go¨do¨ll} o and on a TRNSYS model developed for solar heating systems. According to the results the improved control provides a higher value of utilizability and brings forth fewer switch-ons and switch-offs for the pumps. These advantages nevertheless result in extended operation time and thus extended parasitic consumption of the pumps. This drawback can, however, be moderated or even extinguished by modern pumps with low energy consumption or if supplied by renewable energy source. Comparing the amount of utilized solar energy and consumed parasitic energy increments, the improved control can be generally recommended. Ó 2012 Elsevier Ltd. All rights reserved. Keywords: Solar water heating system; Energetically-based control; On/off control; Simulation; Measurements
1. Introduction In view of the global environment pollution issue it is important to exploit renewable, and as a part of it, solar energy better. For this ambition, one possibility to develop solar heating systems (in this paper we always refer to active solar water heating system using the shorter term solar heating system) is the efficiency enhancement of their control strategy. Several works have been published in the literature on different optimization endeavors for solar heating systems. Substantial early publications for determining the optimal control strategy by pump flow rate modulation are (Kovarik and Lesse, 1976; Winn and Hull, 1979; Badescu, 2008) in case of no heat exchanger and (Badescu, 2008) ⇑ Corresponding author.
E-mail address: [email protected] (R. Kicsiny). 0038-092X/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.solener.2012.08.003
again in case of internal heat exchanger inside the solar storage. The optimal control in case of external heat exchanger can be similarly discussed by customarily taking the effect of the solar collector(s) but now with an adequate corrective coefficient corresponding to the effect of the heat exchanger. As a result the solar heating system is equivalent with a simple, directly connected collector-storage system of reduced collector surface area, with the above coefficient that contains parameters for both the solar collector and the heat exchanger. On the process of optimizing control in this case with counter flow heat exchanger see Hollands and Brunger (1992), on the corrective coefficient see Hollands and Brunger (1992) and Duffie and Beckman (2006). Based on the Pontryagin maximum principle (Pontryagin et al., 1962) it can be demonstrated that the theoretical optimal control which maximizes the difference of the energy utilized by the storage and used up by the pumping
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is a differential (or bang–bang, or on/off) control that depends on the future knowledge of weather data (Kovarik and Lesse, 1976; Orbach et al., 1981). (Here and generally the differential control switches between zero and a maximal flow rate value.) This control cannot be directly put into practice since the meteorological data are of course not known in advance. The problem is partially eased but not fully resolved if we assume the a priori knowledge that only one on and off switches will occur during the time interval under consideration. In this case a feedback differential control stands for the optimal one which, in principle, could be used in practice. See again Orbach et al. (1981). A so-called instantaneous control resolves the problem theoretically which is feasible for optimal flow rate modulation, needing only the most recent measured values of meteorological data (Bejan, 1982) but its application is also difficult and impractical. In case of no heat exchanger, correlating to the theoretically optimal control (Kovarik and Lesse, 1976), Winn and Hull (1979) establish a nearly as effective differential control that is feedback-type and so, in principle, can be used in practice. Applying the Pontryagin maximum principle they take into account the physical and geometrical parameters of the solar collector. This process is fairly technical and charged with inaccuracies since the partial and temporary shading effect of the clouds and the environment, even the physical and geometrical collector parameters, cannot be precisely taken into account. On the detailed calculation see also Lo¨f (1993). In addition, several investigated cases and different optimization approaches bring forth the conclusion that in many cases, the optimal control is the differential type control with an adequately set flow rate value. See e.g. Fritchman and Grantham, 1987 aiming at maximal solar storage temperature for a solar collector system with heat exchanger by a min–max differential game approach in which the solar irradiance is unknown. Furthermore e.g. (Badescu, 2007) achieved similar results by aiming at maximal exergy extraction by optimal flow rate control in significant part of the operation time. A further aspect is the interaction between different physical, geometrical and control parameters, namely the optimal flow rate in the solar heating system. See Farahat et al. (2009) on the common optimization of the flow rate and the collector area as a function of other parameters of the system for maximal exergy extraction. In addition to the emphasized application of the Pontryagin principle further dynamic optimization techniques are reviewed in Dorato (1983) for constructing optimal control for solar heating systems. Several control strategies exist and are used besides the differential type. The perhaps most frequented controls and their comparisons can be found e.g. in the following references: Winn (1983) compares differential, I (integral) and PID (proportional integral differential) controls. Hirsch (1985) compares differential, P (proportional) and
a hybrid of differential and P controls in different operation conditions. Lo¨f (1993) discusses differential, P, I, PID, adaptive as well as certain types optimal controls. In (Morteza et al., 1996) PID and PSD (proportional sum derivative) controls are compared. In different particular cases, different control methods may certainly be suitable in practice considering several aspects. It can be generally stated that the differential control is the simplest, in view of the required equipments, and the least expensive to apply in practice in the field of solar heating systems. On the detailed discussion of this control see Duffie and Beckman (2006) or as a more recent reference Kalogirou (2009). In this paper a new, specific feedback differential control, with variable switch-on and switch-off temperature differences, is introduced for solar heating systems with external heat exchanger, thus the collector and storage loops are separated hydraulically and equipped with two pumps. In the construction of this control the thermal processes of the solar collector are not implemented as the physical and geometrical collector parameters are not required, only the collector outlet temperature directly, thus the operation of the control is not charged with the unavoidable inaccuracies encountered by the solar collector. This control strategy aims to transfer even the least harvestable solar potential and all energy excess correlating to the solar storage into it from the pipes of the storage loop. In this way the control aims to maintain the storage at the all-time maximal energetic level possible, therefore it aims to maintain the potential for the consumer to always extract maximal heat from the storage. Let this improved differential control be called improved control. In this work the improved control is compared with an optimized version of the ordinary differential control used generally in practice (we will refer to this as ordinary control), which operates with prefixed switch-on and switchoff temperature differences. The improved control is a new, modified version of the one developed in Kicsiny (2009). The optimization of the ordinary control was also carried out in the latter work. The comparison, made in this paper, is based on recent measured data of a particular solar heating system and on a physically-based TRNSYS model that was also worked out in the latter work. The comparison is made from the aspect of the utilized solar energy, consumed parasitic (electric) energy by the pumps and the amount of switchons and switch-offs for the pumps. As new research achievements, the new improved control with both measured and simulation results are introduced in this paper to make the conclusions of the work reliable. The control methods and the physically based model are described in this paper. Physical bases corresponding to solar heating systems are well described in details in Duffie and Beckman (2006).
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2. Improved control approach In this section an improved control developed for solar heating systems and the optimized ordinary control used for comparison are introduced (Kicsiny, 2009). Although the controls have been developed for domestic hot water (DHW) heating, the principles and the functioning can be similarly applied in other applications, e.g. in swimming pool heating. During the investigations the following one dimensional partial differential equation relating to energy conservation law in the pipelines is needed: qcA
@T p @T p ¼ qcV_ kðT p T env;p Þ @t @x
ð1Þ
Notation: The l.h.s. of (1) stands for the heat due to the temperature change in time, the firs term on the r.h.s. represents the effect of the temperature change in space and the last term represents the heat loss of the pipe to the environment. The energy balance equation with Bosˇnjakovicˇ-coefficient corresponding to counter flow heat exchangers (see Fig. 1) will also be needed. UðT c;h;in T k;h;in Þ ¼ T k;h;out T k;h;in
ð2Þ
where U is the Bosˇnjakovicˇ-coefficient for heat exchanger, –; Tc,h,in the inlet temperature to heat exchanger in collector loop, °C; Tk,h,in the inlet temperature to heat exchanger in kindergarten loop, °C; Tk,h,out the outlet temperature from heat exchanger in kindergarten loop, °C. Tc,h,in Tk,h,in represents the theoretically maximal temperature change of the heated fluid inside the heat exchanger. The r.h.s. represents the realized value of this temperature change. 2.1. Operation of improved control In contrast with the ordinary control method which operates with fixed switch-on and switch-off temperature differences and generally used in practice, the improved control operates with varying temperature differences. Fig. 1 shows the investigated solar heating system type. Inside the storage there is no heat exchanger, therefore the
T c,out T env,c Tc,h,in collector loop
Tk,s,in Ts
Tk,h,out Tc,h,out
kindergarten loop
Vc
Tk,h,in Vk
Fig. 1. Simplified scheme of the investigated solar heating system type.
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storage is not separated hydraulically from the kindergarten loop. Notation: Tc,out is the outlet temperature from collector field, °C; Tenv,c the environment temperature of collector field, °C; Tk,s,in the inlet temperature to solar storage in kindergarten loop, °C; Ts the solar storage temperature in the lower third of the storage, °C; V_ c the volumetric flow in collector loop, m3/s; V_ k the volumetric flow in kindergarten loop, m3/s. The operation method of the improved control is the following: Case a, the outlet temperature from the collector field Tc,out, the storage temperature Ts and the environment temperature of the collector Tenv,c are measured continually. Assuming switched on pumps the inlet temperature of the heat exchanger in the collector loop Tc,h,in is calculated from Tc,out, Tenv,c and Eq. (1). Then the inlet temperature of the heat exchanger in the kindergarten loop Tk,h,in is calculated from Ts and (1). Then the outlet temperature of the heat exchanger in the kindergarten loop Tk,h,out can be determined from Tc,h,in, Tk,h,in and (2). Finally the inlet temperature of the storage in the kindergarten loop Tk,s,in can be also determined from Tk,h,out and (1). Tk,s,in Ts is the controlling temperature difference for both pumps. This is the one that is compared continuously with the switch-off temperature difference (DToff = 0 °C) and the switch-on temperature difference (DTon), that is the sum of DToff and a prefixed hysteresis value (DThyst = 2 °C). Case b, now not the calculated but the measured value of Tk,s,in is taken along with the measured value of Ts. The pumps are assumed to be switched on. The controlling temperature difference now is Tk,s,in Ts that is compared continuously with the switch-off temperature difference (that is prefixed DToff = 0.3 °C) and the switch-on temperature difference (DTon = DToff + DThyst). In this case the hysteresis temperature difference DThyst is prefixed to be 0.5 °C. The collector pump works according to Case a. The kindergarten pump works according to the logical OR connection between Case a, and b. So if either of the cases orders the kindergarten pump to switch on then the pump is on. 2.2. Operation of optimized ordinary control Generally the ordinary control switches off the pumps if Tc,out Ts is less than a prefixed value (e.g. 5 °C) and switches them on at a higher, also prefixed value (e.g. 7 °C). It is important for the practice and for the fair comparison of the control methods later to maximize the effectiveness of the ordinary control. The ordinary control does not deal with heat loss, it simply uses a prescribed switch-off temperature difference greater than 0 °C to ensure that the pumps work only if they take positive thermo-energy into the solar storage, that is if the cooling down of the storage is surely avoided. Furthermore this value should be as small as possible to gain the most solar potential.
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For the optimization that is the switch-off temperature difference minimization of the ordinary control, let us consider the biggest but still real losses in the system. Let us calculate with 55 °C temperature in the whole kindergarten loop, 10 °C in the ground and 5 °C in the environment of the collector loop. (In case of high system temperatures and low environment temperature the heat losses are characteristically the highest.) Assuming the above storage temperature, the pumps, which always work simultaneously in this control method, have to switch off if the inlet temperature of the storage in the kindergarten loop Tk,s,in decreases to 55 °C. The pumps are assumed to be switched on now also. Assuming the aforementioned Tk,s,in value, the claimed minimal value of the outlet temperature of the heat exchanger in the kindergarten loop Tk,h,out can be determined from (1). The inlet temperature of the heat exchanger in the kindergarten loop Tk,h,in can be also determined from the assumed storage temperature Ts value and (1). Based on these, such minimal value of the inlet temperature of the heat exchanger in the collector loop Tc,h,in by which Tk,h,out is still high enough can be determined from (2). Finally from the minimal value of Tc,h,in and (1) the minimal value of the outlet temperature from the collector field Tc,out can be also determined. The so established value DToff = Tc,out Ts is the switch-off temperature difference used permanently in the ordinary control. The prefixed hysteresis value is the same as in Case a, of the improved control (DThyst = 2 °C), with which DTon = DToff + DThyst. For the calculation of DToff and DTon in a different way, focusing on the positive value of the difference between the instantaneous heat gain and the consumed parasitic power, see Duffie and Beckman (2006) or Hirsch (1985). According to the considerations above for the ordinary control the term optimized corresponds not to some kind of direct or indirect optimal control approach but for the minimization of the switch-off temperature difference. The improved control always means a DToff value less or equal than the ordinary control since the former works with current measured temperature data and not with the possible “worse” conditions as the latter. In the coordinate system of the moving fluid element, Eq. (1) can be transformed into a one dimensional ordinary differential equation which can be explicitly solved. Then an explicit formula is gained for DToff and DTon for the ordinary control and for Case a, of the improved control. DToff is fixed in case of the ordinary control and depends on the measured Tc, Ts, Tenv,c and Tk,s,in temperatures in case of the improved control. Finally the improved control is provided as a directly applicable feedback control.
3. Evaluation This section compares the improved and the optimized ordinary controls using measured data of a real monitored system and simulations with a physically-based model.
Evaluation and summary of the results can be found here as well. The comparison considers the amount of the utilized solar energy, the consumed parasitic energy by the pumps and the amount of the switch-ons (=amount of switch-offs) of the pumps in case of both controls. The consumed parasitic energy is determined by the operation time of the pumps, i.e. the time duration of switched on pump periods. To take into account the operation time of both pumps together, in view of the parasitic consumption, let us introduce the term “equivalent operation time” of the pumps. This is the time, if the pumps simultaneously operate with, as in case of the ordinary control, they would consume the same amount of electric energy as in the real investigated case. By this quantity the operation time of the pumps can be directly compared between the different control cases. The governing equation is the following: tp;eq ¼
P p;c tp;c þ P p;k tp;k P p;c þ P p;k
ð3Þ
where tp,eq is the equivalent operation time of the pumps, h; Pp,c the parasitic consumption of the pump in the collector loop, W; Pp,k the parasitic consumption of the pump in the kindergarten loop, W; tp,c the operation time of collector pump, h; tp,k the operation time of kindergarten pump, h. In case of the ordinary control the pumps always operate simultaneously, so the equivalent operation time is the (equal) operation time of the pumps directly. In case of the improved control the pumps may operate in different times and commonly determine the equivalent operation time. 3.1. System description A monitored combined solar heating system (Farkas et al., 2000) which has been installed at the campus of Szent Istva´n University (SIU), Go¨do¨ll} o, Hungary is sketched in Fig. 2 (referred to as SIU system). The term combined here means that the installation has more than one consumers. It preheats water for an outdoor swimming pool and, in the idle period of this operation, DHW for a kindergarten nearby. The consumers can be independently or, in principle, parallelly served. In practice they are separated in time. The gained solar energy heats only the swimming pool in summer and only a solar storage in the kindergarten at the rest of the year. In both operations auxiliary gas heated boilers work simultaneously with the solar heating if necessary to cover the required heat energy. The main system components are the flat plate solar collector field, with a total area of 33.3 m2, oriented to the south with an inclination angle of 45°, the plate heat exchangers, a 700 m3 outdoor swimming pool with a surface of 350 m2 and a 2000 l solar storage tank. The solar collectors of the collector field are arranged in mixed, partially serial, partially parallel connection. In the modeling of the system described later in this paper, the solar collector field is considered by an equivalent solar
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Ig Collector field
Auxiliary Hot water gas outlet boiler Kindergarten
Collector loop
Solar storage Kindergarten loop
Vl
Vc
Vk Heat exchanger
Tap water inlet Aux. gas heater
Control valve
Pool loop
Vp
Swimming pool
Filter
Fig. 2. Simplified scheme of the combined solar heating system at the campus of SIU.
collector with 33.3 m2. Based on measured flow rate, temperature and pipe volume data, the estimated pipe length is 80 m between the equivalent collector and the kindergarten heat exchanger (in both directions) and 113.7 m between the same heat exchanger and the solar storage (underground in both directions). According to the notation in Fig. 2 temperature (T), flow rate ðV_ Þ and specific global solar irradiance (Ig) values are monitored in the system. The heat exchangers are assumed to operate with counter flows. Physical and geometrical parameters of the SIU system needed for the application of the control methods have been carefully estimated based on available measurements. Namely such measured data have been considered from different measurement times that suggest greater (but certainly rational) heat losses of the system. (Such parameters are the pipe lengths mentioned above, and the U Bosˇnjakovicˇ-coefficient.) In this way we can expect the cooling down of the solar storage to be surely avoided in case of continuously switched on pumps. This precaution affects both controls alike. The such determined parameters are U = 0.56, estimated by measured inlet and outlet temperatures of the heat exchanger, the overall heat loss coefficients of the pipes, estimated from measured data, kc = 0.5 W/(m K) in the collector loop and kk = 0.25 W/(m K) in the kindergarten loop. Other parameters are V_ c ¼ 0 or 0.98 m3/h; V_ k ¼ 0 or 0.63 m3/h. The parasitic consumptions are Pp,c = 60 W; Pp,k = 60 W. Nowadays it is generally achievable by modern, efficient pumps.
The optical efficiency of the collectors is 0.74, the linear heat loss coefficient of the collectors is 3.688 W/(m2 K), the second order heat loss coefficient of the collectors is 0.0207 W/(m2 K2). These values are taken from the technical documentation of the solar collectors (Fiorentini, 2012). Volume of the collector field: 27 l; volume of collector side of the heat exchanger: 2.5 l, volume of kindergarten side of the heat exchanger: 2.6 l. The specific heat of the collector fluid is 3623 J/(kg K), the collector fluid mass density is 1034 kg/m3. The switch-off and switch-on temperature differences arisen from the above parameter values for the ordinary control (see Section 2.2) are DT off ¼ 7:1 C, DT on ¼ 9:1 C. These values are in accordance with the increased heat losses by the system’s long pipelines and fall inside the generally recommended bounds in engineering practice (Duffie and Beckman, 2006; Kalogirou, 2009). 3.2. Experimental results The improved and the ordinary controls, according to the setup above, have been applied on the real, measured SIU system from 24 November 2010 to 23 May 2011, with a technical interruption from 06 May to 12 May. The controls were alternated day by day, so the same control operated every second day. Considering all measured data we have measurements for 88 days in case of the ordinary control and 86 days in case of the improved control. In view of the alternating operation, the nearly equal values of the solar irradiation on the collectors (see firs row in Table 1) and of the heat consumption of the
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kindergarten (see second row of Table 1) during the operation time of each control, they can be considered to operate under a similar environment and consumption circumstances. Thus the comparison of the controls can be considered relevant. The ordinary control transferred 933.3 kW h solar energy into the storage, while the improved control transferred more, 1050.0 kW h that is 116.7 kW h surplus in the utilization of the available solar energy. The time average of the measured solar storage temperature at the 2/3rd of the height of the storage (T21 in Fig. 2) is 25.7 °C in case of the ordinary control and 25.7 °C as well in case of the improved control. The equivalent operation time of the pumps is 174.0 h with the ordinary control and 222.6 h with the improved control. Accordingly the parasitic consumption is 20.9 kW h in case of the ordinary control and 26.7 kW h in case of the improved control, so the parasitic consumption excess is 5.8 kW h. The amount of switch-ons is 718 with the ordinary control for both pumps. This quantity is 543 for the collector pump and 548 for the kindergarten pump with the improved control. Thus the collector pump switched on 175 less, the kindergarten pump switched on 170 less in case of the improved control. It should be mentioned that the above values correspond to a bit different measured solar irradiation and heat consumption data. Nevertheless, these discrepancies are so marginal that, effectively, the results can be directly compared. Even in case of significantly different solar irradiation and heat consumption measurements the following specific quantities can be directly compared: Considering the utilized solar energy by the solar storage and the solar irradiation on the collectors, the utilizability is 16.0% with the ordinary control and 18.5% with the improved control.
Based on the above values the ordinary control needed 22.4 W h parasitic energy on average to transfer 1 kW h solar energy into the storage during the time of the measurements. The corresponding value with the improved control is 25.4 W h. All essential results are summarized in Table 1. 3.3. Simulation results This section contains the physically-based modeling of the investigated solar heating system. Simulation results are also introduced here for the comparison of the discussed control algorithms. 3.3.1. Physically-based modeling On the basis of time-separated operation, according to Fig. 3, a distinct model has been elaborated for kindergarten operation of the SIU system (Kicsiny, 2009). It should be mentioned that the model can easily be adapted to any similar solar heating system. The model was realized using the TRNSYS 16 (Klein et al., 2005) and, for some particular calculations, by the MAPLE 9 (Waterloo Maple Inc., 2003) software packages. The main system units have been located in distinct submodels, that are readily available in TRNSYS and can be used independently as well (see Fig. 4). Such parts are the collector sub-model (Type 832 in TRNSYS (Heimrath and Haller, 2007)), the heat exchanger sub model (Type 5b – counter flow heat exchanger), the stratified solar storage sub-model (Type 60c), the sub-model of the pumps (Type 114), the sub-model of the pipes (Type 31) and the sub-model for the ordinary control (Type 2b). The model part for the improved control has been established by different software elements (Type 2b blocks with the related “Equations” blocks). It is possible to choose either of them manually. Actual operation of the improved control is shown in Fig. 4.
Table 1 Measurement results (24 November 2010–23 May 2011).
Global solar irradiation on the collectors (kW h) Heat consumption of the kindergarten (kW h) Solar energy utilized by the solar storage (kW h) Utilized solar energy surplus (kW h) Utilizability (%) Time average of the solar storage temperature (°C) Operation time of the collector pump (h) Operation time of the kindergarten pump (h) Equivalent operation time of the pumps (h) Parasitic consumption of the pumps (kW h) Parasitic consumption excess (kW h) Specific parasitic consumption to the solar energy utilized by the solar storage (W h/kW h) Switch-ons of the collector pump Reduction in the amount of the switch-ons of the collector pump Switch-ons of the kindergarten pump Reduction in the amount of the switch-ons of the kindergarten pump
Ordinary control
Improved control
5380.2 4561.7 933.3 – 16.0 25.7 174.0 174.0 174.0 20.9 – 22.4 718 – 718 –
5689.1 4813.0 1050.0 116.7 18.5 25.7 214.2 231.0 222.6 26.7 5.8 25.4 543 175 548 170
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11
500
9
400
7 5
300
3
200
1
120
110
90
80
70
-3
60
-1
0
50
100
Environment temperature, ° C
13
600
100
The model can be run with inputs from special components (Fig. 3). One of them is the “Meteorological database” component which calls either a selected weather data file available in the software (Type 109 in Fig. 4) or measured data from an external data file. The other input component is for DHW load (“Load profile” and (Type 9c)) that also calls an external data file. Auxiliary heating after the solar storage could be also implemented serially to afterheat the water to the all-time needed temperature level. It was not needed in our investigations. The specification of the describing equations for the related components can be found in details in the relevant TRNSYS documentation (Klein et al., 2005). The model determines and takes into account all energy components influencing the performance and the efficiency of the solar heating system, such as the irradiated energy on the collectors’ plane, the utilized energy by the collectors, the transferred energy in the heat exchanger as well as the solar energy that is finally used up by the consumers.
15
40
Fig. 3. Flowchart of the model for kindergarten operation. Notation: Tenv is the environment temperature, °C; Ts,c the calculated solar storage temperature, °C.
17
700
30
(arbitrary) outputs
800
Environment temperature
20
Additional
Solar irradiance
0
Vl
Model of the system for kindergarten operation
19
900
10
Load profile
Tenv
T s,c
Solar irradiance, W/m2
Ig Meteorological database
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time, h Fig. 5. Solar temperature.
irradiance
on
collector
surface
and
environment
3.3.2. Calculation results Both the improved and the ordinary controls have also been run in the TRNSYS model. The simulation setup is based on the real consumer (kindergarten) but for meteorological inputs different than in the measurements. Investigated modeled days: 1–5 April. Amongst the geographical sites that can be found in TRNSYS database, the Meteonorm data of Praha have been used. (Praha is the geographically closest place to Go¨do¨ll} o and the same control considerations (see Section 2.2) are reasonable here. The relevant TRNSYS weather file is: CZ-Praha115180.tm2. The solar irradiance on the collector surface and the environment temperature are shown in Fig. 5. The consumption load is based on the realistic profile of Jordan and Vajen (2003) for 5 days without bathtub or
Fig. 4. Flowchart scheme of the model in TRNSYS worksheet.
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Ordinary control
120 100 80 60 40
120
110
100
90
80
70
60
50
V_ c ¼ 0 or 0:98 m =h; V_ k ¼ 0 or 0:63 m =h; P p;c ¼ 60 W; P p;k ¼ 60 W: 3
40
0 3
30
20 20
k k ¼ 0:25 W=ðm KÞ:
Improved control
0
U ¼ 0:56; k c ¼ 0:5 W=ðm KÞ;
140
10
shower with 1990 l/day. The claimed DHW temperature is assumed to be 55 °C. The optical efficiency of the collectors is 0.74, the linear heat loss coefficient of the collectors is 3.688 W/(m2 K), the second order heat loss coefficient of the collectors is 0.0207 W/(m2 K2).
Utilized solar energy, kWh
3496
time, h
Improved control
120
110
100
90
80
70
50
60
40
30
20
Ordinary control
0
37 35 33 31 29 27 25 23 21 19 17 15 13 11
10
Solar storage temperature, ° C
time, h Fig. 6. Average temperature of the stratified solar storage with the different controls.
Improved control
120
110
100
90
80
70
60
50
40
30
20
Ordinary control
0
200 180 160 140 120 100 80 60 40 20 0
10
The heat gain transferred from the pumps to the working fluids is neglected. Initial temperatures: collector field: 5 °C (initial ambience temperature of the day 1st April); both sides of the heat exchanger: 20 °C (assumed temperature of the maintenance house); solar storage: 20 °C (discharged solar storage); all pipelines of the system: 15 °C. Volume of the collector field: 27 l; volume of collector side of the heat exchanger: 2.5 l, volume of kindergarten side of the heat exchanger: 2.6 l. The specific heat of the collector fluid is 3623 J/(kg K), the collector fluid mass density is 1034 kg/m3. The heat loss coefficient between the solar storage and the ambience is assumed to be 1 W/(m2 K). The switch-off and switch-on temperature differences arisen from the above parameter values for the ordinary control (see Section 2.2) are DT off ¼ 7:1 C, DT on ¼ 9:1 C. Figs. 6–8 and Table 2 show the comparative simulation results in case of the ordinary and the improved control in the investigated time period, 1–5 April. Fig. 6 shows, as a function of time, the average solar storage temperature that is the average of the layer temperatures inside the stratified storage. Fig. 7 shows the solar energy utilized by the solar storage. Fig. 8 shows the amount of switch-on (or the equal amount of switch-off) events for both pumps. The ordinary control transferred 136.0 kW h solar energy into the storage, while the improved control trans-
Amount of switch-ons
Fig. 7. Solar energy utilized by the solar storage with the different controls.
time, h Fig. 8. Amount of switch-ons with the different controls.
ferred more, 145.7 kW h that is 9.7 kW h = 7.1% surplus in the utilization of the available solar energy. Considering the ratio of the utilized solar energy by the storage and the available solar irradiation on the surface of the collectors (see first row of Table 2), these values means 24.8% utilizability with the ordinary control and 26.5% utilizability with the improved control. Taking the time average of the mean temperature of the layers inside the solar storage (that is the average values of the graphs in Fig. 6), a similar advantage can be realized. These values are 19.9 °C in case of the ordinary control and 20.7 °C in case of the improved control. The equivalent operation time of the pumps should also be compared. This quantity is 23 h with the ordinary control and 35.3 h with the improved control. Therefore the parasitic consumption is 2.8 kW h in case of the ordinary control and 4.2 kW h in case of the improved control. So the parasitic consumption excess is 1.4 kW h = 50%, which means a drawback. Based on the above values the ordinary control needed 20.6 W h parasitic energy on average to transfer 1 kW h solar energy into the storage during the investigated time period. The corresponding value with the improved control is 28.9 W h. The amount of switch-ons is 203 with the ordinary control for both pumps and 78 with the improved control both for the collector and the kindergarten pumps. Thus both
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Table 2 Simulation results, 1–5 April.
Global solar irradiation on the collectors (kW h) Heat consumption of the kindergarten (kW h) Solar energy utilized by the solar storage (kW h) Utilized solar energy surplus Utilizability (%) Time average of the mean solar storage temperature (°C) Operation time of the collector pump (h) Operation time of the kindergarten pump (h) Equivalent operation time of the pumps (h) Parasitic consumption of the pumps (kW h) Parasitic consumption excess Specific parasitic consumption to the solar energy utilized by the solar storage (W h/kW h) Switch-ons of the collector pump Reduction in the amount of the switch-ons of the collector pump Switch-ons of the kindergarten pump Reduction in the amount of the switch-ons of the kindergarten pump
pumps switched on 125 = 61.6% less in case of the improved control, which means an advantage. Although in the above investigated case the collector and the kindergarten pumps switched on equal times while using the improved control, this is not necessary as the number of their switches may normally differ. All essential results are summarized in Table 2. 4. Conclusions Based on measured and simulated results and different operating circumstances, it can be stated that the improved control results in higher utilizability, i.e. utilizes a higher rate of the available solar energy than the ordinary control in case of the same or slightly different conditions. The significant surplus is obviously caused by the decreased DToff value and the transfer of the all-time heat excess into the storage from the kindergarten loop, in case of the improved control. The latter occurs even if the solar irradiation is too low to start the pumps, so the heat excess does not transfer through the pipes to the environment, but is utilized by the consumer in times of load. Certainly, the longer the pipes are the more advantageous the improved control is, in view of the utilized solar energy. It can be shown (see e.g. Hirsch (1985)) and thought intuitively that in case of prefixed DToff and DTon values, if DToff (and DTon) decreases, then the amount of switches and the utilized solar energy increase. On the contrary, although the improved control always means less or equal DToff value than the ordinary control, it achieves not only increased utilized solar energy, but also fewer pump switches due to the more favorable operation. It holds both for the collector and the kindergarten pumps and facilitates more gentle operation and extended lifetime. It should also be mentioned that the above advantages accompany higher operation time of the pumps and thus extended parasitic consumption. This drawback can be, however, moderated or even extinguished by modern
Ordinary control
Improved control
548.8 499.2 136.0 – 24.8 19.9 23.0 23.0 23.0 2.8 – 20.5 203 – 203 –
548.8 499.2 145.7 9.7 kW h = 7.1% 26.5 20.7 35.28 35.31 35.29 4.2 1.4 kW h = 50% 28.9 78 125 = 61.6% 78 125 = 61.6%
pumps with low energy consumption, or supplied by a renewable energy source. (As an example for a PV driven solar heating system, see Grassie et al. (2002).) Comparing the amount of the utilized solar energy and consumed parasitic energy increments, the improved control can be generally recommended. In particular cases the mentioned advantages and drawbacks should of course be considered in advance. To make a correct decision the expected saving in the auxiliary heating cost and the expected increment in the parasitic energy cost should be considered, in addition to environment protection aspects. As for the applicability of the improved control, it fulfills the general practical requirements (see e.g. Kalogirou (2009)), since only reliable, simple and relatively low cost elements are needed. DToff (and DTon) can be explicitly fed into an ordinary programmable controller available in the market. Two additional temperature sensors (for Tenv,c and Tk,s,in) are needed compared to the case of the ordinary control. Consequently, the improved control is as easy to use, essentially as reliable and nearly as cost effective than the generally used ordinary control. Acknowledgement The authors say special thanks to Dr. Ja´nos Buza´s at the Physics and Process Control Department in the SIU for his contribution to this work by giving advices and valuable help especially in the measurement process. References Badescu, V., 2007. Optimal control of flow in solar collectors for maximum exergy extraction. International Journal of Heat and Mass Transfer 50, 4311–4322. Badescu, V., 2008. Optimal control of flow in solar collector systems with fully mixed water storage tanks. Energy Conversion and Management 49, 169–184. Bejan, A., 1982. Extraction of exergy from solar collectors under timevarying conditions. International Journal of Heat and Fluid Flow 3, 67–72.
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Dorato, P., 1983. Optimal temperature control of solar energy systems. Solar Energy 30, 147–153. Duffie, J.A., Beckman, W.A., 2006. Solar Engineering of Thermal Processes, third ed. John Wiley and Sons, New York. Farahat, S., Sarhaddi, F., Ajam, H., 2009. Exergetic optimization of flat plate solar collectors. Renewable Energy 34 (4), 1169–1174. Farkas, I., Buza´s, J., La´gyma´nyosi, A., Kalma´r, I., Kaboldy, E., Nagy, L., 2000. A combined solar hot water system for the use of swimming pool and kindergarten operation. In: Frankovic, B. (Ed.), Energy and the Environment, vol. I. Croatian Solar Energy Association, Opatija, pp. 81–88. Fiorentini. (2012. 04.) (in Hungarian). Fritchman, B.M., Grantham, W.J., 1987. Differential game control of a bilinear solar collector/heat exchanger system. Mathematical Modelling 8, 399–405. Grassie, T., MacGregor, K., Muneer, T., Kubie, J., 2002. Design of a PV driven low flow solar domestic hot water system and modeling of the system collector outlet temperature. Energy Conversion and Management 43, 1063–1078. Heimrath, R., Haller, M., 2007. Project Report A2 of Subtask A: The reference building, the reference heating system. A Report of IEA SHC – Task 32, Graz University of Technology, Institute of Thermal Engineering. Hirsch, U.T., 1985. Control strategies for solar water heating systems. Master of Science Thesis, University of Wisconsin–Madison. Hollands, K.G.T., Brunger, A.P., 1992. Optimum flow rates in solar water heating systems with a counterflow exchanger. Solar Energy 48, 15–19.
Jordan, U., Vajen, K., 2003. DHWcalc, version 1.10 – Tool for the Generation of Domestic Hot Water (DHW) Profiles on a Statistical Basis. University of Kassel, Institute of Thermal Engineering, Solar and Systems Engineering. Kalogirou, S.A., 2009. Solar Energy Engineering. Academic Press. Kicsiny, R., 2009. Development of an Energetically-Based Control for Solar Thermal Heating Systems, Review of Faculty of Engineering, Analecta Technica Segediensia, 2009, pp. 50–57. Klein, S.A. et al., 2005. A Transient System Simulation Program. Solar Energy Laboratory, University of Madison, USA. Kovarik, M., Lesse, P.F., 1976. Optimal control of flow in low temperature solar heat collectors. Solar Energy 18, 431–435. Lo¨f, G., 1993. Active Solar Systems. MIT Press. Maplesoft, 2003. Maple 9 Learning Guide, Waterloo Maple Inc. Morteza, A., Ardehali, M., Yae, K.H., Smith, T.F., 1996. Development of proportional-sum-derivative control methodology. Solar Energy 57, 251–260. Orbach, A., Rorres, C., Fischl, R., 1981. Optimal control of a solar collector loop using a distributed-lumped model. Automatica 17 (3), 535–539. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., Mishchenko, E.F., 1962. The Mathematical Theory of Optimal Processes. Wiley, New York. Winn, C.B., Hull, D.E., 1979. Optimal controllers of the second kind. Solar Energy 23, 529–534. Winn, C.B., 1983. Controls in Solar Energy Systems, Advances in Solar Energy. American Solar Energy Society Inc.
Solar Energy 86 (2012) 3489–3498 www.elsevier.com/locate/solener
Improved differential control for solar heating systems R. Kicsiny a,⇑, I. Farkas b b
a Department of Mathematics, Szent Istva´n University, Go¨do¨ll}o, Hungary Department of Physics and Process Control, Szent Istva´n University, Go¨do¨ll}o, Hungary
Received 22 July 2011; received in revised form 3 May 2012; accepted 6 August 2012 Available online 24 August 2012 Communicated by: Associate Editor C. Estrada-Gasca
Abstract One possibility to exploit solar energy better is the efficiency enhancement of the control of solar thermal heating systems. In this paper an improved differential control and the generally used ordinary differential control operating with fixed switch-on and switchoff temperature differences are compared in different efficiency viewpoints. The comparison is based on measured data of a particular system at the Szent Istva´n University, Go¨do¨ll} o and on a TRNSYS model developed for solar heating systems. According to the results the improved control provides a higher value of utilizability and brings forth fewer switch-ons and switch-offs for the pumps. These advantages nevertheless result in extended operation time and thus extended parasitic consumption of the pumps. This drawback can, however, be moderated or even extinguished by modern pumps with low energy consumption or if supplied by renewable energy source. Comparing the amount of utilized solar energy and consumed parasitic energy increments, the improved control can be generally recommended. Ó 2012 Elsevier Ltd. All rights reserved. Keywords: Solar water heating system; Energetically-based control; On/off control; Simulation; Measurements
1. Introduction In view of the global environment pollution issue it is important to exploit renewable, and as a part of it, solar energy better. For this ambition, one possibility to develop solar heating systems (in this paper we always refer to active solar water heating system using the shorter term solar heating system) is the efficiency enhancement of their control strategy. Several works have been published in the literature on different optimization endeavors for solar heating systems. Substantial early publications for determining the optimal control strategy by pump flow rate modulation are (Kovarik and Lesse, 1976; Winn and Hull, 1979; Badescu, 2008) in case of no heat exchanger and (Badescu, 2008) ⇑ Corresponding author.
E-mail address: [email protected] (R. Kicsiny). 0038-092X/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.solener.2012.08.003
again in case of internal heat exchanger inside the solar storage. The optimal control in case of external heat exchanger can be similarly discussed by customarily taking the effect of the solar collector(s) but now with an adequate corrective coefficient corresponding to the effect of the heat exchanger. As a result the solar heating system is equivalent with a simple, directly connected collector-storage system of reduced collector surface area, with the above coefficient that contains parameters for both the solar collector and the heat exchanger. On the process of optimizing control in this case with counter flow heat exchanger see Hollands and Brunger (1992), on the corrective coefficient see Hollands and Brunger (1992) and Duffie and Beckman (2006). Based on the Pontryagin maximum principle (Pontryagin et al., 1962) it can be demonstrated that the theoretical optimal control which maximizes the difference of the energy utilized by the storage and used up by the pumping
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is a differential (or bang–bang, or on/off) control that depends on the future knowledge of weather data (Kovarik and Lesse, 1976; Orbach et al., 1981). (Here and generally the differential control switches between zero and a maximal flow rate value.) This control cannot be directly put into practice since the meteorological data are of course not known in advance. The problem is partially eased but not fully resolved if we assume the a priori knowledge that only one on and off switches will occur during the time interval under consideration. In this case a feedback differential control stands for the optimal one which, in principle, could be used in practice. See again Orbach et al. (1981). A so-called instantaneous control resolves the problem theoretically which is feasible for optimal flow rate modulation, needing only the most recent measured values of meteorological data (Bejan, 1982) but its application is also difficult and impractical. In case of no heat exchanger, correlating to the theoretically optimal control (Kovarik and Lesse, 1976), Winn and Hull (1979) establish a nearly as effective differential control that is feedback-type and so, in principle, can be used in practice. Applying the Pontryagin maximum principle they take into account the physical and geometrical parameters of the solar collector. This process is fairly technical and charged with inaccuracies since the partial and temporary shading effect of the clouds and the environment, even the physical and geometrical collector parameters, cannot be precisely taken into account. On the detailed calculation see also Lo¨f (1993). In addition, several investigated cases and different optimization approaches bring forth the conclusion that in many cases, the optimal control is the differential type control with an adequately set flow rate value. See e.g. Fritchman and Grantham, 1987 aiming at maximal solar storage temperature for a solar collector system with heat exchanger by a min–max differential game approach in which the solar irradiance is unknown. Furthermore e.g. (Badescu, 2007) achieved similar results by aiming at maximal exergy extraction by optimal flow rate control in significant part of the operation time. A further aspect is the interaction between different physical, geometrical and control parameters, namely the optimal flow rate in the solar heating system. See Farahat et al. (2009) on the common optimization of the flow rate and the collector area as a function of other parameters of the system for maximal exergy extraction. In addition to the emphasized application of the Pontryagin principle further dynamic optimization techniques are reviewed in Dorato (1983) for constructing optimal control for solar heating systems. Several control strategies exist and are used besides the differential type. The perhaps most frequented controls and their comparisons can be found e.g. in the following references: Winn (1983) compares differential, I (integral) and PID (proportional integral differential) controls. Hirsch (1985) compares differential, P (proportional) and
a hybrid of differential and P controls in different operation conditions. Lo¨f (1993) discusses differential, P, I, PID, adaptive as well as certain types optimal controls. In (Morteza et al., 1996) PID and PSD (proportional sum derivative) controls are compared. In different particular cases, different control methods may certainly be suitable in practice considering several aspects. It can be generally stated that the differential control is the simplest, in view of the required equipments, and the least expensive to apply in practice in the field of solar heating systems. On the detailed discussion of this control see Duffie and Beckman (2006) or as a more recent reference Kalogirou (2009). In this paper a new, specific feedback differential control, with variable switch-on and switch-off temperature differences, is introduced for solar heating systems with external heat exchanger, thus the collector and storage loops are separated hydraulically and equipped with two pumps. In the construction of this control the thermal processes of the solar collector are not implemented as the physical and geometrical collector parameters are not required, only the collector outlet temperature directly, thus the operation of the control is not charged with the unavoidable inaccuracies encountered by the solar collector. This control strategy aims to transfer even the least harvestable solar potential and all energy excess correlating to the solar storage into it from the pipes of the storage loop. In this way the control aims to maintain the storage at the all-time maximal energetic level possible, therefore it aims to maintain the potential for the consumer to always extract maximal heat from the storage. Let this improved differential control be called improved control. In this work the improved control is compared with an optimized version of the ordinary differential control used generally in practice (we will refer to this as ordinary control), which operates with prefixed switch-on and switchoff temperature differences. The improved control is a new, modified version of the one developed in Kicsiny (2009). The optimization of the ordinary control was also carried out in the latter work. The comparison, made in this paper, is based on recent measured data of a particular solar heating system and on a physically-based TRNSYS model that was also worked out in the latter work. The comparison is made from the aspect of the utilized solar energy, consumed parasitic (electric) energy by the pumps and the amount of switchons and switch-offs for the pumps. As new research achievements, the new improved control with both measured and simulation results are introduced in this paper to make the conclusions of the work reliable. The control methods and the physically based model are described in this paper. Physical bases corresponding to solar heating systems are well described in details in Duffie and Beckman (2006).
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2. Improved control approach In this section an improved control developed for solar heating systems and the optimized ordinary control used for comparison are introduced (Kicsiny, 2009). Although the controls have been developed for domestic hot water (DHW) heating, the principles and the functioning can be similarly applied in other applications, e.g. in swimming pool heating. During the investigations the following one dimensional partial differential equation relating to energy conservation law in the pipelines is needed: qcA
@T p @T p ¼ qcV_ kðT p T env;p Þ @t @x
ð1Þ
Notation: The l.h.s. of (1) stands for the heat due to the temperature change in time, the firs term on the r.h.s. represents the effect of the temperature change in space and the last term represents the heat loss of the pipe to the environment. The energy balance equation with Bosˇnjakovicˇ-coefficient corresponding to counter flow heat exchangers (see Fig. 1) will also be needed. UðT c;h;in T k;h;in Þ ¼ T k;h;out T k;h;in
ð2Þ
where U is the Bosˇnjakovicˇ-coefficient for heat exchanger, –; Tc,h,in the inlet temperature to heat exchanger in collector loop, °C; Tk,h,in the inlet temperature to heat exchanger in kindergarten loop, °C; Tk,h,out the outlet temperature from heat exchanger in kindergarten loop, °C. Tc,h,in Tk,h,in represents the theoretically maximal temperature change of the heated fluid inside the heat exchanger. The r.h.s. represents the realized value of this temperature change. 2.1. Operation of improved control In contrast with the ordinary control method which operates with fixed switch-on and switch-off temperature differences and generally used in practice, the improved control operates with varying temperature differences. Fig. 1 shows the investigated solar heating system type. Inside the storage there is no heat exchanger, therefore the
T c,out T env,c Tc,h,in collector loop
Tk,s,in Ts
Tk,h,out Tc,h,out
kindergarten loop
Vc
Tk,h,in Vk
Fig. 1. Simplified scheme of the investigated solar heating system type.
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storage is not separated hydraulically from the kindergarten loop. Notation: Tc,out is the outlet temperature from collector field, °C; Tenv,c the environment temperature of collector field, °C; Tk,s,in the inlet temperature to solar storage in kindergarten loop, °C; Ts the solar storage temperature in the lower third of the storage, °C; V_ c the volumetric flow in collector loop, m3/s; V_ k the volumetric flow in kindergarten loop, m3/s. The operation method of the improved control is the following: Case a, the outlet temperature from the collector field Tc,out, the storage temperature Ts and the environment temperature of the collector Tenv,c are measured continually. Assuming switched on pumps the inlet temperature of the heat exchanger in the collector loop Tc,h,in is calculated from Tc,out, Tenv,c and Eq. (1). Then the inlet temperature of the heat exchanger in the kindergarten loop Tk,h,in is calculated from Ts and (1). Then the outlet temperature of the heat exchanger in the kindergarten loop Tk,h,out can be determined from Tc,h,in, Tk,h,in and (2). Finally the inlet temperature of the storage in the kindergarten loop Tk,s,in can be also determined from Tk,h,out and (1). Tk,s,in Ts is the controlling temperature difference for both pumps. This is the one that is compared continuously with the switch-off temperature difference (DToff = 0 °C) and the switch-on temperature difference (DTon), that is the sum of DToff and a prefixed hysteresis value (DThyst = 2 °C). Case b, now not the calculated but the measured value of Tk,s,in is taken along with the measured value of Ts. The pumps are assumed to be switched on. The controlling temperature difference now is Tk,s,in Ts that is compared continuously with the switch-off temperature difference (that is prefixed DToff = 0.3 °C) and the switch-on temperature difference (DTon = DToff + DThyst). In this case the hysteresis temperature difference DThyst is prefixed to be 0.5 °C. The collector pump works according to Case a. The kindergarten pump works according to the logical OR connection between Case a, and b. So if either of the cases orders the kindergarten pump to switch on then the pump is on. 2.2. Operation of optimized ordinary control Generally the ordinary control switches off the pumps if Tc,out Ts is less than a prefixed value (e.g. 5 °C) and switches them on at a higher, also prefixed value (e.g. 7 °C). It is important for the practice and for the fair comparison of the control methods later to maximize the effectiveness of the ordinary control. The ordinary control does not deal with heat loss, it simply uses a prescribed switch-off temperature difference greater than 0 °C to ensure that the pumps work only if they take positive thermo-energy into the solar storage, that is if the cooling down of the storage is surely avoided. Furthermore this value should be as small as possible to gain the most solar potential.
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For the optimization that is the switch-off temperature difference minimization of the ordinary control, let us consider the biggest but still real losses in the system. Let us calculate with 55 °C temperature in the whole kindergarten loop, 10 °C in the ground and 5 °C in the environment of the collector loop. (In case of high system temperatures and low environment temperature the heat losses are characteristically the highest.) Assuming the above storage temperature, the pumps, which always work simultaneously in this control method, have to switch off if the inlet temperature of the storage in the kindergarten loop Tk,s,in decreases to 55 °C. The pumps are assumed to be switched on now also. Assuming the aforementioned Tk,s,in value, the claimed minimal value of the outlet temperature of the heat exchanger in the kindergarten loop Tk,h,out can be determined from (1). The inlet temperature of the heat exchanger in the kindergarten loop Tk,h,in can be also determined from the assumed storage temperature Ts value and (1). Based on these, such minimal value of the inlet temperature of the heat exchanger in the collector loop Tc,h,in by which Tk,h,out is still high enough can be determined from (2). Finally from the minimal value of Tc,h,in and (1) the minimal value of the outlet temperature from the collector field Tc,out can be also determined. The so established value DToff = Tc,out Ts is the switch-off temperature difference used permanently in the ordinary control. The prefixed hysteresis value is the same as in Case a, of the improved control (DThyst = 2 °C), with which DTon = DToff + DThyst. For the calculation of DToff and DTon in a different way, focusing on the positive value of the difference between the instantaneous heat gain and the consumed parasitic power, see Duffie and Beckman (2006) or Hirsch (1985). According to the considerations above for the ordinary control the term optimized corresponds not to some kind of direct or indirect optimal control approach but for the minimization of the switch-off temperature difference. The improved control always means a DToff value less or equal than the ordinary control since the former works with current measured temperature data and not with the possible “worse” conditions as the latter. In the coordinate system of the moving fluid element, Eq. (1) can be transformed into a one dimensional ordinary differential equation which can be explicitly solved. Then an explicit formula is gained for DToff and DTon for the ordinary control and for Case a, of the improved control. DToff is fixed in case of the ordinary control and depends on the measured Tc, Ts, Tenv,c and Tk,s,in temperatures in case of the improved control. Finally the improved control is provided as a directly applicable feedback control.
3. Evaluation This section compares the improved and the optimized ordinary controls using measured data of a real monitored system and simulations with a physically-based model.
Evaluation and summary of the results can be found here as well. The comparison considers the amount of the utilized solar energy, the consumed parasitic energy by the pumps and the amount of the switch-ons (=amount of switch-offs) of the pumps in case of both controls. The consumed parasitic energy is determined by the operation time of the pumps, i.e. the time duration of switched on pump periods. To take into account the operation time of both pumps together, in view of the parasitic consumption, let us introduce the term “equivalent operation time” of the pumps. This is the time, if the pumps simultaneously operate with, as in case of the ordinary control, they would consume the same amount of electric energy as in the real investigated case. By this quantity the operation time of the pumps can be directly compared between the different control cases. The governing equation is the following: tp;eq ¼
P p;c tp;c þ P p;k tp;k P p;c þ P p;k
ð3Þ
where tp,eq is the equivalent operation time of the pumps, h; Pp,c the parasitic consumption of the pump in the collector loop, W; Pp,k the parasitic consumption of the pump in the kindergarten loop, W; tp,c the operation time of collector pump, h; tp,k the operation time of kindergarten pump, h. In case of the ordinary control the pumps always operate simultaneously, so the equivalent operation time is the (equal) operation time of the pumps directly. In case of the improved control the pumps may operate in different times and commonly determine the equivalent operation time. 3.1. System description A monitored combined solar heating system (Farkas et al., 2000) which has been installed at the campus of Szent Istva´n University (SIU), Go¨do¨ll} o, Hungary is sketched in Fig. 2 (referred to as SIU system). The term combined here means that the installation has more than one consumers. It preheats water for an outdoor swimming pool and, in the idle period of this operation, DHW for a kindergarten nearby. The consumers can be independently or, in principle, parallelly served. In practice they are separated in time. The gained solar energy heats only the swimming pool in summer and only a solar storage in the kindergarten at the rest of the year. In both operations auxiliary gas heated boilers work simultaneously with the solar heating if necessary to cover the required heat energy. The main system components are the flat plate solar collector field, with a total area of 33.3 m2, oriented to the south with an inclination angle of 45°, the plate heat exchangers, a 700 m3 outdoor swimming pool with a surface of 350 m2 and a 2000 l solar storage tank. The solar collectors of the collector field are arranged in mixed, partially serial, partially parallel connection. In the modeling of the system described later in this paper, the solar collector field is considered by an equivalent solar
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Ig Collector field
Auxiliary Hot water gas outlet boiler Kindergarten
Collector loop
Solar storage Kindergarten loop
Vl
Vc
Vk Heat exchanger
Tap water inlet Aux. gas heater
Control valve
Pool loop
Vp
Swimming pool
Filter
Fig. 2. Simplified scheme of the combined solar heating system at the campus of SIU.
collector with 33.3 m2. Based on measured flow rate, temperature and pipe volume data, the estimated pipe length is 80 m between the equivalent collector and the kindergarten heat exchanger (in both directions) and 113.7 m between the same heat exchanger and the solar storage (underground in both directions). According to the notation in Fig. 2 temperature (T), flow rate ðV_ Þ and specific global solar irradiance (Ig) values are monitored in the system. The heat exchangers are assumed to operate with counter flows. Physical and geometrical parameters of the SIU system needed for the application of the control methods have been carefully estimated based on available measurements. Namely such measured data have been considered from different measurement times that suggest greater (but certainly rational) heat losses of the system. (Such parameters are the pipe lengths mentioned above, and the U Bosˇnjakovicˇ-coefficient.) In this way we can expect the cooling down of the solar storage to be surely avoided in case of continuously switched on pumps. This precaution affects both controls alike. The such determined parameters are U = 0.56, estimated by measured inlet and outlet temperatures of the heat exchanger, the overall heat loss coefficients of the pipes, estimated from measured data, kc = 0.5 W/(m K) in the collector loop and kk = 0.25 W/(m K) in the kindergarten loop. Other parameters are V_ c ¼ 0 or 0.98 m3/h; V_ k ¼ 0 or 0.63 m3/h. The parasitic consumptions are Pp,c = 60 W; Pp,k = 60 W. Nowadays it is generally achievable by modern, efficient pumps.
The optical efficiency of the collectors is 0.74, the linear heat loss coefficient of the collectors is 3.688 W/(m2 K), the second order heat loss coefficient of the collectors is 0.0207 W/(m2 K2). These values are taken from the technical documentation of the solar collectors (Fiorentini, 2012). Volume of the collector field: 27 l; volume of collector side of the heat exchanger: 2.5 l, volume of kindergarten side of the heat exchanger: 2.6 l. The specific heat of the collector fluid is 3623 J/(kg K), the collector fluid mass density is 1034 kg/m3. The switch-off and switch-on temperature differences arisen from the above parameter values for the ordinary control (see Section 2.2) are DT off ¼ 7:1 C, DT on ¼ 9:1 C. These values are in accordance with the increased heat losses by the system’s long pipelines and fall inside the generally recommended bounds in engineering practice (Duffie and Beckman, 2006; Kalogirou, 2009). 3.2. Experimental results The improved and the ordinary controls, according to the setup above, have been applied on the real, measured SIU system from 24 November 2010 to 23 May 2011, with a technical interruption from 06 May to 12 May. The controls were alternated day by day, so the same control operated every second day. Considering all measured data we have measurements for 88 days in case of the ordinary control and 86 days in case of the improved control. In view of the alternating operation, the nearly equal values of the solar irradiation on the collectors (see firs row in Table 1) and of the heat consumption of the
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kindergarten (see second row of Table 1) during the operation time of each control, they can be considered to operate under a similar environment and consumption circumstances. Thus the comparison of the controls can be considered relevant. The ordinary control transferred 933.3 kW h solar energy into the storage, while the improved control transferred more, 1050.0 kW h that is 116.7 kW h surplus in the utilization of the available solar energy. The time average of the measured solar storage temperature at the 2/3rd of the height of the storage (T21 in Fig. 2) is 25.7 °C in case of the ordinary control and 25.7 °C as well in case of the improved control. The equivalent operation time of the pumps is 174.0 h with the ordinary control and 222.6 h with the improved control. Accordingly the parasitic consumption is 20.9 kW h in case of the ordinary control and 26.7 kW h in case of the improved control, so the parasitic consumption excess is 5.8 kW h. The amount of switch-ons is 718 with the ordinary control for both pumps. This quantity is 543 for the collector pump and 548 for the kindergarten pump with the improved control. Thus the collector pump switched on 175 less, the kindergarten pump switched on 170 less in case of the improved control. It should be mentioned that the above values correspond to a bit different measured solar irradiation and heat consumption data. Nevertheless, these discrepancies are so marginal that, effectively, the results can be directly compared. Even in case of significantly different solar irradiation and heat consumption measurements the following specific quantities can be directly compared: Considering the utilized solar energy by the solar storage and the solar irradiation on the collectors, the utilizability is 16.0% with the ordinary control and 18.5% with the improved control.
Based on the above values the ordinary control needed 22.4 W h parasitic energy on average to transfer 1 kW h solar energy into the storage during the time of the measurements. The corresponding value with the improved control is 25.4 W h. All essential results are summarized in Table 1. 3.3. Simulation results This section contains the physically-based modeling of the investigated solar heating system. Simulation results are also introduced here for the comparison of the discussed control algorithms. 3.3.1. Physically-based modeling On the basis of time-separated operation, according to Fig. 3, a distinct model has been elaborated for kindergarten operation of the SIU system (Kicsiny, 2009). It should be mentioned that the model can easily be adapted to any similar solar heating system. The model was realized using the TRNSYS 16 (Klein et al., 2005) and, for some particular calculations, by the MAPLE 9 (Waterloo Maple Inc., 2003) software packages. The main system units have been located in distinct submodels, that are readily available in TRNSYS and can be used independently as well (see Fig. 4). Such parts are the collector sub-model (Type 832 in TRNSYS (Heimrath and Haller, 2007)), the heat exchanger sub model (Type 5b – counter flow heat exchanger), the stratified solar storage sub-model (Type 60c), the sub-model of the pumps (Type 114), the sub-model of the pipes (Type 31) and the sub-model for the ordinary control (Type 2b). The model part for the improved control has been established by different software elements (Type 2b blocks with the related “Equations” blocks). It is possible to choose either of them manually. Actual operation of the improved control is shown in Fig. 4.
Table 1 Measurement results (24 November 2010–23 May 2011).
Global solar irradiation on the collectors (kW h) Heat consumption of the kindergarten (kW h) Solar energy utilized by the solar storage (kW h) Utilized solar energy surplus (kW h) Utilizability (%) Time average of the solar storage temperature (°C) Operation time of the collector pump (h) Operation time of the kindergarten pump (h) Equivalent operation time of the pumps (h) Parasitic consumption of the pumps (kW h) Parasitic consumption excess (kW h) Specific parasitic consumption to the solar energy utilized by the solar storage (W h/kW h) Switch-ons of the collector pump Reduction in the amount of the switch-ons of the collector pump Switch-ons of the kindergarten pump Reduction in the amount of the switch-ons of the kindergarten pump
Ordinary control
Improved control
5380.2 4561.7 933.3 – 16.0 25.7 174.0 174.0 174.0 20.9 – 22.4 718 – 718 –
5689.1 4813.0 1050.0 116.7 18.5 25.7 214.2 231.0 222.6 26.7 5.8 25.4 543 175 548 170
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11
500
9
400
7 5
300
3
200
1
120
110
90
80
70
-3
60
-1
0
50
100
Environment temperature, ° C
13
600
100
The model can be run with inputs from special components (Fig. 3). One of them is the “Meteorological database” component which calls either a selected weather data file available in the software (Type 109 in Fig. 4) or measured data from an external data file. The other input component is for DHW load (“Load profile” and (Type 9c)) that also calls an external data file. Auxiliary heating after the solar storage could be also implemented serially to afterheat the water to the all-time needed temperature level. It was not needed in our investigations. The specification of the describing equations for the related components can be found in details in the relevant TRNSYS documentation (Klein et al., 2005). The model determines and takes into account all energy components influencing the performance and the efficiency of the solar heating system, such as the irradiated energy on the collectors’ plane, the utilized energy by the collectors, the transferred energy in the heat exchanger as well as the solar energy that is finally used up by the consumers.
15
40
Fig. 3. Flowchart of the model for kindergarten operation. Notation: Tenv is the environment temperature, °C; Ts,c the calculated solar storage temperature, °C.
17
700
30
(arbitrary) outputs
800
Environment temperature
20
Additional
Solar irradiance
0
Vl
Model of the system for kindergarten operation
19
900
10
Load profile
Tenv
T s,c
Solar irradiance, W/m2
Ig Meteorological database
3495
time, h Fig. 5. Solar temperature.
irradiance
on
collector
surface
and
environment
3.3.2. Calculation results Both the improved and the ordinary controls have also been run in the TRNSYS model. The simulation setup is based on the real consumer (kindergarten) but for meteorological inputs different than in the measurements. Investigated modeled days: 1–5 April. Amongst the geographical sites that can be found in TRNSYS database, the Meteonorm data of Praha have been used. (Praha is the geographically closest place to Go¨do¨ll} o and the same control considerations (see Section 2.2) are reasonable here. The relevant TRNSYS weather file is: CZ-Praha115180.tm2. The solar irradiance on the collector surface and the environment temperature are shown in Fig. 5. The consumption load is based on the realistic profile of Jordan and Vajen (2003) for 5 days without bathtub or
Fig. 4. Flowchart scheme of the model in TRNSYS worksheet.
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Ordinary control
120 100 80 60 40
120
110
100
90
80
70
60
50
V_ c ¼ 0 or 0:98 m =h; V_ k ¼ 0 or 0:63 m =h; P p;c ¼ 60 W; P p;k ¼ 60 W: 3
40
0 3
30
20 20
k k ¼ 0:25 W=ðm KÞ:
Improved control
0
U ¼ 0:56; k c ¼ 0:5 W=ðm KÞ;
140
10
shower with 1990 l/day. The claimed DHW temperature is assumed to be 55 °C. The optical efficiency of the collectors is 0.74, the linear heat loss coefficient of the collectors is 3.688 W/(m2 K), the second order heat loss coefficient of the collectors is 0.0207 W/(m2 K2).
Utilized solar energy, kWh
3496
time, h
Improved control
120
110
100
90
80
70
50
60
40
30
20
Ordinary control
0
37 35 33 31 29 27 25 23 21 19 17 15 13 11
10
Solar storage temperature, ° C
time, h Fig. 6. Average temperature of the stratified solar storage with the different controls.
Improved control
120
110
100
90
80
70
60
50
40
30
20
Ordinary control
0
200 180 160 140 120 100 80 60 40 20 0
10
The heat gain transferred from the pumps to the working fluids is neglected. Initial temperatures: collector field: 5 °C (initial ambience temperature of the day 1st April); both sides of the heat exchanger: 20 °C (assumed temperature of the maintenance house); solar storage: 20 °C (discharged solar storage); all pipelines of the system: 15 °C. Volume of the collector field: 27 l; volume of collector side of the heat exchanger: 2.5 l, volume of kindergarten side of the heat exchanger: 2.6 l. The specific heat of the collector fluid is 3623 J/(kg K), the collector fluid mass density is 1034 kg/m3. The heat loss coefficient between the solar storage and the ambience is assumed to be 1 W/(m2 K). The switch-off and switch-on temperature differences arisen from the above parameter values for the ordinary control (see Section 2.2) are DT off ¼ 7:1 C, DT on ¼ 9:1 C. Figs. 6–8 and Table 2 show the comparative simulation results in case of the ordinary and the improved control in the investigated time period, 1–5 April. Fig. 6 shows, as a function of time, the average solar storage temperature that is the average of the layer temperatures inside the stratified storage. Fig. 7 shows the solar energy utilized by the solar storage. Fig. 8 shows the amount of switch-on (or the equal amount of switch-off) events for both pumps. The ordinary control transferred 136.0 kW h solar energy into the storage, while the improved control trans-
Amount of switch-ons
Fig. 7. Solar energy utilized by the solar storage with the different controls.
time, h Fig. 8. Amount of switch-ons with the different controls.
ferred more, 145.7 kW h that is 9.7 kW h = 7.1% surplus in the utilization of the available solar energy. Considering the ratio of the utilized solar energy by the storage and the available solar irradiation on the surface of the collectors (see first row of Table 2), these values means 24.8% utilizability with the ordinary control and 26.5% utilizability with the improved control. Taking the time average of the mean temperature of the layers inside the solar storage (that is the average values of the graphs in Fig. 6), a similar advantage can be realized. These values are 19.9 °C in case of the ordinary control and 20.7 °C in case of the improved control. The equivalent operation time of the pumps should also be compared. This quantity is 23 h with the ordinary control and 35.3 h with the improved control. Therefore the parasitic consumption is 2.8 kW h in case of the ordinary control and 4.2 kW h in case of the improved control. So the parasitic consumption excess is 1.4 kW h = 50%, which means a drawback. Based on the above values the ordinary control needed 20.6 W h parasitic energy on average to transfer 1 kW h solar energy into the storage during the investigated time period. The corresponding value with the improved control is 28.9 W h. The amount of switch-ons is 203 with the ordinary control for both pumps and 78 with the improved control both for the collector and the kindergarten pumps. Thus both
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Table 2 Simulation results, 1–5 April.
Global solar irradiation on the collectors (kW h) Heat consumption of the kindergarten (kW h) Solar energy utilized by the solar storage (kW h) Utilized solar energy surplus Utilizability (%) Time average of the mean solar storage temperature (°C) Operation time of the collector pump (h) Operation time of the kindergarten pump (h) Equivalent operation time of the pumps (h) Parasitic consumption of the pumps (kW h) Parasitic consumption excess Specific parasitic consumption to the solar energy utilized by the solar storage (W h/kW h) Switch-ons of the collector pump Reduction in the amount of the switch-ons of the collector pump Switch-ons of the kindergarten pump Reduction in the amount of the switch-ons of the kindergarten pump
pumps switched on 125 = 61.6% less in case of the improved control, which means an advantage. Although in the above investigated case the collector and the kindergarten pumps switched on equal times while using the improved control, this is not necessary as the number of their switches may normally differ. All essential results are summarized in Table 2. 4. Conclusions Based on measured and simulated results and different operating circumstances, it can be stated that the improved control results in higher utilizability, i.e. utilizes a higher rate of the available solar energy than the ordinary control in case of the same or slightly different conditions. The significant surplus is obviously caused by the decreased DToff value and the transfer of the all-time heat excess into the storage from the kindergarten loop, in case of the improved control. The latter occurs even if the solar irradiation is too low to start the pumps, so the heat excess does not transfer through the pipes to the environment, but is utilized by the consumer in times of load. Certainly, the longer the pipes are the more advantageous the improved control is, in view of the utilized solar energy. It can be shown (see e.g. Hirsch (1985)) and thought intuitively that in case of prefixed DToff and DTon values, if DToff (and DTon) decreases, then the amount of switches and the utilized solar energy increase. On the contrary, although the improved control always means less or equal DToff value than the ordinary control, it achieves not only increased utilized solar energy, but also fewer pump switches due to the more favorable operation. It holds both for the collector and the kindergarten pumps and facilitates more gentle operation and extended lifetime. It should also be mentioned that the above advantages accompany higher operation time of the pumps and thus extended parasitic consumption. This drawback can be, however, moderated or even extinguished by modern
Ordinary control
Improved control
548.8 499.2 136.0 – 24.8 19.9 23.0 23.0 23.0 2.8 – 20.5 203 – 203 –
548.8 499.2 145.7 9.7 kW h = 7.1% 26.5 20.7 35.28 35.31 35.29 4.2 1.4 kW h = 50% 28.9 78 125 = 61.6% 78 125 = 61.6%
pumps with low energy consumption, or supplied by a renewable energy source. (As an example for a PV driven solar heating system, see Grassie et al. (2002).) Comparing the amount of the utilized solar energy and consumed parasitic energy increments, the improved control can be generally recommended. In particular cases the mentioned advantages and drawbacks should of course be considered in advance. To make a correct decision the expected saving in the auxiliary heating cost and the expected increment in the parasitic energy cost should be considered, in addition to environment protection aspects. As for the applicability of the improved control, it fulfills the general practical requirements (see e.g. Kalogirou (2009)), since only reliable, simple and relatively low cost elements are needed. DToff (and DTon) can be explicitly fed into an ordinary programmable controller available in the market. Two additional temperature sensors (for Tenv,c and Tk,s,in) are needed compared to the case of the ordinary control. Consequently, the improved control is as easy to use, essentially as reliable and nearly as cost effective than the generally used ordinary control. Acknowledgement The authors say special thanks to Dr. Ja´nos Buza´s at the Physics and Process Control Department in the SIU for his contribution to this work by giving advices and valuable help especially in the measurement process. References Badescu, V., 2007. Optimal control of flow in solar collectors for maximum exergy extraction. International Journal of Heat and Mass Transfer 50, 4311–4322. Badescu, V., 2008. Optimal control of flow in solar collector systems with fully mixed water storage tanks. Energy Conversion and Management 49, 169–184. Bejan, A., 1982. Extraction of exergy from solar collectors under timevarying conditions. International Journal of Heat and Fluid Flow 3, 67–72.
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Dorato, P., 1983. Optimal temperature control of solar energy systems. Solar Energy 30, 147–153. Duffie, J.A., Beckman, W.A., 2006. Solar Engineering of Thermal Processes, third ed. John Wiley and Sons, New York. Farahat, S., Sarhaddi, F., Ajam, H., 2009. Exergetic optimization of flat plate solar collectors. Renewable Energy 34 (4), 1169–1174. Farkas, I., Buza´s, J., La´gyma´nyosi, A., Kalma´r, I., Kaboldy, E., Nagy, L., 2000. A combined solar hot water system for the use of swimming pool and kindergarten operation. In: Frankovic, B. (Ed.), Energy and the Environment, vol. I. Croatian Solar Energy Association, Opatija, pp. 81–88. Fiorentini.
Jordan, U., Vajen, K., 2003. DHWcalc, version 1.10 – Tool for the Generation of Domestic Hot Water (DHW) Profiles on a Statistical Basis. University of Kassel, Institute of Thermal Engineering, Solar and Systems Engineering. Kalogirou, S.A., 2009. Solar Energy Engineering. Academic Press. Kicsiny, R., 2009. Development of an Energetically-Based Control for Solar Thermal Heating Systems, Review of Faculty of Engineering, Analecta Technica Segediensia, 2009, pp. 50–57. Klein, S.A. et al., 2005. A Transient System Simulation Program. Solar Energy Laboratory, University of Madison, USA. Kovarik, M., Lesse, P.F., 1976. Optimal control of flow in low temperature solar heat collectors. Solar Energy 18, 431–435. Lo¨f, G., 1993. Active Solar Systems. MIT Press. Maplesoft, 2003. Maple 9 Learning Guide, Waterloo Maple Inc. Morteza, A., Ardehali, M., Yae, K.H., Smith, T.F., 1996. Development of proportional-sum-derivative control methodology. Solar Energy 57, 251–260. Orbach, A., Rorres, C., Fischl, R., 1981. Optimal control of a solar collector loop using a distributed-lumped model. Automatica 17 (3), 535–539. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., Mishchenko, E.F., 1962. The Mathematical Theory of Optimal Processes. Wiley, New York. Winn, C.B., Hull, D.E., 1979. Optimal controllers of the second kind. Solar Energy 23, 529–534. Winn, C.B., 1983. Controls in Solar Energy Systems, Advances in Solar Energy. American Solar Energy Society Inc.