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Hierarchical fuzzy control of low-energy building systems
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Solar Energy 84 (2010) 538–548 www.elsevier.com/locate/solener
Hierarchical fuzzy control of low-energy building systems Zhen Yu, Arthur Dexter * Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK Received 4 September 2008; received in revised form 8 March 2009; accepted 10 March 2009 Available online 9 April 2009 Communicated by: Associate Editor J-L Scartezzini
Abstract A hierarchical fuzzy supervisory controller is described that is capable of optimizing the operation of a low-energy building, which uses solar energy to heat and cool its interior spaces. The highest level fuzzy rules choose the most appropriate set of lower level rules according to the weather and occupancy information; the second level fuzzy rules determine an optimal energy profile and the overall modes of operation of the heating, ventilating and air-conditioning system (HVAC); the third level fuzzy rules select the mode of operation of specific equipment, and assign schedules to the local controllers so that the optimal energy profile can be achieved in the most efficient way. Computer simulation is used to compare the hierarchical fuzzy control scheme with a supervisory control scheme based on expert rules. The performance is evaluated by comparing the energy consumption and thermal comfort. Ó 2009 Elsevier Ltd. All rights reserved. Keywords: Low-energy building system; Fuzzy; Hierarchical control
1. Introduction Over the last few years, there has been increasing interest in low-energy building systems as a consequence of global concern about climate change and energy price increases. The use of novel technologies, the system complexity and the intensive interaction between the natural environment, the occupants and the building services make proper control of such low-energy systems both difficult and important. Traditionally, supervisory control of building energy systems is based on expert rules. Practioners implement heuristic rules based on their own experience or information obtained from engineering manuals. The expert rules for traditional systems work acceptably well because of the abundance of application experience and the relatively simple design of the systems. For modern complex building systems, some advanced control schemes have been proposed *
Corresponding author. Tel.: +44 1865 2 73007; fax: +44 1865 2 73902. E-mail addresses: [email protected], [email protected] (A. Dexter). 0038-092X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2009.03.014
to achieve better energy and comfort performance. Optimization based predictive control is one of the most popular methods in this area. To implement the optimization based method, a building thermal model, equipment models and an occupant model are first constructed using physical modelling techniques (Drees and Braun, 1996; Henze, 2003) or by identifying them from field data. Equations with physical meanings, artificial neural networks or fuzzy models have been used (Lu et al., 2004; Sousa et al., 1997). The second step is to use an optimization algorithm to find the optimal control strategy for the current operating conditions. Generally, the optimizer needs to look forward to the future using the predictions of future weather, usage and building thermal environment information (Braun, 2003; KintnerMeyer and Emery, 1995; Kummert et al., 2000). Dynamic programming (Braun, 2003; Caldas and Norford, 2003; Henze, 2003) and other non-linear optimization algorithms such as genetic algorithms (Lu et al., 2004; Wright et al., 2002) and simulated annealing (Koeppel et al., 1995) are mostly adopted because of the non-linear and discrete characteristics of building energy systems. Although many successful cases have been reported (Kintner-Meyer and
Z. Yu, A. Dexter / Solar Energy 84 (2010) 538–548
Emery, 1995; Lu et al., 2004; Nagai, 1999; Nassif et al., 2005), this has not led to commercial exploitation. One of the major drawbacks is that the optimization process is black-box; not in the sense that there is no physical meaning behind the optimization but that the results are not comprehensible to human beings. Considering the large uncertainties and the inevitable simplifications and assumptions made during the optimization stage, it is unacceptable to use such a technology in practice without expert validation. Besides, the high computational cost of optimization also hinders practical application. In this paper, a hierarchical rule-based control scheme is proposed to make the mathematically rigorous optimization results more comprehensible and the optimal control easier to apply. A simulation of a low-energy building system is first described. The proposed three-level hierarchy of fuzzy rules is then explained as well as the method adopted to design and generate the fuzzy rule bases. A computer simulation is used to compare the results obtained from a set of expert rules with those obtained from the fuzzy hierarchical rules. The performance is evaluated by comparing the energy consumption and thermal comfort. 2. Simulation of a low-energy building system The low-energy building system is based on a real building in Central England (Zhang and Hanby, 2006) (Fig. 1). The original system is a heating system using solar energy and thermal storage. To provide proper cooling for the summer, a solar driven absorption chiller and an evaporative cooling system, which uses the cooling tower as cooling source, are added. The building has three main zones except for a flat on the second floor and the roofspace: an exhibition room (217.9 m2) located at the north end of the building, a dinning area (74.0 m2) located on the first floor in the west end of the building, and a class room (178.6 m2) located on first floor in the south east part of the building. The building energy system is composed of a water circuit and an air circuit. The water circuit includes a heating source, a cooling source, thermal storage, a chilled water
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system, and a cooling tower (Fig. 2). A boiler, a solar water collector and a VPV (Ventilated Photovoltaic) panel are the sources of energy used to heat the system. A stratified hot-water storage tank is used for thermal storage. Active cooling is provided by a solar absorption chiller, which generates chilled water from the hot water in the storage tank. The cooling tower of the absorption chiller can also be used as a direct cooling source when the building needs cooling and the outdoor wet bulb temperature is low enough for evaporative cooling to be used. A water-towater heat exchanger is used to transfer heat directly between the chilled water circuit and the water from the cooling tower, instead of using the absorption chiller for cooling. This approach is frequently used when the cooling load is not high and the outdoor wet bulb temperature is low. The air circuit is composed of a VPV unit, a heat recovery heat exchanger, an AHU, three heated zones, air supply fans, air dampers and an independent heat recovery unit (Fig. 3). The heating and cooling coils of the air handling unit (AHU) act as the interfaces between the water circuit and the air circuit. The system can operate in different modes according to the positions of the dampers and the use of the fans. For example, the main heating system can be run by turning on Fan 1 and Fan 2; or outside air alone can be supplied to the building through the fresh air heat recovery unit by turning on Fan 4. If the main circulation mode is chosen, the inlet air can be preheated by the VPV panel, warmed by the heat recovery unit, heated by the AHU or a combination of them, by selecting different positions of the dampers. The VPV unit can work in four modes: discharge mode, preheat mode, storage mode and bypass mode (Cartmell et al., 2004). An equation based simulation of the low-energy building is implemented in a Matlab/SimulinkÒ environment. The simulation uses a simplified first-order lumped-parameter room model, which is identified from measured data taken from the real building (Zhang and Hanby, 2006). Most of the equipment is modelled using component models from the library of an HVAC toolbox (CSTB, 1998). The absorption chiller is modelled by fitting curves
Fig. 1. Brocks Hill Environment Centre (Photo from Dr Yi Zhang).
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Fig. 2. Water subsystem.
Fig. 3. Air subsystem.
(Muneer and Uppal, 1985) to the manufacturer’s data (EAW, 2006). The expert rules are an extension of those used to control the heating only system studied previously (Zhang and Hanby, 2006). A manual check was made to ensure that the rules are complete and consistent. 3. Hierarchical fuzzy supervisory control 3.1. Re-definition of the output space of the control problem The optimal control of the plant is achieved by finding values of the control signals that minimise the overall operating costs (defined, for example, by Eq. (1) in Section 5) at given operating conditions. The current control actions will
influence future control actions because of the thermal capacity of the building and existence of the thermal storage tank. Thus the optimal control strategy is a series of actions. A control horizon of 24 h and a time-step of 1 h are used for this work. The plant has 5 continuous and 18 on/off control signals as summarized in the Table 1. It is unrealistic to run an optimization program to find the optimal control strategy directly, because the size of the search space is an exponential function of the number of control signals. However, some of the control signals are related and in practice the system can only run in a number of predefined operation modes. A list of possible working modes of the plant, which are based on practitioners’ designs, is given in Table 2.
Z. Yu, A. Dexter / Solar Energy 84 (2010) 538–548 Table 1 Direct control variables. No.
Control signals
Name
Type
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
VPV air–water heat exchanger pump Solar evacuated tube collector pump Boiler pump Hot domestic water pump Heating coil pump Chiller generator pump Cooling tower pump Cooling coil pump Supply fan Exhaust fan VPV circulate fan VPV inlet damper VPV preheat damper VPV bypass damper VPV recirculation damper VPV distract damper Exhaust damper Heat recovery face-bypass damper Heating coil valve Cooling coil valve Boiler Chiller Free cooling heat exchanger
P1 P2 P3 P4 P5 P6 P7 P8 F1 F2 F3 D1 D2 D3 D4 D5 D6 D7 V1 V2 Boiler Chiller Free cooling
On/off On/off On/off On/off On/off On/off On/off On/off On/off On/off On/off On/off Continuous Continuous On/off On/off On/off Continuous Continuous Continuous On/off On/off On/off
Selection of appropriate room temperature and tank temperature set points is important if the plant is to operate efficiently. Further more, the local control of the heat recovery, heating coil, cooling coil and VPV needs to be coordinated in order to achieve the set points efficiently. Priorities must also be assigned to the sequencing of the outputs of the local PI controllers. The different operating
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modes (see Table 3) are used as intermediate variables in the control scheme. The control problem can therefore be re-defined so as to find the most efficient working modes, together with the optimal set points and local control schedules. It is then possible to reduce the search space by over 99%. 3.2. Hierarchy used in the fuzzy rule base The inputs to the controller include information about the current state of the system and the current operating Table 3 Intermediate variables. Type
Name
Description
Set points
Room dT Tank dT
Mode of operation
Mode
Equipment action
Schedule
Change in room temperature set point Change in tank water temperature set point 1. Chiller + boiler 2. Chiller only 3. Free cooling 4. Free cooling + boiler 5. Ventilation only 6. Ventilation + boiler 7. Independent fresh air only 8. Independent fresh air + boiler 1. Recovery ? VPV Preheating 2. VPV Preheating ? Recovery 3. Recovery ? AHU 4. Recovery ? VPV Preheating ? AHU 5. VPV Preheating ? Recovery ? AHU VPV water storage subsystem on/off
VPV mode
Table 2 Working modes of system. No.
Mode
Description
1
Chiller + boiler
2 3
Chiller only Free cooling
4 5
Free cooling + boiler Ventilation only
6 7
Ventilation + boiler Independent fresh air only
8
Independent fresh air + boiler
Chiller and cooling tower are on to provide chilled water for AHU; Boiler is on to raise the tank water temperature; Main air circulation is on; Air recovery and AHU water valve is controlled according to room temperature; Independent fresh air unit is off; VPV switch among Bypass/Discharge/Heater mode Same as mode 1, except that the boiler is turned off Cooling tower and free cooling heat exchanger are used to provide chilled water for AHU; Boiler is off; Main air circulation is on; Air recovery and AHU water valve is controlled according to room temperature; Independent fresh air unit is off; VPV switch among Bypass/Discharge/Heater mode Same as mode 3, except that the boiler is turned on Only main air ventilation is used to control the room temperature; AHU, boiler, chiller, free cooling heat exchanger, cooling tower and associated water distribution systems are off; Independent fresh air unit is off; VPV switches between AHU/Bypass /Discharge/Heater modes Same as mode 5, except for boiler is on The main ventilation and all room temperature control equipment are off; Boiler, chiller, cooling tower and related water system are off; Independent fresh air unit is on; VPV switches between AHU/Bypass/Discharge/Heater modes Same as mode 7, except that the boiler is turned on
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environment, as well as similar information about the future state and the future operating environment. The inputs include time, date, occupancy information, building temperatures, tank water temperatures, outdoor dry bulb temperatures, outdoor wet bulb temperatures, and solar radiation. The results of both simulation and optimization are used to generate the supervisor’s fuzzy rules. Ideally, the rules should be generated from optimization results calculated for all combinations of values of the inputs at the centres of the input fuzzy sets, so that the accuracy of the consequents can be guaranteed for every possible input combination. In that case, even if it is assumed that each of the input variables is described by only three fuzzy sets, the total number of rules would still be extremely large (>1045) and the processing power required to generate them would far exceed that currently available. A hierarchical fuzzy rule-based control scheme is proposed to solve this so called curse of dimensionality. In this scheme, lower level fuzzy rules use the consequents of higher level rules in their antecedents. It has been shown that the hierarchical approach transforms the rule-base from one that is an exponential function of the input spaces to one that is a linear function of the input spaces (Yager, 1998). The hierarchy and intermediate variables are introduced to mimic the decision making processes of experts. At the first level, the date, time and schedule are used to decide which of the second and third level rule-bases will be used. At the second level, predictions of the future solar radiation, outdoor temperatures and internal loads are used to find the optimal values of the tank water temperature set point, the room temperature set point and the mode of operation. At the third level, the room and tank temperature set points are used, together with a measurement of the current solar radiation and outdoor temperature to determine the VPV operating mode and the output schedule to be used by the local controllers. The introduction of a three level hierarchical rule-base decouples the generation of the set points and the selection of the operating modes to be used to control the equipment. Thus a less precise simulation can be used to generate the level 2 rules and a more detailed simulation can be used for the level 3 rules, which shortens significantly the time required to generate the rule base. 3.3. Fuzzy rule reduction techniques Some techniques are also used to reduce the number of rules further. Firstly, the long-term optimization is based on 24-hour average values of future operating conditions. Predictions of the future outdoor temperatures, solar radiation and internal load are used to determine the long term energy profile. Because the future is uncertain, detailed calculation of these values is unnecessary. The average values of the data are used instead, which significantly reduces the number of input variables but maintains the key information. In practice, these values would be obtained using the
weather forecast from a local weather station. The work described in this paper uses 24-averages based on the actual recorded weather data and there are therefore no prediction errors. Secondly, an internal hierarchy is introduced into the level 2 rule-base. In practice, experts use knowledge of the weather conditions and the internal loads to determine the amount of ‘‘free” energy available and to evaluate the current conditions. The same optimal set points will be chosen if different weather conditions lead to similar predictions of the energy demands. Stimulated by this idea, the ability of the system to use renewable energy, and the temperature increase that would occur if that amount of ‘‘free” energy was to be introduced into the building, are used as intermediate variables. The structure of the final rule base is shown in Fig. 4. By using these techniques, the rule-base can be simplified and the final number of rules can be reduced to less than 1000. 4. Generation of the fuzzy rule base 4.1. The level 1 rule base The level 1 fuzzy rules, which select the appropriate set of level 2 rules are based on available expert knowledge. A typical rule at level 1 is of the form: if T out is HIGH & Date is SUMMER & Time is MORNING then Rule Selection is SUMMER MORNING where Tout is the current outdoor temperature, Date and Time are the current date and time, SUMMER MORNING is the name of the set of level 2 rules to be used when the system is operating on a summer morning. HIGH, SUMMER and MORNING are predefined fuzzy sets defined over the universes of discourse of the variables used in the antecedent of the rule. A fuzzy rule is defined for every combination of Tout, Date and Time. 4.2. The level 2 rule base The level 2 fuzzy rules specify the optimal room temperature, tank water set point and the mode of operation of the plant. Level 2.1 The level 2.1 rules specify the heating or cooling capacity that can be achieved from renewable energy sources without turning on the boiler. A typical rule at this level is of the form: if T out is LOW & T out T wet is LOW & Solar is HIGH then CurrentFreeQ ¼ 8:0 where Tout is the outdoor dry bulb temperature; Tout Twet is the difference between the outdoor dry bulb temperature and wet bulb temperature; Solar is the solar radiation,
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Fig. 4. Hierarchical fuzzy rule-base.
CurrentFreeQ is the amount of energy that can be provided without turning on the boiler; and LOW and HIGH are predefined fuzzy sets. Level 2.2 The level 2.2 rules specify the temperature increase that is possible if the ‘‘free” energy acquired from renewable energy sources is put into the building. A typical rule at this level is: if CurrentFreeQ is LOW & T room T out is MEDIUM HIGH & T room T wall is HIGH then dTFreeMax ¼ 0:5
where CurrentFreeQ is the output of the level 2.1 rules; Troom Tout is the temperature difference between the room temperature and the outdoor dry bulb temperature (a measure of the rate of heat loss); Troom Twall is the difference between the room temperature and the building wall temperature (a measure of the rate of heat gain from the building fabric); dTFreeMax is the maximum room temperature increase that can be achieved without turning on the boiler. At level 2.1 and 2.2, fuzzy rules are defined for all the possible combinations of the linguistic values of the inputs. The consequence of each rule is found by running the simulation in open-loop with its inputs set to the crisp values corresponding to the centres of the membership
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X
functions of the fuzzy sets used in the antecedent of the rule.
J¼
Level 2.3
where, EnergyCosti is the energy in kWh purchased from the supplier during the ith hour
The level 2.3 rules specify the optimal room temperature set point, tank water temperature set point and mode of operation of the plant that should be used, given the current state of the HVAC system and the weather and occupancy predictions. A typical rule is of the form: if dTFreeMaxNow is HIGH & dTFreeMaxFuture is LOW & T room is MEDIUM HIGH & T tank is MEDIUM LOW then Mode is 2 & Room dT ¼ 0:2 & Tank dT ¼ 1:0 where DTFreeMaxNow and dTFreeMaxFuture are the consequents of the level 2.2 rules; Troom and Ttank are the current room and tank temperatures; Room dT and Tank dT are the changes in the temperature set points to be achieved at the next time step; and Mode is the overall mode of operation to be used, as defined in Table 3. The crisp values used in the consequents of the rule are found by off-line optimization of the simulated system using Dynamic Programming (Bellman, 1957). 4.3. The level 3 rule base The level 3 rules specify the scheduling priorities for the local controllers and the VPV working mode, given the optimal set points and working mode of the plant specified by the level 2.3 rules. A typical rule at this level is of the form: if Tank dT is LOW & Room dT is MEDIUM HIGH & Mode is 6 & T out is HIGH & Solar is MEDIUM LOW then Schedule is 3 & VPV Mode is On where Tank dT, Room dT and Mode are the outputs of level 2.3 rules; Tout is the current outdoor dry bulb temperature; Solar is the current solar radiation; Schedule is the schedule to be used by the local controllers; VPV Mode is the mode of operation of the VPV panel (in this case, ON or OFF). The values used in the consequent of the rule are found by off-line optimization of the simulated plant using a simple exhaustive search. All of the fuzzy sets used in the antecedents of the rules have triangular membership functions with 50% overlap, evenly spaced over the universes of discourse. 5. Performance analysis The performance of the rule-based controllers is evaluated using a cost function J that takes account of both the energy consumption and the thermal comfort:
ðEnergy Costi þ Comfort Costi Þ:
ð1Þ
i¼1;N
Comfort Costi ¼ 0; 20 < T room < 24 or i 2 unoccupied period Comfort Costi ¼ k minfð20 T room Þ2 ; ð24 T room Þ2 g; otherwise ð2Þ
N is the duration of the performance test in hours, and k is an application dependent comfort-to-energy conversion factor. Here, the value of the conversion factor is chosen to be 100.0, which means that a room temperature 0.5 °C above the higher limit, or below the lower limit, of the comfort zone is equivalent to 25 kWh of energy being consumed. In practice, the value of lambda will be application dependent, differing from building to building, and would need to be chosen by the building manager. The performance of the expert rule-based controller (ERC) and the hierarchical fuzzy rule-based controller (HFRC) are compared on 30 typical days during the winter, transfer season and summer. The results of short-term simulation on three days taken from those 30 days are first presented to show details of the performance of the two controllers. The validation tests are performed using a more detailed computer simulation than that used to generate the fuzzy rules used in the HFRC. The weather data are taken from the UK Mat office database (BADC, 2006). The main characteristics of the outdoor dry bulb temperature, wet bulb temperature and solar radiation conditions over the three day periods are summarised in Table 4. 5.1. Performance over three days in winter Three very cold days are chosen to show the differences in the behaviour of the two control systems in winter. The HFRC outperforms the ERC in terms of both comfort and energy use. As can be seen in Fig. 5, the HFRC uses the hot water stored in the tank to preheat the building in the early morning (for example, on day 1), when the building is unoccupied, in order to avoid the thermal discomfort Table 4 Weather condition of three tested days. Item
Winter
Spring
Summer
Weather Maximum outdoor dry bulb temperature Minimum outdoor dry bulb temperature Average outdoor dry bulb temperature Average outdoor wet bulb temperature Maximum solar irradiance
Clear 7.7 °C
Clear 12.4 °C
Clear 25.6 °C
2.5 °C
6.6 °C
16.0 °C
4.8 °C
10.0 °C
20.7 °C
3.9 °C
8.3 °C
17.9 °C
384 W/ m2 26 W/m2
752 W/ m2 135 W/ m2
851 W/ m2 354 W/ m2
Average solar radiation
Z. Yu, A. Dexter / Solar Energy 84 (2010) 538–548
5.2. Performance over three days in the transfer season
21
HFRC
TRoom ( o C)
20.5
ERC
20 19.5 19 18.5 18
0
10
20
30 40 time (h)
70
HFRC
60
70
60
70
ERC
60
o
TTank ( C)
65
50
55 50 45 40 35 0
10
20
30
40
50
545
The HFRC saves a significant amount of energy, with only a modest reduction in comfort, when the climate is moderate. As can be seen in Fig. 6, the room temperature variations resulting from the two controllers are nearly identical. The HFRC realises that the risk of discomfort is not very great and turns off the main heating system, only using the dedicated ventilation system: an option not considered by the ERC. During the mornings, the HFRC decides that the cost of discomfort will be smaller than the energy cost associated with preheating the building. The different assessment of the energy-comfort trade-off leads to a lower total cost, as can be seen in Table 6. The overall performance of the ERC is not as good as the HFRC but it is good in absolute terms.
time (h)
5.3. Performance over three days in summer 30
HFRC
Energy (kWh)
25
ERC
During the summer test period, the initial temperature of the building is high and it is very hot on all three of the simulated days (Fig. 7). As a result, the HFRC uses more energy and maintains lower indoor temperatures
20 15 10 5
25
0 10
20
30
40
50
60
70
time (h)
Fig. 5. Comparison of room temperature, tank water temperature and energy consumption (winter).
HFRC
24 TRoom ( o C)
0
ERC
23 22 21 20 19
Table 5 Performance comparison over a 72-hour period during winter.
18 0
10
20
30 40 time (h)
50
60
70
60
70
60
70
80
HFRC
TTank ( o C)
70
ERC
60 50 40 30 0
10
20
30
40
50
time (h) 30
HFRC
25 Energy (kWh)
observed on a cold morning when the system is controlled by the ERC. The HFRC turns off the main ventilation system and uses only the lower cost dedicated ventilation system when the weather is warmer and room temperature is higher. To make such a decision, the controller must consider the risk of discomfort if it turns off the main temperature control system. The expert rules are incapable of making such a decision because they do not have any understanding of the thermal behaviour of the building. The simulation results show that the HFRC can handle the trade-off between the comfort and energy relatively well. Table 5 compares the thermal discomfort cost and energy cost of the two controllers over the three winter days.
ERC
20 15 10 5 0
Method ERC HFRC
Energy cost (kWh)
Discomfort cost (kWh)
Total cost (kWh)
590 574
498 317
1088 891
0
10
20
30
40
50
time (h)
Fig. 6. Comparison of room temperature, tank water temperature and energy consumption (spring).
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Table 6 Performance comparison over a 72-hour period during the spring. Method
Energy cost (kWh)
Discomfort cost (kWh)
Total cost (kWh)
ERC HFRC
267 73
11 137
278 209
27
HFRC
TRoom ( C)
26
ERC
o
25 24 23 22 21
o
TTank ( C)
0
10
20
30 40 time (h)
110 105 100 95 90 85 80 75 70
HFRC
0
10
20
30
50
60
70
ERC
40
50
60
tions and to compare the controllers at different times of the year. The low computation cost of the HFRC, which is comparable to that of the ERC, makes it possible to perform the month long validation tests in less than 24 h, which it not the case with other computationally expensive optimization based control schemes. Another advantage of HFRC is that the processing power needed to implement the HFRC on-line in a real building will be much lower than that needed by other optimization based schemes. The room temperature variations produced by the ERC and HFRC in the different seasons are shown in Figs. 8–10. The HFRC maintains a higher room temperature in winter and a lower room temperature in summer, which results in better control of thermal comfort compared to the ERC. In the transfer season, both the HFRC and the ERC keep the room temperature close to the range where there is no associated discomfort cost. However, as can be seen in Table 8, the energy consumption of the building controlled by the HFRC is very much lower. Overall, the percentage savings are large, which demonstrates that improving the control of a low-energy building system can greatly influence its performance. However, the cost of operating the building using expert rules is small and the actual savings may be relatively modest.
70
time (h)
6. Conclusions
35
Energy (kWh)
30
HFRC
ERC
25 20 15 10 5 0 0
10
20
30
40
50
60
70
time (h)
Fig. 7. Comparison of room temperature, tank water temperature and energy consumption (summer).
compared to the ERC. The HFRC uses the boiler more often to raise the tank water temperature during occupancy, which provides the hot-water driven absorption chiller with greater cooling capacity. As can be seen in Table 7, the result is a higher energy cost but a significantly lower thermal discomfort cost. 5.4. Performance evaluation based on one-month simulations during each of the three seasons Monthly simulations for the different seasons are performed in order to reduce the effects of the initial condiTable 7 Performance comparison over a 72-hour period during summer. Method
Energy cost (kWh)
Discomfort cost (kWh)
Total cost (kWh)
ERC HFRC
150 420
1870 176
2020 596
The control of renewable energy building systems is a high dimensional, multi-input–multi-output, non-linear dynamic optimization problem with a large search space. To solve this problem, a hierarchical fuzzy rule-based approach has been proposed. The introduction of fuzzy reasoning and rule hierarchy significantly reduces the search space; making the method of solution feasible and the rules more comprehensible. The performance of the fuzzy rule-based control scheme has been compared to that of an expert rule-based control scheme for different weather conditions. The proposed control scheme handles well the trade-off between the energy costs and thermal discomfort costs and the computational demands associated with its online implementation are similar to those of the expert controller, which are much lower than those of optimization based control schemes. The current hierarchical rule structure has already greatly reduced the number of required rules, thus making the generation of the rule base possible. However, the number of rules is still too large to make it easy for human experts to validate them based on their experience of operating similar buildings. A sensitivity study of the rule base is now being undertaken to reduce the size of rule base further, in order to make it more comprehensible. The current results are based on the assumption that the computer simulation of the low energy building system is an accurate representation of the real system. However, the development of such a simulation may be too time consuming or even impossible in practice. The next phase of
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o
TRoom( C)
22 HFRC
21
ERC
20 19 18 17 0
50
100
150
200
250
300 350 Time (h)
400
450
500
550
600
650
o
TRoom( C)
Fig. 8. Comparison of room temperatures over a 30-day period during winter.
25 24 23 22 21 20 19 18
HFRC
0
50
100
150
200
250
300
350
400
450
ERC
500
550
600
650
Time (h)
Fig. 9. Comparison of room temperatures over a 30-day period during the transfer season.
o
TRoom( C)
27 HFRC
26 25 24 23
ERC
63
22 21 0
50
100
150
200
250
300 350 Time (h)
400
450
500
550
600
650
Fig. 10. Comparison of room temperatures over a 30-day period during summer.
Table 8 Seasonal performance comparisons. Season
Method
Energy cost (kWh)
Discomfort cost (kWh)
Total cost (kWh)
Reduction of cost
Winter
ERC HFRC ERC HFRC ERC HFRC
5288 4601 7285 356 902 1699
7418 4724 391 0 4385 194
12706 9325 7676 356 5287 1893
26.6%
Transfer Season Summer
95.4% 64.2%
the research will consider ways in which the rule-based controller can be adapted on-line. References Bellman, R., 1957. Dynamic Programming, Dover Paperback Edition, 2003 ed. Princeton University Press, pp. 4–9. Braun, J.E., 2003. Load control using building thermal mass. ASME Journal of Solar Energy Engineering 125, 292–301. Caldas, L.G., Norford, L.K., 2003. Genetic algorithms for optimization of building envelopes and the design and control of hvac systems. ASME Journal of Solar Energy Engineering 125, 343–351. Cartmell, B.P., Shankland, N.J., Fiala, D., Hanby, V., 2004. A multioperational ventilated photovoltaic and solar air collector: application, simulation and initial monitoring feedback. Solar Energy 76, 45–53.
CSTB, 1998. Simbad building and hvac toolbox version 3.0 user manual: Centre Scientifique et Technique du Batiment. Drees, K.H., Braun, J.E., 1996. Development and evaluation of a rulebased control strategy for ice storage systems. HVAC&R Research 2 (4), 312–336. EAW, 2006. Absorption chiller wegracal se 15 datasheet. Henze, G.P., 2003. An overview of optimal control for central cooling plants with ice thermal energy storage. ASME Journal of Solar Energy Engineering 125, 302–309. Kintner-Meyer, M., Emery, A.F., 1995. Optimal control of an hvac system using cold storage building thermal capacitance. Energy and Buildings 23, 19–31. Koeppel, E.A., Mitchell, J.W., Klein, S.A., Flake, B.A., 1995. Optimal supervisory control of an absorption chiller system. HVAC&R Research 1 (4), 325–342. Kummert, M., Andre´, P., Nicolas, J., 2000. Optimal heating control in a passive solar commercial building. Solar Energy 69, 103–116. Lu, L., Cai, W., Chai, Y.S., Xie, L., 2004. Global optimization for overall hvac systems – Part I problem formulation and analysis. Energy Conversion and Management 46, 999–1014. Muneer, T., Uppal, A.H., 1985. Modelling and simulation of a solar absorption cooling system. Applied Energy 19, 209–229. Nagai, T., 1999. Dynamic optimization technique for control of hvac system utilizing building thermal storage. Building Simulation Kyoto, Japan, CD-c18. Nassif, N., Kajl, S., Sabourin, R., 2005. Optimization of hvac control system strategy using two-objective genetic algorithm. HVAC&R Research 11 (3), 459–486.
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Sousa, J.M., Babuika, R., Verbruggen, H.B., 1997. Fuzzy predictive control applied to an air-conditioning system. Control Engineering Practice 5, 1395–1406. Wright, J.A., Loosemore, H.A., Farmani, R., 2002. Optimization of building thermal design and control by multi-criterion genetic algorithm. Energy and Buildings 34 (9), 959–972.
Yager, R.R., 1998. On the construction of hierarchical fuzzy systems models. IEEE Transactions on Systems, Man and Cybernetics 28 (1), 55–66. Zhang, Y., Hanby, V.I., 2006. Model-based control of renewable energy systems in buildings. HVAC&R Research Special Issue 12 (3a), 739– 760.
Solar Energy 84 (2010) 538–548 www.elsevier.com/locate/solener
Hierarchical fuzzy control of low-energy building systems Zhen Yu, Arthur Dexter * Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK Received 4 September 2008; received in revised form 8 March 2009; accepted 10 March 2009 Available online 9 April 2009 Communicated by: Associate Editor J-L Scartezzini
Abstract A hierarchical fuzzy supervisory controller is described that is capable of optimizing the operation of a low-energy building, which uses solar energy to heat and cool its interior spaces. The highest level fuzzy rules choose the most appropriate set of lower level rules according to the weather and occupancy information; the second level fuzzy rules determine an optimal energy profile and the overall modes of operation of the heating, ventilating and air-conditioning system (HVAC); the third level fuzzy rules select the mode of operation of specific equipment, and assign schedules to the local controllers so that the optimal energy profile can be achieved in the most efficient way. Computer simulation is used to compare the hierarchical fuzzy control scheme with a supervisory control scheme based on expert rules. The performance is evaluated by comparing the energy consumption and thermal comfort. Ó 2009 Elsevier Ltd. All rights reserved. Keywords: Low-energy building system; Fuzzy; Hierarchical control
1. Introduction Over the last few years, there has been increasing interest in low-energy building systems as a consequence of global concern about climate change and energy price increases. The use of novel technologies, the system complexity and the intensive interaction between the natural environment, the occupants and the building services make proper control of such low-energy systems both difficult and important. Traditionally, supervisory control of building energy systems is based on expert rules. Practioners implement heuristic rules based on their own experience or information obtained from engineering manuals. The expert rules for traditional systems work acceptably well because of the abundance of application experience and the relatively simple design of the systems. For modern complex building systems, some advanced control schemes have been proposed *
Corresponding author. Tel.: +44 1865 2 73007; fax: +44 1865 2 73902. E-mail addresses: [email protected], [email protected] (A. Dexter). 0038-092X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2009.03.014
to achieve better energy and comfort performance. Optimization based predictive control is one of the most popular methods in this area. To implement the optimization based method, a building thermal model, equipment models and an occupant model are first constructed using physical modelling techniques (Drees and Braun, 1996; Henze, 2003) or by identifying them from field data. Equations with physical meanings, artificial neural networks or fuzzy models have been used (Lu et al., 2004; Sousa et al., 1997). The second step is to use an optimization algorithm to find the optimal control strategy for the current operating conditions. Generally, the optimizer needs to look forward to the future using the predictions of future weather, usage and building thermal environment information (Braun, 2003; KintnerMeyer and Emery, 1995; Kummert et al., 2000). Dynamic programming (Braun, 2003; Caldas and Norford, 2003; Henze, 2003) and other non-linear optimization algorithms such as genetic algorithms (Lu et al., 2004; Wright et al., 2002) and simulated annealing (Koeppel et al., 1995) are mostly adopted because of the non-linear and discrete characteristics of building energy systems. Although many successful cases have been reported (Kintner-Meyer and
Z. Yu, A. Dexter / Solar Energy 84 (2010) 538–548
Emery, 1995; Lu et al., 2004; Nagai, 1999; Nassif et al., 2005), this has not led to commercial exploitation. One of the major drawbacks is that the optimization process is black-box; not in the sense that there is no physical meaning behind the optimization but that the results are not comprehensible to human beings. Considering the large uncertainties and the inevitable simplifications and assumptions made during the optimization stage, it is unacceptable to use such a technology in practice without expert validation. Besides, the high computational cost of optimization also hinders practical application. In this paper, a hierarchical rule-based control scheme is proposed to make the mathematically rigorous optimization results more comprehensible and the optimal control easier to apply. A simulation of a low-energy building system is first described. The proposed three-level hierarchy of fuzzy rules is then explained as well as the method adopted to design and generate the fuzzy rule bases. A computer simulation is used to compare the results obtained from a set of expert rules with those obtained from the fuzzy hierarchical rules. The performance is evaluated by comparing the energy consumption and thermal comfort. 2. Simulation of a low-energy building system The low-energy building system is based on a real building in Central England (Zhang and Hanby, 2006) (Fig. 1). The original system is a heating system using solar energy and thermal storage. To provide proper cooling for the summer, a solar driven absorption chiller and an evaporative cooling system, which uses the cooling tower as cooling source, are added. The building has three main zones except for a flat on the second floor and the roofspace: an exhibition room (217.9 m2) located at the north end of the building, a dinning area (74.0 m2) located on the first floor in the west end of the building, and a class room (178.6 m2) located on first floor in the south east part of the building. The building energy system is composed of a water circuit and an air circuit. The water circuit includes a heating source, a cooling source, thermal storage, a chilled water
539
system, and a cooling tower (Fig. 2). A boiler, a solar water collector and a VPV (Ventilated Photovoltaic) panel are the sources of energy used to heat the system. A stratified hot-water storage tank is used for thermal storage. Active cooling is provided by a solar absorption chiller, which generates chilled water from the hot water in the storage tank. The cooling tower of the absorption chiller can also be used as a direct cooling source when the building needs cooling and the outdoor wet bulb temperature is low enough for evaporative cooling to be used. A water-towater heat exchanger is used to transfer heat directly between the chilled water circuit and the water from the cooling tower, instead of using the absorption chiller for cooling. This approach is frequently used when the cooling load is not high and the outdoor wet bulb temperature is low. The air circuit is composed of a VPV unit, a heat recovery heat exchanger, an AHU, three heated zones, air supply fans, air dampers and an independent heat recovery unit (Fig. 3). The heating and cooling coils of the air handling unit (AHU) act as the interfaces between the water circuit and the air circuit. The system can operate in different modes according to the positions of the dampers and the use of the fans. For example, the main heating system can be run by turning on Fan 1 and Fan 2; or outside air alone can be supplied to the building through the fresh air heat recovery unit by turning on Fan 4. If the main circulation mode is chosen, the inlet air can be preheated by the VPV panel, warmed by the heat recovery unit, heated by the AHU or a combination of them, by selecting different positions of the dampers. The VPV unit can work in four modes: discharge mode, preheat mode, storage mode and bypass mode (Cartmell et al., 2004). An equation based simulation of the low-energy building is implemented in a Matlab/SimulinkÒ environment. The simulation uses a simplified first-order lumped-parameter room model, which is identified from measured data taken from the real building (Zhang and Hanby, 2006). Most of the equipment is modelled using component models from the library of an HVAC toolbox (CSTB, 1998). The absorption chiller is modelled by fitting curves
Fig. 1. Brocks Hill Environment Centre (Photo from Dr Yi Zhang).
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Fig. 2. Water subsystem.
Fig. 3. Air subsystem.
(Muneer and Uppal, 1985) to the manufacturer’s data (EAW, 2006). The expert rules are an extension of those used to control the heating only system studied previously (Zhang and Hanby, 2006). A manual check was made to ensure that the rules are complete and consistent. 3. Hierarchical fuzzy supervisory control 3.1. Re-definition of the output space of the control problem The optimal control of the plant is achieved by finding values of the control signals that minimise the overall operating costs (defined, for example, by Eq. (1) in Section 5) at given operating conditions. The current control actions will
influence future control actions because of the thermal capacity of the building and existence of the thermal storage tank. Thus the optimal control strategy is a series of actions. A control horizon of 24 h and a time-step of 1 h are used for this work. The plant has 5 continuous and 18 on/off control signals as summarized in the Table 1. It is unrealistic to run an optimization program to find the optimal control strategy directly, because the size of the search space is an exponential function of the number of control signals. However, some of the control signals are related and in practice the system can only run in a number of predefined operation modes. A list of possible working modes of the plant, which are based on practitioners’ designs, is given in Table 2.
Z. Yu, A. Dexter / Solar Energy 84 (2010) 538–548 Table 1 Direct control variables. No.
Control signals
Name
Type
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
VPV air–water heat exchanger pump Solar evacuated tube collector pump Boiler pump Hot domestic water pump Heating coil pump Chiller generator pump Cooling tower pump Cooling coil pump Supply fan Exhaust fan VPV circulate fan VPV inlet damper VPV preheat damper VPV bypass damper VPV recirculation damper VPV distract damper Exhaust damper Heat recovery face-bypass damper Heating coil valve Cooling coil valve Boiler Chiller Free cooling heat exchanger
P1 P2 P3 P4 P5 P6 P7 P8 F1 F2 F3 D1 D2 D3 D4 D5 D6 D7 V1 V2 Boiler Chiller Free cooling
On/off On/off On/off On/off On/off On/off On/off On/off On/off On/off On/off On/off Continuous Continuous On/off On/off On/off Continuous Continuous Continuous On/off On/off On/off
Selection of appropriate room temperature and tank temperature set points is important if the plant is to operate efficiently. Further more, the local control of the heat recovery, heating coil, cooling coil and VPV needs to be coordinated in order to achieve the set points efficiently. Priorities must also be assigned to the sequencing of the outputs of the local PI controllers. The different operating
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modes (see Table 3) are used as intermediate variables in the control scheme. The control problem can therefore be re-defined so as to find the most efficient working modes, together with the optimal set points and local control schedules. It is then possible to reduce the search space by over 99%. 3.2. Hierarchy used in the fuzzy rule base The inputs to the controller include information about the current state of the system and the current operating Table 3 Intermediate variables. Type
Name
Description
Set points
Room dT Tank dT
Mode of operation
Mode
Equipment action
Schedule
Change in room temperature set point Change in tank water temperature set point 1. Chiller + boiler 2. Chiller only 3. Free cooling 4. Free cooling + boiler 5. Ventilation only 6. Ventilation + boiler 7. Independent fresh air only 8. Independent fresh air + boiler 1. Recovery ? VPV Preheating 2. VPV Preheating ? Recovery 3. Recovery ? AHU 4. Recovery ? VPV Preheating ? AHU 5. VPV Preheating ? Recovery ? AHU VPV water storage subsystem on/off
VPV mode
Table 2 Working modes of system. No.
Mode
Description
1
Chiller + boiler
2 3
Chiller only Free cooling
4 5
Free cooling + boiler Ventilation only
6 7
Ventilation + boiler Independent fresh air only
8
Independent fresh air + boiler
Chiller and cooling tower are on to provide chilled water for AHU; Boiler is on to raise the tank water temperature; Main air circulation is on; Air recovery and AHU water valve is controlled according to room temperature; Independent fresh air unit is off; VPV switch among Bypass/Discharge/Heater mode Same as mode 1, except that the boiler is turned off Cooling tower and free cooling heat exchanger are used to provide chilled water for AHU; Boiler is off; Main air circulation is on; Air recovery and AHU water valve is controlled according to room temperature; Independent fresh air unit is off; VPV switch among Bypass/Discharge/Heater mode Same as mode 3, except that the boiler is turned on Only main air ventilation is used to control the room temperature; AHU, boiler, chiller, free cooling heat exchanger, cooling tower and associated water distribution systems are off; Independent fresh air unit is off; VPV switches between AHU/Bypass /Discharge/Heater modes Same as mode 5, except for boiler is on The main ventilation and all room temperature control equipment are off; Boiler, chiller, cooling tower and related water system are off; Independent fresh air unit is on; VPV switches between AHU/Bypass/Discharge/Heater modes Same as mode 7, except that the boiler is turned on
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environment, as well as similar information about the future state and the future operating environment. The inputs include time, date, occupancy information, building temperatures, tank water temperatures, outdoor dry bulb temperatures, outdoor wet bulb temperatures, and solar radiation. The results of both simulation and optimization are used to generate the supervisor’s fuzzy rules. Ideally, the rules should be generated from optimization results calculated for all combinations of values of the inputs at the centres of the input fuzzy sets, so that the accuracy of the consequents can be guaranteed for every possible input combination. In that case, even if it is assumed that each of the input variables is described by only three fuzzy sets, the total number of rules would still be extremely large (>1045) and the processing power required to generate them would far exceed that currently available. A hierarchical fuzzy rule-based control scheme is proposed to solve this so called curse of dimensionality. In this scheme, lower level fuzzy rules use the consequents of higher level rules in their antecedents. It has been shown that the hierarchical approach transforms the rule-base from one that is an exponential function of the input spaces to one that is a linear function of the input spaces (Yager, 1998). The hierarchy and intermediate variables are introduced to mimic the decision making processes of experts. At the first level, the date, time and schedule are used to decide which of the second and third level rule-bases will be used. At the second level, predictions of the future solar radiation, outdoor temperatures and internal loads are used to find the optimal values of the tank water temperature set point, the room temperature set point and the mode of operation. At the third level, the room and tank temperature set points are used, together with a measurement of the current solar radiation and outdoor temperature to determine the VPV operating mode and the output schedule to be used by the local controllers. The introduction of a three level hierarchical rule-base decouples the generation of the set points and the selection of the operating modes to be used to control the equipment. Thus a less precise simulation can be used to generate the level 2 rules and a more detailed simulation can be used for the level 3 rules, which shortens significantly the time required to generate the rule base. 3.3. Fuzzy rule reduction techniques Some techniques are also used to reduce the number of rules further. Firstly, the long-term optimization is based on 24-hour average values of future operating conditions. Predictions of the future outdoor temperatures, solar radiation and internal load are used to determine the long term energy profile. Because the future is uncertain, detailed calculation of these values is unnecessary. The average values of the data are used instead, which significantly reduces the number of input variables but maintains the key information. In practice, these values would be obtained using the
weather forecast from a local weather station. The work described in this paper uses 24-averages based on the actual recorded weather data and there are therefore no prediction errors. Secondly, an internal hierarchy is introduced into the level 2 rule-base. In practice, experts use knowledge of the weather conditions and the internal loads to determine the amount of ‘‘free” energy available and to evaluate the current conditions. The same optimal set points will be chosen if different weather conditions lead to similar predictions of the energy demands. Stimulated by this idea, the ability of the system to use renewable energy, and the temperature increase that would occur if that amount of ‘‘free” energy was to be introduced into the building, are used as intermediate variables. The structure of the final rule base is shown in Fig. 4. By using these techniques, the rule-base can be simplified and the final number of rules can be reduced to less than 1000. 4. Generation of the fuzzy rule base 4.1. The level 1 rule base The level 1 fuzzy rules, which select the appropriate set of level 2 rules are based on available expert knowledge. A typical rule at level 1 is of the form: if T out is HIGH & Date is SUMMER & Time is MORNING then Rule Selection is SUMMER MORNING where Tout is the current outdoor temperature, Date and Time are the current date and time, SUMMER MORNING is the name of the set of level 2 rules to be used when the system is operating on a summer morning. HIGH, SUMMER and MORNING are predefined fuzzy sets defined over the universes of discourse of the variables used in the antecedent of the rule. A fuzzy rule is defined for every combination of Tout, Date and Time. 4.2. The level 2 rule base The level 2 fuzzy rules specify the optimal room temperature, tank water set point and the mode of operation of the plant. Level 2.1 The level 2.1 rules specify the heating or cooling capacity that can be achieved from renewable energy sources without turning on the boiler. A typical rule at this level is of the form: if T out is LOW & T out T wet is LOW & Solar is HIGH then CurrentFreeQ ¼ 8:0 where Tout is the outdoor dry bulb temperature; Tout Twet is the difference between the outdoor dry bulb temperature and wet bulb temperature; Solar is the solar radiation,
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Fig. 4. Hierarchical fuzzy rule-base.
CurrentFreeQ is the amount of energy that can be provided without turning on the boiler; and LOW and HIGH are predefined fuzzy sets. Level 2.2 The level 2.2 rules specify the temperature increase that is possible if the ‘‘free” energy acquired from renewable energy sources is put into the building. A typical rule at this level is: if CurrentFreeQ is LOW & T room T out is MEDIUM HIGH & T room T wall is HIGH then dTFreeMax ¼ 0:5
where CurrentFreeQ is the output of the level 2.1 rules; Troom Tout is the temperature difference between the room temperature and the outdoor dry bulb temperature (a measure of the rate of heat loss); Troom Twall is the difference between the room temperature and the building wall temperature (a measure of the rate of heat gain from the building fabric); dTFreeMax is the maximum room temperature increase that can be achieved without turning on the boiler. At level 2.1 and 2.2, fuzzy rules are defined for all the possible combinations of the linguistic values of the inputs. The consequence of each rule is found by running the simulation in open-loop with its inputs set to the crisp values corresponding to the centres of the membership
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X
functions of the fuzzy sets used in the antecedent of the rule.
J¼
Level 2.3
where, EnergyCosti is the energy in kWh purchased from the supplier during the ith hour
The level 2.3 rules specify the optimal room temperature set point, tank water temperature set point and mode of operation of the plant that should be used, given the current state of the HVAC system and the weather and occupancy predictions. A typical rule is of the form: if dTFreeMaxNow is HIGH & dTFreeMaxFuture is LOW & T room is MEDIUM HIGH & T tank is MEDIUM LOW then Mode is 2 & Room dT ¼ 0:2 & Tank dT ¼ 1:0 where DTFreeMaxNow and dTFreeMaxFuture are the consequents of the level 2.2 rules; Troom and Ttank are the current room and tank temperatures; Room dT and Tank dT are the changes in the temperature set points to be achieved at the next time step; and Mode is the overall mode of operation to be used, as defined in Table 3. The crisp values used in the consequents of the rule are found by off-line optimization of the simulated system using Dynamic Programming (Bellman, 1957). 4.3. The level 3 rule base The level 3 rules specify the scheduling priorities for the local controllers and the VPV working mode, given the optimal set points and working mode of the plant specified by the level 2.3 rules. A typical rule at this level is of the form: if Tank dT is LOW & Room dT is MEDIUM HIGH & Mode is 6 & T out is HIGH & Solar is MEDIUM LOW then Schedule is 3 & VPV Mode is On where Tank dT, Room dT and Mode are the outputs of level 2.3 rules; Tout is the current outdoor dry bulb temperature; Solar is the current solar radiation; Schedule is the schedule to be used by the local controllers; VPV Mode is the mode of operation of the VPV panel (in this case, ON or OFF). The values used in the consequent of the rule are found by off-line optimization of the simulated plant using a simple exhaustive search. All of the fuzzy sets used in the antecedents of the rules have triangular membership functions with 50% overlap, evenly spaced over the universes of discourse. 5. Performance analysis The performance of the rule-based controllers is evaluated using a cost function J that takes account of both the energy consumption and the thermal comfort:
ðEnergy Costi þ Comfort Costi Þ:
ð1Þ
i¼1;N
Comfort Costi ¼ 0; 20 < T room < 24 or i 2 unoccupied period Comfort Costi ¼ k minfð20 T room Þ2 ; ð24 T room Þ2 g; otherwise ð2Þ
N is the duration of the performance test in hours, and k is an application dependent comfort-to-energy conversion factor. Here, the value of the conversion factor is chosen to be 100.0, which means that a room temperature 0.5 °C above the higher limit, or below the lower limit, of the comfort zone is equivalent to 25 kWh of energy being consumed. In practice, the value of lambda will be application dependent, differing from building to building, and would need to be chosen by the building manager. The performance of the expert rule-based controller (ERC) and the hierarchical fuzzy rule-based controller (HFRC) are compared on 30 typical days during the winter, transfer season and summer. The results of short-term simulation on three days taken from those 30 days are first presented to show details of the performance of the two controllers. The validation tests are performed using a more detailed computer simulation than that used to generate the fuzzy rules used in the HFRC. The weather data are taken from the UK Mat office database (BADC, 2006). The main characteristics of the outdoor dry bulb temperature, wet bulb temperature and solar radiation conditions over the three day periods are summarised in Table 4. 5.1. Performance over three days in winter Three very cold days are chosen to show the differences in the behaviour of the two control systems in winter. The HFRC outperforms the ERC in terms of both comfort and energy use. As can be seen in Fig. 5, the HFRC uses the hot water stored in the tank to preheat the building in the early morning (for example, on day 1), when the building is unoccupied, in order to avoid the thermal discomfort Table 4 Weather condition of three tested days. Item
Winter
Spring
Summer
Weather Maximum outdoor dry bulb temperature Minimum outdoor dry bulb temperature Average outdoor dry bulb temperature Average outdoor wet bulb temperature Maximum solar irradiance
Clear 7.7 °C
Clear 12.4 °C
Clear 25.6 °C
2.5 °C
6.6 °C
16.0 °C
4.8 °C
10.0 °C
20.7 °C
3.9 °C
8.3 °C
17.9 °C
384 W/ m2 26 W/m2
752 W/ m2 135 W/ m2
851 W/ m2 354 W/ m2
Average solar radiation
Z. Yu, A. Dexter / Solar Energy 84 (2010) 538–548
5.2. Performance over three days in the transfer season
21
HFRC
TRoom ( o C)
20.5
ERC
20 19.5 19 18.5 18
0
10
20
30 40 time (h)
70
HFRC
60
70
60
70
ERC
60
o
TTank ( C)
65
50
55 50 45 40 35 0
10
20
30
40
50
545
The HFRC saves a significant amount of energy, with only a modest reduction in comfort, when the climate is moderate. As can be seen in Fig. 6, the room temperature variations resulting from the two controllers are nearly identical. The HFRC realises that the risk of discomfort is not very great and turns off the main heating system, only using the dedicated ventilation system: an option not considered by the ERC. During the mornings, the HFRC decides that the cost of discomfort will be smaller than the energy cost associated with preheating the building. The different assessment of the energy-comfort trade-off leads to a lower total cost, as can be seen in Table 6. The overall performance of the ERC is not as good as the HFRC but it is good in absolute terms.
time (h)
5.3. Performance over three days in summer 30
HFRC
Energy (kWh)
25
ERC
During the summer test period, the initial temperature of the building is high and it is very hot on all three of the simulated days (Fig. 7). As a result, the HFRC uses more energy and maintains lower indoor temperatures
20 15 10 5
25
0 10
20
30
40
50
60
70
time (h)
Fig. 5. Comparison of room temperature, tank water temperature and energy consumption (winter).
HFRC
24 TRoom ( o C)
0
ERC
23 22 21 20 19
Table 5 Performance comparison over a 72-hour period during winter.
18 0
10
20
30 40 time (h)
50
60
70
60
70
60
70
80
HFRC
TTank ( o C)
70
ERC
60 50 40 30 0
10
20
30
40
50
time (h) 30
HFRC
25 Energy (kWh)
observed on a cold morning when the system is controlled by the ERC. The HFRC turns off the main ventilation system and uses only the lower cost dedicated ventilation system when the weather is warmer and room temperature is higher. To make such a decision, the controller must consider the risk of discomfort if it turns off the main temperature control system. The expert rules are incapable of making such a decision because they do not have any understanding of the thermal behaviour of the building. The simulation results show that the HFRC can handle the trade-off between the comfort and energy relatively well. Table 5 compares the thermal discomfort cost and energy cost of the two controllers over the three winter days.
ERC
20 15 10 5 0
Method ERC HFRC
Energy cost (kWh)
Discomfort cost (kWh)
Total cost (kWh)
590 574
498 317
1088 891
0
10
20
30
40
50
time (h)
Fig. 6. Comparison of room temperature, tank water temperature and energy consumption (spring).
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Table 6 Performance comparison over a 72-hour period during the spring. Method
Energy cost (kWh)
Discomfort cost (kWh)
Total cost (kWh)
ERC HFRC
267 73
11 137
278 209
27
HFRC
TRoom ( C)
26
ERC
o
25 24 23 22 21
o
TTank ( C)
0
10
20
30 40 time (h)
110 105 100 95 90 85 80 75 70
HFRC
0
10
20
30
50
60
70
ERC
40
50
60
tions and to compare the controllers at different times of the year. The low computation cost of the HFRC, which is comparable to that of the ERC, makes it possible to perform the month long validation tests in less than 24 h, which it not the case with other computationally expensive optimization based control schemes. Another advantage of HFRC is that the processing power needed to implement the HFRC on-line in a real building will be much lower than that needed by other optimization based schemes. The room temperature variations produced by the ERC and HFRC in the different seasons are shown in Figs. 8–10. The HFRC maintains a higher room temperature in winter and a lower room temperature in summer, which results in better control of thermal comfort compared to the ERC. In the transfer season, both the HFRC and the ERC keep the room temperature close to the range where there is no associated discomfort cost. However, as can be seen in Table 8, the energy consumption of the building controlled by the HFRC is very much lower. Overall, the percentage savings are large, which demonstrates that improving the control of a low-energy building system can greatly influence its performance. However, the cost of operating the building using expert rules is small and the actual savings may be relatively modest.
70
time (h)
6. Conclusions
35
Energy (kWh)
30
HFRC
ERC
25 20 15 10 5 0 0
10
20
30
40
50
60
70
time (h)
Fig. 7. Comparison of room temperature, tank water temperature and energy consumption (summer).
compared to the ERC. The HFRC uses the boiler more often to raise the tank water temperature during occupancy, which provides the hot-water driven absorption chiller with greater cooling capacity. As can be seen in Table 7, the result is a higher energy cost but a significantly lower thermal discomfort cost. 5.4. Performance evaluation based on one-month simulations during each of the three seasons Monthly simulations for the different seasons are performed in order to reduce the effects of the initial condiTable 7 Performance comparison over a 72-hour period during summer. Method
Energy cost (kWh)
Discomfort cost (kWh)
Total cost (kWh)
ERC HFRC
150 420
1870 176
2020 596
The control of renewable energy building systems is a high dimensional, multi-input–multi-output, non-linear dynamic optimization problem with a large search space. To solve this problem, a hierarchical fuzzy rule-based approach has been proposed. The introduction of fuzzy reasoning and rule hierarchy significantly reduces the search space; making the method of solution feasible and the rules more comprehensible. The performance of the fuzzy rule-based control scheme has been compared to that of an expert rule-based control scheme for different weather conditions. The proposed control scheme handles well the trade-off between the energy costs and thermal discomfort costs and the computational demands associated with its online implementation are similar to those of the expert controller, which are much lower than those of optimization based control schemes. The current hierarchical rule structure has already greatly reduced the number of required rules, thus making the generation of the rule base possible. However, the number of rules is still too large to make it easy for human experts to validate them based on their experience of operating similar buildings. A sensitivity study of the rule base is now being undertaken to reduce the size of rule base further, in order to make it more comprehensible. The current results are based on the assumption that the computer simulation of the low energy building system is an accurate representation of the real system. However, the development of such a simulation may be too time consuming or even impossible in practice. The next phase of
Z. Yu, A. Dexter / Solar Energy 84 (2010) 538–548
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TRoom( C)
22 HFRC
21
ERC
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TRoom( C)
Fig. 8. Comparison of room temperatures over a 30-day period during winter.
25 24 23 22 21 20 19 18
HFRC
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Time (h)
Fig. 9. Comparison of room temperatures over a 30-day period during the transfer season.
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TRoom( C)
27 HFRC
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Fig. 10. Comparison of room temperatures over a 30-day period during summer.
Table 8 Seasonal performance comparisons. Season
Method
Energy cost (kWh)
Discomfort cost (kWh)
Total cost (kWh)
Reduction of cost
Winter
ERC HFRC ERC HFRC ERC HFRC
5288 4601 7285 356 902 1699
7418 4724 391 0 4385 194
12706 9325 7676 356 5287 1893
26.6%
Transfer Season Summer
95.4% 64.2%
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