Constrained Fuzzy Logic Approximation for Indoor Comfort and Energy Optimization* S. Ari
I. A. Cosden
H. E. Khalifa
J. F. Dannenhoffer
P. Wilcoxen
C. Isik
Syracuse University Syracuse, NY 13244, USA
[email protected],
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[email protected],
[email protected],
[email protected],
[email protected] Abstract – Indoor environmental satisfaction has been receiving considerable attention by many researchers recently. Research has indicated that allowing building occupants to adjust their local environment to their liking increases satisfaction and human performance. However, concern about the possible increase of energy consumption associated with the wide adoption of distributed localized environmental control has limited the use of such systems. In this study, we show how gradient-based optimization can be used to minimize energy consumption of distributed environmental control systems without increasing occupant thermal dissatisfaction. Fuzzy rules have been generated by data from gradient optimization, showing that a fuzzy logic control scheme based on nearest neighbors approximates closely the gradient-based optimized results.
I. INTRODUCTION A. Problem Definition In current Heating, Ventilating and Air-Conditioning (HVAC) systems, the building thermal environment is regulated through the use of a small number of thermostats placed within relatively large building zones. Such “One-SizeFits-All” (OSFA) systems are usually designed to satisfy the thermal comfort needs of only ~80% of the office occupants [1] and provide sub-optimum thermal conditions for a relatively large fraction of the building occupants. Individual physiological and psychological differences make it impossible for these OSFA systems to satisfy all occupants. In order to increase thermal comfort and satisfaction, individual occupants should have the ability to customize their immediate thermal environments to suit their particular needs. This is tantamount to adopting a “Have-It-Your-Way” (HIYW) philosophy in building thermal environmental design. There is mounting evidence that personal environmental control leads to higher satisfaction and enhanced productivity [2][3][4][5]. Nevertheless, so far such systems have achieved very limited commercial success for two primary reasons: 1) initial cost may be higher than for centralized OSFA systems, and 2) if not optimized globally for the whole-building, HIYW systems may increase building HVAC energy consumption owing to the inherent non-uniformity of the building thermal environment in such systems (e.g., one cubicle heated while the adjacent one cooled). This paper presents an intelligent
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control strategy that approaches the HIYW ideal with no increase, or possibly even a savings, in energy consumption. B. Literature Survey There have been a variety of articles in which different control strategies were applied to reduce energy consumption in HVAC systems. Some of these articles do not take comfort into consideration at all and concentrate on the controller in isolation. For example, Huang has presented an adaptive learning algorithm for automatic tuning of proportional, integral and derivative (PID) control of an HVAC system by using a genetic algorithm to improve HVAC system performance [6]. Mathews has investigated the effect of the changing control strategies by developing a new simulation tool [7]. Comfort of occupants is an important factor in the control of indoor environments. Fanger has published extensively on the estimation of the percentage of a population thermally satisfied under a variety of environmental conditions, specifically under different indoor temperatures. In order to estimate satisfaction of the whole population in a certain environment, Fanger provides a formula for predicted mean vote (PMV) [8], which is a function of metabolic rate (met), clothing (clo), air temperature (oC), radiant temperature (oC), air velocity (m/s), and relative humidity (%). It consists of a 7-point scale, as shown below. -3 -2 -1 0 +1 +2 +3
cold cool slightly cool neutral slightly warm warm hot
In his experiments, he classified the people voting -3, -2, +2 and +3, as dissatisfied and he has pioneered research on thermal comfort and productivity. Comfort has been considered as a fuzzy concept by a number of authors. For example, Dounis has presented the design of a living space comfort regulator by using fuzzy logic without taking into account energy consumption [9].
This work is supported by DoE Grant # DE-FG02-03ER63694 and the New York State Office of Science, Technology and Academic Research.
II. METHODOLOGY
DID(vote ) =
2
+ 3, T > T0 + 2∆T − 3, T < T0 − 2∆T . T − T0 1 .5 , otherwise ∆T
(2)
Fig. 1 shows the satisfaction curve of a given individual. We validated these individual equations by matching the cumulative population curve of this function to that in the American Society of Heating, Refrigerating and AirConditioning Engineers (ASHRAE) Standard 55 [1] as shown in Fig. 2. 1 0.8 T0-∆T
0.6
T0+∆T
0.5 0.4 0.2 0 -3
T0 -2
-1
0
vote (-3, +3)
1
2
3
Fig. 1 Assumed dissatisfaction curve.
100 80 60 40 20
A. Individual Dissatisfaction The occupant comfort (satisfaction) is modeled by a method inspired by Fanger’s PMV and PPD [1]. We introduce a new measure: the Degree of Individual Dissatisfaction (DID):
1 + tanh (2 vote − 3)
vote(T ) =
dissatisfaction
C. Our Approach Consideration of the thermal satisfaction of a population of building occupants, while an improvement over “controlsonly” approaches, does not account for individual thermal satisfaction. For example, when 90% of the population is satisfied, the remaining occupants may be persistently dissatisfied. Our approach prevents persistent individual dissatisfaction, while keeping the population PPD at or below 10%. In order to do this, we developed a model of personal dissatisfaction (Fig. 1) that generates population results that match the well-established PPD-PMV curve (Fig. 2) [1]. Our approach concentrates on a typical office building, which we modeled with a thermal circuit network coupled with a typical HVAC system consisting of a heat pump and a furnace. Gradient optimization has been employed to minimize energy consumption with a constraint on the generated individual dissatisfactions. While providing a control strategy that reconciles energy, population comfort, and individual comfort, our approach, like other global optimization approaches, requires information acquired from all offices and cubicles. We propose using a fuzzy logic approximation approach, with simplified sensor connectivity, which imitates the gradient optimization results. Section II of this paper describes the individual dissatisfaction model, the building model, and the general strategy of optimization. Section III is devoted to fuzzy logic approximation, and finally, the paper is concluded in Section IV with some comparative results depicting energy consumption and dissatisfaction for three US cities.
temperature, and ∆T, the individual’s temperature tolerance, namely:
PPD (%)
Several approaches have been proposed to reconcile comfort and energy consumption. Wright has considered the design of HVAC systems using multi-criteria optimization [10]. Nassif has implemented the non-dominated sorting genetic algorithms to solve an HVAC optimization problem [11]. Another method used by researchers is to employ fuzzy logic to determine classical controller parameters [12]. The common denominator of all these approaches is that they consider population-averaged occupant comfort, by using as a constraint Fanger’s predicted percentage of dissatisfied (PPD) occupants, which is related to PMV.
,
(1)
where an individual’s vote is a function of the surrounding indoor temperature (T) and two parameters describing the individual’s preferences: T0, the desired individual
0 -3
Original PPD Generated PPD
-2
-1
0
PMV (-3, +3)
1
2
3
Fig. 2 Comparison of original and generated PPD.
B. Building Model In order to estimate the yearly energy consumption of a typical building, we needed a thermal model of a building system. A typical 600m2 office building consisting of 49 individual offices was modeled using a temperature-bin-based lumped-parameter approach, where each interior occupied zone is a node in a thermal circuit network. Resistance values for interior walls, exterior walls, and windows were typical of
common building construction materials. Each office contained three sources of internal heat generation: the occupant, a computer, and task lighting. The HVAC system was comprised of a rooftop heat pump and a standard efficiency furnace. The outside temperature was modeled using temperature bins created from the typical meteorological year (TMY2) weather files for three different US climates [13]. Each climate was represented by a US city: Phoenix, AZ (hot-dry), San Francisco, CA (warm-marine), and Chicago, IL (cool-humid). The building HVAC sizing varied in each city depending on the maximum design temperature; otherwise the building model was the same for each city. The conventional HVAC control (OSFA) consisted of placing thermostats in three offices that control the other 46 remaining offices as well (a 3-zone system). The HIYW system provides a thermostat for each office. To determine yearly energy usage, we calculated the energy consumption for every temperature bin, for each city, given the required thermostat set point temperatures in each office. Energy consumption has been optimized with this building model by using gradient-based optimization to modify the thermostat set point temperatures. C. Optimization Our approach uses a gradient-based scheme to minimize energy consumption by varying office temperatures while keeping the overall population dissatisfaction less than 10%, the ASHRAE Standard 55 guideline [1]. In addition to this constraint, each individual’s dissatisfaction was kept under 20% in order to prevent extreme dissatisfaction for any occupant in a given population. The desired temperatures (T0) of each individual have been used as initial conditions. We called this “Optimized HIYW”. Function “fmincon” [14] in the MATLAB optimization toolbox has been used. Energy consumption has been optimized for 32 different outside temperature bins. III. FUZZY LOGIC APPROXIMATION The optimization uses the personal satisfaction curves for all occupants to determine the temperature settings in each office. In the gradient optimization method, temperature settings of each office are the variables, which need to be optimized to minimize whole building energy consumption. As the number of offices increases, the computational complexity of the optimization rises. Fuzzy approximation uses the temperature settings from the neighboring offices only, simplifying the sensor communication requirements. We accomplished this by using the optimum temperature distribution as the target distribution for the fuzzy logic system. We designed a Sugeno-type fuzzy inference system (FIS) [15], which is a rule extraction method, with the help of the MATLAB fuzzy logic toolbox function “genfis2” [14]. This method uses fuzzy subtractive clustering to find the number of rules and membership functions; we used 0.15 of radius of
clusters under the assumption that data falls into a unit hyperbox, and at the next step, it finds the result equations by using a linear least square estimation. The building has three general types of offices (zones): corner, perimeter and interior offices. Perimeter and corner offices are most affected by the outside temperature, while interior offices are most affected by the heat exchange with the neighboring offices. Due to the nature of this kind of building, three different FIS have been generated. These fuzzy systems work for the three types of building zones. In order to derive optimized temperature set points for each office as an output of the fuzzy system, four neighboring office temperatures and its own desired temperature values have been used as inputs. For corner offices, two neighboring office temperatures, two outside temperatures and its own desired temperatures have been used. Unlike the corner offices, perimeter offices used only one outside temperatures and three neighboring-desired temperatures. Fuzzy logic has been used to imitate the results of gradient optimization. The energy consumption of 50 random populations for each outside temperature in the three cities mentioned above has been minimized with the gradient-based scheme with 10% PPD and 20% personal dissatisfaction constraints. The desired temperatures of the populations and their optimized temperature distributions, which are the result of the gradient optimization, have been used to train the FIS for the three zones. Fuzzy approximation has been applied to both the training data (50 populations) and the test data (10 different populations). With this suboptimal system approximation, we tried to reach the satisfaction criteria and energy consumption found in the gradient-based scheme. IV. RESULTS AND CONCLUSION Wide acceptance of individual control is predicated on its associated energy cost relative to the conventional approach. In this implementation, the optimized HIYW has been tested and compared with OSFA. Optimized HIYW has also been compared with an optimized version of OSFA in order to get the best-case comparison with optimized HIYW. The optimized OSFA has been constrained to 10% average population dissatisfaction. Fig. 3 and Fig. 4 summarize our results, which show the significant potential yearly energy savings through gradient optimization, compared to OSFA and optimized OSFA. They also show that a constrained fuzzy approximation is able to mimic these results, thus simplifying sensor connectivity requirements. Energy consumption is strongly related to the cost of building operation, but environmental comfort in a work place, such as a typical cubicle, is strongly related to occupant satisfaction and productivity. Energy consumption and comfort usually affect each other in the opposite way. Unlike the previous studies, individual satisfaction has been the heart of this study. Enhanced thermal comfort and satisfaction has been provided for all occupants, while energy consumption was minimized in our implementation.
Gradient Fuzzy Train Fuzzy Test
25 20 15 10 5 0
Phoenix, AZ
San Francisco, CA
Chicago, IL
Fig. 3 Energy Savings per year with respect to OSFA.
Energy Savings (%/Year)
30
Gradient Fuzzy Train Fuzzy Test
25 20 15 10 5 0
Phoenix, AZ
San Francisco, CA
Chicago, IL
Fig. 4 Energy Savings per year with respect to optimized OSFA.
As shown in Fig. 5 for Phoenix, AZ, neither optimized HIYW nor constrained fuzzy approximation result in a degree of individual dissatisfaction in excess of 20%, as both OSFA and optimized OSFA do. OSFA is likely to cause the degree of individual dissatisfaction (DID) of ~5% of a building population to exceed 20%, and that of ~1% to exceed 50%. Reduction of the energy consumption of conventional (OSFA) HVAC systems through thermostat adjustment could result in an increase in the occupants’ thermal dissatisfaction. Even though the 10% PPD constraint has been met in the OSFA system, relative frequency of individual dissatisfaction is higher. Optimization of OSFA to reduce energy consumption would result in a degree of individual dissatisfaction exceeding 20% for ~15% of a building population and 50% for ~5% of the population. In our approach, population dissatisfaction has been kept under 10% without subjecting any one occupant to thermal discomfort in excess of 20% (DID). Similar trends have been observed for other cities.
Relative Frequency of the Population
Energy Savings (%/Year)
30
0.35
OSFA Optimized OSFA Gradient Fuzzy
0.3 0.25 0.2 0.15 0.1 0.05 0 0
0.2
0.4
0.6
0.8
Degree of Individual Dissatisfaction (DID)
1
Fig. 5 Typical curves of the degree of individual dissatisfaction (DID) for Phoenix, AZ.
This optimized HIYW system improves occupant’s comfort while reducing energy consumption. Since occupants remain thermally comfortable within a certain temperature tolerance that varies from one individual to another, the results of this approach, which takes advantage of the varying thermal comfort tolerances of the occupants, are quite encouraging. The HIYW approach would use all the sensor network connectivity in the building. The communication of all sensors with each other is not required in the fuzzy logic approximation. Reduction of sensor connectivity would reduce system complexity and cost at a modest decrease in energy savings relative to the fully connected HIYW system. REFERENCES [1] ANSI/ASHRAE Standard 55-2004 [2] W. Kroner, J.E. Stark-Martin, and T. Willemain, Using Advanced Office Technology to Increase Productivity, Center for Architectural Research and Center for Services Research and Education, Rensselaer, Troy, New York, 1992. [3] E. Arens and F. Bauman, A Field Study of PEM Performance in Bank of America's San Francisco Office Buildings, Department of Architecture, Center for Environmental Design Research, UC Berkeley, CA, 2000. [4] A. Hedge, M.G. Mitchell, and J. McCarthy, “Effects of a FurnitureIntegrated Breathing-Zone Filtration System on Indoor Air Quality, Sick Building Syndrome, Productivity, and Absenteeism,” Indoor Air, vol. 3(4), pp. 328-336, 1993. [5] A.K. Melikov, “Personalized Ventilation”, Indoor Air, vol. 14(7), pp. 157-167, 2004. [6] W. Huang, and H.N. Lam, “Using genetic algorithms to optimize controller parameters,” Energy and Buildings, vol. 26, pp. 277-282, 1997. [7] E.H. Mathews, C.P. Botha, D.C. Arndt, and A. Malan, “Developing cost efficient control strategies to ensure optimal energy use and sufficient indoor comfort,” Applied Energy, vol. 66, pp. 135-159, June 2000. [8] P.O. Fanger, Thermal Comfort: Analysis and Applications in Environmental Engineering, McGraw-Hill, NY, 1972. [9] A.I. Douinis and D.E. Manolakis, “Design of a fuzzy system for living space thermal-comfort regulation,” Applied Energy, vol. 69, pp. 119-144, June 2001. [10] J.A. Wright, H.A. Loosemore, and R. Farmani, “Optimization of building thermal design and control by multi-criterion genetic algorithm,” Energy and Buildings, vol. 34, pp. 959-972, 2002.
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