Author's personal copy Energy and Buildings 43 (2011) 988–994
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Optimizing the design of a solar cooling system using central composite design techniques Yin Hang, Ming Qu ∗ , Satish Ukkusuri Purdue University, School of Civil Engineering, 550 Stadium Mall Dr. CIVL G243, West Lafayette, IN United States
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Article history: Received 28 October 2010 Received in revised form 9 December 2010 Accepted 16 December 2010 Keywords: Solar cooling Central composite design Experiment design Optimization TRNSYS
a b s t r a c t This paper presents the development of a method to optimize a solar-assisted cooling system with limited budget constraints. Regression analysis is used to identify the relationship between the solar fraction and the system factors according to the data provided by experiments. In order to obtain an accurate model to estimate the problem using small number of experimental trials, the method of central composite design (CCD) from design of experiment (DE) is used as a key technique. The experimental trials are conducted in the transient energy system simulation (TRNSYS) tool. Finally, the optimization problem is formulated and solved by including the model as the objective function, the physical constraints of the system factors, and the budget limit. A case study was conducted to apply this optimization method to the design of a solar-assisted double-effect absorption cooling system installed in a small-sized office building in West Lafayette, IN, USA. The results show the developed optimal model strongly agrees with the physical system model in TRNSYS. This optimization method can be generally applied to different types of solar cooling systems, and other renewable energy systems. Published by Elsevier B.V.
1. Introduction Due to mounting concerns about climate change and resource depletion, meeting building heating and cooling demands with renewable energy has attracted increasing attention in the energy system design of green buildings. One of these approaches, solarassisted cooling, can be a solution to addressing the energy and environmental challenges faced by building designers. Solarassisted thermal cooling systems refer to the systems which use solar energy as the thermal source to drive a special kind of chiller, such as an absorption chiller or adsorption chiller, to provide cooling to the buildings. Till 2007, there were 81 installed large-scale solar cooling systems around the world, most of them are located in Europe, and some are located in Asia. There are few solar cooling systems installed in USA. These installations are applied to different building types, including offices, schools, hospitals, and hotels [1]. Lots of researches have been done about the solar cooling or integrated solar cooling and heating systems in different buildings. Most of researchers use both energetic and economic performances to evaluate a solar cooling system. Tsoutsos et al. [2] designed a solar cooling system for a hospital in Grete based on the energy performance and economic considerations. A detailed methodology
∗ Corresponding author. Tel.: +1 765 494 1714; fax: +1 765 269 7903. E-mail address:
[email protected] (M. Qu). 0378-7788/$ – see front matter. Published by Elsevier B.V. doi:10.1016/j.enbuild.2010.12.024
was also provided in the paper which can be followed. Eicker et al. [3] discussed the design and performance of the solar cooling systems in office buildings. The author selected a typical small office building as the base case, and some key factors of the building, such as the building window surface area and orientation, the shading system and the internal loads were varied to determine the influences of the load distribution on solar fraction. Meanwhile, both the energetic and economic performances were analyzed in this study. Calise [4] investigated the energetic and economic feasibility of an integrated solar heating and cooling system for different types of school buildings and Italian climates. The conclusion showed this system can achieve potential energy saving, but the economic payback only became true when the public funding was applied. To optimize a solar cooling system, one of the important things to know is the relationship between the variable of interest, which is the optimization object (e.g., the solar fraction used to evaluate the energy performance or, the life cycle cost used to evaluate the economic performance), and the system factors, which are the key parameters of a system. Basically there are two methods to explore this relationship: one is to build a mechanical model with the variable of interest and system factors according to their purely physical meaning; and the other is to build the input–output relationship by simply connecting the inputs (factors) and outputs (responses), which is appropriately called the “black-box model” [5]. Ghaddar et al. [6] built a mechanical model for a small-sized solar cooling system with simplified considerations. The variable of interest in this optimization problem is the life cycle cost, and
Author's personal copy Y. Hang et al. / Energy and Buildings 43 (2011) 988–994
Nomenclature ˙ m ˙ sc m rp Asc Qs Li Qo i Vcold Cp Tload n ˛ k ne nc ˇ Vhot IC SF FR NC
mass flow rate of the pump (kg/h) mass flow rate of one panel of solar collector (kg/h) number of array of solar collectors in parallel solar collector area (m2 ) the thermal capacity of the cold storage (kW h) the daily cooling load (kW) the nominal capacity of the chiller (kW) the time interval of the simulation (h) volume of cold storage tank (m3 ) the specific heat of the water (kJ/(kg ◦ C)) density of the water (kg/m3 ) temperature difference of the cold storage tank (◦ C) the total operation period (h) axial points number of factors total number of experimental trials number of center points collector slope above the horizontal plane (◦ ) volume of hot storage tank (m3 ) initial cost ($) solar fraction (%) flow rate of the pump (kg/h) normal capacity (kW)
the system factors are the solar collector area and the volume of the hot storage tank. The study obtained the optimal design of the solar cooling system by minimizing the life cycle cost of the system. Assilzadeh et al. [7], Mateus and Oliveira [8], and Valise et al. [9] explored the “black-box” relationship between the variable of interest and system factors by simulations. Assilzadeh et al. [7] first maximized the system energy performance by varying, one at a time, the value of the key factors, such as the slope of solar collectors, the pump flow rate, the boiler thermostat setting, and the volume of the hot storage tank. Then, the solar collector area was maximized based on the economic considerations. Mateus and Oliveira [8] optimized the tilt angle of collectors by maximizing all year round energy collection and optimized the solar collector area and hot storage tank volume by minimizing the “cost of a unit of produced energy,” – which is expressed as the ratio of the total cost in the life span to the total energy produced in the life span. Valise et al. [9] utilized the three- and four-level factorial design approach to maximize the primary energy savings of solar heating and cooling systems, which resulted in 324 simulation runs. Both Assilzadeh et al. [7] and Mateus and Oliveira [8] utilized the one-change-ata-time traditional technique, which obtains the results by massive simulations. This technique has three major disadvantages. First, it requires tremendous efforts and resources to gain enough useful information. Second, this technique cannot make judgments on the significance of input factors acting alone, or factors acting in combination with one another. Third, the experiment based on this technique can cover only a limited range in the experimental domain; therefore, the optimal results located in that domain may not be the true optimal results in a wider range. Although Valise et al. [9] utilized the advanced technique – design of experiment (DE), a relatively large number of simulation runs were required for the optimization. In this study, a method was created to optimize a solar-assisted cooling system by using a relatively small number of experimental trials. Using concepts from DE, we propose a central composite design (CCD) approach to determine the required number of experimental trials and the locations of the system factors. The experimental trials are conducted in the TRNSYS tool. Regression
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analysis is used to build a statistical model between the variable of interest and the system factors; and this model is also used as an objective function for the optimization problem. The energy performance of the solar cooling system is then maximized by including the budget constraint and other specific constraints related the system’s characteristics. This paper is organized as follows. The next section discusses the optimization method for the solar cooling system. The developed algorithm is then applied to a case study, and the results and some conclusions are presented. 2. Optimization method Solar fraction is generally used to evaluate system energy performance. Solar fraction is the ratio of the cooling energy provided by the solar system to the total cooling energy required by the building. Solar cooling systems usually cost more than conventional cooling systems. It is believed that system performance should be further improved within budgets limits. Therefore, an optimal design should seek to allocate a limited budget to the solar cooling system so that the energy performance, indicated by the solar fraction, is maximized. In a solar cooling system, since the nature of the relationship between the solar fraction and the factors that are required to be optimized in a system are not known exactly, regression analysis can be utilized to identify the relationship between them, according to the samples generated by the experimental trials. In order to build this relationship, DE was adopted in this study, and the experiments are conducted using the TRNSYS simulation tool. The system factors of a solar cooling system should be initially screened in order to select the key factors on which to build the relationship with the solar fraction. The size of the design is constrained by the resources, usually cost and time. The precision of the parameter estimates can increase with the number of trials, but also depends on the location of the design points. Therefore, the selection of a suitable approach from DE is important. The CCD approach was utilized in this study. The suitable range for each factor is also an important consideration for an experiment. If the range is too small, the final model will not cover the whole relationship; if the range is too large, the accuracy of the final model cannot be guaranteed. The TRNSYS simulation tool was used to conduct the experiments. Once all of the samples are collected, the model between the solar fraction and the system factors can be identified by regression analysis. The residual test and other statistical tests are needed to test the regression model. If all the tests are satisfied, the next step, – optimization, can be conducted by adding other relevant constraints including the budget limit. The optimization results are then input into the TRNSYS model to evaluate and compare them with the simulation results. If the error is in an acceptable range, the optimal design is considered satisfactory; otherwise, the experiments should be re-conducted. The detailed explanations are illustrated in the following sections. And a case study is conducted in Section 3 with detailed procedures. 2.1. The choice of factors Fig. 1 shows the schematic diagram for a typical solar cooling system, which includes the solar collectors, hot storage tank(s), auxiliary heater(s), thermal chiller(s) (e.g., absorption chiller or adsorption chiller), and cold storage tank(s) [10]. The solar collectors receive solar radiation from the sun, and transfer the energy to the hot storage tank. The hot energy is then used to drive a thermal chiller, such as an absorption chiller, or an adsorption chiller, which can generate chilled water via thermal energy. The chilled water can be stored in the cold storage tank or provided to the building.
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Y. Hang et al. / Energy and Buildings 43 (2011) 988–994
r cto lle o C
s
P3
P4
P2 Hot storage tank
Aux. Heater
Cold storage tank
Chiller
Building
P1 Fig. 1. Schematic diagram for a solar-assisted absorption cooling system.
The hot storage tank and the cold storage tank not only store the hot and cold energy for the system, but also make the system more stable. Besides, the cold storage tank can reduce the capacity of the chiller, – by storing the extra cooling energy in the tank during partial load period. The auxiliary heater can provide the hot water to drive the chiller when the solar energy is not available. At the beginning of an experimental program there are many factors which, separately or jointly, have an effect on the response (i.e., solar fraction in this study). For a typical solar cooling system, there will be many variables related to the solar fraction, for example: (1) slope of the solar collectors, (2) area of the solar collectors, (3) volume of hot storage tank, (4) nominal capacity of the chiller, (5) volume of cold storage tank, (6) pumps flow rate, (7) fluid water temperature set points, such as heat source temperature, chilled water temperature, and cooling water temperature, (8) type of solar collectors, (9) type of storage tanks, 10) type of the chiller, (11) whether installing VFD on the pumps or not. Some initial efforts are often spent in screening out those dependent factors from those independent factors [11]. Among all the variables, some of them are continuous ones, and the rest of them are discrete ones. Normally, the pumps flow rate can be determined by equipment requirements, such as chiller, solar collectors (see Eq. (1)). Therefore, the pumps flow rate are dependent factors, which can be screened out. The set point of the heat source temperature is related to the chiller selection and the characteristics of the solar collectors. The optimization of the set point of the chilled water temperature and the set point of the cooling temperature is the same as a conventional cooling system, which is not a unique problem for the solar cooling system. Furthermore, these two set point temperatures also depend on the requirements of the building design condition. Therefore, all the temperature set points are also dependent variables. The parameters (8)–(10) are selections for system equipment and whether they are included in an experiment will depend on the purpose of the study. If the study focuses on the equipment selection, these factors should be included in the final selected factors; and if the study focuses on the system optimization, these factors are normally determined beforehand. Also, the chiller capacity and the lower bound of the volume of cold storage tank can be determined. In order to maintain the cooling load for an entire day, the chiller should be capable of handling the capability to cover the daily cooling load even if the system includes a cold storage tank. The chiller’s capacity can be determined based on Eq. (2) [12], and the volume of the cold storage tank can be determined according to Eqs. (3) and (4) [13]:
Qs =
n
Vcold =
(1)
h=24 Capacitychiller =
h=1
Cooling load
Hours which the cooling load is available
(2)
if
Li > Qo
3600Qs Cp Tload
(3)
(4)
Therefore, the following factors should be included in the experiment: (i) slope of solar collectors, (ii) area of solar collectors, (iii) volume of hot storage tanks, and (iv) volume of cold storage tank. The decision to include the other parameters depends on the specific project.
2.2. Design of experiment (DE) DE guarantees the accuracy and efficiency of the experiments [14]. DE is commonly used in complex real-world experiments [15,16]; however, it is also applicable for simulation-based experiments [8,17], which only requires a single repetition for each experiment. Simulated experiments are obviously not affected by the errors commonly encountered in real experiments. Optimum experimental designs depend upon the model relating the response to the factors. The model needs to be sufficiently complicated to approximate the main features of the data, without being so complicated that unnecessary effort is involved in estimating a multitude of parameters. Usually, the model is a first-order or second-order polynomial equation, and the key ingredient in choosing a design that minimizes the variances is the concept of orthogonality [18]. The first-order model is represented in Eq. (5), and its orthogonal design is generally used for two-level factorial design, which means each factor has two levels. The total experiment sets will be 2k plus the central runs, where k denotes the number of factors. yˆ = a0 +
n
aj xj
(5)
j=1
However, the first-order design should not only consider the main effects of the factors, but also often need to include the interaction items, which would mean the model is then represented as in Eq. (6).
yˆ = a0 + ˙ vp = rp · m ˙ sc = f (Asc ) · m ˙ sc m
(Li − Qo )i
i=1
n j=1
aj xj +
aij xi xj
(6)
1
