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Multi-objective optimization of solar assisted absorption cooling system Berhane H. Gebreslassiea, Mélanie Jimeneza, Gonzalo Guillén-Gosálbezb, Laureano Jiménezb and Dieter Boera a

Department of Mechanical Engineering, University Rovira i Virgili Department of Chemical Engineering, University Rovira i Virgili Av. Països Catalans, 26, 43007-Tarragona, Spain, [email protected]

b

Abstract This work presents a multi-period and multi-objective optimization based on mathematical programming of solar assisted absorption cooling systems. Seven solar collector models combined with a gas fired heater and an absorption cooling cycle are considered. The optimization task is formulated as a multi-objective multi-period mixed-integer nonlinear programming (MINLP) problem that accounts for the minimization of the total cost of the cooling system and the associated environmental impact. The environmental performance is measured following the Life Cycle Assessment (LCA) principles. The capabilities of the proposed method are illustrated in a case study that addresses the design of a solar assisted ammonia-water absorption cooling system using the weather conditions of Tarragona (Spain). Keywords: Solar assisted cooling, MINLP, multi-objective optimization, life cycle assessment (LCA), absorption cycle.

1. Introduction Air conditioning and refrigeration have a significant contribution to the total energy consumption. The growing demand for air conditioning and refrigeration has caused a significant increase in the consumption of primary energy resources, to the end that it currently threatens the stability of electricity grids. Thus, a change in the energy structure should be made, promoting energy efficient technologies and renewable energies. A more sustainable concept, known as solar assisted refrigeration, is based on the use of absorption cooling cycles driven by thermal energy provided by solar collectors. The use of solar energy for cooling applications has a high potential to replace partially conventional cooling systems, given the fact that the cooling demand matches the availability of solar irradiation [1]. These technologies use renewable energy sources, thus decreasing the associated environmental impact. However, their cost is still higher compared to conventional cooling systems (i.e., vapor compression cooling system). The objective of this work is to provide a quantitative decision support tool for the optimal design of solar assisted absorption cycles. The model presented optimizes the operating and structural decisions of the absorption cycle taking into account simultaneously its environmental and economic performance. The environmental performance is measured based on the Eco-indicator 99, which follows the life cycle assessment (LCA) methodology.

B.H Gebreslassie et al.

2. Problem statement The problem addressed is formally stated as follows. Given are the cooling capacity of the system, the inlet and outlet temperatures of the external fluids (chilled water and cooling water), capital cost data, monthly-averaged weather conditions, the performance characteristics of the solar collectors, and life cycle inventory data associated with the construction and operation of the cooling system. The goal is to determine the optimal design and associated operating conditions that simultaneously minimize the total cost and the environmental impact of the system.

3. Solar assisted absorption cycle Figure 1 depicts the solar assisted absorption cooling system under study. The absorption cycle operation is discussed in detail in Berhane et al. [2]. The heat production subsystem includes two main units: a gas fired heater (GFH), and solar collectors (Col). GFH is a low pressure heater consuming natural gas. The solar collector panels used in this work are: evacuated tube collectors (ETC), flat plate collectors (FPC) and compound parabolic collectors (CPC). Within each collector type, we consider different possible alternatives and the associated models that describe their performance.

Fig. 1. Ammonia-water solar assisted absorption cooling system

4. Mathematical model The mathematical model of the absorption cycle is based on the formulation introduced by the authors in previous works [2, 3]. The original formulation has been extended in order to integrate the heat production subsystem model. 4.1. General constraints The model considers that the time horizon can be divided into t periods. The cycle can then operate in a different manner in each of these periods in order to get adapted to the specific solar radiation of that time interval. Without loss of generality, we consider that each of these periods corresponds to one month, although in general we could specify any other length. The model is based on energy and materials balances applied to each unit of the system.

Multi-Objective Optimization of Solar Assisted Absorption cooling system

4.2. Heat production subsystem The heat supplied to the absorption cycle is generated in the solar collectors and the gas fired heater. 4.2.1. Collector performance constraints The selection of n solar collectors of type i is represented by the following disjunction [4]: ª « Yi « « Yn º ª « » « Col Col Ki ,t nAi GBt »¼ i 1,... I « i 1,... I « ¬Qt « « T av Tt amb T av Tt amb C2 , i t «Ki ,t IAM 4 C0 ,i C1, i t GBt GBt ¬ Yi , Yn ^True, False` i, n

º » » » » » » 2 » » ¼

(1)

where Yi and Yn are Boolean variables that decide whether the given disjunctive terms i and n inside the disjunctions are true or false. They are true if n collectors of type i are selected and zero otherwise. If the collector is chosen, then the equations inside the disjunction, which determine the heat supplied by the solar system, are active. If the collector is not selected, the corresponding equations are all set to zero. The useful heat collected from the solar system in each time-period t ( QtCol ) is determined from the collector performance, which is calculated from the collector efficiency (Și,t), its area and the global solar incident radiation on the collector surface in month t (GBt) [1]. The area of the collectors is obtained by multiplying the size of the collector type i available in the market ( AiCol ) with the corresponding number of collectors (n) installed in the system. The second equation inside the disjunction allows to determine the efficiency of the collector i in month t [1]. 4.2.2. Linking constraints Eqn. (2) links the heat provided by the collectors and the gas fired heater with that consumed by the cycle. Hence, the heat consumed by the generator of the cycle in month t ( QtD ) should be less than or equal to the sum of the heat collected from the Col

collector ( Qt

) and the heat supplied by the gas fired heater ( QtGFH ) t in the same

month:

QtD d QtCol QtGFH

(2)

4.3. Objective functions Our model includes two contradicting objective functions: 1) minimize the total cost; and 2) minimize the environmental impact of the cooling system. 4.3.1. Economic performance objective function The total cost of the system (TC) accounts for the capital and operating costs (Cc and Cop, respectively) as shown in eqn. (3).

TC

C c C op

(3)

B.H Gebreslassie et al.

4.3.2. Environmental performance objective function The environmental performance of the system is measured based on the principles of Life Cycle Assessment (LCA) using the Eco-Indicator 99 framework. The total EcoIndicator 99 (ECO99tot) is given by the sum of the Eco-Indicator 99 of the manufacturing part (ECO99man) and the operational part (ECO99op) shown in eqn. (4).

ECO99tot

ECO99man ECO99op

(4)

5. Solution method The design problem can be finally formulated as a multi-objective mixed-integer nonlinear programming (MINLP) of the following form: ( P)

^TC x, y , ECO x, y `

min

U x, y

s.t.

h ( x, y ) 0 g ( x, y ) d 0

x, y

tot 99

(5)

x R, y ^0,1`

In this formulation, x represents the state or design variables such as thermodynamic properties, mass flows and equipment sizes. The discrete variables are denoted by y, and are used in the selection of a specific number of collectors n of type i. TC (x, y) and ECO99tot denote the economic and environmental performances of the solar heat integrated absorption cooling system, respectively. The solution to (P) is given by a set of Pareto optimal points that represent the trade off between the economic and environmental performance of the system. For the calculation of the optimal trade off solutions, the İ-constraint solution method is used. This method is coupled with a customized branch and bound algorithm that reduces the computational burden of the model. This strategy relies on branching on the Boolean variables that denote the type of collector. In every node of the tree, lower and upper bounds on the optimal solution are obtained by relaxing the integer variables that denote the number of collectors selected (lower bound) and then rounding them up and solving again the problem with fixed values of the integers (upper bound). The nodes of the tree for which the lower bound exceeds the current best upper bound are pruned, and the procedure is repeated until all the collector types are analyzed.

6. Case study The capabilities of our approach are illustrated through a case study that addresses the design of a solar assisted absorption cooling system with a cooling capacity of 100 kW. The process data for the ammonia-water absorption cycle are taken from [2, 3]. Concerning the solar collectors, there are several types which can be used in solar air conditioning systems. We consider seven models of non-tracking collectors assuming the weather conditions of Tarragona (Spain).

7. Results and discussions The non-convex bi-criteria mixed integer nonlinear programming (MINLP) and the associated solution procedure is implemented in GAMS [5]. Figure 3 shows for the extreme solutions the single damage categories that contribute to the total Eco-indicator 99. In all the cases, the main contributor to the overall environmental damage is the

Multi-Objective Optimization of Solar Assisted Absorption cooling system

depletion of natural resources. On the other hand, the eco-system quality damage is rather low, mainly because the cooling system does not use hydrochlorofluorocarbons (HCFC).

Fig. 2. Pareto set of solutions of the case study

Fig. 3. Contribution of single damage categories to the total Eco-indicator at the extreme Pareto designs

The CPU time required to obtain the complete Pareto set of solutions is 88.33 seconds in a 2.29 GHz machine. The Pareto points are depicted in Figure 2, which shows the single damage categories as well as the total Eco-indicator 99 value associated with each Pareto solution. Each point of the curve represents a different absorption cycle design. In the minimum total cost solution, the heat required by the cycle is exclusively supplied by the gas fired heater. However, as we move towards the minimum impact solution, the energy needs are gradually fulfilled using a larger number of collectors. Near to the minimum total cost Pareto design, flat plate collectors are selected. The reason is that they show performance improvement at lower temperatures more than the evacuated tube collectors. Moreover, they are cheaper than the evaluated tube collectors. On the other hand, near to the minimum environmental impact Pareto designs, the heat demand is covered by the evacuated tube solar collectors. The reason is at higher temperature the performance of evacuated tube collectors is better than the flat plate collectors. Figures 4 and 5 depict the contribution that the manufacturing and operation of the subsystems of the cycle (i.e., absorption cycle itself, collectors and heater) have on its environmental performance for each of the extreme Pareto designs. In general, the construction of the equipment units has very little impact on the overall environmental damage. In fact, in the minimum total cost Pareto design, the main source of impact is the operating of the gas fired, whereas the contribution due to the manufacturing of the cooling system is negligible. However, in the minimum environmental impact solution, the main contributor to the total impact is the operation of the solar collectors. These are operated using pumps that consumes electricity, the impact of which is determined assuming the Spanish electricity grid that is mainly based on fuel oil and coal. In this latter case, the magnitude of the impact due to the manufacturing of the cooling system is larger, mainly because of the emissions of heavy metals that take place during the construction of the collectors. Hence, it is worthwhile to consider this part in the calculation of the life cycle impact of the solar assisted cooling system.

B.H Gebreslassie et al.

Note: The subscripts m, op and t represents the manufacturing, operation and total Ecoindicator respectively.

Fig. 4. Main sources of impact in the minimum environmental impact solution

Fig. 5. Main sources of impact in the minimum cost solution

8. Conclusions Based on mathematical programming, the design of more sustainable solar assisted absorption cooling systems has been presented. The method introduced relies on formulating a bi-criteria MINLP problem that accounts for the minimization of the total cost and the environmental impact of the cooling system. The capabilities of the proposed approach have been illustrated through its application to the design of a solar assisted ammonia-water absorption cooling system. Reductions up to 70 % in the environmental impact are feasible by replacing the consumption of primary energy resources by renewable solar energy sources. The tool presented in this work is intended to guide decision-makers towards more sustainable design alternatives for fulfilling the current cooling demand.

9. Acknowledgements Berhane H. Gebreslassie expresses his gratitude for the financial support received from the University Rovira i Virgili. The authors wish to acknowledge support from the Spanish Ministry of Education and Science (projects DPI2008-04099 and CTQ200914420-C02) and the Spanish Ministry of External Affairs (projects A/016473/08 and HS2007-0006).

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H. M. Henning. Solar-assisted air-conditioning in buildings. Springer Wien/New York; 2004. B. H. Gebreslassie, G. Guillén-Gosálbez, L. Jiménez, and D. Boer. Design of environmentally friendly absorption cooling systems via multi-objective optimization and life cycle assessment. Computer Aided Chemical Engineering, 26:1099-1103, 2009. B. H. Gebreslassie, G. Guillén-Gosálbez, L. Jiménez, and D. Boer. Economic performance optimization of an absorption cooling system under uncertainty. Applied Thermal Engineering, 29:3491-3500, 2009. M. Türkay and I. E. Grossmann. Structural flow sheet optimization with complex investment cost functions. Computers & Chemical Engineering, 22:673-686, 1998. A. Brooke, D. Kendrik, A. Meeraus, R. Raman, and R. E. Rosenthal. GAMS - A User's Guide. GAMS Development Corporation, Washington, 1998.

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