A New Thermoeconomic Methodology for Energy Systems,
D. J., Energy, 2010. 35. 410–422.
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Thermoeconomics, or exergoeconomics, can be classified into the three fields: cost allocation, cost optimization, and cost analysis. In this study, a new thermoeconomic methodology for energy systems is proposed in the three fields. The proposed methodology is very simple and clear. That is, the number of the proposed equation is only one in each field, and it is developed with a wonergy newly introduced in this paper. The wonergy is defined as an energy that can equally evaluate the worth of each product. Any energy, including enthalpy or exergy, can be applied to the wonergy and be evaluated by this equation. In order to confirm its validity, the CGAM problem and various cogenerations were analyzed. Seven sorts of energy, including enthalpy and exergy, were applied for cost allocation. Enthalpy, exergy, and profit were applied for cost optimization. Enthalpy and exergy were applied for cost analysis. Exergy is generally recognized as the most reasonable criterion in exergoeconomics. By the proposed methodology, however, exergy is the most reasonable in cost allocation and cost analysis, and all of exergy, enthalpy, and profit are reasonable in cost optimization. Therefore, we conclude that various forms of wonergy should be applied to the analysis of thermoeconomics.
Keywords: Thermoeconomics; Exergoeconomics;
Exergy; Optimization; CGAM; Power Plant
Thermoeconomics, or exergoeconomics, is a technique for analyzing the cost flow of energy through a combination of the second law of thermodynamics and economic principles. This can be classified into three fields: cost allocation, cost optimization, and cost analysis.
The objective of cost allocation is to estimate each unit cost of the product and divide the overall input cost flow into each production cost flow. This technique is especially important in cogeneration or CHP producing electricity and heat at the same time, which is needed for the determination of sale price, the calculation of profit and loss, and the economic evaluation of each product. The objective of optimization is to minimize the input cost flow of the overall system and maximize the output cost flow of the products under the given constraints. Using this technique, a system designer can determine the optimal operating conditions of the energy system. The objective of cost analysis is to find the cost formation process and calculate the amount of cost flow for each state, each component, and the overall system. This information can be useful for evaluating each component and improving the cost flow of targeted components.
Many thermal engineers have studied thermoeconomics or exergoeconomics, and various methodologies have been suggested. As representative methods introduced in a review paper  on exergoeconomics, there is the theory of the exergetic cost (TEC) [2,3], the theory of exergetic cost-disaggregating methodology (TECD) [2,4], thermoeconomic functional analysis (TFA) [5-7], intelligent functional approach (IFA) [8,9], last-in-first-out principle (LIFO) , specific exergy costing/average cost approach (SPECO/AVCO) [11-14], modified productive structure analysis (MOPSA) [15-17], engineering functional analysis (EFA) [18,19], and the structural theory of thermoeconomics (STT) . The main feature of the above methods is that they propose a cost balance equation applying the exergetic unit cost to the exergy balance equation according to a specific principle. However, there is a disadvantage in that it is not easy to apply these methodologies to actual systems and solve thermoeconomic problems, because too many equations are needed.
On the other hand, various alternative methodologies in the cost allocation of cogeneration or CHP have also been suggested in the field of accounting. As representative methodologies introduced in the technical paper of The World Bank , there is the energy method, the proportional method, the work method, the equal distribution method, and the benefit distribution method. These alternative methodologies have the advantage that the equation of cost allocation is very simple. However, there is a disadvantage in that they analyze not the actual system but an alternative system.
The aim of this paper is to propose a new methodology in the fields of cost allocation, cost optimization, and cost analysis. It is the main characteristic that various indexes or energies can be easily applied to the proposed methodology. This methodology is termed the wonergy method. In this methodology, various energies, including enthalpy and exergy, can be integrated with ¡°wonergy¡±, a portmanteau of ¡°worth¡± and ¡°energy¡±. Here, wonergy is defined as an energy that can equally evaluate the worth of each product, and worth is not an absolute number but a relative concept. That is, this means that there is no right answer in the thermoeconomics. In order for the proposed methodology to be compared with the conventional exergetic methodologies, the CGAM problem [22,23] was applied in this study.
2. CGAM problem
The name of the CGAM is derived from the initials of a group of concerned specialists (C. Frangopoulos, G. Tsatsaronis, A. Valero, and M. von Spakovsky) in the field of exergoeconomics who decided to compare their methodologies by solving a predefined and simple problem of optimization. The results of thermoeconomics by each methodology can be compared from the CGAM problem.
The CGAM system in Fig. 1 consists of an air compressor (AC), an air pre-heater (APH), a combustion chamber (CC), a gas turbine (GT), and a heat recovery steam generator (HRSG), which produces 30 MW of electrical power and 14 kg/s of saturated steam at 20 bar as a fixed condition. In the HRSG, the minimum temperature difference of the pinch point is given as 1.64 ¡É, and the minimum outlet temperature of the flue gas is given as 105 ¡É. The components of the environment and a fuel injector are used in the proposed methodology, since they are newly added in Fig. 1.
Fig. 1. Flow diagram of
the CGAM cogeneration system.
In the CGAM problem,the decision variables are the compressor pressure ratio , the isentropic efficiencies of the compressor and turbine , and the temperatures at theoutlet of the preheater and combustion chamber . All the other thermodynamicvariables can be calculated as the functions of the decision variables, and the function of capital cost flow for each component is expressed in terms ofthe thermodynamic variables. All the detailed equations and variables can be found in the definition of the CGAM problem [22,23].
In the CGAM problem, the values of =10, =0.86, =0.86, =850 K, and =1520 K are given as thestate before optimization. The values of mass flow rate, temperature, pressure, enthalpy, and exergy, which are calculated from the functions of decision variables, are shown in Table 1. The pinch point temperature difference is calculated as 67.39 oC in the state before optimization.
The energy balance equation for the k-th component and the overall system can be rearranged as follows:
where and are the amount of electricity and heat as the finalproducts, is the amount of heat input of fuel, is the difference of the enthalpy flow rate at the stream that inputs the energy to another stream, is the difference of the enthalpy flow rate at the stream that outputs the energy from another stream, and is the lost heat into the environment.
In Eqs. (1)-(2), the heat product must be calculated as thedifference of the outlet enthalpy and inlet enthalpy, and the other terms must be calculated as the difference of the inlet enthalpy and outlet enthalpy. The values of each term in Eqs. (1)-(2) are calculated in Table 2.
The exergy balance
equation for the k-th component and the overall system can be rearranged as follows:
where and are the amount of electricity and steam exergy as the final products, is the amount of exergy input of fuel, is the difference of the exergy flow rate at the stream that inputs the exergy to another stream, is the difference of the exergy flow rate at the stream that outputs the exergy from another stream, and is the lost exergy (exergy destruction or exergy loss).
In Eqs. (3)-(4), the heat product must be calculated as the difference of the outlet exergy and inlet exergy, and the other terms must be calculated as the difference of the inlet exergy and outlet exergy. The values of each term in Eqs. (3)-(4) are calculated in Table 3.
As the fixed
conditions, the CGAM system produces 30 MW of electrical power and 14 kg/s of
saturated steam at 20 bar. Therefore, the optimization problem is to minimize
the overall cost flow of fuel and capital. The conventional objective function
is as follows:
where is the objective function, is the heat purchase unit price of fuel, is the mass flow rate of fuel, LHV is the low heating value of fuel, and is the capital cost flow rate of the k-th component. In the CGAM problem, the value of is 4.0 $/GJ and the LHV is 50,000 kJ/kg.
Various numerical analysis techniques or software tools can be used to solve the optimization problem of Eq. (5). In this study, the gradient search technique in numerical analysis was used. In Table 4, the optimized values in this calculation are compared with the optimum values in the definition of the CGAM problem.
The values of fuel, capital, and overall cost flow as a function of the mass flow rate of fuel are illustrated in Fig. 2. In the case that the mass flow rate of fuel is lower than the optimal condition, the capital cost flow in particular rises rapidly due to the increase of the efficiency of each component.
At the optimal conditions, the values of mass flow rate, temperature, pressure, enthalpy, and exergy are shown in Table 5, the values of the energy balance equation are calculated in Table 6, and the values of the exergy balance equation are calculated in Table 7.
The values of the capital cost flow of each component before and after optimizations are calculated in Table 8.
Table 1 Properties before optimization Table 5 Properties after optimization
Table 2 Energy balance before optimization Table 6 Energy balance after
Table 3 Exergy balance before
optimization Table 7 Exergy balance after
Table 4 Optimized values in this calculation (a) and Optimum
values in the definition of CGAM problem (b)
Table 8 Capital cost flow optimization Fig. 2. Fuel, capital, and overall cost flow rates.
new cost allocation methodology
new optimization methodology
The objective functions of the conventional optimization can be expressed as the cost optimization of Eq. (65) and the performance optimization of Eq. (66).
where is the input cost of fuel, is the sum of all capital cost, and is the amount of wonergy output of the i-th product. Applying enthalpy to wonergy, the can be replaced with or , and applying exergy to wonergy, the can be replaced with or .
In the case of cogeneration, the fixed conditions and the optimal objects are the fuel cost flow , the capital cost flow , the amount of electricity , and the amount of heat . Therefore, the optimization problem involves the number of combinations of these terms. In the cost optimization of Eq. (65), the fixed conditions are and , and the optimal objects are and . In the performance optimization of Eq. (66), the fixed conditions are and , and the optimal objects are and . Here, a new optimization equation that can analyze the cost and the performance at the same time is needed.
4.1 Design optimization
Multiplying the both sides of Eq. (7) by the wonergetic unit purchase cost of fuel, the cost balance equation for energy flow is equal to the following:
where is the output cost flow of electricity, is the output cost flow of heat, is the input cost flow of fuel, and is the sum of the lost cost flows for all the components including the environment.
In Eq. (67), both the minimization of and the maximization of and are equal to the minimization of the lost cost flows . Therefore, the objective function for design optimization can be suggested such as follows:
where is the wonergetic overall efficiency, such as or .
In the case that enthalpy is applied to wonergy, is the unit heat purchase price and is the sum of the lost heat at all components, including the environment. In the case that exergy is applied to wonergy, is the unit exergy purchase price and is the sum of lost exergy for all components, including the environment.
In the CGAM problem, it is given that the unit heat purchase price of fuel is 4.0 $/GJ, the low heating value of fuel is 50,000 kJ/kg, and the specific exergy of fuel is 51,850 kJ/kg. Therefore, the unit exergy purchase price of fuel can be calculated by Eq. (69), and this value is 3.857 $/GJ.
If the optimal object is only electricity in cogeneration, the term for the heat cost flow is added in Eq. (68), and the amount of heat product becomes the minimum.
4.2 Profit optimization
From Eq. (68), the minimization of the input cost flows and the maximization of the production amounts can be attained at the same time. This methodology is approached from the viewpoint of system design, where there are the lost cost flows. An optimization methodology approached from the viewpoint of economics is needed, and this methodology can determine the operating conditions creating the maximum profit.
The equation of the profit optimization is as follows:
where is the unit sale price determined by the market, is the amount of the p-th product, and is the input cost flow.
Applying Eq. (70) to a cogeneration system producing electricity and heat , the equation of profit optimization is rearranged as follows:
where is the ratio of the profit obtained from production and sale.
4.3 Results and discussion
The results of the optimization are shown in Table 17. Here, the 9.0 $/GJ of unit electricity sale price and the 3.4 $/GJ of unit heat sale price in a market are applied to each and respectively.
In the case that and are the fixed conditions and the others are the optimal objects, the results of enthalpic, exergetic, and profit optimizations in Table 17 are exactly equal to the results of the conventional optimization in Table 4. In the case of other combinations, each result of optimization is somewhat different. Exergy has been generally recognized as the most reasonable criterion in exergoeconomics. From these results, however, it can be concluded that enthalpy and profit are also reasonable for cost optimization.
In the CGAM problem, the independent variables are , , , , , , , , and . This optimization problem involves the number of combinations of the fixed conditions and the optimal objects for nine variables, and the proposed methodologies can perform the design and profit optimizations of any combination.
Table 17 Results of optimization according to the
combination of the fixed conditions and the optimal objects
5. A new cost analysis methodology
5.1 Cost analysis
In order to find the cost formation process and calculate the amount of cost flow in each state, each component, and the overall system, a methodology that can analyze the cost flow of the system is needed. The proposed methodology is very clear. That is, all the unit costs of state are equal to the unit wonergy purchase price of fuel. This equation is formulated as follows:
The cost flow of the i-th state is calculated by Eq. (73), the cost flow of the k-th component is analyzed by Eq. (74), and the cost flow of the overall system is analyzed by Eq. (75).
Analyzing the cost flow of Eqs. (73)-(75) from the energy balance equation, is the unit heat purchase price of fuel, and analyzing the cost flow of Eqs. (73)-(75) from the exergy balance equation, is the unit exergy purchase price of fuel. In the case of the CGAM problem, is 4.0 $/GJ and is 3.857 $/GJ.
5.2 Results and discussion
At each state of Table 1 or Table 5, the enthalpic cost flow can be calculated from multiplying the term by , and the exergetic cost flow can be calculated from multiplying the term by . For each component and the overall system in Table 2, Table 3, Table 6, and Table 7, the enthalpic and the exergetic cost flows can be calculated by multiplying all the terms by and respectively.
The results of the enthalpic analysis and the exergetic analysis of the cost improvement before and after optimization are shown in Table 18. From these results, the exergetic analysis is more reasonable than the enthalpic analysis.
Table 18 Results of the cost improvement between
before and after optimization
In this study, a new methodology for cost allocation, cost optimization, and cost analysis was proposed. Various forms of energies including exergy can be integrated to wonergy as a new term, and the proposed equations are expressed in terms of wonergy. Cost allocation and profit optimization are the methodologies from the viewpoint of economics, where there are no lost cost flows. Enthalpic optimization, exergetic optimization, and cost analysis are the methodologies from the viewpoint of thermodynamics, where there are lost cost flows.
In the cost allocation, enthalpy, alternative heat, alternative electricity, equal fuel-saving, alternative fuel, compensated fuel, and exergy can be applied to the wonergy. From the results of the analysis for various cogeneration systems, we conclude that the exergy method is the most reasonable.
In the cost optimization, the proposed function can perform the enthalpic, exergetic, and profit optimizations in any combination of the fixed conditions and the optimal objects. The enthalpic and exergetic optimizations can determine the operating conditions with the minimization of the input cost flows and the maximization of the amount of products at the same time, and the profit optimization can determine the operating conditions with the maximization of profit. The profit optimization can be more reasonable, because the purpose of the system installation is to obtain more profit, and this analysis is clearly the right answer for any combination.
In the cost analysis, enthalpy and exergy can be applied to the wonergy, and the exergetic results are reasonable.
The new methodology is very simple and clear. Therefore, the equations and results can be easily compared with those of conventional methodologies. Moreover, the proposed methodology can be applied to any complex energy system including cogeneration. In future work, various complex energy systems will be analyzed and evaluated with this new methodology.
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