Property values and thermal, and mechanical exergy flows and entropy production rates at various state points in the gasturbine power plant at 100% load condition.
Abstract
Exergy costing to estimate the unit cost of products from various power plants and refrigeration system is discussed based on modifiedproductive structure analysis (MOPSA) method. MOPSA method provides explicit equations from which quick estimation of the unit cost of products produced in various power plants is possible. The unit cost of electricity generated by the gasturbine power plant is proportional to the fuel cost and inversely proportional to the exergetic efficiency of the plant and is affected by the ratio of the monetary flow rate of nonfuel items to the monetary flow rate of fuel. On the other hand, the unit cost of electricity from the organic Rankine cycle power plant with heat source as fuel is proportional to the unit cost of heat and the ratio of the monetary flow rate of nonfuel items to the generated electric power, independently. For refrigeration system, the unit cost of heat is proportional to the consumed electricity and inversely proportional to the coefficient of performance of the system, and is affected by the ratio of the monetary flow rate of nonfuel items to the monetary flow rate of consumed electricity.
Keywords
 exergy
 thermoeconomics
 unit exergy cost
 power plant
 refrigeration system
1. Introduction
Exergy analysis is an effective tool to accurately predict the thermodynamic performance of any energy system and the efficiency of the system components and to quantify the entropy generation of the components [1, 2, 3]. By this way, the location of irreversibilities in the system is determined. Furthermore, thermoeconomic analysis provides an opportunity to estimate the unit cost of products such as electricity and/or steam from thermal systems [4, 5] and quantifies monetary loss due to irreversibility for the components in the system [6]. Also, thermoeconomic analysis provides a tool for optimum design and operation of complex thermal systems such as cogeneration power plant [7] and efficient integration of new and renewable energy systems [8]. Recently, performance evaluation of various plants such as sugar plant [9], drying plant [10], and geothermal plant [11] has been done using exergy and thermoeconomic analyses. In this chapter, a procedure to obtain the unit cost of products from the power plants and refrigeration system is presented by using modifiedproductive structure analysis (MOPSA) method. The power plants considered in this chapter are gasturbine power plant and organic Rankine cycle power plant. These systems generate electricity as a product by consuming the heat resultant from combustion of fuel and by obtaining heat from any hot stream as fuel, respectively. In addition, MOPSA method is applied to an aircooled air conditioning system, which removes heat like a product while the consumed electricity is considered as fuel. Explicit equations to estimate the unit cost of electricity generated by the gasturbine power plant and organic Rankine cycle plant, and the unit cost of heat for the refrigeration system are obtained and the results are presented.
2. A thermoeconomic method: modified productive structure analysis (MOPSA)
2.1. Exergybalance and cost balance equations
A general exergybalance equation that can be applied to any component of thermal systems may be formulated by utilizing the first and second law of thermodynamics [12]. Including the exergy losses due to heat transfer through the nonadiabatic components, and with decomposing the material stream into thermal and mechanical exergy streams, the general exergybalance equation may be written as [6]
The fourth term in Eq. (1) is called the negentropy which represents the negative value of the rate of lost work due to entropy generation, which can be obtained from the second law of thermodynamics. The term
However, the quantity
Exergy, which is the ability to produce work, can be defined as the differences between the states of a stream or matter at any given particular temperature and pressure and the state of the same stream at a reference state. The exergy stream per unit mass is calculated by the following equation:
where T is temperature, P is pressure, and the subscript ref denotes reference values. The exergy stream per unit mass can be divided into its thermal (T) and mechanical (P) components as follows [3]:
and
Assigning a unit exergy cost to every exergy stream, the costbalance equation corresponding to the exergybalance equation for any component in a thermal system [13] may be written as
The term
2.2. Levelized cost of system components
All costs due to owning and operating a plant depend on the type of financing, the required capital, the expected life of components, and the operating hours of the system. The annualized (levelized) cost method of Moran [1] was used to estimate the capital cost of components in this study. The amortization cost for a particular plant component is given by
The present worth of the component is converted to annualized cost by using the capital recovery factor CRF(i, n):
The capital cost rate of the kth component of the thermal system can be obtained by dividing the levelized cost by annual operating hours δ.
The maintenance cost is taken into consideration through the factor
3. Gasturbine power plant
A schematic of a 300 MW gasturbine power plant considered in this chapter is shown in Figure 1. The system includes five components: air compressor (1), combustor (2), gas turbines (3), fuel preheater (5), and fuel injector (6). A typical mass flow rate of fuel to the combustor at full load condition is 8.75 kg/s and the air–fuel mass ratio is about 50.0. Thermal and mechanical exergy flow rates and entropy flow rate at various state points shown in Figure 1 are presented in Table 1. These flow rates were calculated based on the values of measured properties such as pressure, temperature, and mass flow rate at various state points.
3.1. Exergybalance equation for gasturbine power plant
The following exergybalance equations can be obtained by applying the general exergybalance equation given in Eq. (1) to each component in the gasturbine power plant.
Air compressor
Combustor
Turbine
Fuel preheater
Steam injector
Boundary
The net flow rates of the various exergies crossing the boundary of each component in the gasturbine power plant at 100% load condition are shown in Table 2. Positives values of exergies indicate the exergy flow rate of “products,” while negative values represent the exergy flow rate of “resources” or “fuel.” The irreversibility rate due to entropy production in each component acts as a product in the exergybalance equation. The sum of exergy flow rates of products and resources equals to zero for each component and the overall system; this zero sum indicates that perfect exergy balances are satisfied.
States 






1  862.722  0.103  15.000  0.000  −0.558  0.121 
2  862.722  1.025  323.589  88.176  164.572  0.193 
23  862.722  1.025  323.589  88.176  164.572  0.193 
24  891.056  1.025  1130.775  702.452  173.550  1.201 
25  891.056  1.025  1130.775  702.452  173.550  1.201 
26  891.056  0.107  592.700  261.996  2.661  1.262 
51  17.500  0.103  15.000  0.000  0.018  0.001 
52  17.500  0.103  185.000  1.563  0.018  0.018 
53  17.500  0.103  185.000  1.563  0.018  0.018 
54  17.500  1.025  415.314  7.735  5.337  0.021 
55  17.500  1.025  415.314  7.735  5.337  0.021 
63  10.833  0.103  (1.000)  6.064  0.000  0.004 
64  10.833  1.025  418.176  12.338  0.010  0.006 
65  10.883  1.025  418.176  12.338  0.010  0.006 
221  11.111  3.540  220.100  2.417  0.038  0.028 
222  11.111  3.540  72.941  0.239  0.038  0.011 
Component  Net exergy flow rates (MW)  Irreversibility rate (MW)  






Compressor  −274.04  0.00  88.18  165.13  20.73 
Combustor  0.00  −881.22  594.20  3.63  283.39 
Gas turbine  593.74  0.00  −440.46  −170.89  17.61 
Fuel preheater  0.00  0.00  −0.61  0.00  0.61 
Steam injector  −18.68  0.00  11.91  5.33  1.44 
Boundary  0.00  0.00  −253.22  −3.20  
Total  301.02  −881.22  253.22  3.20  323.78 
3.2. Costbalance equation for gasturbine power system
When the costbalance equation is applied to a component, a new unit cost must be assigned to the component’s principle product, whose unit cost is expressed as Gothic letter. After a unit cost is assigned to the principal product of each component, the costbalance equations corresponding to the exergybalance equations are as follows:
Air compressor
Combustor
Turbine
Fuel preheater
Steam injector
Applying the general costbalance equation to the system components, five costbalance equations are derived. However, these equations present eight unknown unit exergy costs, which are C_{T}, C_{S}, C_{W}, C_{1P}, C_{2T}, C_{P}, C_{5T}, and C_{6P}. To calculate the value of these unknown unit exergy costs, three more costbalance equations are required. These additional equations can be obtained from the thermal and mechanical junctions and boundary of the plant.
Thermal exergy junction
Mechanical exergy junction
Boundary
In Table 3, initial investments, the annuities including the maintenance cost, and the corresponding monetary flow rates for each component are given. The cost flow rates corresponding to a component’s exergy flow rates at 100% load condition are given in Table 4. The same sign convention for the cost flow rates related to products and resources was used as the case of exergy balances shown in Table 2. The lost cost due to the entropy production in a component is consumed cost. The fact that the sum of the cost flow rates of each component in the plant becomes zero, as verified in Table 4, shows that all the cost balances for the components are satisfied.
Component  Initial investment cost (US$10^{6}) 
Annualized cost (×US$10^{3}/year) 
Monetary flow rate (US$/h) 

Compressor  36.976  4744.997  628.712 
Combustor  2.169  278.340  36.880 
Gas turbine  29.213  3748.799  496.716 
Fuel preheater  7.487  960.780  127.303 
Steam injector  14.787  1897.562  251.427 
Total  90.542  11,630.478  1531.038 
Component 







Compressor  −17732.47  0.00  4217.91  15,071.00  −927.63  −628.71 
Combustor  0.00  −15861.96  28238.85  341.28  −12681.19  −36.88 
Gas turbine  38419.49  0.00  −21068.79  −16066.19  −787.79  −496.72 
Fuel preheater  0.00  0.00  154.92  0.00  −27.52  −127.30 
Steam injector  −1208.41  0.00  569.65  954.76  −64.44  −251.43 
Boundary  0.00  0.00  −12112.54  −300.85  14488.57  −2075.18 
Total  19478.61  −15861.96  0.00  0.00  0.00  −3616.22 
The overall costbalance equation for the power system is simply obtained by summing Eqs. (17)–(24).
From the above equation, the unit cost of electricity for the gasturbine power system is given as [1]
The production cost depends on fuel cost and the exergetic efficiency of the system, and is affected by the ratio of the monetary flow rate of nonfuel items to the monetary flow rate of fuel. With the unit cost of fuel, C_{o} = 5.0 $/GJ, an exergetic efficiency of the gasturbine power plant, 0.341, and a value of the ratio of the monetary flow rate of nonfuel items to the monetary flow rate of fuel, 0.22, the unit cost of electricity estimated from Eq. (26) is approximately 17.97 $/GJ. However, one should solve Eqs. (17)–(24) simultaneously to obtain the unit cost of electricity and the lost cost flow rate occurred in each component.
4. Organic Rankine cycle power plant using heat as fuel
A schematic of the 20kW ocean thermal energy conversion (OTEC) plant [20] operated by organic Rankine cycle, which is considered to apply MOPSA method, is illustrated in Figure 2. Five main components exist in the system: the evaporator (1), turbine (2), condenser (3), receiver tank (4) and pump (5). The refrigerant stream is heated by a heat source in the evaporator, and then the refrigerant stream is divided into two streams. A portion of this stream is passed through the throttling valve and reaches the receiver tank, while the remaining part of the refrigerant stream leaving from evaporator is sent to turbine. A portion of the stream flowing to turbine is throttled and bypassed to turbine outlet. The “pipes” are introduced into the analysis as a component to consider the heat and pressure losses in the pipes and the exergy removal during the throttling processes. Refrigerant of R32 is used as a working fluid in the organic Rankine cycle. At the full load condition, the mass flow rate of the refrigerant is 3.62 kg/s. The warm sea water having mass flow rate of 86.99 kg/s is used as a heat source for the plant, while the cold sea water having mass flow rate of 44.85 kg/s is used as a heat sink for the plant. The reference temperature and pressure for the refrigerant R32 are −40°C and 177.60 kPa, respectively. For water, the reference point was taken as 0.01°C, the triple point of water.
4.1. Exergybalance equations for the organic Rankine cycle power plant
The exergybalance equations obtained using Eq. (1) for each component in the organic Rankine cycle plant shown in Figure 2 are as follows.
Evaporator
Turbine
Condenser
Receiver tank
Pump
Pipes
Boundary
The α term given in Eq. (32) is the ratio of the bypass streams from state 103 to 108. The value of the α term can be calculated by applying the mass and energy conservation equations to the receiver tank. The stream bypassed from state 103 to 105 may be neglected. An example of exergy calculation for the organic Rankine cycle plant using a stream of warm water at 28°C as a heat source to the evaporator [20] is shown in Table 5. As mentioned in the previous section, a positive value of exergy flow rate represents “product,” while a negative value of exergy flow rate indicates “fuel.” The last two columns clearly indicate that the electricity comes from expenditure of heat input.
Component  Refrigerant  Water stream  Irreversibility rate  Heat transfer rate  Work input/output rate 

Evaporator  224.59  −233.21  17.52  −8.90  — 
Turbine  −24.24  —  3.31  0.83  20.10 
Condenser  −178.00  171.26  5.22  1.51  — 
Receiver tank  −2.52  —  −11.68  14.20  — 
Pump  1.50  —  1.69  −0.15  −3.04 
Pipes  −21.33  —  20.31  1.02  — 
Boundary  —  61.95  −36.36  −25.58  — 
Total  0.00  0.00  0.00  −17.06  17.06 
4.2. Costbalance equations for the organic Rankine cycle power plant
By assigning a unit cost to every thermal exergy of the refrigerant stream (C_{1T}, C_{2T}, C_{3T}, and C_{T}), mechanical exergy for the refrigerant stream (C_{P}), cold water (C_{3}), negentropy (C_{s}), and electricity (C_{W}), the costbalance equations corresponding to the exergybalance equations which are Eqs. (27)–(33) are given as follows. When the costbalance equation is applied to a specific component, one may assign a unit cost to its main product, which is represented by a Gothic letter.
Evaporator
Turbine
Condenser
Receiver tank
Pump
Pipes
Boundary
Seven costbalance equations for the five components of the plant, pipes, and the boundary were derived with eight unknown unit exergy costs of C_{1T}, C_{2T}, C_{3T}, C_{T}, C_{P}, C_{3}, C_{S}, and C_{W}. We can obtain an additional costbalance equation for the junction of thermal exergy of the refrigerant stream.
Thermal junction
With Eq. (41), we have all the necessary costbalance equations to calculate the unit cost of all exergies (C_{1T}, C_{2T}, C_{3T}, C_{T}, and C_{3}, negentropy (C_{s}) and a product (electricity, C_{W}) by input (given) of thermal energy (C_{2}) to the evaporator. The overall costbalance equation for the Rankine power plant can be obtained by summing Eqs. (34)–(41), which is given by
where
where
Figure 3 shows that the unit cost of electricity from the organic Rankine cycle plant and the net cost flow rate due to the heat transfer rate to the plant vary depending on the unit cost of warm water in the evaporator, C_{2}, appeared in Eq. (34). As the unit cost of warm water increases, the net cost flow rate due to heat transfer to the plant decreases while the unit cost of electricity increases. The cross point between the line for the unit cost of electricity and the line for the total cost flow rate due to heat transfer determines unit cost of electricity. The unit cost of electricity and the net cost flow rate due to heat transfer for a case whose detailed calculation results shown in Table 6 are $0.205 and −$0.941/kWh, respectively. The value of the unit cost C_{2} appeared in the cost balance equation, Eq. (34), is approximately $0.117/kWh for this particular case, which may be considered as a fictional one.
Component 









Evaporator  27.502  −0.026  0.967  −0.491  —  −27.285  —  −0.666 
Turbine  −3.101  −0.613  0.183  0.046  4.126  —  —  −0.640 
Condenser  −23.569  −0.004  0.288  0.084  —  —  23.867  −0.666 
Receiver tank  0.021  0.012  −0.645  0.784  —  —  —  −0.172 
Pump  0.079  0.678  0.093  −0.008  −0.624  —  —  −0.218 
Pipes  −0.932  −0.048  1.121  0.056  —  —  —  −0.198 
Boundary  —  —  −2.006  −1.412  —  27.285  −23.867  — 
Total  −0.000  0.000  −0.000  −0.941  3.502  —  —  −2.561 
Detailed calculation results reveal that the unit cost of electricity from an organic Rankine cycle plant can be obtained from the following equation:
From Eqs. (43) and (44), one can deduce that
The calculated value of
5. 200 kW aircooled air conditioning unit
Even though the performance evaluation of a household refrigerator using thermoeconomics was performed [21], estimation of the unit cost of heat supplied to the room by air conditioning unit was never tried. In this section, the unit cost of heat for a 120kW aircooled air conditioning unit is obtained, which is helpful for the cost comparison between air conditioning unit operated by electricity and absorption refrigeration system running by heat [22].
5.1. Exergybalance equations for the air conditioning units
The exergybalance equations obtained using Eq. (1) for each component in an aircooled air conditioning units shown in Figure 4 are as follows. The heat transfer interactions with environment for the compressor, TXV, and suction line are neglected.
Compressor
Condenser
TXV
Evaporator
Suction line
Superscripts
In Eqs. (47) and (49), the difference in the exergy and entropy for air stream is just the difference in the enthalpy so that these terms can be written with help of Eq. (2) as
The deposition of heat into the environment and the heat transferred to room are hardly considered to be dissipated to the environment. For such heat delivery system, it may be reasonable that the delivered heat rather than its exergy is contained in the exergybalance equation. With help of Eqs. (51) and (52), the exergybalance equation for the condenser and evaporator become
The terms,
The simulated data for the difference in the thermal and mechanical exergy flow rates at each component under normal operation for a 120kW aircooled air conditioning system [24] is displayed in Table 7. The cooling capacity of the system (
Component 






Compressor  0.18  22.85  −32.10  9.07  
Condenser  −8.95  −0.09  (−88.92)  (88.92) 9.04 

TXV  18.29  −21.97  3.68  
Evaporator  −9.52  −0.66  (121.02)  (−121.02) 10.18 

Suction line  −0.13  0.13  
Total  0.0  0.0  32.10  −32.10  0.0 
5.2. Costbalance equations for the aircooled air conditioning units
By assigning a unit cost to every thermal and mechanical exergy stream of the refrigerant (C_{T}, C_{P}), lost work (C_{S}), heat (C_{H}), and work (C_{W}), the costbalance equations corresponding to the exergybalance equations, i.e., Eqs. (46), (47’), (48), (49’), and (50), are as follows. In this particular thermal system, a unit to a principal product for each component is not applied because the working fluid that flows through all the components makes a thermodynamic cycle.
Compressor
Condenser
TXV
Evaporator
Suction line
We now have five costbalance equations to calculate two unit costs of exergies (C_{T} and C_{P}), negentropy (C_{S}), and a product, heat (C_{H}) by input of electricity (C_{W}). So, it is better to combine the costbalance equation for the evaporator and suction line, which can be written as
The overall costbalance equation for the air conditioning units can be obtained by summing Eqs. (53)–(55) and (58);
Table 8 lists the initial investment, the annuities including the maintenance cost, and the corresponding monetary flow rates for each component of the aircooled air conditioning system. Currently, the installation cost of an aircooled air conditioning system with a 120kW cooling capacity is approximately $17,000 in Korea. The levelized cost of the air conditioning units was calculated to be 0.3122$/h with an expected life of 20 years, an interest rate of 5% and salvage value of $850. The operating hours of the air conditioning system, which is crucial in determining the levelized cost, were taken as 4500 h. The maintenance cost was taken as 5% of the annual levelized cost of the system.
Component  Initial investment ($)  Annualized cost ($/year)  Monetary flow rate ($/h) 

Compressor  5000  393.4  0.0918 
Condenser  4000  314.8  0.0735 
TXV  2000  157.4  0.0367 
Evaporator + Suction line  6000  472.1  0.1102 
Total  17,000  1337.7  0.3122 
The cost flow rates of various exergies and irreversibility rate at each component in the air conditioning system at the normal operation are shown in Table 9. The sign convention for the cost flow rates is that minus and plus signs indicate the resource and product cost flow rates, respectively. Erroneously, reverse sign convention was used in their study on the thermoeconomic analysis of groundsource heat pump systems [25]. The lost cost flow rate due to the entropy generation appears as consumed cost in the evaporator; on the other hand, it appears as production cost in other components. The unit cost of heat delivered to the room or the unit cost of the cooling capacity is estimated to be 0.0344$/kWh by solving the four costbalance equations given from Eqs. (53) to (59) with unit cost of electricity of 0.120 $/kWh. The unit cost of thermal and mechanical exergies and the irreversibility are C_{T} = 0.1948, C_{P} = 0.1636, and C_{S} = 0.0187 $/kWh at the normal operation. It is noted that the unit cost of heat C_{H} can be obtained from Eq. (60) directly with known values of C_{W}, COP (β) and the ratio of the monetary flow rate of nonfuel items to the monetary flow rate of input (electricity). Table 9 confirms that costbalance balance is satisfied for all components and the overall system.
Component 







Compressor  0.03506  3.73914  −3.8520  0.16960  −0.09180  
Condenser  −1.74352  −0.01473  1.83175  −0.07350  
TXV  3.56302  −3.59513  0.06881  −0.03670  
Evaporator+ Suction line  −1.85456  −0.12928  4.16420  −2.07016  −0.11020  
Total  0.0  0.0  4.16420  −3.8520  0.0  −0.3122 
Rewriting Eq. (59), we have [25]
where β is the COP of the air conditioning units. Equation (60) provides the unit cost of cooling capacity as 0.0344 $/kWh with a unit cost of electricity of 0.120 $/kWh, β of 3.77, and a value of 0.081 for the ratio of the monetary flow rate of nonfuel items to the monetary flow rate of consumed electricity.
6. Conclusions
Explicit equations to obtain the unit cost of products from gasturbine power plant and organic Rankin cycle plant operating by heat source as fuel and the unit cost heat for refrigeration system using the modifiedproductive structure analysis (MOPSA) method were obtained. MOPSA method provides two basic equations for exergycosting method: one is a general exergybalance equation and the other is costbalance equation, which can be applicable to any components in power plant or refrigeration system. Exergybalance equations can be obtained for each component and junction. The costbalance equation corresponding to the exergybalance equation can be obtained by assigning a unit cost to the principal product of each component. The overall exergycosting equation to estimate the unit cost of product from the power plant and refrigeration system is obtained by summing up all the costbalance equations for each component, junctions, and boundary of the system. However, one should solve the costbalance equations for the components, junctions, and system boundary simultaneously to obtain the lost cost flow rate due to the entropy generation in each component. It should be noted that the lost work rate due to the entropy generation plays as “product” in the exergybalance of the component, while the lost cost flow rate plays as “consumed resources” in the costbalance equation. This concept is very important in the research area of thermoeconomic diagnosis [18, 26, 27, 28].
Nomenclature
C  unit cost of exergy ($/kJ) 
Ci  initial investment cost ($) 
CH  unit cost of heat ($/kWh) 
Co  unit cost of fuel ($/kWh) 
CS  unit cost of lost work due to the entropy generation ($/kWh) 
CW  unit cost of electricity ($/kWh) 
C ̇  monetary flow rate ($/h) 
COP  coefficient of performance 
CRF  capital recovery factor 
ex  exergy per mass 
E ̇ x  exergy flow rate (kW) 
h  enthalpy per mass 
H ̇  enthalpy flow rate (kW) 
i  interest rate 
I ̇  irreversibility rate (kW) 
m ̇  mass flow rate 
PW  amortization cost 
PWF(i,n)  present worth factor 
Q ̇ cv  heat transfer rate (kW) 
S ̇  entropy flow rate (kW/K) 
Sn  salvage value (KRW) 
To  ambient temperature (°C) 
W ̇ cv  work production rate (kW) 
Z ̇ k  capital cost flow rate of unit k ($/h) 
β  coefficient of performance 
δ  operating hours 
ηe  exergy efficiency 
ϕ k  maintenance factor of unit k 
a  air stream 
comp  compressor 
con  condenser 
env  environment 
evap  evaporator 
H  heat 
k  kth component 
r  refrigerant stream 
ref.  reference condition 
room  room 
s  entropy 
sl  suction line 
W  work or electricity 
a  air stream 
CHE  chemical exergy 
H  heat 
P  mechanical exergy 
r  refrigerant stream 
T  thermal exergy 
W  work or electricity 
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