Thermoeconomic evaluation of the feasibility of highly efficient combined cycle power plants

Energy 29 (2004) 1963–1982 www.elsevier.com/locate/energy

Thermoeconomic evaluation of the feasibility of highly efficient combined cycle power plants Alessandro Franco
, Claudio Casarosa Dipartimento di Energetica ‘‘L.Poggi’’, University of Pisa, Via Diotisalvi, 2-56126 Pisa, Italy

Abstract The paper proposes an analysis of the feasibility of highly efficient combined plants. The aim of the paper is to discuss and analyze different strategies for the increase of the efficiency of the combined cycle power plants with respect to those usually proposed in the literature. Resorting to the optimization of the components, joined with the use of regeneration and postcombustion (reheat) in the topping cycle it is shown how the combined plant efficiency can rise well over the actually well known limit of 60%. The possibility of obtaining such a high efficiency value is confirmed also by the proposed thermoeconomic optimization, based on the minimization of the total cost of the plant per unit power, obtained referring to a common economic basis the cost of the exergy losses and the costs of the components. The feasibility of obtaining combined plant with efficiency higher than 62%, simply by best fitting the available technology and without waiting for meaningful technological improvement of the gas turbines, is demonstrated. # 2004 Elsevier Ltd. All rights reserved.

1. Introduction The combined cycle power plants actually represent the most effective energy conversion technology and the favourite option chosen to satisfy the growing electric energy demand all over the world. All major gas turbine (GT) manufacturing companies offer last generation combined plants of power 250–400 MW, with efficiency claimed up to 58–59% and the purpose of the most part of the world manufacturers is to reach in short times thermal efficiencies of 60%. This value is very high indeed but remains quite far from the Carnot factor, that is, of about 0.8 conv sidering a turbine inlet temperature (TIT) of 1250 C, typical of the F series GT. In spite of such a high efficiency value just available today, innovative cycles can be proposed to approach the aforesaid Carnot level, and also to obtain similar efficiency at a smaller scale.


Corresponding author. Tel.: +39-050-2217154, fax: +39-050-2217160. E-mail address: [email protected] (A. Franco).

0360-5442/$ - see front matter # 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2004.03.047

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Nomenclature specific heat of the exhaust gas at Ta (J/kg K) cpa D economic life of the plant (years) H number of working hours of the plant in a year I exergy losses (W) K cost (4) annual cost (4) K0 specific cost of HRSG sections in Eq. 6 (4/m2) kj specific cost of the exergy losses (4/kW h) kI specific cost of the regenerator section (4/m2) kR dimensionless cost K

dimensionless cost for unit power KW m mass flow of the water stream (kg/s) mass flow of the gas stream (kg/s) Mg p pressure (bar) PP pinch point (K) RW ratio between gas turbine and steam turbine power S heat exchange surface (m2) T temperature (K) inlet temperature of water to HRSG (K) Tlin environmental temperature (K) Ta inlet temperature of the gas to HRSG (REG) Tgin thermal power (W) Wth W power (W) Wtot total output power of the combined plant (W) b ¼ pmax =pmin total pressure ratio bint ¼ pmax =pint intermediate compression pressure ratio k ¼ pint =pmin intermediate expansion pressure ratio g efficiency l ratio between the total plant input thermal power and the gas cycle input thermal power defined by Eq. (1) Pedices, acronyms and abbreviations B Brayton cycle CC combined cycle comp of the components e economizer g of the gas G, GT gas turbine HE heat exchanger HP, IP, LP high (H), intermediate (I), low (L) pressure

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HRSG heat recovery steam generator in inlet I intercooling P postcombustion or reheat R,REG regeneration, regenerator rh reheater sh superheater S,ST steam turbine TMD thermodynamic TME thermoeconomic v evaporator 2PRSH two pressure levels with reheat HRSG 3PRSH three pressure levels with reheat HRSG

Notwithstanding the efforts of the major part of the manufacturers are dedicated to the increase of the TIT (or firing temperature), it is possible to approach the level of 60% of efficiency just by best fitting and optimizing the components available in the existing technology [1,2]. A thermodynamic analysis of the combined cycle reveals that though if the largest exergy losses occur in the combustion chamber, a process responsible for exergy losses is the heat transfer between exhaust gas and water stream that occur in the heat recovery steam generator (HRSG). In order to provide the reduction of the exergy losses in the HRSG, a recovery with more than one pressure level is used. It is a generally accepted idea that the recovery would be performed with a two or three pressure levels HRSG. The optimization of the HRSG operating parameters permits a not meaningless increase of the combined plant efficiency [2]. Regarding the GT technology, considerable investments in material research are aimed at increasing the firing temperature and the isentropic efficiency, which are the major constraints on the increase of the GT efficiency. An increase of the efficiency of the combined plants to values of 60%, with the new ‘G’ and ‘H’ technology turbines, characterized by an increase of the TIT that leads one to arrive at valv ues of about 1450–1500 C, is considered a result achievable by 2010. But research and development work, carried out by GT manufacturers and research centers, offers various ways of improving cycle performance. A critical review of advanced GT cycles for power generation has been recently given in [3,4], while a comprehensive thermodynamic and economic analysis of combined cycles is contained in [5]. An interesting perspective of increasing the efficiency can be achieved joining reheat, intercooling and regeneration with the aforementioned HRSG optimization, without waiting for different technologies in the GT cooling systems and firing temperature increase. It is yet reasonable to think that the development of such ideas will get, in more short times, to obtain efficiencies of the combined plant higher than 60%, as shown by the authors, with limitation to a thermodynamic analysis, in a previous paper [1].

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After those preliminary remarks, the objective of the present paper is to revise the perspectives for increasing the efficiency available using different configurations of the combined plant and to propose a method for a thermoeconomic optimization of these plants, in order to investigate the feasibility of the proposed new highly efficient combined plant configurations. All this maintaining the use of water as fluid for the bottom cycle and referring to an usual TIT v value of 1200–1250 C, typical of the actual F series GTs. 2. Thermodynamic analysis of a combined cycle plant A thermodynamic analysis of the combined plants reveals that the unconditional increase of the GT firing temperature, maintaining the use of water as bottoming cycle, determines a shift from the ideal thermodynamic conditions, represented by the Carnot factor, even if increase of the efficiency of the whole plant can be obtained, the results are not proportional to the efforts. The analysis of the performance of a combined cycle plant can be carried out defining the ratio between the total input thermal power of the plant and the input thermal power of the gas cycle l¼

Wth Wth;G

(1)

The first law efficiency of the combined plant gCC, assuming lower heating value as commonly used in the market of combined cycles and the output power ratio, RW, can be both expressed as a function of the efficiency of the GT gG, of the steam turbine (ST), gS and of the HRSG, gHRSG so that gCC ¼

Wtot gG þ gS ½gHRSG ð1  gG Þ þ ðl  1Þ ¼ l Wth

(2)

RW ¼

WG gG ¼ WS gS ½gHRSG ð1  gG Þ þ ðl  1Þ

(3)

It is simple to show that the maximum efficiency is obtained when l ¼ 1. So, from a thermodynamic point of view, it is correct to introduce all the chemical energy of fuel in the top cycle and the introduction of heat in the bottom cycle (refiring), after the discharge from the GT, can be justified only from an economic point of view, when cheap fuels and fuels with a lower calorific value as biomass are used. For a fixed steam cycle efficiency, the GT efficiency would be the maximum and vice versa. It must be considered a general strategy to perform not only an increase of the GT efficiency but also the contemporary increase of the steam plant efficiency. Fig. 1 shows the convenience of equally increasing gas and steam cycle efficiency, when it is possible to obtain an increase of the combined cycle efficiency. Moreover, basing on Eq. (3), the rule that power ratio between GT and ST is 2:1, exactly applied in the actual plants, seems convenient if both the efficiency of GT and ST cycle approach 40%. But it must be questioned if the gas cycle efficiency grows to higher values. In these cases, the combined plant would result with a higher power ratio, as obtained by Eq. (3).

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Fig. 1. Combined cycle plant efficiency and power ratio as a function of gas and steam cycle efficiencies (gHRSG ¼ 0:9, l ¼ 1).

3. Combined plant efficiency increase based on the HRSG and steam cycle optimization The technology of the combined plants leads to the use of GT with outlet temperatures (corv responding to the HRSG inlet temperature) higher than 580 C (853 K) and in particular cases v (ABB GT24 and GT26) of 640 and 647 C (913 and 920 K) [6]. The key element for increasing the output power of the steam cycle, seems to be an increase of the inlet temperature of the exhaust gas to the HRSG and this agrees well with the increase of the firing temperature. Excluding the opportunity of increasing the GT firing temperature and pursuing the aim of optimizing the use of the available technology, a first important step in order to increase the combined cycle efficiency states in the optimization of the HRSG and of the bottoming cycle. A thermodynamic optimization of the HRSG yielding the minimization of exergy losses due to the

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temperature difference between hot and cold streams [7] leads to a systematic use of sections with two or more water streams, exchanging with the exhaust gas stream, limited in the existing plants to the superheater sections, and to the approach of the upper steam temperature to the critical value (647 K) [8]. This approach to the critical condition that is not found in the existing plants, where satuv rated steam stays below 160 bar and 350 C, [9], joined with the use of sections with two parallel water streams, seems to be a key element for each further increase of the efficiency of the combined plant. But using these particular HRSG configurations with two or three pressure levels with reheaters, it can be observed that the efficiency of the steam bottom cycle does not meaningfully increase, due to technological constraint on the ST isentropic efficiency, if the inlet temperature to the HRSG superates a certain values (Fig. 2). So an upper limit for the HRSG inlet temperature can be assumed, where its increase over such value leads to a not meaningful increase of the steam cycle efficiency. The existence of an upper limit is confirmed by the analysis of the total exergy losses in the HRSG comparing those due to steam expansion and the residual steam exergy at the exit of the ST with those due to heat transfer [2]. If water is the fluid used in the bottom cycle, and isentropic efficiency of the ST is assumed to be of the order of 0.9 and a two and three pressure levels HRSG with reheater (2PRSH and 3PRSH) are used for the recovery, when the inlet temperature of the exhaust gas to the HRSG approaches 820–830 K, the exergy losses become lower than those due to steam expansion in the turbine. So, this last temperature can be considered as upper limit for the gas entering the HRSG. For higher temperatures, no reduction of the whole exergy losses is possible. However, it seems a general result that by joining an optimized Brayton cycle and an optimized 3PRSH HRSG it is possible to approach a thermodynamic efficiency of 60%. This result can be modified considering a themoeconomic optimization. The thermoeconomic optimization, as discussed in [2], has been carried out with the objective of minimizing the total

Fig. 2. Steam cycle efficiency as a function of the inlet temperature (case of 3PRSH HRSG).

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annual cost of the HRSG, obtained as sum of the costs of exergy losses in the component plus the costs of the heat exchange sections: 0 KHRSG ¼ KI0 þ

KHRSG D

(4)

KI0 ¼ kI HlHRSG

(5)

where kI is the cost of the exergy losses. The cost of HRSG has been considered as the sum of the cost of the single heat exchange sections. This is in general a complex function depending mainly on pressure and temperature and can be considered proportional to the heat exchange surface. Based on a real costs analysis, referred in [2], it has been established that the dependence of the cost of the HRSG sections on the surface S is linear. Distinguishing for the HRSG four different kinds of heat exchange section (economizers, evaporators, reheaters, superheaters), the total HRSG cost can be expressed as X X X X KHRSG ¼ ke Se þ k v Sv þ ksh Ssh þ krh Srh (6) e

v

sh

rh

where kj are the specific costs of the HRSG sections. Thermodynamic and thermoeconomic optimization carried out on the 2PRSH and 3PRSH HRSG used in two commercial combined plants, indicated in Table 1 as (P1) and (P2), confirms the possibility to obtain interesting Table 1 Operating parameters of HRSG configurations and relative plant efficiencies after thermodynamic (TMD) and thermoeconomic (TME) optimization

HP

IP

LP

RH

WG (MW) WS (MW) WCC (MW) gCC

p (bar) Tsh (K) m (kg/s) PP (K) p (bar) m (kg/s) PP (K) p (bar) Tsh (K) m (kg/s) PP (K) p (bar) Trh (K) PP (K)

P1 (2PRSH)

P2 (3PRSH)

Tgin HRSG ¼ 920 K Mg ¼ 386:7 kg=s

Tgin HRSG ¼ 852 K Mg ¼ 653:1 kg=s

Real

TMD

TME

Real

TMD

TME

164 836 58.9 n.a. – – – 6.9 593 11.4 n.a. 38.2 835 58.9 183 97.0 280.0 57.6

220 829 67.3 4.6 – – – 1.6 sat. 4.53 0 69.7 829 67.3 183 106.4 289.4 59.5

220 820 68.0 5.3 – – – 2.2 403 4.10 0.3 73.2 820 68.0 183 105.9 288.9 59.4

117 813 65.7 n.a. 15.2 22.1 n.a. 3.7 615 8.92 n.a 14.6 813 82.9 249 131 380 57.1

217 852 79.8 0 17.4 3.96 0 1.2 503 14.3 0 17.4 852 83.8 249 150 399 59.9

216 835 76.4 14.6 28.2 8.22 8.5 2.2 504 16.3 4.2 28.2 835 84.6 249 146 395 59.5

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increase of the efficiency, only working on HRSG and bottoming cycle [2,8]. Using a realistic cost structure the thermoeconomic optimization allows an increase of the power output of about 9% for the 2PRSH steam plant (P1) and of 11–12% for the 3PRSH steam plant (P2), with respect to the real applications. Thus, the efficiency of the plants increases from 57.6% to 59.4% in the former case (B þ 2PRSH) and from 57.1% to 59.5% in the latter one (B þ 3PRSH) [2]. Table 1 provides the optimized operating parameters of the two HRSG in comparison with those of the real applications, both in the case of a thermodynamic optimization (TMD) and for the thermoeconomic optimization (TME). As a consequence of this last optimization, the output of the steam cycle and of the whole combined plant increases by 9 MW (on a total of 280 MW) and by 15 MW (on a total of 380 MW), respectively. It is remarkable that HRSG optimization, as described in [2], remains a basic element for each further increase of the efficiency. Moreover, it appears evident that the efficiency of 60% is an ideal limit that cannot be reached for both the analyzed GT (the thermodynamic optimization gives in both the cases a limit of the efficiency lower than 60%), as can be pointed out considering the results of the thermodynamic optimization in Table 1.

4. Thermodynamic optimization of advanced combined cycle configurations It has been previously shown that with the optimization of the HRSG and of the bottom cycle, with the GT of available technology, the level of 60% for the plant efficiency seems to be a limit and further increase are possible, without expecting for advanced technology, only modifying the gas cycle, so changing the point of view, previously discussed, of increasing equally the two efficiencies. Joining some ideas available in the technology, together with the optimization of the HRSG previously exposed, it is possible to get an increase in the performances of the combined plants without awaiting meaningful improvements in the GTs technology and the increase of the TIT. Interesting modifications of the cycle include recuperation, reheat and intercooling [10]. It is well known that efficiency can be raised when recuperation of the enthalpy of the exhaust gas is applied, joined with intercooling, diminishing the work of compression, as in the 21 MW WR21 GT [11]. In the major part of the GTs used for the combined plants the temperature of the turbine exhaust gas is higher with respect to that required by the HRSG optimization. Some of the GTs on the market used for combined plants schedule the presence of a postcombustion (reheat) and their outlet temperatures is higher than 900 K (e.g. model ABB GT24-26). Those GT models, like the ABB GT24, had no particular market success, but propose an interesting idea. With these GTs concepts, a joined use of HRSG and of the regenerator can be an interesting strategy to perform the increase of the efficiency of the whole combined plant. Strictly speaking, in the combined cycle it is convenient to join the HRSG with gas to gas recuperation v when the GT exhaust temperature is sufficiently higher than 550 C (823 K), temperature for which the steam cycle efficiency can be sufficiently high (about 38%). So the temperature ‘‘surplus’’ of the exhaust gas at the discharge from the GT can be used in a gas to gas regenerator to increase the efficiency of the Brayton cycle. It must be observed that the feasibility of gas to gas recuperation is due to the fact that the regenerators are rather simple to be constructed and the surfaces are not particularly high,

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because inside the exhaust gas that leaves the turbine at temperature of 900–1000 K is processed, to heat the air after compression (at temperature of 500–600 K) of an amount of the order of 100–200 K. So these regenerators are exchangers, of gas–gas type, operating under high temperature drop. The exhaust gas can be used for regeneration till the upper limit temperature necessary for the optimization of the HRSG (820–850 K). Then the exhaust gas can be used in the HRSG to transfer its residual enthalpy to water streams. The whole plant is so composed by the following four main elements: – GT based on a optimized Brayton cycle, with the possibility of involving one reheat and one intercooling. – Regenerator for the GT recuperation. – Optimized 3PRSH HRSG structure, with operating parameters independently optimized as a function of the inlet gas temperature (the values of 650, 673, 700, 725, 750, 773, 800, 823, 850, 873, 900 and 920 K are considered as discrete values for the inlet gas temperature to the HRSG). – High and low pressure STs. In particular, three configurations have been considered and for them an optimization can be performed: 1. Brayton cycle, gas to gas recuperation and optimized HRSG (B R þ 3PRSH). 2. Brayton cycle, postcombustion, recuperation and optimized HRSG (B P R þ 3PRSH). 3. Brayton cycle, intercooling, postcombustion, regeneration and optimized HRSG (B I P R þ 3PRSH). In the following calculations results are obtained for the various analyzed configurations joining a GT with a thermodynamic optimized HRSG with null pinch points, assuming the following parameters: TIT: 1500 K; maximum pressure: 30 bar; isentropic efficiency of compressor: 87%; isentropic efficiency of GT: 88%; pressure loss of the gas flow in the recuperator: 5%; minimal temperature drop in the recuperator: 40 K; isentropic efficiency of ST: 90%; reference mass gas flow: 386.7 kg/s; maximum temperature of the inlet gas to the regenerator: 1100 K. The method carried out to perform the thermodynamic optimization is not a rigorous mathematical one, but it corresponds to a quasi-optimum design strategy. The objective function of the thermodynamic optimization is represented by the maximization of the efficiency with the constraint of the reference mass gas flow, characteristic of a commercial GT on which is based a combined plant with power output of 280 MW size [4]. The constraint on the mass gas flow

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permits to maintain the power output of the plant in a range in the proximity of 280 MW in order to obtain, in each case, optimized plants of similar size. In the next paragraphs a detailed analysis of the three available solutions is summarized. 4.1. Brayton cycle with gas to gas recuperation and optimized HRSG The first strategy to obtain an increase of the combined cycle efficiency is to join an optimized HRSG structure with the gas to gas recuperation (regeneration) in the Brayton cycle. In this case the number of independent variables of the optimum design process are two: – the pressure ratio b; – the inlet temperature of the gas to the HRSG. Fig. 3 provides the results of the thermodynamic optimization of this plant structure obtained varying the pressure ratio and the inlet temperature to the HRSG. In each case, for a given inlet temperature to the HRSG an 3PRSH optimized structure, obtained as shown in [2], is used. In this case the best performances can be obtained operating with a pressure ratio in the range between 8 and 15. Moreover, it is possible to see that, for each pressure ratio the maximum of the efficiency can be obtained in two different ways; in the first case with a low temperature drop in the regenerator and high inlet temperature to the HRSG; in the second case operating with a more remarkable temperature drop in the regenerator. To better clarify, the first maximum is relative to a value of the inlet temperature to the HRSG of about 800–820 K (limited temperature drop in the regenerator and large heat recovery). The second maximum is relative to an inlet temperature to the HRSG of 650–670 K (high temperature drop in the regenerator and limited heat recovery). In both the cases it is possible to obtain an increase of the whole plant efficiency of 1.5% in comparison with the Brayton cycle without regeneration but with an optimized HRSG structure. It is interesting to underline that for pressure ratios

Fig. 3. Efficiency of the B R þ 3PRSH plant configuration as a function of the inlet gas temperature to HRSG for different values of the gas turbine pressure ratio b.

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higher than 20, the regenerator does not influence the GT efficiency because the output temperature of the compressor is similar to the output temperature of the GT. 4.2. Brayton cycle with postcombustion, gas to gas recuperation and optimized HRSG An opportunity to furtherly increase the efficiency of the combined cycle plant can be obtained by joining the concept of gas to gas recuperation and postcombustion, with an optimized HRSG structure, obtaining the schemes of Fig. 4. The postcombustion or reheat has been already applied in the actual GT technology, in the ABB GT24/26 series turbine but starting from a quite high pressure ratio (30:1). In this case the number of independent variables of the optimum design process is 3 and it is possible to select: – the pressure ratio b; – the intermediate expansion pressure ratio k; – the inlet temperature of the gas to the HRSG. Optimizing the pressure ratio and the intermediate pressure in the gas cycle, it is possible to obtain an increase of about 7–8% with respect to the classical arrangement of the combined cycle. At the end, resorting to a Brayton cycle with postcombustion, regeneration and an optimized 3PRSH HRSG, it seems possible to obtain for the combined plant, a thermodynamic efficiency up to 65%. All this for a pressure ratio of 20–26, limiting the TIT at 1500 K, available for ‘‘D’’ and ‘‘F’’ technology GTs. Table 2 provides the results for an B P R þ 3PRSH plant with a limit on the inlet temperature to regenerator fixed at 1100 K, while Table 3 reports results relative to an inlet temperatures in the regenerators not limited at 1100 K, allowing the possibility of further increases in the efficiency. To maintain the inlet temperature of the exhaust

Fig. 4. Scheme of a Brayton cycle with postcombustion, gas to gas recuperation and three pressure level HRSG (B P R þ 3PRSH).

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Table 2 Thermodynamic opitmization of a B P R þ 3PRSH HRSG (with T gin REG < 1100 K) b

k

Tgin

18 20 22 24 26 28 30

3.8 4.2 4.6 5.0 5.5 5.9 6.3

1098 1097 1096 1095 1099 1098 1097

R

(K)

Tgin HRSG (K)

gCC

WCC (MW)

RW

773 773 800 800 823 850 850

0.646 0.649 0.649 0.651 0.652 0.648 0.649

254.6 256.9 266.1 267.2 274.8 281.6 281.6

2.81 2.85 2.58 2.59 2.38 2.21 2.21

Table 3 Thermodynamic optimization of a B P R þ 3PRSH HRSG (pressure ratio b ¼ 30) without a limit on Tgin b

k

Tgin

30 30 30 30

5 6 8 10

1084 1124 1198 1258

R

(K)

Tgin

HRSG

(K)

823 823 823 823

gCC

WCC (MW)

RW

0.649 0.653 0.658 0.660

273.5 272.4 267.5 261.0

2.37 2.35 2.29 2.21

REG

gas to the regenerator under 1100 K permits the use of regenerators of conventional technology v of stainless steel, that has an upper temperature capability of 820 C. Nickel-based superalloys v v allow operation at 850 C, while advanced materials permit temperatures of 950 C and higher, [12,13], so that the solution proposed in the last two rows of Table 3, with a thermodynamic efficiency higher than 65% are also available. Considering the results of Tables 2 and 3 it must be remarked that all the optimized solutions correspond to values of the power ratio RW higher than 2. 4.3. Brayton cycle with intercooling, postcombustion, regenerator and optimized HRSG This one is the more complex configuration for the combined plant even if it represents the most promising method to further increase the plant efficiency. Schemes with two compression steps and one intercooler have been analyzed. The number of independent variables of the optimization is four. Among the design variables the independent are: – – – –

the the the the

pressure ratio b; intermediate compression pressure ratio bint; intermediate expansion pressure ratio k; inlet temperature of the gas to the HRSG.

The thermodynamic optimization shows that with intercooling it is possible to further increase the plant efficiency or to obtain efficiencies similar to those proposed in Tables 2 and 3 but with a higher specific work. Only to show the perspectives of this kind of plant configuration, the results relative to two cases, reported in Tables 4 and 5 are considered.

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Table 4 Combined cycle with a modified ABB GT24 (case 1) with intercooling, regeneration and optimized 3PRSH HRSG k

bint

Tgin

2.8 2.8 2.8 2.8 2.8

3 5 5.47 6 8

920 920 920 920 920

R

(K)

Tgin

HRSG

(K)

850 850 850 850 850

gCC

WCC (MW)

RW

0.648 0.649 0.649 0.648 0.645

316.6 323.7 323.0 322.8 321.4

2.61 2.69 2.68 2.68 2.66

Table 5 Combined cycle with a modified ABB GT24 (case 2) with intercooling, regeneration and optimized 3PRSH HRSG k

bint

Tgin

2.8 2.8 2.8 2.8 2.8

5.47 5.47 5.47 5.47 5.47

920 920 920 920 920

R

(K)

Tgin 750 700 673 650 625

HRSG

(K)

gCC

WCC (MW)

RW

0.654 0.663 0.669 0.674 0.682

294.5 282.7 276.7 271.6 267.0

3.96 4.95 5.67 6.45 7.40

Table 4 provides results relative to the use of a GT with a pressure ratio equal to 30 and discharge gas temperature of 920 K (like the model ABB GT24) with intercooling, limiting the regeneration to a temperature drop of 70 K on the gas side. The results of Table 5 are relative to a modified ABB GT24 GT with intercooling, without imposing a constraint on the temperature drop in the regeneration process. The configuration examined is characterized by a predominant heat recovery (Table 4—case 1), or by a predominant regeneration (Table 5—case 2), as can be seen by RW values. While in the first case an efficiency similar to that obtained with the case of Section 4.2, in the second case a remarkable increase of the efficiency can be obtained, even if the result of the contribution of the steam plant to the whole output power of the plant is very low (the ratio RW varies from 4 to 7) and an unusual plant configuration results. 5. Thermoeconomic optimization of the advanced combined cycle configurations In paragraph 4 it has been shown how it is possible to obtain high efficient combined plants associating HRSG optimization with regeneration and postcombustion. The efficiency increase can vary between 2%, by resorting only to HRSG optimization and 6–7%, with the combined use of postcombustion, regeneration and HRSG optimization, defining an upper limit to the plant efficiency values of 64–65%. Higher efficiencies (68%) are available with intercooling, even if this last solution appears to be not technically available and economically convenient like the previous one with postcombustion and regeneration and will not be considered in the following thermoeconomic analysis. The main results of the analysis are reported in Fig. 5, which provides efficiencies and power outputs for three different complex optimized configurations in comparison with the basic one (B þ 3PRSH).

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Fig. 5. Comparison among the various optimized combined cycle plant configurations (1: B þ 3PRSH; 2: B R þ 3PRSH; 3: B P R þ 3PRSH; 4: B I P R þ HRSG).

In order to furnish a more realistic evaluation on the opportunity of an improvement of a combined cycle, an analysis of the plant configuration that considers also economic elements must be carried out. On the same line of the strategy defined for the optimization of the HRSG operating parameters recalled in paragraph 3, an optimization strategy that permits to combine energy saving and economic costs, using some of the most important ideas of the ‘‘Thermoeconomics’’ from a different point of view can be proposed. The resulting optimization strategy is a sequential optimization, because it is structured to search, in successive steps, two different solutions for a given configuration of the power plant. The first one is a pure thermodynamic optimization, the second step is the modification of the thermodynamic solution, integrating economical factor. In this way it is possible to evaluate the difference between the two different solutions, which is obviously dependent on the weight of the economic elements. In particular, thermodynamic optimization of the whole plant can be based on the minimization of the exergy loss, while the objective function of the thermoeconomic optimization, in analogy with the strategy considered for the thermoeconomic optimization of the HRSG, [2], is the total cost of the combined plant, that results as the sum of two terms: KCC ¼ KI þ Kcomp

(7)

where KI is the cost of the exergy losses, while Kcomp is the economic cost of the components of the plant, related to their purchase, installation and maintenance. So the total cost of the combined plant is equal to the sum of the costs of the exergy losses plus the operative costs of each component considering GT, regenerator, HRSG and ST. This approach can be considered a possible alternative to the classical ‘‘Thermoeconomic’’ analysis, well defined in [14,15] for what concerns two of the most important alternatives.

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The real difference of this approach from the others present in the literature is that the inefficiencies of all the components are not considered on the basis of an economic value where they take place, but according to a fixed cost. So the cost of the exergy losses can be considered independent from the part of the plant where they occur. Obviously, the cost of the exergy losses, that is the key element of this approach can range between the cost of natural gas (input fuel) and the selling price of electric energy. In particular, in the last case (cost of the exergy losses equal to the selling price of energy), the basic idea of the method is that a higher plant efficiency (lower exergy losses) corresponds to a higher gain in electric power production and the selling price of energy is higher (till to 3–4 times) than the fuel cost. Anyway, the final result is that the optimal thermoeconomic solution is shifted towards optimal thermodynamic less than the analogous solutions obtained with a classical exergoeconomic analysis. In the next paragraph and example of the application of this method to the configuration previously examined in paragraph 4.2 is proposed. 5.1. The objective function for the thermoeconomic optimization of the Brayton cycle with postcombustion, gas to gas recuperation and optimized HRSG The objective function of the thermoeconomic optimization is the minimization of the operative cost of the plant, with a constraint on the total output power of the plant or alternatively the minimization of the cost of the plant for unit output power. The operative cost of the plant is defined as sum of the cost of the exergy loss plus the cost of the components (GT, ST, heat exchangers sections, like HRSG and regenerator): 0 0 KCC ¼ KI0 þ KHE þ KG0 þ KS0

(8)

The first term can be calculated using an expression analogous to that of Eq. (5) where the total exergy losses of the plant are considered. Important is the selection of the term kI, which is the cost of the exergy losses. On this coefficient depends the weight attributed to the thermodynamic efficiency (and so to the energy saving) with respect to the investment. For what concerns the groups GT and ST, their annual cost, after a market analysis, referred to 80–300 MW range, can be expressed by means of a quadratic law, as  00 2  0 kG WG þ kG WG þ kG 0 KG ¼ þ km;G WG H (9) D  00 2  kS WS þ kS0 WS þ kS 0 þ km;S WS H (10) KS ¼ D where the first coefficients k00 are both negative and km,G and km,S are the maintenance cost of the GT and ST groups, respectively. On the other hand, the total cost of the heat exchangers, KHE is equal to the cost of the regenerator KR plus those of the HRSG, KHRSG, given by Eq. (6): 0 KHE ¼

KHE kR SR þ KHRSG ¼ D D

(11)

Considering the whole combined plant objective function, which has to be minimized, is the total cost of the plant, obtained as sum of the cost of the exergy losses and the costs of GT, ST,

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HRSG and regenerator. In dimensionless terms, the total cost is given by K
¼

0 KCC kI Mg cpa Ta H

(12)

or referred to the unit output power of the plant
¼ K
=Wtot KW

(13)

The optimized thermoeconomic solution is the plant with the operating parameters that permits to minimize the cost defined by Eq. (13). The result of the thermodynamic optimization can be used as the starting point for the thermoeconomic optimization. The design variables described in paragraph 4.2 are joined to the economic variables related to the gas and ST, to the heat exchanger sections (in this case average values of the heat transfer coefficients are considered) and to the exergy losses. The result of the optimum design process has been obtained with an iterative step by step procedure. 5.2. Results of thermoeconomic optimization The thermoeconomic optimization determines some differences in the results with respect to those obtained with the thermodynamic optimization. An effect of the thermoeconomic optimization is the shift of the optimum towards more limited structures of the HRSG and finite pinch point values, as well as of the regenerator. Second, the thermoeconomic optimization gives different GT configurations. In this paragraph some of the results obtained with the optimization are referred. These results have been obtained with the cost structure of Table 6. A cost of the exergy losses kI ¼ 0:077 4=kW h, coincident with an average value of the selling price of the electric energy in Italy, has been fixed, while the maintenance costs km,G and km,S are considered equal for simplicity. As economic life of the plant D, the value of 10 years is used while the reference environmental temperature Ta is 293 K. The selection of a cost structure is fundamental in order to modify the results of the thermodynamic optimization and the difference introduced by the thermoeconomic optimization strongly depends on it. The position of attributing to the cost of the exergy losses equal to the selling price of electrical energy leads obviously to favour the energy saving. Figs. 6 and 7 report the results of the thermoeconomic optimization in terms of efficiency and cost of the plant per unit output power as a function of the pressure ratio, for the combined plant with postcombustion, regeneration and triple pressure level HRSG (B P R þ 3PRSH HRSG configuration). The absolute optimum of the efficiency is obtained with a pressure ratio

Table 6 Cost structure used for the thermoeconomic optimization 0 kG (4/kW)

00 kG kS (4) (4/kW2)

kS0 (4/kW)

kS00 km,G,S kv ke ksh krh kR (4/kW2) (4/kW h) (4/m2) (4/m2) (4/m2) (4/m2) (4/m2)

kI (4/kW h)

kG (4)

0.077

9:22 106 1:8 105 0.0026 4:61 106 8:9 104 0.0014 0.05

39.66

51.56

71.39

63.46

63.46

A. Franco, C. Casarosa / Energy 29 (2004) 1963–1982

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Fig. 6. Efficiency of the thermoeconomic optimum for different values of the pressure ratio (B P R þ 3PRSH configuration).

of about 22, lower than those obtained with the thermodynamic optimization that is 26. Table 7 shows a comparison between the operating parameters of the plant obtained with the thermodynamic optimization and the modifications determined by the thermoeconomic optimization. Among the various results it can be observed that the maximum efficiency shifts from 65.2%, obtained with the thermodynamic optimization to 62.5%. The total output power of the optimized plant is reduced from 274.8 MW, obtained for the thermodynamic optimization, to

Fig. 7. Minimum dimensionless costs for unit power as a function of the pressure ratio (B P R þ 3PRSH configuration).

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Table 7 Comparison between the results of thermodynamic (TMD) and thermoeconomic (TME) optimization for the configuration B P R þ 3PRSH HRSG

gCC gG WCC (MW) WG (MW) WS (MW) b k TginHRSG (K) HP p (bar) Tsh (K) m (kg/s) IP p (bar) Tsh (K) m (kg/s) LP p (bar) Tsh (K) m (kg/s) REG TginR (K)

TMD Opt. B P R þ 3PRSH

TME Opt. B P R þ 3PRSH

65.2 45.8 274.8 193.5 81.3 26 5.5 900

62.5 41.7 263.2 163.7 99.5 22 7.7 900

220 822 45.6

220 887 51.5

16.8 647 1.2

20.1 509 4.2

1.05 423 9.1

1.05 422 8.2

1099

1100

263.2 MW, characteristic of the solution of the thermoeconomic optimization. The trend of the output power of the plant configuration relative to the optimized thermoeconomic solution varies, with the pressure ratio b, as described in Fig. 8. The results obtained with the previously defined cost structure, fully described in [16], represent only a possible example of application of the procedure previously described but gives some interesting suggestions for a practical design of the plant, combining thermodynamic and economic aspects. The minimization of the function given by Eq. (8) can be extended to consider also the effect of the advances in the technology of the components. In this case a cost structure similar to that proposed in [17] can be used, where the dependence on some technological elements as the pressure ratio, the isentropic efficiency of compressor and turbine and the firing temperature can be considered as design variables. Moreover, it is possible to make a few remarks on the thermoeconomic analysis. – As the thermodynamic optimum corresponds to infinite surfaces of the HRSG and a variable GT pressure ratio, the thermoeconomic one is a compromise between high thermodynamic efficiency and reduced heat exchange surface of the HRSG as well as of the regenerator. – The thermoeconomic optimum is obtained with lower pressure ratio (b ¼ 22) than the thermodynamic one (b ¼ 26), corresponding to a lower temperature of the gas after compression.

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Fig. 8. Output power of the plant relative to the optimized solution (B P R þ 3PRSH configuration).

– The thermoeconomic optimum corresponds to lower GT efficiency, higher steam cycle power output (99.5 MW) and lower total output (263.2 MW) with respect to that of the thermodynamic optimum (81.5 and 274.8 MW, respectively). – The thermoeconomic optimum is obtained with large use of regeneration. The regenerator inlet temperature in the case of the optimized solution is 1100 K (upper limit imposed as constraint), while the HRSG inlet temperature is in the proximity of 900 K.

6. Conclusions The paper analyzes a series of available strategies promising in order to reach the objective of increasing in a meaningful way the efficiency of the combined power plants together with methods to perform a thermoeconomic optimization. The conclusions of the present study can be summarized in the following statements: 1. Thermoeconomic optimization of the HRSG with systematic use of sections with parallel water stream allows obtaining efficiency of the basic combined cycle configurations close to 60% with an increase of 1.5–2%. But the break of the barrier of 60% seems to be not possible resorting to the actually available GT technology. 2. The actual temperature of the turbine exhaust gas is higher with respect to the temperature required to perform an HRSG optimization so that a joined use of HRSG and regenerator can be considered an interesting perspective in order to obtain a meaningful increase of efficiency.

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3. Thermodynamic optimization involving the use of postcombustion, regeneration and optimized HRSG permits to obtain, resorting to the actually available GT technology, an efficiency of 65%, that can be extended up to the 68% with intercooling. 4. The thermoeconomic optimization, carried out assuming that the total cost of the combined plant is equal to the sum of the costs related to the exergy losses plus the costs of each component, shifts the results of thermodynamic optimization but confirms the possibility of conceiving combined plants with an efficiency well higher than 60%, without requiring further advancement in the GT technology, but simply resorting to an optimization of the conventional components, like the HRSG and accepting the idea of modifying the classical structure of the combined cycle plant. References [1] Franco A, Casarosa C. On some perspectives for increasing the efficiency of combined cycle power plants. Applied Thermal Engineering 2002;22(13):1501–18. [2] Casarosa C, Donatini F, Franco A. Thermoeconomic optimization of the HRSG operative parameters for combined plants. Proceedings of ECOS 2001 Conference, vol. II, Istanbul. 2001, p. 80–13. [3] Heppenstall T. Advanced gas turbine cycles for power generation: a critical review. Applied Thermal Engineering 1998;18:837–46. [4] Korobitsyn MA. New and advanced energy conversion technologies. PhD thesis. Enschede, The Netherlands: University of Twente-Enschede, 1998. [5] Horlock JH. Combined power plants—past, present, and future. ASME Journal of Engineering for Gas Turbines and Power 1995;117:608–16. [6] Schultz R, Bachmann R. KA24-1CST—market success for a standardized power plant. Report M489, ABB, 1999. [7] Kotas TJ. The exergy method of thermal plant analysis. London: Butterworths; 1985. [8] Casarosa C, Franco A. Thermodynamic optimisation of the operative parameters for the heat recovery in combined plants. International Journal of Applied Thermodynamics 2001;4(1):43–52. [9] Deschamps PJ. Advanced combined cycle alternatives with the latest gas turbines. ASME Journal of Engineering for Gas Turbines and Power 1998;120:350–7. [10] McDonald CF. Heat exchanger ubiquity in advanced gas turbines cycles, IGTI, vol. 9. Proceedings of the ASME Cogen Turbo Power ‘94, Portland, Oregon. 1994, p. 681–703. [11] Weiler C, Broadbelt A, Law B. WR-21 design and maintenance. ASME Paper 96-GT-328, ASME Turbo Expo ‘96, Birmingham, England, 1996. [12] Klara JM, Izsak MS, Wherley M. Advanced power generation: the potential of indirectly-fired combined cycles. ASME Paper 95-GT-261, ASME Turbo Expo ‘95, Houston, Texas, 1995. [13] Solomon P, Serio M, Cosgrove J, Zhao Y, Buggeln R, Shamroth S. Coal-fired heat exchanger for an externally fired gas turbines. ASME Journal of Engineering for Gas Turbines and Power 1996;118:22–31. [14] Bejan A, Tsatsaronis G, Moran M. Thermal design and optimization. New York: John Wiley and Sons; 1996. [15] Valero A, Lozano MA. An introduction of thermoeconomics. Developments in the design of thermal systems. Cambridge (UK): Cambridge University Press; 1997, p. 203–23. [16] Giannini N. Thermoeconomic criteria for combined cycle plants design. Master thesis, Pisa, Italy: University of Pisa, Engineering Faculty, 2001 [in Italian]. [17] Valero A, Lozano MA, Serra L, Tsatsaronis G, Pisa J, Frangopoulos Ch, et al. CGAM problem: definition and conventional solution. Energy 1994;19:279–86.