The characteristics of ultramodern combined cycle power plants

Energy xxx (2015) 1e15

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The characteristics of ultramodern combined cycle power plants Janusz Kotowicz, Marcin Job*, Mateusz Brze˛ czek Institute of Power Engineering and Turbomachinery, Silesian University of Technology, Konarskiego 18, 44-100 Gliwice, Poland

a r t i c l e i n f o

a b s t r a c t

Article history: Received 12 January 2015 Received in revised form 3 April 2015 Accepted 7 April 2015 Available online xxx

In the paper are presented methods to improve the efficiency of combined cycle power plants. The efficiency increase is sought by the improvement of the gas turbine characteristics and by proposed effective utilization of heat from the turbine cooling air. The calculation methodology in a wide range of compression ratios and temperatures, far beyond currently applied values, with an assumed constant turbine outlet gas temperature, is presented. It is revealed that the efficiency rise without the use of this heat may be achieved only by improving the gas turbine characteristics. By introducing the additional steam cycle, an efficiency growth of 2e3 percentage points is gained, although this results in a corresponding increase in the compression ratio. An economic analysis is performed, which confirms that the presented development direction of gas turbines may be feasible under the condition of maintaining reasonably low gas turbine investment costs. © 2015 Published by Elsevier Ltd.

Keywords: Combined cycle power plant Gas turbine Efficiency Turbine cooling

1. Introduction CCPP (combined cycle power plants) are one of the fastest developing technologies of electricity production, currently achieving efficiencies, based on a LHV (lower heating value), exceeding 60%. The thermal efficiency of combined cycle gas turbine units is defined as the ratio of the internal power NiGT, NiST to the heat supplied to the unit Q_ in .

htCC

N þ NiST ¼ iGT Q_

DhtCC ¼ (1)

in

Using the thermal efficiencies of a gas turbine htGT and a steam cycle htSC, equation (1) can be written as follows:

htCC ¼ htGT þ htSC ð1  htGT Þ htGT ¼

(2)

NiGT Q_

(3)

NiST Q_

(4)

in

htSC ¼

4a

Relationship (2) is presented in graphical form in Fig. 1. The currently achieved thermal efficiency of the gas turbines is

* Corresponding author. Tel.: þ48 32 237 1745. E-mail address: [email protected] (M. Job).

approximately 40% and that of the steam cycle is higher than 35%. Therefore, the left side of vertical axis shows the currently achieved thermal efficiency of the CCPP, whereas the right side presents the potential to increase this efficiency. By differentiation of equation (2), the condition to improve the CCPP efficiency can be easily obtained [1,2]:

vhtCC vh Dh þ tCC Dh vhtGT tGT vhtSC tSC

(5)

Based on equation (5) and using values of htGT ¼ 0.4 and vhtCC htSC ¼ 0.35, the derivatives are determined to be vh y0:65 and tGT vhtCC vhtSC y0:6.

This implies that an increase in gas turbine efficiency

leads to a greater growth of the CCPP efficiency than a corresponding increase in steam cycle efficiency. Moreover, the unit investment cost for the gas turbine installation is 4e5 times lower than for the steam cycle [3e5]. These arguments indicate a preferred direction for CCPP development by improving gas turbine efficiency. The gas turbine thermal efficiency depends primarily on the compressor pressure ratio and the highest temperature in the cycle, which is the COT (combustor outlet temperature). However, due to the significant role of turbine cooling, a more important parameter is thought to be the average TIT (turbine inlet temperature), defined by ISO 2314 [6]. Stoichiometric combustion would be the most effective way to produce power in gas turbines, but under these conditions, the COT would far exceed 2000  C. Most producers currently set the COT to 1500  C. One leading

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Nomenclature a A b B cp c C CEA be Cel CF Cop COT D Eel F h i I J k L LHV m_ N p Q_ r R S St t TIT

t a ab b gc h r m ~

n

z

pressure loss, e

purchase cost factor, e surface area, m2 cooling efficiency parameter, e coefficient of construction costs, e specific heat capacity at constant pressure, kJ/(kg K) unit cost of purchase, V/kW cost of purchase, V price of CO2 emission allowances, V/MgCO2 break-even price of electricity, V/MWh fuel price, V/GJ operation costs, V combustor outlet temperature,  C depreciation charge, V sold electric energy, MWh interest specific enthalpy, kJ/kg unit investment costs, V/kW income tax, V total investment costs, V surface area ratio, e salvage value, % lower heating value, kJ/kg mass flow rate, kg/s power, MW pressure, MPa

Subscripts a air b expander blade c cooling air C compressor CC combined cycle CO additional steam cycle utilizing cooling air el electric f fuel g flue gas G generator GT gas turbine i isentropic, internal in inlet m mechanical max maximum min minimal opt optimal out outlet p polytropic SC steam cycle ST steam turbine t thermal T turbine

heat energy flow, MW discount rate, % individual gas constant, kJ/(kg K) profit, V Stanton number, e temperature,  C number of iteration, e turbine inlet temperature,  C year from project start, e rate of energy flow, e average heat transfer coefficient of the blade, W/(m2 K) pressure ratio, e cooling air mass flow ratio, e efficiency, e density, kg/m3 average isentropic exponent, e velocity, m/s

Acronyms 3 PR triple pressure HRSG with reheating C compressor CAC cooling air cooler CCH combustion chamber CCPP combined cycle power plant CND condenser DEA deaerator F air filter G generator HRSG heat recovery steam generator P pump ST steam turbine T turbine TBC thermal barrier coating

manufacturer introduced a COT equal to 1600  C and is doing research towards the use of 1700  C [7,8]. By comparison, TIT values are in range of 1300e1400  C, and rarely reach 1500  C. Changes of allowable blade temperature and COT in the past sixty years are presented in Fig. 2. These temperatures are limited by the materials used in gas turbines. Elements exposed to the highest temperatures are covered by TBCs (thermal barrier coatings). It is assumed that existing TBCs allow continuous work at a temperature not exceeding 1200  C. Currently used cooling technologies allow the reduction of the flue gas temperature on a cooled surface by Dt ¼ 300e400 K, so the highest temperature (COT) may reach 1500e1600  C. Further increase of COT by another 100e200 K is associated with a corresponding increase of Dt to the range of Dt ¼ 500e600 K. Producers were focused on such operations more than 10 years ago [9,10], but there is no information in the literature about their execution. An article by Satoshi Hada et al. [11] from

Mitsubishi Heavy Industries is an exception, as it indicates that the key to the creation of the J-class turbine with COT ¼ 1600  C (M701J for 50 Hz and M501J for 60 Hz), i.e., 100  C higher than the G-class, was the improvement of cooling technology and the reduction of the thermal conductivity of the TBC. Each allowed raising the COT by 50  C. Data provided there also suggest that cooling technologies allow raising the COT by Dt ¼ 550 K in a G-class turbine, whereas the TBC raised this temperature by 50 K, which in turn enabled using alloys with allowable temperatures of 700e900  C. In the Jclass turbine, the cooling technology raises COT by Dt ¼ 600 K and TBC by 100 K (COT ¼ 900 þ 600 þ 100 ¼ 1600  C). In Japan, there is ongoing research on turbines with COT ¼ 1700  C [12]. There is a number of studies in the field of potential and possible directions of gas turbines development, particularly in terms of work in CCPP, presented in the recent literature. These studies involve modifications in the gas turbine basic structure to evaluate the potential to increase efficiency in full-load [13] and also in

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Table 1 Gas turbine operation parameters.

Fig. 1. Thermal efficiency of the combined cycle as a function of the gas turbine and steam cycle thermal efficiencies.

part-load operation [14]. The turbine blade cooling technology is an object of analyzes presented in Refs. [15,16]. There are also concepts of inlet air cooling [17], intercooling of the air in compressor [18,19] and cooling of the turbine cooling air [19].

2. Gas turbine model The basic assumption for the calculations presented in this article is a constant gas turbine outlet temperature of 630  C. The constant temperature t4a is maintained by the variation of the combustor outlet temperature t3a depending on the compression ratio b. Fig. 3 shows a scheme of the gas turbine. The main parameters of the gas turbine installation are summarized in Table 1. The model of the gas turbine was made using GateCycle™ software from GE Energy. The isentropic efficiencies of the compressor and the turbine are determined on the basis of the compressor polytropic efficiency as a function of b and the turbine polytropic efficiency as a function of b and TIT. Algorithms to calculate the isentropic efficiency characteristics are described in Section 5.

Value

Gas turbine power, NelGT, MW Mechanical efficiency, hm Generator efficiency, hG Gas turbine outlet temperature, t4a,  C Cooling air cooler outlet temperature, t2c,  C Compressor inlet pressure loss (air filter), zin Combustion chamber pressure loss, zCCH Turbine outlet pressure loss (including HRSG), zout

200 0.995 0.985 630 100 0.01 0.045 0.038

The composition and parameters of the ambient air are set in accordance with ISO 2314 (t0a ¼ 15  C, p0a ¼ 101.325 kPa, relative humidity 60%). The gas turbine is fed by natural gas with a purity of 100% CH4, with the temperature and pressure at the combustion chamber inlet equal to 15  C and 3.5 MPa, respectively. The lower heating value of the fuel is LHV ¼ 50.049 MJ/kg (in accordance with to ISO 2314). The turbine outlet gas pressure is based on the outlet pressure loss:

p4a ¼

Fig. 2. Allowable blade temperature and achieved COT in a timeline.

Parameter

p0a 1  zout

(6)

Convective air cooling is applied to the turbine blades in the gas turbine. The cooling air cooler is used to reduce the temperature of the cooling air. The heat from the cooling air is effectively used in the steam cycle. The implemented turbine cooling model results from the heat flow balance in the turbine blading system and is presented in Refs. [15,16]. The heat flow balance between the hot flue gas, the cooled blade and the cooling air is expressed by the relationship:



Q_ ¼ m_ g $cp:g $ tg:in  tg:out ¼ ab $Ab $ tg:in  tb ¼ m_ c $cp:c $ðtc:out  tc:in Þ

(7)

In the convective cooling model, relationship (8) for the flue gas mass flow rate (ṁg), relation (9) for the Stanton number (St) and definition (10) of the cooling efficiency (hc) are applied.

m_ g ¼ Ag $vg $rg

(8)

St ¼

ab cp:g $vg $rg

(9)

hc ¼

tc:out  tc:in tb  tc:in

(10)

Relationship (11), describing the mass flow ratio of cooling air to the flue gas, is obtained using equations (7)e(10).

  m_ c $cp:c k$St tg:in  tb ¼ $ hc tb  tc:in m_ g $cp:g k¼

Ab Ag

(11)

(12)

By introducing parameter b described by equation (13) and rearranging relation (11), equation (14) is obtained, which defines the cooling air flow demand for the turbine stage.

b¼

Fig. 3. Scheme of a gas turbine.

k$St hc

  tg:in  tb cp:g $m_ g $ m_ c ¼ b$ tb  tc:in cp:c

(13)

(14)

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Presented in (14), the specific heat capacities cp.g and cp.c can be obtained from the following equations:

cp:g ¼

hg:in  hg:b tg:in  tb

(15)

cp:c ¼

hc:b  hc:in tb  tc:in

(16)

where hg.b and hc.b are the specific enthalpy of flue gas and cooling air at the turbine blade temperature tb, respectively. Parameter b is associated with the effectiveness of cooling, and for convective air cooling, it is generally around b ¼ 0.1e0.2 [16]. This approach allows determining the cooling air mass flow rate separately for each turbine stage, which is important for turbine analysis over a wide range of COT values. The turbine is composed of four stages, out of which one to even three stages may require cooling, depending on the COT. Important in the analysis is the application of the CAC, which reduces the cooling air temperature to t2c ¼ tc.in ¼ 100  C. This leads to the reduction of the required cooling air mass flow, particularly at high b, when the temperature of the compressed air is very high. However, the reduction of tc.in leads to increased thermal stress in the blades caused by the high temperature difference between its two sides. This solution may therefore significantly reduce the durability of the turbine blades, so the design of a turbine with a cooling air cooler will necessitate solutions to rectify this undesirable effect.

A structure of the unit with the steam part and air cooling heat recovery shown in detail is presented in Fig. 4. The classic steam cycle 3 PR is based on the work of a three-section steam turbine with steam reheating before the intermediate-pressure section. A deaerator is fed by extraction steam from the low-pressure steam turbine section. The deaeration economizer replaces the lowpressure economizer in the HRSG. The high-pressure economizer is divided into two sections. Assumed in the steam part is a condenser pressure of 5 kPa, a deaerator pressure of 200 kPa, a 90% isentropic efficiency of the steam turbine, and a 99% mechanical and generator efficiency. Pressure losses in the steam cycle are 1% in the economizers, 4% in the evaporators, 3% in the superheaters, and 2% at the inlet to subsequent steam turbine sections. The model of steam cycle was made using a GateCycle™ application. Essential for the 3 PR steam cycle analysis is the assumption of constant turbine outlet temperature t4a ¼ 630  C. This allows for the optimization of the steam cycle parameters independently of the pressure ratio in the gas turbine. For the assumptions described above, the steam cycle efficiency is a function of the following HRSG parameters:  Pressures of live steam for each pressure level p3s(Y) (Y ¼ h,i,l, where h e high, i e intermediate, l e low pressure levels),  Temperatures of live steam t3s(Y), or alternatively, temperature differences at the hot ends of the superheaters Dthe(Y) (Y ¼ h,i,l,R),  Pinch point temperature differences in evaporators Dtpp(Y) (Y ¼ h,i,l),  Underheating of water at the economizer outlet Dtap(Y) (Y ¼ h,i,l,D, where D e deaeration economizer).

3. Steam part model The steam part of the power plant consists of a) a classic steam cycle fed through a triple-pressure HRSG (heat recovery steam generator) with reheating (3 PR) and b) an additional steam cycle utilizing the heat from air cooling (CO).

Thus, for the analyzed triple-pressure HRSG with reheating, there are 12 decision variables. Their research ranges in the optimization trial are presented in Table 2. The optimization of the 3 PR steam cycle was performed by means of a genetic algorithm. It is a probabilistic algorithm that imitates the principles of evolution in nature to solve optimization

Fig. 4. Structure of a combined cycle unit with a three-pressure HRSG with reheating ((h) e refers to high, (i) e intermediate, (l) e low pressure level).

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J. Kotowicz et al. / Energy xxx (2015) 1e15 Table 2 Ranges of decision variables in the optimization of the 3 PR steam cycle. Decision variable

Min

Max

p3s(h), MPa p3s(i), MPa p3s(l), MPa t3s(h),  C t3s(i),  C Dthe(i),  C Dtpp(h),  C Dtpp(i),  C Dtpp(l),  C Dtap(h),  C Dtap(i),  C Dtap(D),  C

10.0 1.0 0.3 500 500 5 5 5 5 5 5 10

18.0 5.0 1.0 600 600 20 20 20 20 20 20 50

problems, thereby obtaining high effectiveness in multidimensional tasks. A block scheme of the optimization algorithm is presented in Fig. 5. In the genetic algorithm, a population of solutions PðtÞ ¼ fxt1 ; …; xtn g is generated. Each solution is the set of all decision variables. All solutions are evaluated on the basis of an obtained objective function value. The objective function is the parameter for which an optimal value is sought; in the analyzed case, it is the steam cycle electric power. The solution with the highest value is stored, and a new population of solutions (tþ1 iteration) is then created by treating the current population with the genetic operators of selection, crossing and mutation. The new population is evaluated, and the cycle is repeated. When a new solution with a higher objective function value appears, it replaces the previously saved solution. Operation parameters of the genetic algorithm are listed in Table 3. The genetic operators are applied on the binary code of solutions, forming a binary chain called a chromosome, and single bits are called genes. First, the best solutions are selected by random chance, as the probability of selecting solutions with a higher value is greater, so statistically the next iteration is better than the previous one. Subsequently, random solutions of the new population, based on the crossing probability, are subjected to crossing. This combines the features of parental solutions by

5

Table 3 Operation parameters of the genetic algorithm. Parameter

Value

Population size, n Minimal number of iterations Termination condition e iterations without result improvement, Wt Crossing probability Mutation probability Binary code length of decision variables

20 1000 300 0.250 0.003 10

creating descendants in their place through the exchange of segments of the parents' chromosomes. Mutation is the last step, in which the change of random gene values according to the mutation probability is realized. Optimization results are presented in Section 6. The principles of operation of genetic algorithms are described in detail in Ref. [20]. They are used to solve similar optimization problems, among others, in Refs. [4,5,21,22]. The additional steam cycle CO utilizes the heat from air cooling. Two different structures of the cooling air cooler to utilize the heat, depending on the available temperature level, are analyzed. A basic CAC consisting of three heat exchangers, a deaerative economizer, a low-pressure evaporator and an intermediatepressure evaporator, is proposed for lower compressor pressure ratios. This structure is presented in Fig. 4. Steam part parameters in the heat exchangers are the same as in the corresponding exchangers of the 3 PR HRSG, thereby producing additional steam flows to feed the common steam turbine and increasing the power without affecting the classic steam cycle parameters. This solution is characterized by the use of received heat with a relatively low efficiency, largely depending on the cooling air inlet temperature t1c. For higher pressure ratios in the compressor, when the outlet temperature is not lower than the turbine outlet temperature (t1c  630  C), the advanced structure of CAC can be applied. This structure is the same as that of the classic 3 PR HRSG and produces steam with identical parameters. The efficiency of heat utilization in the advanced structure is considerably higher than in the basic CAC. 4. Thermodynamic evaluation methodology 4.1. Efficiency evaluation The effectiveness of the analyzed CCPP (combined cycle power plant) is expressed by the efficiency of electricity generation. The gross electric efficiency hel is determined by the following equation:

hel ¼

Nel N þ NelSC þ DNelSC ¼ elGT m_ f LHV m_ f LHV

(17)

The electric efficiency of the gas turbine helGT and the classic steam cycle helSC are expressed by relations:

helGT ¼

NelGT m_ f LHV

(18)

helSC ¼

NelSC Q_

(19)

4a

The efficiency of the additional steam cycle hel.CO is defined as:

hel:CO ¼ Fig. 5. Block scheme of the genetic algorithm.

DNelSC Q_

(20)

1c

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The turbine outlet heat energy flow Q_ 4a and cooling air heat energy flow Q_ 1c related to the gas turbine electric power are expressed as a and aCO, respectively.

a¼

Q_ 4a NelGT

aCO ¼

(21)

Q_ 1c NelGT

(22)

Including relations (20)e(22), the gross electric efficiency hel can be written as:

hel ¼ helGT $ð1 þ a$helSC þ aCO $helCO Þ

(23)

4.2. Cases and scope of analysis The key parameter governing gas turbine operation is the pressure ratio. Currently available gas turbines have pressure ratios in the range of b ¼ 15e30, with the highest pressure ratio, 50, applied in the Rolls Royce Trent 1000 aviation turbine. To verify the theoretical potential of the air cooled gas turbines in the combined cycle, analysis is performed over the range of b ¼ 10e100. Analysis include three cases, conservative (C), optimistic (O) and super-optimistic (S). Cases O and S are characterized by higher compressor and turbine polytropic efficiencies and also by higher maximum temperatures of the turbine blades. Case S is further distinguished by a lower value of parameter b, related to the cooling effectiveness. The value of b ¼ 0.1 in Cases C and O refers to the currently achieved effectiveness of convective cooling, whereas the value of b ¼ 0.07 in Case S corresponds to air cooling with improved effectiveness. The differences between the analyzed cases are shown in Table 4. 5. Thermodynamic analysis of gas turbine 5.1. Calculation algorithm for the compressor

Fig. 6. The compressor polytropic efficiency as a function of b.

m ~C ¼

~cpC

R ~cpC

     cp ðt1a Þ$ln tt1a0  cp ðt2a Þ$ln tt2a0 ¼   ln tt1a 2a

(25)

(26)

The values of cp(t) are read for known temperatures (t1a and t2a), gas composition and the reference temperature (t0) from the ideal gas parametric tables [23,24]. A block diagram of the calculation algorithm for the compressor isentropic efficiency is presented in Fig. 7. At first, the compressor polytropic efficiency hpC is read for the analyzed pressure ratio b. With the initial assumption of cp ðt1a Þ ¼ ~cpC , the

The compressor work is independent from the turbine operating parameters, but the compressed air parameters have an impact on the turbine work. Therefore, calculations for the air compressor to produce the characteristics of isentropic efficiency hiC ¼ f(b) are first performed. The calculations are based on the compressor polytropic efficiency, presented in Fig. 6, adopted from Wettstein [19] for the conservative (C) and optimistic (O, S) cases. The isentropic efficiency of the compressor is determined using the relationships described in Ref. [18]. The average isentropic ~ C is the ratio of the individual gas conexponent for compression m stant R to the average specific heat for isentropic compression ~cpC .

hiC ¼

bm~ C  1

(24)

m ~C

bhpC  1

Table 4 Differences between analyzed Cases C, O and S. Case parameter

Conservative (C)

Optimistic (O)

Polytropic efficiency of compressor and turbine Maximum temperature of blades in turbine, tb Cooling effectiveness parameter, b

Conservative

Optimistic

900  C

1000  C

0.1

0.1

Superoptimistic (S)

0.07

Fig. 7. Block diagram of the calculation algorithm for the compressor isentropic efficiency.

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Fig. 8. The compressor isentropic efficiency and compressed air temperature as a function of b.

isentropic efficiency hiC is obtained using equations 24e26. The air compression simulation for the first iteration is then conducted to give the current outlet temperature t2a, ~cpC values and revised isentropic efficiency (hiC)t. The calculations are complete when the absolute difference between the revised and previous isentropic efficiencies is lower than the predefined precision of calculations. Otherwise, for the revised efficiency, the next iteration of the air compression simulation is executed until it reaches the predefined precision. The resulting characteristics of the compressor isentropic efficiency and the temperature of compressed air are shown in Fig. 8. The isentropic efficiency significantly decreases with an increase in the compression ratio. Over the entire analyzed b range, the drop is from 89.7% to 84.1% in the conservative case and from 90.5% to 85.6% in the optimistic cases. Due to design restrictions, it is assumed that the maximum acceptable compressed air temperature is approximately 600  C, which is exceeded for b > 40. Therefore, to apply a higher b, a solution that reduces this temperature is needed, such as the use of an intercooled compressor, steam or water injection, or the use of new materials or technologies that enable the compressor to operate at higher temperatures. These solutions are not a part of this paper.

7

Fig. 9. The expander polytropic efficiency as a function of TIT for b ¼ 0.

The TIT calculation method is illustrated in Fig. 10, wherein scheme B is applied in the paper. The turbine isentropic efficiency is obtained from the relationship presented in Ref. [23]:

hiT ¼

~ m ~T ¼

1  b~mT $hpT

R ~cpT

1  b~mT

(28)

(29)

5.2. Calculation algorithm for the turbine The calculations of the turbine isentropic efficiency, similar to the compressor, are based on the polytropic efficiency hpT, also adopted from Ref. [19]. It depends primarily on the turbine inlet temperature, and secondarily on the pressure ratio. The theoretical hpT with no impact from b is shown in Fig. 9. The actual hpT is obtained by adding an appropriate value, taking into account the impact of b, according to the relation:

hpT ðb; TITÞ ¼ hpT ðTITÞ  0; 000225$b

(27)

The turbine inlet temperature is calculated according to the ISO 2314 standard. It is a theoretical temperature before the first stage stationary blades, with a simplification assuming that the total turbine cooling air flow is mixed with the flue gas before entering the turbine. Such an approach to TIT is caused by the technical inability to measure the physical TIT in the actual gas turbines [6].

Fig. 10. A diagram showing the TIT calculation approach (A e real system, B e system according to ISO 2314).

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 ~cpT ¼

cp ðTITÞ$ln





TIT t0

   cp ðt4a Þ$ln tt4a0

  ln TIT t4a

(30)

The values of cp(t) for known temperatures and gas composition are read from ideal gas parametric tables. When the simplification according to ISO 2314 is not applied, the calculations should be performed for each turbine stage due to the cooling air, which when mixed with the flue gas changes its composition and temperature, thereby affecting the parameters ð~cpT Þ. Calculations of hiT are performed according to the algorithm presented in Fig. 11. With known compressed air parameters for assumed b, the expansion simulation can be performed. The main assumption in the gas turbine is that the constant turbine outlet temperature t4a.est ¼ 630  C, so the proper t3a value must be found. That requires an initial assumption of t3a and the resulting TIT. Subsequently, for the obtained polytropic efficiency hpT(TIT,b), the isentropic efficiency hiT is calculated on the basis of relationships (28)e(30). The expansion simulation is then performed and t4a is obtained, which is compared with the established value. If the condition t4a ¼ t4a.est is not met, the small loop is realized by adjusting t3a and repeating the simulation. When the temperature condition is met and the proper t3a is found, the hpT(TIT,b) value is obtained, and the revised isentropic efficiency (hiT)t is calculated. The next iteration of the expansion simulation in the large loop for (hiT)t are then executed, in the same manner as for the compressor, until it reaches the predefined precision.

Fig. 12. The expander isentropic efficiency as a function of b.

The obtained characteristics of turbine isentropic efficiency are presented in Fig. 12. The resultant hiT values depends on TIT, t4a and gas composition, and thus they are valid only for the analyzed cases. For different assumptions, the resulting hiT would be different. The efficiency decreases with the increase of the pressure ratio; however, the drop is lower than in the compressor isentropic efficiency. The values vary from 90.6% to 86.1% in the conservative case (C) and from 91% to 86.8% in the optimistic cases (O, S). The difference between Case O and Case S is insufficient to be shown on the graph. 5.3. Results of gas turbine analysis

Fig. 11. Block diagram of the calculation algorithm for the turbine isentropic efficiency.

In the applied approach, the temperatures COT and TIT depend primarily on b, but also on hiT and turbine cooling effectiveness. For Case C, the COT reaches the highest value, exceeding the currently highest applied temperature of 1600  C at only b ¼ 25, whereas at b ¼ 100, the COT is over 2400  C with close to stoichiometric combustion. Case S produces the lowest temperatures, but even here, COT exceeds 1600  C at b ¼ 30. For all cases, the values of TIT are very similar, which is a result of the constant turbine outlet temperature approach. The resulting COT and TIT values are shown in Fig. 13. The gas turbine electric efficiency of helTG ¼ 40% is reached, depending on the case, at b ¼ 18e26, which corresponds to the parameters of currently used gas turbines. For example, the most recent J-class gas turbine from MHI achieves an electric efficiency of 41% with a pressure ratio b ¼ 23, COT ¼ 1600  C, and the turbine outlet temperature is t4a ¼ 638  C, so it is similar to that established in a previously analyzed model [8]. Maximum efficiencies are within the range of 41.57% at b ¼ 51 in Case C to 45.14% at b ¼ 74 in Case S, although efficiencies close to the maximum are achieved in the range of b ¼ 40e50. The gas turbine efficiency is presented in Fig. 14. At high compression ratios and temperatures, the cooling technology and its effectiveness have a significant impact on the gas turbine parameters. The turbine cooling system in the analysis is regulated by the maximal blade temperature tb and parameter b. In Case O, the cooling air flow is lower than in Case C due to the higher tb. That difference is almost constant over the range of b. Apart from increasing tb in Case S, the cooling effectiveness is improved by the reduction of b; thus, the cooling air flow is even

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Fig. 13. TIT and COT as a function of b.

Fig. 15. The cooling air flow ratio gc as a function of b.

Fig. 14. Gas turbine electric efficiency helGT as a function of b.

Fig. 16. Heat energy flow in the turbine outlet flue gas and the a ratio as a function of b.

lower than in Case O. With increasing b, the difference in favor of Case S grows. The ratio gCO of cooling air flow m_ 1c to compressor inlet air flow m_ 1a is presented in Fig. 15. The turbine outlet gas heat energy flow Q_ 4a and its ratio a are shown in Fig. 16. The heat energy flow in the cooling air at the cooler inlet Q_ 1c and its ratio aCO are presented in Fig. 17. Heat energy flow Q_ 1c strongly depends on b and the parameters of the analyzed case. At lower b, the heat energy flow is low, but with increasing b, it becomes a significant heat source in combination with high temperature (t1c > t4a at b  46), having a high potential for effective use.

6. Thermodynamic analysis of the steam cycle and the whole unit 6.1. Steam cycle optimization The values of the decision variables obtained from the optimization algorithm for the classic 3 PR steam cycle are presented in

Table 5. In the optimization process, all the variables except the intermediate pressure level have reached their limits. The live steam pressure and the live steam and reheated steam temperatures reached their peak, whereas the low pressure level and all temperature differences reached the bottom of their ranges. The optimal intermediate pressure level is 4.0 MPa. These results indicate that the maximum efficiency of the steam part is related primarily to the flue gas temperature and structural or economic restrictions, such as available alloys and limited dimensions of heat exchangers. The obtained steam parameters are the maximal currently applicable in modern CCPP units. The calculations were performed for all cases with classic steam part 3 PR and expanded with the additional steam cycle CO, leading to the steam cycle power increase DNelSC. The approach using a constant turbine outlet temperature ensures that the optimized steam cycle efficiency is also constant, equal to helSC ¼ const ¼ 35.71% for all cases and within the entire range of analyzed pressure ratios. Therefore, the combined cycle efficiency hel depends only on the gas turbine parameters, helGT, a and aCO, and also on the additional steam cycle efficiency helCO.

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J. Kotowicz et al. / Energy xxx (2015) 1e15

Fig. 17. Cooling air heat energy flow at the cooling air cooler inlet and the aCO ratio as a function of b.

Fig. 18. Steam cycle electric power NelSC as a function of b.

Table 5 Ranges of decision variables in optimization of the 3 PR steam cycle. Decision variable

Value

p3s(h), MPa p3s(i), MPa p3s(l), MPa t3s(h),  C t3s(i),  C Dthe(i),  C Dtpp(h),  C Dtpp(i),  C Dtpp(l),  C Dtap(h),  C Dtap(i),  C Dtap(D),  C

18.0 4.0 0.3 600 600 5 5 5 5 5 5 10

The 3 PR power NelSC and the CO power increase DNelSC for all cases are presented in Fig. 18. The DNelSC grows with the increase in b. A step increase of DNelSC resulting from the change of the basic CAC to an advanced structure occurs at b ¼ 45 in Case C and at b ¼ 46 in Cases O and S. That change is noted in the additional steam cycle efficiency helCO characteristics as a function of b, shown in Fig. 19. This efficiency depends primarily on the cooling air temperature t1c for the basic CAC structure applied at a lower b not exceeding 30%, whereas with an advanced CAC, it is 35.5% and increasing with b up to 39.5%. 6.2. Results of the combined cycle unit thermodynamic analysis The CCPP gross electric efficiency for all cases is presented in Fig. 20. The selected parameters for all cases at an optimal pressure ratio bopt without and including the additional steam cycle are summarized in Table 6. bopt is the b for which the highest CCPP efficiency hel.max is achieved. bmin and bmax are defined as the values at which the electric efficiency is close to the maximum (hel  hel.max0.002). For the classic 3 PR structure, the electric efficiency reaches a maximum at a relatively low pressure ratio. In Cases C and O the optimal pressure ratio is around b ¼ 30, with COT approximately 1700  C. However, efficiency close to maximum is reached even at b ¼ 22, when COT is limited to 1540e1570  C. These results correspond to the parameters currently used by leading

Fig. 19. Classic steam cycle efficiency helSC and additional steam cycle efficiency helCO as functions of b.

producers. Case S stands out here with bopt ¼ 46 as a result of the significantly reduced cooling air mass flow rate (Fig. 17). This case at bmin ¼ 35 achieves hel ¼ 61.55% with COT ¼ 1674  C. Increasing the thermal resistance of the turbine blade (Case O compared with C) as well as the improvement of the cooling technology (Case S compared with O) provide a significant improvement in the CCPP parameters. They allow achieving a higher efficiency while lowering COT through using higher pressure ratios to obtain a higher hel while maintaining COT at an acceptable level. The use of additional steam cycle CO causes a significant increase in hel in all cases. The optimal pressure ratio moved to a range of bopt ¼ 69e81. However, there is a wide range of b with efficiency achieved close to maximum, starting from around bmin ¼ 52e64. Such high pressure ratios are connected with very high temperatures at the level of COT ¼ 1950e2040  C. Fig. 21 shows the unit CO2 emission per 1 MWh of generated gross electricity.

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J. Kotowicz et al. / Energy xxx (2015) 1e15

Fig. 20. Gross electric efficiency of the CCPP hel as a function of b.

Fig. 21. Unit CO2 emission per every 1 MWh of gross energy produced eCO2 as a function of b.

Table 6 Selected parameters of the analyzed case without and with the additional steam cycle DNelSC. Parameter

DNelSC ¼ 0 bmin

Super-optimistic case b, e 35 hel, % 61.55 COT,  C 1674 TIT,  C 1540 Optimistic case (O) b, e 23 hel, % 60.20  COT, C 1541 TIT,  C 1413 Conservative case (C) b, e 22 hel, % 58.72 COT,  C 1570 TIT,  C 1392

bopt

DNelSC s 0 bmax

bmin

bopt

bmax

46 61.73 1796 1622

63 61.54 1942 1716

64 64.28 1949 1721

81 64.48 2061 1790

100 64.44 2163 1851

32 60.36 1703 1510

44 60.19 1871 1604

56 63.28 2037 1690

73 63.48 2162 1751

97 63.28 2335 1831

29 58.89 1707 1472

39 58.69 1863 1557

52 62.15 2025 1640

69 62.34 2192 1720

87 62.14 2334 1784

(S)

7. Economic analysis

The total unit investment costs for currently built CCPP units is estimated to be in the range of 700e1100 V/kW, on the basis of data presented in Refs. [25,26]. The crucial factor here is coefficient B, which depends largely on the plant location and can range from B ¼ 1.8 to even B > 3, although usually it is B ¼ 2.0e2.3 [25,27]. In the analysis, it is assumed that B ¼ 2.15. Determining the costs of combined cycle units with such a wide range of gas turbine operation parameters is associated with high uncertainty, which results mainly from the lack of commercially, or even pilot-scale, operating gas turbines with the analyzed parameters. To estimate the cost of purchasing gas turbine CGT, relationships are used for the costs of the individual elements: compressor CC, expander CT and combustion chamber CCCH. The relationships are described in Refs. [22], and the general forms of the equations used are:

CGT ¼ CC þ CT þ CCCH

The economic analysis is performed only for the super-optimistic case (S) with the additional steam cycle. This case is characterized by the most favorable efficiency characteristics with the lowest required COT. It represents the higher thermal resistance of blade materials and an improved turbine air cooling system. Without development in those fields, the evolution of gas turbines towards higher pressure ratios and temperatures will be very limited. The total investment costs for the combined cycle power plant J can be written using the cost of purchasing equipment for the gas turbine CGT and steam cycle CSC, and coefficient B, responsible for the cost of construction and all indirect costs associated with the construction of the power plant:

(31)

This equation may be converted to a form using unit costs of purchasing the devices:

i$Nel:gross ¼ B$c$Nel:gross ¼ B$ðcGT $Nel:GT þ cSC $Nel:SC Þ

(32)

(33)

CC ¼

a1 $m_ 1a $b $ln bC a2  hiC C

(34)

CT ¼

a3 $m_ 3a $ln bT $½1 þ expða5 $T3a  a6 Þ a4  hiT

(35)

7.1. Economic evaluation model

J ¼ B$C ¼ B$ðCGT þ CSC Þ

11

CCCH ¼

a7 $m_ 2a $½1 þ expða5 $T3a  a6 Þ a8  ð1  z2 Þ

(36)

The selection of factors a1ea8 is based on the cost of purchasing gas turbines from manufacturers, such as General Electric or Alstom [28]. The applied values of a1ea8 are summarized in Table 7. The results from equations 34e36 are expressed in USD. The constant turbine outlet gas temperature approach and consequent constant steam cycle parameters allows setting up a constant unit cost of purchasing the steam turbine and equipment in steam part cSC. With the use of data in Refs. [25e28], it is assumed that the unit cost of the steam part is cSC ¼ 643 V/kW, which is proper for a modern steam part using a 3 PR HRSG. The economic calculations are in EUR, so the reference data presented in USD are converted to EUR using the average annual exchange rate from 2013 (1 USD ¼ 0.753 EUR). The total unit investment costs

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J. Kotowicz et al. / Energy xxx (2015) 1e15 Table 7 Values of factors in equations (34)e(36). Factor a1, a2, a3, a4, a5, a6, a7, a8,

e e e e e e e e

Table 8 Assumptions for economic analysis.

Value

Parameter

Value

53.6 0.93 279.88 0.93 0.0042 7.35 26.91 0.995

Annual operation time, h Exploitation time, years Construction time, years Division of investment for subsequent years of construction, % Share of own means, e Share of commercial credit, e Payback time of commercial credit, years Actual interest of commercial credit, % Discount rate, % Depreciation rate, %/year Income tax rate, % Liquidation value related to the investment, % Maintenance and repairs (related to the investment) in subsequent years of exploitation, %

8000 20 3 30/50/20

Natural gas price, V/GJ Employment, person/MW Monthly salary including related costs, V/ person/month Price of CO2 emission allowances, V/Mg Power plant own needs related to Nel, e

Fig. 22. Unit plant cost i as a function of b.

for analyzed unit i and the unit costs of equipment c, cGT and cSC, are shown in Fig. 22. The economic analysis presented in the article is based on the NPV (net present value) method, which is one of the most frequently used indicators to assess the commercial profitability of an investment. It is the sum of discounted net cash flows realized over the whole period of analysis (CFt) and calculated at the known discount rate (r). Cash flow includes the profit S, the investment costs J, the operating costs Cop, the income tax I, the depreciation D, the interest F, and the liquidation value L. It is described by the equations:

NPV ¼ St¼N t¼0

CFt ð1 þ rÞt

1e5 6e10 11e15 16e20

0.2 0.8 10 6 6.2 6.67 19 20 0.5 1.0 1.5 2.0 9.04 0.2 1191 0 0.02

The main assumptions necessary for the economic calculations are presented in Table 8. These assumptions are relevant for the economic conditions in Poland and may vary considerably, depending mainly on the location of the power plant. A crucial factor impacting economic results is the price of fuel, which could vary by up to tens of percentage points, depending on fuel availability and politics in the considered locations. Also important is the rate of income tax. The discount rate was determined using the WACC (weighted average cost of capital method). In the basic analysis, the CO2 emission allowances are not included. 7.2. Results of the economic analysis The resulting break-even price of electricity and its components for the analyzed unit are presented in Fig. 23. The lowest be equal to 64.85 V/MWh is achieved at b ¼ 31. However, the Cel price function is flattened around the minimal value, so

(37)


 CFt ¼ S  J  Cop þ I þ D þ F þ L t

(38)

To evaluate the electricity generation system investment, the be is used. This is the price of break-even price of electricity Cel electricity for which the net present value equals zero (NPV ¼ 0), so the investment brings no gain or loss. The break-even price of electricity can be written as a relationship:

be Cel ¼

St¼N t¼0

⌊JþðC

⌋

ÞDFL ð1þrÞt ðEel Þt St¼N t¼0 ð1þrÞt op þI

t

(39)

be can also be Cel be CJ , the fuel part

divided into components: the investment part CFbe , and the non-fuel part that includes all be : remaining production costs CNF be be Cel ¼ CJbe þ CFbe þ CNF

(40)

Fig. 23. Break-even price of electricity and its components for Case S as a function of b.

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be < 66 V/MWh is obtained over a wide range of b ¼ 18e53. Cel be , repreThe further increase in b leads to an increase in Cel senting a significant increase in the investment cost with a relatively slight decrease in fuel costs, which are related to the electric efficiency. There is performed the sensitivity analysis of the break-even price of electricity to the change in factors such as:

   

Investment costs J in the range of (0.8e1.2) J, Fuel price CF in the range of (0.8e1.2) CF, Annual operation time for values 7200e8400 h/year. Price of CO2 emission allowances CEA for values 0e40 V/MgCO2,

The change of investment costs by 20% causes a correspondbe by 3.2e5.6%, depending on b. The fuel price ing change in Cel component CFbe in the analyzed case ranges from 71% to over 83% of total price of electricity. Thus, it is an essential component in determining the profitability of investment in power plants fed by natural gas. A fuel price change by 20% brings a corresponding be by 14.2e16.7%. The annual time of operation has change of Cel little effect on the price of electricity, but the reduction of the be , e.g., a 10% operation time always leads to an increase of Cel reduction from 8000 to 7200 h/year increases the price by 1.8e3.2%. All analyzed changes have insignificant influence on the optimal compression ratio, which is always within b ¼ 29e33. The European Union Emissions Trading System will be the driving force for the implementation of CCS (carbon capture and storage) technology. The introduction of CO2 capture is expected to be justified with the price of CO2 emission allowances on the level of CEA ¼ 40 V/MgCO2. With this CEA for the analyzed power plan, be will increase by 12.5e14.1 V/MWh. This increase depends on Cel the quantity of the emitted gas, so the highest efficiency units are the least charged by the allowances. The results of the sensitivity analysis are shown in Figs. 24e27.

Fig. 25. Break-even price of electricity for a change of fuel price CF as a function of b.

8. Conclusions This paper presents the methodology and results of CCPP (combined cycle power plant) efficiency with an assumed constant turbine outlet temperature t4a ¼ 630  C. The efficiency

Fig. 26. Break-even price of electricity for a change of annual time of operation as a function of b.

characteristics as a function of the pressure ratio b are prepared. The change of b is connected with the change of the combustor outlet temperature COT and turbine inlet temperature TIT. Three cases are analyzed: conservative (C), optimistic (O) and superoptimistic (S). The cases differ by the compressor and turbine isentropic efficiencies, which are better for Cases O and S than for Case C. Moreover, the maximum blade temperature is set to tb ¼ 900  C in Case C and to tb ¼ 1000  C in Cases O and S. Additionally, the turbine cooling efficiency in Case S is improved by lowering the value of parameter b. The steam part in the analyzed unit may include:

Fig. 24. Break-even price of electricity for a change of investment cost J as a function of b.

1) A classic steam cycle with a triple-pressure HRSG (heat recovery steam generator) with reheating (3 PR) and 2) The classic 3 PR steam cycle with an additional steam cycle utilizing the heat from air cooling (CO).

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J. Kotowicz et al. / Energy xxx (2015) 1e15

For the super-optimistic case (S), an economic analysis is performed, which is based on determining the break-even price be. The lowest price C be ¼ 64.85 V/MWh is obof electricity Cel el tained at b ¼ 31. However, the range of close to optimal pressure ratios is within the wide range of b ¼ 18e53. The analysis of sensitivity to changes of such factors as the investment, price of fuel, annual operation time and price of CO2 emission allowances revealed the minor influence of these factors on the optimal pressure ratio. The increase of the CCPP efficiency from the currently achieved hel ¼ 60e61% at b ¼ 25e30 is dependent by the development of cooling technology and by effective integration of the gas turbine installation, in particular the cooling system, with the steam part. Only then would it be reasonable to move towards the compression ratio of b ¼ 45e50 to improve the efficiency by 2e3pp to the values of hel ¼ 62e64%. The economic analysis confirms this direction, but it indicates that the condition of the use of b  45 is to maintain a reasonably low investment costs for the gas turbine, competitive with currently used gas turbines. Fig. 27. Break-even price of electricity for a change in the price of CO2 emission allowances CEA as a function of b.

The efficiency of the classic steam cycle obtained in the optimization is 35.71%, and it is constant in all cases, regardless of the applied gas turbine pressure ratio. Thus, the increase in the CCPP efficiency may be sought only by: a) The improvement of gas turbine characteristics (hel, a) or b) The incorporation of an additional steam cycle. The gas turbine characteristics can also be improved through better organization of the cooling process, in presented calculations expressed by the reduction of b, affecting the cooling air mass flow (equations (13) and (14)). The incorporation of an additional steam cycle causes a significant increase in the steam turbine power, e.g., for Cases C and O at b ¼ 50, the increases are DNelSC ¼ 18.7 MW and DNelSC ¼ 14.5 MW, respectively. Currently, gas turbines achieve efficiencies of 40%, with maximum COT ¼ 1500  C, rarely 1600  C. The primary limitation for the further development of gas turbines is the durability of the materials exposed to high temperatures. Leading producers mainly opt for the development of turbine cooling technology, allowing for raising COT and TIT without distinct improvements in the field of material technologies. The potential for further efficiency improvement is on the side of high pressure ratios in the range of b ¼ 40e60 and high temperatures, far exceeding COT ¼ 1700  C. Further increase in the pressure ratio above b ¼ 40e60 gives a minor efficiency improvement over the maximum achieved at b ¼ 70e80, but it is associated with an increase in both the temperature and cooling air mass flow, and therefore it is not currently reasonable. Moreover, the compressor outlet temperature for such high b is far beyond the limitation of 600  C resulting from presently used materials. The analysis of cases with different effectivenesses of turbine air cooling (by variation of parameter b) revealed a significant improvement of the gas turbine performance in many aspects upon to the reduction of cooling air flow, including a gas turbine efficiency increase (Fig. 5) and significant reduction of COT (Fig. 4), but it is also associated with a drop in the a ratio (Fig. 7) and the aCO ratio (Fig. 8). However, in consequence, the CCPP efficiency hel improves (Fig. 11).

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