off-design conditions for its efficient design and operation

Energy Conversion and Management 126 (2016) 76–88

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Thermodynamic analysis of combined cycle under design/off-design conditions for its efficient design and operation Guoqiang Zhang, Jiongzhi Zheng, Angjun Xie, Yongping Yang ⇑, Wenyi Liu National Thermal Power Engineering and Technology Research Center, Beijing Key Laboratory of Emission Surveillance and Control for Thermal Power Generation, North China Electric Power University, Changping District, Beijing 102206, China

a r t i c l e

i n f o

Article history: Received 31 May 2016 Received in revised form 25 July 2016 Accepted 26 July 2016 Available online 3 August 2016 Keywords: Design/off-design performance Combined cycle Compressor redesigning Off-design characteristic of the topping and bottoming cycles

a b s t r a c t To achieve a highly efficient design and operation of combined cycles, this study analyzed in detail the off-design characteristics of the main components of three combined cycles with different compressor pressure ratios (PRs) based on real units. The off-design model of combined cycle was built consisting of a compressor, a combustor, a gas turbine, and a heat recovery steam generator (HRSG). The PG9351FA unit is selected as the benchmark unit, on the basis of which the compressor is redesigned with two different PRs. Then, the design/off-design characteristics of the three units with different design PRs and the interactive relations between topping and bottoming cycles are analyzed with the same turbine inlet temperature (TIT). The results show that the off-design characteristics of the topping cycle affect dramatically the combined cycle performance. The variation range of the exergy efficiency of the topping cycle for the three units is between 11.9% and 12.4% under the design/off-design conditions. This range is larger than that of the bottoming cycle (between 9.2% and 9.5%). The HRSG can effectively recycle the heat/heat exergy of the gas turbine exhaust. Comparison among the three units shows that for a traditional gas-steam combined cycle, a high design efficiency results in a high off-design efficiency in the usual PR range. The combined cycle design efficiency of higher pressure ratio is almost equal to that of the PG9351FA, but its off-design efficiency is higher (maximum 0.42%) and the specific power decreases. As for the combined cycle with a design PR of 12.73, the decrement of the efficiency under the design/offdesign conditions is in the range of 0.20–0.39%, however, its specific power increases. Thus, for the efficient design of a combined cycle, its optimal efficiency and maximum specific power, instead of that of the topping cycle, should be considered. For the operation strategy, the performance of the topping cycle should be kept at a high level first (the turbine inlet temperature should be as high as possible), followed by the high setting of the turbine exhaust temperature. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Gas turbines own many advantages, including rapid startup, high thermodynamic efficiency, and excellent load regulating capacity. Heavy-duty gas turbines, in particular, are developing rapidly, as evidenced by the continuous increase in their design pressure ratio (PR) and turbine inlet temperature (TIT) and the improvement in their efficiency and power output [1]. With the increase in the gas turbine exhaust parameters, the pattern of heat recovery steam generators (HRSGs) has developed from a singlepressure reheat to a dual-/triple-pressure reheat, so that the gas turbine exhaust heat can be recycled effectively [2].

⇑ Corresponding author. E-mail address: [email protected] (Y. Yang). http://dx.doi.org/10.1016/j.enconman.2016.07.066 0196-8904/Ó 2016 Elsevier Ltd. All rights reserved.

Thermodynamic analysis and optimization for Brayton cycles [3–5] and combine cycles [6] have been widely investigated in previous literatures under design condition. However, the combined cycle gas turbine (CCGT) often runs at partial load conditions because it is frequently constrained to peak regulation in a power grid. Thus, investigating CCGT off-design thermodynamic performance is necessary. The off-design performance prediction of gas-steam combined cycle depends on the off-design modelling of each component of overall thermodynamic system. Therefore, the off-design simulation methodologies of main components of gas-steam combined cycle should be discussed and analyzed. The compressor is the ‘‘heart” of a gas turbine, and its off-design performance prediction is vital. The traditional stage stacking method is often applied to predict the performance of multi-stage axial flow compressors with geometry angle variations [7–10]. Kim et al. [11] proposed an improved method that

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Nomenclature A h L n m Ma PR p Q ar;net;p R T Y Dp

area [m2] enthalpy [kJ/kg] theoretical air quantity [kg/kg] rotational speed [r/min] mass flow [kg/s] Mach number [–] pressure ratio [–] pressure [MPa] lower heating value of the fuel [kJ/kg] gas constant temperature [K] constant pressure loss [kPa]

Greek letters absolute flow angle b excess air coefficient d expansion ratio / flow coefficient

a

u ¼ ðc  1Þ=c specific heat ratio c g efficiency j comprehensive parameter r constant 1 mixing loss coefficient w

pressure coefficient

Subscripts and superscripts 0 environment condition 2 compressor outlet 3 combustion chamber outlet a air

incorporates governing equations and stage characteristics, can calculate all inter-stage variables simultaneously, and evaluates the off-design performance of various multi-stage compressors. In recent years, to improvement the off-design performance prediction accuracy of gas turbines, various mathematical methods adopted to generate the compressor map have attracted remarkable attention [12,13]. Tsoutsanis et al. [14] proposed a novel compressor map tuning method to improve the accuracy and fidelity of gas turbine models for performance prediction and diagnostics in steady-state and transient conditions. The off-design model of turbines is often based on the Stodola equation or Flugel formula [15], which can be found in many studies on the off-design performance prediction of gas turbines or combined cycles. HRSG off-design modelling mainly focuses on the overall heat transfer coefficient calculation methods. The relatively simplified methodology, which only relates to gas turbine exhaust mass flow and temperature, is applied in Refs. [16,17]. For another similar overall heat transfer coefficient formula, it is affected by gas turbine exhaust temperature, mass flow rate, and pressure [18]. The relationship between the overall heat transfer coefficient and the thermodynamic parameters of gas/(water, steam) sides was also described for each heating surface [19,20]. Ganapathy [21] proposed an HRSG off-design performance prediction method, in which relatively detailed thermodynamic design parameters of HRSG and off-design gas turbine exhaust parameters (e.g., temperature, flow, gas composition, and several physical properties) are considered in estimating the overall heat transfer coefficients of

c cc ca d f g in opt t 

compressor, combustion chamber cooling air, design condition fuel gas inlet maximum efficiency points gas turbine stagnation parameter

Acronyms C compressor CC combustion chamber CCGT combine cycle gas turbine CP condensate pump EV evaporator FP feed water pump GT gas turbine HP high pressure HRSG heat recover steam generator IGV inlet guide vane IP intermediate pressure LP low pressure ORC Organic Rankine Cycle PR pressure ratio RH reheater RP recycle pump SH surperheater TIT turbine initial temperature TET turbine exhaust temperature TEF turbine exhaust flow

different heating surfaces. In addition, Zhang et al. [22] proposed concise semi-theoretical, semi-empirical formulas to predict the off-design performance of the bottoming cycle of the gas-steam turbine combined cycle. The off-design characteristics of steam turbines, including off-design performance prediction [23,24] and cylinder efficiency calculation [25], were also studied. To achieve relatively high design/off-design efficiencies of power plants, the thermodynamic performance of gas turbine/ combined cycle with different equipment/system configurations and various operation strategies are analyzed comprehensively and corresponding thermodynamic systems were optimally integrated. Goodarzi [26] investigated a new regenerative Brayton cycle and the results shown that the new regenerative Brayton cycle has higher thermal efficiency than the original one at the same pressure ratio, and also lower heat absorption and exhausted heat per unite output power. The influence of shaft configurations on the design/off-design point performances of simple, regenerative, and intercooled-regenerative gas turbines was also studied [27]. For a recuperated gas turbine cycle, a single-shaft configuration with variable speed operation is the best combination, followed by the double-shaft configuration with a variable area nozzle (VAN) [28]. For alternative recuperated gas turbine cycles with divided turbine expansion, a single-shaft configuration is less sensitive to compressor PR in comparison with a double-shaft configuration, and variable speed control is recommended [29]. The variable inlet guide vane modulation positively affects the singleshaft combined cycle performance, especially at high load ranges,

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but is not effective to improve the double-shaft engine performance [30]. A comparison of single/combined cycle plants with different design parameters (TIT) at part load revealed that gas turbines with high parameters exhibit superior performance at part load [31]. Haglind [20] studied the effects of variable geometry controls on the part load efficiencies of combined cycles and found that VAN control is effective in combined cycles at part loads and that the variable guide vane control of compressors is an equally good choice for the combined cycles used in tankers and carriers. In addition, some novel techniques also were adopted to enhance the performance of power plants at partial loads. Coolant modulation minimizes coolant consumption at part loads and can thus improve the part load thermal efficiencies of gas turbines [32] and combined cycles [19]. Barelli and Ottaviano [33] proposed an innovative combined cycle with a small compressor installed in the gas turbine inlet, which improves the operational flexibility of the combined cycle and its overall efficiency under off-design conditions. Rovira et al. [34] presented a methodology to achieve thermoeconomic optimizations of CCGT power plants taking into account the frequent off-design operation of the plant. Dynamic simulation of power plants is important for stable operation [35], residual life estimation and fault diagnosis [36]. In recent years, the regeneration technology are increasingly considered to improve the thermo-economic performance and operation flexibility of combined cycle under design/off-design conditions. Carapellucci and Giordano [37] illustrated that thermodynamic regeneration has the potential to markedly enhance energy and economic performances of combined cycle based on advanced gas-turbine technology. Moreover, the off-design operation flexibility of CCGTs can be improved, provided that the regenerator and bottoming steam cycle are properly designed. Gogoi [38] simulated the performances of a CCGT combining air and fuel preheating and compared to the case of simple CCGT, varying the gas turbine pressure ratio. Cao et al. [39] designed a gas turbine and Organic Rankine Cycle (ORC) combined cycle with recuperator and conducted thermodynamic performance analysis, the results shown that compared with the GT-Rankine combined cycle, the GT-ORC combined cycle had better thermodynamic performance. With regard to present gas-steam combined cycle power plants, the matching steam turbine units are subcritical units with a main steam temperature in the range of 480–565 °C and pressure between 4 and 9.98 MPa [15]. However, steam turbine technologies have reached a relatively advanced level. Supercritical and ultra-supercritical technologies are widely applied in coal-fired power plants, with the steam parameters reaching 27.56 MPa/605 °C [40]. At present, B&W PGG and Toshiba Corporation have designed an advanced ultra-supercritical unit with an initial temperature range of 700–760 °C to fire Indian coal [41]. Therefore, for the design of an advanced combined cycle, technology advancements in gas turbine cycles and bottoming cycles should be considered. Gas turbines often run under part load conditions because of peak load regulations. Therefore, modern gas-steam combined cycle power plants with high design and off-design efficiency should be developed. Although many studies have investigated the design/off-design performance of gassteam combined cycle power plants and proposed some methods to enhance the design/off-design performance of combined cycle, currently there is no simulation studies that explores the influence of diverse topping/bottoming cycle temperature utilization intervals (e.g., for same gas turbine inlet temperature and HRSG out temperature, the whole temperature interval of combined cycle is divided into different two half segments for topping and bottoming cycles) on combined cycle design/off-design performance and the interactions among the topping, bottoming, and combined cycles based on practical operation unit under design/off-design

conditions. Such analysis can provide comprehensive suggestions for the highly efficient design and operation of combined cycles. In the current study, we aim to address the aforementioned issue by performing a detailed analysis of the off-design characteristics of the main parts of a combined cycle with different PRs. A PG9351FA unit is selected as the benchmark unit, on the basis of which the compressor is redesigned with two redesigned PRs (one larger PR and one smaller PR). Then, the design/off-design characteristics of three units with different design PRs are analyzed under the same TIT. The characteristics of the topping and bottoming cycles are evaluated, and the interaction relationship among the topping, bottoming (including HRSG, steam turbine, and bottoming cycles), and combined cycles is studied. Finally, the key factors that affect the off-design characteristics of combined cycles are summarized, and suggestions for the efficient design and operation of combined cycles are proposed. 2. Gas-steam combined cycle modelling 2.1. Compressor modelling The stage-stacking method is adopted to calculate the offdesign characteristics of compressor [7–10]. The stage-stacking method is based on the mean-line one-dimensional flow continuity equation and the generalized stage characteristic curves [42,43]. This method is convenient to simulate the off-design performance and obtain the key parameters (the stage inlet/outlet parameters (pressure, temperature, and velocity) and overall parameters of compressor) of compressor under different operation conditions, such as the inter-stage bleeding performance and the characteristics of the startup/shutdown process. The geometry variation, including the changing inlet guide vane (IGV) and the nozzle vanes of several front stages, can also be calculated by this method. In this work, the solution for the performance prediction of a compressor with IGV regulation is described as follows. The relationship between flow coefficient and vane exit absolute flow angles if the rotor inlet incidences are equivalent under different operating conditions is shown below [7].


 1 ¼ dðtan aÞ d /

ð1Þ

where a is the vane exit absolute flow angle. / is flow coefficient. Assuming that the relative rotor exit flow angle and stage efficiency are mere functions of rotor incidence, the relationship between the flow and pressure coefficients can be expressed as follows [11]:

w ¼ constant /

ð2Þ

where / is flow coefficient, w is pressure coefficient. The off-design calculation model of rotatable nozzle vanes and compressor inter-stage bleeding are provided in Refs. [11,44]. 2.2. Combustion chamber modelling The thermodynamic calculation of combustion chamber is aimed to determine the excess air coefficient and combustion temperature using the following thermal balance equation [15]: 3

0

ð1 þ bLÞðhg  hg Þ ¼

h   i 2 0 2 0 hf  hf þ bL ha  ha þ gcc  Q ar;net;p

ð3Þ

where b is the excess air coefficient, L is the theoretical air quantity, h is the enthalpy, g is the efficiency, and Qar,net,p is the low heating value of the fuel. Subscripts/Superscripts: 0 is the environment con-

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dition, g is the gas, f is the fuel, a is the air, cc is the combustion chamber, 2 is the compressor outlet, and 3 is the combustion chamber outlet. The thermo-physical properties of gas turbine flue gas mainly rely on its composition and temperature. The method proposed by Zhang [45] is used to calculate the thermo-physical properties of flue gas in different states in combustion chamber and turbine. 2.3. Gas turbine modelling A simplified off-design gas turbine model with separate turbine stage cooling is considered (Fig. 1). The gas turbine is composed of three stages, each of which contains a pair of nozzle vanes and rotor blade rows. The following blade cooling model and expansion processes are assumed to simplify the thermodynamic calculation (Fig. 2). The cooling air of the nozzle vanes is mixed with the main flue gas at the inlet. The mixed flue gas expands in both the nozzle vanes and the rotor blade rows. Finally, the cooling air of the corresponding rotor blade rows is mixed with the expanded flue gas at the outlet of this stage. The expansion ratios of the first and second turbine stages are almost the same; however, the expansion ratios of the third stage vary with the change in the turbine inlet pressure under off-design conditions [15]. The cooling air quantity at each turbine stage at design condition is estimated by Zhang [46]. We assume that the ratio of the cooling air quantity to the total air quantity of compressor inlet is equal to that of the benchmark unit at design condition because the TIT of the redesigned units are equal to that of the benchmark unit. The cooling air quantity of each turbine stage at off-design conditions can be adjusted according to the temperature and pressure of the bleeding stage [47].

mca ¼ mca;d

pc;out pc;out;d

!

T c;out;d T c;out

!0:5

where Dp is the pressure loss, p is the pressure, m is the mass flow, c is the specific heat capacity, Ma is the Mach number, 1 is the mixing loss coefficient, and j is the comprehensive parameter that ranges from 0.15 to 0.5 and is set to 0.404 in this work [46]. Subscripts: t is the turbine, g is the gas, ca is the cooling air, and in is the inlet. Superscripts: ⁄ is the stagnation parameter. The turbine efficiency of each stage under off-design conditions is corrected with the following semi-empirical formula [49]:

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi   u 1  du opt =ð1  d Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi

  u Y  ðY  1Þðn=nd Þ T 3d =T 3 1  du opt =ð1  d Þ

gt =gt;max ¼ ðn=nd Þ T 3d =T 3

ð6Þ

ð4Þ

where m is mass flow, p is pressure, and T is temperature. Subscripts: c is the compressor, d is design condition, ca is the cooling air, and out is the outlet. Superscripts: ⁄ is the stagnation parameter. The cooling air is accelerated during the mixing with the mainstream flue gas such that its velocity and direction are consistent with those of the mainstream flue gas. The pressure drop during this process is evaluated with the following formula [48]:

Dp mca m ¼ c Ma2 1 ¼  ca j; DP < 0 pt;in mg g g mg

Fig. 2. Turbine thermodynamic calculating using diagram.

ð5Þ

where g is the efficiency, n is the rotational speed, T is the temperature, d is the expansion ratio, Y is the constant (set to 2.083 in this work) [49], and u = (c  1)/c, where c is the specific heat ratio. Subscripts/Superscripts: d is the design condition, t is the turbine, max and opt are the maximum efficiency points, 3 is the combustion chamber outlet, and ⁄ is the stagnation parameter. Under off-design conditions, the turbine and compressor should satisfy certain relationships. In the absence of a turbine characteristic curve, the simplified Flugel formula can be used to describe the relationship between the turbine inlet pressure, temperature, and mass flow rate [47,50].

Fig. 1. Diagram of gas turbine air cooling system.

80

r

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mt;in

qffiffiffiffiffiffiffiffi T t;in

AP t;in

¼ con;

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u
ccþ1 uc 1 2 r¼t R cþ1

ð7Þ

where r is a constant, m is the mass flow, A is the turbine inlet area, and P is the pressure, c is the specific heat ratio and R is the gas constant. Subscripts: t is the gas turbine, and in is the inlet. Superscripts: ⁄ is the stagnation parameter. 2.4. HRSG and steam turbine modelling The triple-pressure reheat HRSG was modelled by adopting and modifying the simplified method for single-pressure HRSG proposed by Ganapathy [21]. Off-design calculation was performed based on the thermodynamic design parameters and the gas turbine exhaust temperature, mass flow, flue gas composition, and feed water temperature at off-design conditions. The steam parameters produced in the HRSG must satisfy the off-design characteristic of the steam turbine, and these desired parameters must be reached in the HRSG, hence the inseparable combination of the HRSG and the steam turbine. The off-design characteristic of the steam turbine can be described by the Flügel formula [51]. The detailed off-design calculation process of triple-pressure reheat HRSG can refer to Ref. [22].

3. Design parameters of the benchmark and redesigned units 3.1. Description of the three units The PG9351FA gas turbine unit selected as the benchmark, which generates a power output of 255.6 MW, is composed of an 18-stage axial flow compressor and a three-stage turbine. The redesigned units are based on the benchmark unit; hence, the basic configuration is similar, whereas the key parameters may be different. The general configuration and the redesigned units are described below. The compressor of the benchmark unit is equipped with four inter-stage bleeding holes that are located behind the ninth- and thirteenth-stage nozzle vanes of the compressor. The inter-stage bleeding air of the ninth and thirteenth stages acts as the cooling air resource of the second and third turbine nozzle vanes. The cooling air of the first-stage turbine nozzle vanes is extracted from the compressor outlet chamber and directed through to the root of the nozzle vanes and then to the interior of the nozzle vanes. The cooling air of the rotor blade rows is extracted from the inner cylinder of the compressor (after the sixteenth stage) and is then passed through the cooling air channel of the shaft to cool the relative parts, the blade root, and the first/second rotor blade rows. Some cooling air is split from the compressed air out of the compressor to cool the transition section and is then made to flow to the combustor; the remaining air cools the fire cylinder. The third stage of the turbine rotor blade rows is not equipped with air cooling. The HRSG is a triple-pressure, single-reheat, horizontal, nonsupplementary firing, natural circulation boiler. There are economizers before the different pressure (high-, intermediate-, and low-pressure) boiler drums, below which are the corresponding evaporators and after which are the corresponding superheaters. In the high-pressure superheater and reheater, attemperators are present to prevent the overtemperature of the steam. The exhaust steam of the high-pressure cylinder mixes with the intermediatepressure superheated steam and then goes to the reheater and finally to the intermediate-pressure cylinder. The exhaust steam of the intermediate-pressure cylinder and the low-pressure superheated steam undergo the same process. The steam turbine selected is a triple-pressure, single intermediate reheat, single-

axis, double-cylinder double-exhaust steam, condensation-type steam turbine. A diagram of triple-pressure reheat combined cycle power plant is shown in Fig. 3. The benchmark structure and thermodynamic design parameters of the compressor, turbine, HRSG, and steam turbine are derived from Ref. [52]. With the development of steam turbine technology, the initial parameters of steam turbine (e.g. steam turbine inlet temperature, pressure, and mass flow) augment accordingly. At present, the initial steam temperature of existing steam turbines reaches 603 °C. Assuming that the TIT remains the same, we study three combined cycle units that match the common bottoming cycle (the main steam initial temperatures are 603 °C, 567.5 °C, and 538 °C). The design parameters of the benchmark gas turbine need to be redesigned accordingly to match the bottoming cycle parameters of 603 °C and 538 °C, and a gas turbine design calculation program is coded using Excel according to the calculation method proposed by Zhong [53]. With regard to the gas turbine that matches the initial steam temperature of 603 °C, assuming that the initial temperature (1327 °C) and exhaust pressure of the gas turbine are unchanged, the design PR of compressor should be reduced accordingly. If the difference between the turbine exhaust and the HRSG main steam temperatures is kept constant, the design PR of redesigned compressor should be 12.73 which is determined through an iterative design calculation. Accordingly, the PG9351FA unit removes the first stage of the compressor and adjusts the PR of each stage. Thus, the overall design PR becomes 12.73. After the redesign, only the first stage lies in the transonic speed region. However, the inlet air mass flow rate and air bleeding ratios of the redesigned unit should be equal to those of the benchmark unit to enable the comparison between the redesigned and benchmark units. Finally, the air extraction points are set after the 8th, 12th, and 15th stages. The end-stage expansion ratio of the turbine varies correspondingly to match the PR of the redesigned compressor. The flow chart of the HRSG does not change. The selected steam turbine is the unit with the initial temperature of 603 °C, and its flow chart remains the same. On the contrary, the gas turbine that matches the initial steam temperature of 538 °C requires an increase in the design PR of compressor. After repeated design calculations, the design PR is set to 18. On the basis of PG9351FA unit, the compressor adjusts the total PR to 18 and does not remove or add stages. The air extraction points and ratios remain the same as those of the benchmark unit, and the inlet air flow rate and exhaust pressure of gas turbine remain unchanged. The flow charts of the HRSG and steam turbine remain the same as that of the benchmark unit, whereas the steam turbine selects the unit with the initial steam temperature of 538 °C. 3.2. Operation strategy With regard to gas turbine control strategy, the TIT remains constant when the gas turbine load is 80–100%, however, the compressor IGV angle does not change when the gas turbine load is lower than 80%. The sliding pressure operation mode is set for the bottoming cycle when the steam turbine load is 45–100%. In the thermodynamic calculation process of HRSG, the main steam pressure is specified according to the HRSG and steam turbine. The controlled expansion operation mode (operation at constant pressure) is implemented when the steam turbine load is less than 45%. 3.3. Design parameters of the three units The main assumptions for the simulations are presented in Table 1. The design and corresponding simulation performance parameters of the three units are shown in Table 2.

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Fig. 3. Schematic of the triple-pressure reheat combined cycle.

Table 1 Main assumptions for the simulation.

Table 2 Design parameters of the gas turbine and HRSG.

Items/unit

PG9351FA unit

High pressure unit

Fuel Lower heating value

LHV = 48685 kJ/kg

Pressure loss Inlet pressure loss/% Combustor pressure loss/% Exhaust pressure loss/%

0.61 3.5 1.32

Thermal losses Mechanical loss/% Generator loss/% Combustor heat loss/%

1 1 0.5

Low pressure unit

Items/unit TIT/°C PR Compressor stage numbers Inlet air flow/kg/s TET/°C Compressor outlet temperature/°C Cooling air parameters of turbine (first to last stage)a First rotor height of compressor/mb First rotor hub diameter of compressor/mb Last rotor height of compressor/mb Last rotor hub diameter of compressor/mb Gas turbine power/MW Gas turbine efficiency/% Combined cycle power/MW Combined cycle efficiency/%

Environmental condition and parameters 15 °C 101.3 kPa, 60%RH Compressor design parameter Compressor efficiency/% Cooling air ratio/% Turbine design parameter Turbine efficiency Steam turbine efficiency/% efficiency/% Speed/r/min

88.1

88.2 18.45

88.6

First/second stage 0.900, third stage 0.908 HP cylinder 87,IP cylinder 93,LP cylinder 89 3000

HRSG design parameterc Main-steam temperature/°C Reheat steam temperature/°C Main steam pressure/MPa Reheat steam pressure/MPa Main steam flow/kg/s Steam turbine power/MW

4. Off-design characteristic analysis of three combined cycle units 4.1. Operation characteristic curves of three compressors a

On the basis of the relationship between the compressor flow and pressure coefficients, the characteristic curves of compressors and the corresponding thermodynamic parameters can be obtained with the stage-stacking method. The IGV angle ranges from 27° to 88° to control the compressor inlet air flow. In this study, the IGV controls the gas turbine load from 100% to 80%; the IGV angle decreases constantly, and the TIT is kept constant until the load of 80%. Subsequently, the fuel control mode is used

b c

PG9351FA unit 15.4 18 617.5 390.67

High pressure unit 1327 18 18 645 587.94 421

Low pressure unit 12.73 17 652.3 352.17

Stator: 0.08, 0.0313, 0.0184 Rotor: 0.0313, 0.0235, 0 0.504

0.437

1.474

1.474 0.147 1.701

258.74 37 404.02 57.79

260.93 38.36 393.37 57.83

255.21 35.89 417.02 57.58

567.5 567.6 9.88 2.3 80.97 145.28

538 538 8.87 1.87 73.39 132.44

603 603 12.01 2.86 88.19 161.82

Corresponding coolant flowrate divided by compressor inlet air flowrate. These parameters are derived from Ref. [52]. More detailed design parameters of HRSG can refer to Ref. [22].

for the load below 80%. In this control scheme (Figs. 4–6), the IGV opening of PG9351FA, high-pressure, and low-pressure units are in the range of 88–64.9°, 88–63.5°, and 88–65.7°, respectively. In addition, each characteristic curve in the figures possesses its

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and then along the curve bc. During the line ab period, the variation of the PR is proportional to that of the mass flow. The highest pressure point of each characteristic curve is set as the surge boundary point. 4.2. Off-design calculation and analysis of the topping cycle

Fig. 4. Operation characteristic curve of PG9351FA compressor.

Fig. 5. Operation characteristic curve of low-pressure compressor.

4.2.1. Off-design characteristic of the gas turbine unit The predicted off-design parameters of the gas turbine cycles are shown in Figs. 7–9. The variation trend of this prediction is consistent with that (a prediction of GE 7F) presented in Ref. [54]. Hence, the calculation model of the gas turbine is reliable. When the gas turbine load decreases from 100% to 80%, the TIT remains the same, the PR decreases, and the turbine exhaust temperature (TET) increases, as shown in Figs. 7–9. The IGV regulation is employed, and the inlet air flow of compressors decrease from 100% to 84%, 83.3%, and 82%, respectively. When the gas turbine load decreases from 80% to 30%, the inlet air flow remains almost the same (without IGV regulation and with the decrease of PR, the air flow increases slightly), and the TIT decreases constantly, resulting in the constant decrease in the TET. The curve trends of the three gas turbines are similar, and the difference between the corresponding relative values at the same load is derived mainly from the effect of the IGV regulation on the inlet air flow at different design PRs. The figures show that the relative value of the turbine exhaust mass flow with a high design compressor ratio changes significantly. The relationship between the power output and the relative load is shown in Fig. 10. The design PR of compressor slightly affects the maximum power output of gas turbine. The gas turbine power output is higher than that of PG9351FA unit by 0.66– 2.19 MW when the compressor PR is 18 and is lower than that of PG9351FA unit by 1.06–3.53 MW when the PR is 12.73. 4.2.2. Topping cycle design/off-design characteristic analysis The variation in gas turbine (topping cycle) efficiency with relative power output is shown in Fig. 11. The design efficiencies of the three gas turbine cycles are consistent with those presented by Ref. [31], thus indicating that the bleeding air ratio of the three units remains constant is reliable at design condition in this work. Fig. 11 shows that if the efficiency of the conventional gas turbine cycle under the design condition is higher than that of the other one, its efficiency under the off-design conditions is also higher. For example, when the design PR of compressor reaches 18 regardless of the design condition or off-design conditions,

Fig. 6. Operation characteristic curve of high-pressure compressor.

own IGV opening, with a rotational speed of 3000 r/min. The operation characteristic curves depend on the matching relationship between the compressor and turbine. The change trends of the pressure and flow are the same, that is, initially along the line ab

Fig. 7. Off-design operation characteristic curve of low-pressure gas turbine.

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Fig. 8. Off-design operation characteristic curve of the high-pressure gas turbine. Fig. 11. Variation in gas turbine thermal efficiency with power output.

Fig. 9. Off-design operation characteristic curve of PG9351FA gas turbine. Fig. 12. Variation in compressor outlet temperature with power output.

Fig. 10. Gas turbine power output of three units during off-design operation process. Fig. 13. Variation in gas turbine fuel consumption flow with power output.

the outlet temperature of compressor shown in Fig. 12 increases, and the fuel consumption decreases, as shown in Fig. 13. In addition, the exhaust temperature decreases for the same gas turbine inlet temperature, and the net power output increases. Therefore, the efficiency of high-pressure unit is higher than that of the

PG9351FA unit. With a load of 100–30%, the increment of the thermal efficiency of high-pressure unit, compared with PG9351FA unit, ranges from 1.38% to 1.70%. On the contrary, if the design PR of compressor is 12.73, the reduction of the gas turbine

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efficiency ranges from 1.25% to 1.75%. As the design PR decreases when the load decreases from 100% to 30%, the thermal efficiency drops dramatically by 12.1%, 12.6%, and 12.8%. Therefore, a high design compressor PR can narrow down the variation range of thermal efficiency. The exergy efficiency of topping cycle versus the relative gas turbine load is shown in Fig. 14. The variation intervals of the exergy efficiency of topping cycle are 25.8–37.6%, 23.9–36.3%, and 22.6–34.6% for the high-pressure, PG9351FA, and lowpressure units, respectively. In terms of the comparison of the three units, a high design PR results in high exergy efficiency. Compared with the PG9351FA unit, the exergy efficiency of topping cycle increases by 1.33–1.84% if the design PR is 18, whereas the exergy efficiency decreases by 1.30–1.71% as the design PR becomes 12.73. It is beneficial to the topping cycle performance with a relatively high design PR. The main reason for the decrease in the exergy efficiency of topping cycle at part load conditions is the reduction in the inlet air temperature and outlet flue gas of combustion chamber. The low design PR of compressor lowers the outlet air temperature; hence, more fuel is consumed to gain the given TIT. Thus, the exergy destruction of the combustion chamber increases (fuel exergy

+ compressed air exergy  exergy of the flue gas to the first stage rotor blade rows), as shown in Fig. 15. The exergy destruction of the combustion chamber decreases linearly under design/offdesign conditions. Fig. 16 shows the variation trend of the exergy destruction rate of the combustion chamber (the exergy destruction of the combustion chamber/the fuel exergy). When the gas turbine load decreases from 100% to 80%, the exergy destruction rate of the combustion chamber rises gradually because of the decrease in the inlet compressed air temperature. The corresponding decrements for high-pressure, PG9351FA, and low-pressure units are 0.69%, 0.66%, and 0.59%, respectively. However, when the load is below 80%, the exergy destruction rate of the combustion chamber reduces dramatically with the TIT at decrements of 7.12%, 7.43%, and 8.03%. Therefore, the TIT affects dramatically the exergy efficiency of topping cycle. By ignoring the change in the cooling air amount for blades, the high design PR of gas turbine is highly suitable for the pitch peak.

Fig. 14. Variation in gas turbine exergy efficiency with power output.

Fig. 16. Variation in combustor exergy destruction ratio with gas turbine power output.

Fig. 15. Variation in combustor exergy destruction with gas turbine power output.

Fig. 17. Variation in HRSG thermal efficiency with gas turbine power output.

4.3. Bottoming cycle design/off-design characteristic analysis 4.3.1. HRSG design/off-design characteristics Figs. 17 and 18 show the variation trend of the thermal efficiency of HRSG and the exergy efficiency (the exergy absorption

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of steam and water/the exergy of gas turbine outlet flue gas exergy), respectively. The variation intervals of the thermal efficiency of high-pressure, PG9351FA, and low-pressure units are 78.4–89.1%, 80.2–89.5%, and 80.7–90.1%, respectively. Therefore, under design/off-design conditions, the heat loss caused by the HRSG exhaust gas is in the range of 10–21%, which is relative to the HRSG inlet temperature of the flue gas. The variation intervals of the corresponding exergy efficiency are 77.5–80.9%, 78.6– 81.8%, and 79.6–83.0%, respectively. This variation is relatively small, and the differences between the different units are close. On the basis of the data mentioned above, the thermal/exergy efficiencies of the HRSG under design/off-design conditions remain at a high level and change slightly. This condition indicates that the HRSG can recover effectively the heat/heat exergy of the gas turbine exhaust to the steam under most of load conditions. Therefore, increasing the exhaust temperature and the design parameters of the bottoming cycle alone cannot effectively increase the thermal/exergy efficiency of HRSG. Fig. 19. Variation in steam turbine power output with gas turbine power output.

4.3.2. Steam turbine design/off-design characteristics The variation curves of the steam turbine power output during the gas turbine off-design operations are shown in Fig. 19. The available heat and final power output of steam turbine decrease as the designed PR increases. The decrement of the steam turbine power output compared with that of PG9351FA unit is in the range of 6.94–12.84 MW as the design PR of compressor increases to 18. On the contrary, if the design PR decreases to 12.73, then the increment of the power output falls in the range of 5.66–16.54 MW. The decrement of the relative power output of steam turbine is less than that of the gas turbine as the load decreases. For example, when the gas turbine load is reduced to 30%, the steam turbine load decreases to about 40% (PG9351FA unit). The variation curves of the thermal and exergy efficiency (the power output of steam turbine/the exergy absorption of steam and water) of steam turbine are shown in Figs. 20 and 21. Fig. 20 shows that the variation intervals of the thermal efficiency of high-pressure, PG9351FA, and low-pressure units are 28.5–36.8%, 29.3–37.8%, and 30.3–39.3% with corresponding variations of 8.3%, 8.5%, and 9.0%, respectively. The change in the steam temperature (caused by the change in the flue gas temperature) affects the thermal efficiency of steam turbine. A high flue gas temperature results in a high thermal efficiency. Fig. 21 shows that the exergy efficiency of steam turbine, similar to its thermal efficiency, depends on the flue gas/steam temperature of HRSG. For example,

Fig. 20. Variation in steam turbine thermal efficiency with gas turbine power output.

Fig. 21. Variation in steam turbine exergy efficiency with gas turbine power output.

Fig. 18. Variation in HRSG exergy efficiency with gas turbine power output.

under the load of 100–80%, the variation intervals of the exergy efficiency of the corresponding steam turbine are very small. The steam cycle is in a passive position in the gas-steam combined cycle. In terms of the design condition, high steam

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parameters result in high steam turbine performance. However, the complete combined cycle should be considered in the selection of steam parameters. As the steam temperature decreases under off-design conditions, the exergy efficiency of the steam turbine decreases apparently. The off-design parameters of the steam cycle rely on the exhaust of gas turbine. Thus, comprehensively summarizing and analyzing the off-design characteristics of topping cycle and maintaining a high exhaust temperature is very important for the off-design operation of the steam cycle. 4.3.3. Bottoming cycle design/off-design characteristics The variations in bottoming cycle thermal efficiencies of the three units with gas turbine power are shown in Fig. 22. Under design/off-design conditions, the variation intervals of highpressure, PG9351FA, and low-pressure units are 22.3–32.0%, 23.5–33.2%, and 24.4–34.8% with the corresponding variations of 9.7%, 9.7%, and 10.4%, respectively. For both the design and offdesign conditions, a high exhaust temperature can result in a high thermal efficiency. The variation trend of the exergy efficiency (the power output of steam turbine/the exergy of gas turbine outlet flue gas exergy) of the bottoming cycle is similar to that of the thermal efficiency, as shown in Fig. 23. The variation intervals of highpressure, PG9351FA, and low-pressure units are 57.9–67.3%, 59.2–68.4%, and 60.3–69.8% with the corresponding variations of 9.4%, 9.2%, and 9.5%, respectively. The decrements in the thermal and exergy efficiencies of the bottoming cycle are less than those of the topping cycle. As indicated in the results, the characteristic parameters of the topping cycle affect the thermodynamic performance of bottoming cycle under design/off-design conditions. The HRSG can almost efficiently transfer the heat exergy of the gas turbine exhaust flue gas to the steam/water of steam turbine. However, the conversion efficiency of the steam heat/exergy to power is highly dependent on the steam temperature. For a given topping cycle, a high gas turbine exhaust temperature is important to the efficient operation of the bottoming cycle and combined cycle.

Fig. 23. Variation in bottoming cycle exergy efficiency with gas turbine power output.

4.4. Combined cycle design/off-design characteristics The variation curves of the thermal efficiency and power output for combined cycles are presented in Figs. 24 and 25. The variation intervals of the thermal efficiency of high-pressure, PG9351FA, and low-pressure units are 42.8–57.8%, 42.2–57.8%, and 41.9–57.6% with the corresponding variations of 15.0%, 15.6%, and 15.7%, respectively. Therefore, a high design PR of compressor can narrow

Fig. 22. Variation in bottoming cycle thermal efficiency with gas turbine power output.

Fig. 24. Variation in combined cycle thermal efficiency with gas turbine power output.

Fig. 25. Variation in combined cycle power output with gas turbine power output.

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down the variation range of the combined cycle thermal efficiency. In addition, the combined cycle efficiency decreases dramatically as the gas turbine load falls below 80% because TIT starts to decrease. After increasing the design PR of the compressor, the design/off-design performance of high-pressure unit is better than that of PG9351FA unit. Compared with PG9351FA unit, the increment of the efficiency of high-pressure unit is in the range of 0.03–0.42%. This increment of the off-design efficiency rises, and the maximum value reaches 0.42% at 80% gas turbine load. Furthermore, when the gas turbine load is below 80%, the increase in the combined cycle efficiency remains at 0.4%. The TIT is a very important parameter in design and off-design conditions. To reduce the load of gas turbine/combined cycle, either the TIT or the mass flow of the working medium should be reduced. As the design PR increases, the relative air flow decreases significantly when the IGV regulation is applied, which results in a relatively high performance. Therefore, for the combined cycle unit that always participates in the pitching peak, increasing the design PR properly can result in satisfactory design/off-design characteristics. As for the combined cycle with a design PR of 12.73, the decrement of the efficiency under the design/off-design conditions is in the range of 0.20–0.39%. A low design PR results in high specific work. For the combined cycle unit with a design PR of 12.73, the power output increases by 4.80–13.20 MW (1.19–3.27%) relative to the PG9351FA unit (Fig. 25). For the combined cycle unit with a design PR of 18, although the overall efficiency increases relative to the benchmark unit, the power output decreases by 6.70–11.00 MW (1.66–2.72%). We find in the comparison of the topping and bottoming cycles that the variation of the thermal/exergy efficiency of the topping cycle is higher than that of the bottoming cycle and that the power output of the topping cycle holds the main part. Therefore, the thermodynamic efficiency degree of the topping cycle exerts a significant influence on the combined cycle. Meanwhile, the exhaust temperature of the topping cycle affects the thermodynamic performance of bottoming cycle. Thus, thermodynamic efficiency itself should be considered first in designing a reasonable topping cycle, followed by a proper exhaust temperature for bottoming cycle. Such consideration shows the reasonable relationship between the topping and bottoming cycles for the traditional gas-steam combined cycle. For an efficient operation, keeping TIT first and then the inlet temperature of HRSG as high as possible is very important. Comparing the three units, if the design efficiency of a traditional gas-steam combined cycle is high, the off-design efficiency is also high in the range of the general PR. For PG9351FA unit, increasing the design PR properly can result in good design and off-design performance, but the design power output decreases.

5. Conclusions On the basis of the design parameter of the given PG9351FA gas turbine and the matching HRSG, two redesigned combined cycles are designed by increasing or decreasing the design PR of compressor. The interaction relationship between the topping and bottoming cycles and the combined cycle is studied by analyzing their detailed design/off-design condition characteristics. The main conclusions can be summarized as follows: (1) The thermal efficiency decrements of the topping cycles for the high-pressure, PG9351FA, and low-pressure units are 12.1%, 12.6%, and 12.8% with the corresponding exergy efficiency decrements of 11.9%, 12.4%, and 12.0%, respectively. The TIT affects dramatically the exergy efficiency of topping cycle. The thermal efficiency decrements of the

(2)

(3)

(4)

(5)

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corresponding bottoming cycle are 9.6%, 9.7%, and 10.3% with exergy efficiency decrements of 9.4%, 9.2%, and 9.5%, respectively. The variations of the thermal/exergy efficiencies of the topping cycle are higher than those of the bottoming cycle, and the power output of the topping cycle holds the main part. Thus, the off-design characteristics of the topping cycle plays a dominant role in the combined cycle. The exergy efficiency of HRSG is at a high level and changes slightly (77.5–80.9%, 78.6–81.8%, and 79.6–83.0%) under design/off-design conditions, therefore, the HRSG can effectively recover the heat/heat exergy of the gas turbine exhaust to the steam under most of the load conditions. Therefore, increasing the exhaust temperature and the design parameters of bottoming cycle alone cannot effectively increase the thermal/exergy efficiency of the HRSG. Compared with PG9351FA unit, the increment of the combined cycle efficiency of the high-pressure unit is in the range of 0.03–0.42%. However, as for the combined cycle with a design PR of 12.73, the decrement of the efficiency under the design/off-design conditions is in the range of 0.20–0.39%. Thus, for the combined cycle unit that often participates in pitch peak, the design PR of the compressor should be relatively high, but the specific power decreases. For a traditional gas-steam combined cycle, a high design efficiency results in a high off-design efficiency in the usual range of PR. For the efficient design of a combined cycle, the optimal efficiency and maximum specific power of combined cycle, instead of that of topping cycle, should be considered. The topping cycle thermodynamic performance should be first considered, followed by a proper exhaust temperature for bottoming cycle. Such considerations highlights the reasonable relationship between the topping and bottoming cycles. For an efficient operation, keeping first the TIT and then the inlet temperature of HRSG as high as possible is very important. To obtain relatively high design/off-design efficiencies of traditional gas-steam combined cycle, the TIT, which has been reached in modern advanced heavy-duty gas turbine (about 1327–1427 °C), cannot match the bottoming cycle with the initial temperature of over 603 °C. Therefore, the relatively high steam turbine initial temperature is not always beneficial to improve the traditional gas-steam combined cycle efficiency.

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