Thermoeconomic Optimization of Steam Pressure of Heat Recovery Steam Generator in Combined Cycle Gas Turbine under Different Operation Strategies

: The optimization of the steam parameters of the heat recovery steam generators (HRSG) of Combined Cycle Gas Turbines (CCGT) has become one of the important means to reduce the power generation cost of combined cycle units. Based on the structural theory of thermoeconomics, a thermoeconomic optimization model for a triple pressure reheat HRSG is established. Taking the minimization of the power generation cost of the combined cycle system as the optimization objective, an optimization algorithm based on three factors and six levels of orthogonal experimental samples to determine the optimal solution for the high, intermediate and low pressure steam pressures under different gas turbine (GT) operation strategies. The variation law and inﬂuencing factors of the system power generation cost with the steam pressure level under all operation strategies are analyzed. The research results show that the system power generation cost decreases as the GT load rate increases, T 4 plays a dominant role in the selection of the optimal pressure level for high pressure (HP) steam and, in order to obtain the optimum power generation cost, the IGV T3-650-F mode should be adopted to keep the T 4 at a high level under different GT load rates.


Introduction
As we know, the Combined Cycle Gas Turbine (CCGT) power plant has become one of the main development directions of future thermal power generation. Improving the economic performance of the unit operation and reducing the cost of power generation have become urgent needs for CCGT power plants.
In the CCGT system, both the heat recovery steam generator (HRSG) and gas turbine (GT) are important devices and the key equipment for system performance optimization and control. The thermodynamic performances of GT and HRSG also have a great impact on its power generation cost. Therefore, it is very important to optimize the performance of GT and HRSG. When the GT system is determined, the choice of GT operation strategy is a key factor in improving the thermodynamic performance of the combined cycle. When the GT operates under different operation modes, the variation rules of the thermodynamic performance of the CCGT are different under the off-design conditions [1]. The common off-design regulation strategies of CCGT include the inlet guided valve (IGV) regulation, GT guide vane regulation, speed regulation and fuel quantity regulation. Kim et al. [2] found that the IGV regulation was beneficial in improving the off-design performance of the single shaft GT with a bottom cycle, but the improvement effect on the thermodynamic performance of the double shaft unit was limited. Domachovski and Dzida [3] compared the off-design thermodynamic performance of the IGV regulation and the pure fuel regulation by the software simulation. Song et al. [4] studied the influence of the IGV regulation on a single shaft GT. It was found that although the IGV regulation could improve the exhaust temperature of the turbine and improve the system efficiency, it would also result in an increase in exergy loss during the first stage compression process of the air compressor.
The parameter optimization of the steam bottoming cycle is also a key measure in improving the combined cycle performance. There are many thermodynamic parameters that affect the CCGT system efficiency, including the flue gas-side parameters such as GT exhaust flue gas temperature and mass flow rate, the pinch point temperature differences, the approach point temperature differences and the steam-side parameters such as high, intermediate and low pressure (HP, IP and LP) steam pressures and temperatures. These parameters have different effects on the CCGT system efficiency. The literature [5,6] has used the traditional CCGT system as the research object, and the influences of each parameter on its thermodynamic performance were studied. The results showed that the steam pressure values played a major role in the effect of the bottoming cycle efficiency.
The literature [7] shows that the steam pressure was the major parameter for getting the maximum energy from the exhaust flue gas of the GT, and that the steam pressure strongly influenced the overall power and thermal efficiency of CCGT. The optimization objective was to maximize the exergy recovery of the HRSG. By using the ε-NTU analysis method, the model of a heat exchanger in a triple pressure reheat HRSG was established, and the pressure values of high, intermediate and low pressure steam in the HRSG were optimized with the aim of the highest system efficiency of CCGT [8]. Hui et al. [9], with the aim of three objective functions (higher efficiency, less cost and lower emission), optimized the pressure values of HP, IP and LP steam in the HRSG based on a genetic algorithm. Yang [10] aimed to maximize the efficiency of the combined cycle and used genetic algorithms to optimize the pressure values of the HP, IP and LP steam in the HRSG.
With the rapid development of CCGT, its thermoeconomic analysis has received extensive attention. The cost calculation and benefit analysis of the CCGT have become a hot spot in recent years. Thermoeconomics is a cross-discipline that combines thermodynamics and economics. Not only can it calculate the efficiency of the system from a local perspective and determine the number and distribution of the irreversible losses of each component in the unit, it can also can calculate and analyze the production costs of each component of the unit, so as to price the products and control the fuel consumption and equipment investment costs of each component of the unit [11]. The concept of thermoeconomics was first proposed by Tribus and Evans [12,13] in the exergy cost calculation of the desalination process in 1962. Valero et al. [14] defined the conceptions of the fuel and products of each component of the unit in the production structure diagram and proposed the principles and methods of introducing auxiliary equations. Hunkun Li et al. [11] established the thermoeconomic model of a CCGT to calculate the non-energy costs of each component in the system. Carlo et al. [15] used the thermoeconomic analysis method to study the effects of steam pressure on the CCGT performance. Xiong et al. [16] conducted a thermoeconomic analysis by establishing a 600 MW coal-fired power plant model. The thermoeconomic structural theory unifies all thermoeconomic methods with a universal linear mathematical model. It adopts physical and production structure diagrams through the analysis of the system, establishes a product cost calculation model equation set, calculates the product cost distribution and analyzes the results [14].
The current thermoeconomic optimization of the CCGT system mainly focuses on a certain GT operation strategy [11,15], and the system performances under different GT operation strategies are only analyzed by using the thermoeconomic method [17]. There is no literature on the optimization of the thermoeconomic performance of the system under different GT operation strategies. Therefore, it is of great significance to study the variation law of the steam pressure level under different operation strategies for the reduction of the thermoeconomic cost of CCGT.
The literature [5,18] has optimized the steam pressure values of the HRSG to maximize the efficiency of the CCGT. However, this optimization did not consider energy costs and non-energy costs and did not fully reflect the economic benefits of the optimization on the system. Therefore, it is necessary to carry out a study on the optimization of the parameters of a triple pressure reheat HRSG by considering the energy costs and the non-energy costs.
Based on the thermoeconomic structure theory modeling method, this paper establishes a thermoeconomic optimization model for the steam parameters of the triple-pressure reheat HRSG in a CCGT system. Aiming at the minimum power generation cost of the CCGT system, an optimization algorithm based on three factors and six levels of orthogonal experimental samples is proposed to determine the optimal solution for the steam parameters under different operation strategies. The variation rules and influencing factors of the system power generation cost under all operation strategies are analyzed.

System Description
The research object is a CCGT system composed of a PG9351FA GT and a steam bottom cycle system with a triple-pressure reheat HRSG [1]. Figure 1 is the CCGT system flowchart. The GT design data [19] are shown in Table 1. The detailed full-condition model of the CCGT system used in this article is described in the literature [1], so this article will not go into details about the construction of the CCGT unit model. Table 2 shows the comparison between the simulation results of the CCGT and operation data (IGV T3-F operation mode) under 100%, 75%, 50% and 25% GT load rates. The relative errors are less than 3%, so the simulation models are effective and feasible.

GT Modeling
The GT is divided into three stages, and the stage by stage turbine cooling off-design calculation model is adopted. The main equations of the GT cooling air flow are as follows [20][21][22]: where T is the temperature, K; k cool stands for the cooling flow factor; Bi is the Biot number; m is the mass flow rate, kg/s; η is the efficiency; and ε is the cooling coefficient. Superscript/subscript: met is the metal; tbc is the thermal barrier coating; g is the gas; b is the blade; int is the internal; c is the cooling air; and f is film.

HRSG Modeling
The off-design model of the HRSG is based on the energy conservation equation and heat transfer equation. The pressure loss of the heating surface is 3.5% [23]. The main equations are as follows [24,25]: Superheater(S) and Re-heater(RH): Economizer(E) and Evaporator(Ev): F g = c 0.33 p k 0.67 /µ 0.32 (10) where, c p is the specific heat capacity, kJ/(kg·K); k is the gas thermal conductivity, N·s/m 2 ; (UA) p is the product of the heat transferring area and overall heat transfer coefficient; t is the temperature, K; and µ is the gas dynamic viscosity, W/(m·K −1 ). Superscript/subscript: s is the steam; 1 is the inlet; 2 is the outlet; and d is the design.

ST Modeling
The ST adopts the sliding pressure mode, and its operating pressure is determined by the operating characteristics of the HRSG and the ST. The main equations are as follows [25]: LP cylinder: HP and IP cylinder: The ST efficiency is as follows [21]: where p is the pressure, MPa. Superscript/subscript: red is the reduction and tur is the turbine.

CCGT Thermodynamic Performance Evaluation Indexex
The heat balance analysis of the CCGT is developed based on the first law of thermodynamics-the conservation of mass and energy. The thermodynamic performance evaluation indexes in the CCGT are defined as follows [26]: where P GT is the GT output power, MW; P ST is the ST output power, MW; P gt is the turbine output power, MW; and ac is the air compressor power consumption, MW. The thermal efficiency of the CCGT system is as follows: where P CCGT is the CCGT output power, MW; LHV is the fuel low heating value, kJ/kg; and m fuel is the fuel consumption, kg/s.

Unit Thermoeconomic Cost Modeling
Thermoeconomic structural theory uses physical and production structure diagrams to establish a system of product cost calculation model equations through system analysis in order to calculate product cost distribution [11]. This paper builds on the thermoeconomic model based on the thermoeconomic structural theory in order to make a reasonable evaluation of the economic operation of the thermal system.

Physical Structure and Productive Structure
The physical structure of the CCGT system is presented in Figure 2. According to the description of the fuel product definition, the physical structure diagram is transformed into the production structure diagram. The productive structure of the CCGT system is presented in Figure 3.  AC is the air compressor; CC is the combustion chamber; GT is the gas turbine; HRSG is the heat recovery steam generator; HPT is the high pressure turbine; IPT is the intermediate pressure turbine; LPT is the low pressure turbine; GEN is the generator; CND is the condenser; FB is the fuel exergy; FS is the fuel negentropy; and PB is the product exergy. The rhombus stands for the collection component and the circle stands for the branch component.

Thermoeconomic Cost Equations
When the fuel cost and non-energy cost in a CCGT system are given, the thermoeconomic cost equation can be established according to Figure 3.
The thermoeconomic cost equation is as follows: where C PB,i is the unit thermoeconomic cost of the product exergy; C FB,i is the unit thermoeconomic cost of the fuel exergy; C FS,i is the unit thermoeconomic cost of the fuel negentropy; kB i is defined as the ratio between the fuel exergy and the product exergy in a component, which is the unit exergy consumption; kS i is defined as the ratio of the fuel negentropy to the product exergy in a component, which is the unit negentropy consumption; and kZ i is defined as the unit product non-energy cost, $/GJ.
The calculation formula of the equipment investment cost is selected from [27][28][29][30]. Using the above equations, the investment costs of each piece of equipment in the system can be obtained, as shown in Table 3. In CCGT non-energy cost calculations, the depreciation, repair and personnel costs of the equipment should also be included. This paper uses the method employed in the literature [8] to calculate the annual non-energy cost. The main equations used are as follows: where ϕ is the maintenance factor; H is the total operation time, h; f is the annualized factor; CP is the construction cycle of the CCGT, year; AP is the amortization period, year; in is the rate of interest; ri is the rate of inflation; and Z is the investment cost, $. Superscript/subscript: e is each component and t is all components.

Optimization of High, Intermediate and Low Steam Pressures
The thermodynamic performance of the combined cycle has a great influence on the cost of power generation. Therefore, in order to obtain the minimum cost of power generation, this paper adopts the orthogonal experimental design method. The orthogonal experimental design method is a high-efficiency experimental design method that uses orthogonal tables to scientifically arrange and analyze multi-factor experiments and to seek the optimal level combination. It has the advantages of fewer tests, the uniform distribution of data points, a simple method and the strong reliability of the conclusions.
The bottom cycle parameters affecting the thermodynamic performance of the combined cycle are mainly HP, IP and LP steam pressure values. According to the relevant data of the triple pressure reheat HRSG [31,32], the pressure variation ranges of HP, IP and LP steam are 95.00~185.25 bar, 20.00~38.75 bar and 2.00~4.50 bar, respectively.
Since different GT operation strategies have different influences on the thermodynamic performance of the combined cycle, in order to obtain the minimum cost of power generation, this paper adopts four common operation modes of the CCGT unit [1]: to 82% of the GT full load by regulating the IGV angle and fuel flow, then the IGV angle keeps unchangeable and the GT load rate changes from 82% to 19% by only regulating the fuel flow.
IGVT4-F: T 4 is kept constant from 100% to 38% of the GT full load by regulating both the IGV angle and fuel flow, then IGV angle keeps unchangeable and the GT load rate changes from 38% to 22% by only regulating the fuel flow IGVT3-650-F: T 3 is kept constant from 100% to 82% of the GT full load by regulating both the IGV angle and fuel flow, then T 4 is kept 650 • C constant when the GT load rate changes from 82% to 41% by regulating both the IGV angle and fuel flow. Lastly, the IGV angle is kept unchangeable and the GT load rate changes from 41% to 22% by only regulating the fuel flow.
IGVT4 gradual rise-F: T 4 gradually rises to 650 • C from 100% to 43% of the GT full load by regulating both the IGV angle and fuel flow. Lastly, the IGV angle is kept unchangeable and the GT load rate changes from 41% to 22% by only regulating the fuel flow.
Here, T 3 and T 4 stand for the turbine inlet temperature and turbine exhaust gas temperature, respectively. The regulation process of the four GT operation modes is explained in detail in reference [1]. Figure 4 shows the variation rules of T 4 . The maximum allowable temperature of a gas turbine outlet is 650 • C. Within the range of the simulated operating conditions, the variation range of T 4 is 650-397 • C. Under the four GT off-design operation modes (except for the IGVT4-F mode), the T 4 first increases to the maximum allowable temperature (650 • C) and then decreases. The thermodynamic performance changes of the reference CCGT system under the whole working conditions are explained in detail in the literature [1], so the thermodynamic performance changes of the other off-design parameters of the CCGT unit are not discussed in this paper. In this paper, the optimal solution for the HP, IP and LP steam pressures under different GT operation strategies under four loads of 100%, 75%, 50% and 25%.

Optimization Algorithm Based on the Orthogonal Experiment
The optimization algorithm based on the orthogonal experiment includes the following steps [33]: (1) Orthogonal experimental design: determining the optimal variables and the number of value levels; (2) Preliminary optimization: based on the sample points of orthogonal experiment, the corresponding thermoeconomic costs are calculated respectively, and the minimum level is determined by using the principle of minimizing the average thermoeconomic cost at each level; (3) Optimal solution: the optimal solution is determined in the minimum horizontal solution.

The Experiment of Orthogonal Design
In this paper, the orthogonal experimental method is used to optimize the HP, IP and LP steam pressures of the triple pressure HRSG. The index of the orthogonal experiment is the system power generation cost. The purpose of the experiment is to find out the optimal solution of HP, IP and LP steam pressure values, so as to minimize the power generation cost.
Firstly, the pressure values of HP, IP and LP steam are selected as three factors in the orthogonal experiment, and each factor includes six levels, as shown in Table 4. There are six levels of these three factors in this question. If we match the different levels, we need to conduct 6 3 = 216 experiments, which will take a lot of time. The problem can be solved by the orthogonal experiment, and the orthogonal table can be selected according to the design requirements.
(1) Choose the orthogonal table according to the design requirements. In this paper, the orthogonal table L 36 (6 6 ) is selected. The subscript 36 in L 36 (6 6 ) indicates that 36 experiments need to be done; the superscript 6 indicates that experiments with a number of factors less than or equal to 6 can be arranged in this table; and the number 6 indicates that each element has 6 levels.

Analysis of Orthogonal Test Results
(3) Analysis of the orthogonal experiment results. Based on the structural theory of thermoeconomics, a thermoeconomic optimization model for the steam parameters of the HRSG is established. The simulated values and designed values from the reference [18] are list in Table 8. The relative errors are less than 3%, which shows that the design of the thermoeconomic model is reasonable. The intuitive analysis method is used to analyze the calculated results [35]. Since the optimization objective of this paper is to obtain the lowest cost of power generation, the corresponding level with the smaller average value of each factor is the optimal level. For example, as can be seen from Table 6 Table 9 shows the average power generation cost (GT 100% load rate) for each level of the three pressure steams. Figure 5 shows the average power generation cost under all levels (GT 100% load rate). In the average value of LP steam pressure, the level 5 is the smallest and the 0.4 MPa is selected. In the average value of IP steam pressure, the level 2 is the smallest and the 2.375 MPa is selected. In the average value of HP steam pressure, the level 5 is the smallest and the 16.5 MPa is selected.
According to the intuitive analysis results of the orthogonal experiment, we select the level corresponding to the minimum system power generation cost as the optimal parameter of each factor and then obtain the optimal steam pressure values with different GT operation models. Figures 5-8 are the average power generation costs at all levels under these four GT operation modes with 75%, 50% and 25% GT load rates, respectively. In Figures 5-8, the system power generation cost decreases as the GT load rate increases. Under the same GT load rate, the system power generation cost variations under all levels of steam pressures (HP, IP and LP) with different operating strategies are roughly the same. Under four GT load rates, the system power generation cost under the IGV T3 650-F is the lowest.     When the GT load rate is constant, the change of the IGV operating strategy is conducive to the improvement of the CCGT system economic performance. This is because when the GT model number is determined, changing the GT operation strategy will change the T 4 in the operation process when the GT load rate is fixed. In order to find out the key factors affecting the optimal solution of steam pressure, it is necessary to further analyze the optimal steam pressure level at all levels under different operation strategies. Figure 9 shows the optimal steam pressure levels under all operation strategies. In Figure 9, the optimal steam level of the HP steam pressure value increases and the optimal levels of IP and LP steam pressure remain unchanged under a 75% GT load rate for these four GT operation strategies. This is due to the increase of T 4 under the 75% GT load rate in Figure 4. In Figure 9a, the optimal steam level of the HP steam pressure value decreases under a 50% GT load rate. This is due to the fact that the T 4 is lower under the 50% GT load rate. The optimal steam levels of the HP, IP and LP steam pressures remain unchanged under a 50% GT load rate for the other three GT operation strategies. This is due to the larger T 4 under the 50% GT load rate in Figure 4. Under a 25% GT load rate, due to the low T 4 , the optimal steam level of the HP steam pressure value decreases. The optimal steam level of the IP steam pressure remains unchanged. The optimal steam level of the LP steam pressure increases. This is due to the decrease of T 4 under the 25% GT load rate in Figure 4. So, the optimal steam pressure level at all levels is different under different operating strategies, and T 4 plays a dominant role in the selection of the optimal pressure level for the HP steam. The higher the T 4 is and the higher the optimal pressure level of the HP steam is, the lower the system power generation cost is. Therefore, in order to obtain optimum power generation cost, the IGV regulation strategy (IGV T3-650-F) should be adopted to keep the T 4 at a high level.  Table 10 shows the optimal generation costs under different GT operation modes. Under four GT load rates, the system power generation cost under the IGV T3 650-F is the lowest, which is less than the 216 groups of experiments mentioned above. It is significantly lower than the cost of power generation before optimization. Therefore, the optimal pressure values of the HP, IP and LP steam of HRSG are 18.25 MPa, 2.375 MPa and 0.4 MPa, respectively. Under 75% and 50% GT load rates, the system power generation costs are 9.3922 × 10 −2 $/kWh and 1.0828 × 10 −1 $/kWh, respectively. The optimal pressure levels of the HP, IP and LP steam of HRSG are 13.00 MPa, 2.375 MPa and 0.45 MPa, respectively. Under a 25% GT load rate, the system power generation cost is 1.0828 × 10 −1 $/kWh. Since this paper is based on the conventional CCGT considering energy cost and non-energy cost, the optimization of the steam pressure parameters is performed for the CCGT. Compared to those before optimization, the CCGT power generation costs are decreased by 1.57%, 2.92%, 8.42% and 13.18%, respectively. As the GT load factor decreases, the reduction of the CCGT power generation cost is more prominent when the CCGT system operates with the IGVT3-650-F operation strategy. In addition to the parameter optimization, the optimization of the bottom cycle steam flow structure is also important. As shown in Table 3, the investment cost of CCGT system bottom cycle is higher, so the heat exchanger structure configuration design of the bottom cycle system based on the optimized waste heat boiler can further reduce the system power generation cost.

Conclusions
Based on the structural theory of thermoeconomics, a thermoeconomic optimization model for a triple pressure reheat HRSG is established. Taking the minimization of system power generation cost as the optimization objective, an optimization algorithm based on three factors and six levels of orthogonal experimental samples to determine the optimal solution for the HP, IP and LP steam pressures under different gas turbine (GT) operation strategies is developed. The variation law and influencing factors of the system power generation cost with the steam pressure levels under different operation strategies are revealed.
(1) The system power generation cost decreases as the GT load rate increases. The T 4 plays a dominant role in the selection of the optimal pressure level for HP steam. The GT regulation strategy of IGV participating in the regulation is conducive to maintaining higher T 3 and T 4 , so as to ensure the better economic performance of the CCGT system. The GT regulation strategy with a higher T 4 is more favorable to the system power generation cost. (2) The optimal steam pressure values at all levels are different under different operating strategies. Under a 100% GT load rate, the optimal pressure values of HP, IP and LP steam are obtained respectively as 16.5 MPa, 2.375 MPa and 0.4 MPa, the system power generation cost is 8.8590 × 10 −2 $/kWh. Under 75% and 50% GT load rate, the optimal pressure values of HP, IP and LP steam are obtained respectively as 16.5 MPa, 2.375 MPa and 0.4 MPa, the system power generation costs are 9.3922 × 10 −2 $/kWh and 1.0828 × 10 −1 $/kWh, respectively. Under 25% GT load rate, the optimal pressure values of HP, IP and LP steam are obtained respectively as 13.00 MPa, 2.375 MPa and 0.45 MPa. The system power generation cost is 1.0828 × 10 −1 $/kWh. Compared to those of before optimization (the IGV T 3 -650-F operation mode is not adopted), the CCGT power generation costs decreased by 1.57%, 2.92%, 8.42% and 13.18%, respectively. As the GT load factor decreases, the reduction of the CCGT power generation cost is more prominent when the CCGT system operates with the IGVT3-650-F operation strategy. (3) Under four GT load rates, the system generation cost under the IGV T3 650-F is the lowest. Therefore, in order for the CCGT to obtain the optimum power generation cost, the IGV regulation strategy (IGV T3-650-F) should be adopted to keep the T 4 at a high level. The economic performance of the CCGT can be improved by increasing the T 4 .
Author Contributions: Conceived and analyzed data, prepared the manuscript draft, writing, Z.W.; Conceptualization, methodology, review, editing, supervision, L.D. Both authors have read and agreed to the published version of the manuscript.
Funding: This study has been supported by the National Science and Technology Major Project (2017-I-0002-0002).