# Implementation of Adaptive Neuro-fuzzy Model to Optimize Operational Process of Multiconfiguration Gas-Turbines

Authors: Chao Deng; Ahmed N. Abdalla; Thamir K. Ibrahim; MingXin Jiang; Ahmed T. Al-Sammarraie; Jun Wu
Journal: Advances in High Energy Physics
 (2020)

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## Abstract

In this article, the adaptive neuro-fuzzy inference system (ANFIS) and multiconfiguration gas-turbines are used to predict the optimal gas-turbine operating parameters. The principle formulations of gas-turbine configurations with various operating conditions are introduced in detail. The effects of different parameters have been analyzed to select the optimum gas-turbine configuration. The adopted ANFIS model has five inputs, namely, isentropic turbine efficiency (Teff), isentropic compressor efficiency (Ceff), ambient temperature (T1), pressure ratio (rp), and turbine inlet temperature (TIT), as well as three outputs, fuel consumption, power output, and thermal efficiency. Both actual reported information, from Baiji Gas-Turbines of Iraq, and simulated data were utilized with the ANFIS model. The results show that, at an isentropic compressor efficiency of 100% and turbine inlet temperature of 1900 K, the peak thermal efficiency amounts to 63% and 375 MW of power resulted, which was the peak value of the power output. Furthermore, at an isentropic compressor efficiency of 100% and a pressure ratio of 30, a peak specific fuel consumption amount of 0.033 kg/kWh was obtained. The predicted results reveal that the proposed model determines the operating conditions that strongly influence the performance of the gas-turbine. In addition, the predicted results of the simulated regenerative gas-turbine (RGT) and ANFIS model were satisfactory compared to that of the foregoing Baiji Gas-Turbines.


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## Body

## 1. Introduction

Energy management, performance analysis, and economic evaluation of a combined heating, cooling, and power system are complicated tasks and often woven into a major project requiring teams of engineers from multidisciplinary backgrounds [1]. The large-scale power and industrial plants have proven the reliability of a combined heat and power (CHP) technology for more than 100 years as the ones that generate electric power and recycle by-product heat from the primary source [2–4]. The conventional implementation of CHP technology is done with large combined cycle gas-turbine (CCGT) systems. Widely successful since the 1950s, the CCGT (also known as cogeneration) systems typically add an unfired waste heat recovery steam generator [5]. The number of available complementary technologies, site specifics, various utility electric rates, and interconnection agreements would only add to the complexity and the cost of the design project [6]. Thus, a preliminary analysis is frequently started with evaluating mathematical models of CHP systems. Mathematical models are not only useful for such decision-making but also invaluable tools to evaluate hypothetical scenarios that would be prohibitively costly or risky to diagnose otherwise [7].Gas-turbines (GT) are extensively used in several industries which require consumption of considerable power, and this circumstance is often referred to as GT power plants. The GT efficiency is about thermal circulation that has been strongly affected by the overall profitability of electrical energy. The GT plants often must function for extended phases even at situations that are not compatible with their planned operating conditions [8]. The relationship between energy utilization and economic growth significantly matters in the current world [9, 10]. Moreover, improving the thermal efficiency of a power plant includes the joining optimization of disciplines and capacities which are required to achieve operational competitiveness. The design and the efficiency of the plant components identify the combustors, turbine, and compressors [11]. Therefore, understanding the efficiency of GT power plants at such working conditions is crucial, particularly in a deregulated market [12, 13].Gas-turbines are well suited for integrating with CHP technology due to high-quality exhaust heat [14, 15], lower initial costs, and shorter construction time compared to other contemporary power generation technologies [16]. The heat coming off the gas-turbine engine is usually converted into steam by the heat recovery steam generator (HRSG) for processing heat or other uses. The conventional application here is to operate the gas-turbine in the combined cycle on base load for maximum thermal efficiency [17]. The simplified physics are captured in the forms of governing equations with the time-dependent conservation laws for each gas-turbine component. The dynamic capability of the developed models is intended to be accurate to simulate the transient operating characteristics of components and the fully integrated gas-turbine system without being too computationally intensive. The models are built in MATLAB-Simulink® environment for ease of development and testing control algorithms and strategies.Computational models are necessary tools in the development and testing of gas-turbine engines. The size and complexity of these models vary from simple zero-dimensional curve-fitted expressions to three-dimensional computational fluid dynamics (CFD) simulation packages. The gas-turbine engine in a CHP system is but one of the several important operating cornerstones of a large cogeneration plant, whose overall performance is dictated by the dynamic change of the energy demands from the end-user. As a general rule, computational complexity should be minimized without sacrificing important modeling accuracy to be temporally concise for analysis. The modeling approach is a bottom-up approach in which the fundamental operating unit of a system is developed individually and the parts eventually assemble into an integrated system model [2, 18]. For the gas-turbine, the major components are simulated individually as control volumes described by time-dependent conservation equations. This equipment combination led to increasing pressure losses at the front and rear of the gas-turbine, incurring performance losses at the compressor and turbine section [19]. Furthermore, additional efficiency losses can occur in the gas-turbine due to plant equipment such as an air filtering system, heat recovery steam generator, and selective catalyst reduction.There are only two methods to examine the performance of the GT plant and its elements at the beginning of the developmental stage, which is either to assess the prototypes of the whole GT energy plant or to consider its primary components. However, these methods are time-consuming to execute [20]. Furthermore, the GT plant works at full load for a significant part of its life. Consequently, it is suggested that the pattern of its performance should be analyzed in detail before it is run. A mathematical model is used with the help of analytical methodology to get the most effective solution for increasing the performance of the plant [21, 22]. Since the sources and consequences of the primary failure of this whole system need to be addressed as efficiently as possible, more research work is required to improve the performance of power plants with the improvement of energy productivity and the reduction in fuel consumption. For this purpose, computerized mathematical modeling of the GT plant will be very useful. Thus, parametric studies on the effect of operating conditions and gas-turbine configurations are required to control those conditions of the system [23, 24]. Lazzaretto and Toffolo [25] developed a physical zero-dimensional relation of a twin-shaft gas-turbine based on experimental data. The study was aimed at simulating the performance and emissions of the variable speed General Electric LM2500-PE Gas-Turbine. Najjar [26] provided a qualitative comparison between the performance of twin-shaft and single-shaft gas-turbines as prime movers of cogeneration plants. This fundamental study reaffirmed the idea that single-shaft gas-turbines are more suitable for a combined cycle plant due to their high efficiency.Several CHP models still utilize the classical linear programming technique to determine optimal operating strategies, maximize energy management, and minimize the overall cost of energy [27, 28]. In addition, the major components of soft computing, neural networks, genetic algorithms, and fuzzy logic have been also wildly used as successful and capable tools to identify and solve complex mathematical problems [29]. Most notably, the study conducted by Wang et al. [30] has developed a generic algorithm to optimize the configuration of a CHP system for a hotel application. Their model evaluated a comprehensive set of operational parameters including the annual changes in monthly electricity and natural gas prices to deduce the optimal primary energy consumption for the most efficient and highest cost savings [30]. The ANFIS technique was also successfully studied and developed based on the diagnostics of health indices of a 255 MW single-shaft gas-turbine (La Spezia, Italy) [31, 32]. The analyses mostly focused on optimizing the ANFIS structure, in terms of computational training time, accuracy, and robustness towards measurement uncertainty during simulations. Further, an artificial neural network (ANN) has been proposed to improve the performance and the heat rate of a power plant [33, 34].The present work mainly focuses on the adaptive neural fuzzy system to predict the operating conditions which are associated with the performance enhancement of the gas-turbine power plant. Details of the development of power-generation technologies using simple gas-turbines, complex gas-turbines (regenerative, two-shaft, reheat, and intercooler), and gas-turbine auxiliary systems have comprehensively been investigated, particularly those aimed at enhancing the performance of gas-turbines. The proposed ANFIS model consists of five layers, where the input layer has five neurons representing, namely, isentropic turbine efficiency (Teff), isentropic compressor efficiency (Ceff), ambient temperature (T1), pressure ratio (rp), and turbine inlet temperature (TIT), and the output layer has three neurons representing fuel consumption, power output, and thermal efficiency. Both the simulated gas-turbine model and ANFIS coding were developed using MATLAB-Simulink® software. Finally, this study validates the employed ANFIS model to single out the parameters associated with the optimal performance of actual operation data for the Baiji Gas-Turbines in Iraq.


## 2. Related Work

### 2.1. The Power Plant

The Baiji Gas-Turbine power plant is located in Baiji city, Iraq. It has 4 single-cycle gas-turbines. The turbines are SGT5200E Siemens AG (previously known as V94.2). Each one has a design capacity of 150 MW and runs on light fuel oil and heavy fuel oil. The construction work of the power plant was performed by Bharat Heavy Electricals Limited (BHEL) between the years of 2000 and 2003.


### 2.2. Simple Gas-Turbine Cycle

The gas-turbine is a type of internal combustion engine that converts the heat of combustion into mechanical energy. It does this job by means of first compressing the air in a compressor, then injecting air into a combustor where air and fuel are mixed. Fuel is burned at relatively constant pressure, and heat is released into the hot product gases. As the hot air enters the turbine, it expands, in the process turning the turbine blades and producing mechanical power [23, 24]. The turbine provides a suitable power to drive the compressor, and whatever power is left is considered as the engine output. The gas-turbine cycle can be represented by a thermodynamic cycle called the Brayton cycle.Figure1(a) shows that the overall gas-turbine system mainly consists of four components, i.e., the generator, turbine, combustion chamber, and compressor. The simple gas-turbine diagram shows that the air of the compressor is delivered to the combustion chamber, the fuel increases the compressed air temperature through a combustion process, and the mechanical energy is produced by expanding the hot combustion gases in the turbine and then discharging them to the atmosphere.Figure 1
Schematic diagram of different gas-turbine cycles.
(a)
SGT cycle(b)
TGT cycle(c)
IGT cycle(d)
RGT cycle(e)
HGT cycleThe work net of the gas-turbine (WGnet) is expressed as follows [35]:
(1)WGnet=Cpg×TIT×ηt1−1rpγg−1/γg−Cpa×T1rpγa−1/γaηmηc,where rp is the pressure ratio, TIT (T3) is the turbine inlet temperature, ηm is the mechanical efficiency, and γg=1.33 and γa=14.The specific heat of air (Cpa) is determined as [35]
(2)Cpa=1.0189×103−0.1378Ta+1.984×10−4Ta2+4.24×10−7Ta3−3.7631×10−10Ta4,and the specific heat of flue gas (Cpg) is determined as
(3)Cpg=1.80828−2.31269×10−3T+4.04501×10−6T2−1.73626×10−9T3,where the ambient temperature is measured in Kelvin.The turbine output power (P) is defined as
(4)P=mg×WGnet.The turbine exhaust gas mass flow rate (ṁg) is presented by
(5)ṁg=ṁa+ṁf,where the mass flow rate of inlet air and fuel are ṁa and ṁf, respectively.The specific fuel consumption (SFC) is determined as follows:(6)SFC=3600frWnet,where fr is the fuel-to-air ratio.The additional supplied heat (Qadd) is determined by the following equation [(10)]:
(7)Qadd=Cpg×TIT−T1×1+rpγa−1/γa−1ηc,while the overall gas-turbine thermal efficiency (ηth) is expressed as [36]
(8)ηth=WGnetQadd.


### 2.3. Gas-Turbine Configuration Cycle

The efficiency of the simple gas-turbine cycle is low compared to that of steam and diesel turbines. Therefore, different improvements are proposed by many research works which focus on the concept of optimal configuration to enhance the performance of a combined cycle gas-turbine station. The most used methods are discussed in the following section.


#### 2.3.1. Two-Shaft Gas-Turbine

Figure1(b) shows the process of a two-shaft gas-turbine configuration (TGT) operation. The air is compressed adiabatically, and then the fuel is burned with air through the combustion chamber to the maximum cycle temperature which occurs at state 3. The exhaust gases produced by the combustion process are used to drive the compressor [37, 38]. The low gas-turbine exhaust gases temperature (T5) is defined as
(9)T5=T41−ηt1−T5sT4,where T5s is the exit low-pressure turbine temperature.The work net is expressed as(10)Wnet=CpgT4−T5,and the heat addition (Qadd) is expressed as
(11)Qadd=CpgTIT−T4.


#### 2.3.2. Intercooled Gas-Turbine (IGT)

Intercooling is important to reduce the power consumption of air compression and maintain the second stage compressor inlet temperature as low as possible. Figure1(c) shows a single-shaft gas-turbine plant with intercooler. In this cycle, the first-stage compressor, the compressed air enters and is cooled in the intercooler. The second stage compressor compresses the cooled air for a specific pressure rate and then transmits it to the combustion chamber to a maximum permissible temperature [39]. The cycle work net output is directly proportional to the turbine temperature drop. The work net is expressed as follows [40]:
(12)WGnet=CpgTIT·ηtηm1−1rp2γa−1/γa−CpaT1rpγa−1/γa−1ηmηc2+1−xrpγa−1/γa−1ηc,In the combustion chamber, the heat absorbed by air is equal to the fuel-supplied heat. The fuel-supplied heat is determined by the following equation [41]:
(13)Qadd=CpgTIT−T1+T2rpγa−1/γa−1ηc2−x+1−xrpγa−1/γa−1ηc.


#### 2.3.3. Regenerative Gas-Turbine

The single-shaft gas-turbine produces the necessary power required to run the compressor. Figure1(d) shows the regenerative gas-turbine (RGT) cycle where the compressed air enters into a regenerator to be heated by the exhaust gases coming from the turbine. Then, the air is additionally preheated to a maximum permissible temperature in the combustion chamber [21]. The work net can be defined as follows:
(14)WGnet=Cpg×TIT×ηtηm1−1rpγg−1/γg−CpaT1rpγa−1/γaηmηc.In the combustion chamber, the fuel-supplied heat is equal to the absorbed air heat, which can be expressed as(15)Qadd=Cpg×TIT−T11−ε×1+rpγa−1/γa−1ηc−ε×TIT×1−ηt1−1rpγa−1/γa.


#### 2.3.4. Reheat Gas-Turbine

The principle of improving the performance of the SGT cycle can be implemented by means of reheating the gases at some intermediate points to the maximum cycle temperature [40]. Figure 1(e) depicts a reheat gas-turbine (HGT) cycle. For the isentropic process, the work of the gas-turbine is expressed as
(16)WGnet=CpgTIT−T6,where the turbine inlet temperature is TIT=T3=T5, and T4 is the HP turbine outlet temperature.The exhaust gas temperature from the LP gas-turbine is obtained by(17)T6=TIT1−ηt1−TITrpγg−1/γg×T4a=1,and the heat supplied for HGT is expressed as
(18)Qadd=CpgTIT−T2+TIT−T4.


## 2.1. The Power Plant

The Baiji Gas-Turbine power plant is located in Baiji city, Iraq. It has 4 single-cycle gas-turbines. The turbines are SGT5200E Siemens AG (previously known as V94.2). Each one has a design capacity of 150 MW and runs on light fuel oil and heavy fuel oil. The construction work of the power plant was performed by Bharat Heavy Electricals Limited (BHEL) between the years of 2000 and 2003.


## 2.2. Simple Gas-Turbine Cycle

The gas-turbine is a type of internal combustion engine that converts the heat of combustion into mechanical energy. It does this job by means of first compressing the air in a compressor, then injecting air into a combustor where air and fuel are mixed. Fuel is burned at relatively constant pressure, and heat is released into the hot product gases. As the hot air enters the turbine, it expands, in the process turning the turbine blades and producing mechanical power [23, 24]. The turbine provides a suitable power to drive the compressor, and whatever power is left is considered as the engine output. The gas-turbine cycle can be represented by a thermodynamic cycle called the Brayton cycle.Figure1(a) shows that the overall gas-turbine system mainly consists of four components, i.e., the generator, turbine, combustion chamber, and compressor. The simple gas-turbine diagram shows that the air of the compressor is delivered to the combustion chamber, the fuel increases the compressed air temperature through a combustion process, and the mechanical energy is produced by expanding the hot combustion gases in the turbine and then discharging them to the atmosphere.Figure 1
Schematic diagram of different gas-turbine cycles.
(a)
SGT cycle(b)
TGT cycle(c)
IGT cycle(d)
RGT cycle(e)
HGT cycleThe work net of the gas-turbine (WGnet) is expressed as follows [35]:
(1)WGnet=Cpg×TIT×ηt1−1rpγg−1/γg−Cpa×T1rpγa−1/γaηmηc,where rp is the pressure ratio, TIT (T3) is the turbine inlet temperature, ηm is the mechanical efficiency, and γg=1.33 and γa=14.The specific heat of air (Cpa) is determined as [35]
(2)Cpa=1.0189×103−0.1378Ta+1.984×10−4Ta2+4.24×10−7Ta3−3.7631×10−10Ta4,and the specific heat of flue gas (Cpg) is determined as
(3)Cpg=1.80828−2.31269×10−3T+4.04501×10−6T2−1.73626×10−9T3,where the ambient temperature is measured in Kelvin.The turbine output power (P) is defined as
(4)P=mg×WGnet.The turbine exhaust gas mass flow rate (ṁg) is presented by
(5)ṁg=ṁa+ṁf,where the mass flow rate of inlet air and fuel are ṁa and ṁf, respectively.The specific fuel consumption (SFC) is determined as follows:(6)SFC=3600frWnet,where fr is the fuel-to-air ratio.The additional supplied heat (Qadd) is determined by the following equation [(10)]:
(7)Qadd=Cpg×TIT−T1×1+rpγa−1/γa−1ηc,while the overall gas-turbine thermal efficiency (ηth) is expressed as [36]
(8)ηth=WGnetQadd.


## 2.3. Gas-Turbine Configuration Cycle

The efficiency of the simple gas-turbine cycle is low compared to that of steam and diesel turbines. Therefore, different improvements are proposed by many research works which focus on the concept of optimal configuration to enhance the performance of a combined cycle gas-turbine station. The most used methods are discussed in the following section.


### 2.3.1. Two-Shaft Gas-Turbine

Figure1(b) shows the process of a two-shaft gas-turbine configuration (TGT) operation. The air is compressed adiabatically, and then the fuel is burned with air through the combustion chamber to the maximum cycle temperature which occurs at state 3. The exhaust gases produced by the combustion process are used to drive the compressor [37, 38]. The low gas-turbine exhaust gases temperature (T5) is defined as
(9)T5=T41−ηt1−T5sT4,where T5s is the exit low-pressure turbine temperature.The work net is expressed as(10)Wnet=CpgT4−T5,and the heat addition (Qadd) is expressed as
(11)Qadd=CpgTIT−T4.


### 2.3.2. Intercooled Gas-Turbine (IGT)

Intercooling is important to reduce the power consumption of air compression and maintain the second stage compressor inlet temperature as low as possible. Figure1(c) shows a single-shaft gas-turbine plant with intercooler. In this cycle, the first-stage compressor, the compressed air enters and is cooled in the intercooler. The second stage compressor compresses the cooled air for a specific pressure rate and then transmits it to the combustion chamber to a maximum permissible temperature [39]. The cycle work net output is directly proportional to the turbine temperature drop. The work net is expressed as follows [40]:
(12)WGnet=CpgTIT·ηtηm1−1rp2γa−1/γa−CpaT1rpγa−1/γa−1ηmηc2+1−xrpγa−1/γa−1ηc,In the combustion chamber, the heat absorbed by air is equal to the fuel-supplied heat. The fuel-supplied heat is determined by the following equation [41]:
(13)Qadd=CpgTIT−T1+T2rpγa−1/γa−1ηc2−x+1−xrpγa−1/γa−1ηc.


### 2.3.3. Regenerative Gas-Turbine

The single-shaft gas-turbine produces the necessary power required to run the compressor. Figure1(d) shows the regenerative gas-turbine (RGT) cycle where the compressed air enters into a regenerator to be heated by the exhaust gases coming from the turbine. Then, the air is additionally preheated to a maximum permissible temperature in the combustion chamber [21]. The work net can be defined as follows:
(14)WGnet=Cpg×TIT×ηtηm1−1rpγg−1/γg−CpaT1rpγa−1/γaηmηc.In the combustion chamber, the fuel-supplied heat is equal to the absorbed air heat, which can be expressed as(15)Qadd=Cpg×TIT−T11−ε×1+rpγa−1/γa−1ηc−ε×TIT×1−ηt1−1rpγa−1/γa.


### 2.3.4. Reheat Gas-Turbine

The principle of improving the performance of the SGT cycle can be implemented by means of reheating the gases at some intermediate points to the maximum cycle temperature [40]. Figure 1(e) depicts a reheat gas-turbine (HGT) cycle. For the isentropic process, the work of the gas-turbine is expressed as
(16)WGnet=CpgTIT−T6,where the turbine inlet temperature is TIT=T3=T5, and T4 is the HP turbine outlet temperature.The exhaust gas temperature from the LP gas-turbine is obtained by(17)T6=TIT1−ηt1−TITrpγg−1/γg×T4a=1,and the heat supplied for HGT is expressed as
(18)Qadd=CpgTIT−T2+TIT−T4.


## 2.3.1. Two-Shaft Gas-Turbine

Figure1(b) shows the process of a two-shaft gas-turbine configuration (TGT) operation. The air is compressed adiabatically, and then the fuel is burned with air through the combustion chamber to the maximum cycle temperature which occurs at state 3. The exhaust gases produced by the combustion process are used to drive the compressor [37, 38]. The low gas-turbine exhaust gases temperature (T5) is defined as
(9)T5=T41−ηt1−T5sT4,where T5s is the exit low-pressure turbine temperature.The work net is expressed as(10)Wnet=CpgT4−T5,and the heat addition (Qadd) is expressed as
(11)Qadd=CpgTIT−T4.


## 2.3.2. Intercooled Gas-Turbine (IGT)

Intercooling is important to reduce the power consumption of air compression and maintain the second stage compressor inlet temperature as low as possible. Figure1(c) shows a single-shaft gas-turbine plant with intercooler. In this cycle, the first-stage compressor, the compressed air enters and is cooled in the intercooler. The second stage compressor compresses the cooled air for a specific pressure rate and then transmits it to the combustion chamber to a maximum permissible temperature [39]. The cycle work net output is directly proportional to the turbine temperature drop. The work net is expressed as follows [40]:
(12)WGnet=CpgTIT·ηtηm1−1rp2γa−1/γa−CpaT1rpγa−1/γa−1ηmηc2+1−xrpγa−1/γa−1ηc,In the combustion chamber, the heat absorbed by air is equal to the fuel-supplied heat. The fuel-supplied heat is determined by the following equation [41]:
(13)Qadd=CpgTIT−T1+T2rpγa−1/γa−1ηc2−x+1−xrpγa−1/γa−1ηc.


## 2.3.3. Regenerative Gas-Turbine

The single-shaft gas-turbine produces the necessary power required to run the compressor. Figure1(d) shows the regenerative gas-turbine (RGT) cycle where the compressed air enters into a regenerator to be heated by the exhaust gases coming from the turbine. Then, the air is additionally preheated to a maximum permissible temperature in the combustion chamber [21]. The work net can be defined as follows:
(14)WGnet=Cpg×TIT×ηtηm1−1rpγg−1/γg−CpaT1rpγa−1/γaηmηc.In the combustion chamber, the fuel-supplied heat is equal to the absorbed air heat, which can be expressed as(15)Qadd=Cpg×TIT−T11−ε×1+rpγa−1/γa−1ηc−ε×TIT×1−ηt1−1rpγa−1/γa.


## 2.3.4. Reheat Gas-Turbine

The principle of improving the performance of the SGT cycle can be implemented by means of reheating the gases at some intermediate points to the maximum cycle temperature [40]. Figure 1(e) depicts a reheat gas-turbine (HGT) cycle. For the isentropic process, the work of the gas-turbine is expressed as
(16)WGnet=CpgTIT−T6,where the turbine inlet temperature is TIT=T3=T5, and T4 is the HP turbine outlet temperature.The exhaust gas temperature from the LP gas-turbine is obtained by(17)T6=TIT1−ηt1−TITrpγg−1/γg×T4a=1,and the heat supplied for HGT is expressed as
(18)Qadd=CpgTIT−T2+TIT−T4.


## 3. Proposed Method

The fundamental mechanism for the Sugeno model and its corresponding ANFIS architecture is illustrated in Figure2 [42]. The ANFIS model consists of five layers and each layer with a number of the node. Figure 2 shows the general adaptive model that has two inputs x and y and one output f.Figure 2
The basic equivalent architecture of ANFIS (a) two-input first-order (b) Sugeno fuzzy model with two rules.
(a)(b)Layer 1 is adaptive nodes producing linguistic-label membership grades as expressed by(19)O1,i=μAix=11+x−ci/ai2bi,where the input node is presented by x and y, the layer output node is presented by O1,i, and the fuzzy membership function set=a1,a2,b1,b2 related to the node [43].Layer 2 presents the fixed nodes of all the input indications which are determined by [43]
(20)O2,i=Wi=μAixμBiy,i=1,2.Layer 3 presents the normalized firing strengths in which each node is a fixed rule labeledN node output which is determined by
(21)O3,i=W¯t=WiW1+W2,i=1,2,where W¯iis the normalized firing strength.In layer 4, the output rule is determined for each node by(22)O4,i=W¯ifi=W¯ipix+qiy+ri,where pi,qi,ri presented the resultant parameter set of the node.Layer 5 is the sum of the node outputs of the overall ANFIS output determined by [42]
(23)O5,i=∑iW¯ifi=∑iWifi∑iWi.Figure3 exhibits the proposed ANFIS model which has five inputs, namely, isentropic turbine efficiency (Teff), isentropic compressor efficiency (Ceff), ambient temperature (T1), pressure ratio (rp), and turbine inlet temperature (TIT), and three single outputs, namely, thermal efficiency, power output, and fuel consumption.Figure 3
Proposed ANFIS architecture for equivalent GT model.


## 4. Results and Discussion

### 4.1. Modeling and Simulation

This section investigates the performance of gas-turbine configurations based on various operating conditions such as isentropic turbine efficiency (Teff), ambient temperature (T1), isentropic compressor efficiency (Ceff), turbine inlet temperature (TIT), and pressure ratio (rp). A comparison between the simulated thermal efficiency of the simple GT and the Boyce model [44] is demonstrated in Figure 4. This figure shows an increase in thermal efficiency with the increase in pressure ratio. Compared to the Boyce model of the simple GT, we can confirm that our simulation results are adequate. This is because of an incomplete combustion caused by the usage of fuel oil instead of natural gas in the Baiji plant, thus decreasing the thermal efficiency of the GT power plant. Furthermore, the compressor is much more intolerant to dirt build up in the inlet air filter and on the compressor blades which creates large drops in the cycle efficiency and performance of the Baiji GT power plant. Furthermore, a comparative analysis of the simulated thermal efficiency of the regenerative GT and the Bassily model [45] together with the effect of different values of the pressure ratio and TIT is shown in Figure 5. It is obvious from this figure that there is an increase in thermal efficiency until the pressure ratio reaches 6. The thermal efficiency starts to decrease with the increase in the pressure ratio after the compression value reaches 7 due to the rise in the compressor outlet temperature as a result of the increased pressure ratio. Therefore, the thermal efficiency was reduced due to the reduction in the heat exchange between the air and the flue gases in the regenerative gas-turbine [45]. It is also noticed that increasing the TIT has led to an increase in thermal efficiency. Compared to the Bassily model of the regenerative GT, our simulation results are adequate, as well.Figure 4
The relation of thermal efficiency and pressure ratio of the simple GT and Boyce model.Figure 5
The relation of thermal efficiency and pressure ratio of the regenerative gas-turbine and Bassily model.The effect of pressure ratio on the performance of the GT plants is exhibited in Figure6. The impact of the pressure ratio on the temperature of the exhaust gases from different configurations of the GT is shown in Figure 6(b). It is evident that the decrease in the temperature of the exhaust gases for all the models, except the regenerative GT model, is increased from 590 to 796 K, as an increase in the pressure ratio. Also, when the pressure ratio increases according to the configuration of the GT for other models, so does the exhaust temperature decreases about 220 to 400 K. The heat recovered from the flue gases to increase the temperature of the air entering the combustion chamber leads to a reduction in the temperature of the exhaust with the regenerative GT model [45]. The two-shaft GT model causes a high exhaust temperature, owing to the presence of the two-shaft GT with one shaft that drives the compressor, while the other drives the generator. It should be mentioned that the increase in the exhaust gas temperature stems from the decrease in the total isentropic turbine efficiency and the work of the turbines [26].Figure 6
The impact of pressure ratio on the performance of the gas-turbine.
(a)(b)The effect of the pressure ratio on the thermal efficiency of the GT plants is displayed in Figure6(a). In the case of all the configurations, except the regenerative GT, increasing the compressor ratio creates a linear increase in the thermal efficiency. On the other hand, the thermal efficiency of the regenerative GT rises up to 46.5% at a pressure ratio value of 7. Afterward, it starts to decrease till 37.3% when the pressure ratio soars to 30. More waste heat can be recovered due to the low outlet temperature of the compressor and the low pressure ratio. Less waste heat needs to be retrieved as the high outlet temperature was obtained at a high pressure ratio [46]. As a consequence, there is an increase in the thermal efficiency of the pressure ratio for other configurations. Compared to the lower pressure ratio, the higher pressure ratio has a significant variation in the thermal efficiency of the GT.Moreover, Figure6(a) shows the effect of the pressure ratio on the fuel consumption for the different studied configurations. At a pressure ratio of 7, the specific fuel consumption has a minimum value (0.159 kg/kWh) in the regenerative GT. This value starts to increase after passing the value of the pressure ratio. In the case of the other configurations, the specific fuel consumption always decreases with the increment in the pressure ratio. In comparison with the lower pressure ratio, the deviation of the specific fuel consumption is higher at the higher pressure ratio. When the pressure ratio increases from 3 to 30 for all configurations, except the regenerative one, the specific fuel consumption decreases (about 0.32 kg/kWh to 0.17 kg/kWh).As indicated in Figure6(b), this is a result of the decrease in the exhaust temperature with the increase in the pressure ratio. In addition, the variation of GT cycles’ output power with the pressure ratio is shown in Figure 6(a). As is evident, increasing the pressure ratio leads to an increase in the output power depending on the configuration of the GT. However, it is noticed that the higher pressure ratio is significant on the output power variation. Due to the burning of more fuel in the additional combustion chamber, the higher output power is obtained in the reheated GT configuration [47]. It can be seen that the lower pressure ratio was insignificant on the output power.The effect of ambient temperature on the performance of the GT plants is depicted in Figure7. The variation of the exhaust temperature of the GT power plants with the effect of the ambient temperature is demonstrated in Figure 7(b). In the case of all the configurations, except the regenerative GT, the increase in the ambient temperature leads to a gradual rise in the exhaust temperature by about 10 K. The regeneration applied to recover heat from the flue gases and increase the air temperature entering the combustion chamber is the main reason behind it. Therefore, for the RGT compared to the other GT configurations, the temperatures of the exhaust gases are increased with increase of the ambient temperature [13, 48]. The lowest exhaust temperature of about 655 K is obtained in the regenerative GT, while the highest temperature of about 1200 K is obtained in the two-shaft GT. Furthermore, the effect of ambient temperature on the thermal efficiency of the GT cycle for different configurations is shown in Figure 7(a). The rising ambient temperature causes a reduction in thermal efficiency. Increasing the ambient temperatures also results in the increased losses of the exhaust gases, which is also a reason for the reduction of the thermal efficiency [49, 50]. The maximum thermal efficiency for the GT configurations is obtained at an ambient temperature of 273 K with the regenerative GT configuration, while at an ambient temperature of 327 K, a minimum thermal efficiency of 33% for the intercooler gas-turbine (IGT) configuration is observed. The work of the compressor increases as the ambient temperature increases. Therefore, there is a reduction in the thermal efficiency of all the configurations. The design of the compressor of the GT is such that it maintains a constant air volume, while the mass is reduced with the increase in the ambient temperature [51]. The mass flow is reduced to maintain the same volumetric flow, which leads to a reduction in the output power of the GT and an increase in the temperature at the inlet of the combustion chamber [26, 51]. The GT thermal efficiency eventually decreases as there is a decrease in the burning fuel and the TIT. Figure 7(b) indicates the variation of the specific fuel consumption of the GT power plant with the effect of the ambient temperature. The specific fuel consumption and the ambient temperature are directly proportional to each other [52]. For all the configurations of the GT, the specific fuel consumption increases with the increase in the ambient temperature. In the presence of the regenerative GT configuration at an ambient temperature of 273 K, the lowest specific fuel consumption occurs at 0.156 kg/kWh. While with the reheated GT configuration at ambient temperature of 327 K, the highest specific fuel consumption occurs at 0.223 kg/kWh.Figure 7
The impact of ambient temperature (°C) on the performance of the gas-turbine.
(a)(b)The predicted output power of the GT configurations with the actual data from the Baiji GT power plant versus the ambient temperature is shown in Figure8. For all the configurations, the output power has been observed to decrease with the increase in the ambient temperature. It is observed that, at any ambient temperature, the lowest and highest output powers obtained are for the regenerative and reheated GT configurations, respectively. Likewise, for all the configurations, except the intercooler GT configuration, a decrease in the output power by 296 MW is observed when the ambient temperatures increased from 273 K to 327 K. The rise in exhaust temperatures is the main reason behind this behavior [53]. Moreover, compared to the output power data of the Baiji GT power plant, enhanced output power has been obtained utilizing the studied GT configurations. The Baiji GT plant uses the fuel oil, which when burned creates a loss in the output power due to the incomplete combustion. On the contrary, the models proposed for the GT plant are designed to work on complete combustion of the natural gas.Figure 8
The relation between the output power and the ambient temperature for the predicted results and the actual data from the Baiji Gas-Turbine power plant.The effect of the TIT on the performance of the GT plants is shown in Figure9. The effect of the TIT on the exhaust temperature of the GT plants is displayed in Figure 9(a). It observed that increasing the TIT causes a rise in exhaust temperature which means that enough heat is supplied by the high TIT to the power turbine, which is then able to produce higher exhaust gases and work net from the GT [54]. Therefore, when the TIT increases from 1100 to 1900 K for all configurations, except for the regenerative GT, the exhaust temperature of the GT also increases by about 700 K. In fact, there is an increase of 150 K in the exhaust temperature of the regenerative model though. At low TIT, there is a minor variation in the exhaust temperature, while at the higher TIT, the exhaust temperature is significant for all the GT configurations. The variation of the thermal efficiency against the TIT for various configurations of the GT is shown in Figure 9(b). It is observed that with the increase in the TIT, there is an increase in thermal efficiency. There is a nominal deviation in the thermal efficiency at the lower TIT, while the deviation is significant at the higher TIT. This occurs owing to the increased work that the GT cycle has to do [13].Figure 9
The impact of the TIT on the performance of the gas-turbine.
(a)
Exhaust temperature(b)
Thermal efficiency(c)
Specific fuel consumption(d)
Power outputTherefore, to increase the thermal efficiency of the GT, the TIT becomes a very critical factor. Except for the regenerative GT, there is an increase in the thermal efficiency of about 3.1% in all the configurations, while for the regenerative GT configuration, the thermal efficiency increased from 33.4 to 52.3%. Furthermore, the effect of the TIT on the specific fuel consumption of the GT plant for different configurations is shown in Figure9(c). The specific fuel consumption decreases from 0.218 to 0.137 kJ/kWh with the increase of the TIT for all configurations, except for the regenerative GT which reduced by about 0.01 kJ/kWh. Figure 9(a) shows the variation of output power versus TIT. As is evident, the increment in the TIT leads to an increase in the output power. But the TIT is significant at the higher values on the output power variation. Due to the burning of more fuel in the additional combustion chamber, the output power obtained in the reheated GT configuration is higher [47]. The less the fuel burned in the combustion chamber of the regenerative GT, the lower the output power obtained in this configuration which is consistent with the results of Figure 9(d).The effect of the isentropic compressor efficiency (Ceff) on the performance of the GT plants is shown in Figure 10. The variation of the exhaust temperature of the GT with the Ceff for different configurations is demonstrated in Figure 10(b). In the case of all the configurations, except the regenerative GT configuration, at a constant TIT, there is no evident effect of the exhaust temperature on the Ceff. This occurs since the exhaust temperature is a function of the TIT [54], while the rise in the Ceff leads to a decrease in the exhaust temperature from 780 to 631 K for the regenerative GT configuration. The effect of this isentropic efficiency on the thermal efficiency for different configurations of the GT plant is depicted in Figure 10(a). Increasing the Ceff leads to an increase in thermal efficiency. According to [35], reducing the thermal loss in the compressor increases the output power and thermal efficiency. At the maximum Ceff, it is noticed that the lowest thermal efficiency of 36.8% occurs in the case of the reheated GT configuration, whereas the highest thermal efficiency of 52.3% occurs in the case of regenerative GT configuration. Moreover, a deviation in the thermal efficiency of the highest Ceff is observed, while an insignificant deviation in this efficiency is obtained at the lowest Ceff. The variation of specific fuel consumption and Ceff for various GT configurations is shown in Figure 10(b). For all the configurations, the specific fuel consumption decreases with the increase in the Ceff, which can be attributed to the decline in compressor losses [40, 55]. At the regenerative GT configuration, the lowest specific fuel consumption of 0.14 kg/kWh is noted, while at the reheated GT configuration, the highest specific fuel consumption is 0.2 kg/kWh. Further, the effect of the Ceff on the output power for different configurations is exhibited in Figure 10(a). In the case of all the configurations, the rise in the Ceff leads to an increase in the output power which is due to the reduction in energy losses in the compressor of the GT [56]. At the maximum Ceff, although the lowest output power (200 MW) occurs in the regenerative GT, the highest output power (about 253 MW) occurs in the reheated GT.Figure 10
The impact of the isentropic compressor efficiency (Ceff) on the performance of the gas-turbine.
(a)(b)The effect of the isentropic turbine efficiency (Teff) on the performance of the GT plants is shown in Figure 11. The effect of this isentropic efficiency on the exhaust temperature for different configurations is displayed in Figure 11(b). For all the configurations, increasing the Teff leads to a decrease in the exhaust temperature. This is because of the conversion of the extra heat from the exhaust gases to create more useful power with the increase of the Teff [36]. The two-shaft GT has the highest exhaust temperature of 1251 K, while the lowest exhaust temperature of 665 K is obtained in the regenerative GT. In addition, the variation of the thermal efficiency with the Teff of different GT configurations is shown in Figure 11(a). There is an apparent increase in the thermal efficiency of all the configurations with the increase in the Teff. The increased work done by the turbine of the GT plant is the reason behind it [57]. The regenerative GT has the highest thermal efficiency of 50.8% at the maximum Teff. Similar trends were observed for the thermal efficiency of other configurations of the GT; however, the low energy losses with the exhaust gases resulted in this high value of thermal efficiency for the regenerative model. Therefore, the thermal efficiency is incredibly significant at higher isentropic turbine efficiency of the GT plants. Furthermore, the effect of the Teff on the specific fuel consumption for different configurations is represented in Figure 11(b).Figure 11
The impact of the isentropic turbine efficiency (Teff) on the performance of the gas-turbine.
(a)(b)As theTeff increases, the specific fuel consumption decreases. It should be mentioned here that at a constant TIT, the output power is increased with the increase in the Teff [36]. Thus, under the effect of these parameters, the specific fuel consumption is reduced. At the maximum Teff, the regenerative GT has the lower specific fuel consumption of 0.145 kg/kWh since more heat energy is recovered from the exhaust gases. This leads to a reduction in fuel consumption in the case of the regenerative GT configuration. Similar behavior has been observed for the other GT configurations. Figure 11(a) shows the variation of the output power with the Teff for different configurations of the GT. It is observed that increasing the Teff linearly increases the output power. The variations in the output power are significant at the highest isentropic turbine efficiency.Since fewer fuel burns in the combustion chamber of the regenerative model, the lowest output power is obtained in this configuration. On the other hand, although there is more fuel burned in the additional combustion chamber as shown in Figure11(a), the highest output power (268 MW, at the maximum Teff) is achieved in the reheated GT configuration. Therefore, in the case of the huge Teff of the GT plants, there is significant output power. According to the trends described in the previous studies, the validity of our models and their foregoing results has been strongly emphasized [56].


### 4.2. Optimization Techniques

In this section, an optimization of the ANFIS model structure utilizing the actual data of the best simulation cases is shown (from the Baiji Gas-Turbines in Iraq). A total of 420 samples from both real field experimental and simulation data used for training and testing the ANFIS model are utilized. The experimental data were divided into two groups in which 85% is used for training and the remainder for testing the performance of the fuzzy inference model.Table1 summarizes the convergence characteristics of the constant and linear outputs for eight different membership functions in which the linear function shows less RMSE compared to the other membership function for the three model outputs.Table 1
Training error of different MFs.
Membership function (MF)RMSE output MF typeConstantLinearProduct sigmoidal (psigmf)0.080710.004006Difference sigmoidal (dsigmf)0.1520210.0050048Pi curve (pimf)0.1220820.0091116Gaussian (gaussmf)0.0118670.00017438Gaussian 2 (gauss2mf)0.0502650.0022592Generalized bell (gbellmf)0.0761380.0033531Trapezoidal (trapmf)0.2581620.0098235Triangular (trimf)0.080710.004005Figure12 compares the actual data and the optimum predicted outputs of the SFC, output power, and thermal efficiency. It is clear that the deviation between the actual and predicted data is very low. That is, the maximum deviations are about 4.8%, 2.51%, and 2.91% for SFC, output power, and thermal efficiency, respectively.Figure 12
The comparison between the real and predicted data using the ANFIS model.
(a)
Specific fuel consumption (SFC)(b)
Power output(c)
Thermal efficiencyThe root-mean-square error (RMSE) parameter for testing the ANFIS model on the whole set of test data in the calculation of the respective output (exhaust temperature, specific fuel consumption (SFC), power output, and thermal efficiency) is shown as follows [28]:
(24)RMSEj=1npatt∑i=1npattOi−yiOi2j=1,⋯,nS,where Oi is the target outputs, yi is the computed outputs, npatt is the pattern numbers used for testing the ANFIS model, and nS is the number of the sample in each pattern.Therefore, the result is represented in Figure13, which demonstrates the comparison of the root-mean-square error (RMSE) of the testing parameters between the predicted and actual plant data. Meanwhile, the maximum error that occurred with the power output was about 3.2% at sample no. 4. Also, the minimum error that appeared with the thermal efficiency was about 0.44%. Therefore, the results show that the ANFIS model showed superior prediction for the performance of the Baiji Gas-Turbine power plant.Figure 13
The RMSE for comparison of predicted and experimental performance data.Furthermore, Figure14 demonstrates the optimum performance of the regenerative GT based on the ANFIS model to select the optimal parameters for the Baiji Gas-Turbine power plant. The effect of the TIT and the Ceff on thermal efficiency is shown in Figure 14(a). It is noticed that the thermal efficiency decreased with increasing TIT at low Ceff. This may be due to the increased fuel consumption, which subsequently leads to an increase in the TIT [19]. The peak thermal efficiency obtained is about 63% when the TIT and the Ceff are 1900 K and 100%, respectively. Figure 13(b) depicts the output power, which is affected by the TIT and the Ceff. It is apparent that the power is increased when both the TIT and the Ceff are increased [58]. The maximum output power is about 375 MW at the same aforesaid maximum values of the TIT and the Ceff. Furthermore, the variation of the specific fuel consumption with the selected optimum parameters is described in Figure 13(c). It is noted that the drop in fuel consumption occurs when increasing both the pressure ratio and the isentropic turbine efficiency. This behavior stems from the fact that the losses of the GT reduce with the increase of the isentropic turbine efficiency (Teff), and then the output power increases at a constant TIT; thus, the specific fuel consumption decreases [59]. Hence, the optimum value of the specific fuel consumption is about 0.033 kg/kWh, when the pressure ratio and the isentropic turbine efficiency are 30 and 100%, respectively. Good agreement can be seen with the results of the previous studies [59].Figure 14
Predicted performance of the RGT with optimum parameters: (a) thermal efficiency, (b) power, and (c) specific fuel consumption.
(a)(b)(c)


## 4.1. Modeling and Simulation

This section investigates the performance of gas-turbine configurations based on various operating conditions such as isentropic turbine efficiency (Teff), ambient temperature (T1), isentropic compressor efficiency (Ceff), turbine inlet temperature (TIT), and pressure ratio (rp). A comparison between the simulated thermal efficiency of the simple GT and the Boyce model [44] is demonstrated in Figure 4. This figure shows an increase in thermal efficiency with the increase in pressure ratio. Compared to the Boyce model of the simple GT, we can confirm that our simulation results are adequate. This is because of an incomplete combustion caused by the usage of fuel oil instead of natural gas in the Baiji plant, thus decreasing the thermal efficiency of the GT power plant. Furthermore, the compressor is much more intolerant to dirt build up in the inlet air filter and on the compressor blades which creates large drops in the cycle efficiency and performance of the Baiji GT power plant. Furthermore, a comparative analysis of the simulated thermal efficiency of the regenerative GT and the Bassily model [45] together with the effect of different values of the pressure ratio and TIT is shown in Figure 5. It is obvious from this figure that there is an increase in thermal efficiency until the pressure ratio reaches 6. The thermal efficiency starts to decrease with the increase in the pressure ratio after the compression value reaches 7 due to the rise in the compressor outlet temperature as a result of the increased pressure ratio. Therefore, the thermal efficiency was reduced due to the reduction in the heat exchange between the air and the flue gases in the regenerative gas-turbine [45]. It is also noticed that increasing the TIT has led to an increase in thermal efficiency. Compared to the Bassily model of the regenerative GT, our simulation results are adequate, as well.Figure 4
The relation of thermal efficiency and pressure ratio of the simple GT and Boyce model.Figure 5
The relation of thermal efficiency and pressure ratio of the regenerative gas-turbine and Bassily model.The effect of pressure ratio on the performance of the GT plants is exhibited in Figure6. The impact of the pressure ratio on the temperature of the exhaust gases from different configurations of the GT is shown in Figure 6(b). It is evident that the decrease in the temperature of the exhaust gases for all the models, except the regenerative GT model, is increased from 590 to 796 K, as an increase in the pressure ratio. Also, when the pressure ratio increases according to the configuration of the GT for other models, so does the exhaust temperature decreases about 220 to 400 K. The heat recovered from the flue gases to increase the temperature of the air entering the combustion chamber leads to a reduction in the temperature of the exhaust with the regenerative GT model [45]. The two-shaft GT model causes a high exhaust temperature, owing to the presence of the two-shaft GT with one shaft that drives the compressor, while the other drives the generator. It should be mentioned that the increase in the exhaust gas temperature stems from the decrease in the total isentropic turbine efficiency and the work of the turbines [26].Figure 6
The impact of pressure ratio on the performance of the gas-turbine.
(a)(b)The effect of the pressure ratio on the thermal efficiency of the GT plants is displayed in Figure6(a). In the case of all the configurations, except the regenerative GT, increasing the compressor ratio creates a linear increase in the thermal efficiency. On the other hand, the thermal efficiency of the regenerative GT rises up to 46.5% at a pressure ratio value of 7. Afterward, it starts to decrease till 37.3% when the pressure ratio soars to 30. More waste heat can be recovered due to the low outlet temperature of the compressor and the low pressure ratio. Less waste heat needs to be retrieved as the high outlet temperature was obtained at a high pressure ratio [46]. As a consequence, there is an increase in the thermal efficiency of the pressure ratio for other configurations. Compared to the lower pressure ratio, the higher pressure ratio has a significant variation in the thermal efficiency of the GT.Moreover, Figure6(a) shows the effect of the pressure ratio on the fuel consumption for the different studied configurations. At a pressure ratio of 7, the specific fuel consumption has a minimum value (0.159 kg/kWh) in the regenerative GT. This value starts to increase after passing the value of the pressure ratio. In the case of the other configurations, the specific fuel consumption always decreases with the increment in the pressure ratio. In comparison with the lower pressure ratio, the deviation of the specific fuel consumption is higher at the higher pressure ratio. When the pressure ratio increases from 3 to 30 for all configurations, except the regenerative one, the specific fuel consumption decreases (about 0.32 kg/kWh to 0.17 kg/kWh).As indicated in Figure6(b), this is a result of the decrease in the exhaust temperature with the increase in the pressure ratio. In addition, the variation of GT cycles’ output power with the pressure ratio is shown in Figure 6(a). As is evident, increasing the pressure ratio leads to an increase in the output power depending on the configuration of the GT. However, it is noticed that the higher pressure ratio is significant on the output power variation. Due to the burning of more fuel in the additional combustion chamber, the higher output power is obtained in the reheated GT configuration [47]. It can be seen that the lower pressure ratio was insignificant on the output power.The effect of ambient temperature on the performance of the GT plants is depicted in Figure7. The variation of the exhaust temperature of the GT power plants with the effect of the ambient temperature is demonstrated in Figure 7(b). In the case of all the configurations, except the regenerative GT, the increase in the ambient temperature leads to a gradual rise in the exhaust temperature by about 10 K. The regeneration applied to recover heat from the flue gases and increase the air temperature entering the combustion chamber is the main reason behind it. Therefore, for the RGT compared to the other GT configurations, the temperatures of the exhaust gases are increased with increase of the ambient temperature [13, 48]. The lowest exhaust temperature of about 655 K is obtained in the regenerative GT, while the highest temperature of about 1200 K is obtained in the two-shaft GT. Furthermore, the effect of ambient temperature on the thermal efficiency of the GT cycle for different configurations is shown in Figure 7(a). The rising ambient temperature causes a reduction in thermal efficiency. Increasing the ambient temperatures also results in the increased losses of the exhaust gases, which is also a reason for the reduction of the thermal efficiency [49, 50]. The maximum thermal efficiency for the GT configurations is obtained at an ambient temperature of 273 K with the regenerative GT configuration, while at an ambient temperature of 327 K, a minimum thermal efficiency of 33% for the intercooler gas-turbine (IGT) configuration is observed. The work of the compressor increases as the ambient temperature increases. Therefore, there is a reduction in the thermal efficiency of all the configurations. The design of the compressor of the GT is such that it maintains a constant air volume, while the mass is reduced with the increase in the ambient temperature [51]. The mass flow is reduced to maintain the same volumetric flow, which leads to a reduction in the output power of the GT and an increase in the temperature at the inlet of the combustion chamber [26, 51]. The GT thermal efficiency eventually decreases as there is a decrease in the burning fuel and the TIT. Figure 7(b) indicates the variation of the specific fuel consumption of the GT power plant with the effect of the ambient temperature. The specific fuel consumption and the ambient temperature are directly proportional to each other [52]. For all the configurations of the GT, the specific fuel consumption increases with the increase in the ambient temperature. In the presence of the regenerative GT configuration at an ambient temperature of 273 K, the lowest specific fuel consumption occurs at 0.156 kg/kWh. While with the reheated GT configuration at ambient temperature of 327 K, the highest specific fuel consumption occurs at 0.223 kg/kWh.Figure 7
The impact of ambient temperature (°C) on the performance of the gas-turbine.
(a)(b)The predicted output power of the GT configurations with the actual data from the Baiji GT power plant versus the ambient temperature is shown in Figure8. For all the configurations, the output power has been observed to decrease with the increase in the ambient temperature. It is observed that, at any ambient temperature, the lowest and highest output powers obtained are for the regenerative and reheated GT configurations, respectively. Likewise, for all the configurations, except the intercooler GT configuration, a decrease in the output power by 296 MW is observed when the ambient temperatures increased from 273 K to 327 K. The rise in exhaust temperatures is the main reason behind this behavior [53]. Moreover, compared to the output power data of the Baiji GT power plant, enhanced output power has been obtained utilizing the studied GT configurations. The Baiji GT plant uses the fuel oil, which when burned creates a loss in the output power due to the incomplete combustion. On the contrary, the models proposed for the GT plant are designed to work on complete combustion of the natural gas.Figure 8
The relation between the output power and the ambient temperature for the predicted results and the actual data from the Baiji Gas-Turbine power plant.The effect of the TIT on the performance of the GT plants is shown in Figure9. The effect of the TIT on the exhaust temperature of the GT plants is displayed in Figure 9(a). It observed that increasing the TIT causes a rise in exhaust temperature which means that enough heat is supplied by the high TIT to the power turbine, which is then able to produce higher exhaust gases and work net from the GT [54]. Therefore, when the TIT increases from 1100 to 1900 K for all configurations, except for the regenerative GT, the exhaust temperature of the GT also increases by about 700 K. In fact, there is an increase of 150 K in the exhaust temperature of the regenerative model though. At low TIT, there is a minor variation in the exhaust temperature, while at the higher TIT, the exhaust temperature is significant for all the GT configurations. The variation of the thermal efficiency against the TIT for various configurations of the GT is shown in Figure 9(b). It is observed that with the increase in the TIT, there is an increase in thermal efficiency. There is a nominal deviation in the thermal efficiency at the lower TIT, while the deviation is significant at the higher TIT. This occurs owing to the increased work that the GT cycle has to do [13].Figure 9
The impact of the TIT on the performance of the gas-turbine.
(a)
Exhaust temperature(b)
Thermal efficiency(c)
Specific fuel consumption(d)
Power outputTherefore, to increase the thermal efficiency of the GT, the TIT becomes a very critical factor. Except for the regenerative GT, there is an increase in the thermal efficiency of about 3.1% in all the configurations, while for the regenerative GT configuration, the thermal efficiency increased from 33.4 to 52.3%. Furthermore, the effect of the TIT on the specific fuel consumption of the GT plant for different configurations is shown in Figure9(c). The specific fuel consumption decreases from 0.218 to 0.137 kJ/kWh with the increase of the TIT for all configurations, except for the regenerative GT which reduced by about 0.01 kJ/kWh. Figure 9(a) shows the variation of output power versus TIT. As is evident, the increment in the TIT leads to an increase in the output power. But the TIT is significant at the higher values on the output power variation. Due to the burning of more fuel in the additional combustion chamber, the output power obtained in the reheated GT configuration is higher [47]. The less the fuel burned in the combustion chamber of the regenerative GT, the lower the output power obtained in this configuration which is consistent with the results of Figure 9(d).The effect of the isentropic compressor efficiency (Ceff) on the performance of the GT plants is shown in Figure 10. The variation of the exhaust temperature of the GT with the Ceff for different configurations is demonstrated in Figure 10(b). In the case of all the configurations, except the regenerative GT configuration, at a constant TIT, there is no evident effect of the exhaust temperature on the Ceff. This occurs since the exhaust temperature is a function of the TIT [54], while the rise in the Ceff leads to a decrease in the exhaust temperature from 780 to 631 K for the regenerative GT configuration. The effect of this isentropic efficiency on the thermal efficiency for different configurations of the GT plant is depicted in Figure 10(a). Increasing the Ceff leads to an increase in thermal efficiency. According to [35], reducing the thermal loss in the compressor increases the output power and thermal efficiency. At the maximum Ceff, it is noticed that the lowest thermal efficiency of 36.8% occurs in the case of the reheated GT configuration, whereas the highest thermal efficiency of 52.3% occurs in the case of regenerative GT configuration. Moreover, a deviation in the thermal efficiency of the highest Ceff is observed, while an insignificant deviation in this efficiency is obtained at the lowest Ceff. The variation of specific fuel consumption and Ceff for various GT configurations is shown in Figure 10(b). For all the configurations, the specific fuel consumption decreases with the increase in the Ceff, which can be attributed to the decline in compressor losses [40, 55]. At the regenerative GT configuration, the lowest specific fuel consumption of 0.14 kg/kWh is noted, while at the reheated GT configuration, the highest specific fuel consumption is 0.2 kg/kWh. Further, the effect of the Ceff on the output power for different configurations is exhibited in Figure 10(a). In the case of all the configurations, the rise in the Ceff leads to an increase in the output power which is due to the reduction in energy losses in the compressor of the GT [56]. At the maximum Ceff, although the lowest output power (200 MW) occurs in the regenerative GT, the highest output power (about 253 MW) occurs in the reheated GT.Figure 10
The impact of the isentropic compressor efficiency (Ceff) on the performance of the gas-turbine.
(a)(b)The effect of the isentropic turbine efficiency (Teff) on the performance of the GT plants is shown in Figure 11. The effect of this isentropic efficiency on the exhaust temperature for different configurations is displayed in Figure 11(b). For all the configurations, increasing the Teff leads to a decrease in the exhaust temperature. This is because of the conversion of the extra heat from the exhaust gases to create more useful power with the increase of the Teff [36]. The two-shaft GT has the highest exhaust temperature of 1251 K, while the lowest exhaust temperature of 665 K is obtained in the regenerative GT. In addition, the variation of the thermal efficiency with the Teff of different GT configurations is shown in Figure 11(a). There is an apparent increase in the thermal efficiency of all the configurations with the increase in the Teff. The increased work done by the turbine of the GT plant is the reason behind it [57]. The regenerative GT has the highest thermal efficiency of 50.8% at the maximum Teff. Similar trends were observed for the thermal efficiency of other configurations of the GT; however, the low energy losses with the exhaust gases resulted in this high value of thermal efficiency for the regenerative model. Therefore, the thermal efficiency is incredibly significant at higher isentropic turbine efficiency of the GT plants. Furthermore, the effect of the Teff on the specific fuel consumption for different configurations is represented in Figure 11(b).Figure 11
The impact of the isentropic turbine efficiency (Teff) on the performance of the gas-turbine.
(a)(b)As theTeff increases, the specific fuel consumption decreases. It should be mentioned here that at a constant TIT, the output power is increased with the increase in the Teff [36]. Thus, under the effect of these parameters, the specific fuel consumption is reduced. At the maximum Teff, the regenerative GT has the lower specific fuel consumption of 0.145 kg/kWh since more heat energy is recovered from the exhaust gases. This leads to a reduction in fuel consumption in the case of the regenerative GT configuration. Similar behavior has been observed for the other GT configurations. Figure 11(a) shows the variation of the output power with the Teff for different configurations of the GT. It is observed that increasing the Teff linearly increases the output power. The variations in the output power are significant at the highest isentropic turbine efficiency.Since fewer fuel burns in the combustion chamber of the regenerative model, the lowest output power is obtained in this configuration. On the other hand, although there is more fuel burned in the additional combustion chamber as shown in Figure11(a), the highest output power (268 MW, at the maximum Teff) is achieved in the reheated GT configuration. Therefore, in the case of the huge Teff of the GT plants, there is significant output power. According to the trends described in the previous studies, the validity of our models and their foregoing results has been strongly emphasized [56].


## 4.2. Optimization Techniques

In this section, an optimization of the ANFIS model structure utilizing the actual data of the best simulation cases is shown (from the Baiji Gas-Turbines in Iraq). A total of 420 samples from both real field experimental and simulation data used for training and testing the ANFIS model are utilized. The experimental data were divided into two groups in which 85% is used for training and the remainder for testing the performance of the fuzzy inference model.Table1 summarizes the convergence characteristics of the constant and linear outputs for eight different membership functions in which the linear function shows less RMSE compared to the other membership function for the three model outputs.Table 1
Training error of different MFs.
Membership function (MF)RMSE output MF typeConstantLinearProduct sigmoidal (psigmf)0.080710.004006Difference sigmoidal (dsigmf)0.1520210.0050048Pi curve (pimf)0.1220820.0091116Gaussian (gaussmf)0.0118670.00017438Gaussian 2 (gauss2mf)0.0502650.0022592Generalized bell (gbellmf)0.0761380.0033531Trapezoidal (trapmf)0.2581620.0098235Triangular (trimf)0.080710.004005Figure12 compares the actual data and the optimum predicted outputs of the SFC, output power, and thermal efficiency. It is clear that the deviation between the actual and predicted data is very low. That is, the maximum deviations are about 4.8%, 2.51%, and 2.91% for SFC, output power, and thermal efficiency, respectively.Figure 12
The comparison between the real and predicted data using the ANFIS model.
(a)
Specific fuel consumption (SFC)(b)
Power output(c)
Thermal efficiencyThe root-mean-square error (RMSE) parameter for testing the ANFIS model on the whole set of test data in the calculation of the respective output (exhaust temperature, specific fuel consumption (SFC), power output, and thermal efficiency) is shown as follows [28]:
(24)RMSEj=1npatt∑i=1npattOi−yiOi2j=1,⋯,nS,where Oi is the target outputs, yi is the computed outputs, npatt is the pattern numbers used for testing the ANFIS model, and nS is the number of the sample in each pattern.Therefore, the result is represented in Figure13, which demonstrates the comparison of the root-mean-square error (RMSE) of the testing parameters between the predicted and actual plant data. Meanwhile, the maximum error that occurred with the power output was about 3.2% at sample no. 4. Also, the minimum error that appeared with the thermal efficiency was about 0.44%. Therefore, the results show that the ANFIS model showed superior prediction for the performance of the Baiji Gas-Turbine power plant.Figure 13
The RMSE for comparison of predicted and experimental performance data.Furthermore, Figure14 demonstrates the optimum performance of the regenerative GT based on the ANFIS model to select the optimal parameters for the Baiji Gas-Turbine power plant. The effect of the TIT and the Ceff on thermal efficiency is shown in Figure 14(a). It is noticed that the thermal efficiency decreased with increasing TIT at low Ceff. This may be due to the increased fuel consumption, which subsequently leads to an increase in the TIT [19]. The peak thermal efficiency obtained is about 63% when the TIT and the Ceff are 1900 K and 100%, respectively. Figure 13(b) depicts the output power, which is affected by the TIT and the Ceff. It is apparent that the power is increased when both the TIT and the Ceff are increased [58]. The maximum output power is about 375 MW at the same aforesaid maximum values of the TIT and the Ceff. Furthermore, the variation of the specific fuel consumption with the selected optimum parameters is described in Figure 13(c). It is noted that the drop in fuel consumption occurs when increasing both the pressure ratio and the isentropic turbine efficiency. This behavior stems from the fact that the losses of the GT reduce with the increase of the isentropic turbine efficiency (Teff), and then the output power increases at a constant TIT; thus, the specific fuel consumption decreases [59]. Hence, the optimum value of the specific fuel consumption is about 0.033 kg/kWh, when the pressure ratio and the isentropic turbine efficiency are 30 and 100%, respectively. Good agreement can be seen with the results of the previous studies [59].Figure 14
Predicted performance of the RGT with optimum parameters: (a) thermal efficiency, (b) power, and (c) specific fuel consumption.
(a)(b)(c)


## 5. Conclusion

Several configurations of the gas-turbine cycle have been assessed with the influence of some operational parameters, including the isentropic turbine efficiency, ambient temperature, turbine inlet temperature, isentropic compressor efficiency, and pressure ratio. Moreover, the proposed ANFIS model improves the performance of the gas-turbine cycle and leads to the following conclusions, as well:(1)
The structure of the ANFIS model shows accurate enough outcomes to predict the SFC, power, and thermal efficiency, with the triangular MF and the linear output MF, and achieve the best results(2)
The pressure ratio, ambient temperature, and isentropic turbine efficiency strongly influence the predicted model results(3)
The conjunction of the ANFIS model with the regenerative GT offers superior performance compared to that of the actual power plant



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*Source: 6590138-2020-07-03.xml*