Fault diagnosis analysis of combined cycle based on the structural theory of thermo-economics

Abstract

In this paper, an improved thermo-economic diagnosis model based on the structural theory of thermo-economics combined with advanced exergy analysis is proposed in a combined cycle fault diagnosis model. Diagnosis model simulation of a 590 MW combined cycle unit is implemented by EBSILON Professional in terms of advanced exergy analysis method. The characteristic fault value (CFV) required for diagnosis is quantitatively presented and precisely located in the diagnosis model. The results show that with 3% performance deterioration fault of the compressor, gas turbine and intermediate pressure cylinder of the turbine, gas turbine failure leads to three times fuel consumption to the unit compared to the compressor. In contrast, multiple fault diagnosis results show that the fault value generated by each component under multiple faults is not a simple superposition of a single fault. The impact of some component faults is partially offset or increased. However, the increased fuel consumption of the whole unit under multiple faults or malfunctions must be greater than the sum of the increased fuel consumption under a single fault. CFV can effectively perform precise positioning and quantitative analysis on single and multiple fault scenarios of the combined cycle unit. In addition, CFV has strong sensitivity and changes linearly with the performance deterioration of the components, which paves the way for a reliable approach for early-stage warning and diagnosis.

INTRODUCTION

When energy system malfunction or process failure is identified and diagnosed in an early stage, it can prevent further malfunction development and minimize potential economic losses. Therefore, it is pivotal to develop a method that can effectively diagnose the faults in the operation of the energy system. Thermo-economics theory is a comprehensive combination of thermodynamic and economic analysis, widely applied to describe the cost formation process of the thermal system as a whole. It has a strong advantage in dealing with the cost analysis, fault diagnosis, and system optimization of the energy system.^1–3 thermo-economic diagnosis is a general, methodology that can be used to identify the equipment with faults in energy systems and quantify the additional fuel consumption of the system due to component degradation. At present, it has been successfully applied to diagnose various energy systems, such as pulverized coal power plants,^4,5 combined cycle power plants,^6,7 membrane fuel cell systems,⁸ and air conditioning cycle systems of buildings.⁹

In the 1990s, Valero et al.¹⁰ first proposed the concept of malfunction cost (or failure cost) and defined faults and obstacles, marking the beginning of research on thermo-economics in the field of fault diagnosis. Lozano et al.¹¹ deduced the malfunction cost equation based on disturbance theory and applied this method to fault diagnosis of energy conversion systems. Valero and Torres et al.^12,13 built the dysfunction table to determine the location of the fault. Thermo-economic diagnosis methods are used to identify the system fault source. However, due to the highly coupling relationship between components, the control system's intervention and multiple faults, they cannot locate the malfunctions accurately.¹⁴

In recent decades, many scholars have developed methods to solve the problem of thermo-economic diagnosis, such as coordination method, characteristic curve method of malfunction cost method, gradual scaling of production structure, thermo-economic input–output analysis, and other methods. However, while improving the thermo-economic practice, some methods also show their limitations. Zaleta-Aguilar et al.¹⁵ proposed a coordination method, which can obtain the impact of system failure by coordinating data from simulators with data from power plant instruments. However, the limitation of this method lies in that the analysis of complex energy systems requires a large amount of computing resources and the installation of instruments in the system. Reini et al.¹⁶ used the malfunction cost method to quantify the impact of degradation, but this method did not accurately detect the existence of multiple intrinsic anomalies. Toffolo et al.^17,18 proposed a new diagnostic index considering that the influence of anomalies would spread to the whole system. This index accurately analyzed the parts with a degraded performance by comparing the deviation of characteristic curves of fault conditions and reference conditions. Still, this method did not provide the fuel influence generated by each component. Verda et al.¹⁹ proposed a diagnostic method of gradually scaling the production structure, effectively separating induced effects. However, this method could not provide accurate diagnostic results when multiple unit faults are produced simultaneously. Rocco and Keshavarzian et al.^20,21 proposed a thermal economy input-output analysis diagnosis method, and decomposed the diagnosis index fault. This method provides useful information for determining the actual strategy to reduce the negative impact of the malfunction.

Compared with the above methods, many scholars have adopted a combination of thermo-economic diagnosis methods and other methods to solve the problem of thermo-economic diagnosis, and achieved good results. Verda²² introduced the concept of memory into the thermo-economic diagnostic, improved the fault diagnosis procedure, and effectively separated the induced fault interference. Uson and colleafues^23,24 combined the improved causal analysis with the traditional thermo-economic malfunction cost method to quantify the intrinsic and induced effects systematically. Zhangchao et al.²⁵ proposed a progressive separation method based on the inductive effect of the combination of structural theory and characteristic curve. This method is suitable for single-fault diagnosis and can give good diagnosis results for multiple-fault scenarios. Pacheco et al.²⁶ proposed a method based on the concept of fuel shock formula and analytical coordination method, which modified the reference state, integrated the modified fuel shock formula, and introduced filtering technology to eliminate the influence caused by the control and regulation system. Orozco et al.²⁷ combined the thermo-economic method with the artificial neural network method. They used the neural network to eliminate the control system's intervention, effectively identifying and quantifying the faulty components’ influence and their fuels. It is more suitable for single-fault and multiple-fault scenarios.

Because of the above research ideas, a new methodology combining the thermo-economic diagnosis methods, and the advanced exergy analysis is proposed. The method can deconstruct the malfunction cost of each component in the system into three parts: intrinsic fault, induced fault, and dysfunction, and the diagnosis method is applied to a 590 MW combined cycle unit. EBSILON Professional software was used for fault simulation in specified condition with one or more inherent faults relative to the reference conditions.

STRUCTURAL THEORY OF THERMO-ECONOMICS

The structural theory of thermo-economics was developed by Spanish scholar A Valero et al, who developed a general model based on the concept of “fuel”–“product,” which is used to analyze the relationship between various equipment in the energy system and resource allocation. In the structural theory, the system's physical structure diagram and production structure diagram should be drawn first. The physical structure diagram is obtained by the functional division of each process in the thermal system, which reflects the physical relationship between each component. The production structure diagram is obtained according to the production process among the processes. In the production structure diagram, two virtual components are added, namely, the assembly component and the branch component, so that the characteristic equation of each actual component is simplified to a homogeneous equation.

In the production structure diagram, the energy input into the subsystem is defined as fuel F, and the energy output from the subsystem to the outside or into other subsystems is defined as product P. The loss caused by irreversibility is called irreversible loss I. According to the exergy balance relationship, it can be expressed as: [Image Omitted. See PDF]

Between fuel and product, the unit exergy consumption is usually expressed as¹²: [Image Omitted. See PDF]where k_ij is the technical product coefficient, as $${k}_{ij}=\frac{{F}_{ij}}{{P}_{j}}$$, it refers to the part paid by the ith component when obtaining a unit product of the jth component; F_ij is the part of the ith component product that is used as the fuel of the jth component; P_j is the product of component j.

The characteristic equation is the mathematical model of components. The production relationship between components can be established from the characteristic equation. The technical product coefficient can be expressed as¹²: [Image Omitted. See PDF]where P_0,i is the final product that the ith component outputs to the outside of the system.

FAULT DIAGNOSIS MODEL OF STRUCTURAL THEORY OF THERMO-ECONOMICS Basic idea

The use of thermo-economics diagnostic tools is to study the system's behavior under abnormal conditions by comparing the actual operating and reference conditions. Any influence that increases fuel is defined as a fault by thermo-economics fault diagnosis. The quantification of fault impact is characterized by the amount of extra fuel consumed,¹² namely: [Image Omitted. See PDF]where $${\rm{\Delta }}{P}_{ex{t}_{i}}$$ is the variation in the overall plant product, which component i contributes to.

The first term on the right is the malfunction cost associated with the specific behavior of the components, calculated by the change in their unit exergy consumption. In contrast, the second term is the change in fuel consumption caused by the change in the production of the entire plan.

If the same final production characterizes the actual operating conditions and reference conditions, and can also be expressed as the sum of the irreversible loss increases of each element, then the last term of formula (4) is zero: [Image Omitted. See PDF]where $${k}_{p,j}^{* }$$ is the unit exergy cost of the product of the jth component, calculated at the operating condition. It can be calculated by irreversibility dysfunction coefficients $${\phi }_{ij}$$.¹² Namely: [Image Omitted. See PDF]

Characteristic fault value Component failures and malfunction cost

Irreversible loss and increase of fuel consumption caused by the change of unit exergy consumption of component i are defined as component failure MF_i, which is expressed as¹²: [Image Omitted. See PDF]where $${\rm{\Delta }}{k}_{i}$$ represents the change value of the unit exergy consumption of component i; $${\rm{\Delta }}{k}_{ji}$$ represents the change value of the jth fuel unit exergy consumption in component i; $${P}_{i}^{0}$$ represents the product of component i under the reference working condition.

Thus, this component requires an additional external fuel consumption, which is called fault cost or malfunction cost $${{\text{MF}}}_{i}^{* }$$ is expressed by the equation²³: [Image Omitted. See PDF]

The malfunction cost indicator reflects the change in component fuel consumption. If a component fails, it will consume more fuel and generate a greater irreversible loss, which will inevitably lead to a greater impact on the total fuel consumption of the system. At the same time, the malfunction cost of this component must be relatively large, so the malfunction cost indicator is selected to judge whether the system has failed.

Inherent and induced faults

The irreversible loss of components is decomposed into endogenous irreversible loss I^EN and exogenous irreversible loss I^EX according to the advanced exergy analysis method. The endogenous irreversible loss is caused by the irreversibility of the component itself, while the exogenous irreversible loss is caused by the low efficiency of the remaining components.²⁸ The irreversible loss of the ith component can be decomposed into two parts expressed in Equation (9). [Image Omitted. See PDF]

Substituting Equations (1) and (9) into Equation (2) can be deformable: [Image Omitted. See PDF]where $${k}_{i}^{L}=\frac{{I}_{i}^{\mathrm{EN}}}{{P}_{i}}$$ is defined as endogenous exergy consumption; $${k}_{i}^{G}=\frac{{I}_{i}^{\mathrm{EX}}}{{P}_{i}}$$ is defined as exogenous exergy consumption.

When comparing the unit exergy consumption time of the component under the reference working condition and the operating working condition, the new expression of the unit exergy consumption variation of the component can be obtained, as shown in Equation (11): [Image Omitted. See PDF]where $${k}_{i,op}$$ and $${k}_{i,ref}$$, respectively, represent the unit energy consumption of component i under operating conditions and reference conditions.

The fault can be further separated from the inherent fault MF^L and induced fault MF^G by using the new expression of the change value of unit energy consumption; that is, the fault of component i can be decomposed into two parts as shown in Equation (12).²⁵ [Image Omitted. See PDF]where, $$M{F}^{L}=\Delta {k}_{i}^{L}{P}_{i}^{0}$$ represents the inherent fault of the ith component; $$M{F}^{G}=\Delta {k}_{i}^{G}{P}_{i}^{0}$$ represents the induced failure of the ith component.

Inherent fault MF^L is obtained by advanced exergy analysis, which not only excluded the induced fault caused by the intervention of the control system but also directly reflects the actual status of the component. MF^L was only related to the change of nearby components. When a component fails, MF^L must be relatively large, so the inherent fault MF^L is selected as the accurate location of the fault source.

Diagnostic model

Figure 1 shows the flow chart of fault diagnosis. The model selects two characteristic fault value (CFV); inherent fault and induced fault. The CFV's are calculated, and the value changes are analyzed. If the value changes significantly and the direction is positive, the component can be confirmed as the fault location.

Figure 1. Fault diagnosis flow chart.

RESULTS AND DISCUSSION

To verify the accuracy of the above diagnosis model, a 590 MW combined cycle unit of a power plant was used for fault simulation analysis. The gas turbine model was 9HA, the low calorific value of natural gas was 45033 kJ/kg, the atmospheric pressure was 98.95 kPa, the temperature was 24°C, and the relative humidity was 70%. EBSILON simulation software is used to build the simulation model. The thermal balance diagram of the unit is shown in Appendix A1. The main operating parameters of the unit are 100% load condition, and the design and simulation values of the unit are shown in Table 1. It can be seen that the relative error is within 2%, so the system model is validated. With the help of this model, fault data required for thermal economic diagnosis are obtained. The physical structure of the system is shown in Figure 2, and the production structure is shown in Figure 3.²⁹

Table 1 Main operating parameters of gas-steam combined cycle unit.

Parameter	Design value	Simulation value	Relative error (%)
Total power (MW)	590.065	590.166	0.017
Gas turbine power (MW)	395.640	396.012	0.094
Steam turbine power (MW)	194.425	194.154	−0.139
Natural gas flow (t/h)	75.100	75.100	0.000
Gas turbine exhaust flow (t/h)	2939.900	2939.660	−0.008
Gas turbine exhaust temperature (°C)	629.400	629.255	−0.023
High pressure steam temperature (°C)	585.300	585.360	0.010
High pressure steam pressure (MPa)	16.290	16.130	−0.982
Medium pressure steam temperature (°C)	584.900	583.460	−0.246
Medium pressure steam pressure (MPa)	3.454	3.458	0.116
Low pressure steam temperature (°C)	317.600	317.026	−0.181
Low pressure steam pressure (MPa)	0.652	0.653	0.153
Exhaust temperature (°C)	98.400	98.930	0.539

Figure 2. Physical structure diagram of a 590 MW combined cycle unit.

Figure 3. Production structure drawing of a 590 MW combined cycle unit.

The above diagnosis model is used to diagnose single-faults and multiple-faults of a combined cycle system. Table 2 describes the common faults related to the performance parameters of the combined cycle unit.

Table 2 Common faults and causes of combined cycle unit.

Subassembly	Performance parameter	Common fault causes
Air compressor	Isentropic efficiency/pressure ratio	Blade scaling, abrasion, and inlet icing
Combustion chamber	Combustion efficiency	Fuel nozzle blocked and coking
Gas turbine	Isentropic efficiency	Scaling, wear, and corrosion of blades
Heat recovery steam generator	End difference/pressure drop	Scaling and leakage of flue gas heat exchange surface
Steam turbine	Isentropic efficiency	Wear, erosion, and leakage of cylinder and blade

In this paper, three typical common faults of combined cycle power plants are considered, with the combination of faults, different multifault cases of the unit are simulated.

Case 1: the isentropic efficiency of the compressor decreases by 3% compared with the reference working condition due to the scaling of the air compressor blades.

Case 2: the isentropic efficiency of the gas turbine decreases by 3% compared with the reference working condition due to the corrosion of the blade surface of the gas turbine.

Case 3: the moving blades of the intermediate pressure cylinder of the steam turbine are eroded, resulting in the isentropic efficiency of the intermediate pressure cylinder being reduced by 5% compared with the reference working condition.

Case 4: the faults of air compressor and gas turbine occur simultaneously.

Case 5: two faults of gas turbine and intermediate pressure cylinder of steam turbine occur simultaneously.

Case 6: three kinds of faults occur simultaneously in air compressor, gas turbine, and steam turbine medium pressure cylinder.

Single fault diagnosis results and discussion

The irreversible loss of each component under the corresponding working conditions is decomposed according to the advanced exergy analysis method, which is divided into endogenous irreversible loss I^EN and exogenous irreversible loss I^EX. When using the exergy balance method to calculate the endogenous/exogenous irreversible loss of components, it is necessary to simulate and model the unit. By defining the ideal operating state of different components, n mixed cycles are established. According to the exergy balance equation of components, the endogenous irreversible loss of each component is solved one by one. The ideal state of each component in the combined cycle system is defined as follows:

For compressor, gas turbine, steam turbine, and other rotating machinery, the ideal state is defined as that the isentropic efficiency and mechanical efficiency are both 1 to ensure operation without irreversible loss.

For heat exchange equipment such as waste heat boiler, due to pinch points, it is basically difficult to achieve a loss of 0. Only the minimum temperature difference and pressure drop of pinch point in the heat exchanger are set to be 0, so as to minimize the irreversible loss.

It is difficult to define the ideal state of combustion chamber due to chemical reaction. This paper adopts the idealized definition scheme of combustion chamber described in Petrakopoulou et al.,³⁰ which has proved to be effective for most complex systems. According to the literature, the ideal state of combustion chamber is defined as follows: (1) In the ideal state, the outlet parameters and flue gas composition of the combustion chamber are consistent with the actual state; (2) The combustion efficiency in the combustion chamber is 1, and the pressure drop is 0; (3) The excess air coefficient under ideal condition is consistent with that under actual condition.

The results of endogenous/exogenous irreversible losses of each component of the combined cycle are shown in Table 3. As shown in Table 3, under the design condition, most components with a more significant proportion of endogenous exergy loss in the plant occurred in the top cycle. The exergy loss in the combustion chamber accounted for 60.6% of the total endogenous exergy loss in the unit, gas turbine for 18.9%, and air compressor for 7.8%. The endogenous heat loss in the combustion chamber is mainly caused by the high-temperature difference between the fuel before and after combustion and the irreversible loss in the combustion process, which can be reduced by increasing the fuel inlet temperature. In addition, it can be seen from Cases 1–3 that their own failure does not cause the increase in irreversible loss of some components, but in many cases is caused by the induction of other components in this component. For example, in Case 2, the turbine is the real source of failure, but the increase in irreversible loss of the combustion chamber and waste heat boiler is also very large. The reason for the increase in irreversible loss of these components can be quantified by using the first analysis.

Table 3 Advanced performance analysis results of each component under single-fault.

No.	Subassembly	Design condition		Fault 1		Fault 2		Fault 3
		IEN	IEX	IEN	IEX	IEN	IEX	IEN	IEX
1	AC	22.335	5.827	27.671	7.221	22.345	7.549	22.335	5.829
2	CC	173.170	12.328	173.090	11.387	173.179	17.323	173.170	12.342
3	FH	0.239	0.105	0.239	0.112	0.239	0.129	0.239	0.106
4	GT	54.186	7.090	54.176	6.992	63.179	8.088	54.186	7.089
5	HRSG	17.439	9.517	17.48	11.403	17.48	16.280	17.439	9.501
6	HPST	2.050	0.771	2.050	0.761	2.050	0.758	2.050	0.772
7	IPST	1.567	1.802	1.567	1.945	1.567	2.335	2.250	2.624
8	LPST	8.309	−2.196	8.309	−1.828	8.309	−0.772	8.209	−3.631
9	CP	0.002	0.003	0.002	0.003	0.002	0.004	0.002	0.003
10	FWP	0.123	0.212	0.123	0.225	0.123	0.263	0.123	0.212
11	GEN	6.110	0.192	6.110	0.095	6.110	−0.182	6.110	0.190

Under the design condition, when the unit fails, the fault characteristic values of each element calculated by the above fault diagnosis model method are shown in Tables 4 and 5. The chimney and condenser are dissipative components, because the same final waste variation the actual operating conditions and reference conditions, so their CFV's are not listed in the table. As seen from the table, the combination of improved fault eigenvalues ML_i^L and $$M{F}_{i}^{* }$$ can accurately locate the real fault source of the system and eliminate the induced fault source. Compared with the traditional combination of MF_i and $$M{F}_{i}^{* }$$ the interference of induced fault can be avoided during diagnosis and location. For example, in Case 2, due to the corrosion of gas turbine blades and the decrease of efficiency, the waste heat boiler of downstream components had a fault of 4.101 MW, which increased the fuel consumption by 5.7805 MW. However, in practice, the waste heat boiler did not have a fault, but its inherent fault value was −2.205 MW which can directly eliminate the induced fault waste heat boiler and improve the accuracy of thermo-economics diagnosis.

Table 4 Single-fault diagnosis results.

No.	Subassembly	Fault 1				Fault 2				Fault 3
		MFi	DFi	MFiL	MFiG	MFi	DFi	MFiL	MFiG	MFi	DFi	MFiL	MFiG
1	AC	5.522	1.153	4.379	1.143	0.763	0.968	−0.707	1.470	0.001	−0.002	−0.001	0.002
2	CC	−3.290	2.110	−2.284	−1.007	−0.594	4.658	−5.072	4.478	0.006	−0.014	−0.007	0.013
3	FH	0.001	0.005	−0.004	0.005	0.004	0.019	−0.013	0.017	0.000	0.000	0.000	0.000
4	GT	−1.409	1.264	−1.171	−0.239	9.782	0.066	8.807	0.974	−0.004	−0.003	−0.003	−0.001
5	HRSG	1.232	0.555	−0.356	1.588	4.101	2.052	−1.339	5.440	−0.015	−0.008	0.001	−0.015
6	HPST	0.000	−0.011	0.007	−0.007	−0.010	−0.008	0.002	−0.012	0.002	−0.001	0.000	0.001
7	IPST	0.042	0.098	−0.045	0.087	0.154	0.357	−0.153	0.306	1.852	−0.346	0.843	1.009
8	LPST	0.205	0.158	−0.209	0.415	0.790	0.562	−0.700	1.489	−1.687	0.152	−0.373	−1.314
9	CP	0.000	0.000	0.000	0.000	0.000	0.001	0.000	0.000	0.000	0.000	0.000	0.000
10	FWP	0.000	0.012	−0.005	0.005	−0.002	0.047	−0.017	0.015	0.000	0.000	0.000	0.000
11	GEN	0.631	0.001	−0.001	−0.097	−0.378	0.004	−0.004	−0.374	−0.002	0.000	0.000	−0.002
TOTAL		2.204	5.347	0.311	1.893	14.608	8.725	0.803	13.805	0.152	−0.221	0.459	−0.307

Note: Bold and italic values indicate the key CFV to be identified and distinct with other results.

Table 5 Influence of single-fault fuel.

No.	Subassembly	Fault 1		Fault 2		Fault 3
		MFi*	ΔIi	MFi*	ΔIi	MFi*	ΔIi
1	AC	8.3633	6.6749	2.1653	1.7309	−0.1393	−0.0015
2	CC	−3.2903	−1.1799	−0.5937	4.0643	0.0062	−0.0082
3	FH	0.0015	0.0064	0.0059	0.0221	0.0000	0.0003
4	GT	0.0251	−0.1451	13.8924	9.8478	−0.0052	−0.0067
5	HRSG	2.2283	1.7870	5.7805	6.1531	−0.0203	−0.0224
6	HPST	0.0008	−0.0117	−0.0097	−0.0180	0.0027	0.0011
7	IPST	0.0674	0.1404	0.2447	0.5104	2.8701	1.5052
8	LPST	0.3268	0.3638	1.2560	1.3511	−2.6171	−1.5350
9	CP	0.0003	0.0004	0.0002	0.0010	0.0003	0.0003
10	FWP	−0.0003	0.0122	−0.0035	0.0449	−0.0002	−0.0001
11	GEN	−0.1715	−0.0971	0.5952	−0.3744	−0.1663	−0.0020
TOTAL		7.5513	7.5513	23.3331	23.3331	−0.0690	−0.0690

Note: Bold and italic values indicate the key CFV to be identified and distinct with other results.

At the same time, it is also found that when a component fails, it will induce influence on other nonfailed components, especially the components closer to the fault source. Due to the large coupling between components, the impact of induced failure will affect the failed components in turn. For example, under the working condition of Case 1, due to the scaling of the compressor blade, the airflow separation area of the compressor blade expanded. The energy loss increased, resulting in a failure of 5.522 MW. Still, but the inherent failure of the compressor was only 4.378 MW, which indicates that the redundant 1.143 MW failure was caused by the induced influence of other components, not due to the performance degradation of the components themselves. And sometimes in the fault performance of components, the induced fault is even larger than the inherent fault of the components themselves. For example, in Case 3, the induced fault of intermediate pressure cylinder accounts for 54.5% of the fault performance.

In the diagnosis of some components, the characteristic fault value is negative, which is because the performance of the component has been improved to some extent due to the influence of the faulty component. For example, in the combustion chamber in Case 1, as the intake air volume of the compressor decreases and the exhaust temperature increases, the internal chemical reaction rate in the combustion chamber increases and the irreversible loss decreases. Hence, the characteristic fault value of the combustion chamber assumes a negative value, reducing the fuel consumption by 3.2903 MW. In addition, by comparing Fault 1, Fault 2, and Fault 3, it is found that the compressor and turbine have the same 3% performance deterioration, but the turbine failure leads to 23.3331 MW fuel added to the unit, while the compressor failure leads to 7.5513 MW fuel added to the plant. The increase in turbine fuel consumption is about three times that of compressor failure, which indicates that turbine failure has a more significant impact on the plant than compressor failure. However, the fuel increase of the unit is −0.069 MW due to the 5% performance deterioration of the medium-pressure cylinder of the turbine, which indicates that in the actual operation of the combined cycle power plant, the performance deterioration of the components in the overhead cycle has a more significant impact on the fuel of the plant. More attention should be paid to the influence of turbine deterioration.

In the actual power plant, the component efficiency reduction caused by blade corrosion, scaling, and other factors is a slow cumulative process. If it can be found early and corresponding maintenance measures can be taken, the unit loss can be reduced. Therefore, by gradually changing the efficiency parameters of the fault components, the influence of the fault variation degree of compressor and turbine components on fault characteristic values is studied. The variation curve is shown in Figure 4: In Fault 1, with the gradual decrease of the compressor fault degree, the compressor fault eigenvalues ML_i^L and $$M{F}_{i}^{* }$$ decrease from 4.378 to 0.684 and 8.363 to 1.387, respectively. In Fault 2, with the gradual reduction of turbine fault degree, turbine fault eigenvalues ML_i^L and $$M{F}_{i}^{* }$$ also change from 8.808 to 2.079 and 13.8924 to 2.255, respectively. The CFV changes linearly with the fault degree of the component, indicating that the CFV has a good sensitivity for detecting unit faults and provides a reliable technology for the early warning and diagnosis of subsequent units.

Figure 4. Performance deterioration curves of compressor and gas turbine under single malfunction.

Multiple fault diagnosis results and discussion

Due to the complex structure of the combined cycle system, it is more difficult to accurately diagnose the real fault source of the unit because of the possibility of multiple faults occurring simultaneously during unit operation. This paper lists three representative multifault cases for diagnosis and analysis. The diagnosis results are shown in Tables 6–8, among which Table 7 is the malfunction cost table of fault 6.

Table 6 Multiple-fault diagnosis results.

No.	Subassembly	Fault 4				Fault 5				Fault 6
		MFi	DFi	MFiL	MFiG	MFi	DFi	MFiL	MFiG	MFi	DFi	MFiL	MFiG
1	AC	6.296	2.214	3.507	2.789	0.764	0.828	−0.708	1.472	6.297	2.214	3.506	2.791
2	CC	−3.920	6.856	−7.310	3.390	−0.628	4.763	−5.145	4.517	−3.911	6.854	−7.316	3.405
3	FH	0.005	0.025	−0.017	0.022	0.004	0.019	−0.014	0.017	0.005	0.025	−0.017	0.022
4	GT	8.251	1.537	7.437	0.814	9.778	0.054	8.804	0.975	8.248	1.536	7.435	0.813
5	HRSG	4.970	3.091	−1.722	6.691	4.087	2.285	−1.329	5.416	4.954	3.088	−1.721	6.676
6	HPST	−0.021	0.013	−0.016	−0.005	−0.010	−0.008	0.002	−0.012	−0.021	0.013	−0.015	−0.005
7	IPST	0.197	0.488	−0.193	0.390	1.952	0.185	0.600	1.352	1.957	0.350	0.535	1.422
8	LPST	1.012	0.824	−0.883	1.895	−0.857	0.665	−0.948	0.092	−0.613	0.840	−1.122	0.509
9	CP	0.000	0.001	0.000	0.000	0.000	0.001	0.000	0.000	0.000	0.001	0.000	0.000
10	FWP	−0.002	0.066	−0.022	0.020	−0.003	0.049	−0.017	0.015	−0.004	0.065	−0.022	0.018
11	GEN	−0.512	0.005	−0.006	−0.506	−0.380	0.004	−0.004	−0.376	−0.512	0.005	−0.006	−0.506
TOTAL		16.276	15.120	0.776	15.500	14.707	8.843	1.239	13.468	16.400	14.990	1.256	15.144

Note: Bold and italic values indicate the key CFV to be identified and distinct with other results.

Table 7 Fuel impact table in case 6.

MFi	6.297	−3.911	0.005	8.248	4.954	−0.021	1.957	−0.613	0.000	−0.004	−0.512	ΔIi
6.297	0.410	0.000	0.000	1.237	0.469	−0.001	0.120	−0.037	0.000	0.000	0.016	8.511
−3.911	2.107	0.000	0.002	2.757	1.485	−0.005	0.616	−0.188	0.000	−0.001	0.082	2.943
0.005	0.004	0.000	0.000	0.014	0.005	0.000	0.001	0.000	0.000	0.000	0.000	0.030
8.248	0.358	0.000	0.000	1.156	0.438	0.002	0.107	−0.027	0.000	0.000	−0.498	9.783
4.954	1.183	0.000	0.001	0.546	0.207	−0.008	0.323	−0.114	0.000	0.000	0.951	8.042
−0.021	−0.008	0.000	0.000	0.046	0.017	0.000	0.005	−0.001	0.000	0.000	−0.046	−0.008
1.957	0.133	0.000	0.000	0.092	0.035	0.000	0.009	−0.002	0.000	0.000	0.082	2.306
−0.613	0.356	0.000	0.000	0.103	0.039	0.000	0.010	−0.002	0.000	0.000	0.333	0.227
0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.001
−0.004	0.013	0.000	0.000	0.006	0.002	0.006	0.012	0.014	0.000	0.000	0.011	0.061
−0.512	0.001	0.000	0.000	0.000	0.000	0.000	0.001	0.001	0.000	0.000	0.001	−0.507
MFi*	10.856	−3.911	0.008	14.205	7.652	−0.025	3.161	−0.969	0.000	−0.006	0.420

Table 8 Influence of multifault fuel.

No.	Subassembly	Fault 4		Fault 5		Fault 6
		MFi*	ΔIi	MFi*	ΔIi	MFi*	ΔIi
1	AC	10.9479	8.5101	2.1357	1.5923	10.8561	8.5110
2	CC	−3.9202	2.9360	−0.6284	4.1345	−3.9111	2.9430
3	FH	0.0085	0.0294	0.0062	0.0228	0.0084	0.0297
4	GT	14.2094	9.7883	13.9697	9.8320	14.2050	9.7835
5	HRSG	7.6737	8.0611	5.7930	6.3716	7.6516	8.0422
6	HPST	−0.0256	−0.0075	−0.0102	−0.0187	−0.0253	−0.0078
7	IPST	0.3219	0.6852	3.1161	2.1372	3.1612	2.3065
8	LPST	1.6545	1.8357	−1.3516	−0.1918	−0.9690	0.2270
9	CP	−0.0005	0.0007	0.0002	0.0010	−0.0003	0.0009
10	FWP	−0.0028	0.0638	−0.0041	0.0459	−0.0062	0.0613
11	GEN	0.5295	−0.5066	0.5238	−0.3764	0.4204	−0.5066
TOTAL		31.3962	31.3962	23.5504	23.5504	31.3908	31.3908

It can be seen from the diagnosis results that when multiple components fail simultaneously in the system, the coupling effect between faults leads to greater induced faults in nonfaulty components. For example, in Fault 4, due to the failure of the compressor and turbine, the plant's fuel consumption increased by 31.3962 MW, and the fault value resulted in induced faults of 4.97 and 1.012 MW in the waste heat boiler and low-pressure cylinder. If the traditional thermo-economic diagnostic index MF_i is used, it can only narrow the search range of faults and cannot eliminate the interference of induced faults. As for the characteristic fault value MF_i^L obtained by an advanced exergic analysis method, the waste heat boiler showed an inherent fault of −1.722 MW, while the low-pressure cylinder showed an inherent fault of −0.833 MW. The two components did not meet the fault identification conditions. It can be seen that the improved fault eigenvalue is more accurate than the traditional eigenvalue in dealing with multiple faults of the unit. In addition, by comparing the diagnosis results of single fault and multiple faults in Tables 4–8, it is found that the fault value generated by each component under multiple faults is not a simple superposition of a single fault, and the impact of some component faults is partially offset or increased. For example, in Case 6, the fault value generated by the compressor increases by 0.775 MW from a single fault, the fault value generated by the intermediate pressure cylinder increases by 0.105 MW, but the fault generated by the gas turbine decreases by 1.534 MW. However, the increased fuel consumption of the whole unit under multiple faults must be greater than the sum of the increased fuel consumption under a single fault. For example, the increased fuel consumption of the plant in Case 4 is 0.5118 MW more than the sum of Case 1 and Case 2. The increased fuel consumption of the plant in Case 5 is 0.2863 MW more than the sum of Case 2 and Case 3, and the increased fuel consumption of the plant in Case 6 is 0.5754 MW more than the sum of the three single faults.

To further study the internal influence relationship between components, the compressor and turbine fault degree will be gradually changed by controlling 3% of the turbine and compressor fault degree respectively, and the influence between compressor fault and turbine fault will be studied in case of multiple faults. The performance degradation curve is shown in Figure 5. It can be seen from the figure that with the gradual increase of the compressor fault, the turbine fault performance will continue to decrease, and the two changes in reverse. It indicates that the occurrence of the compressor fault will weaken the impact of the turbine fault to a certain extent. However, with the gradual increase of the turbine fault degree, the compressor fault performance is also increasing. The two changes in a positive direction indicate that the occurrence of the turbine fault will, to a certain extent, strengthen the impact of the compressor fault. The analysis results correspond exactly to the plant performance in actual operation. When the compressor's fault degree increases continuously, its outlet temperature increases continuously, increasing turbine inlet temperature and efficiency, thereby weakening the fault performance of the turbine itself.

Figure 5. Performance deterioration curves of compressor and gas turbine under multiple malfunction.

CONCLUSIONS

Based on the traditional diagnosis method based on thermo-economic, this paper puts forward with the help of advanced exergy analysis method for diagnosis of the fault characteristic value, and the numerical analysis method, develops a simulation model of 590 MW combined cycle unit in quantitative analysis and detection units of single and multiple faults, main conclusions are as follows:

• (1)

  By using the advanced exergy analysis method, the improved thermo-economic diagnosis characteristic fault value ML_i^L and $$M{F}_{i}^{* }$$, in the diagnosis of the unit on the question of a single fault and multiple faults, through the analysis of compressor, turbine, steam turbine intermediate pressure cylinder three single-fault condition and the compressor and turbine, turbine and steam turbine intermediate pressure cylinder, more than three kinds of compressor and turbine and steam turbine intermediate pressure cylinder fault condition, It can not only accurately detect the fault source location of the unit, improve the accuracy of thermal economic diagnosis, but also further quantify the impact caused by the fault.

• (2)

  Through the compressor and turbine fault degree of change and the relationship between characteristic value analysis shows that the characteristic fault value $$M{L}_{i}^{L}$$ and $$M{F}_{i}^{* }$$ unit to detect the fault has strong sensitivity. The performance degradation defined as a linear relation, leads that the diagnosis model can provide reliable technology for subsequent early warning and diagnosis of the unit.

• (3)

  By analyzing the multifault diagnosis of the unit, it can be seen that in the multifault condition, the malfunction cost of each component is not the simple superposition under a single fault, but the partial offset or phase increase among faults. In the further study of the internal influence relationship between components, it is found that with the gradual increase of fault degree, compressor fault can weaken the fault performance of the turbine to some extent. In contrast, turbine fault can strengthen the fault performance of the compressor to some extent, and the fault performance of the turbine is roughly twice that of the compressor, resulting in three times of fuel consumption of the unit. In the operation of combined cycle power plants, more attention should be paid to the influence of turbine deterioration.

NOMENCLATURE ACRONYMS AND SCALARS

• AC
• air compressor
• CC
• combustion chamber
• FH
• fuel heater
• GT
• gas turbine
• HRSG
• heat recovery steam generator
• STA
• stack
• HPST
• high pressure cylinder of steam turbine
• IPST
• intermediate pressure cylinder of steam turbine
• LPST
• low pressure cylinder of steam turbine
• CND
• condenser
• CP
• condensate pump
• FWP
• feed water pump
• GEN
• generator
• J₁-J₄
• pooled component
• B₁-B₆
• branch component
• FB, PB
• fuel and products exergy of a component
• FS, PS
• fuel and products negentropy of a component
• MF
• malfunction of a component
• P
• products
• F
• fuel
• I
• irreversible loss
• k*
• unit exergy cost
• k
• unit exergy consumption

SUBSCRIPTS

• 0
• system environment
• i, j
• index for number of components
• ref
• reference conditions
• op
• operation condition
• T
• total
• P
• products
• F
• fuel

SUPERSCRIPTS

• 0
• reference conditions
• ∗
• exergy cost/malfunction cost
• L, G
• intrinsic and induced malfunction
• EN, EX
• endogenous and external irreversibility

ACKNOWLEDGEMENTS

This research was supported by the Science and Technology Innovation Project of the Shanghai Municipal Science and Technology Commission (20dz1205208).

CONFLICT OF INTEREST STATEMENT

The authors declare no conflict of interest.