CN109655275B - Gas turbine cycle heat economy diagnosis method based on sensitivity coefficient method - Google Patents

Gas turbine cycle heat economy diagnosis method based on sensitivity coefficient method Download PDF

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CN109655275B
CN109655275B CN201811439330.5A CN201811439330A CN109655275B CN 109655275 B CN109655275 B CN 109655275B CN 201811439330 A CN201811439330 A CN 201811439330A CN 109655275 B CN109655275 B CN 109655275B
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王雷
张瑞青
姜阳
杨倩玉
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Shenyang Institute of Engineering
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Abstract

The invention relates to a method for diagnosing the circulating heat economy of a gas turbine based on a sensitivity coefficient method, which comprises the following steps of; establishing a state space description equation for describing the efficiency characteristic of the unit according to parameters influencing the efficiency characteristic of the gas turbine, wherein the efficiency characteristic state of the unit at a certain moment can be represented as an n-dimensional space with each state variable as a coordinate axis, and the efficiency characteristic of the gas turbine is represented by efficiency; according to the obtained state space description equation and the state parameters, the sensitivity coefficient of each parameter to the efficiency change is calculated one by one, the parameter with small influence on the efficiency is eliminated from the maximum parameter which influences the efficiency change, and the state space description equation is simplified. The method can not only qualitatively judge the heat economy problem of the gas turbine, but also more timely and accurately judge the main parameters influencing the change of the gas turbine, avoid the misguidance of false data or wrong data to operators, and simultaneously provide a referable model for the operation optimization, the state monitoring, the fault diagnosis and the like of a gas turbine monitoring information system.

Description

Gas turbine cycle heat economy diagnosis method based on sensitivity coefficient method
Technical Field
The invention belongs to the technical field of gas turbines, and particularly relates to a gas turbine cycle heat economy diagnosis method based on a sensitivity coefficient method.
Background
With the increase of the number of the operating gas turbines for large power generation in China, the heat economy of the gas turbines for large power generation is diagnosed on the premise of ensuring the safe operation of the gas turbines, the operation benefit of the gas turbines is improved to the maximum extent, and the method is an important target of power generation enterprises. At present, the method for analyzing the thermal economy of the large-scale power generation gas turbine is a diagnosis direction of calculating the economical efficiency change from the parameter change, namely, the method focuses on the research of the influence of the state parameter change on the cyclic thermal economy (thermal efficiency), and is mainly based on two methods: the method is characterized in that a thermal equilibrium method based on a first law of thermodynamics, such as a traditional thermal efficiency method, an equivalent steam extraction method, a cyclic function method and the like, and the essence of the analysis method is energy conservation; the second is a fire analysis method based on the second law of thermodynamics. The existing literature analyzes the influence of the gas turbine parameters on the unit economy from different aspects and different angles by using the method, and constructs a functional relation of the thermal economy of the combined cycle unit changing along with the state parameters and the like. Although these analysis methods can determine the magnitude of the thermal economy change of the gas turbine cycle unit when the state parameter changes, they are only suitable for performance monitoring or design optimization, and what is more concerned about the running unit is how to find out the specific state parameter that causes the thermal economy change, i.e. implementing the diagnosis method of "determining the main parameter that affects the change by the thermal economy change", and the existing methods all focus on a small deviation method based on the parameter target value, and obtain the relationship between the unit state parameter deviation and the gas turbine cycle thermal economy to qualitatively determine the parameter that causes the thermal economy change.
In summary, the existing thermal economy diagnosis method from parameter change to economy change has rationality, but for exploiting the energy-saving potential of the unit, the operation benefit of the unit is improved to the maximum extent, and a more effective analysis and diagnosis method is needed.
Therefore, it is necessary to effectively analyze the deviation of the state parameter of the gas turbine cycle plant and the thermal economy of the combined cycle plant, and on the basis of this, establish a diagnostic method for determining the main parameter affecting the change from the change in the thermal economy. The method has very important value for improving the unit operation level and the economic efficiency to the maximum extent.
Disclosure of Invention
In view of the above problems, it is an object of the present invention to provide a method for diagnosing thermal economy of a gas turbine cycle based on a coefficient of sensitivity method, which can quantitatively analyze the contribution of a plant thermodynamic system parameter to a change in thermal economy to determine which parameters are main parameters affecting the change in thermal economy. The optimization method comprises the following steps:
and (1) establishing a state space description equation for describing the efficiency characteristic of the unit according to the parameters influencing the efficiency characteristic of the gas turbine, wherein the efficiency characteristic state of the unit at a certain moment can be represented as an n-dimensional space with each state variable as a coordinate axis. This space is determined by the topology, operating conditions, and operating mode of the gas turbine system. And establishing a state space description equation, and determining state parameters of each part and the efficiency characteristic of the unit.
The state parameters comprise fuel property f and atmospheric temperature TaAtmospheric pressure paInlet temperature T of compressor1 *Inlet pressure of compressor
Figure BDA0001884313220000021
Compressor outlet temperature
Figure BDA0001884313220000022
Compressor outlet pressure
Figure BDA0001884313220000023
Combustion chamber outlet pressure
Figure BDA0001884313220000024
Turbine inlet temperature
Figure BDA0001884313220000025
Turbine exhaust temperature
Figure BDA0001884313220000026
Turbine outlet pressure
Figure BDA0001884313220000027
Pressure loss epsilon of inlet air of air compressorcPressure loss epsilon of turbine exhausttPressure loss epsilon of combustion chamberbCompression efficiency eta of gas compressorcExpansion efficiency eta of turbinetCombustion chamber efficiency etab(ii) a The efficiency characteristic of a gas turbine may be expressed in terms of a combination of the efficiencies of its component parts.
The efficiency of a gas turbine can be expressed as a combination of the three component efficiencies of the compressor, the combustion chamber and the gas turbine, i.e. the efficiency η of the gas turbinegtCalculating an index, using compressor efficiency etacCombustion chamber efficiency etabGas turbine etatThe combined form of efficiency represents:
Figure BDA0001884313220000031
wherein: x is 1+ f, the mass flow rate ratio of fuel gas to air, and f is the amount of fuel added into the combustion chamber when the compressor sucks unit mass of air, and is called the fuel-air ratio;
wherein:
Figure BDA0001884313220000032
wherein
Figure BDA0001884313220000036
Respectively representing the average specific constant pressure heat capacity of air in the compression process, the air stagnation temperature of the outlet of a compressor in the isentropic compression process, the average specific constant pressure heat capacity of gas in the expansion process and the gas stagnation temperature of the outlet of a turbine in the isentropic expansion process; qnetExpressed as the lower heating value of the fuel;
wherein:
Figure BDA0001884313220000033
is the temperature ratio of the gas turbine,
Figure BDA0001884313220000034
is the pressure ratio of the gas compressor,
wherein:
Figure BDA0001884313220000035
therefore, the gas turbine efficiency characteristic state space description equation can be expressed as:
ηgt＝f(τ,π,ηc,ηt,ηb,εc,εb,εt)
calculating a proportional relation between each parameter change and the efficiency change according to a thermodynamic theory according to the state space description equation obtained in the step and the state parameters contained in the state space description equation, calculating sensitive coefficients of each parameter to the efficiency change one by one, eliminating parameters with small influence on the efficiency, and simplifying the state space description equation;
an efficiency function describing an equation by a state space is expressed as η ═ f (x)1,x2,...,xi,xn)。
And (3): when all the parameter factors are changed, x is respectively used1,x2,...,xiBecome x'1,x′2,...,x′iThe variation amounts are respectively Δ x1,Δx2,...,ΔxiX'1＝x1+Δx1,x′2＝x2+Δx2,...,x′i＝xi+ΔxiThe efficiency η also changes accordingly from η to η ', and the variation Δ η, which represents η represented by all the factor variations, is equal to η' - η.
And (4): the efficiency variation is linearized with a taylor expansion of a multivariate function:
Figure BDA0001884313220000041
in the formula
Figure BDA0001884313220000042
Is xiThe partial derivative to η; Δ xiIs xiThe amount of change in (c).
If only xiThe factor changes, and none of the other factors changes, i.e. Δ xi≠0,ΔxjWhen j ≠ i is 0, the variation of the efficiency η is represented as Δ η ≠ iiIs Δ xiThe influence on η is expressed as
Figure BDA0001884313220000043
It is clear that,
Figure BDA0001884313220000044
and (5): the sensitivity coefficient to efficiency variation for each parameter is calculated. Variation of definition eta and factor xiThe ratio of the variation of (a) to (b) is eta to xiInfluence coefficient A ofiThen, then
Figure BDA0001884313220000045
The meaning of which is the ith factor xiA change of one percent will cause a change in efficiency AiAnd (4) percent. A. theiIs positive to represent Δ ηiAnd Δ xiThe direction of change of (2) is the same. | AiThe larger |, the factor x is indicatediThe greater the impact on efficiency.
And (6): using AiCalculating a in step (4)i：
Figure BDA0001884313220000046
And (7): calculating the influence of each parameter change on the efficiency:
Figure BDA0001884313220000047
and (8): by comparing Δ ηiIs used for judging the maximum parameter x influencing the change of the parameteri。
The invention has the advantages that:
the method can not only qualitatively judge the heat economy problem of the gas turbine, but also more timely and accurately judge the main parameters influencing the change of the gas turbine, avoid false data or wrong data from giving wrong guidance to operators, and simultaneously provide a referable model for operation optimization, state monitoring, fault diagnosis and the like of a gas turbine monitoring information system.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The invention provides a method for diagnosing the circulating heat economy of a gas turbine based on a sensitivity coefficient method, which comprises the following steps of:
and (1) establishing a state space description equation for describing the efficiency characteristic of the unit according to the parameters influencing the efficiency characteristic of the gas turbine, wherein the efficiency characteristic state of the unit at a certain moment can be represented as an n-dimensional space with each state variable as a coordinate axis. This space is determined by the topology, operating conditions, and operating mode of the gas turbine system. And establishing a state space description equation, and determining state parameters of each part and the efficiency characteristic of the unit.
The state parameters include fuel characteristicsProperty f, atmospheric temperature TaAtmospheric pressure paInlet temperature T of compressor1 *Inlet pressure of compressor
Figure BDA0001884313220000051
Compressor outlet temperature
Figure BDA0001884313220000052
Compressor outlet pressure
Figure BDA0001884313220000053
Combustion chamber outlet pressure
Figure BDA0001884313220000054
Turbine inlet temperature
Figure BDA0001884313220000055
Turbine exhaust temperature
Figure BDA0001884313220000056
Turbine outlet pressure
Figure BDA0001884313220000057
Pressure loss epsilon of inlet air of air compressorcPressure loss epsilon of turbine exhausttPressure loss epsilon of combustion chamberbCompression efficiency eta of gas compressorcExpansion efficiency eta of turbinetCombustion chamber efficiency etab(ii) a The efficiency characteristic of a gas turbine may be expressed in terms of a combination of the efficiencies of its component parts.
The efficiency of a gas turbine can be expressed as a combination of the three component efficiencies of the compressor, the combustion chamber and the gas turbine, i.e. the efficiency η of the gas turbinegtCalculating an index, using compressor efficiency etacCombustion chamber efficiency etabGas turbine etatThe combined form of efficiency represents:
Figure BDA0001884313220000061
wherein: x is 1+ f, the mass flow rate ratio of fuel gas to air, and f is the amount of fuel added into the combustion chamber when the compressor sucks unit mass of air, and is called the fuel-air ratio;
wherein:
Figure BDA0001884313220000062
wherein
Figure BDA0001884313220000066
Respectively representing the average specific constant pressure heat capacity of air in the compression process, the air stagnation temperature of the outlet of a compressor in the isentropic compression process, the average specific constant pressure heat capacity of gas in the expansion process and the gas stagnation temperature of the outlet of a turbine in the isentropic expansion process; qnetExpressed as the lower heating value of the fuel;
wherein:
Figure BDA0001884313220000063
is the temperature ratio of the gas turbine,
Figure BDA0001884313220000064
is the pressure ratio of the gas compressor,
wherein:
Figure BDA0001884313220000065
therefore, the gas turbine efficiency characteristic state space description equation can be expressed as:
ηgt＝f(τ,π,ηc,ηt,ηb,εc,εb,εt)
and (2) according to the state space description equation obtained in the step (1) and the state parameters contained in the state space description equation, calculating the proportional relation between the change of each parameter and the change of the efficiency according to a thermodynamic theory, eliminating the parameters with small influence on the efficiency, and simplifying the state space description equation.
And (3): an efficiency function describing an equation by a state space is expressed as η ═ f (x)1,x2,...,xi,xn)；
When all the factors occurChange, respectively, by x1,x2,...,xiBecome x'1,x′2,...,x′iThe variation amounts are respectively Δ x1,Δx2,...,ΔxiX'1＝x1+Δx1,x′2＝x2+Δx2,...,x′i＝xi+ΔxiThe efficiency η also changes accordingly from η to η ', and the variation Δ η, which represents η represented by all the factor variations, is equal to η' - η.
And (4): the efficiency variation is linearized with a taylor expansion of a multivariate function:
Figure BDA0001884313220000071
in the formula
Figure BDA0001884313220000072
Is xiThe partial derivative to η; Δ xiIs xiThe amount of change in (c).
If only xiThe factor changes, and none of the other factors changes, i.e. Δ xi≠0,ΔxjWhen j ≠ i is 0, the variation of the efficiency η is represented as Δ η ≠ iiIs Δ xiThe influence on η is expressed as
Figure BDA0001884313220000073
It is clear that,
Figure BDA0001884313220000074
and (5): the sensitivity coefficient to efficiency variation for each parameter is calculated. Variation of definition eta and factor xiThe ratio of the variation of (a) to (b) is eta to xiInfluence coefficient A ofiThen, then
Figure BDA0001884313220000075
The meaning of which is the ith factor xiA change of one percent will cause a change in efficiency AiAnd (4) percent. A. theiIs positively representedΔηiAnd Δ xiThe direction of change of (2) is the same. | AiThe larger |, the factor x is indicatediThe greater the impact on efficiency.
And (6): using AiCalculating a in step (4)i：
Figure BDA0001884313220000076
And (7): calculating the influence of each parameter change on the efficiency:
Figure BDA0001884313220000077
and (8): by comparing Δ ηiIs used for judging the maximum parameter x influencing the change of the parameteri。
The invention realizes the thermal economy diagnosis of the gas turbine circulating unit 'the main parameters influencing the change of the gas turbine circulating unit are judged by the thermal economy change'. The method is based on the characteristic space of the unit running state and the variables thereof, and based on the combined cycle running characteristic and from the structure and mechanism of a thermodynamic system, the thermodynamic method is adopted to calculate the influence degree of the state parameters on the gas turbine heat economic performance change, the influence degree on other parameters and the contribution degree to the overall heat economic performance change; decoupling the coupling relation among the parameters by using a Taylor formula, quantitatively calculating the influence of parameter change on the cyclic thermal efficiency and the influence sequence thereof by using a sensitive coefficient method, and judging which state parameter causes the largest change of the thermal economy.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims (1)

1. A method for diagnosing the heat economy of a gas turbine cycle based on a coefficient of sensitivity method is characterized by comprising the following steps of:
the method comprises the following steps: establishing a state space description equation for describing the efficiency characteristic of the unit according to parameters influencing the efficiency characteristic of the gas turbine, wherein the efficiency characteristic state of the unit at a certain moment can be represented as an n-dimensional space with each state variable as a coordinate axis; the efficiency characteristic of a gas turbine can be expressed in terms of a combination of the efficiencies of its component parts;
step two: calculating the proportional relation between each parameter change and the efficiency change according to the obtained state space description equation and the state parameters contained in the state space description equation, calculating the sensitivity coefficient of each parameter to the efficiency change one by one, judging the maximum parameter influencing the efficiency change, and eliminating the parameter with small influence on the efficiency, thereby simplifying the state space description equation; the state parameters in the step one specifically comprise fuel property f and atmospheric temperature TaAtmospheric pressure paInlet temperature T of compressor1 *Inlet pressure of compressor
Figure FDA0002921749610000011
Compressor outlet temperature
Figure FDA0002921749610000012
Compressor outlet pressure
Figure FDA0002921749610000013
Combustion chamber outlet pressure
Figure FDA0002921749610000014
Turbine inlet temperature
Figure FDA0002921749610000015
Turbine exhaust temperature
Figure FDA0002921749610000016
Turbine outlet pressure
Figure FDA0002921749610000017
Pressure loss epsilon of inlet air of air compressorcPressure loss epsilon of turbine exhausttPressure loss epsilon of combustion chamberbCompression efficiency eta of gas compressorcExpansion efficiency eta of turbinetCombustion chamber efficiency etab；
A state space description equation is established, specifically as follows,
the efficiency of a gas turbine can be expressed as a combination of the three component efficiencies of the compressor, the combustion chamber and the gas turbine, i.e. the efficiency η of the gas turbinegtCalculating index, using compressor compression efficiency etacCombustion chamber efficiency etabExpansion efficiency eta of gas turbinetThe combination of (a) and (b) represents:
Figure FDA0002921749610000018
wherein: x is 1+ f, the mass flow rate ratio of fuel gas to air, and f is the amount of fuel added into the combustion chamber when the compressor sucks unit mass of air, and is called the fuel-air ratio;
wherein:
Figure FDA0002921749610000021
wherein c ispa、
Figure FDA0002921749610000027
cpg、
Figure FDA0002921749610000028
Respectively representing the average specific constant pressure heat capacity of air in the compression process, the air stagnation temperature of the outlet of a compressor in the isentropic compression process, the average specific constant pressure heat capacity of gas in the expansion process and the gas stagnation temperature of the outlet of a turbine in the isentropic expansion process; qnetExpressed as the lower heating value of the fuel;
wherein:
Figure FDA0002921749610000022
is the temperature ratio of the gas turbine,
Figure FDA0002921749610000023
is the pressure ratio of the gas compressor,
wherein:
Figure FDA0002921749610000024
therefore, the gas turbine efficiency characteristic state space description equation can be expressed as:
ηgt＝f(τ,π,ηc,ηt,ηb,εc,εb,εt)；
the state space description equation is simplified in the following way,
1) the efficiency function of the equation described by the state space is expressed as η ═ f (x)1,x2,...,xi,xn) (ii) a When all parameters are changed, x is respectively used1,x2,...,xiBecome x'1,x′2,...,x′iThe variation amounts are respectively Δ x1,Δx2,...,ΔxiIs x'1＝x1+Δx1,x′2＝x2+Δx2,...,x′i＝xi+ΔxiThe efficiency η also changes correspondingly from η to η ', and the variation Δ η of η, which is expressed by the variation of all parameters, is equal to η' - η;
2) the efficiency variation is linearized with a taylor expansion of a multivariate function:
Figure FDA0002921749610000025
in the formula
Figure FDA0002921749610000026
Is xiThe partial derivative to η; Δ xiIs xiThe amount of change in (c);
when only xiChange, no other parameter being changed, i.e. Δ xi≠0,Δxj0, j ≠ i, then variation of efficiency ηThe chemical quantity is recorded as Δ ηiIs Δ xiThe influence on η is expressed as
Figure FDA0002921749610000031
3) Calculating the sensitivity coefficient to the efficiency change of each parameter: variation of definition eta and parameter xiThe ratio of the variation of (a) to (b) is eta to xiInfluence coefficient A ofiThen, then
Figure FDA0002921749610000032
4): using AiCalculating a in step 2)i，
Figure FDA0002921749610000033
5): calculating the influence of each parameter change on the efficiency:
Figure FDA0002921749610000034
by comparing Δ ηiIs used for judging the maximum parameter x influencing the change of the parameteri。
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