CN113420404A - Gas turbine performance simulation self-adaption method - Google Patents

Gas turbine performance simulation self-adaption method Download PDF

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CN113420404A
CN113420404A CN202110412226.2A CN202110412226A CN113420404A CN 113420404 A CN113420404 A CN 113420404A CN 202110412226 A CN202110412226 A CN 202110412226A CN 113420404 A CN113420404 A CN 113420404A
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闫斌斌
冯坤
李周正
江志农
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Beijing University of Chemical Technology
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Abstract

Accurate performance simulation is critical to gas turbine early warning and adaptive diagnostics, and performance simulation accuracy depends on the accuracy of the component map. The patent provides a performance simulation self-adaptive method based on a particle swarm algorithm aiming at the deviation of a component characteristic diagram caused by the manufacturing tolerance, assembly and maintenance operation of a gas turbine. And selecting a general analytic solution as an analytic expression of the part characteristic diagram, extracting key sensitive coefficients of the general analytic solution, and defining the key sensitive coefficients as update factors. And successfully determining an accurate expression of the improved general analytic solution by adopting an updating factor optimization method based on the improved particle swarm optimization algorithm. The method can supplement the deficiency of the current component characteristic parameter nonlinear relation identification means, improve the performance simulation precision of the gas turbine, and provide theoretical support for early warning and self-adaptive diagnosis of the gas turbine.

Description

Gas turbine performance simulation self-adaption method
Technical Field
The invention relates to the field of gas turbine performance simulation and self-adaptation, in particular to performance simulation self-adaptation.
Background
Accurate performance prediction is crucial to gas turbine early warning and adaptive diagnostics, and performance prediction is highly correlated with accuracy of component property maps.
The component maps are the result of expensive bench tests and are proprietary information of the gas turbine manufacturer, the gas turbine customer cannot obtain actual component maps, and the component customer may obtain generic component maps for the same model gas turbine. However, due to slight differences in the results of manufacturing tolerances, assembly and maintenance of gas turbines, the component maps of the same model gas turbines necessarily differ. In addition, disassembly or modification operations performed during engine maintenance or repair can also affect the shape of the real part map. Part of gas turbine users cannot acquire the gas turbine component characteristic diagram, only can acquire part of gas turbine performance discrete data, and even can acquire only gas turbine performance simulation data. The non-linear relationship between the component characteristic parameters is therefore still worth further investigation.
Disclosure of Invention
In view of this, the patent designs a gas turbine performance simulation adaptive method, selects a general analytic solution as an analytic expression of a component characteristic diagram, extracts a key sensitive coefficient of the general analytic solution, defines the key sensitive coefficient as an update factor, and adopts an update factor optimization method based on an improved particle swarm optimization algorithm to successfully determine an accurate expression of the improved general analytic solution, so that the adaptive of the component characteristic diagram can be realized through the scheme, and the technical scheme content is as follows:
1. a gas turbine performance simulation self-adaptive method is characterized in that key sensitive parameters of a general analytic solution are extracted and defined as update factors, the update factors are optimized based on a particle swarm optimization, the general analytic solution is determined and improved, and the nonlinear relation of component characteristic parameters is accurately captured, and the method comprises the following steps:
1) selecting a universal analytic solution with strong robustness as an initial expression of a gas turbine component characteristic diagram, wherein the universal analytic solution comprises a gas compressor universal analytic solution, a gas turbine universal analytic solution and a power turbine universal analytic solution, the universal analytic solutions of all the components are respectively composed of a flow analytic solution and an isentropic efficiency analytic solution, describing the mass flow characteristic of the gas compressor by cutting a parabolic two-dimensional curved surface, describing the mass flow characteristic of the turbine by adopting a Freuger formula, and describing the isentropic efficiency characteristic of all the components by adopting a complete parabolic two-dimensional curve.
2) Extracting key sensitive parameters of the general analytic solution, defining the parameters as update factors, and selecting an auxiliary coefficient (alpha)t,mt,pt) As an update factor of the compressor mass flow analytic solution, constant coefficients 1.54 and 0.54 of the compressor efficiency analytic solution are converted into variable coefficients (gamma)tAnd gammat-1) and defining as an update factor of the compressor efficiency characteristic, converting the constant 0.232 of the turbine mass flow analytic solution into a variable coefficient χtAnd defined as the turbine mass flow characteristic update factor, and converts the constants 1.61 and 0.61 of the turbine efficiency analytic solution into variable coefficients (phi)tAnd phit-1) and is defined as a turbine efficiency characteristic update factor, the power turbine characteristic update factor being consistent with the turbine.
3) Acceleration constants c1 and c2 of the particle swarm algorithm are set to be c 1-c 2-1.2, r1 and r2 are set to be random values in the range of 0-1, the population is set to be 60, algebra is set to be 80, the traditional particle swarm algorithm is improved, constraints are added to the inertia weight W, and the inertia weight is limited from the maximum inertia weight WmaxLinear reduction to minimum inertial weight WminAnd searching the global optimal value of the characteristic updating factor of the component.
4) Optimizing the component characteristic updating factor, adjusting the component characteristic updating factor by adopting an improved particle swarm algorithm, and matching the actually measured performance data of the reference gas turbine until the fitness reaches the required precision or the maximum algebra, alphaiHas an optimization range from alphaiTo alphai+3δk，mtIs from mt-δkTo mt+δk，ptHas an optimization range of pt-δkTo pt+δk，γtHas an optimization range from gammat-δkTo gammat+δk，χtThe optimizing range is from xt-δkTo xt+δk，φtIs from phit-δkTo phit+δk，δk＝1。
2. The gas turbine performance simulation adaptive method according to claim 1, wherein in the step 1,
selecting a universal analytic solution with strong robustness as an initial expression of a gas turbine component characteristic diagram, and characterizing the reduced rotation speed (n) by adopting the universal analytic solutionc,nt) Pressure ratio (pi)c,πt) Reduced flow (G)c,Gt) And isentropic efficiency (η)c,ηt) The general analytic solutions comprise a flow analytic solution and an isentropic efficiency analytic solution, the mass flow characteristic of the compressor is described by cutting a parabolic two-dimensional curved surface, the mass flow characteristic of the turbine is described by using a Flrogger formula, the isentropic efficiency characteristic of each component is described by using a complete parabolic two-dimensional curve, and the general analytic solutions adopt normalized parameters (such as normalized reduced flow)
Figure BDA0003024299890000031
It is shown that,
1) general analytic solution for gas compressor
General analytic solution for compressor to express reduced rotation speed
Figure BDA0003024299890000032
Pressure ratio
Figure BDA0003024299890000033
Reduced flow
Figure BDA0003024299890000034
And isentropic efficiency
Figure BDA0003024299890000035
The non-linear mathematical relationship between them, the formula is as follows,
Figure BDA0003024299890000036
Figure BDA0003024299890000041
wherein
Figure BDA0003024299890000042
Figure BDA0003024299890000043
Figure BDA0003024299890000044
Figure BDA0003024299890000045
Wherein
Figure BDA0003024299890000046
p＝0.5。
2) Turbo universal analytic solution
Approximate description of mass flow characteristics of a turbine using a modified Fligger formula, the turbine general analytic solution representing reduced rotational speed
Figure BDA0003024299890000047
Pressure ratio
Figure BDA0003024299890000048
Reduced flow
Figure BDA0003024299890000049
And isentropic efficiency
Figure BDA00030242998900000410
The non-linear mathematical relationship between them, the formula is as follows,
Figure BDA00030242998900000411
Figure BDA00030242998900000412
the general analytic solution form of the power turbine is consistent with that of the turbine and is not described in detail.
3. The adaptive method for simulating the performance of a gas turbine according to claim 1, wherein in the step 2,
extracting key sensitive parameters of a general analytic solution of each part of the gas turbine, defining the key sensitive parameters as update factors,
1) selecting an auxiliary coefficient (alpha)t,mt,pt) As an update factor of the mass flow analytic solution of the compressor, the formula is as follows,
Figure BDA00030242998900000413
αt＝(αi+3δk)·e-q (6)
Figure BDA0003024299890000051
mt＝(mi+δk)·e-q (8)
p＝pt＝(pi+δk)·e-q (9)
wherein alpha isi＝0.1，mi＝1.25，pi＝0.5，δk＝0.1。
2) Constant coefficients 1.54 and 0.54 of the compressor efficiency analytical solution are converted into variable coefficients (gamma)tAnd gammat-1) and is defined as an update factor of the compressor efficiency characteristic, the formula being as follows,
Figure BDA0003024299890000052
γt＝(γi+δk)·e-q (11)
wherein gamma isi＝1.54,δk＝0.1。
3) Converting constant 0.232 of turbine mass flow analytic solution into variable coefficient chitAnd defined as the turbine mass flow characteristic update factor, while converting constants 1.61 and 0.61 of the turbine efficiency analytical solution into variable coefficients (phi)tAnd phit-1) and is defined as a turbine efficiency characteristic update factor, the formula being as follows,
Figure BDA0003024299890000053
χt＝(χi+δk)·e-q (13)
wherein xi＝0.232,δk＝0.1。
Figure BDA0003024299890000054
φt＝(φi+δk)·e-q (15)
Wherein phii＝1.61,δk＝0.1。
The power turbine characteristic update factor is kept consistent with the turbine.
4. The gas turbine performance simulation adaptive method according to claim 1, wherein in the step 3:
the particle swarm algorithm is adopted to search the update factors, the position and the speed of each particle are obtained by tracking two extreme values, namely the individual optimal pBest and the global optimal gBest, the formula is as follows,
Figure BDA0003024299890000061
Figure BDA0003024299890000062
where c1 and c2 are constant rotational speeds, typically set at c 1-c 2-1.2; r1 and r2 are random values in the range of 0 to 1; w is an inertial weight, and its value is set in the range of 0.1 to 0.9.
Figure BDA0003024299890000063
Is the iththThe particles are in the (k +1) ththThe rotational speed of the generation;
Figure BDA0003024299890000064
displaying the position of each particle;
Figure BDA0003024299890000065
is the previous best position of each particle at the particle best position, gBestkIs the optimal position for all the particles,
the traditional particle swarm algorithm is improved, the constraint is added to the inertia weight W, and the inertia weight is limited from the maximum inertia weight WmaxLinear reduction to minimum inertial weight WminThe formula is as follows,
Figure BDA0003024299890000066
wherein iter is the current generation number; itermaxIs the total number of the generation,
by continuously updating the position, the particles tend to the position of the optimal solution in the solution space, the search process is completed, and the global optimal solution of the update factor is finally output.
5. The gas turbine performance simulation adaptive method according to claim 1, wherein in the step 4:
1) the gas turbine performance models are tuned until they accurately predict engine performance under the same environmental conditions and fuel flow, expressed as,
Y＝f(X,u) (19)
wherein, Y represents the engine performance vector and is composed of the measured values of pressure, temperature and the like at different engine gas path positions, namely Y is [ P, T ═ P]Component feature vectors include unmeasurable quantities, e.g. in terms of mass and efficiency, i.e. X ═ G, η, n, pi]U is composed of ambient conditions and fuel flow, and is called an engine model control variable (u ═ Pamb,Tamb,handle]) The parameter being used as input to a model for engine performance simulation, and the control variable may be the useful power P output by the power turbine, depending on the selected simulation methodptReduced rotational speed NcorOr any other variable of the number of variables,
2) adjusting the characteristic update factor of the component by adopting an improved particle swarm algorithm, matching the actually measured performance data of the reference gas turbine until the fitness reaches the required precision or the maximum algebra, adjusting the independent parameter vector X, and realizing the output parameter Y of the gas turbine model and the output parameter Y of the reference gas turbinerMinimization of the difference between, evaluation of the predicted Y and observation of the measured YrThe objective function of the difference between is as follows,
Figure BDA0003024299890000071
where n denotes the total number of measured parameters, γiIndicating the relative error of the measured parameter, Yi-YriRepresentation model simulation data YiAnd field measurement data YriDifference between, field measurement data YriSelecting performance measurement data of the continuous loading process of the gas turbine,
3) the accuracy of fitness is set to eps 1 × 10-1，αiHas an optimization range from alphaiTo alphai+3δk，mtIs from mt-δkTo mt+δk，ptHas an optimization range of pt-δkTo pt+δk，γtHas an optimization range from gammat-δkTo gammat+δk，χtThe optimizing range is from xt-δkTo xt+δk，φtIs from phit-δkTo phit+δk，δk＝1。
Advantageous effects
(1) The invention selects the initial component characteristic diagram of the general analytic solution gas turbine performance simulation model, can cover the full rotating speed range of the component characteristic, and can realize the full working condition performance simulation self-adaptation.
(2) The key sensitive coefficient of the general analytic solution is extracted and defined as an update factor, so that the complex nonlinear characteristics of gas turbine compressor, turbine and power turbine parts can be captured more accurately, and the characteristic deviation caused by the manufacturing tolerance, assembly and maintenance operation of the gas turbine is reduced.
(3) And improving an inertia weight coefficient of the particle swarm algorithm, and finally outputting a global optimal solution of the update factor. The limitation that the traditional particle swarm algorithm jumps back and forth when the optimal update factor is converged is overcome.
(4) By adopting the update factor optimization method based on the improved particle swarm optimization algorithm, the accurate expression of the improved general analytical solution is successfully determined, the defects of the current component characteristic parameter nonlinear relation identification means can be overcome, the performance simulation precision of the gas turbine is improved, and the theoretical support is provided for early warning and self-adaptive diagnosis of the gas turbine.
Drawings
FIG. 1 is a flow chart of a performance simulation adaptation method
FIG. 2 gas turbine Performance model schematic
FIG. 3 in situ measurement of parameters
FIG. 4 convergence diagram of particle swarm optimization algorithm
FIG. 5 measured data for a field gas turbine loading process
FIG. 6 comparison of predicted trends for different adaptation methods
FIG. 7 prediction error comparison of different adaptive methods
Detailed Description
The adaptive method for simulating the performance of the gas turbine is further described below.
1. General analytic solution for gas turbine component characteristics
The performance of the components of the same model gas turbine is expressed by constructing a general analytical solution, the shape of a component characteristic diagram can be accurately captured, and the reduced rotating speed (n) is representedc,nt) Pressure ratio (pi)c,πt) Reduced flow (G)c,Gt) And isentropic efficiency (η)c,ηt) The mathematical analytical relationship between the parameters. The analytical relationship is a function of the reduced parameters, i.e., G ═ f (n, pi) and η ═ G (n, G). Another way of expressing the isentropic efficiency η ═ h (n, pi) is to characterize it as a function of the reduced speed n and the pressure ratio pi, which is advantageous for the nearly vertical speed line in the high-speed range. The general analytic solutions of the gas turbine comprise a flow analytic solution and an isentropic efficiency analytic solution, and are in a three-dimensional curved surface form. The flow characteristic diagrams of the compressor and the turbine are obviously different in shape, and the efficiency characteristic diagrams are similar.
An accurate component analysis solution is a prerequisite for accurate simulation of gas turbine performance. First, they must be sufficiently concise or else an explicit analytical solution to the entire operating conditions may not be derivable. Secondly, as a standard solution, the analytical solution of the component should be as close as possible to a typical practical analytical solution. How to make a trade-off between these two factors is the key to derive a common analytical solution for the same model gas turbine. The component performance expression may take many forms. The universal analytic solution selected by the patent adopts normalized folding parameters (such as normalized folding flow)
Figure BDA0003024299890000091
The patent uses a split-shaft gas turbine as an example to describe the general analytic solution in detail.
1) General analytic solution for gas compressor
General analytic solution for compressor to express reduced rotation speed
Figure BDA0003024299890000092
Pressure ratio
Figure BDA0003024299890000093
Reduced flow
Figure BDA0003024299890000094
And isentropic efficiency
Figure BDA0003024299890000095
The method selects a general analytic solution with the highest robustness according to the mathematical relationship, and the formula is as follows:
Figure BDA0003024299890000096
Figure BDA0003024299890000101
wherein
Figure BDA0003024299890000102
Figure BDA0003024299890000103
Figure BDA0003024299890000104
Figure BDA0003024299890000105
Wherein
Figure BDA0003024299890000106
p＝0.5。
2) Turbo universal analytic solution
The turbine section features are more uniform in shape than the compressor section features because the turbine is operating in a blocked condition most of the time. Therefore, constructing a turbine analytical solution is mathematically simpler than a compressor analytical solution. Using modified Flegur's formulaApproximately describing the mass flow characteristics of the turbine. This patent gives the reduced rotational speed of the turbine
Figure BDA0003024299890000107
Pressure ratio
Figure BDA0003024299890000108
Reduced flow
Figure BDA0003024299890000109
And isentropic efficiency
Figure BDA00030242998900001010
The analytical formula (2). The formula is as follows:
Figure BDA00030242998900001011
Figure BDA00030242998900001012
2. universal analytic solution update factor extraction
In order to realize the nonlinear matching characteristic of the universal analytic solution in the full rotating speed range and further reduce the deviation caused by manufacturing, assembly tolerance and maintenance of the gas turbine, the initial universal analytic solution of the gas turbine is updated. Update factors are first defined, including compressor, turbine and power turbine update factors. Since the analytic solutions of the turbine and power turbine are similar, only the turbine update factor is given here.
The mass flow characteristic coefficients (alpha, m, p) of the compressor are designed as update factors (alpha)t,mt,pt) To efficiently adapt the analytical solution. The formula is as follows:
Figure BDA0003024299890000111
αt＝(αi+3δk)·e-q (6)
Figure BDA0003024299890000112
mt＝(mi+δk)·e-q (8)
p＝pt＝(pi+δk)·e-q (9)
wherein alpha isi＝0.1，mi＝1.25，pi＝0.5，δk＝0.1。
Defining a constant variation of the compressor efficiency characteristic as an update factor (gamma)t) To effectively accommodate component characteristic variations. The formula is as follows:
Figure BDA0003024299890000113
γt＝(γi+δk)·e-q (11)
wherein gamma isi＝1.54,δk＝0.1。
Similarly, a turbine (χ) is definedt,φt) To effectively accommodate component characteristic variations. The formula is as follows:
Figure BDA0003024299890000114
χt＝(χi+δk)·e-q (13)
wherein xi＝0.232,δk＝0.1。
Figure BDA0003024299890000115
φt＝(φi+δk)·e-q (15)
Wherein phii＝1.61,δk＝0.1。
3. Particle swarm algorithm improvement
Particle Swarm Optimization (PSO) is a biomimetic heuristic derived from the collective behavior of clusters of birds, consisting of a set of particles called a population, each particle representing a candidate solution. The elements of the particle represent the parameters to be optimized. The particles are updated in the solution space at a specified rate to search for the optimal solution. Each particle has a memory that helps it track the previous best position. The position of each particle is distinguished into an individual best pBest and a global best gBest; when updated in the solution space, the velocity of each particle is adjusted according to its history and its neighborhood. Each update of a particle is affected by its memory of previous useful parameters, its current location, and the population memory of the population. Thus, during the search, the particles tend to move to the optimized search area.
During the search, the position and velocity of each particle is determined by tracking two extrema, the individually optimal pBest and the globally optimal gBest. The formula is as follows:
Figure BDA0003024299890000121
Figure BDA0003024299890000122
where c1 and c2 are constant rotational speeds, typically set at c 1-c 2-1.2; r1 and r2 are random values in the range of 0 to 1; w is an inertial weight, and its value is set in the range of 0.1 to 0.9. Vi k+1Is the iththThe particles are in the (k +1) ththThe rotational speed of the generation;
Figure BDA0003024299890000123
displaying the position of each particle;
Figure BDA0003024299890000124
is the previous one of each particle at the optimal position of the particlePosition of good, gBestkIs the optimal position for all particles.
By continuously updating the position, the particles tend to the position of the optimal solution in the solution space, the search process is completed, and the global optimal solution is finally output.
Compared with a genetic algorithm, the PSO algorithm has no cross and variation operation, the algorithm structure is simpler, and the calculation speed is faster. However, the conventional particle swarm optimization is prone to search back and forth near the global optimal solution at the end of the search process. To address this problem, the inertial weight W may be selected from a maximum inertial weight W during the search processmaxLinear reduction to minimum inertial weight WminSince a relatively large inertial weight favors global searches and a relatively small inertial weight favors local searches. The formula is as follows:
Figure BDA0003024299890000131
wherein iter is the current generation number; itermaxIs the total generation number.
4. Component characteristic update factor optimization
Aiming at the problem of performance simulation self-adaption of the gas turbine, a performance simulation self-adaption method based on a general analytical solution and particle swarm optimization is provided, and the whole framework of the method is shown in figure 1.
The performance simulation adaptation is related to the reverse performance analysis, in which the general analytical solution schemes are adjusted until they accurately predict the engine performance under the same environmental conditions and fuel flow. In general, the engine performance assuming no measurement noise or bias is expressed as:
Y＝f(X,u) (19)
wherein, Y represents the engine performance vector and is composed of the measured values of pressure, temperature and the like at different engine gas path positions, namely Y is [ P, T ═ P]. Component feature vectors include unmeasurable quantities, such as, for example, mass and efficiency, i.e., X ═ G, η, n, pi]U is made up of ambient conditions and fuel flow, called hairEngine model control variable (u ═ P)amb,Tamb,handle]) This parameter is used as an input to a model of the engine performance simulation. Depending on the selected simulation method, the control variable may be the useful power P output by the power turbineptReduced rotational speed NcorOr any other variable.
The gas turbine performance parameters are represented by measured data of an in-service gas turbine or by simulation results of a gas turbine model. For testing the method proposed by this patent, the reference gas turbine is a gas turbine model with an initial generic analytical solution built in based on the method of this patent. Instead, the gas turbine model employs an improved generic analytic solution. The initial generic analytic solution is discretized into a two-dimensional interpolation table with reference to the gas turbine to determine the reduced mass flow and the isentropic efficiency of the compressor.
The performance simulation adaptive method described in FIG. 1 implements gas turbine model output parameter Y and reference gas turbine output parameter Y by adjusting independent parameter vector XrMinimization of the difference between. To evaluate the predicted Y and observed measurements YrThe difference between them, the patent defines the objective function as follows:
Figure BDA0003024299890000141
the constraint function is: formulas (6), (8), (9), (11), (13), (15).
Where n represents the total number of measured parameters. Gamma rayiIndicating the relative error of the measured parameter. Y isi-YriRepresentation model simulation data YiAnd field measurement data YriThe difference between them. Since the above-described adaptation process involves a plurality of measured parameters, the objective function is modified. The number of the measurement parameters to be matched depends on the test case, and the patent selects all the measurement parameters to perform parameter optimization.
The improved particle swarm optimization algorithm can realize the minimization of the target function, can effectively search the neighborhood of the initial point and converge to the global minimum of the target function. Mathematically, multiple solutions are possible because the optimization results of improving the particle swarm optimization algorithm are not necessarily global minima. To address the above limitations, matching is first performed at the design point of the gas turbine, and then at the non-design point. Another approach is to place no constraints on the number of subsystems of the optimization process, which can increase the search space. The last condition for successful implementation of the optimization algorithm is to obtain optimal solution convergence before the maximum number of iterations is reached. The above steps may ensure that the obtained solution is a global minimum of (of).
The method proposed by this patent assumes that there is an initial generic analytical solution. There is no similarity requirement between the initial generic analytical solution built into the gas turbine model and the actual component map of the reference gas turbine. Since the component characteristic curve is controlled by mathematical analysis, the method can reconstruct a component characteristic diagram of an arbitrary shape. The adaptation process will now be described as follows:
1. an initial generic analytical solution is selected from a public literature or other source.
2. Adjusting the cyclic reference point to a standard value (G) of the component performance parametermap,ηmap,πmap) Design point performance (G) at rated operating conditions with reference gas turbinedes,ηdes,πdes) And (5) performing anastomosis.
3. The initial generic analytical solution is analyzed and an appropriate update factor is selected for each part property map. The coefficients of the generic analytic solution are typically selected as update factors.
4. In the gas turbine model, the generic analytic solution is integrated with the update factor of the initial generic analytic solution.
5. An update factor in the adaptation process is adjusted based on the measured parameters of the reference gas turbine, and the adapted analysis solution is further modified to match all measured parameters. Notably, prior to the adaptive process being implemented, the gas turbine simulation parameters deviate significantly from the reference engine measurements. In addition, in some cases, the engine model may fail to converge before the particle swarm algorithm is invoked.
The finally obtained universal analytic solution is an improved universal analytic solution and can output the same result as the field measured data. The resulting generic analytical solution is only an approximation of the unknown part characteristic curve because there are many uncertainties not accounted for, such as measurement noise and humidity.
5. The effectiveness of the patent is verified based on a gas turbine performance model and performance monitoring data of a split-shaft gas turbine, the gas turbine performance model is shown in figure 2, the gas turbine performance measurement parameters are shown in figure 3, the gas turbine performance model is developed in a Matlab/Simulink environment, and verification is performed through actually measured data. The in-situ measurement position of the gas turbine is shown in FIG. 3, wherein
Figure BDA0003024299890000161
The output parameters are represented by a number of output parameters,
Figure BDA0003024299890000162
representing a control parameter. And extracting the optimal update factor from the general analytic solution by using an improved particle swarm optimization algorithm. The convergence of the optimization process is shown in fig. 4, where the 73 rd generation reached a minimum adaptation value of 0.94%. In the global optimization process, the fitness monotonically decreases, which shows that the error caused by the update factor is further reduced in the optimization process.
In order to evaluate the accuracy of the UGAS method proposed by the present patent, comparison with the characteristic diagram scaling method and the characteristic diagram generation method was made. To evaluate the method of the patent over a larger operating range, the measured data during the loading of the gas turbine are selected, wherein the fuel mass flow G is determinedfCompressor inlet temperature T1And compressor inlet pressure P1As input parameters of the gas turbine model, fig. 5 shows.
Based on the simulation trend graph of the three adaptive methods, as shown in fig. 6, from the perspective of trend matching, the adaptive method provided by the patent has the best matching effect, and the matching between the performance simulation trend in the whole rotating speed area and the field measured data is superior to that of the other two adaptive methods. In addition, the newly proposed method cannot occur also in the low speed region at the maximum.
The simulation errors of the three adaptive methods are shown in fig. 7. When the operating point is far from the design point, the prediction error of the gas turbine model by the characteristic map scaling method increases. This is because the successful application of the method presupposes that the shape of the component map to be adjusted is very similar to the shape of the component map used with reference to the gas turbine. On the other hand, the simulation error of the characteristic diagram generation method is in a quadratic parabolic distribution, and the deviation between the low-speed and high-speed regions is mainly caused by the specific shapes near the two side edges of the elliptic curve. The simulation error distribution of the UGAS method is more balanced, and the error is lower than that of the two self-adaptive methods in the whole working condition range.
As can be seen from FIG. 7, the peak value of the simulation error of the map scaling method is in the range of-6.9% to 4.3%, the peak value of the simulation error of the map generation method is between-5.32% to 5.12%, and the peak value of the simulation error of the newly proposed UGAS method is in the range of-1.55% to 1.6%, where the peak value of the simulation error of the turbine outlet pressure of the gas turbine model is 1.3% with the minimum. On the other hand, the simulation error of the outlet pressure of the compressor is the largest and is 1.6%.
In conclusion, the gas turbine performance simulation based on the UGAS method reduces the simulation error at the design point and the non-design point at the same time. In addition, the UGAS method overcomes the limitation of the existing self-adaptive method due to the two self-adaptive methods in the simulation precision, and provides a theoretical basis for the self-adaptation of the gas turbine components.

Claims (5)

1. A gas turbine performance simulation self-adaptive method is characterized in that key sensitive parameters of a general analytic solution are extracted and defined as update factors, the update factors are optimized based on a particle swarm optimization, the general analytic solution is determined and improved, and the nonlinear relation of component characteristic parameters is accurately captured, and the method comprises the following steps:
1) selecting a universal analytic solution with strong robustness as an initial expression of a gas turbine component characteristic diagram, wherein the universal analytic solution comprises a gas compressor universal analytic solution, a gas turbine universal analytic solution and a power turbine universal analytic solution, each component universal analytic solution is respectively composed of a flow analytic solution and an isentropic efficiency analytic solution, describing the mass flow characteristic of the gas compressor by cutting a parabolic two-dimensional curved surface, describing the mass flow characteristic of the turbine by adopting a Flegul formula, describing the isentropic efficiency characteristic of each component by adopting a complete parabolic two-dimensional curve,
2) extracting key sensitive parameters of the general analytic solution, defining the parameters as update factors, and selecting an auxiliary coefficient (alpha)t,mt,pt) As an update factor of the compressor mass flow analytic solution, constant coefficients 1.54 and 0.54 of the compressor efficiency analytic solution are converted into variable coefficients (gamma)tAnd gammat-1) and defining as an update factor of the compressor efficiency characteristic, converting the constant 0.232 of the turbine mass flow analytic solution into a variable coefficient χtAnd defined as the turbine mass flow characteristic update factor, and converts the constants 1.61 and 0.61 of the turbine efficiency analytic solution into variable coefficients (phi)tAnd phit-1) and is defined as a turbine efficiency characteristic update factor, the power turbine characteristic update factor being in agreement with the turbine,
3) acceleration constants c1 and c2 of the particle swarm algorithm are set to be c 1-c 2-1.2, r1 and r2 are set to be random values in the range of 0-1, the population is set to be 60, algebra is set to be 80, the traditional particle swarm algorithm is improved, constraints are added to the inertia weight W, and the inertia weight is limited from the maximum inertia weight WmaxLinear reduction to minimum inertial weight WminSearching for a global optimum value of the component characteristic update factor,
4) optimizing the component characteristic updating factor, adjusting the component characteristic updating factor by adopting an improved particle swarm algorithm, and matching the actually measured performance data of the reference gas turbine until the fitness reaches the required precision or the maximum algebra, alphaiHas an optimization range from alphaiTo alphai+3δk，mtIs from mt-δkTo mt+δk，ptHas an optimization range of pt-δkTo pt+δk，γtHas an optimization range from gammat-δkTo gammat+δk，χtThe optimizing range is from xt-δkTo xt+δk，φtIs from phit-δkTo phit+δk，δk＝1。
2. The gas turbine performance simulation adaptive method according to claim 1, wherein in the step 1,
selecting a universal analytic solution with strong robustness as an initial expression of a gas turbine component characteristic diagram, and characterizing the reduced rotation speed (n) by adopting the universal analytic solutionc,nt) Pressure ratio (pi)c,πt) Reduced flow (G)c,Gt) And isentropic efficiency (η)c,ηt) The general analytic solutions comprise a flow analytic solution and an isentropic efficiency analytic solution, the mass flow characteristic of the compressor is described by cutting a parabolic two-dimensional curved surface, the mass flow characteristic of the turbine is described by using a Flrogger formula, the isentropic efficiency characteristic of each component is described by using a complete parabolic two-dimensional curve, and the general analytic solutions adopt normalized parameters (such as normalized reduced flow)
Figure FDA0003024299880000021
It is shown that,
1) general analytic solution for gas compressor
General analytic solution for compressor to express reduced rotation speed
Figure FDA0003024299880000022
Pressure ratio
Figure FDA0003024299880000023
Reduced flow
Figure FDA0003024299880000024
And isentropic efficiency
Figure FDA0003024299880000025
The non-linear mathematical relationship between them, the formula is as follows,
Figure FDA0003024299880000026
Figure FDA0003024299880000031
wherein
Figure FDA0003024299880000032
Figure FDA0003024299880000033
Figure FDA0003024299880000034
Figure FDA0003024299880000035
Wherein
Figure FDA0003024299880000036
p＝0.5，
2) Turbo universal analytic solution
Approximate description of mass flow characteristics of a turbine using a modified Fligger formula, the turbine general analytic solution representing reduced rotational speed
Figure FDA0003024299880000037
Pressure ratio
Figure FDA0003024299880000038
Reduced flow
Figure FDA0003024299880000039
And etcEntropy efficiency
Figure FDA00030242998800000310
The non-linear mathematical relationship between them, the formula is as follows,
Figure FDA00030242998800000311
Figure FDA00030242998800000312
the general analytic solution form of the power turbine is consistent with that of the turbine and is not described in detail.
3. The adaptive method for simulating the performance of a gas turbine according to claim 1, wherein in the step 2,
extracting key sensitive parameters of a general analytic solution of each part of the gas turbine, defining the key sensitive parameters as update factors,
1) selecting an auxiliary coefficient (alpha)t,mt,pt) As an update factor of the mass flow analytic solution of the compressor, the formula is as follows,
Figure FDA00030242998800000313
αt＝(αi+3δk)·e-q (6)
Figure FDA0003024299880000041
mt＝(mi+δk)·e-q (8)
p＝pt＝(pi+δk)·e-q (9)
wherein alpha isi＝0.1，mi＝1.25，pi＝0.5，δk＝0.1；
2) Constant coefficients 1.54 and 0.54 of the compressor efficiency analytical solution are converted into variable coefficients (gamma)tAnd gammat-1) and is defined as an update factor of the compressor efficiency characteristic, the formula being as follows,
Figure FDA0003024299880000042
γt＝(γi+δk)·e-q (11)
wherein gamma isi＝1.54,δk＝0.1；
3) Converting constant 0.232 of turbine mass flow analytic solution into variable coefficient chitAnd defined as the turbine mass flow characteristic update factor, while converting constants 1.61 and 0.61 of the turbine efficiency analytical solution into variable coefficients (phi)tAnd phit-1) and is defined as a turbine efficiency characteristic update factor, the formula being as follows,
Figure FDA0003024299880000043
χt＝(χi+δk)·e-q (13)
wherein xi＝0.232,δk＝0.1。
Figure FDA0003024299880000044
φt＝(φi+δk)·e-q (15)
Wherein phii＝1.61,δk＝0.1；
The power turbine characteristic update factor is kept consistent with the turbine.
4. The gas turbine performance simulation adaptive method according to claim 1, wherein in the step 3:
the particle swarm algorithm is adopted to search the update factors, the position and the speed of each particle are obtained by tracking two extreme values, namely the individual optimal pBest and the global optimal gBest, the formula is as follows,
Figure FDA0003024299880000051
Figure FDA0003024299880000052
where c1 and c2 are constant rotational speeds, typically set at c 1-c 2-1.2; r1 and r2 are random values in the range of 0 to 1; w is the inertial weight, and the value of W is set in the range of 0.1 to 0.9i k+1Is the iththThe particles are in the (k +1) ththThe rotational speed of the generation;
Figure FDA0003024299880000053
displaying the position of each particle;
Figure FDA0003024299880000054
is the previous best position of each particle at the particle best position, gBestkIs the optimal position for all the particles,
the traditional particle swarm algorithm is improved, the constraint is added to the inertia weight W, and the inertia weight is limited from the maximum inertia weight WmaxLinear reduction to minimum inertial weight WminThe formula is as follows,
Figure FDA0003024299880000055
wherein iter is the current generation number; itermaxIs the total number of the generation,
by continuously updating the position, the particles tend to the position of the optimal solution in the solution space, the search process is completed, and the global optimal solution of the update factor is finally output.
5. The gas turbine performance simulation adaptive method according to claim 1, wherein in the step 4:
1) the gas turbine performance models are tuned until they accurately predict engine performance under the same environmental conditions and fuel flow, expressed as,
Y＝f(X,u) (19)
wherein, Y represents the engine performance vector and is composed of the measured values of pressure, temperature and the like at different engine gas path positions, namely Y is [ P, T ═ P]Component feature vectors include unmeasurable quantities, e.g. in terms of mass and efficiency, i.e. X ═ G, η, n, pi]U is composed of ambient conditions and fuel flow, and is called an engine model control variable (u ═ Pamb,Tamb,handle]) The parameter being used as input to a model for engine performance simulation, and the control variable may be the useful power P output by the power turbine, depending on the selected simulation methodptReduced rotational speed NcorOr any other variable of the number of variables,
2) adjusting the characteristic update factor of the component by adopting an improved particle swarm algorithm, matching the actually measured performance data of the reference gas turbine until the fitness reaches the required precision or the maximum algebra, adjusting the independent parameter vector X, and realizing the output parameter Y of the gas turbine model and the output parameter Y of the reference gas turbinerMinimization of the difference between, evaluation of the predicted Y and observation of the measured YrThe objective function of the difference between is as follows,
Figure FDA0003024299880000061
where n denotes the total number of measured parameters, γiIndicating the relative error of the measured parameter, Yi-YriRepresentation model simulation data YiAnd field measurement data YriDifference between, number of field measurementsAccording to YriSelecting performance measurement data of the continuous loading process of the gas turbine,
3) the accuracy of fitness is set to eps 1 × 10-1，αiHas an optimization range from alphaiTo alphai+3δk，mtIs from mt-δkTo mt+δk，ptHas an optimization range of pt-δkTo pt+δk，γtHas an optimization range from gammat-δkTo gammat+δk，χtThe optimizing range is from xt-δkTo xt+δk，φtIs from phit-δkTo phit+δk，δk＝1。
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