Method for estimating surge margin of gas-steam combined cycle generator set

Abstract

The application discloses a surge margin estimation method for a gas-steam combined cycle generator set and belongs to the technical field of gas-steam combined cycle power generation, wherein the method estimates the surge margin based on steady-state identification-dynamic correction, divides the identification process into two steps in order: the first step is to identify the steady-state process; and the second step is to identify dynamic parameters, namely a state space matrix, by using a dynamic process. The method converts a difficult-to-implement nonlinear model identification into a linear least square problem of static parameter fitting and dynamic parameter correction, identifies by the two-step method of steady-state identification-dynamic correction, reduces the number of undetermined coefficients by analyzing the constraint conditions between the identified parameters, thereby makes the engineering implementation of the complex identification problem possible, realizes the surge margin estimation, and ensures the safe and stable operation of the unit.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of gas-steam combined cycle power generation, and particularly relates to a surge margin estimation method for a gas-steam combined cycle power generating unit. BACKGROUND

[0002] Surge is a kind of aerodynamic unstable working state in a compressor, and is an important source of hindering the working efficiency improvement and stable operation of a turbomachinery. With the improvement of performance requirements of a gas-steam combined cycle power generating unit, it is required to fully exert the potential capacity of a gas turbine, and the unit parameters are closer to the limit state, and the surge margin is more nervous. Therefore, if the signs of surge of the unit can be measured, a real-time estimation model of the surge margin is established, and a signal is provided to a surge control system, the surge can be more effectively controlled, and the anti-surge capacity of the unit is improved.

[0003] A traditional method starts from the aerodynamic and thermodynamic process of a compressor, one of which is to obtain characteristic interface output parameters by using a mature aerodynamic and thermodynamic model of a turbine engine, and then to perform surge margin estimation. The other is to use a one-dimensional model of a compression component to describe a surge dynamic process, to establish a dynamic model of a compression system surge according to the momentum conservation of a compressor channel, the mass conservation of gas in a cavity, the angular momentum conservation of a main shaft, and the thermodynamic equation of gas, to calculate the characteristic parameters of the compressor, and then to obtain the surge margin. The dynamic model obtained by this method can better simulate the surge dynamics of a turbocompression system, and is also applied to the design of a surge control system. However, since the aerodynamic and thermodynamic model is composed of a series of complex differential equations, the calculation amount is large, and it is difficult to realize real-time calculation.

[0004] An existing technology proposes a modeling method of engine surge margin (see “Wang, H., Zhang, H., Chen, K., et al. High stability control of engine based on surge margin estimation model[J]. Journal of Aerospace Power, 2013, 28(09): 2145-2154. DOI:10.13224 / j.cnki.jasp.2013.09.024.”). The model of the surge margin is divided into two parts of a non-distortion model in regular flight and a loss amount model in supermaneuver flight. The non-distortion model is based on a surge margin characteristic selection algorithm to screen the optimal model input, and is modeled and realized by a nonlinear fitting method; the loss amount model is based on an online angle of attack prediction model to evaluate the inlet distortion degree of the engine in real time, and then to obtain. The disadvantages of this method are that the online angle of attack prediction model is designed based on the OSP-LSSVR algorithm, and then the D c60 =D c60 (Ma, a) is an inlet distortion index, which is converted into a surge pressure ratio loss by converting the inlet distortion degree into the surge pressure ratio loss, and then the surge margin loss amount in distortion is obtained. This method has more complicated steps, and has weak generalization ability.

[0005] Therefore, the surge margin estimation of the gas-steam combined cycle generator set is a technical problem that needs to be solved. SUMMARY

[0006] The purpose of the present application is to solve the problem that the important parameter of surge margin cannot be measured during the operation of the gas-steam combined cycle generator set, and a surge margin estimation method for the gas-steam combined cycle generator set based on steady-state identification-dynamic correction is proposed to realize surge margin estimation and ensure safe and stable operation of the unit.

[0007] To achieve the above purpose, the present application adopts the following technical solution: a surge margin estimation method for a gas-steam combined cycle generator set, which estimates the surge margin based on steady-state identification-dynamic correction, and divides the identification process into two ordered steps: the first step is to identify the steady-state process; the second step is to identify the dynamic parameters, i.e. the state space matrix, using the dynamic process;

[0008] The method specifically includes:

[0009] Step 1: determine the simplest structure of the steady-state model expansion model of the gas-steam combined cycle generator set, so as to determine the parameters to be identified;

[0010] The simplest structure of the steady-state model expansion model is:

[0011]

[0012] Among them, the characteristic variable α representing the steady-state model is selected, and the steady-state model is expressed as a function of α; the gas turbine rotor speed n is selected as the characteristic variable α, and n is the state variable of the steady-state model; mf q represents the fuel flow, which is the input variable of the steady-state model, f1 represents the mapping relationship of q mf to ; SM represents the surge margin of the compressor, which is the output variable of the steady-state model, SM e (α) represents the surge margin of the compressor parameterized by the characteristic variable α;

[0013] Step 2: determine the identification signal and establish the identification data

[0014] The state variable of the steady-state model is the gas turbine rotor speed n, the input variable is the fuel flow q mf ; the output variable is the surge margin SM, and a step signal is selected as the input signal during identification;

[0015] Step 3: find the parameterized expression n e (α) of the steady-state model, and SM e (α), n e (α), and SM e (α) respectively represent state variable, input variable and output variable of steady-state model parameterized by characteristic variable α;

[0016] Step 4: Obtain deviation quantity Δn = n - n e (α), Δq mf = q mf - q mfe (α) and ΔSM = SM - SM e (α) in dynamic process;

[0017] Step 5: Obtain parameterized expression of state space matrix

[0018] Bring dynamic process deviation quantity of step 4 into steady-state model expansion model to determine parameterized Jacobian matrix coefficients A1(α) and C(α) of steady-state model expansion model; dynamic parameters A1(α) and C(α) at parameterization point of characteristic variable α are obtained through numerical calculation;

[0019] Specific method for obtaining A1(α) and C(α) is as follows:

[0020] Obtain variation of rotor speed and each output quantity through steady-state balance calculation by extracting power on rotor shaft of unit and sequentially changing input variable of unit, and calculate each partial derivative according to obtained variation of each parameter;

[0021] Or;

[0022] Obtain through data identification method by using test data or simulation output data of non-linear component level model;

[0023] Up to now, the method for estimating surge margin of gas-steam combined cycle generating unit based on steady-state identification-dynamic correction is completed.

[0024] The method for estimating surge margin of gas-steam combined cycle generating unit uses compressor pressure ratio and air flow to define compressor surge margin SM:

[0025]

[0026] Wherein π w is pressure ratio of current working point; π s is pressure ratio of corresponding surge boundary point under same reduced speed; m aw is air flow of current working point; m as is air flow of corresponding surge boundary point under same reduced speed.

[0027] The surge margin estimation method of the gas-steam combined cycle generator set, in step 3, utilizes the polyfit function in MATLAB to perform polynomial fitting on the characteristic variable alpha of each steady state point, so as to obtain the state variable, input variable and output variable of the steady state model, that is, to fit other variables by using the function of the characteristic variable alpha.

[0028] Through the above design scheme, the gas-steam combined cycle generator set surge margin estimation method based on steady state identification-dynamic correction provided by the application can bring the following beneficial effects: the method converts a difficult-to-implement nonlinear model identification into a linear least square problem of static parameter fitting and dynamic parameter correction, identifies through the two-step method of steady state identification-dynamic correction, and reduces the number of undetermined coefficients by analyzing the constraint conditions between the identified parameters, so as to make the engineering implementation of the complex identification problem possible. The fuel oil command is selected as the input signal, and the signal remains for 100s after each step, which is enough to make the system reach a good steady state to meet the identification needs of the steady state model. The command signal drives the fuel oil actuator, so that the unit speed increases by 2% to 6% each time, and the final system dynamic process can cover the entire operating area. The gas-steam combined cycle generator set surge margin estimation method based on steady state identification-dynamic correction realizes surge margin estimation and ensures safe and stable operation of the unit. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 is a general characteristic map of the compressor;

[0030] Figure 2 is a principle diagram of the estimation method based on steady state identification-dynamic correction;

[0031] Figure 3 is a schematic diagram of the steady state model expansion model;

[0032] Figure 4 is a surge margin estimation result diagram;

[0033] Figure 5 is a speed estimation result diagram;

[0034] Figure 6 is a flowchart of the surge margin estimation method of the gas-steam combined cycle generator set. DETAILED DESCRIPTION

[0035] In order to make the purpose, features and advantages of the application more obvious and easy to understand, the following will combine the specific embodiments of the application with the drawings to further describe the application. Figure 1 , Figure 2 , Figure 3 , Figure 4 , Figure 5 and Figure 6The technical solutions in the present application are described clearly and completely. Obviously, the present application is not limited by the following examples, and the specific implementation can be determined according to the technical solutions of the present application and the actual situation. In order to avoid confusion of the essence of the present application, the well-known methods, processes and procedures are not described in detail.

[0036] Method principle:

[0037] For the surge boundary of the compressor, it is generally determined by the experimental method. The present application adopts the method of curve fitting with the limit value of the component characteristic data to give the surge boundary of the compressor. First, according to the compressor characteristic data points, the corresponding each constant specific speed characteristic line is drawn on the general characteristic diagram of the compressor, and the extreme value point on each constant specific speed characteristic line in the direction close to the surge boundary of the compressor is selected. It is assumed that each extreme value point obtained is the intersection point of the corresponding constant specific speed characteristic line and the surge boundary of the compressor. In order to increase the fitting data points and improve the accuracy of the surge boundary fitting, according to the working principle of the compressor, there must be a theoretical starting working point of the compressor: the pressure ratio is 1 and the air flow is 0. Its meaning is that when the air flow through the compressor is 0, the pressure ratio of the compressor must be 1, that is, there is no any pressure increasing effect. The data points obtained above can make the surge boundary of the compressor as shown in Figure 1 ; Figure 1 The middle solid line shown in Figure 1 , the horizontal coordinate m a,cor represents the specific flow, and the vertical coordinate represents the pressure ratio.

[0038] In order to facilitate the use in actual calculation, the explicit expression of the surge boundary of the compressor is given by the method of curve fitting. Under the premise of ensuring the fitting accuracy, the third order is selected for fitting, and the result is shown by the dotted line in Figure 1 . After determining the surge boundary line, the present application adopts the pressure ratio and the air flow of the compressor to define the surge margin:

[0039]

[0040] Wherein: SM is the degree of deviation of the working point of the compressor at a certain equivalent speed from the surge boundary, that is, the surge margin; π w is the pressure ratio of the current working point; π s is the pressure ratio of the corresponding surge boundary point at the same equivalent speed; m aw is the air flow of the current working point; m as is the air flow of the corresponding surge boundary point at the same equivalent speed.

[0041] The surge margin estimation method based on steady-state identification and dynamic correction breaks down the identification process into two ordered steps: the first step is to identify the steady-state process; the second step is to identify the dynamic parameters, i.e., the state-space matrix. Although the identification process is completed in only two steps, the detailed modeling process still involves many issues.

[0042] The typical structure of a gas-steam combined cycle generator set model is as follows:

[0043]

[0044] Where X represents the unit's state variables; U represents the unit's input variables, i.e., control variables; and Y represents the unit's output variables, including all unit parameters. f and g represent the corresponding mapping relationship. The mapping relationship is abstracted into f and g. This invention aims to solve for this specific mapping relationship between f and g.

[0045] The steady-state model for a gas-steam combined cycle generator set is as follows:

[0046] {(X e (α),U e (α),Y e (α))|f(X e (α),U e (α))=0,Y e (α)=g(X e (α),U e (α))}(3)

[0047] Choose a characteristic variable α to represent the steady-state model, express the steady-state model as a function of α, and write the steady-state model in parameterized form: X e (α), U e (α) and Y e (α) represents the state variables, input variables, and output variables of the steady-state model parameterized by the characteristic variable α, respectively. The polyfit function in MATLAB is used to perform polynomial fitting on the characteristic variable α at each steady-state point to obtain the state variables, input variables, and output variables of the steady-state model; that is, fitting other variables with a function of the characteristic variable α. The expanded structure of the steady-state model of the gas-steam combined cycle generator unit is as follows:

[0048]

[0049] Where: each partial derivative represents the corresponding parameter of the Jacobian matrix at the steady-state point parameterized by α, i.e. It is expressed as the first derivative of the mapping relation f with respect to the state variable X. It is expressed as the first derivative of the mapping relation f with respect to the input variable U. This can be expressed as the first derivative of the mapping relation g with respect to the state variable X. The first order derivative of the mapping relationship g with respect to the input variable U, and each deviation is: e (α) and ΔU = U - U e (α).

[0050] For the gas-steam combined cycle generator set with fuel flow q mf as the control variable, the state variable is the gas turbine rotor speed n; the input variable is the fuel flow q mf ; and the output variable is the characteristic parameter at any cross section, such as the compressor outlet pressure, the turbine inlet temperature, the turbine outlet temperature, and the compressor surge margin SM. The steady-state model of the system satisfies the following set:

[0051]

[0052] The steady-state model is written in a parameterized form: n e (α), and Y e (α) represent the state variable, the input variable, and the output variable of the steady-state model parameterized by the characteristic variable α, respectively.

[0053] The steady-state model expansion model structure of the gas-steam combined cycle generator set is obtained as:

[0054]

[0055] where each partial derivative represents the corresponding parameter of the Jacobian matrix at the steady-state point parameterized by the characteristic variable α, that is, represents the first order derivative of the mapping relationship f1 with respect to the gas turbine rotor speed n, represents the first order derivative of the mapping relationship f1 with respect to the fuel flow q mf , represents the first order derivative of the mapping relationship g with respect to the gas turbine rotor speed n, represents the first order derivative of the mapping relationship g with respect to the fuel flow q mf , and each deviation is:

[0056]

[0057] In order to make the model structure simpler, the gas turbine rotor speed n is selected as the characteristic variable α, and then n e (α) = n, and Δn = 0 is obtained by substituting equation (7).

[0058] By substituting Δn = 0 into equation (6), the steady-state model expansion model structure of the gas-steam combined cycle generator set is simplified as:

[0059]

[0060] For the convenience of representation, record:

[0061]

[0062] Substitute formula (7), formula (9) into formula (8), and the steady-state model expansion model structure of the built gas-steam combined cycle generator set and its output parameters can be obtained:

[0063]

[0064] The steady-state model expansion model can be obtained from the complex nonlinear aerodynamic thermal model, and n e (α), q mfe (α) and Y e (α) The polyfit function in MATLAB is used for polynomial fitting of the characteristic variable α of each steady-state point, and the state variable, input variable and output variable of the steady-state model are obtained, that is, other variables are fitted by the function of the characteristic variable α. The dynamic parameters A1(α) and C(α) parameterized by the characteristic variable α on the steady-state model can be obtained by numerical calculation. The specific calculation method can obtain the change of the rotor speed and each output variable by extracting the power on the rotor shaft of the unit and sequentially changing the steady-state balance calculation of the input variable of the unit, and calculating each partial derivative according to the change of each parameter. It can also be obtained by using the test data or the simulation output data of the nonlinear component level model to obtain the dynamic parameters by using the data identification method.

[0065] The surge margin estimation method based on steady-state identification-dynamic correction proposed in the application converts a difficult nonlinear model identification into a linear least square problem of static parameter fitting and dynamic parameter correction, identifies through the two-step method of steady-state identification-dynamic correction, and reduces the number of undetermined coefficients by analyzing the constraint conditions between the identification parameters, so that the engineering implementation of the complex identification problem becomes possible.

[0066] Figure 2 The principle diagram of the estimation method based on steady-state identification-dynamic correction is shown, and the surge margin estimation method based on steady-state identification-dynamic correction divides the identification process into an orderly two-step: the first step is to identify the steady-state process; the second step is to identify the dynamic parameters, that is, the state space matrix, by using the dynamic process. Figure 3 The steady-state model expansion model diagram is shown.

[0067] The implementation method of the method is:

[0068] Referring to Figure 6 The specific process of the surge margin estimation method of the gas-steam combined cycle generator set based on steady-state identification-dynamic correction proposed in the application is as follows:

[0069] Step 1: Determine the simplest structure of the unit. Determine the simplest structure of the steady-state model expansion model of the gas-steam combined cycle generator unit to be identified, so as to determine the parameters to be identified.

[0070] Step 2: Determine the identification signal and establish the identification data. The steady-state identification-dynamic correction two-step method identification requires that the data used for identification contain both the steady-state characteristics and the dynamic characteristics of the system, so a step signal is generally selected as the input signal during identification.

[0071] Step 3: Obtain the parameterized representation of the steady-state model e (α), q mfe (α) and Y e (α). The relationship between the steady-state parameters is established, that is, other variables are fitted by the function of the characteristic variable.

[0072] Step 4: Obtain the deviation amount in the dynamic process. For the gas-steam combined cycle generator unit, it is to obtain Δn = n-n e (α), Δq mf = q mf -q mfe (α) and ΔSM = SM-SM e (α).

[0073] Step 5: Obtain the parameterized representation of the state space matrix.

[0074] The input signal selected by the present application, that is, the fuel command signal, keeps the signal for 100s after each step, which is sufficient to make the system reach a good steady state to meet the identification needs of the steady-state model. The command signal drives the fuel actuator, so that the unit speed increases by 2% to 6% each time, and the final system dynamic process can cover the entire operating area.

[0075] Next, the dynamic identification effect of the steady-state model expansion model is verified. In this process, the IGV position does not change, simulating the process of rapid change of fuel flow in the actual gas turbine during acceleration and deceleration. In the case that the IGV is fully opened and the fuel flow signal is continuously stepped input, the system state parameters calculated by the component-level nonlinear model (NCL) and the simulation results of the system state parameters based on the steady-state identification-dynamic correction are shown in Figs. Figure 4 and Figure 5 It can be seen that the estimation result of the surge margin of the present application can well follow the component-level nonlinear model (NCL), that is, accurately give the dynamic law of the gas-steam combined cycle generator unit in the operating area.

Claims

1. A method for estimating surge margin of a gas-steam combined cycle generator set, characterized in that, This method estimates surge margin based on steady-state identification and dynamic correction, and breaks down the identification process into two ordered steps: the first step is to identify the steady-state process; The second step is to identify dynamic parameters, i.e., the state-space matrix, using the dynamic process; The method specifically includes: Step 1: Determine the simplest structure of the steady-state model expansion model of the gas-steam combined cycle generator set, thereby determining the parameters to be identified; The simplest structure of the expanded steady-state model is: In this model, the characteristic variable α is selected to represent the steady-state model as a function of α. The rotor speed n of the gas turbine is selected as the characteristic variable α, and n is used as the state variable of the steady-state model. mf This represents fuel flow rate, which serves as an input variable for the steady-state model. f1 represents q mf arrive The mapping relationship, The characteristic variable α represents the parameterized fuel flow rate; SM represents the compressor surge margin, which is the output variable of the steady-state model. e (α) represents the compressor surge margin parameterized by the characteristic variable α; Step 2: Determine the identification signal and establish identification data. The state variable of the steady-state model is the gas turbine rotor speed n, and the input variable is the fuel flow rate q. mf The output variable is the surge margin SM, and a stepped signal is selected as the input signal for identification. Step 3: Find the parameterized representation n of the steady-state model e (α), and SM e (α), n e (α), and SM e (α) represent the state variables, input variables, and output variables of the steady-state model parameterized by the feature variable α, respectively; Step 4: Calculate the deviation Δn = nn in the dynamic process. e (α), Δq mf =q mf -q mfe (α) and ΔSM=SM-SM e (α); Step 5: Obtain the parameterized representation of the state space matrix. The dynamic process deviation from step 4 is substituted into the steady-state model expansion model to determine the parameterized Jacobian matrix coefficients A1(α) and C(α) of the steady-state model expansion model; the dynamic parameters A1(α) and C(α) of the parameterized points of the characteristic variable α are obtained through numerical calculation. Thus, the surge margin estimation method for gas-steam combined cycle generator sets based on steady-state identification and dynamic correction is completed.

2. The surge margin estimation method for gas-steam combined cycle generator sets according to claim 1, characterized in that, The compressor surge margin SM is defined using the compressor pressure ratio and air flow rate. Where π w It is the pressure ratio at the current operating point; π s It is the pressure ratio at the surge boundary point corresponding to the same reduced rotational speed; m aw This is the airflow rate at the current work point; m as It is the airflow rate at the surge boundary point corresponding to the same equivalent rotational speed.

3. The surge margin estimation method for gas-steam combined cycle generator sets according to claim 1, characterized in that, In step 3, the polyfit function in MATLAB is used to perform polynomial fitting on the characteristic variable α at each steady-state point to obtain the state variables, input variables, and output variables of the steady-state model. That is, the other variables are fitted with a function of the characteristic variable α.

4. The surge margin estimation method for gas-steam combined cycle generator sets according to claim 1, characterized in that, The specific methods for obtaining A1(α) and C(α) are as follows: The changes in rotor speed and output quantities are obtained by extracting the power on the rotor shaft and sequentially changing the input variables of the unit in steady-state balance calculation. The partial derivatives of each parameter are then calculated based on the obtained changes in each parameter.

5. The surge margin estimation method for gas-steam combined cycle generator sets according to claim 1, characterized in that, The specific methods for obtaining A1(α) and C(α) are as follows: they are obtained by using test data or simulation output data of nonlinear component-level models through data identification methods.

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