Method for calculating efficiency curve of nuclear turbine based on data driving

Abstract

The invention belongs to the technical field of nuclear turbines, and particularly relates to a nuclear turbine efficiency curve calculation method based on data driving. Comprising the following steps: step 1, collecting and sorting historical measurement data to obtain working condition data; 2, obtaining the uncertainty grade of the power plant measuring instrument, and generating a covariance matrix; 3, establishing a low-pressure cylinder-condenser system heat balance model; step 4, establishing a redundancy balance equation, and calculating a Jacobian matrix of the residual relative to the measuring point data; 5, calculating a low-pressure cylinder efficiency correction result; 6, fitting a final-stage efficiency curve of the low-pressure cylinder; and 7, iterating the final-stage efficiency curve of the low-pressure cylinder until the final-stage efficiency curve converges. The method has the advantages that according to an existing classical calculation method, the turbine efficiency under the current working condition is calculated through measurement data, measurement results are usually adopted, enthalpy values, entropy and other data are obtained by inquiring the physical property of water, and then the turbine efficiency value is calculated and deduced through mass or energy balance.

Description

Technical Field

[0001] The present invention belongs to the technical field of nuclear power steam turbines, and particularly relates to a method for calculating the efficiency curve of a nuclear power steam turbine based on data driving. Background Art

[0002] The nuclear power steam turbine is a key core component of a nuclear power plant and is the focus of on-site operators and technical researchers. A condenser is connected to the end of the nuclear power steam turbine. The condenser provides a low-pressure environment for the steam turbine, reducing the exhaust back pressure to increase the unit output. The condenser is a component that condenses the exhaust of the nuclear power steam turbine into condensate. The condensation effect of the condenser is directly related to the exhaust back pressure of the nuclear power steam turbine. However, the circulating water used for cooling in the condenser is often taken from the environment, such as rivers or the sea. Therefore, the condensation effect of the condenser will change with the environment, and correspondingly, the back pressure will also change. For the last stage of the nuclear power steam turbine, the change in back pressure will change the operating conditions, causing the efficiency of the nuclear power steam turbine to vary.

[0003] When the nuclear power steam turbine unit leaves the factory, the manufacturer often provides the operating characteristics of the steam turbine under different operating conditions. However, the actual operating nuclear power steam turbine faces problems such as changes in characteristics and performance degradation after long-term operation. Since the working medium in the low-pressure cylinder of the nuclear power steam turbine is in the wet steam region, it is difficult to obtain the steam turbine efficiency parameters by direct or indirect measurement using traditional temperature and pressure sensors. Therefore, a method is needed to deduce the steam turbine efficiency of the nuclear power steam turbine under different back pressures and obtain the actual operating condition curve to help operators and researchers better control the operating state of the nuclear power steam turbine. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for calculating the efficiency curve of a nuclear power steam turbine based on data driving, which can calculate the steam turbine efficiency of the nuclear power steam turbine under different back pressures, thereby obtaining the operating condition curve. The present invention can utilize a large amount of real historical data and combine data correction and data driving methods to realize the correction and iteration of the steam turbine efficiency. The method proposed by the present invention can analyze the historical data generated during actual operation to obtain the steam turbine efficiency curve in the recent period, and can be widely applied to the operation monitoring of nuclear power steam turbines.

[0005] The technical solution of the present invention is as follows: A method for calculating the efficiency curve of a nuclear power steam turbine based on data driving includes the following steps:

[0006] Step 1: Collect and sort out historical measurement data to obtain operating condition data;

[0007] Step 2: Obtain the uncertainty level of the power plant measurement instrument and generate a covariance matrix;

[0008] Step 3: Establish a heat balance model for the low-pressure cylinder-condenser system;

[0009] Step 4: Establish a redundant balance equation and calculate the Jacobian matrix of the residuals with respect to the measured point data;

[0010] Step 5: Calculate the correction result of the low-pressure cylinder efficiency;

[0011] Step 6: Fit the efficiency curve of the last stage of the low-pressure cylinder;

[0012] Step 7: Iterate the efficiency curve of the last stage of the low-pressure cylinder until convergence.

[0013] The sources of historical measurement data in Step 1 include: historical measured values of measurement points and design values of equipment characteristic parameters. Among them, the historical measured values of measurement points come from the measurement data in the nuclear power plant data system, and the mean value of short-term measured values is used as the historical measured value of a measurement point under a certain working condition.

[0014] In Step 2, the uncertainty level of the measurement is obtained when selecting the instrument. For the covariance matrix X of the measurement points c , its elements can be calculated as follows:

[0015]

[0016] where x ij is the element in the covariance matrix; is the uncertainty of the measured value of the measurement point; r ij is the correlation coefficient between measurement points.

[0017] In Step 3, the unknown parameters are calculated from the known basic data. The unknown parameters include: enthalpy value, entropy value at a certain state point, and temperature, pressure, and flow rate at a certain place in the system. These unknown parameters are defined as vector y, and the following calculation is established:

[0018] y = h(x, s) (5)

[0019] where g is the heat balance function, which measures the relationship between the unknown parameter y and the measured point data x and characteristic parameter s. The system heat balance model is established based on the two principles of mass balance and energy balance. For a certain component with serial number i, there is the following mass balance equation:

[0020] f m，i = m in，i - m out，i = 0 (6)

[0021] where f m，i represents the residual of the mass balance equation of component i, m in，i represents the total mass flow rate of the working fluid input to component i, m out，iDenote the total mass flow rate of the working fluid flowing out of component \(i\). The flow rates are all calculated in absolute values. For a certain component, the following energy balance equation holds:

[0022] f e，i = e in，i - e out，i = 0 (7)

[0023] where \(f\) e，i denotes the residual of the energy balance equation of a certain component \(i\), \(e\) in，i denotes the total input energy of a certain component \(i\), and \(e\) out，i denotes the total output energy of a certain component \(i\).

[0024] In step 4, the redundant balance equation is established to calculate the residual:

[0025] \(R = y'-x'\) (8)

[0026] where \(R\) represents the residual vector of the redundant balance equation, \(y'\) represents part of the data in the unknown parameters, \(x'\) represents part of the data in the measured point data, the known parameter vector \(l\) is the sum of the known data composed of the measured point data vector \(x\) and the characteristic parameter data vector \(s\), and the Jacobian matrix \(J\) of the redundant balance equation \(R\) with respect to the known parameter vector \(l\) R，l To calculate the above Jacobian matrix, the Jacobian matrix \(J\) of the unknown parameters \(z\) of the power station with respect to the known parameters \(l\) is calculated respectively z，l , and the Jacobian matrix \(J\) of the redundant balance equation with respect to the unknown parameters \(z\) of the power station R，z . According to the chain rule, the Jacobian matrix \(J\) R，l can be calculated as:

[0027] \(J\) R，l = J R，z J z，l (9).

[0028] In step 5, according to the calculated Jacobian matrix \(J\) R，x , and the mean value of the known parameter variables and the elements of the covariance matrix are used to calculate the residual of the system redundant balance equation. The correction amount of all the known parameters in the system is calculated according to the above conditions. According to the mean value of the known parameters of the system, the mean values of the unknown parameters and the residual of the system balance equation in the system can be calculated:

[0029]

[0030] where and are the mean value vectors of the unknown parameters and the measured point data in the system respectively; and are the mean value vectors of the residuals and part of the measured point data in the system respectively. From this, the covariance matrix \(X\) of the residual vector of the system balance equation is calculated R:

[0031]

[0032] If a correction amount c is applied to all known parameters l such that the residual of the system balance equation is zero, in the case of the minimum correction amount, there is the following constrained optimization problem:

[0033]

[0034] Applying the Lagrange multiplier method to the above optimization problem and introducing the Lagrange multiplier variable λ, then the problem can be equivalently transformed into the following form:

[0035]

[0036] When the constant coefficient of the additional term introduced by the Lagrange multiplier method is -2, simplifying the expression and solving according to the stationary point condition, the correction amount expression is obtained as:

[0037]

[0038] Left-multiply both sides of the above equation by the Jacobian matrix J R，l , and convert the above equation into the following form:

[0039] J R，l c = X c λ (16)

[0040] According to the constraint conditions of this optimization problem The Lagrange multiplier is solved as:

[0041]

[0042] Substituting the above equation back into equation (16), the final solution of the correction amount is obtained as:

[0043]

[0044] Then the corrected result of the known parameter vector l is:

[0045]

[0046] In the case of obtaining the correction result of a certain working condition in step 6 described above, obtaining the operation data of the nuclear power plant for a period of time, obtaining k sets of working condition results, and extracting the low-pressure cylinder last-stage efficiency l in the correction result of the known parameter vector η , and combining the results of k working conditions into a last-stage efficiency vector η as:

[0047] η = (l η，1 , l η，2 , …, l η，k ) (20)

[0048] In the formula, η is the last-stage efficiency vector, corresponding to the extraction steam turbine back pressure l pb , and the steam turbine back pressure vector P is obtained b as follows:

[0049] P b =(l pb，1 , l pb，2 , …, l bp，k ) (21)

[0050] In the formula, P b is the steam turbine back pressure vector, the last-stage efficiency vector η and the steam turbine back pressure vector P b have elements that correspond one by one, and the following approximate fitting relationship is constructed between the two:

[0051]

[0052] There is the following calculation formula:

[0053]

[0054] According to the following formula, the four coefficients of the fitting relationship can be solved:

[0055]

[0056] The fitting curve of the last-stage efficiency of the low-pressure cylinder for one calculation is obtained.

[0057] In step 7 described above, the last-stage efficiency vector η and the steam turbine back pressure vector P are obtained through steps 1 to 6 b of the fitting relationship curve. The calculated curve is re-substituted into steps 1 to 6 for repeated calculation to obtain an iterative fitting curve. When the above operation is repeated g times, the following relationship curve is obtained:

[0058]

[0059] By measuring the back pressure distribution in the data vector x, it is obtained that the back pressure distribution is in the interval [P mn , P mx . The efficiency curve loss value Loss is defined as:

[0060]

[0061] When the efficiency curve loss value Loss < 0.001, the curve converges, and the final fitting curve of the last-stage efficiency of the low-pressure cylinder is obtained.

[0062] The beneficial effects of the present invention are as follows: The existing classical calculation methods calculate the steam turbine efficiency under the current working conditions based on the measured data. Usually, the measured results are used to obtain data such as enthalpy and entropy by querying the physical properties of water, and then the steam turbine efficiency value is deduced through mass or energy balance calculations. However, for nuclear power steam turbines, the working fluid is in the wet steam region. Therefore, data such as enthalpy values cannot be directly obtained by querying through temperature and pressure. The method of inversely calculating the exhaust enthalpy of the low-pressure cylinder through the heat transfer of other components such as condensers will face problems such as no measuring points for the circulating water volume, or if there are measuring points, the measurement error will be transmitted to the exhaust enthalpy of the low-pressure cylinder due to the large flow rate, resulting in large errors and obvious distortion in the calculated data. Especially when calculating with a large amount of historical data, the existence of errors will cause the obtained efficiency results to fluctuate greatly, and the continuous working condition curve of the nuclear power steam turbine cannot be obtained, indicating that the reliability of this method is relatively low. This method combines data correction methods in the processing of original data through data driving, fully utilizes the measured data in a large amount of historical working condition data and performs fitting, and on this basis, iterates multiple times, so that the calculated value of the steam turbine efficiency is continuously updated to stable convergence, effectively avoiding the problems of errors caused by measurement and data fluctuations, and can effectively obtain a reasonable operation curve under real data and restore the real operation situation. Brief Description of the Drawings

[0063] Figure 1 It is a flow chart of a method for calculating the efficiency curve of a nuclear power steam turbine based on data driving provided by the present invention;

[0064] Figure 2 It is a low-pressure cylinder-condenser system of a certain nuclear power plant, and the measuring point types and layout positions in this system. Detailed Embodiment

[0065] The present invention will be further described in detail below with reference to the drawings and specific embodiments.

[0066] As Figure 1 shown, a method for calculating the efficiency curve of a nuclear power steam turbine based on data driving includes the following steps:

[0067] Step 1: Collect and organize historical measurement data to obtain working condition data

[0068] The basic data sources of the present invention include: historical measurement values of measuring points, design values of equipment characteristic parameters, and uncertainty levels of measuring instruments. Among them, the historical measurement values of measuring points come from the measurement data in the nuclear power plant data system. The nuclear power plant is usually in a steady-state operation, but in order to avoid errors caused by accidental and normal fluctuations, the average value of short-time measurement values is used as the historical measurement value of a certain working condition for the measuring point. Specifically, in the low-pressure cylinder-condenser system, the operating parameter M i A total of n measurement results are selected to obtain a series of measurement values: M i,1 , Mi,2 , …, M i,n , the mean value of the measured value at this measurement point is:

[0069]

[0071] In the formula, is the estimated value of the mean value at this measurement point. There are many measurement points in the steam turbine - condenser system of concern, and these measurement points together constitute the measurement point data vector x:

[0072]

[0073] It should be noted that the boundary parameters of the selected system can be obtained by external calculation and input into this method for calculation, and can be equally regarded as measurement point data here. The design values of the equipment characteristic parameters are also necessary calculation conditions for subsequent solutions. When the unit leaves the factory, the manufacturer will provide a total of m characteristic parameters of the steam turbine characteristics of the equipment under the design conditions. S m , and this type of data together constitutes the characteristic parameter data vector s:

[0074] s = (S1, S2, …, S m ) (3)

[0075] In the formula, Si represents the i-th characteristic parameter of the steam turbine, such as isentropic efficiency, pressure ratio, flow area, etc.

[0076] Step 2: Obtain the uncertainty level of the power plant measurement instrument and generate the covariance matrix

[0077] In addition to obtaining the measured values of the measurement points, it is necessary to obtain the corresponding uncertainty of this measurement point. The uncertainty level of the measurement can be obtained when selecting the instrument, and it is usually selected according to engineering experience during calculation. For the covariance matrix X of the measurement points c , its elements can be calculated as follows:

[0078]

[0079] In the formula, x ij is the element in the covariance matrix; is the uncertainty of the measured value of the measurement point; r ij is the correlation coefficient between measurement points, and this coefficient is determined according to the fluctuation situation of the historical operation data of the nuclear power plant and combined with engineering experience. represents the row index and column index of the element in the matrix.

[0080] Step 3: Establish a heat balance model for the low-pressure cylinder - condenser system

[0081] Unknown parameters in a nuclear power plant can be calculated from known basic data. These unknown parameters include: enthalpy and entropy values at a certain state point, as well as data such as temperature, pressure, and flow rate at a certain location in the system. Here, these unknown parameters are defined as vector y, and the following calculation can be established:

[0082] y = h(x, s) (5)

[0083] In the formula, h is a heat balance function, which measures the relationship between the unknown parameter y and the measured point data x and characteristic parameter s. It should be noted that not all data participates in the heat balance calculation. Some data is redundant after the calculation, such as repeated measurements and variable transfer between pipelines, which makes the number of known conditions greater than the need to solve unknown variables. In a nuclear power plant, the number of measurement points is large, and there will be measurement redundancy. The system heat balance model is established based on the two major principles of mass balance and energy balance. For a certain component (with serial number i), the following mass balance equation exists:

[0084] f m，i = m in，i - m out，i = 0 (6)

[0085] In the formula, f m，i represents the residual of the mass balance equation of component i, m in，i represents the total mass flow rate of the working fluid input to component i, and m out，i represents the total mass flow rate of the working fluid flowing out of component i. The flow rates are all calculated using absolute values and do not require the use of positive or negative signs to represent the direction relationship. For a certain component, the following energy balance equation exists:

[0086] f e，i = e in，i - e out，i = 0 (7)

[0087] In the formula, f e，i represents the residual of the energy balance equation of a certain component i, e in，i represents the total energy input to a certain component i, and e out，i represents the total energy flowing out of a certain component i. For a certain component, the total energy not only includes that carried by the working fluid but also includes input and output work, etc. The energies are all calculated using absolute values and do not require the use of positive or negative signs to represent the direction relationship.

[0088] Step 4: Establish a redundancy balance equation and calculate the Jacobian matrix of the residual with respect to the measured point data

[0089] After obtaining the results through heat balance calculation, some of the parameters coincide with certain parameters in the known dataset. However, due to actual measurement errors, the coincident parameter data is not consistent. Therefore, a redundancy balance equation can be established to calculate the residual:

[0090] R = y' - x' (8)

[0091] In the formula, R represents the residual vector of the redundancy balance equation, y' represents part of the data in the unknown parameters, and x' represents part of the data in the measured point data. The known parameter vector l is the sum of the known data composed of the measured point data vector x and the characteristic parameter data vector s. The Jacobian matrix of the redundancy balance equation R with respect to the known parameter vector l is J R，l . To calculate the above Jacobian matrix, it is necessary to calculate the Jacobian matrix J z，l of the power station unknown parameter z with respect to the known parameter l, and the Jacobian matrix J R，z of the redundancy balance equation with respect to the power station unknown parameter z. The Jacobian matrix J R，l can be calculated by the chain rule as follows:

[0092] J R，l = J R，z J z，l (9)

[0093] Step 5: Calculate the correction result of the low-pressure cylinder efficiency

[0094] According to the Jacobian matrix J R，x calculated in Steps 1 - 4, and using the elements of the mean and covariance matrix of the known parameter variables to calculate the residual of the system redundancy balance equation, the correction amount of all the known parameters in the system can be calculated based on the above conditions. According to the mean of the system known parameters, the means of the unknown parameters and the system balance equation residual in the system can be calculated:

[0095]

[0096] In the formula, and are the mean vectors of the unknown parameters and the measured point data in the system respectively; and are the mean vectors of the residual and part of the measured point data in the system respectively, and y' is the mean vector of the system unknown parameters calculated from x' according to Equation (10). Thus, the covariance matrix X R of the system balance equation residual vector can be calculated as follows:

[0097]

[0098] J R,l is the Jacobian matrix of the redundancy equation R with respect to the known parameter vector l.

[0099] If a correction amount c is applied to all the known parameters l to make the system balance equation residual zero. In the case of the minimum correction amount, there is the following constrained optimization problem:

[0100]

[0101] T represents the transpose of a vector, and s.t. is the abbreviation of subject to, indicating that the optimal solution should satisfy the subsequent equality constraint conditions;

[0102] Applying the Lagrange multiplier method to the above optimization problem and introducing the Lagrange multiplier variable λ, the problem can be equivalently transformed into the following form:

[0103]

[0104] When the constant coefficient of the additional term introduced by the Lagrange multiplier method is -2, the expression can be simplified without affecting the calculation result. The correction quantity expression obtained by solving according to the stationary point condition is:

[0105]

[0106] Premultiply both sides of the above equation by the Jacobian matrix J R，l , and the above equation can be transformed into the following form:

[0107] J R，l c = X c λ (16)

[0108] According to the constraint conditions of this optimization problem the Lagrange multiplier can be solved as:

[0109]

[0110] Substituting the above equation back into equation (16), the final solution of the correction quantity can be obtained as:

[0111]

[0112] Then the corrected result of the known parameter vector l is:

[0113]

[0114] Step 6: Fit the efficiency curve of the last stage of the low-pressure cylinder.

[0115] Through the above calculation process, the correction result of a certain working condition can be obtained. On this basis, the operation data of the nuclear power plant for a period of time is obtained, and k groups of working condition results are obtained. It should be noted that in order to make the last stage curve of the low-pressure cylinder cover different working conditions of the unit, the data range should include the operation results of each period of the year. Extract the last stage efficiency l of the low-pressure cylinder from the corrected result of the known parameter vector in the middle η Extract it, and combine the results of k working conditions into a last stage efficiency vector η as:

[0116] η = (l η，1 , l η，2, …, l η，k ) (20)

[0117] The i-th parameter l in the vector n,i represents the last-stage efficiency of the low-pressure cylinder under the i-th operating condition in the above-mentioned formed operating condition dataset.

[0118] In the formula, η is the last-stage efficiency vector. Similarly, the extraction of the turbine back pressure l pb results in the turbine back pressure vector P b which is:

[0119] P b =(l pb，1 , l pb，2 ,..., l pb，k ) (21)

[0120] The i-th parameter l in the vector pb,i represents the turbine back pressure under the i-th operating condition in the above-mentioned formed operating condition dataset.

[0121] In the formula, P b is the turbine back pressure vector. The elements in the last-stage efficiency vector η and the turbine back pressure vector P b correspond one by one. According to engineering experience, an approximate fitting relationship can be constructed between the two as follows:

[0122]

[0123] a0 to a3 are the coefficients corresponding to each term in the above fitting polynomial

[0124] There is the following calculation formula:

[0125]

[0126] v represents the sum of squared residuals between the fitted last-stage low-pressure cylinder efficiency vector and the actual last-stage low-pressure cylinder efficiency vector; the meaning of k has been explained before and represents the number of nuclear power operating conditions selected above.

[0127] The four coefficients of the fitting relationship can be solved according to the following formula:

[0128]

[0129] Thus, the fitting curve of the last-stage efficiency of the low-pressure cylinder for the first calculation is obtained.

[0130] Step 7: Iterate the last-stage efficiency curve of the low-pressure cylinder until convergence

[0131] Through Steps 1 to 6, the last-stage efficiency vector η and the turbine back pressure vector P can be obtained bFor the fitting relationship curve, substituting the calculated curve back into Steps 1 to 6 for repeated calculation can obtain an iterated fitting curve. Thus, when the above operation is repeated g times, the following relationship curve is obtained:

[0132]

[0133] In the formula, q g+1 represents the fitting function of the (g + 1)-th time.

[0134] It can be obtained by measuring the back pressure distribution in the data vector x of the measured values. The back pressure distribution is in the interval [P mn , P mx . Define the efficiency curve loss value Loss as:

[0135]

[0136] When the efficiency curve loss value Loss < 0.001, it is considered that the curve converges, and the final fitting curve of the last stage efficiency of the low-pressure cylinder is obtained.

[0137] Example:

[0138] There is a low-pressure cylinder - condenser system in a certain nuclear power plant. The types and layout positions of the measuring points in this system are as shown in the appendix Figure 2 . There are three types of measuring points in the power plant: temperature measuring points (T), pressure measuring points (P), and flow measuring points (M). It should be noted that the measuring units of the same type of measuring points in the power plant may not be consistent, and all measured data need to be converted into the same unit system before calculation. When selecting the measured data of the measuring points, the measured data under relatively stable working conditions should be selected as much as possible, and large fluctuations in the measured values of the measuring points should be avoided.

[0139] In this embodiment, the actual data of each component in the involved thermal system is corrected, and the specific steps are as follows:

[0140] 1) Collect and sort historical measurement data to obtain working condition data. For the low-pressure cylinder - condenser system, sort out the layout of the measuring points in the actual system and sort them in turn: INT-P, INT-T, EX1-P, EX1-T, EX2-P, EX2-T, EX3-P, EX3-T, CO-M, CO-T. As Figure 2 shown, according to formula (1) and the known boundary parameters, the known parameter vector x can be obtained, and it has the following form:

[0141]

[0142] In addition to the above nine measurement points, the known parameter vector x also includes the parameters transmitted from the boundary, which are the inlet steam flow rate of the low-pressure cylinder, the extraction steam flow rate of the first stage of the low-pressure cylinder, and the extraction steam flow rate of the second stage of the low-pressure cylinder obtained from the reheating system. The corresponding relationships of the above parameters are shown in the following table:

[0143]

[0144] The turbine efficiency and condenser parameter S are obtained according to the design data of the unit at the time of factory shipment m , and they form the equipment characteristic parameter data vector s:

[0145] s = (S1, S2, S3) (29)

[0146] It should be noted that in this example, the turbine stages given are equivalent turbine stages separated by extraction points. Among them, the efficiency of the third-stage low-pressure cylinder is only used in the first calculation, and it will be replaced with the fitting curve obtained later for iterative calculation

[0147] Efficiency parameter Meaning <![CDATA[S1]]> Efficiency of the first-stage low-pressure cylinder <![CDATA[S2]]> Efficiency of the second-stage low-pressure cylinder <![CDATA[S3]]> Efficiency of the third-stage low-pressure cylinder

[0148] 2) Obtain the uncertainty level of the power plant measuring instruments and generate the covariance matrix. Through Equation (4), the covariance matrix X of the measurement points is constructed c .

[0149] 3) Establish a heat balance model for the low-pressure cylinder-condenser system. The unknown parameter vector y represents the enthalpy values at various places in the low-pressure cylinder, the ideal enthalpy value in the isentropic process, and the exhaust steam flow rate. The corresponding relationships of the above parameters are shown in the following table:

[0150] Unknown parameter Meaning Unknown parameter Meaning <![CDATA[y1]]> Enthalpy value of the low-pressure cylinder inlet <![CDATA[y6]]> Ideal enthalpy value of the first-stage extraction of the low-pressure cylinder <![CDATA[y2]]> Enthalpy value of the first-stage extraction of the low-pressure cylinder <![CDATA[y7]]> Ideal enthalpy value of the second-stage extraction of the low-pressure cylinder <![CDATA[y3]]> Enthalpy value of the second-stage extraction of the low-pressure cylinder <![CDATA[y8]]> Ideal enthalpy value of the low-pressure cylinder exhaust <![CDATA[y4]]> Enthalpy value of the low-pressure cylinder exhaust <![CDATA[y9]]> Saturation temperature of the first-stage extraction pressure <![CDATA[y5]]> Low-pressure cylinder exhaust flow rate <![CDATA[y 10 > Saturation temperature of the second-stage extraction pressure

[0151] The above components have the following balance relationships according to Equations (6) and (7):

[0152]

[0153] Among them, the enthalpy value can be obtained by querying the water vapor property library using the measured value

[0154] 4) Establish redundant balance equations and calculate the Jacobian matrix of the residuals with respect to the measurement point data. In addition to the known parameters used in the above basic solution, the remaining part can be used to establish redundant balance equations to obtain the residual vector R = (R1, R2, R3) of the system, and the calculation methods of its components are as follows:

[0155]

[0156] 5) Calculate the correction result of the low-pressure cylinder efficiency. Calculate the mean values of the unknown parameters in the system and the residuals of the system balance equation according to equations (10) and (11) respectively, and thus obtain the covariance matrix X of the residual vector of the system balance equation. R :

[0157]

[0158] If a correction amount c is applied to all known parameters l such that the residual of the system balance equation is zero. In the case of the minimum correction amount, establish the following constrained optimization problem:

[0159]

[0160] The constant coefficient of the additional term introduced by the Lagrange multiplier method is -2, and the formula can be simplified without affecting the calculation result. Solve according to the stationary point condition to obtain the correction amount expression as:

[0161]

[0162] Multiply both sides of the above formula by the Jacobian matrix J R，l , and the above formula can be converted into the following form:

[0163] J R，l c = X c λ (35)

[0164] According to the constraint conditions of this optimization problem The Lagrange multiplier can be solved as:

[0165]

[0166] Substitute the above formula back into equation (35), and the final solution of the correction amount can be obtained as:

[0167]

[0168] Then the corrected result of the known parameter vector l is:

[0169]

[0170] Among them, the corrected known parameter vector contains the corrected low-pressure cylinder efficiency.

[0171] 6) Fit the efficiency curve of the last stage of the low-pressure cylinder

[0172] Obtain the operation data of the nuclear power plant for a period of time to get k sets of operating conditions results. It should be noted that in order to make the last stage curve of the low-pressure cylinder cover different operating conditions of the unit, the data range should include the operating results of each period of the year. The correction result of the known parameter vector The low-pressure cylinder last stage efficiency l inη Extract them and combine the results of k operating conditions into a final-stage efficiency vector η as follows:

[0173] η = ( lη，1 , l η，2 , …, l η，k ) (39)

[0174] In the formula, η is the final-stage efficiency vector. Similarly, extract the turbine back pressure l pb to obtain the turbine back pressure vector P b as follows:

[0175] P b = (l pb，1 , l pb，2 , …, l pb，k ) (40)

[0176] In the formula, P b is the turbine back pressure vector. The elements in the final-stage efficiency vector η and the turbine back pressure vector P b correspond one by one. According to engineering experience, an approximate fitting relationship can be constructed between the two as follows:

[0177]

[0178] The coefficients of the fitting relationship can be solved using the above relationship.

[0179] 7) Iterate the final-stage efficiency curve of the low-pressure cylinder until convergence. After repeating the above results g - 1 and g times for k groups of operating conditions, the fitting curve is obtained:

[0180]

[0181] Calculate the loss value of the efficiency curve according to Equation (26).

[0182] When

[0183]

[0184] it is considered that the turbine efficiency fitting curve has converged. Among them, [P mn , P mx is the low-pressure cylinder back pressure distribution interval. The final fitting curve of the low-pressure cylinder final-stage efficiency is obtained.

Claims

1. A data-driven calculation method for the efficiency curve of a nuclear power steam turbine, characterized in that, It includes the following steps: Step 1: Collect and organize historical measurement data to obtain operating condition data; Step 2: Obtain the uncertainty level of the power plant measurement instruments and generate a covariance matrix; Step 3: Establish a thermal balance model for the low-pressure cylinder-condenser system; Step 4: Establish redundant balance equations and calculate the Jacobian matrix of the residuals with respect to the measured point data; Step 5: Calculate the correction result of the low-pressure cylinder efficiency; Step 6: Fit the efficiency curve of the last stage of the low-pressure cylinder; Step 7: Iterate the efficiency curve of the last stage of the low-pressure cylinder until convergence.

2. The method for calculating the efficiency curve of a nuclear power steam turbine based on data driving according to claim 1, wherein: The sources of historical measurement data in the above-mentioned step 1 include: measured point historical measurement values and equipment characteristic parameter design values. Among them, the measured point historical measurement values are from the measurement data in the nuclear power plant data system, and the mean value of short-term measurement values is used as the measured point historical measurement value for a certain working condition. The equipment characteristic parameter design values are the steam turbine characteristic parameters S under the design working condition provided by the manufacturer at the time of factory shipment m , which together constitute the characteristic parameter data vector s: s = (S1, S2, …, S m ) (3) 3. A data-driven calculation method for the efficiency curve of a nuclear power steam turbine according to claim 1, characterized in that: In step 2, the uncertainty level of measurement is obtained when selecting the instrument. For the covariance matrix X of the measurement points c , its elements can be calculated as follows: where x ij is an element in the covariance matrix; is the uncertainty of the measured value at the measurement point; r ij is the correlation coefficient between measurement points.

4. A data-driven method for calculating the efficiency curve of a nuclear power steam turbine according to claim 1, characterized in that: The unknown parameters in Step 3 are calculated from the known basic data. The unknown parameters include: the enthalpy value, entropy value at a certain state point, and the temperature, pressure, and flow rate at a certain place in the system. Define these unknown parameters as vector y and establish the following calculation: y = h(x, s) (5) In the formula, h is a thermal balance function, which measures the relationship between the unknown parameter y and the measured point data x and characteristic parameter s. The system thermal balance model is established based on the two principles of mass balance and energy balance. For a certain component with the serial number i, there is the following mass balance equation: f m,i = m in,i - m out,i = 0 (6) where f m,i represents the residual of the mass balance equation for component i, m in,i represents the total mass flow rate of the working fluid input to component i, m out,i represents the total mass flow rate of the working fluid flowing out of component i. The flow rates are all calculated using absolute values. For a certain component, there is the following energy balance equation: f e,i = e in,i - e out,i = 0 (7) where f e,i represents the residual of the energy balance equation for a certain component i, and e in,i represents the total energy input to a certain component i, and e out,i represents the total energy flowing out of a certain component i.

5. The method for calculating the efficiency curve of a nuclear power steam turbine based on data driving according to claim 1, characterized in that: In Step 4, redundant balance equations are established to calculate the residuals: R = y' - x' (8) In the formula, R represents the residual vector of the redundancy balance equation, y′ represents part of the data in the unknown parameters, x′ represents part of the data in the measurement point data, the known parameter vector l is the sum of the known data composed of the measurement point data vector x and the characteristic parameter data vector s, and the Jacobian matrix J of the redundancy balance equation R with respect to the known parameter vector l R,l To calculate the above Jacobian matrix, the Jacobian matrix J of the unknown parameters z of the power station with respect to the known parameter l is calculated respectively z,l , and the Jacobian matrix J of the redundancy balance equation with respect to the unknown parameters z of the power station R,z , and the Jacobian matrix J can be calculated by the chain rule R,l as follows: J R,l = J R,z J z,l (9).

6. A data-driven method for calculating the efficiency curve of a nuclear power steam turbine according to claim 1, characterized in that: The said step 5 is based on the calculated Jacobian matrix J R,x , and calculates the residual of the system redundancy balance equation by using the elements of the mean value and covariance matrix of the known parameter variables. According to the above conditions, the correction amount of all the known parameters in the system is calculated, and the mean values of the unknown parameters and the system balance equation residual in the system can be calculated according to the mean value of the known parameters in the system: In the formula, and are the mean vectors of the unknown parameters and the measured point data in the system respectively; and are the mean vectors of the residuals and part of the measured point data in the system respectively, and the covariance matrix X of the residual vector of the system balance equation is calculated therefrom R : If a correction amount c is applied to all known parameters l to make the residuals of the system balance equations zero, in the case of the smallest correction amount, there is the following constrained optimization problem: Apply the Lagrange multiplier method to the above optimization problem and introduce the Lagrange multiplier variable λ. Then this problem can be equivalently transformed into the following form: When the constant coefficient of the additional term introduced by the Lagrange multiplier method is -2, simplify the formula and solve according to the stationary point condition to obtain the expression of the correction amount: Left-multiply the Jacobian matrix J on both sides of the above equation R,l to convert the above equation into the following form: J R,l c = X c λ (16) According to the constraints of this optimization problem The Lagrange multipliers are obtained as follows: Substitute the above formula into Equation (16) to obtain the final solution of the correction amount: Then the corrected result of the known parameter vector l is:

7. A data-driven calculation method for the efficiency curve of a nuclear power steam turbine according to claim 1, characterized in that: In the case that the correction result of a certain working condition is obtained in step 6, obtain the nuclear power plant operation data for a period of time to obtain k sets of working condition results, and correct the known parameter vector result The efficiency l of the last stage of the intermediate and low pressure cylinders η Extract it, and combine the results of k working conditions into a last stage efficiency vector η as: η = (l η,1 , l η,2 , …, l η,k ) (20) where η is the last-stage efficiency vector corresponding to the extraction steam turbine back pressure l pb , and the extraction steam turbine back pressure vector P is obtained b as follows: P b ＝(l pb,1 ,l pb,2 ,…,l pb,k ) (21) Where, P b is the back pressure vector of the steam turbine, the last stage efficiency vector η and the back pressure vector P of the steam turbine b have elements that correspond one by one, and an approximate fitting relationship is constructed between the two as follows: There is the following calculation formula: The four coefficients of the fitting relationship can be solved according to the following formula: Obtain the fitting curve of the efficiency of the last stage of the low-pressure cylinder for one calculation.

8. The method for calculating the efficiency curve of a nuclear power steam turbine based on data driving according to claim 1, characterized in that: The aforesaid step 7 obtains the final-stage efficiency vector η and the steam turbine back pressure vector P through steps 1 to 6 b of the fitting relationship curve, and re-introduces the calculated curve into steps 1 to 6 to repeat the calculation to obtain an iterated fitting curve. After repeating the above operation g times, the following relationship curve is obtained: The backpressure distribution in the interval [P mn , P mx is obtained by measuring the backpressure distribution in the data vector x, and the loss value Loss of the efficiency curve is defined as: When the loss value Loss of the efficiency curve < 0.001, the curve converges to obtain the final fitting curve of the efficiency of the last stage of the low-pressure cylinder.

Images