Quantitative evaluation method for wide-load stability of mixed-flow water turbine

Abstract

The invention discloses a quantitative evaluation method for wide-load stability of a mixed-flow water turbine. The quantitative evaluation method specifically comprises the following steps: step 1, collecting horizontal and vertical throw data of an upper guide bearing measuring point, a lower guide bearing measuring point and a turbine guide bearing measuring point through an eddy current displacement sensor; 2, horizontal and vertical vibration displacement of the upper rack measuring point, the lower rack measuring point and the top cover measuring point and horizontal vibration displacement of the stator base measuring point are collected through a speed displacement sensor; 3, collecting pressure pulsation of the top cover inlet measuring point, the volute inlet measuring point and the draft tube inlet measuring point through a pressure sensor; 4, constructing an evaluation matrix A; and 5, processing data in the matrix A through a principal component analysis method to obtain a unit operation risk rate. According to the method, principal component analysis is carried out on vibration, throw and pressure pulsation data of the water turbine under different loads, and the stability change of the water turbine under the wide-load operation condition can be accurately quantified.

Description

Technical Field

[0001] The invention belongs to the technical field of hydraulic machinery and relates to a quantitative evaluation method for wide load stability of a Francis turbine. Background Art

[0002] At present, the world is facing the dual challenges of economic development and climate change. It has become a consensus to promote the transformation of energy systems towards low-carbon and sustainable directions. With the rapid decline in the cost of clean energy such as wind and solar energy, their installed capacity has increased significantly, becoming the main source of clean energy in the world. However, wind and solar energy themselves have significant intermittent and volatile characteristics, which poses a huge challenge to the stability and flexibility of the power system. In response to these problems, multi-energy complementary systems have gradually emerged. By combining different types of renewable energy such as hydropower, wind power, and solar energy, energy output can be stabilized and the safety and reliability of the power system can be improved. In multi-energy complementary systems, hydropower is often used as an important support for balancing wind power and photovoltaic fluctuations due to its strong adjustability and fast response speed. However, with the expansion of wind and solar energy applications, the demand for hydropower has increased significantly. In order to balance the load fluctuations in the system, hydropower units need to frequently adjust power, even operating in a lower load area. Low-load operation and frequent adjustment conditions will aggravate the vibration of the turbine and fatigue damage of key components, resulting in an increased risk of turbine failure and a shortened service life. In response to this demand, traditional turbine stability assessment methods are mostly based on a single characteristic parameter or rely on simple signal analysis methods, which makes it difficult to effectively cope with the data characteristics under multiple measurement points and multiple operating conditions. Summary of the invention

[0003] The purpose of the present invention is to provide a method for quantitatively evaluating the wide-load stability of a mixed flow turbine. The method performs principal component analysis (PCA) on the vibration, swing and pressure pulsation data of the turbine under different loads, and combines the approximate ideal solution (TOPSIS) method to quantitatively analyze the operating stability of the unit, so as to accurately quantify the stability changes of the turbine under wide-load operating conditions.

[0004] The technical solution adopted by the present invention is a method for quantitatively evaluating the wide load stability of a Francis turbine, which specifically comprises the following steps:

[0005] Step 1, collecting horizontal and vertical swing data of the upper guide bearing measuring point, the lower guide bearing measuring point and the water guide bearing measuring point through an eddy current displacement sensor, and inputting the measured swing data into a matrix A1;

[0006] Step 2, collecting the horizontal and vertical vibration displacements of the upper frame measuring point, the lower frame measuring point and the top cover measuring point, and the horizontal vibration displacement of the stator base measuring point through the speed displacement sensor, and inputting the measured vibration displacement data into the matrix A2;

[0007] Step 3, collecting pressure pulsation at the top cover inlet measuring point, the volute inlet measuring point and the draft tube inlet measuring point through a pressure sensor, and inputting the measured pressure pulsation data into the matrix A3;

[0008] Step 4, merge matrices A1, A2 and A3 into an evaluation matrix A;

[0009] Step 5: Process the data in matrix A through principal component analysis to obtain the unit operation risk rate.

[0010] The present invention is also characterized in that:

[0011] In step 1, the matrix A1 is shown in the following formula (1):

[0012]

[0013] in, It represents the swing value of the j1th measuring point index under the i-th load value.

[0014] In step 2, the matrix A2 is shown in the following formula (2):

[0015]

[0016] in, It represents the vibration value of the j2th measuring point under the i-th load value.

[0017] In step 3, the matrix A3 is shown in the following formula (3):

[0018]

[0019] in, It represents the pressure pulsation value of the j3th measuring point indicator under the i-th load value.

[0020] In step 4, the matrix A is shown in the following formula (4):

[0021]

[0022] Among them, n represents the test index, m represents the load value in each test index, and a ij It represents the test value of the index at the jth measuring point under the i-th load value.

[0023] The specific process of step 5 is:

[0024] Step 5.1, perform forward processing on each element in the evaluation matrix A through formula (5), and obtain the normalized matrix B through formula (6):

[0025]

[0026] Among them, b ij It represents the normalized value of the index of the jth measuring point under the i-th load value;

[0027] Step 5.2, calculate the covariance matrix H of the matrix B, as shown in formula (7), and extract the eigenvalues ​​and eigenvectors of the matrix H, which satisfy the relationship of formula (8):

[0028]

[0029] Hv r =λ r v r (8)

[0030] Among them, B T is the transposed matrix of matrix B, n is the number of columns of matrix B, λ r is the rth eigenvalue, v r is λ r The corresponding eigenvector;

[0031] Step 5.3, arrange the eigenvalues ​​of the covariance matrix H in descending order, and select the eigenvector corresponding to each eigenvalue to form the principal component direction matrix F;

[0032] Step 5.4, calculate the variance ratio E of each principal component using the following formula (9): r :

[0033]

[0034] Step 5.5, calculate the cumulative variance percentage E by the following formula (10): C , and select the k value where the cumulative variance percentage exceeds 90%:

[0035]

[0036] Step 5.6: After determining the number of principal components k, update the matrix F to be the matrix F k ;

[0037] Step 5.7, by combining the original data matrix B with the eigenvector matrix F k Multiply to get the principal component score S:

[0038] S=B·F k (11)

[0039] Step 5.8, reconstruct the evaluation matrix Q through formula (12):

[0040]

[0041] Where S is the principal component score matrix, FTk is the eigenvector matrix F of the selected k principal componentsk The transpose of

[0042] Step 5.9, determine the positive ideal solution Q + and negative ideal solution Q - , as shown in the following formulas (13) and (14):

[0043]

[0044] in, is the optimal normalized value of the index of the jth measuring point under the i-th load value, that is, the maximum value and is the worst normalized value of the index of the jth measuring point under the i-th load value, that is, the minimum value;

[0045] Step 5.10, calculate the distance from the evaluation object to the positive ideal solution and the negative ideal solution;

[0046] Step 5.11, calculate the relative closeness coefficient C of each indicator i , according to C i Calculate the unit operation risk rate R i .

[0047] The specific process of step 5.10 is: Calculate the distance D from the evaluation object to the positive ideal solution and the negative ideal solution by using the following formula (15) and formula (16): + and D - :

[0048]

[0049] The specific process of step 5.11 is: Calculate the relative closeness coefficient C of each indicator by the following formula (17): i , through formula (18) the computer group operation risk rate R i :

[0050]

[0051] R i =1-C i (18).

[0052] The beneficial effect of the present invention is that the present invention improves the accuracy and reliability of the operation status evaluation by comprehensively analyzing the vibration, swing and pressure pulsation data of the turbine under different loads. The method extracts key features through PCA, reduces data redundancy, and uses the TOPSIS method for quantitative analysis, so that the stability changes of the turbine under wide load conditions can be more accurately quantified and identified. Compared with traditional methods, the present invention can identify potential vibration anomalies and unstable factors earlier, provide a scientific basis for the early maintenance and optimized operation of the turbine, and avoid the accumulation of operating failures and the occurrence of sudden failures. In addition, the method of the present invention is suitable for the stability management of hydropower units in multi-energy complementary systems, which can significantly improve the operating reliability and service life of the equipment and reduce downtime and maintenance costs. Its strong versatility also makes the method suitable for promotion and application in other complex mechanical systems, and provides an efficient solution for the comprehensive evaluation of multi-point and multi-feature data, thereby enhancing the safety and long-term effectiveness of the equipment under complex working conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 It is a schematic diagram of the measurement point positions of the online monitoring system of the Francis turbine unit in the method for quantitatively evaluating the wide load stability of the Francis turbine of the present invention;

[0054] FIG. 2( a ) is a diagram showing the main shaft swing of a Francis turbine under different loads in the method for quantitatively evaluating wide load stability of the present invention;

[0055] FIG. 2( b ) is a diagram showing the vibration of each component unit under different loads in the method for quantitatively evaluating the wide load stability of a Francis turbine according to the present invention;

[0056] FIG2( c ) is a diagram showing the pressure pulsations of various components under different loads in the method for quantitatively evaluating the wide load stability of a Francis turbine according to the present invention;

[0057] Figure 3 is the principal component analysis result of the Francis turbine unit in the method for quantitatively evaluating the wide load stability of the Francis turbine of the present invention;

[0058] Figure 4 It is the unit risk coefficient of the Francis turbine under different loads in the method for quantitatively evaluating the wide load stability of the Francis turbine of the present invention.

[0059] In the figure, 1. upper guide bearing measuring point, 2. upper frame measuring point, 3. stator base measuring point, 4. lower guide bearing measuring point, 5. lower frame measuring point, 6. water guide bearing measuring point, 7. top cover inlet measuring point, 8. top cover measuring point, 9. volute inlet measuring point, 10. tailwater pipe inlet measuring point. DETAILED DESCRIPTION

[0060] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0061] Example 1

[0062] The invention discloses a quantitative evaluation method for wide load stability of a Francis turbine, and adopts an online test system for vibration and pressure pulsation data of a hydropower unit. The system includes 10 key measuring points: upper guide bearing measuring point 1, upper frame measuring point 2, stator base measuring point 3, lower guide bearing measuring point 4, lower frame measuring point 5, water guide bearing measuring point 6, top cover inlet measuring point 7, top cover measuring point 8, volute inlet measuring point 9, and tailwater pipe inlet measuring point 10. In the variable load test, the test system gradually increases from no load to 400MW with a step size of 20MW, and collects data according to national standards (GB / T 11348.5-2008, GB / T 32584-2016 and GB / T15468-2020). The measurement adopts an XYZ orthogonal coordinate system, in which the Z axis represents the vertical direction, and the X and Y axes are horizontal orthogonal directions, wherein the Y direction is parallel to the volute inlet, and the X direction is perpendicular to the Y direction. The swing data is collected by the eddy current displacement sensor of model 85745 of Beizhen Factory, measuring the horizontal and vertical swing of the upper guide bearing measuring point 1, the lower guide bearing measuring point 4 and the water guide bearing measuring point 6; the vibration data is collected by the Tsinghua MLS-9 low-frequency velocity displacement sensor, measuring the horizontal and vertical vibration of the upper frame measuring point 2, the stator base measuring point 3, the lower frame measuring point 5 and the top cover measuring point 8; the pressure pulsation data is collected by the Druck model pressure sensor, measuring the pressure pulsation of the top cover inlet measuring point 7, the volute inlet measuring point 9 and the tailwater pipe inlet measuring point 10. The vibration, swing and pressure pulsation data collected by all sensors are the peak-to-peak values ​​of the 97% confidence interval, and the data are input into the computer through the data acquisition card.

[0063] Example 2

[0064] The method for quantitatively evaluating wide load stability of a Francis turbine of the present invention is specifically implemented according to the following steps:

[0065] Step 1: In the variable load test, the test system gradually increases from no load to 400MW in steps of 20MW, and collects data according to national standards. The horizontal and vertical swings of the upper guide bearing measuring point 1, the lower guide bearing measuring point 4 and the water guide bearing measuring point 5 are collected by using the eddy current displacement sensor model 85745 of Beizhen Factory. The data is shown in Figure 2(a). The measured swing data is input into matrix A1:

[0066]

[0067] in, It represents the swing value of the j1th measuring point index under the i-th load value.

[0068] Step 2: Use the Tsinghua MLS-9 low-frequency velocity displacement sensor to collect the horizontal and vertical vibration displacements of the upper frame measuring point 2, the lower frame measuring point 5, and the top cover measuring point 8, and the horizontal vibration displacement of the stator base measuring point 3. The data is shown in Figure 2(b). The measured vibration displacement data is input into the matrix A2:

[0069]

[0070] in, It represents the vibration value of the j2th measuring point under the i-th load value.

[0071] Step 3: Use a Druck pressure sensor to collect the pressure pulsation at the top cover inlet point 7, the volute inlet point 9, and the draft tube inlet point 10. The data is shown in Figure 2(c). The measured pressure pulsation data is input into matrix A3:

[0072]

[0073] in, It represents the pressure pulsation value of the j3th measuring point indicator under the i-th load value.

[0074] Step 4: Combine matrices A1, A2, and A3 into a matrix A, and define matrix A as the evaluation matrix.

[0075]

[0076] Where n represents the test index, n = 16, m represents the load value in each test index, m = 400MW / 20MW = 20, a ij It represents the test value of the index at the jth measuring point under the i-th load value.

[0077] Step 5: Process the data in matrix A through principal component analysis to obtain the unit operation risk rate.

[0078] Example 3

[0079] The specific process of step 5 is:

[0080] Step 5.1, perform forward processing on each element in the evaluation matrix A through formula (5), and obtain the normalized matrix B through formula (6):

[0081]

[0082] Among them, b ij It represents the normalized value of the index of the jth measuring point under the i-th load value.

[0083] Step 5.2, calculate the covariance matrix H of the matrix B, as shown in formula (7), and extract the eigenvalues ​​and eigenvectors of the matrix H, which satisfy the relationship of formula (8).

[0084]

[0085] Hv r =λ r v r (8)

[0086] Among them, B T is the transposed matrix of matrix B, n is the number of columns of matrix B, λ r is the rth eigenvalue, v r is λ r The corresponding feature vector.

[0087] Step 5.3, sort the eigenvalues ​​of the covariance matrix H in descending order, and select the eigenvector corresponding to each eigenvalue. These eigenvectors constitute a new principal component direction matrix F, which contains the directions of all principal components.

[0088] Step 5.4, calculate the variance proportion E of each principal component r is to transform each eigenvalue λ r This is done by dividing by the sum of all eigenvalues, which represents the proportion of the rth principal component in the total variance.

[0089]

[0090] Step 5.5, Cumulative variance percentage E C By gradually accumulating the variance proportion E of the first k principal components r Calculation indicates the proportion of the total variance retained by the first k principal components to all variances. The minimum number of principal components selected by the present invention is the k value when the cumulative variance percentage exceeds 90%.

[0091]

[0092] Step 5.6, after determining the number of principal components k, the matrix F will be updated to a new matrix F k , which only contains the eigenvectors of the first k principal components. k are the first k columns extracted from the original F, indicating the selected principal component directions.

[0093] Step 5.7, by combining the original data matrix B with the eigenvector matrix F k Multiply them together to get the principal component score S.

[0094] S=B·F k (11)

[0095] Step 5.8, the evaluation matrix Q is reconstructed through formula (12), and the process of converting the data representation in the principal component space back to the original feature space is aimed at making the reconstructed data retain the most critical information.

[0096]

[0097] Where S is the principal component score matrix, FTk is the eigenvector matrix F of the selected k principal components k The transpose of .

[0098] Step 5.9, determine the positive ideal solution Q + and negative ideal solution Q - , as shown in equations (13) and (14).

[0099]

[0100] in, is the optimal normalized value of the index of the jth measuring point under the i-th load value, that is, the maximum value and It is the worst normalized value of the index of the jth measuring point under the i-th load value, that is, the minimum value.

[0101] Step 5.10, calculate the distance from the evaluation object to the positive ideal solution and the negative ideal solution;

[0102] Step 5.11, calculate the relative closeness coefficient C of each indicator i , according to C i Calculate the unit operation risk rate R i .

[0103] Example 4

[0104] The specific process of step 5.10 is: Calculate the Euclidean distance D + and D - , that is, the distance from the evaluation object to the positive ideal solution and the negative ideal solution, as shown in equations (15) and (16).

[0105]

[0106] Example 5

[0107] The specific process of step 5.11 is: Calculate the relative closeness coefficient C of each indicator i , as shown in formula (17). Since in the TOPSIS evaluation system, the closer the relative closeness coefficient is to 1, the better, therefore, the computer group operation risk rate R is obtained through formula (18). i .

[0108]

[0109] Ri =1-C i (18)

[0110] Example 6

[0111] By carrying out a variable load test on the Francis turbine unit, the peak-to-peak values ​​of the swing, vibration and pressure pulsation of each component are collected through the test acquisition system, as shown in Figure 2(a)-(c). The collected data are classified according to swing, vibration and pressure pulsation, and their evaluation matrix A is constructed through steps 1-4. Figure 3 The process of selecting the number of principal components k is shown. The unit risk coefficient of the Francis turbine under different loads is obtained through step 5, such as Figure 4 As shown. Figure 4 It can be seen that the unit risk factor shows a wave-like change trend with the increase of load. The peak appears at 160MW, and the trough appears at 140MW and 260MW. This shows that under the load of 160MW, the risk of unit operation is in the unsafe operation area.

[0112] The method for quantitatively evaluating the wide-load stability of a Francis turbine of the present invention can quantitatively analyze the operating stability of a Francis turbine unit under different load conditions, and has higher evaluation accuracy and stability identification capability, thereby improving the reliability and service life of the hydropower unit in a multi-energy complementary system.

Claims

1. A quantitative evaluation method for wide load stability of Francis turbine, characterized by: The specific steps include: Step 1, collecting horizontal and vertical swing data of the upper guide bearing measuring point, the lower guide bearing measuring point and the water guide bearing measuring point through an eddy current displacement sensor, and inputting the measured swing data into a matrix A1; Step 2, collecting the horizontal and vertical vibration displacements of the upper frame measuring point, the lower frame measuring point and the top cover measuring point, and the horizontal vibration displacement of the stator base measuring point through the speed displacement sensor, and inputting the measured vibration displacement data into the matrix A2; Step 3, collecting pressure pulsation at the top cover inlet measuring point, the volute inlet measuring point and the draft tube inlet measuring point through a pressure sensor, and inputting the measured pressure pulsation data into the matrix A3; Step 4, merge matrices A1, A2 and A3 into an evaluation matrix A; Step 5: Process the data in matrix A through principal component analysis to obtain the unit operation risk rate.

2. The method for quantitatively evaluating wide load stability of a Francis turbine according to claim 1, characterized in that: In step 1, the matrix A1 is shown in the following formula (1): in, It represents the swing value of the j1th measuring point index under the i-th load value.

3. The method for quantitatively evaluating wide load stability of a Francis turbine according to claim 2, characterized in that: In step 2, the matrix A2 is shown in the following formula (2): in, It represents the vibration value of the j2th measuring point under the i-th load value.

4. The method for quantitatively evaluating wide load stability of a Francis turbine according to claim 3, characterized in that: In step 3, the matrix A3 is shown in the following formula (3): in, It represents the pressure pulsation value of the j3th measuring point indicator under the i-th load value.

5. The method for quantitatively evaluating wide load stability of a Francis turbine according to claim 4, characterized in that: In step 4, the matrix A is shown in the following formula (4): Among them, n represents the test index, m represents the load value in each test index, and a ij It represents the test value of the index at the jth measuring point under the i-th load value.

6. The method for quantitatively evaluating wide load stability of a Francis turbine according to claim 5, characterized in that: The specific process of step 5 is as follows: Step 5.1, perform forward processing on each element in the evaluation matrix A through formula (5), and obtain the normalized matrix B through formula (6): Among them, b ij It represents the normalized value of the index of the jth measuring point under the i-th load value; Step 5.2, calculate the covariance matrix H of the matrix B, as shown in formula (7), and extract the eigenvalues ​​and eigenvectors of the matrix H, which satisfy the relationship of formula (8): Hv r =λ r v r (8) Among them, B T is the transposed matrix of matrix B, n is the number of columns of matrix B, λ r is the rth eigenvalue, v r is λ r The corresponding eigenvector; Step 5.3, arrange the eigenvalues ​​of the covariance matrix H in descending order, and select the eigenvector corresponding to each eigenvalue to form the principal component direction matrix F; Step 5.4, calculate the variance ratio E of each principal component using the following formula (9): r : Step 5.5, calculate the cumulative variance percentage E by the following formula (10): C , and select the k value where the cumulative variance percentage exceeds 90%: Step 5.6: After determining the number of principal components k, update the matrix F to be the matrix F k ; Step 5.7, by combining the original data matrix B with the eigenvector matrix F k Multiply to get the principal component score S: S=B·F k (11) Step 5.8, reconstruct the evaluation matrix Q through formula (12): Where S is the principal component score matrix, FTk is the eigenvector matrix F of the selected k principal components k The transpose of Step 5.9, determine the positive ideal solution Q + and negative ideal solution Q - , as shown in the following formulas (13) and (14): in, is the optimal normalized value of the index of the jth measuring point under the i-th load value, that is, the maximum value and is the worst normalized value of the index of the jth measuring point under the i-th load value, that is, the minimum value; Step 5.10, calculate the distance from the evaluation object to the positive ideal solution and the negative ideal solution; Step 5.11, calculate the relative closeness coefficient C of each indicator i , according to C i Calculate the unit operation risk rate R i .

7. The method for quantitatively evaluating wide load stability of a Francis turbine according to claim 6, characterized in that: The specific process of step 5.10 is: calculate the distance D from the evaluation object to the positive ideal solution and the negative ideal solution by the following formula (15) and formula (16): + and D - :

8. The method for quantitatively evaluating wide load stability of a Francis turbine according to claim 7, characterized in that: The specific process of step 5.11 is: calculate the relative closeness coefficient C of each indicator by the following formula (17): i , through formula (18) the computer group operation risk rate R i : R i =1-C i (18)。

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