Compensation type differential expansion calculation method for steam turbine

Abstract

The invention discloses a method for calculating the compensation type expansion difference of a steam turbine. The method comprises the following steps of: oppositely mounting two differential expansion sensors, namely a differential expansion sensor I and a differential expansion sensor II, on cylinders on two sides of a to-be-detected surface of a rotor; determining the length L11 and the length L21 of the non-overlapping area; the output voltage V11 of the sensor 1 is collected at the position, away from the sensor I by the distance L11, of the measured surface, and the output voltage V21 of the sensor 2 is collected at the position, away from the sensor II by the distance L21, of the measured surface; collecting the output voltage V1 of the sensor I and the output voltage V2 of the sensor 2; and defining weights k1 (x) and K2 (x) of the sensor I and the sensor II related to the differential expansion quantity x in a measurement range overlapping region, and solving the differential expansion quantity in a weighted summation expression of the differential expansion. According to the method, the situation that in compensation type differential expansion measurement, the differential expansion measurement error is large due to data sudden change in a transition area caused by the difference between the sensitivities of different differential expansion sensors and the sensitivity error of the sensors is reduced.

Description

Technical Field

[0001] The invention relates to a calculation method for compensating expansion difference of a steam turbine. Background Art

[0002] During the start-up and shutdown process, the turbine will experience thermal expansion due to heat. The rotor and cylinder will expand axially from the dead point. Usually, the temperature rise of the rotor is faster than that of the cylinder, so there will be relative expansion between the rotor and the cylinder. The expansion difference between the two is called the expansion difference. By installing an expansion difference sensor (usually an eddy current displacement sensor) on the cylinder, the output voltage of the sensor is proportional to the distance between the sensor and the surface to be measured within the linear range. The monitor can calculate the relative displacement between the sensor (cylinder reference surface) and the surface to be measured (rotor reference surface) by collecting the output voltage of the sensor. When the distance exceeds a certain range, the monitor sends an alarm signal to avoid axial friction and damage to the unit. For some medium and large units, the expansion difference is large, and a single eddy current sensor cannot cover the entire range to be measured. Therefore, it is generally necessary to use inclined expansion difference measurement or compensated expansion difference measurement.

[0003] Compensated differential expansion refers to the expansion differential measurement by compensating the ranges of two sensors. During the measurement process, the sensitivity of the two sensors may be inconsistent due to different manufacturers, production processes, production batches, sensor aging, etc., resulting in data jumps and large errors in the transition area of ​​the two sensors. Summary of the invention

[0004] In order to solve the problem of data jump and large error in the overlap area in the compensation differential expansion measurement, the present invention proposes an improved algorithm for the overlap area.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A method for calculating the compensating expansion difference of a steam turbine comprises the following steps:

[0007] 1) Two differential expansion sensors are installed on the cylinder and on both sides of the rotor surface to be measured, namely differential expansion sensor I and differential expansion sensor II;

[0008] 2) Determine the lengths L11 and L21 of the non-overlapping areas within the corresponding measuring ranges of differential expansion sensor I and differential expansion sensor II;

[0009] 3) Collect output voltages V11 and V21 at the locations where the differential expansion sensor I and differential expansion sensor II are displaced L11 and L21 from the corresponding measured surface, respectively;

[0010] 4) Collect the output voltage V1 of differential expansion sensor I and the output voltage V2 of differential expansion sensor II;

[0011] 5) Define the weights k1(x) and K2(x) of differential expansion sensor I and differential expansion sensor II related to the differential expansion x in the overlapping range;

[0012] 6) Solve the expansion difference x based on the weighted sum of the expansion difference, the expression is as follows:

[0013] x=L11+k1(x)*L12_Sensor1+k2(x)*L12_Sensor2,where

[0014] L12_Sensor1=(V1-V11) / S1_nominal

[0015] L12_Sensor2=(L12+L22)-(V2-V21) / S2_nominal,

[0016] S1_nominal and S2_nominal are the nominal sensitivities of sensor 1 and sensor 2 respectively.

[0017] Furthermore, the constraints that the weights k1(x) and K2(x) must satisfy in step (5) are:

[0018] k1(x)=1,x=L11

[0019] k1(x)=0,x=L11+L12+L22

[0020] k2(x)=0,x=L11

[0021] k2(x)=1,x=L11+L12+L22,

[0022] in,

[0023] L12=L1-L11

[0024] L22=L2-L21,

[0025] L1 and L2 are the distances from differential expansion sensor Ⅰ and differential expansion sensor Ⅱ to the corresponding measured surface respectively.

[0026] The weights k1(x) and K2(x) can be set as constants according to actual conditions.

[0027] Or focus on the displacement calculation of the overlapping area and make the following settings:

[0028] Let x′=x-L11, then the constraints of k1(x) and k2(x) are rewritten as

[0029] k1(x′)=1,x′=0

[0030] k1(x′)=0,x′=L12+L22

[0031] k2(x′)=0,x′=0

[0032] k2(x′)=1,x′=L12+L22

[0033] And define k1(x′) and k2(x′) as:

[0034]

[0035] The solution method for the expansion difference x in step (6) is as follows:

[0036] The differential expansion in the overlapping area can be expressed as:

[0037] x′=k1(x′)*L12_Sensor1+k2(x′)*L12_Sensor2

[0038] The expression of the expansion difference x is:

[0039] x=x′+L11.

[0041] Furthermore, the combined measuring range of the two differential expansion sensors does not exceed the sum of the measuring ranges of the two differential expansion sensors; L11 and L21 do not exceed the measuring ranges of the corresponding differential expansion sensors, respectively.

[0042] Compared with the prior art, the present invention has the following advantages:

[0043] 1) When there is a certain difference in the sensitivity of the differential expansion sensor, the calculation method of the present invention can avoid the problem of data jump in the transition zone in the compensation differential expansion measurement;

[0044] 2) When the sensitivity of the differential expansion sensor has a certain error, the error in a part of the overlapping area can be eliminated through the calculation method of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 A schematic diagram of the installation positions of two differential expansion sensors used in the steam turbine compensating differential expansion calculation method of the present invention;

[0046] Figure 2 A comparison diagram of the calculated displacement and the actual displacement value of the compensation differential expansion in Example 2 of the present invention;

[0047] Figure 3 This is a comparison chart of the calculated displacement and the actual displacement value of the compensating differential expansion in Example 3 of the present invention. DETAILED DESCRIPTION

[0048] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0049] Example 1

[0050] like Figure 1 As shown, the present invention relates to a method for realizing compensated differential expansion calculation, which can avoid the problem of data jump in the transition zone of compensated differential expansion measurement when there is a certain difference in sensitivity between two differential expansion sensors in compensated differential expansion measurement, and eliminate part of the measurement error caused by the sensor sensitivity error. The method comprises the following steps:

[0051] A method for realizing compensatory differential expansion calculation of a steam turbine, comprising:

[0052] 1) Two differential expansion sensors are installed on the cylinder and on both sides of the measured surface of the rotor 1, namely differential expansion sensor I4 and differential expansion sensor II5;

[0053] 2) Determine the lengths L11 and L21 of the non-overlapping areas within the corresponding measuring ranges of the differential expansion sensor Ⅰ4 and the differential expansion sensor Ⅱ5;

[0054] 3) The output voltages V11 and V21 are collected at the positions where the differential expansion sensor Ⅰ4 and the differential expansion sensor Ⅱ5 are respectively displaced L11 and L21 from the rotor surface to be measured Ⅰ2 and the rotor surface to be measured Ⅱ3;

[0055] 4) collecting the output voltage V1 of the differential expansion sensor Ⅰ4 and the output voltage V2 of the differential expansion sensor Ⅱ5;

[0056] 5) defining weights k1(x) and K2(x) of the differential expansion sensor Ⅰ4 and the differential expansion sensor Ⅱ5 in the measurement overlap area related to the differential expansion x;

[0057] 6) Solve the weighted summation expression of the expansion difference to obtain the expansion difference amount.

[0058] Among them, the constraints that weights k1(x) and K2(x) need to satisfy are

[0059] k1(x)=1,x=L11

[0060] k1(x)=0,x=L11+L12+L22

[0061] k2(x)=0,x=L11

[0062] k2(x)=1,x=L11+L12+L22

[0063] The weighted summation expression of the expansion difference is:

[0064] x=L11+k1(x)*L12_Sensor1+k2(x)*L12_Sensor2

[0065] In the formula,

[0066] S1_nominal and S2_nominal are the nominal sensitivities of sensor 1 and sensor 2 respectively.

[0067] The combined measuring range shall not exceed the sum of the measuring ranges of the two sensors; L11 and L21 shall not exceed the measuring ranges of the differential expansion sensor Ⅰ4 and the differential expansion sensor Ⅱ5 respectively.

[0068] Example 2

[0069] This embodiment focuses on the displacement calculation of the overlapping area. Let x′=x-L11, then the constraints of k1(x) and k2(x) are rewritten as:

[0070] k1(x′)=1,x′=0

[0071] k1(x′)=0,x′=L12+L22

[0072] k2(x′)=0,x′=0

[0073] k2(x′)=1,x′=L12+L22

[0074] It is not general, and k1(x′) and k2(x′) can be defined as

[0075]

[0076] The differential expansion in the overlap zone is expressed as the weighted sum of the readings of the two differential expansion sensors:

[0077] x′=k1(x′)*L12_Sensor1+k2(x′)*L12_Sensor2

[0078] Among them, L12_Sensor1 and L12_Sensor2 are the displacement L12 calculated by sensor 1 and sensor 2 respectively. The weighted sum of the two is obtained to obtain the weighted sum expression of the expansion difference.

[0079] in

[0080] L12_Sensor1=(V1-V11) / S1_nominal

[0081] L12_Sensor2=(L12+L22)-(V2-V21) / S2_nominal

[0082] S1_nominal and S2_nominal are the nominal sensitivities of sensor 1 and sensor 2 respectively.

[0083] Since the weight is a function of the expansion difference, it is necessary to solve the expression of the expansion difference x. Substituting the expression of the weight into the expression of the expansion difference x′ in the overlap region yields

[0084] x′=k1(x′)*L12_sensor1+k2(x′)*L12_sensor2

[0085]

[0086] Let ΔL=L12+L22

[0087]

[0088] Solved

[0089]

[0090] x=x′+L11

[0091] Figure 2 It is a comparison between the displacement calculated by the compensation differential expansion in the invention and the real displacement value. Assuming that the combined range is 20mm, the overlapping area is 8-12mm, and the sensitivity of the two differential expansion sensors is ±1% compared with the nominal value (nominal sensitivity), if direct range compensation is used, it is possible that when the two sensors are at the maximum positive deviation and the maximum negative deviation, a 2% measured displacement jump will be obtained. However, the differential expansion value actually measured by the method of the present invention has no jump in the entire range, and the relative error in the entire range is not greater than the sensitivity error of a single differential expansion sensor.

[0092] Example 3

[0093] This embodiment considers a case where the weight coefficient is a constant, and the weighted summation expression of the expansion difference is:

[0094] x=L11+k1*L12_Sensor1+k2*L12_Sensor2

[0095] In the formula,

[0096] S1_nominal and S2_nominal are the nominal sensitivities of sensor 1 and sensor 2 respectively.

[0097] The combined measuring range shall not exceed the sum of the measuring ranges of the two sensors; L11 and L21 shall not exceed the measuring ranges of the differential expansion sensor Ⅰ4 and the differential expansion sensor Ⅱ5 respectively.

[0098] Figure 3The comparison between the displacement calculated by the compensation differential expansion and the real displacement value when the weight coefficients k1 and k2 in the invention are both constants of 0.5. Assuming that the combined range is 20mm and the overlapping area is 8-12mm, the sensitivity of the two differential expansion sensors has an error of ±1% compared with the nominal value (nominal sensitivity). If direct range compensation is used, a 2% measured displacement jump may be obtained when the two sensors are at the maximum positive deviation and the maximum negative deviation, respectively. In this embodiment, although there is a jump at the starting point and the end point of the overlapping area, the jump amount is smaller than that of the direct range compensation.

[0099] The above implementation method should not be understood as limiting the scope of protection of the present invention. The key to the present invention is to adopt a novel calculation method to solve the problem of data mutation and large error in the overlapping area caused by the difference in sensitivity between different differential expansion sensors, as well as the technical details involved. Any form of modification made to the present invention without departing from the spirit or scope of the present invention shall be included in the scope of protection of the present invention.

[0100] The above description is only a preferred embodiment of the present invention. It should be pointed out that a person skilled in the art can make several improvements without departing from the principle of the present invention, and these improvements should also be regarded as within the protection scope of the present invention.

Claims

1. A method for calculating the compensatory expansion difference of a steam turbine, characterized in that: The following steps are involved: 1) Two differential expansion sensors are installed on the cylinder and on both sides of the rotor surface to be measured, namely differential expansion sensor I and differential expansion sensor II; 2) Determine the lengths L11 and L21 of the non-overlapping areas within the corresponding measuring ranges of differential expansion sensor I and differential expansion sensor II; 3) Collect output voltages V11 and V21 at the locations where the differential expansion sensor I and differential expansion sensor II are displaced L11 and L21 from the corresponding measured surface, respectively; 4) Collect the output voltage V1 of differential expansion sensor I and the output voltage V2 of differential expansion sensor II; 5) Define the weights k1(x) and K2(x) of differential expansion sensor I and differential expansion sensor II related to the differential expansion x in the overlapping range; 6) Solve the expansion difference x based on the weighted sum of the expansion difference, the expression is as follows: x=L11+k1(x)*L12_Sensor1+k2(x)*L12_Sensor2, in L12_Sensor1=(V1-V11) / S1_nominal L12_Sensor2=(L12+L22)-(V2-V21) / S2_nominal, S1_nominal and S2_nominal are the nominal sensitivities of sensor 1 and sensor 2 respectively.

2. The method for calculating the compensatory expansion difference of a steam turbine according to claim 1, characterized in that: The constraints that the weights k1(x) and K2(x) must satisfy in step (5) are: k1(x)=1,x=L11 k1(x)=0,x=L11+L12+L22 k2(x)=0,x=L11 k2(x)=1,x=L11+L12+L22, in, L12=L1-L11 L22=L2-L21, L1 and L2 are the distances from differential expansion sensor Ⅰ and differential expansion sensor Ⅱ to the corresponding measured surface respectively.

3. The calculation method of the steam turbine compensating expansion difference according to claim 2 is characterized in that: The definitions of k1(x) and K2(x) in step (5) are as follows: Considering the displacement calculation of the overlapping area, let x′=x-L11, then the constraints of k1(x) and k2(x) are rewritten as k1(x′)=1,x′=0 k1(x′)=0,x′=L12+L22 k2(x′)=0,x′=0 k2(x′)=1,x′=L12+L22 And define k1(x′) and k2(x′) as: The method for solving the expansion difference x in step (6) is as follows: The differential expansion in the overlapping area can be expressed as: x′=k1(x′)*L12_Sensor1+k2(x′)*L12_Sensor2 The expression of the expansion difference x is: x=x′+L11.

4. The method for calculating the compensating expansion difference of a steam turbine according to claim 1, characterized in that: The combined measuring range of the two differential expansion sensors does not exceed the sum of the measuring ranges of the two differential expansion sensors; L11 and L21 do not exceed the measuring ranges of the corresponding differential expansion sensors respectively.

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