CN110489801B - Generator shaft system multi-mass-block parameter simplification method by utilizing particle swarm optimization algorithm - Google Patents
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Abstract
The invention discloses a generator shaft system multi-mass-block parameter simplification method by utilizing a particle swarm optimization algorithm, belonging to the field of modeling and analysis of a power system. The method specifically relates to parameter simplification of a shafting multi-mass model for the sub-synchronous oscillation analysis of the thermal power generating unit, the generator mass is combined successively, the section of the mass where a sub-synchronous frequency mode is located is judged, the rest masses are combined, a simplified model without high-frequency mode components is obtained, model parameters are corrected based on a particle swarm optimization algorithm, the simplified shafting multi-mass model and simulation calculation are obtained, the establishment of the multi-mass model in power system simulation software is simplified, and the dynamic characteristics of the sub-synchronous oscillation of the thermal power generating unit of the power system can be reflected. The simplified shafting multi-mass model does not contain the high-frequency component of shafting torsional vibration. The research efficiency and the reliability of the research result are greatly improved. The method can meet the requirement of the subsynchronous oscillation characteristic analysis of the thermal power generating unit of the power system.
Description
Technical Field
The invention belongs to the field of modeling and analysis of power systems, and particularly relates to a generator shafting multi-mass parameter simplification method by utilizing a particle swarm optimization algorithm, in particular to a shafting multi-mass parameter simplification method based on successive combination and particle swarm optimization algorithm adjustment.
Background
The generator shafting multi-mass model determines the natural torsional vibration frequency of the shafting, so that establishment of a reasonable unit shafting model is the basis for researching the subsynchronous oscillation problem. In practice, the shafting length of a large-capacity unit is very long, and the shafting model is a continuous infinite element shafting model and is not easy to analyze. The model adopted for calculating the inherent characteristics of the torsional vibration of the shafting of the unit mainly comprises a simple centralized model, a multi-section centralized quality model and a continuous quality model. The calculation result of the continuous mass model has high precision, although the calculation result can accurately reflect higher-order torsional vibration characteristics and mechanical characteristics, the calculation amount is large, the influence of the local structure of the shafting is mainly calculated, and the method is not suitable for the dynamic analysis of the electromechanical coupling system. The calculated amount of the multi-section concentrated mass model is smaller than that of the multi-section concentrated mass model, the calculation accuracy can be guaranteed, however, in practice, the multi-section concentrated mass model divides the shafting into dozens of sections to hundreds of sections, the specific details of the shafting are considered, the key and non-key sections are analyzed finely, and the calculated amount is still very large. The simplified method for simplifying the mass model of the simple concentrated mass has a good effect when the qualitative analysis of the inherent characteristics of the torsional vibration of the shafting of the unit is carried out, and although the simplified simple concentrated mass model brings some errors, the rationality of the simplification can be ensured as long as the subsynchronous torsional vibration frequencies calculated by the simplified mass model and the subsynchronous torsional vibration frequencies calculated by the simplified mass model are consistent and the overall trend of the simplified vibration mode is consistent. Some documents calculate that some adjacent rigid roulette plates have no influence on the torsional vibration characteristics of the model after being combined, so that many researchers model the unit shafting into a Jian Shanji middle mass model according to the cylinder positions. In the research aiming at the problem of the sub-synchronization of the thermal power generating unit, a multi-mass block axial system torsional vibration model provided by a manufacturer may contain a high-frequency component, but only a torsional vibration mode of the sub-synchronization frequency component is concerned in the sub-synchronization vibration research, so that the torsional vibration analysis and calculation are simplified, and the torsional vibration analysis and calculation are further effectively combined to obtain a low-order simple mass model without the high-frequency mode of the multi-mass block model. In the analysis of the subsynchronous oscillation problem, the shafting design frequency provided by a power plant generally has a slight difference with the actual measurement frequency, and in addition, the model is a simplified equivalent model, and the calculated natural torsional oscillation frequency possibly has a deviation with the field actual measurement frequency, so that the parameters of the simplified shafting model need to be corrected.
Disclosure of Invention
The invention aims to provide a generator shaft system multi-mass parameter simplification method by utilizing a particle swarm optimization algorithm; the method is characterized in that the method for simplifying the parameters of the generator shafting multi-mass block is a method for further simplifying a turboset shafting multi-mass block shafting model into a shafting equivalent model only containing subsynchronous torsional vibration frequency components based on a successive combination principle, and parameter correction is carried out by utilizing a particle swarm algorithm, and the specific process comprises the following steps:
(1) Inputting an inertia time constant M of the multiple mass blocks of the generator and a rigidity coefficient K between the mass blocks;
(2) Combining the generator multi-mass blocks one by one, calculating new torsional vibration frequency by using the combined inertia time constant M and the rigidity coefficient K between the mass blocks, and comparing the new torsional vibration frequency with the reserved subsynchronous torsional vibration frequency component;
(3) Obtaining a shafting equivalent model only containing subsynchronous torsional vibration frequency components, and calculating an inertia time constant M after combination and a rigidity coefficient K between the mass blocks;
(4) Correcting the rigidity coefficient among the mass blocks by utilizing a particle swarm algorithm;
(5) The precision is satisfied:
if the precision requirement is met, the next step (6) is carried out; if not, returning to the step (4);
(6) And outputting the optimized parameters.
Inputting an inertia time constant M of a plurality of mass blocks of the generator and a rigidity coefficient K between the mass blocks, wherein the shafting torsional vibration frequency of the steam turbine unit refers to natural frequency generated between the mass blocks of a rotor shafting of the steam turbine generator after the unit is disturbed, and the natural frequency is only related to the inherent characteristics of a mechanical system; therefore, if two adjacent mass blocks are combined, one natural frequency is reduced, and the cross section where the subsynchronous frequency component is located is obtained by judging the value of the reduced natural frequency; the inertia time constant of the new mass block is the sum of the two mass blocks before combination, the stiffness coefficients of the combined mass blocks are distributed in proportion, and the specific calculation formula is as follows:
M j ＝M i +M i+1 (1-1)
in the above formula, M represents the inertia time constant of the mass block, K represents the stiffness coefficient parameter between the mass blocks, i represents the position number of the mass block before combination of the mass blocks, and j represents the position number of the mass block after combination, that is, M 1 Is the inertial time constant of the first mass, K 1 Is the stiffness coefficient between mass 1 and mass 2.
The remaining subsynchronous frequency components can be selected from the provided torsional vibration frequencies provided by the power plant and are recorded as:
rest_f＝[rest_f 1 ，rest_f 2 ，…，rest_f k ] (1-4)
where rest _ f is the reserved subsynchronous frequency, rest _ f k The k-th frequency reserved.
And (3) combining two adjacent mass blocks, and calculating the inertia time constant after combination and the rigidity coefficient between the mass blocks according to the formulas (1-1), (1-2) and (1-3). When two adjacent mass blocks are combined, the combined natural frequency is recorded as:
f＝[f 1 ,f 2 ,…,f h ] (1-5)
in the above formula, f h Is the h-th frequency reserved.
And (3) respectively subtracting the reserved frequency components in the formulas (1-4) from the h frequencies in the formulas (1-5), and taking the minimum value of the absolute values of the reserved frequency components as T:
T＝[T 1 ,T 2 ,…,T k ] (1-6)
wherein T is k Comprises the following steps:
T k ＝min{|rest_f k -f 1 |,|rest_f k -f 2 |,…,|rest_f k -f h |} (1-7)
rest _ f in the above equation k I.e. the retained kth frequency component, f h The same formula (1-5).
At this time, if T k If the value of (d) is close to zero, it represents that the frequency components are not merged, otherwise, it represents that the frequency components exist between the adjacent masses, and thus it is determined that the position needs to be preserved; judging whether the combined mass blocks contain the low-frequency components to be reserved or not according to whether the maximum value in the T is close to zero or not, and if the maximum value of the T is close to zero, not containing the low-frequency components;
if the number of the mass blocks is n, the merging times are n-1 times, and n-1 maxTs can be obtained correspondingly, and the number is denoted as S:
S＝[S 1 ,S 2 ,…,S n-1 ] (1-8)
in the above formula S n-1 Represents the maximum value corresponding to the formula (1-6) after each combination.
And determining the position of the reserved subsynchronous frequency component according to the position of the maximum value of the number of the first k reserved frequencies in the S, combining the rest mass blocks, and simultaneously calculating corresponding inertia time constants and stiffness coefficients among the mass blocks according to the formulas 1-1 to 1-3.
In the step (4), in order to take into account that the preliminarily combined parameters generate certain errors, the parameters are corrected based on a particle swarm optimization algorithm, the value of the inertia time constant is mainly determined by the mass of the shafting mass block, and the value of the inertia time constant is easily and accurately obtained, so that the rigidity coefficient between the mass blocks is corrected more reasonably, the value of the inertia time constant is reserved, and the rigidity coefficient between the mass blocks is corrected to correspondingly check the equivalent shafting model, so that the consistency of the vibration mode trend of the equivalent shafting model is ensured;
in each iteration process, the particle updates the speed and position of the particle through an individual extremum and a group extremum, and the updating formula is as follows:
in the formula, each coefficient represents the following meaning:
c 1 ,c 2 -acceleration constant, adjusting the maximum step size of learning;
r 1 ,r 2 -two random functions, value range [0,1]To increase search randomness;
omega-inertial weight, non-negative number, adjusts the search range for the solution space;
to ensure the rapidity of the search, the inertia weight ω is set to the formula 1-11, and the inertia weight is ensured to be decreased, so that the search range can be ensured to be reduced when the vicinity of the optimal solution is reached (as shown in fig. 3).
In the formula, ω start ＝0.9，ω end =0.4,maxgen is the population size.
The specific operation of the step (5) is to use the sum of the absolute values of the difference values of the measured frequency and the calculated frequency as the fitness function value, i.e. the sum of the absolute values of the difference values of the measured frequency and the calculated frequency is used as the fitness function value
fitness＝|f 1 -real_f 1 |+|f 2 -real_f 2 |+…+|f r -real_f s | (1-12)
In the formula, real _ f s For the measured frequency value, f r To calculate the frequency.
Setting a jump-out circulation condition:
fitness＝ε＜10 -4 (1-13)
the whole searching and updating process of the particle swarm algorithm is a process following the current optimal solution, so that the convergence speed of the particle swarm algorithm is high generally, and when the maximum iteration number is reached, maxgen =50 is set; or jumping out of the cycle after the formula (1-13) is satisfied to obtain the current optimal solution, namely the rigidity coefficient among the mass blocks.
The method has the advantages that according to the requirement of analyzing the shafting parameters for the subsynchronous oscillation stability analysis of the thermal power generating unit of the electric power system, a mass model containing high-frequency components is further simplified into a shafting model only containing subsynchronous torsional oscillation frequency components, parameter correction is carried out on the simplified model based on a particle swarm optimization algorithm, shafting model establishment of power system simulation software PSCAD is simplified, a simplified steam turbine shafting equivalent model without high-frequency components and simulation calculation are obtained, and the requirement of subsynchronous oscillation characteristic analysis of the thermal power generating unit of the electric power system can be met.
Drawings
FIG. 1 is a simplified mass flow diagram.
FIG. 2 is a schematic diagram of mass consolidation.
FIG. 3 is a graph of inertial weight versus number of iterations.
Fig. 4 is a schematic diagram of a shafting structure of a typical large-scale steam turbine generator unit.
FIG. 5 is a flow chart of mass preliminary merging.
FIG. 6 is a flow chart of a particle swarm optimization algorithm for correcting stiffness coefficients between the masses.
FIG. 7 is a block diagram of a north two power plant axis multi-mass system.
FIG. 8-1 is a graph of the 38.30Hz mode shape provided by the North two Power plant.
FIG. 8-2 is a simplified diagram of the post-38.30 Hz mode shape.
FIG. 9-1 provides a 29.91Hz mode pattern for the second North Power plant.
FIG. 9-2 is a simplified 29.91Hz mode pattern diagram.
FIG. 10-1 provides a 17.49Hz mode shape for the second North Power plant.
FIG. 10-2 is a simplified diagram of the 17.49Hz mode shape.
Detailed Description
The invention provides a generator shaft system multi-mass parameter simplification method. The invention will be further described with reference to the accompanying drawings.
A simplified mass flow diagram is shown in fig. 1. The generator shafting multi-mass-block parameter simplification method is a method for further simplifying a turboset shafting multi-mass-block shafting model into a shafting equivalent model only containing subsynchronous torsional vibration frequency components based on a successive combination principle, and utilizes a particle swarm algorithm to correct parameters, and the specific process comprises the following steps of
(1) Inputting an inertia time constant M of the multiple mass blocks of the generator and a rigidity coefficient K between the mass blocks;
(2) Combining the generator multi-mass blocks one by one, calculating new torsional vibration frequency by using the combined inertia time constant M and the rigidity coefficient K between the mass blocks, and comparing the new torsional vibration frequency with the reserved subsynchronous torsional vibration frequency component;
(3) Obtaining a shafting equivalent model only containing subsynchronous torsional vibration frequency components, and calculating an inertia time constant M after combination and a rigidity coefficient K between the mass blocks;
(4) Correcting the rigidity coefficient K between the mass blocks by utilizing a particle swarm algorithm;
(5) The precision is satisfied:
if the precision requirement is met, the next step (6) is carried out; if not, returning to the step (4);
(7) And outputting the optimized parameters.
Inputting an inertia time constant M of a plurality of mass blocks of the generator and a rigidity coefficient K between the mass blocks, and a shafting structure schematic diagram (shown in figure 4) of a typical large-scale steam turbine generator unit, wherein the shafting torsional vibration frequency of the steam turbine generator unit refers to natural frequency generated between the mass blocks of a rotor shafting of the steam turbine generator after the unit is disturbed, and the natural frequency are only related to the inherent characteristics of a mechanical system; therefore, if two adjacent blocks are combined (as shown in fig. 2), a natural frequency is reduced, and a cross section where the sub-synchronization frequency component is located is obtained by judging and reducing the value of the natural frequency; the inertia time constant of the new mass block is the sum of the two mass blocks before combination, the stiffness coefficients of the combined mass blocks are distributed in proportion, and the specific calculation formula is as follows:
M j ＝M i +M i+1 (1-1)
in the above formula, M represents the inertia time constant of the mass block, K represents the stiffness coefficient parameter between the mass blocks, i represents the position number of the mass block before combination of the mass blocks, and j represents the position number of the mass block after combination, (i.e. M 1 Is the inertial time constant of the first mass, K 1 Is the stiffness coefficient between mass 1 and mass 2).
The remaining subsynchronous frequency components can be selected from the provided torsional vibration frequencies provided by the power plant and are recorded as follows:
rest_f＝[rest_f 1 ，rest_f 2 ，…，rest_f k ] (1-4)
where rest _ f is the reserved subsynchronous frequency, rest _ f k The reserved kth frequency.
And (3) combining two adjacent mass blocks, and calculating the inertia time constant of a shafting system and the rigidity coefficient between the mass blocks after combination according to the formulas (1-1), (1-2) and (1-3). When two adjacent mass blocks are combined, recording the natural frequency after combination:
f＝[f 1 ,f 2 ,…,f h ] (1-5)
in the above formula, f h The h-th frequency reserved.
And (3) respectively subtracting the reserved frequency components in the formulas (1-4) from the h frequencies in the formulas (1-5), and taking the minimum value of the absolute values of the reserved frequency components as T:
T＝[T 1 ,T 2 ,…,T k ] (1-6)
in the above formula, T k Comprises the following steps:
T k ＝min{|rest_f k -f 1 |,|rest_f k -f 2 |,…,|rest_f k -f h |} (1-7)
rest _ f in the above equation k I.e. the retained k-th frequency component, f h The same formula (1-5).
At this time, if T k If the value of (d) is close to zero, it represents that the frequency components are not merged, otherwise, it represents that the frequency components exist between the adjacent masses, and thus it is determined that the position needs to be preserved; judging whether the combined mass blocks contain the low-frequency components to be reserved or not according to whether the maximum value in the T is close to zero or not, and if the maximum value of the T is close to zero, not containing the low-frequency components;
here, if the number of the mass blocks is n, the number of merging times is n-1 times, and n-1 maxT can be obtained correspondingly, which is denoted as S:
S＝[S 1 ,S 2 ,…,S n-1 ] (1-8)
in the above formula S n-1 Represents the maximum value corresponding to the formula (1-6) after each combination.
The positions of the reserved subsynchronous frequency components can be determined according to the positions of the first k maximum values (the number of reserved frequencies) in the S, the rest mass blocks are combined, and the corresponding inertia time constants and the stiffness coefficients among the mass blocks are calculated according to the formulas 1-1 to 1-3.
In the step (4), in order to take into account that the preliminarily combined parameters generate certain errors, the parameters are corrected based on a particle swarm optimization algorithm, the value of the inertia time constant is mainly determined by the mass of the shafting mass block, and the value of the inertia time constant is easily and accurately obtained, so that the rigidity coefficient between the mass blocks is corrected more reasonably, the value of the inertia time constant is reserved, and the rigidity coefficient between the mass blocks is corrected to correspondingly check the equivalent shafting model, so that the consistency of the vibration mode trend of the equivalent shafting model is ensured;
in each iteration process, the particle updates the speed and position of the particle through the individual extremum and the group extremum, and the updating formula is as follows:
in the formula, each coefficient represents the following meaning:
c 1 ,c 2 -acceleration constant, adjusting the maximum step size of learning;
r 1 ,r 2 -two random functions, value range [0,1]To increase search randomness;
omega-inertial weight, non-negative number, adjusts the search range for the solution space;
to ensure the rapidity of the search, the inertia weight ω is set to the formula 1-11, and the inertia weight is ensured to be decreased, so that the search range can be ensured to be narrowed when the vicinity of the optimal solution is reached (as shown in fig. 3).
In the formula, ω start ＝0.9，ω end =0.4,maxgen is the population size.
The specific operation of the step (5) is to use the sum of the absolute values of the difference values of the measured frequency and the calculated frequency as the fitness function value, i.e. the sum of the absolute values of the difference values of the measured frequency and the calculated frequency is used as the fitness function value
fitness＝|f 1 -real_f 1 |+|f 2 -real_f 2 |+…+|f r -real_f s | (1-12)
In the formula, real _ f s For the measured frequency value, f r To calculate the frequency.
Setting a jumping-out circulation condition:
fitness＝ε＜10 -4 (1-13)
the whole searching and updating process of the particle swarm algorithm is a process following the current optimal solution, so that the convergence speed of the algorithm is high generally, and when the maximum iteration times are reached, maxgen =50 is set; or jumping out of the cycle after the formula 1-13 is satisfied to obtain the current optimal solution, namely the rigidity coefficient among the mass blocks.
The simplified steam turbine shafting equivalent model without high-frequency components is obtained according to the method, and can be used for simplifying the building of a generator shafting multi-mass model in PSCAD and simulation calculation.
According to the schematic diagram of the shafting structure of the typical large-scale steam turbine generator unit shown in FIG. 4, the mathematical expression of the shafting sectional concentrated mass-spring model of the column-writing unit is as follows
In the formula, each coefficient has the following meaning. (the points above the variables represent differential equations)
δ is the electrical twist angle vector:
δ＝[δ 1 δ 2 … δ N ] Τ
wherein, delta N Is the electrical torsion angle of the Nth mass relative to the reference axis of synchronous rotation, in arcDegree (rad).
ω is the electrical angular velocity: ω = [ ω ] 1 ω 2 … ω N ] Τ Wherein ω is N Electrical angular velocity of the nth mass is given in radians per second (rad/s).
Δ T is the difference between the mechanical torque and the electromagnetic torque.
M is an inertia time constant matrix: m = diag [ M [ ] 1 M 2 … M N ](ii) a Wherein M is N Is the inertia time constant of the Nth mass in kilograms-meters 2 (kg·m 2 )。
K is the rigidity coefficient among the mass blocks, namely an elastic coefficient matrix:
wherein, K p,p+1 Is the stiffness coefficient between the masses, and N is the number of masses in newton-meters per radian (N · m/rad).
D is a damping coefficient matrix:
wherein D is qq And D q-1,q Is the self-damping and mutual damping coefficient between turbine blocks, and N is the number of blocks and has the unit of N.m.s/rad.
By calculating M -1 The eigenvalues of K can yield the mode frequency.
Fig. 5 shows a flow chart of mass preliminary combination. The method comprises the following steps:
1) Selecting the subsynchronous frequency components needing to be reserved, and calculating as follows:
1.1 inputting the parameters of the generator multi-mass block: inertia time constant and rigidity coefficient among each mass block;
1.2, combining two adjacent mass blocks, and calculating an inertia time constant and a rigidity coefficient parameter between the mass blocks after combination according to the method in the formulas 1-3;
1.3, carrying out mode frequency calculation on the combined parameters;
1.4 subtracting the subsynchronous frequency component to be preserved from the frequency in 1.3, and solving the minimum value, namely
T k ＝min{|rest_f k -f 1 |,|rest_f k -f 2 |,…,|rest_f k -f h |} (1-15)
1.5 to find T = [ T = 1 ,T 2 ,…,T k ]The maximum value of (2) is denoted as S;
1.6 the number of the mass blocks is n, and after n-1 times of combination, S = [ S ] is obtained 1 S 2 …S n-1 ]Judging the section of the subsynchronous frequency by judging the position of the first k maximum values (the number of reserved frequencies) in the S, combining the positions without subsynchronous components according to the methods in the formulas 1-1 to 1-3, and calculating a preliminary inertia time constant and a stiffness coefficient between the mass blocks;
2) Parameter correction was performed based on particle swarm optimization (as shown in fig. 6):
2.1 initializing and optimizing the value (+/-25% change) of the stiffness coefficient among the mass blocks according to the inertia time constant obtained in the step (3) and the stiffness coefficient among the mass blocks, setting the population size to be 100, setting the iteration times to be 50 times, and initializing the iteration speed weight omega;
2.2 taking the sum of the absolute values of the difference between the measured frequency and the calculated frequency as the fitness function value, i.e.
fitness＝|f 1 -real_f 1 |+|f 2 -real_f 2 |+…+|f r -real_f s | (1-16)
In the formula, real _ f s For the measured frequency value, f r To calculate the frequency.
2.3 calculating the optimal solution of the current individual extremum and the group extremum, namely the stiffness coefficient among the mass blocks;
2.4, iteration is carried out until the fitness function value condition is met or the maximum iteration times are reached, and then a loop is skipped;
2.5, outputting an optimal solution, namely the rigidity coefficient among the mass blocks.
Examples
In order to verify the correctness of the above shafting equivalent model, the shafting model of the northbound power plant of the east direct current transmission end power grid is simplified, and after the rigidity coefficients among the mass blocks are corrected according to the actual measurement frequency, vibration mode verification is carried out, so that the rationality of the simplified model is ensured.
As shown in fig. 7, the shafting structure diagram provided by the north-second power plant, the inertia time constant provided by the host manufacturer, and the stiffness coefficient between the mass blocks are shown in table 1.
TABLE 1 shafting parameter model of turbo generator set in the north two power plants
The natural oscillation frequency of the concentrated mass-spring model of the power plant of the second north can be calculated according to the provided data, and is shown in table 2.
TABLE 2 inherent oscillation frequency of concentrated mass-spring model of the north two power plants
1) Obtaining a preliminary simplified model
From the natural frequency, the subsynchronous frequency mode components which should be kept are 17.49hz,29.91hz and 38.30Hz, 9 mass blocks provided by the power plant are respectively combined for 8 times, the kept subsynchronous frequency components are respectively differed from 7 frequencies combined for 8 times, so that the S in the step (2) can be obtained, the result is shown in table 3, the positions of the first three maximum values are easily obtained to be 3, 4 and 5, so that the mass blocks 1, 2 and 3 are combined into one mass block, the mass blocks 4 and 5 are respectively used as a single mass block, and the positions 6, 7 and 8 are combined into a fourth mass block, the combination method is detailed in the invention, and the combined inertia time constant, the rigidity coefficient between the mass blocks and the natural torsional vibration frequency are shown in table 4.
TABLE 3 judgment of preliminary block merger criterion based on S value
TABLE 4 preliminary combined inertia time constant, stiffness coefficient and natural torsional frequency
2) Correcting stiffness coefficients between masses
The mass model after the preliminary combination has a certain deviation from the natural torsional vibration frequency corresponding to the actual model, the stiffness coefficients of the obtained mass blocks are optimized by a particle swarm optimization algorithm, and the optimized parameters and the torsional vibration frequency are shown in table 5.
TABLE 5 optimized stiffness coefficients and torsional frequencies between masses
3) Model correction
In order to prove the effectiveness of the simplified model, because the vibration mode of the simple mass model is formed by line segments connected by a few points, and the vibration modes of the multi-mass model are relatively smooth curves, the former can be regarded as the simplified curve of the latter, the overall trends of the two are consistent, and the vibration modes of the three subsynchronous frequency components which are reserved are compared with the vibration modes provided by the power plant (as shown in figures 8-1, 8-2, 9-1, 9-2, 10-1 and 10-2), the trend of the vibration modes before and after simplification can be obviously seen to be consistent, so that the effectiveness of the simplified model is proved.
Claims (4)
1. The method for simplifying the parameters of the multiple mass blocks of the generator shafting by using the particle swarm optimization algorithm is characterized in that the method for simplifying the parameters of the multiple mass blocks of the generator shafting is a method for further simplifying a turboset shafting model into an equivalent model only containing subsynchronous torsional vibration frequency component shafting based on a successive combination principle, and parameter correction is performed by using the particle swarm optimization algorithm, and the specific flow comprises the following steps:
(1) Inputting parameters of the generator multi-mass block: inertia time constant M and rigidity coefficient K among the mass blocks; the inertia time constant M of the input generator multi-mass blocks and the rigidity coefficient K between the mass blocks are the shafting torsional vibration frequency of the turbine generator set, which means the natural frequency generated between the mass blocks of the turbine generator rotor shafting after the turbine generator set is disturbed, and the natural frequency is only related to the inherent characteristic of a mechanical system; therefore, if two adjacent mass blocks are combined, one natural frequency is reduced, and the cross section of the subsynchronous frequency component is obtained by judging the value of the reduced natural frequency; the inertia time constant of the new mass block is the sum of the two mass blocks before combination, the stiffness coefficients of the combined mass blocks are distributed in proportion, and the specific calculation formula is as follows:
M j ＝M i +M i+1 (1-1)
in the above formula, i represents the position number of the prime block before merging, j represents the position number of the merged prime block, and M 1 Is the inertial time constant of the first mass, K 1 Is the stiffness coefficient between mass 1 and mass 2;
selecting reserved subsynchronous frequency components from torsional vibration frequencies provided by a power plant, and recording as follows:
rest_f＝[rest_f 1 ，rest_f 2 ，…，rest_f k ] (1-4)
where rest _ f is the reserved subsynchronous frequency, rest _ f k For the reserved kth frequency;
(2) Combining the generator multi-mass blocks one by one, calculating new torsional vibration frequency by using the combined inertia time constant M and the rigidity coefficient K between the mass blocks, and comparing the new torsional vibration frequency with the reserved subsynchronous torsional vibration frequency component;
(3) Obtaining a shafting equivalent model only containing subsynchronous torsional vibration frequency components, and calculating an inertia time constant M after combination and a rigidity coefficient K between the mass blocks;
(4) Correcting the rigidity coefficient K between the mass blocks by utilizing a particle swarm algorithm;
(5) The precision is satisfied: if the precision requirement is met, the next step (6) is carried out; if not, returning to the step (4);
(6) And outputting the optimized parameters.
2. The method for simplifying the parameters of the multiple mass blocks of the generator shaft system by using the particle swarm optimization algorithm according to claim 1, wherein the steps (2) and (3) are specifically to combine two adjacent mass blocks, and calculate the inertia time constant of the shaft system after combination and the stiffness coefficient between the mass blocks according to the formulas (1-1), (1-2) and (1-3); when two adjacent masses are combined, the combined natural frequency is recorded as:
f＝[f 1 ,f 2 ,…,f h ] (1-5)
in the above formula, f h For the reserved h frequency;
and (3) respectively subtracting the reserved frequency components in the formulas (1-4) from the h frequencies in the formulas (1-5), and taking the minimum value of the absolute values of the reserved frequency components as T:
T＝[T 1 ,T 2 ,…,T k ] (1-6)
in the above formula, T k Comprises the following steps:
T k ＝min{|rest_f k -f 1 |,|rest_f k -f 2 |,…,|rest_f k -f h |} (1-7)
rest _ f in the above equation k I.e. the retained k-th frequency component, f h The same formula (1-5);
at this time, if T k If the value of (A) is close to zero, it means that the frequency components are not merged, otherwise, it means that the frequency components exist in the neighboring massTo determine that the location needs to be reserved; judging whether the merged mass blocks contain the low-frequency components to be reserved or not according to whether the maximum value in the T is close to zero or not, and if the maximum value of the T is close to zero, not containing the low-frequency components to be reserved; here, if the number of the mass blocks is n, the number of merging times is n-1 times, and n-1 maxT can be obtained correspondingly, which is denoted as S:
S＝[S 1 ,S 2 ,…,S n-1 ] (1-8)
in the above formula S n-1 Represents the maximum value corresponding to the formula (1-6) after each combination;
and determining the position of the reserved subsynchronous frequency component according to the position of the maximum value of the number of the first k reserved frequencies in the S, combining the rest of the mass blocks, and simultaneously calculating corresponding inertia time constants and rigidity coefficients among the mass blocks according to the formulas 1-3.
3. The method for simplifying parameters of multiple mass blocks of a generator shaft system by using a particle swarm optimization algorithm according to claim 1, wherein in the step (4), in order to take the parameters after preliminary combination into consideration, certain errors are generated, the parameters are corrected based on the particle swarm optimization algorithm, the value of an inertia time constant is mainly determined by the mass of the mass block of the shaft system, the value is easily and accurately obtained, the rigidity coefficient among the mass blocks is corrected more reasonably, the value of the inertia time constant is reserved, and the rigidity coefficient among the mass blocks is corrected to correspondingly check an equivalent shaft system model, so that the consistency of the vibration mode trend of the equivalent shaft system is ensured;
in each iteration process, the particle updates the speed and position of the particle through the individual extremum and the group extremum, and the updating formula is as follows:
in the formula, each coefficient represents the following meaning:
c 1 ,c 2 -acceleration constant, adjusting the maximum step size of learning;
r 1 ,r 2 -two random functions, value range [0,1]To increase search randomness;
omega-inertial weight, non-negative number, adjusts the search range for the solution space;
in order to ensure the rapidity of the search, the inertia weight omega is set to be the formula 1-11, the inertia weight is ensured to be decreased, so that the search range can be ensured to be reduced when the vicinity of the optimal solution is reached,
in the formula, ω start ＝0.9，ω end =0.4,maxgen for population size.
4. The method for simplifying generator shaft system multi-mass block parameters by using particle swarm optimization algorithm as claimed in claim 1, wherein the specific operation of step (5) is to use the sum of the absolute values of the difference between the measured frequency and the calculated frequency as the fitness function value
fitness＝|f 1 -real_f 1 |+|f 2 -real_f 2 |+…+|f r -real_f s | (1-12)
In the formula, real _ f s For the measured frequency value, f r To calculate the frequency;
setting a jump-out circulation condition:
fitness＝ε<10 -4 (1-13)
the whole searching and updating process of the particle swarm algorithm is a process following the current optimal solution, the convergence speed of the algorithm is high, and when the maximum iteration times are reached, maxgen =50 is set; or jumping out of the cycle after the formula 1-13 is satisfied to obtain the current optimal solution, namely the rigidity coefficient among the mass blocks.
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