CN113514784B - Method for detecting and judging mechanical state of transformer winding under no-load closing - Google Patents
Method for detecting and judging mechanical state of transformer winding under no-load closing Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/50—Testing of electric apparatus, lines, cables or components for short-circuits, continuity, leakage current or incorrect line connections
- G01R31/72—Testing of electric windings
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01H—MEASUREMENT OF MECHANICAL VIBRATIONS OR ULTRASONIC, SONIC OR INFRASONIC WAVES
- G01H17/00—Measuring mechanical vibrations or ultrasonic, sonic or infrasonic waves, not provided for in the preceding groups
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/50—Testing of electric apparatus, lines, cables or components for short-circuits, continuity, leakage current or incorrect line connections
- G01R31/62—Testing of transformers
Abstract
The invention relates to a method for detecting and judging a mechanical state of a transformer winding under no-load closing, and belongs to the technical field of safety monitoring of power transformers. According to the method, time domain vibration acceleration signals generated by testing transformers of the same type in four states under no-load closing are decomposed by WOA-VMD to obtain IMF1 component spectrum peaks at three frequencies of 100Hz, 200Hz and 400Hz respectively, and four conditions of the transformers of the same type in four states are obtained; and then collecting time domain vibration acceleration signals of the transformer to be detected when no-load switching-on is performed, obtaining IMF1 component spectrum peaks at three frequencies of 100Hz, 200Hz and 400Hz after WOA-VMD decomposition, and comparing the IMF1 component spectrum peaks at the three frequencies of the transformer to be detected by taking the four conditions obtained in the previous step as judgment conditions to judge that the mechanical state of the winding of the transformer to be detected belongs to one of the four states. The detection and judgment method provided by the invention is timely, accurate, reliable, simple, convenient and easy to implement.
Description
Technical Field
The invention relates to a method for detecting and judging a mechanical state of a transformer winding under an idle load closing condition. Belongs to the technical field of safety monitoring of power transformers.
Background
The power transformer is used as important equipment in the power system, plays roles of voltage conversion, electric energy distribution and electric energy transmission, and the normal operation of the power transformer is an important guarantee of safe, reliable, high-quality and economic operation of the power system. Statistical analysis shows that a significant number of transformer faults result from winding loosening deformations. The loose deformation of the winding is used as a latent defect of the transformer winding, and early warning is an effective means for preventing fault expansion. At present, a diagnosis transformer winding has an online method such as a short-circuit reactance method, a steady-state current vibration method and the like. Based on the poor early warning capability of the characteristic offline diagnosis method caused by the disturbance of the short circuit fault in the operation of the transformer, the diagnosis is lagged; the transformer winding fault diagnosis method based on the steady-state vibration signals has weak anti-interference capability, and the sensitivity and accuracy of fault diagnosis and fault degree identification are low.
The vibration signal of the transformer in operation is mainly superposition of core vibration and winding vibration. When the transformer is impacted by exciting surge, the amplitude of the impact current is far higher than the rated current, the vibration of the winding is far greater than the vibration of the iron core, and the vibration of the transformer is considered to be mainly caused by the vibration of the winding when the surge is impacted. Existing vibration analysis methods detect the winding state of a transformer by measuring vibration signals transmitted to the wall of a tank, but lack a method of judging the mechanical state of the winding by analyzing the vibration signals.
Disclosure of Invention
The invention aims to solve the technical problems that: and judging the mechanical state of the transformer winding by utilizing the vibration signal of the transformer.
The technical scheme provided by the invention for solving the technical problems is as follows: a method for detecting and judging the mechanical state of a transformer winding under no-load closing is carried out by the following steps:
1) The same type of transformer in the following four states is selected for testing,
(1) the winding 100% normal compression force is in a first state of normal mechanical condition without looseness,
(2) the winding 90% standard compression is in the second state of 10% slightly loose mechanical state,
(3) the winding 70% normal compression is in the third state of 30% moderate loosening mechanical state,
(4) a fourth state in which 50% of the normal compaction force of the winding is at 50% of the severely loose mechanical state;
arranging vibration acceleration sensors on the transformers of the same type in four states respectively, and collecting time domain vibration acceleration signals of the transformers of the same type in four states when in idle load closing respectively;
2) The time domain vibration acceleration signal acquired in the step 1) is decomposed by WOA-VMD to obtain IMF1 component spectrum peaks at three frequencies of 100Hz, 200Hz and 400Hz, and four conditions of the same type of transformers in the four states are respectively as follows:
A. in the first state, the IMF1 component spectral peak value at 100Hz is greater than 3 times the IMF1 component spectral peak value at 400Hz, or the IMF1 component spectral peak value at 200Hz is greater than 7 times the IMF1 component spectral peak value at 400 Hz;
B. in the second state, the IMF1 component spectral peak value at 100Hz is greater than 5 times the IMF1 component spectral peak value at 400Hz, or the IMF1 component spectral peak value at 200Hz is greater than 7 times the IMF1 component spectral peak value at 400 Hz; the method comprises the steps of carrying out a first treatment on the surface of the
C. In the third state, the IMF1 component spectral peak at 400Hz is greater than 4 times the IMF1 component spectral peak at 100Hz or greater than 7 times the IMF1 component spectral peak at 200 Hz; the method comprises the steps of carrying out a first treatment on the surface of the
D. In the fourth state, the IMF1 component spectral peak value at 400Hz is greater than 25 times the IMF1 component spectral peak value at 100Hz or greater than 14 times the IMF1 component spectral peak value at 200 Hz;
3) Arranging a vibration acceleration sensor on a transformer to be detected, which is actually ready to be put into operation, and collecting vibration acceleration signals of the transformer to be detected during idle load closing;
4) And 3) decomposing the vibration acceleration signal acquired in the step 3) through WOA-VMD to obtain IMF1 component spectrum peaks at three frequencies of 100Hz, 200Hz and 400Hz, and comparing the IMF1 component spectrum peaks at the three frequencies of the transformer to be detected by taking the four conditions obtained in the step 2) as judgment conditions to judge that the winding mechanical state of the transformer to be detected belongs to one of the four states.
Further, the specific steps of WOA-VMD decomposition are as follows:
(1) the whale algorithm is utilized to optimize the VMD parameter decomposition layer number k and the penalty factor alpha, and the initial values of k and alpha are respectively set to be 5 and 2000.
(2) Initializing population scale, iteration times and self-adaptive weight values of a whale optimization algorithm, taking an adaptation function F, wherein IMF energy entropy is shown as the following formula (1) fit The inverse of the energy entropy average value of each IMF is expressed as the following formula (2),
wherein E is k For the energy of the kth order IMF component,the energy of the k-th order IMF component accounts for the total energy specific gravity of the signal;
(3) calculating the fitness value of each whale, and comparing the fitness values with each other to determine the optimal whale with the current fitness;
(4) entering an algorithm main loop, and updating the position according to the values of p and |G|;
(5) evaluating the whole population, and determining the global optimal whale position;
(6) repeating the steps (3) to (5) until the maximum iteration number is reached, and outputting the optimal combination of k and alpha;
(7) VMD is initialized with the optimal k and alpha parameters and the vibration signal is decomposed into IMF1 component spectral peaks at three frequencies, 100Hz, 200Hz and 400 Hz.
Still further, the whale optimization algorithm is as follows:
1) Assuming that the population size of whales is N, the position of the ith whale in the solution space for solving the D-dimensional optimization problem isThe algorithm assumes the location of the problem variable to be optimized and its solution to the optimal whale (prey);
2) In the surrounding prey stage, assuming that the current best-after-optimal solution is close to the best whale position, then the other whales automatically update their own positions, and the position update equation is as follows (3):
in the formula (3), D is the optimal candidate solution position, G and C are coefficients, n E (1, n) max ) Is the current iteration number, X * (n) is the optimal solution for the nth iteration, X (n) is the position of the whale for the nth iteration, r.epsilon.0, 1]Is a random number, a decreases linearly from 2 to 0 with increasing iteration number;
3) In the local search stage, a surrounding mechanism or a spiral bubble mode is selected, and then the local search position update equation is as follows (4):
in the formula (4), p is [0,1 ]]Is a random number, D' = |x * (n) -X (n) | is the distance between the ith whale and the optimal whale, l.epsilon. -1,1]Is a random number, b is a spiral constant, e is a base of a natural logarithmic function;
4) In the global search stage, the algorithm is allowed to perform global search by using the convergence factor |G| and when |G| > 1, the position update equation for performing global search is as follows (5):
D＝|CX rand (n)-X(n)|
X(n+1)＝X rand (n)-AD (5)；
in the formula (5), X rand Is the position of a whale randomly in the current iterative population.
In the above searching scheme, the vibration acceleration sensors are three of A, B, C three phases arranged on the transformer, and are equidistantly distributed between the high-voltage insulation terminal and the low-voltage insulation terminal of the transformer.
The beneficial effects of the invention are as follows: and decomposing the acquired time domain vibration acceleration signal of the transformer winding under no-load closing by using WOA-VMD (variation modal decomposition optimized by whale optimization algorithm) to obtain IMF1 component spectrum peaks at three frequencies of 100Hz, 200Hz and 400Hz respectively, and judging the mechanical state of the transformer winding by taking the relation of the respective duty ratios of the IMF1 component spectrum peaks at the three frequencies as the condition. Compared with the existing detection and analysis method for the mechanical state of the transformer winding, the detection and judgment method provided by the invention has the advantages of timely, accurate, reliable, simple, convenient and easy diagnosis.
Furthermore, it should be noted that: according to the invention, the mechanical state of the transformer winding is judged by measuring the time domain vibration acceleration signal of the transformer winding under no-load closing and then decomposing the time domain vibration acceleration signal by a WOA-VMD algorithm to obtain an IMF1 component spectrum peak value, and the invention is based on the fact that the internal relation exists between the axial acceleration of the transformer winding and the power frequency of the transformer winding under short circuit impact. The inventors have derived by theory that the expression of the transformer winding axial acceleration under short-circuit impact with respect to time t is as follows (6),
in the formula (6), a y Is the axial acceleration of the winding, A y 、B 1 、B 3 、G y Is a dimensionless coefficient, C' y Is the damping coefficient, M is the total mass of winding wire cake, gamma is the initial phase angle of voltage during closing, omega 0 Is the power angular frequency at the closing moment, beta is the breaking angle of excitation surge current in one period, omega is the power angular frequency, T is the circuit time constant, and θ=arctan [ (1-omega) 2 T 2 )/2ωT]And
is a function of ω, K' y Is the stiffness coefficient and e is the base of the natural logarithmic function.
From (6), it is known that the vibration signal characteristic quantity (a) of the vibration characteristic (axial acceleration) of the winding when the transformer receives the surge current y ) Is an even harmonic of the power supply frequency (ω). Thus, changes in the mechanical dynamics of the transformer winding due to loosening or deformation of the transformer winding can be reflected by the vibrational acceleration signal of the transformer winding under a short circuit impact.
The formula (6) reflects the scientific and theoretical findings of the inventor, and the derivation process of the formula is complex and does not belong to the scope of patent, so that the invention only indicates that the winding vibration acceleration signal is related to the power frequency through the formula (6), and the specific derivation process of the formula is not described herein.
Drawings
The method for detecting and judging the mechanical state of the transformer winding under no-load closing is further described below with reference to the accompanying drawings.
Fig. 1 is a schematic diagram of a structure in which a vibration acceleration sensor is mounted on a transformer in the first embodiment.
Fig. 2 is a graph of vibration acceleration signals collected by a transformer a phase 1.
Fig. 3 is a graph of time domain signals of IMF1 components of each order after WOA-VMD decomposition of winding vibration time domain signals measured for phase 1 of a transformer of example one.
Fig. 4 is a graph of frequency domain signals of the vibration acceleration signal in the first state after the fast fourier transform.
Fig. 5 is a graph of a frequency domain signal of the vibration acceleration signal in the second state after the fast fourier transform.
Fig. 6 is a graph of a frequency domain signal of a vibration acceleration signal in a third state after a fast fourier transform.
Fig. 7 is a graph of a frequency domain signal of the vibration acceleration signal in the fourth state after the fast fourier transform.
Detailed Description
Examples
The method for detecting and judging the mechanical state of the transformer winding under no-load closing comprises the following steps:
1) The same type of transformer in the following four states is selected for testing,
(1) the winding 100% normal compression force is in a first state of normal mechanical condition without looseness,
(2) the winding 90% standard compression is in the second state of 10% slightly loose mechanical state,
(3) the winding 70% normal compression is in the third state of 30% moderate loosening mechanical state,
(4) the winding 50% standard pinch force is in the fourth state of 50% severely loose mechanical state.
Vibration acceleration sensors are respectively arranged, and vibration acceleration signals of the transformers of the same model in four states during no-load closing are respectively collected;
as shown in fig. 1, vibration acceleration sensors 10 are respectively arranged on the same type of transformer in four states, three vibration acceleration sensors are respectively arranged on each phase of a transformer A, B, C, nine vibration acceleration sensors are respectively numbered 1, 2, 3, 4, 5, 6, 7, 8 and 9 in the figure, and the positions of the nine vibration acceleration sensors are equidistantly distributed between a high-voltage insulation terminal 11 and a low-voltage insulation terminal 12. After closing, time domain vibration acceleration signals of the four transformers during no-load closing are respectively acquired; in this embodiment, for convenience of explanation, a vibration acceleration signal collected by a vibration acceleration sensor denoted by the a-phase reference numeral 1 is taken as an example.
2) The time domain vibration acceleration signal acquired in the step 1) is decomposed by WOA-VMD to obtain IMF1 component spectrum peaks at three frequencies of 100Hz, 200Hz and 400Hz respectively, the acquired vibration acceleration signal is decomposed by WOA-VMD to obtain IMF1 component spectrum peaks at three frequencies of 100Hz, 200Hz and 400Hz respectively as shown in figure 2, WOA is a whale optimization algorithm, VMD is a variation modal decomposition, and WOA-VMD combines and applies the whale optimization algorithm and the variation modal decomposition, and the method is as follows:
(1) the whale algorithm is utilized to optimize the VMD parameter decomposition layer number k and the penalty factor alpha, and the initial values of k and alpha are respectively set to be 5 and 2000.
(2) Initializing population scale, iteration times and self-adaptive weight values of a whale optimization algorithm, taking an adaptation function F, wherein IMF energy entropy is shown as the following formula (1) fit The inverse of the energy entropy average value of each IMF is expressed as the following formula (2),
in the formula (1), E k For the energy of the kth order IMF component,the energy of the k-th order IMF component accounts for the total energy specific gravity of the signal;
(3) calculating the fitness value of each whale, and comparing the fitness values with each other to determine the optimal whale with the current fitness;
(4) entering an algorithm main loop, and updating the position according to the values of p and |G|;
(5) evaluating the whole population, and determining the global optimal whale position;
(6) repeating the steps (3) to (5) until the maximum iteration number is reached, and outputting the optimal combination of k and alpha;
(7) VMD is initialized with the optimal k and α parameters and the vibration signal is decomposed into IMF component spectral peaks at 100Hz, 200Hz and 400Hz frequencies as shown in table 1 below:
TABLE 1
The following four cases can be derived from table 1:
A. for the first transformer, the IMF1 component spectral peak value of 100Hz is more than 3 times of the IMF1 component spectral peak value of 400Hz, or the IMF1 component spectral peak value of 200Hz is more than 7 times of the IMF1 component spectral peak value of 400 Hz;
B. for the second transformer, the IMF1 component spectrum peak value of 100Hz is more than 5 times of the IMF1 component spectrum peak value of 400Hz, or the IMF1 component spectrum peak value of 200Hz is more than 7 times of the IMF1 component spectrum peak value of 400 Hz; the method comprises the steps of carrying out a first treatment on the surface of the
C. For the third transformer, the IMF1 component spectrum peak value of 400Hz is more than 4 times of the IMF1 component spectrum peak value of 100Hz or more than 7 times of the IMF1 component spectrum peak value of 200 Hz; the method comprises the steps of carrying out a first treatment on the surface of the
D. For the fourth transformer, its IMF1 component spectral peak at 400Hz is greater than 25 times or more than the IMF1 component spectral peak at 100Hz or greater than 14 times or more than the IMF1 component spectral peak at 200 Hz.
3) Arranging a vibration acceleration sensor on a transformer to be detected, which is actually ready for input, and collecting vibration acceleration signals of the transformer during no-load closing;
4) And 3) decomposing the vibration acceleration signal acquired in the step 3) through WOA-VMD to obtain IMF1 component spectrum peaks at three frequencies of 100Hz, 200Hz and 400Hz, wherein the specific decomposition process is as described above and is not repeated here.
And (2) comparing the IMF1 component spectrum peaks of the three frequencies by taking the four conditions obtained in the step (2) as judging conditions to judge which of the four transformers the mechanical state of the transformer winding to be detected belongs to. The IMF component spectral peaks of the decomposed vibration signal of this example into 100Hz, 200Hz and 400Hz frequencies are shown in table 2 below:
TABLE 2
As can be seen from comparison, the present embodiment meets the above condition B, so that it can be determined that the mechanical state of the transformer winding detected in the present embodiment is slightly loose.
FIG. 3 is a graph showing the vibration time domain signal of the transformer winding obtained from the measuring point No. 1 of the phase A of the present embodiment, and the time domain signal of each IMF component after the decomposition of WOA-VMD; fig. 4-7 are graphs of frequency domain signals of IMF component time domain signals of four states after fast fourier transform.
The whale optimization algorithm in step 2) above is conventional (see Mirjallii S, lewis A. The whale optimization algorithm whale optimization algorithm [ J ]. Advances in engineering software software engineering development, 2016, 95:51-67). The present embodiment gives the algorithm as follows:
1) Assuming that the population size of whales is N, the position of the ith whale in the solution space for solving the D-dimensional optimization problem isThe algorithm assumes the location of the problem variable to be optimized and its solution to the optimal whale (prey);
2) In the surrounding prey stage, assuming that the current best-after-optimal solution is close to the best whale position, then the other whales automatically update their own positions, and the position update equation is as follows (3):
in the formula (3), D is the optimal candidate solution position, G and C are coefficients, n E (1, n) max ) Is the current iteration number, X * (n) is the optimal solution for the nth iteration, X (n) is the position of the whale for the nth iteration, r.epsilon.0, 1]Is a random number, a decreases linearly from 2 to 0 with increasing iteration number;
3) In the local search stage, a surrounding mechanism or a spiral bubble mode is selected, and then the local search position update equation is as follows (4):
in the formula (4), p is [0,1 ]]Is a random number, D' = |x * (n) -X (n) | is the distance between the ith whale and the optimal whale, l.epsilon. -1,1]Is a random number, b is a spiral constant, e is a base of a natural logarithmic function;
4) In the global search stage, the algorithm is allowed to perform global search by using the convergence factor |G| and when |G| > 1, the position update equation for performing global search is as follows (5):
in the formula (5), X rand Is the position of a whale randomly in the current iterative population.
Example two
The method for detecting and judging the mechanical state of the transformer winding under no-load closing in this embodiment is the same as that in the first embodiment, except that: the vibration acceleration signal in the 4) step is decomposed by WOA-VMD to obtain IMF1 component spectrum peaks at three frequencies of 100Hz, 200Hz and 400Hz as shown in the following table 3:
TABLE 3 Table 3
As can be seen from comparison, the present embodiment meets the above condition C, so that it can be determined that the mechanical state of the transformer winding detected in the present embodiment is moderately loose.
The foregoing description is only of the preferred embodiments of the invention, but the invention is not limited thereto, and all equivalents and modifications according to the concept of the invention and the technical solutions thereof are intended to be included in the scope of the invention.
Claims (4)
1. A method for detecting and judging the mechanical state of a transformer winding under no-load closing is carried out by the following steps:
1) The same type of transformer in the following four states is selected for testing,
(1) the winding 100% normal compression force is in a first state of normal mechanical condition without looseness,
(2) the winding 90% standard compression is in the second state of 10% slightly loose mechanical state,
(3) the winding 70% normal compression is in the third state of 30% moderate loosening mechanical state,
(4) a fourth state in which 50% of the normal compaction force of the winding is at 50% of the severely loose mechanical state;
arranging vibration acceleration sensors on the transformers of the same type in four states respectively, and collecting time domain vibration acceleration signals of the transformers of the same type in four states when in idle load closing respectively;
2) The time domain vibration acceleration signal acquired in the step 1) is decomposed by WOA-VMD to obtain IMF1 component spectrum peaks at three frequencies of 100Hz, 200Hz and 400Hz, and four conditions of the same type of transformers in the four states are respectively as follows:
A. in the first state, the IMF1 component spectral peak value at 100Hz is greater than 3 times the IMF1 component spectral peak value at 400Hz, or the IMF1 component spectral peak value at 200Hz is greater than 7 times the IMF1 component spectral peak value at 400 Hz;
B. in the second state, the IMF1 component spectral peak value at 100Hz is greater than 5 times the IMF1 component spectral peak value at 400Hz, or the IMF1 component spectral peak value at 200Hz is greater than 7 times the IMF1 component spectral peak value at 400 Hz;
C. in the third state, the IMF1 component spectral peak at 400Hz is greater than 4 times the IMF1 component spectral peak at 100Hz or greater than 7 times the IMF1 component spectral peak at 200 Hz;
D. in the fourth state, the IMF1 component spectral peak value at 400Hz is greater than 25 times the IMF1 component spectral peak value at 100Hz or greater than 14 times the IMF1 component spectral peak value at 200 Hz;
3) Arranging a vibration acceleration sensor on a transformer to be detected, which is actually ready to be put into operation, and collecting a time domain vibration acceleration signal of the transformer to be detected when the transformer to be detected is in idle load closing;
4) And 3) decomposing the time domain vibration acceleration signal acquired in the 3) through WOA-VMD to obtain IMF1 component spectrum peaks at three frequencies of 100Hz, 200Hz and 400Hz, and comparing the IMF1 component spectrum peaks at the three frequencies of the transformer to be detected by taking the four conditions obtained in the 2) as judging conditions to judge that the winding mechanical state of the transformer to be detected belongs to one of the four states.
2. The method according to claim 1, wherein: the specific steps of WOA-VMD decomposition are as follows:
(1) optimizing the number k of VMD parameter decomposition layers and the penalty factor alpha by using a whale algorithm, and setting the initial values of k and alpha to be 5 and 2000 respectively;
(2) initializing population scale, iteration times and self-adaptive weight values of whale optimization algorithm, and IMF energy entropyAnd is of the following formula (1)Taking fitness function F fit For each IMF energy entropy->The inverse of the average value is expressed as (2),
in the formula (1), E k For the energy of the kth IMF component, p k ＝E k the/E is the energy specific gravity of the kth IMF component to the total energy of the signal,
(3) calculating the fitness value of each whale, and comparing the fitness values with each other to determine the optimal whale with the current fitness;
(4) entering an algorithm main loop, and updating the position according to the values of p and |G|;
(5) evaluating the whole population, and determining the global optimal whale position;
(6) repeating the steps (3) to (5) until the maximum iteration number is reached, and outputting the optimal combination of k and alpha;
(7) VMD is initialized with the optimal k and alpha parameters and the vibration signal is decomposed into IMF1 component spectral peaks at three frequencies, 100Hz, 200Hz and 400 Hz.
3. The method according to claim 2, characterized in that: the whale optimization algorithm is as follows:
1) Assuming that the population size of whales is N, the position of the ith whale in the solution space for solving the D-dimensional optimization problem isThe algorithm assumes the problem variables to be optimized and the locations where the solution to the problem variables is the optimal whale prey;
2) In the surrounding prey stage, assuming that the current best-after-optimal solution is close to the best whale position, then the other whales automatically update their own positions, and the position update equation is as follows (3):
in the formula (3), D is the optimal candidate solution position, G and C are coefficients, n E (1, n) max ) Is the current iteration number, X * (n) is the optimal solution for the nth iteration, X (n) is the position of the whale for the nth iteration, r.epsilon.0, 1]Is a random number, a decreases linearly from 2 to 0 with increasing iteration number;
3) In the local search stage, a surrounding mechanism or a spiral bubble mode is selected, and then the local search position update equation is as follows (4):
in the formula (4), p is [0,1 ]]Is a random number, D' = |x * (n) -X (n) | is the distance between the ith whale and the optimal whale, l.epsilon. -1,1]Is a random number, b is a spiral constant, e is a base of a natural logarithmic function;
4) In the global search stage, the algorithm is allowed to perform global search by using the convergence factor |G| and when |G| > 1, the position update equation for performing global search is as follows (5):
D＝|CX rand (n)-X(n)|
X(n+1)＝X rand (n)-AD (5)；
in the formula (5), X rand Is the position of a whale randomly in the current iterative population.
4. The method according to claim 1, wherein: the vibration acceleration sensor is three of A, B, C three phases arranged on the transformer and is equidistantly distributed between a high-voltage insulating terminal and a low-voltage insulating terminal of the transformer.
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