CN110221147B - Power quality detection and analysis method based on multi-composite optimization algorithm - Google Patents

Power quality detection and analysis method based on multi-composite optimization algorithm Download PDF

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CN110221147B
CN110221147B CN201910501158.XA CN201910501158A CN110221147B CN 110221147 B CN110221147 B CN 110221147B CN 201910501158 A CN201910501158 A CN 201910501158A CN 110221147 B CN110221147 B CN 110221147B
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李征
詹振辉
刘帅
孟浩
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Donghua University
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Abstract

The invention relates to a power quality detection and analysis method of a multi-composite optimization algorithm. The invention firstly adopts EEMD method to denoise and decompose the sampled electric signal. The amplitude, frequency, attenuation factor and initial phase angle of each of the decomposed IMFs are then processed using the Prony algorithm. In order to improve the accuracy and precision of calculation, the improved dragonfly algorithm is added in the calculation process to be combined with the Prony algorithm to obtain a new intelligent algorithm (temporarily called DP algorithm in the invention) to solve the IMF. In order to obtain better effect, the invention introduces signal-to-noise ratio in DP algorithm, so as to judge the accuracy of the algorithm, and the final result is more accurate.

Description

Power quality detection and analysis method based on multi-composite optimization algorithm
Technical Field
The invention relates to a power quality detection and analysis method based on a multi-composite optimization algorithm, and belongs to the technical field of power quality detection and analysis of a power grid.
Background
In recent years, rapid development of social economy and continuous improvement of social productivity rapidly improve the living standard of people and rapidly increase the power load of a power supply network. Various impact loads and nonlinear loads in a power grid are rapidly increased, various high-precision equipment is widely applied to a power system, particularly, the condition of electric energy quality in the power system is more and more complicated along with the grid connection of new energy, such as wind power generation, photovoltaic power generation and the like, which has low stability and high randomness, and the electric energy quality problem has attracted more and more attention of various social circles. Therefore, the detection problem of the power quality by related departments is more and more emphasized. However, in reality, discrete data of a power system is often affected by a plurality of error causes at the same time, and the data includes attenuated dc components, inter-harmonics, noise, and the like. Accurately extracting parameters such as amplitude, frequency and the like of periodic signals in the power fault transient signals is important for state analysis, fault diagnosis, control and protection of a power system. The study of scholars at home and abroad has been extensively and intensively conducted. How to extract the characteristic information of the power quality disturbance signal is the basis of the identification and correct classification of the power quality disturbance signal.
Disclosure of Invention
The invention aims to provide a method for detecting and analyzing the quality of electric energy.
In order to achieve the above object, the technical solution of the present invention is to provide a power quality detection and analysis method of a multi-composite optimization algorithm, which is characterized by comprising the following steps:
step 1, EEMD decomposition is carried out after denoising a sampled power failure transient signal by adopting an EEMD method, each IMF component is obtained after EEMD decomposition, and the ith IMF component is recorded as cki(t), performing integration average processing on the IMF components obtained each time, and recording the ith IMF component obtained after processing as ci(t)，
Figure BDA0002090262620000011
N is the total number of the Gaussian white noise, the larger N is, the larger the corresponding IMF sum of the Gaussian white noise tends to be 0, and the more the decomposition result approaches to the true value;
step 2, setting the maximum iteration times TmaxSetting a signal-to-noise ratio threshold SNR', and setting the iteration number t to be 0;
and 3, substituting each IMF component obtained in the step 1 as an initial value of a dragonfly algorithm to calculate the separation degree, the alignment degree, the cohesion degree, the food attraction force and the natural enemy repulsion force of each dragonfly individual, wherein:
the separation degree of the ith dragonfly individual is SiThen, there are:
Figure BDA0002090262620000021
wherein X represents the position of the ith dragonfly individual, and X represents the position of the ith dragonfly individualjThe position of the dragonfly individuals adjacent to X is shown, and N dragonfly individuals adjacent to X are shared;
the ith dragonfly individualAlignment degree of AiThen, there are:
Figure BDA0002090262620000022
in the formula, VjRepresenting the speed of the dragonfly individual adjacent to X;
the cohesion degree of the ith dragonfly individual is CiThen, there are:
Figure BDA0002090262620000023
the food attraction of the ith dragonfly individual is FiThen, there are:
Fi＝X+-X
in the formula, X+Indicating a food source location;
the repulsive force of the ith individual dragonfly is EiThen, there are:
Ei＝X-+X
in the formula, X-Representing the position of the natural enemy;
step 4, setting an alignment degree weight a, a separation degree weight s, a cohesion degree weight c and an inertia factor w, and calculating to obtain an improved natural enemy factor e 'and an improved food factor f':
f'＝λ·f
e'＝β·e
wherein f represents a food factor before improvement, e represents a natural enemy factor before improvement,
Figure BDA0002090262620000024
Figure BDA0002090262620000031
step 5, obtaining the updated position X of the improved dragonfly according to the improved natural enemy factor e' and the food factor ft+1Then, there are:
ΔXt+1＝(sSi+aAi+cCi+f'Fi+e'Ei)+wΔXt
Xt+1＝Xt+ΔXt+1
in the formula,. DELTA.XtIndicates the update step size, XtThe current position of the ith dragonfly individual;
step 6, setting the new position parameter Xt+1Bringing in
Figure BDA0002090262620000032
To solve for
Figure BDA0002090262620000033
Bring results into
Figure BDA0002090262620000034
To find an objective function, wherein:
Figure BDA0002090262620000035
denotes the fitting estimate of x (n), akCoefficient of expression characteristic equation, bkDenotes the complex number corresponding to x (n) fitting estimate,
Figure BDA0002090262620000036
representing the complex number corresponding to the fitting estimated value x (n), and z represents an objective function;
step 7, calculating to obtain ak、Ak、θkAnd fk，AkIs the amplitude of the k order, fkIs the k-th order frequency, θkFor the k-th phase:
Ak＝|bk|
Figure BDA0002090262620000037
Figure BDA0002090262620000038
Figure BDA0002090262620000039
in the formula, zkRepresenting the root obtained by solving the polynomial, and delta t representing the sampling interval;
step 8, calculating to obtain the SNR,
Figure BDA00020902626200000310
t＝t+1；
step 9, if T is more than or equal to TmaxOr SNR < SNR', ending the method, otherwise, returning to the step 3.
The invention firstly adopts EEMD method to denoise and decompose the sampled electric signal. The amplitude, frequency, attenuation factor and initial phase angle of each of the decomposed IMFs are then processed using the Prony algorithm. In order to improve the accuracy and precision of calculation, the improved dragonfly algorithm is added in the calculation process to be combined with the Prony algorithm to obtain a new intelligent algorithm (temporarily called DP algorithm in the invention) to solve the IMF. In order to obtain better effect, the invention introduces signal-to-noise ratio in DP algorithm, so as to judge the accuracy of the algorithm, and the final result is more accurate.
Drawings
Fig. 1 and 2 are flow charts of the present invention.
Detailed Description
The invention is further elucidated with reference to the drawing. It should be understood that these examples are for illustrative purposes only and are not intended to limit the scope of the present invention. Further, it should be understood that various changes or modifications of the present invention may be made by those skilled in the art after reading the teaching of the present invention, and such equivalents may fall within the scope of the present invention as defined in the appended claims.
The invention provides a power quality detection analysis method of a multi-composite optimization algorithm, which is based on the following algorithm:
first) Prony algorithm
The Prony algorithm has been widely applied in signal analysis in recent years, and the feasibility of the Prony algorithm has been proved. The Prony algorithm can directly estimate the amplitude, frequency, attenuation factor, and initial phase angle in the signal.
Let x (0), x (1).. and x (N-1) be the sampled data. Then:
Figure BDA0002090262620000041
wherein N is 0,1,2, …, N-1; k is 1,2, …, P
Figure BDA0002090262620000042
Figure BDA0002090262620000043
bkRepresents the complex number corresponding to the fitting estimation value of x (n),
Figure BDA0002090262620000044
denotes the complex number, A, corresponding to the fitting estimate of x (n)kIs the amplitude of the k order, alphakIs a damping factor of the k-th order, fkIs the k-th order frequency, θkAt is the k-th order phase and Δ t is the sampling interval.
Constructing an objective function:
Figure BDA0002090262620000045
the solution using the difference equation is given below:
equation (1) is a homogeneous solution of the following constant coefficient linear difference equation:
Figure BDA0002090262620000051
assuming the estimation error is e (n), then
Figure BDA0002090262620000052
Therein
Figure BDA0002090262620000053
Thus, x (n) can be viewed as the output of a P-th order AR model excited by noise u (n). Solving the regular equation of the AR model can obtain the parameter akSubstituting the formula and obtaining z by root finding of polynomialkWhere k is 1,2, …, P, the order P may be determined according to the AIC criterion of the AR model.
Figure BDA0002090262620000054
According to formula (1), then
Figure BDA0002090262620000055
Using least squares solution to obtain [ b1,b2…bP]T. B is formed bykIt is possible to obtain:
Ak＝|bk| (4)
Figure BDA0002090262620000056
Figure BDA0002090262620000057
Figure BDA0002090262620000058
in the above formula: k is 1,2, …, P
The fitted signal and the original signal have certain errors, and the signal-to-noise ratio is used for representing that: the larger the better, the signal-to-noise threshold SNR' is set as a criterion for evaluation.
Figure BDA0002090262620000059
Second) EEMD Process
When the power system normally operates, the waveform is relatively stable. The frequency, the amplitude, the initial phase and the attenuation factor of the signal are analyzed by using a Prony algorithm, the analysis process is simple, and the accuracy of the analysis result is high. However, when the harmonic pollution of the power system is serious, the Prony algorithm is susceptible to noise interference, so that the result analysis is inaccurate. In this case, noise-aided analysis can be applied to EMD by the improved EEMD method to promote anti-aliasing decomposition, and good noise reduction can be achieved while suppressing mode aliasing. The inherent modal component of the noise signal after EEMD decomposition better reveals the physical connotation of the original signal, so that the physical essence of the noise signal is clearer. Therefore, the invention firstly carries out EEMD decomposition on the signal and then carries out Prony analysis on each decomposed IMF component, thereby rapidly and accurately identifying the oscillation mode parameters.
The problem of aliasing of the traditional mode can be solved through multiple EMD after Gaussian white noise is superimposed. When the original signal is added to a white noise background with uniform frequency, signal regions with different time scales can be automatically mapped to a proper scale related to the white noise of the background. After the overall average value after noise is added for many times is averaged by using the principle that the statistical average value of an uncorrelated random sequence is 0, the noise is eliminated, and the overall average value is considered as a signal per se so as to eliminate the modal aliasing phenomenon. The algorithm steps are as follows.
(1) Normally distributed white noise sequence nk(t) to the time series x (t);
x'k(t)＝x(t)+nk(t) (9)
(2) adding the time sequence x after the normal distribution white noise sequencek(t) EMD decomposition is carried out on the whole to obtain each IMF component and the component is recorded as cki(t) and a remainder denoted as rkn(t)。
Figure BDA0002090262620000061
(3) Repeating the steps (1) and (2) for 100 times, and adding a new normal distribution white noise sequence each time;
(4) and performing integrated average processing on the IMF components obtained each time.
Figure BDA0002090262620000062
In the formula ci(t) represents the final i-th IMF component after EEMD decomposition. And N is the total number of the Gaussian white noise. The larger N is, the larger IMF sum of the corresponding white noise tends to be 0, and the more the decomposition result tends to be a true value.
Third) dragonfly algorithm
In the dragonfly algorithm, the individual dragonfly behaviors mainly include: the main functions of the actions are respectively to avoid mutual collision among individuals around the dragonfly group, ensure the speed consistency among the individuals around the group, ensure the movement of the individuals around the group to an average position, ensure the individuals in the group to be close to a food source and ensure the individuals in the group to avoid natural enemies. The specific meaning and mathematical expression method of these individual behaviors are as follows:
(1) the separation degree means avoiding collision between dragonfly and adjacent individual
Figure BDA0002090262620000071
(2) Registration refers to the tendency of adjacent individuals to maintain the same velocity.
Figure BDA0002090262620000072
(3) Cohesion means that the dragonfly tends to gather towards the centre of the adjacent individual.
Figure BDA0002090262620000073
(4) The food attraction refers to the attraction of food to dragonflies.
Fi＝X+-X (15)
(5) The repulsive force of natural enemy means the repulsive force of dragonfly to natural enemy
Ei＝X-+X (16)
Wherein, X represents the position of the current dragonfly individual; xjRepresents the position of the jth adjacent dragonfly individual; vjRepresenting the speed of the jth adjacent dragonfly individual; n represents the number of individuals adjacent to the ith dragonfly individual; x+Indicating a food source location; x-Indicating the location of the natural enemy. According to the 5 dragonfly behaviors, the step length and the position of the next generation dragonfly are calculated as follows:
Figure BDA0002090262620000074
in the above formula, t represents the current iteration number; i represents the ith dragonfly individual; xtRepresenting the current position of the t generation population; Δ Xt+1Representing the next generation population position updating step length; xt+1Representing the individual position of the next generation population; s represents a separation degree weight; a represents an alignment weight; c represents a cohesion weight; f represents a food factor; e represents a natural enemy factor; w represents the inertial weight.
Fourth) improved dragonfly algorithm:
the method aims to improve the rapidity and the accuracy of the dragonfly optimization algorithm. So as to better solve the target optimization problem, the following improvement strategies are proposed:
for f, a food factor; e represents the natural enemy factor to improve
Figure BDA0002090262620000081
Figure BDA0002090262620000082
The updated position of the improved dragonfly can be obtained according to the new weight factor as follows:
Figure BDA0002090262620000083
based on the above algorithm, the specific process of the electric energy quality detection and analysis method based on the multi-composite optimization algorithm provided by the invention is shown in the flow chart 1, and the steps are as follows:
(1) firstly, EEMD decomposition processing is carried out on the collected electric signals, specifically according to a formula x'k(t)＝x(t)+nk(t) adding normally distributed white noise. Adding the time sequence x after the normal distribution white noise sequencek(t) EMD decomposition is carried out on the whole to obtain each IMF component and the component is recorded as cki(t) and a remainder denoted as rkn(t) is that
Figure BDA0002090262620000084
And performing integrated average processing on the IMF components obtained each time.
Figure BDA0002090262620000085
In the formula ci(t) represents the final jth IMF component obtained after EEMD decomposition. N is the total number of the added Gaussian white noise, the larger N is, the IMF sum of the corresponding white noise tends to be 0, and the more the decomposition result approaches to the true value.
(2) Each c isi(t) as an initial value for the dragonfly algorithm
Figure BDA0002090262620000086
Figure BDA0002090262620000087
Fi＝X+-X；Ei＝X-+ X. Wherein X represents the position of the current dragonfly individual; xjRepresents the position of the jth adjacent dragonfly individual; vjIs shown asThe speed of j adjacent dragonfly individuals; n represents the number of individuals adjacent to the ith dragonfly individual; x+Indicating a food source location; x-represents the location of a natural enemy.
(3) Setting an alignment degree weight a, a separation degree weight s, a cohesion degree weight c and an inertia factor w according to a formula
f'＝λ·f
Figure BDA0002090262620000091
e'＝β·e
Figure BDA0002090262620000092
The coefficients e ', f' are calculated to update the coefficients.
(4) According to
Figure BDA0002090262620000093
To calculate the position of the next generation and to bring the new position parameters into the formula
Figure BDA0002090262620000094
To solve for
Figure BDA0002090262620000095
Substituting the result into a formula
Figure BDA0002090262620000096
To find the objective function.
(5) Let t be t +1 at the same time according to the formula
Figure BDA0002090262620000097
And calculating the signal-to-noise ratio, and judging whether the iteration times and the signal-to-noise ratio meet the conditions. Until the requirements are met, according to the formula:
Ak＝|bk|
Figure BDA0002090262620000098
Figure BDA0002090262620000099
Figure BDA00020902626200000910
to calculate Ak,ak,θk,fkAnd storing and outputting the result.
Through verification, the electric energy quality detection and analysis method based on the multi-composite optimization algorithm can better detect and analyze the electric energy quality of the power grid, and has relatively simple implementation process and good practical value.

Claims (1)

1. A power quality detection analysis method of a multi-composite optimization algorithm is characterized by comprising the following steps:
step 1, EEMD decomposition is carried out after denoising a sampled power failure transient signal by adopting an EEMD method, each IMF component is obtained after EEMD decomposition, and the ith IMF component is recorded as cki(T), performing integration average processing on the IMF components obtained each time, and recording the ith IMF component obtained after processing as ci(T)，
Figure FDA0002822064590000011
N is the total number of the Gaussian white noise, the larger N is, the larger the corresponding IMF sum of the Gaussian white noise tends to be 0, and the more the decomposition result approaches to the true value;
step 2, setting the maximum iteration times TmaxSetting a signal-to-noise ratio threshold SNR', and setting the iteration number t to be 0;
and 3, substituting each IMF component obtained in the step 1 as an initial value of a dragonfly algorithm to calculate the separation degree, the alignment degree, the cohesion degree, the food attraction force and the natural enemy repulsion force of each dragonfly individual, wherein:
the separation degree of the ith dragonfly individual is SiThen, there are:
Figure FDA0002822064590000012
wherein X represents the position of the ith dragonfly individual, and X represents the position of the ith dragonfly individualjThe position of the dragonfly individuals adjacent to X is shown, and N dragonfly individuals adjacent to X are shared;
the alignment degree of the ith dragonfly individual is AiThen, there are:
Figure FDA0002822064590000013
in the formula, VjRepresenting the speed of the dragonfly individual adjacent to X;
the cohesion degree of the ith dragonfly individual is CiThen, there are:
Figure FDA0002822064590000014
the food attraction of the ith dragonfly individual is FiThen, there are:
Fi＝X+-X
in the formula, X+Indicating a food source location;
the repulsive force of the ith individual dragonfly is EiThen, there are:
Ei＝X-+X
in the formula, X-Representing the position of the natural enemy;
step 4, setting an alignment degree weight a, a separation degree weight s, a cohesion degree weight c and an inertia factor w, and calculating to obtain an improved natural enemy factor e 'and an improved food factor f':
f'＝λ·f
e'＝β·e
wherein f represents a food factor before improvement, e represents a natural enemy factor before improvement,
Figure FDA0002822064590000021
Figure FDA0002822064590000022
step 5, obtaining the updated position X of the improved dragonfly according to the improved natural enemy factor e' and the food factor ft+1Then, there are:
ΔXt+1＝(sSi+aAi+cCi+f'Fi+e'Ei)+wΔXt
Xt+1＝Xt+ΔXt+1
in the formula,. DELTA.XtIndicates the update step size, XtThe current position of the ith dragonfly individual;
step 6, setting the new position parameter Xt+1Bringing in
Figure FDA0002822064590000023
To solve for
Figure FDA0002822064590000024
Bring results into
Figure FDA0002822064590000025
To find an objective function, wherein:
Figure FDA0002822064590000026
denotes the fitting estimate of x (n), akCoefficient of expression characteristic equation, bkDenotes the complex number corresponding to x (n) fitting estimate,
Figure FDA0002822064590000027
representing the complex number corresponding to the fitting estimated value x (n), and z represents an objective function;
step 7, calculating to obtain ak、Ak、θkAnd fk，AkIs the amplitude of the k order, fkIs the k-th order frequency, θkFor the k-th phase:
Ak＝|bk|
Figure FDA0002822064590000028
Figure FDA0002822064590000031
Figure FDA0002822064590000032
in the formula, zkRepresenting the root obtained by solving the polynomial, and delta t representing the sampling interval;
step 8, calculating to obtain the SNR,
Figure FDA0002822064590000033
t＝t+1；
step 9, if T is more than or equal to TmaxOr SNR<SNR', the method is ended, otherwise, step 3 is returned.
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