CN111523635A - Harmonic detection method based on combination of artificial bee colony algorithm and least square method - Google Patents

Harmonic detection method based on combination of artificial bee colony algorithm and least square method Download PDF

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CN111523635A
CN111523635A CN202010210558.8A CN202010210558A CN111523635A CN 111523635 A CN111523635 A CN 111523635A CN 202010210558 A CN202010210558 A CN 202010210558A CN 111523635 A CN111523635 A CN 111523635A
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聂晓华
胡方亮
万晓凤
余运俊
王淳
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Abstract

The invention discloses a harmonic detection method based on combination of an artificial bee colony algorithm and a least square method, relates to the technical field of electric power, and solves the problem that the artificial bee colony algorithm is easy to be premature by introducing Tent chaotic mapping; on the basis, Tent chaotic mapping is improved, and the problems of small cycle and unstable cycle points of chaotic mapping are solved. The Tent chaos improved artificial bee colony algorithm solves the problem that the artificial bee colony algorithm is easy to fall into a local optimum point, improves the solving precision and the convergence speed of the algorithm, is good in robustness, combines the improved artificial bee colony algorithm with a least square method, detects harmonic signals by using the fused algorithm, solves the problems that the least square algorithm is sensitive to an initial value and poor in detection precision, achieves quick, effective, accurate and stable detection of harmonic waves in load current, and has great reference value for effectively governing the harmonic waves and improving the power quality.

Description

Harmonic detection method based on combination of artificial bee colony algorithm and least square method
Technical Field
The invention relates to the technical field of electric power, in particular to a harmonic detection method based on combination of an artificial bee colony algorithm and a least square method.
Background
Due to the increase of the nonlinear load, a large amount of harmonics are injected into the grid system. The harmonic waves of the power grid system seriously affect the power quality of the power grid, and if the harmonic waves in the power grid are not treated, the harmonic waves cause great troubles and even economic losses for users and power suppliers. Harmonic suppression has an important historical position for supporting economic and social development by high-quality electric energy, and the significance of the harmonic suppression is self-evident. For harmonic suppression, firstly, the harmonic needs to be detected, the harmonic components are analyzed, and the harmonic components are detected. And then, according to the harmonic detection result, a harmonic treatment scheme is pertinently provided. The traditional algorithm for detecting the harmonic waves at present has the problems of sensitivity to initial values, spectrum leakage, barrier effect, frequency aliasing and the like.
Disclosure of Invention
In order to solve the problems in the prior art, the initial value of the least square algorithm is optimized by using a Tent chaos improved artificial Bee Colony (CABC) algorithm to obtain a chaos improved artificial Bee Colony algorithm on the basis of a traditional least square algorithm harmonic detection method (CIABC), so that the problem that the traditional least square algorithm is sensitive to the initial value is solved, the accuracy and the real-time performance of harmonic detection are greatly improved, and the steady-state error is reduced.
The invention specifically adopts the following technical scheme:
a harmonic detection method based on an artificial bee colony algorithm combined with a least square method comprises the following steps:
s1: on the basis of a standard Artificial Bee Colony algorithm, Tent Chaotic mapping is introduced into the Artificial Bee Colony algorithm for algorithm improvement, and a Chaotic Artificial Bee Colony (CABC) algorithm is provided; the CABC algorithm generates a chaotic sequence on the basis of the optimal food source searched by the whole bee colony;
s2: on the basis of the CABC algorithm, an improved Tent Chaotic map is introduced, and a chaos improved Artificial Bee Colony algorithm (CIABC) is provided;
s3: and optimizing unknown parameters by using a CIABC algorithm, taking an optimal value output by the algorithm as an initial value of the RLS algorithm, performing parameter estimation by using the RLS algorithm, and finally updating the weight to obtain the amplitude and the phase of the harmonic wave.
Further, the CABC algorithm is implemented by the following steps:
step 1: in the D-dimensional space, given iteration times M and a total number S of food sources, each hiring bee corresponds to one food source position, the number of the hiring bees is the same as that of the observation bees, and the hiring bees generate new positions in the field positions; all hiring bees share food source location information to the observing bees;
food source location update basis
Figure BDA0002422654020000021
Carrying out the following steps;
in the formula (I), the compound is shown in the specification,
Figure BDA0002422654020000022
a j dimension value representing the position of the ith honey source is initialized; i 1,2, … …, S, j 1,2, … …, D,
Figure BDA0002422654020000023
respectively the minimum value and the maximum value of the honey source position corresponding to the j dimension, wherein R is a random number between 0 and 1;
step 2: determining and selecting a food source by the observation bees according to the quality of the food source, and recording the position and the fitness value of the selected optimal food source;
performing a neighborhood search of the selected employer bee and observer bee locations based on
Figure BDA0002422654020000024
Position updating is carried out, wherein t is iteration times,
Figure BDA0002422654020000025
representing the t +1 th iterationThe position value of the j-th dimension of the newly generated first food source,
Figure BDA0002422654020000026
representing the j-dimensional position value of the ith food source at the t time of iteration; k is a randomly assigned individual, and k ≠ 1; r is [ -1, 1]A random number within a range;
and calculating and comparing fitness values of the new food sources, and replacing the original food source positions with honey source positions with more excellent food source quality.
And step 3: and the observation bees are greedy selected after each new position attempt, the positions are updated if the attempt succeeds, the original positions are maintained if the attempt fails, and if the failed times exceed the preset limit value, the quality of the food source is considered to be lower than the mining threshold. And if the position of the food source is kept unchanged, finishing the observation honeycomb search task. The corresponding employed bee discards the food source and no longer memorizes its location; hiring bees to become scout bees to start to randomly search for new food source positions;
and 4, step 4: recording the current optimal solution and position, finishing the algorithm when the iteration times of the algorithm reach the maximum M times, and outputting the fitness value of the optimal food source; if the maximum iteration times are not reached, judging whether the global optimal food source is updated or not; if so, repeating the step 2 to the step 3; otherwise according to
Figure BDA0002422654020000027
For conventional variables
Figure BDA0002422654020000028
Mapping transformation is carried out to obtain a chaotic variable which is between 0 and 1]Then pass through
Figure BDA0002422654020000029
To pair
Figure BDA00024226540200000210
Mapping to obtain a chaotic variable
Figure BDA0002422654020000031
Finally, theBy passing
Figure BDA0002422654020000032
To make chaotic variable
Figure BDA0002422654020000033
Conversion to conventional variables
Figure BDA0002422654020000034
And repeating the steps 2 to 3.
The further scheme is that the Tent chaotic mapping introduced in the step S1 is used for carrying out algorithm improvement, specifically, the Tent chaotic mapping is introduced for carrying out algorithm improvement
Figure BDA0002422654020000035
The Tent chaotic mapping is improved, and small cycle and unstable cycle points of the Tent chaotic mapping are overcome.
The further scheme is that the fitness value of the new food source is calculated and compared in the step 2, and the position of the honey source with more excellent quality of the food source replaces the position of the original food source, and the specific operation rule is as follows:
let fiThe method comprises the following steps of (1) carrying out an objective function of a nonlinear optimization problem, wherein when a maximum value is solved, the fitness function is the objective function; when solving the minimum problem, the fitness function is a transformation form of the objective function by
Figure BDA0002422654020000036
Calculating to obtain;
employing bees to select a better quality honey source by comparing fitness values, and observing the rules of bees selecting food sources:
Figure BDA0002422654020000037
wherein t is 1,2, … …, M; fi(t) is the fitness value of the ith food source at the time of the t iteration.
Further, the specific operation process of S3 is as follows: estimating harmonics, namely sampling a signal at first, wherein the sampling frequency meets the Nyquist criterion; the equivalent linear model of the sampling system is expressed as:
y' (K) ═ h (K) · a + v (K), K ═ 1,2.., K, where Y (K) is the kth noisy signal measurement, a ═ a · K1A2……AN]TIs amplitude vector matrix, v (k) is the additive noise of the k-th sampling, and H (k) is the k-th row of the system structure matrix; the structural matrix of the system is represented as:
Figure BDA0002422654020000041
the harmonic detection problem is reduced to search for the optimum phinMaking the difference between Y (k) and Y (k) tend to a minimum value, wherein Y (k) H (k) A, and determining different phase information phi by using CIABC algorithmnThe amplitude estimation is performed in conjunction with the use of the RLS algorithm.
The invention has the beneficial effects that:
on the basis of a harmonic detection method of a traditional least square algorithm, the chaos improved Artificial Bee Colony (CABC) algorithm is used for optimizing an initial value of the least square algorithm, so that the problem that the traditional least square algorithm is sensitive to the initial value is solved, accuracy and real-time performance of harmonic detection are greatly improved, and steady-state errors are reduced.
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FIG. 1 is a flow chart of a harmonic detection method based on an artificial bee colony algorithm combined with a least square method according to an embodiment of the invention;
FIG. 2 is a flow chart of the chaos improved artificial bee colony algorithm in the embodiment of the invention;
FIG. 3 is a waveform diagram of fundamental wave signal detection on an MTALAB simulation platform by a hybrid algorithm of an artificial bee colony Algorithm (ABC) and a least square method (RLS);
FIG. 4 is a waveform diagram of fundamental wave signal detection by a hybrid algorithm of a chaotic artificial bee Colony Algorithm (CABC) combined with a least square method (RLS) on an MTALAB simulation platform;
FIG. 5 is a waveform diagram of fundamental wave signal detection by a hybrid algorithm of chaos improved artificial bee colony algorithm (CIABC) combined with least square method (RLS) on an MTALAB simulation platform;
FIG. 6 is a waveform diagram of multi-frequency harmonic signal detection on MTALAB software using experimental platform data for a hybrid algorithm of an artificial bee colony Algorithm (ABC) combined with a least squares method (RLS);
FIG. 7 is a waveform diagram of multi-frequency harmonic signal detection by a hybrid algorithm of a chaotic artificial bee Colony Algorithm (CABC) combined with a least square method (RLS) on MTALAB software by using experimental platform data;
fig. 8 is a waveform diagram of multi-frequency harmonic signal detection by a hybrid algorithm of chaos improved artificial bee colony algorithm (CIABC) combined with least square method (RLS) on MTALAB software using experimental platform data.
Detailed Description
The technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.
As shown in fig. 1-2, an embodiment of the present invention discloses a harmonic detection method based on an artificial bee colony algorithm combined with a least square method, comprising the following steps:
s1: on the basis of a standard Artificial Bee Colony algorithm, Tent Chaotic mapping is introduced into the Artificial Bee Colony algorithm for algorithm improvement, and a Chaotic Artificial Bee Colony (CABC) algorithm is provided; the CABC algorithm generates a chaotic sequence on the basis of the optimal food source searched by the whole bee colony; the traversal uniformity characteristic of Tent chaotic mapping is utilized, the optimization speed of the algorithm is improved, and the algorithm is more efficient;
s2: on the basis of the CABC algorithm, an improved Tent Chaotic map is introduced, and a chaos improved Artificial Bee Colony algorithm (CIABC) is provided; after the algorithm is iterated for two times continuously, the position of the employed bee is not updated, namely the chaotic mapping is introduced, and other steps are not changed only by replacing the limit.
S3: and optimizing unknown parameters by using a CIABC algorithm, taking an optimal value output by the algorithm as an initial value of the RLS algorithm, performing parameter estimation by using the RLS algorithm, and finally updating the weight to obtain the amplitude and the phase of the harmonic wave.
In this embodiment, the CABC algorithm is implemented as follows:
step 1: in the D-dimensional space, given iteration times M and a total number S of food sources, each hiring bee corresponds to one food source position, the number of the hiring bees is the same as that of the observation bees, and the hiring bees generate new positions in the field positions; all hiring bees share food source location information to the observing bees;
food source location update basis
Figure BDA0002422654020000051
Carrying out the following steps;
in the formula (I), the compound is shown in the specification,
Figure BDA0002422654020000052
a j dimension value representing the position of the ith honey source is initialized; i 1,2, … …, S, j 1,2, … …, D,
Figure BDA0002422654020000053
respectively the minimum value and the maximum value of the honey source position corresponding to the j dimension, wherein R is a random number between 0 and 1;
step 2: determining and selecting a food source by the observation bees according to the quality of the food source, and recording the position and the fitness value of the selected optimal food source;
performing a neighborhood search of the selected employer bee and observer bee locations based on
Figure BDA0002422654020000054
Position updating is carried out, wherein t is iteration times,
Figure BDA0002422654020000055
represents the j-th dimension of the newly generated first food source at the t +1 th iteration,
Figure BDA0002422654020000061
representing the j-dimensional position value of the ith food source at the t time of iteration; k is a randomly assigned individual, and k ≠ 1; r is [ -1, 1]A random number within a range;
and calculating and comparing fitness values of the new food sources, and replacing the original food source positions with honey source positions with more excellent food source quality.
And step 3: and the observation bees are greedy selected after each new position attempt, the positions are updated if the attempt succeeds, the original positions are maintained if the attempt fails, and if the failed times exceed the preset limit value, the quality of the food source is considered to be lower than the mining threshold. And if the position of the food source is kept unchanged, finishing the observation honeycomb search task. The corresponding employed bee discards the food source and no longer memorizes its location; hiring bees to become scout bees to start to randomly search for new food source positions;
and 4, step 4: recording the current optimal solution and position, finishing the algorithm when the iteration times of the algorithm reach the maximum M times, and outputting the fitness value of the optimal food source; if the maximum iteration times are not reached, judging whether the global optimal food source is updated or not; if so, repeating the step 2 to the step 3; otherwise according to
Figure BDA0002422654020000062
For conventional variables
Figure BDA0002422654020000063
Mapping transformation is carried out to obtain a chaotic variable which is between 0 and 1]Then pass through
Figure BDA0002422654020000064
To pair
Figure BDA0002422654020000065
Mapping to obtain a chaotic variable
Figure BDA0002422654020000066
Finally pass through
Figure BDA0002422654020000067
To make chaotic variable
Figure BDA0002422654020000068
Conversion to conventional variables
Figure BDA0002422654020000069
And repeating the steps 2 to 3.
In this embodiment, Tent chaotic mapping also has the problem of small-cycle and unstable-cycle points, for example, at points (0.2,0.4,0.6,0.8), the Tent mapping generates chaotic attractors; at points (0.25,0.5,0.75) the chaotic map will iterate to motionless 0[66-67], through
Figure BDA00024226540200000610
The Tent chaotic mapping is improved, and small cycle and unstable cycle points of the Tent chaotic mapping are overcome.
Tent chaotic mapping is also called Tent mapping, and is named after the fact that an image is similar to a Tent, and is a piecewise linear mapping in mathematics. The mapping has uniform power spectral density, probability density and ideal correlation characteristics, and the iteration speed is higher, and the mathematical expression is as follows: x is the number ofn+1＝a-1-a|xn|,a∈(1,2)；
When a is less than or equal to 1, the Tent hybrid map is in a stable state;
when a is larger than 1, the Tent chaotic map is in a chaotic state;
when a is 2, for the center Tent mapping, the mathematical expression is:
Figure BDA0002422654020000071
in this embodiment, the fitness value of the new food source is calculated and compared in step 2, and the honey source position with better quality of the food source is used to replace the original food source position, and the specific operation rules are as follows:
let fiThe method comprises the following steps of (1) carrying out an objective function of a nonlinear optimization problem, wherein when a maximum value is solved, the fitness function is the objective function; when solving the minimum problem, the fitness function is a transformation form of the objective function by
Figure BDA0002422654020000072
Calculating to obtain;
employing bees to select a better quality honey source by comparing fitness values, and observing the rules of bees selecting food sources:
Figure BDA0002422654020000073
wherein t is 1,2, … …, M; fi(t) is the fitness value of the ith food source at the time of the t iteration.
In this embodiment, the specific operation process of S3 is as follows: estimating harmonics, namely sampling a signal at first, wherein the sampling frequency meets the Nyquist criterion; the equivalent linear model of the sampling system is expressed as:
y' (K) ═ h (K) · a + v (K), K ═ 1,2.., K, where Y (K) is the kth noisy signal measurement, a ═ a · K1A2……AN]TIs amplitude vector matrix, v (k) is the additive noise of the k-th sampling, and H (k) is the k-th row of the system structure matrix; the structural matrix of the system is represented as:
Figure BDA0002422654020000074
the harmonic detection problem is reduced to search for the optimum phinMaking the difference between Y (k) and Y (k) tend to a minimum value, wherein Y (k) H (k) A, and determining different phase information phi by using CIABC algorithmnCombined with estimation of amplitude using RLS algorithm, e.g. a ═ HT(k)·H(k)]-1HT(k) Y' (k) achieves this by minimizing the performance function E,
Figure BDA0002422654020000081
for each bee, the performance function EiExpressed as:
Figure BDA0002422654020000082
finally, the average estimation error is
Figure BDA0002422654020000083
In this embodiment, the load voltage signal detected for the fundamental wave signal on the MTALAB simulation platform is:
y(t)＝0.95sin(100πt-2.02)+0.09sin(500πt+82.1)+0.043sin(700πt+7.9)+0.03sin(1100πt-147.1)+0.033sin(1300πt+162.6)
in this embodiment, the load voltage signal detected for the multi-frequency harmonic signal on the MTALAB software using the experimental platform data is: the voltage fundamental wave effective value is 220V, and the 3 rd harmonic content is 10%, the 5 th harmonic content is 8% and the 7 th harmonic content is 5% of the alternating current voltage signal.
The swarm parameters of the CIABC and RLS hybrid algorithm are set as follows: the colony size was 32, the number of iterations 20, and 50 seeks were performed.
The harmonic wave is detected by adopting the hybrid algorithm of the chaos improved artificial bee colony algorithm (CIABC) least square method (RLS) of the invention and compared with the harmonic wave detection of the hybrid algorithm of the artificial bee colony Algorithm (ABC) combined with the least square method (RLS) and the harmonic wave detection of the hybrid algorithm of the chaos artificial bee Colony Algorithm (CABC) combined with the least square method (RLS), and the comparison of the experimental results shown in figures 3, 4 and 5 and figures 6, 7 and 8 shows that the invention has high detection precision on the harmonic wave and high algorithm convergence speed. Compared with two other mixed algorithms, the method has obvious advantages.
Finally, only specific embodiments of the present invention have been described in detail above. The invention is not limited to the specific embodiments described above. Equivalent modifications and substitutions by those skilled in the art are also within the scope of the present invention. Accordingly, equivalent alterations and modifications are intended to be included within the scope of the invention, without departing from the spirit and scope of the invention.

Claims (5)

1. A harmonic detection method based on the combination of an artificial bee colony algorithm and a least square method is characterized in that: the method comprises the following steps:
s1: on the basis of a standard Artificial Bee Colony algorithm, Tent Chaotic mapping is introduced into the Artificial Bee Colony algorithm for algorithm improvement, and a Chaotic Artificial Bee Colony (CABC) algorithm is provided; the CABC algorithm generates a chaotic sequence on the basis of the optimal food source searched by the whole bee colony;
s2: on the basis of the CABC algorithm, an improved Tent Chaotic map is introduced, and a chaos improved Artificial Bee Colony algorithm (CIABC) is provided;
s3: and optimizing unknown parameters by using a CIABC algorithm, taking an optimal value output by the algorithm as an initial value of the RLS algorithm, performing parameter estimation by using the RLS algorithm, and finally updating the weight to obtain the amplitude and the phase of the harmonic wave.
2. The harmonic detection method based on the artificial bee colony algorithm combined with the least square method as claimed in claim 1, wherein:
the CABC algorithm is implemented by the following steps:
step 1: in the D-dimensional space, given iteration times M and a total number S of food sources, each hiring bee corresponds to one food source position, the number of the hiring bees is the same as that of the observation bees, and the hiring bees generate new positions in the field positions; all hiring bees share food source location information to the observing bees;
food source location update basis
Figure FDA0002422654010000011
Carrying out the following steps;
in the formula (I), the compound is shown in the specification,
Figure FDA0002422654010000012
a j dimension value representing the position of the ith honey source is initialized; i 1,2, … …, S, j 1,2, … …, D,
Figure FDA0002422654010000013
respectively the minimum value and the maximum value of the honey source position corresponding to the j dimension, wherein R is a random number between 0 and 1;
step 2: determining and selecting a food source by the observation bees according to the quality of the food source, and recording the position and the fitness value of the selected optimal food source;
performing a neighborhood search of the selected employer bee and observer bee locations based on
Figure FDA0002422654010000014
Position updating is carried out, wherein t is iteration times,
Figure FDA0002422654010000015
represents the j-th dimension of the newly generated first food source at the t +1 th iteration,
Figure FDA0002422654010000016
representing the j-dimensional position value of the ith food source at the t time of iteration; k is a randomly assigned individual, and k ≠ 1; r is [ -1, 1]A random number within a range;
and calculating and comparing fitness values of the new food sources, and replacing the original food source positions with honey source positions with more excellent food source quality.
And step 3: and the observation bees are greedy selected after each new position attempt, the positions are updated if the attempt succeeds, the original positions are maintained if the attempt fails, and if the failed times exceed the preset limit value, the quality of the food source is considered to be lower than the mining threshold. And if the position of the food source is kept unchanged, finishing the observation honeycomb search task. The corresponding employed bee discards the food source and no longer memorizes its location; hiring bees to become scout bees to start to randomly search for new food source positions;
and 4, step 4: recording the current optimal solution and position, finishing the algorithm when the iteration times of the algorithm reach the maximum M times, and outputting the fitness value of the optimal food source; if the maximum iteration times are not reached, judging whether the global optimal food source is updated or not; if so, repeating the step 2 to the step 3; otherwise according to
Figure FDA0002422654010000021
For conventional variables
Figure FDA0002422654010000022
Mapping transformation is carried out to obtain a chaotic variable which is between 0 and 1]Then pass through
Figure FDA0002422654010000023
To pair
Figure FDA0002422654010000024
Mapping to obtain a chaotic variable
Figure FDA0002422654010000025
Finally pass through
Figure FDA0002422654010000026
To make chaotic variable
Figure FDA0002422654010000027
Conversion to conventional variables
Figure FDA0002422654010000028
And repeating the steps 2 to 3.
3. The harmonic detection method based on the artificial bee colony algorithm combined with the least square method as claimed in claim 1, wherein:
the Tent chaotic mapping introduced in S1 is used for algorithm improvement, specifically, the Tent chaotic mapping is introduced for algorithm improvement
Figure FDA0002422654010000029
The Tent chaotic mapping is improved, and small cycle and unstable cycle points of the Tent chaotic mapping are overcome.
4. The harmonic detection method based on the artificial bee colony algorithm combined with the least square method as claimed in claim 2, wherein:
calculating and comparing fitness values of the new food sources in the step 2, and replacing the original food source position with a honey source position with more excellent food source quality, wherein the specific operation rule is as follows:
let fiThe method comprises the following steps of (1) carrying out an objective function of a nonlinear optimization problem, wherein when a maximum value is solved, the fitness function is the objective function; when solving the minimum problem, the fitness function is a transformation form of the objective function by
Figure FDA0002422654010000031
Calculating to obtain;
employing bees to select a better quality honey source by comparing fitness values, and observing the rules of bees selecting food sources:
Figure FDA0002422654010000032
wherein t is 1,2, … …, M; fi(t) is the fitness value of the ith food source at the time of the t iteration.
5. The harmonic detection method based on the artificial bee colony algorithm combined with the least square method as claimed in claim 1, wherein:
the specific operation process of S3 is as follows: estimating harmonics, namely sampling a signal at first, wherein the sampling frequency meets the Nyquist criterion; the equivalent linear model of the sampling system is expressed as: y' (K) ═ h (K) · a + v (K), K ═ 1,2.., K, where Y (K) is the kth noisy signal measurement, a ═ a · K1A2……AN]TIs amplitude vector matrix, v (k) is the additive noise of the k-th sampling, and H (k) is the k-th row of the system structure matrix; the structural matrix of the system is represented as:
Figure FDA0002422654010000033
the harmonic detection problem is reduced to search for the optimum phinMaking the difference between Y (k) and Y (k) tend to a minimum value, wherein Y (k) H (k) A, and determining different phase information phi by using CIABC algorithmnThe amplitude estimation is performed in conjunction with the use of the RLS algorithm.
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