CN110222429A - The optimization method of more line current Reconstructions - Google Patents
The optimization method of more line current Reconstructions Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B7/00—Measuring arrangements characterised by the use of electric or magnetic techniques
- G01B7/003—Measuring arrangements characterised by the use of electric or magnetic techniques for measuring position, not involving coordinate determination
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R19/00—Arrangements for measuring currents or voltages or for indicating presence or sign thereof
- G01R19/0092—Arrangements for measuring currents or voltages or for indicating presence or sign thereof measuring current only
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R25/00—Arrangements for measuring phase angle between a voltage and a current or between voltages or currents
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Abstract
A kind of optimization method of more line current Reconstructions, including model foundation step, inversion step, optimizing step, parameter verification step, the model foundation step, inversion step, optimizing step, parameter verification step successively carry out, in the model foundation step, three axis cartesian coordinate systems are established, setting includes the long straight line current model of location parameter, angle parameter, magnitude parameters.The beneficial effect is that: this method is combined with giant magneto-resistance sensor measurement array, line current measurement scheme as novel non-intervention type, line current measurement method traditional at present can be substituted to a certain extent, in the case where all line current parameters are unknown, accurate Reconstruction result is directly obtained simultaneously.
Description
Technical field
The present invention relates to a kind of optimization methods of more line current Reconstructions, belong to Operation of Electric Systems monitoring and measure
Calculating field.
Background technique
There are extensive current measurement demand in electric system, in different application scene the amplitude, frequency of measurement signal,
There are greatest differences for sensitivity, required precision: current amplitude is related to mA grades of leakage current to tens of kA grades of short circuit currents, thunder
Electric current, power frequency are related to the corona current from DC current up to 100MHz.More difficult in the directly measurement magnitude of current
In the case of, generally inverting can be carried out to current parameters by the space magnetic field value that non-intervention type measurement obtains, in all kinds of magnetic fields
In measurement method, giant magneto-resistance sensor can integrated level, small size, the spies such as cheap because of its high sensitivity, broadband, small temperature drift, height
Point, has vast potential for future development, it has also become the preferred embodiment of magnetic field and current monitoring in smart grid.
Line current is most common one kind current source in electric system, and the parametric inversion for line current is electric system electricity
Flow the basis of inverting.According to biot savart's law, the magnetic field and line current parameter that line current generates are closed in nonlinear function
System.It, can be by nonlinear functional relation according to different types of parameter characteristic in the inverting of solid wire current parameters is rebuild
Multiple linear regression problems are converted into, to greatly simplifie difficulty in computation, improve computational accuracy.But for more line currents
Parametric inversion, since magnetic field strength is the magnetic field strength superposition value that more line currents generate, and all parameters in electric current are equal
In the case where unknown, the nonlinear optimal problem can not be converted to the form of linear problem.Directly nonlinear optimization is being asked
In the solution of topic, traditional optimization algorithm and single heuritic approach are influenced by computational instability, it is easy to fall into office
Portion's optimal solution, and it is unable to get globally optimal solution, to make the solving result of line current parameter that larger offset occur, rebuild effect
Poor, therefore, the three-dimensional parameter of more line currents rebuilds the research of optimization method, becomes in the measurement of electric system line current and needs
It solves the problems, such as.
Summary of the invention
The purpose of the present invention is to solve the above problems, devise a kind of optimization side of more line current Reconstructions
Method.Specific design scheme are as follows:
A kind of optimization method of more line current Reconstructions, including model foundation step, inversion step, optimizing step,
Parameter verification step, the model foundation step, inversion step, optimizing step, parameter verification step successively carry out, the model
In establishment step, three axis cartesian coordinate systems are established, setting includes the long straight-line electric of location parameter, angle parameter, magnitude parameters
Flow model,
In the inversion step, according to each component of magnetic vector and the relationship of line current, it is non-linear to establish single goal
Optimization method,
In the optimizing step, is exchanged and is solved using the coupling of meta-heuristic algorithm,
In the parameter verification step, using Nonlinear Convex optimize in interior point method, obtained according to meta-heuristic algorithm
Initial optimal solution calculates output by a step and obtains the globally optimal solution under this method frame as initial value, i.e. more line electricity
The parameters value of stream.
In the model foundation step,
If N root long straight line current model, parameter are divided into location parameter, angle parameter and magnitude parameters three classes, wherein the
The location parameter of k root line current is with the intersecting point coordinate (x of itself and z=0 planesk,ysk, 0) and it indicates, wherein k=1 ..., N, angle
Parameter is with the unit direction vector dl of electric currentk=(mk,nk,pk) indicate, magnitude parameters are with current amplitude IkIt indicates.According to ampere ring
Road law derives more line currents in ith measurement point (xi0,yi0, 0) at the three-dimensional magnetic field intensity non-linear side as follows that generates
Shown in journey are as follows:
COEFFICIENT K in formulakFollowing formula indicates are as follows:
Wherein:
In the inversion step, if sharing M magnetic-field measurement point, amplitude, position and the angle parameter point of k-th of line current
Not with Ik, PkAnd OrikIt indicates, magnetic field strength expression formula indicates that the single goal thus set under two norms is excellent with function f in (1)
Change function are as follows:
Calculating is optimized to above formula, to obtain the parameters value of line current simultaneously.
In the optimizing step, using including genetic algorithm, differential evolution algorithm, simulated annealing and particle swarm algorithm
The coupling of four kinds of meta-heuristic algorithms, which is exchanged, to be solved.
The upper and lower limits for setting solution first generate multiple groups initial solution according to the range of solution at random, are referred to as population
(population), each of these group of solution is known as an individual, and each of every group of solution element is known as one
Member is randomly assigned all individuals in population, using four kinds of algorithms to majorized function simultaneously
It is calculated, this process is known as the coupling (Linking) of heuritic approach.In algorithmic statement or after reaching default calculating limit,
Correspondence is obtained an individual (individual) by each algorithm, randomly selects different number in each individual
Member is added in other individual, is interchangeable (Interchanging) processing, original optimization solves convergence at this time
It is destroyed, therefore calculating is optimized using every kind of algorithm again.By the iteration to above-mentioned coupling, interchange process and follow
Ring, after the calculating of each heuritic approach reaches and stablizes, output obtains final about the initial optimal of more line current parameters
Solution.
The optimization method for the more line current Reconstructions that above-mentioned technical proposal through the invention obtains, its advantages
It is:
This method is combined with giant magneto-resistance sensor measurement array, the line current measurement side as novel non-intervention type
Case can substitute line current measurement method traditional at present to a certain extent, be unknown feelings in all line current parameters
Under condition, accurate Reconstruction result is directly obtained simultaneously.
Detailed description of the invention
Fig. 1 is long straight line current illustraton of model of the present invention；
Fig. 2 is the optimization method flow diagram of more line current Reconstructions of the present invention.
Specific embodiment
The present invention is specifically described with reference to the accompanying drawing.
Embodiment 1
Fig. 1 is long straight line current illustraton of model of the present invention, as shown in Figure 1, setting N root long straight line current model, parameter
It is divided into location parameter, angle parameter and magnitude parameters three classes, wherein the location parameter of kth root line current is with itself and z=0 plane
Intersecting point coordinate (xsk,ysk, 0) and it indicates, wherein k=1 ..., N, angle parameter is with the unit direction vector dl of electric currentk=(mk,
nk,pk) indicate, magnitude parameters are with current amplitude IkIt indicates.According to Ampere circuit law, more line currents are derived in ith measurement
Point (xi0,yi0, 0) at generate the following nonlinear equation of three-dimensional magnetic field intensity shown in are as follows:
COEFFICIENT K in formulakFollowing formula indicates are as follows:
Wherein:
In the inversion step, if sharing M magnetic-field measurement point, amplitude, position and the angle parameter point of k-th of line current
Not with Ik, PkAnd OrikIt indicates, magnetic field strength expression formula indicates that the single goal thus set under two norms is excellent with function f in (1)
Change function are as follows:
Calculating is optimized to above formula, to obtain the parameters value of line current simultaneously.
Embodiment 2
Fig. 2 is the optimization method flow diagram of more line current Reconstructions of the present invention, as shown in Fig. 2, described seek
In excellent step, calculated using comprising four kinds of genetic algorithm, differential evolution algorithm, simulated annealing and particle swarm algorithm meta-heuristics
The coupling of method, which is exchanged, to be solved.
Global optimizing is carried out using meta-heuristic algorithm first, it is contemplated that single meta-heuristic algorithm solution procedure may not
Stablize, therefore is calculated using comprising four kinds of genetic algorithm, differential evolution algorithm, simulated annealing and particle swarm algorithm meta-heuristics
Solver is exchanged in the coupling of method.The upper and lower limits for estimating true line current parameters solution first generate at random according to the range of solution
Multiple groups initial solution is referred to as population (population), and each of these group of solution is known as an individual, in every group of solution
Each element is known as a member, is randomly assigned to all individuals in population, using four kinds
Algorithm calculates majorized function simultaneously, this process is known as the coupling (Linking) of heuritic approach.In algorithmic statement or reach
To after default calculating limit, each algorithm will correspondence obtain an individual (individual), in each individual with
The member that machine extracts different number is added in other individual, is interchangeable (Interchanging) processing, at this time
Original optimization solution convergence is destroyed, therefore optimizes calculating again using every kind of algorithm.By to above-mentioned coupling, exchange
The iteration and circulation of process, after the calculating of each heuritic approach reaches stable, output obtains final about more line currents
The initial optimal solution of parameter.
Embodiment 3
Genetic algorithm (GA)
// initialization generated for the 0th generation
// population scale is set as N, the probability for intersecting generation is χ, and the probability for the generation that makes a variation is μ
N=0；
P (n): the 0th generation population population is randomly generated
// assessment P (n)
Calculate the fitness fitness (i) of each individual individual in population P (n)
do
{ // generate population of new generation
// 1. reproduction processes:
(1- χ) in P (n) × individual is selected to be added in P (n+1)；
// 2. crossover process:
χ × individual in selection P (n) executes crossover operation two-by-two, will generate new individual and is added in P (n+1)；
// 3. mutation processes:
μ × individual in P (n+1) is selected to execute mutation operation；
// assessment P (n+1)
Calculate the fitness fitness (i) of each individual in population P (n+1)
// increment
N=n+1；
}
While P (n) not up to sets fitness or n is not up to maximum setting number
Return optimal individual values P (n)
Embodiment 4
Differential evolution algorithm (DE)
// initialization generated for the 0th generation
// population scale is set as N, the probability for intersecting generation is χ
N=0；Generate the 0th generation population
P (0, i)=Pmin (0)+rand (0,1) (Pmax (0)-Pmin (0))
// assessment P (n)
Calculate the fitness fitness (i) of each individual individual in population P (n)
do
{ // generate population of new generation
// 1. mutation processes:
V (n+1, i)=P (n, r1)+K (P (n, r2)-Pmin (n, r3)), wherein K is the scaling factor, in guarantee
Mesosome v (n+1, i) meets preset boundary conditions；
// 2. crossover process:
χ × individual in selection P (n) and its variation intermediate v (n+1) executes crossover operation two-by-two, will generate new
Body is added in u (n+1)；
// 3. selection courses:
Using greedy algorithm, selection enters the individual of next-generation population from the u (n+1) after intersection；
// assessment P (n+1)
Calculate the fitness fitness (i) of each individual in population P (n+1)
// increment
N=n+1；
}
While P (n) not up to sets fitness or n is not up to maximum setting number
Return optimal individual values P (n).
Embodiment 5
Particle swarm algorithm (PSO)
// initialization generated for the 0th generation
// population scale is set as N
N=0；
P (n): the 0th generation population is randomly generated, and is arranged
Pp_best (n): the optimal solution that particle itself is found so far
Pg_best (n): the optimal solution that full population is found so far
// assessment P (n)
Calculate the fitness fitness (i) of each individual in population P (n)
do
{ // generate population of new generation
// 1. update particle rapidity:
V (n+1)=fun (v (n), Pp_best (n), Pg_best (n))
// 2. update particle position:
P (n+1)=fun (v (n+1), P (n))
// assessment P (n+1)
Calculate the fitness fitness (i) of each individual in population P (n+1)
// update optimal solution:
The fitness (i) of Pp_best (n)=P (n+1) if P (n+1) is better than the fitness (i) of Pp_best (n)
Pg_best (n)=Pp_best (n) ifPp_best (n) fitness (i) is better than the fitness of Pg_best (n)
(i)
// increment
N=n+1；
}
While P (n) not up to sets fitness or n is not up to maximum setting number
Return optimal individual values P (n).
Embodiment 6
Simulated annealing (SA)
// initialization generated for the 0th generation
// population scale is set as N, systemic presupposition temperature is T, and temperature control coefficient is r (0 < r < 1)
N=0；
P (n): the 0th generation population is randomly generated
// assessment P (n)
Calculate the fitness fitness (i) of each individual in population P (n)
do
{ // generate population of new generation
// generated in neighborhood and sound out population
P'(n)=neighbor (P (n))
// compare the fitness of two populations, and selected:
IfP'(n) and fitness1 (i) be better than P (n) fitness2 (i)
P (n+1)=P'(n)
DE=fitness1 (i)-fitness2 (i)
elseifexp(dE/T)>rand(0,1)
P (n+1)=P'(n)
else
P (n+1)=P (n)
}
T=rT
// increment
N=n+1；
}
While P (n) not up to sets fitness or n is not up to maximum setting number
Return optimal individual values P (n).
In embodiment 2-6, in the solution of first step meta-heuristic algorithm, by coupling process by optimization method distribute to
In four kinds of meta-heuristic algorithms, since meta-heuristic algorithm does not guarantee that output globally optimal solution, certain in four kinds of algorithms
A result may fall into locally optimal solution, and using four kinds of algorithms while when calculating, the advantage of each algorithm is strengthened, and disadvantage obtains
To complementation, the probability of globally optimal solution is obtained to be promoted.It exchanges in operation, by destroying the convergence of former result, increases
A possibility that new optimal solution, i.e. globally optimal solution.By cycle calculations, initial globally optimal solution is obtained.Since member opens
For hairdo algorithm when calculating the locally optimal solution within the scope of some, the more traditional optimization algorithm of effect is poor, therefore is calculated knot
Fruit is finally solved as initial solution, using interior point method, while obtaining position and the current parameters of line current.Whole process knot
The advantage for having closed meta-heuristic algorithm and traditional optimization algorithm, ensure that and obtain globally optimal solution on to greatest extent, have compared with
Strong robustness.This method is combined with giant magneto-resistance sensor measurement array, the line current as novel non-intervention type measures
Scheme can substitute line current measurement method traditional at present to a certain extent, be unknown in all line current parameters
In the case of, accurate Reconstruction result is directly obtained simultaneously.
Above-mentioned technical proposal only embodies the optimal technical scheme of technical solution of the present invention, those skilled in the art
The principle of the present invention is embodied to some variations that some of them part may be made, belongs to the scope of protection of the present invention it
It is interior.
Claims (4)
1. a kind of optimization method of more line current Reconstructions, including model foundation step, inversion step, optimizing step, ginseng
Number verification step, the model foundation step, inversion step, optimizing step, parameter verification step successively carry out, and feature exists
In,
In the model foundation step, three axis cartesian coordinate systems are established, setting includes location parameter, angle parameter, amplitude ginseng
Several long straight line current models,
In the inversion step, according to each component of magnetic vector and the relationship of line current, single goal nonlinear optimization is established
Equation,
In the optimizing step, is exchanged and is solved using the coupling of meta-heuristic algorithm,
In the parameter verification step, using Nonlinear Convex optimize in interior point method, obtained according to meta-heuristic algorithm initial
Optimal solution calculates output by a step and obtains the globally optimal solution under this method frame as initial value, i.e. more line currents
Parameters value.
2. the optimization method of more line current Reconstructions according to claim 1, which is characterized in that the model is built
In vertical step,
If N root long straight line current model, parameter are divided into location parameter, angle parameter and magnitude parameters three classes, wherein kth root
The location parameter of line current is with the intersecting point coordinate (x of itself and z=0 planesk,ysk, 0) and it indicates, wherein k=1 ..., N, angle parameter
With the unit direction vector dl of electric currentk=(mk,nk,pk) indicate, magnitude parameters are with current amplitude IkIt indicates.It is fixed according to Ampere ring road
Rule derives more line currents in ith measurement point (xi0,yi0, 0) at generate the following nonlinear equation institute of three-dimensional magnetic field intensity
It is shown as:
COEFFICIENT K in formulakFollowing formula indicates are as follows:
Wherein:
。
3. the optimization method of more line current Reconstructions according to claim 1, which is characterized in that the inverting step
In rapid, if sharing M magnetic-field measurement point, amplitude, position and the angle parameter of k-th of line current are respectively with Ik, PkAnd OrikTable
Show, magnetic field strength expression formula is indicated in (1) with function f, thus sets the single object optimization function under two norms are as follows:
Calculating is optimized to above formula, to obtain the parameters value of line current simultaneously.
4. the optimization method of more line current Reconstructions according to claim 1, which is characterized in that the optimizing step
In rapid, using including four kinds of genetic algorithm, differential evolution algorithm, simulated annealing and particle swarm algorithm meta-heuristic algorithms
Coupling, which is exchanged, to be solved.
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