CN104965134B - Grounding net of transformer substation surface potential distribution calculation method based on echo state network - Google Patents
Grounding net of transformer substation surface potential distribution calculation method based on echo state network Download PDFInfo
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Abstract
The present invention relates to a kind of grounding net of transformer substation surface potential distribution calculation method based on echo state network, including：Step 1, the surface potential distribution using numerical computation method calculating grounding net of transformer substation；Step 2, determine echo state network structure；Step 3, according to grounding net of transformer substation surface potential result of calculation echo state network is trained, the grounded screen surface potential computation model based on echo state network after being trained；Step 4, to grounding net of transformer substation power frequency exciting current is injected, by power frequency parameter test instrument along measurement surface potential above grounded screen；Step 5, according to the echo state network structure after training to grounded screen carry out region division；Step 6, the surface potential curve to grounding grids and mesh are fitted, and obtain the distribution of grounding net of transformer substation surface potential.Compared with prior art, the present invention has the advantages that calculating the surface potential for obtaining grounding net of transformer substation effectively, exactly is distributed.
Description
Technical field
The present invention relates to grounding net of transformer substation surface potential computing technique field, echo state is based on more particularly, to one kind
The grounding net of transformer substation surface potential distribution calculation method of network.
Background technology
Grounded screen is the important component of transformer station, the safe and stable operation shadow of the reliability of its work to power system
Sound is great.Because grounding net of transformer substation is embedded in underground for a long time, inevitably by the electrochemical corrosion of soil.It is same with this
When, flow through the stray electrical current of earth conductor can also cause ground net corrosion in addition be broken, down conductor section diminish, grounding body
Between loose contact the problems such as.Further, since construction reason, grounded screen there is likely to be the potential faults such as sealing-off or rosin joint.This
A little failures can cause grounded screen performance to decline to a great extent, and then may trigger major accident and bring huge economic loss.
How timely and effective detection grounding net of transformer substation potential faults so that take corresponding safeguard procedures existing as power industry
There are in grounded screen maintenance work distinct issues the most.
At present, based on electric field theory, by injecting exciting current to grounded screen, it is distributed according to the surface potential that detection is obtained
It is more conventional Failure Diagnosis of Substation Ground Network method to carry out fault diagnosis to grounded screen.This method is by comparing transformer station
The calculated results and field actual measurement results of grounded screen surface potential distribution, carry out fault diagnosis to grounded screen and are commented with state
Estimate.Therefore, it is necessary to study the computational methods that grounding net of transformer substation surface potential is distributed, so as to accurate, efficient
Ground obtains the surface potential distribution theory result of grounded screen, and then carries out fault diagnosis and state estimation to grounding net of transformer substation.
The existing research to grounding net of transformer substation surface potential distribution theory value is concentrated mainly on two aspects, one is root
According to electric field or Circuit theory, based on the equipotential of grounded screen or non-equipotential model, theory is directly carried out to earth's surface Potential distribution
Calculate, but this method operand is big, and different shape grounded screen changes more in calculating process, it is difficult to form fitness higher
Algorithm；The second is in-situ measurement directly is carried out to it at the beginning of grounding net of transformer substation is built up, enough measuring points by setting
To obtain more complete surface potential distribution, but this method workload is big and can not eliminate in-site measurement error to grounded screen
Influence caused by table Potential distribution result.
The content of the invention
It is an object of the present invention to overcome the above-mentioned drawbacks of the prior art and provide one kind is based on echo state
The grounding net of transformer substation surface potential distribution calculation method of network, this method, which integrates on-the-spot test and calculates analysis, can realize change
Efficient, the accurate calculating of power station grounded screen surface potential distribution.
The purpose of the present invention can be achieved through the following technical solutions：
A kind of grounding net of transformer substation surface potential distribution calculation method based on echo state network, it is characterised in that bag
Include following steps：
Step 1, the surface potential distribution using numerical computation method calculating grounding net of transformer substation；
Step 2, determine echo state network structure, using grounded screen by boundary's subdivision of node as n sections of conductors after, by grounded screen
At node, the surface potential of each conductor midpoint and mesh center be input quantity；Output quantity is made up of two parts, and one is to connect
Earthed conductor part, it is output quantity to take surface potential at its six Along ent；Secondly being mesh-portion, its parallel conductor correspondence six etc. is taken
Surface potential is output quantity at six Along ents of branch line；
Step 3, according to grounding net of transformer substation surface potential result of calculation echo state network is trained, obtains echo
State network exports weight matrix, the grounded screen surface potential computation model based on echo state network after being trained；
Step 4, using AC signal generator by one can and node to grounding net of transformer substation inject power frequency exciting current,
By power frequency parameter test instrument surface potential is measured along above grounded screen；Grounded screen is divided into n sections of conductors by cut-point of node, selected
Take at node, each conductor midpoint and mesh center are measuring point；
Step 5, region division carried out to grounded screen according to the echo state network structure after training, division principle is ensures
The mesh count in each region is consistent with the mesh count of training network；Using the measuring point measured value in each region as input number
According to input echo state network, the output valve of network is read, you can obtain surface potential at each Along ent of conductor six of grounded screen, and
Surface potential at six Along ents of mesh parallel conductor six Along ent lines of correspondence, and then obtain grounding net of transformer substation generally
Table Potential distribution；
Step 6, using least square method the surface potential curve of grounding grids and mesh is fitted, so as to obtain
Grounding net of transformer substation surface potential is distributed.
The surface potential that described step 1 calculates grounding net of transformer substation by numerical computation method is distributed, and is specifically：
Interstitial content 1a) is divided into n sections of conductors for m grounded screen, the mutual resistance matrix R between this n sections of conductor is calculated, its
In, matrix element RijThe mutual impedance between i sections of conductors and j sections of conductors is represented, its calculation formula is：
I=1 ..., n；J=1 ..., n
In formula, σEFor soil conductivity；ε0For permittivity of vacuum；εrFor soil relative dielectric constant；εE=ε0·εrFor
Soil dielectric constant；liWith ljRespectively i-th section and jth section conductor length；li'For the image length of i-th section of conductor；Di,jTo incite somebody to action
The distance between i-th section and jth section conductor；Di',jFor by i-th section of conductor mirror image and jth section the distance between conductor；
This n sections of conductor 1b) is represented respectively using T-shaped equivalent circuit, i.e., 1 section conductor 1 T-shaped equivalent circuit of correspondence is described
Self-inductance L, self-resistance Z of the T-shaped equivalent circuit by i-th section of conductor0, i-th section of mutual inductance M between jth section conductor, i-th section
The direct-to-ground capacitance C of conductor and over the ground conductance G are constituted, wherein i=1 ..., n, j=1 ..., n；It is described to connect after T-shaped circuit equivalent
Earth mat has m+n node and 2n sections of conductors；
Incidence matrix A of the grounded screen through T-shaped equivalent circuit each section of conductor after equivalent 1c) is calculated, wherein, incidence matrix A's
Row corresponds to number of branches 2n corresponding to grounded screen the interstitial content m+n through T-shaped equivalent circuit after equivalent, incidence matrix A row,
Arbitrary element a in incidence matrix Ai,jDefinition be：
The impedance matrix Z of the grounded screen after equivalent through T-shaped equivalent circuit with m+n node and 2n bar branch roads 1d) is calculated,
Its calculation formula is：
In formula, Mi,jFor each branch road of grounded screen through it is T-shaped it is equivalent after mutual inductance matrix；kiFor through it is T-shaped it is equivalent after i-th section of conductor
Length, wherein i=1 ..., 2n；hi,jFor the distance between i-th section of conductor and jth section conductor；Z0iFor the internal resistance of i-th section of conductor
It is anti-；μ0For soil magnetic conductivity, and assume that soil is identical with air permeability；μ=μ0μrFor conductor magnetic conductance
Rate；μrFor conductor relative permeability；ρcFor conductor resistance rate；r0For conductor radius；I0(γr0)、I1(γr0) be respectively zeroth order and
First-order bessel function；
It is Y 1e) according to incidence matrix A and impedance matrix Z calculate node admittance matrixsn+m=AZ-1AT；According to impedance matrix
R calculates admittance matrix, is G=R-1；
1f) calculate the midpoint potential of n sections of conductors of grounding gridsAnd node potentialBy solving grounded screen mathematics
The fundamental equation of model is obtained, and the fundamental equation of described grounded screen mathematical modeling is：
In formula, G is n × n matrix；For n midpoint potential column vector；For m node column vector；For m node Injection Current column vector；
The leakage current distribution of n sections of conductors of grounding grids 1g) is calculated, passes through equationTry to achieve, wherein, mutually
Impedance matrix R is n × n matrix；It is the leakage current on every section of conductor for n dimensional vectors
Vector；For n midpoint potential column vector；
The Potential distribution on ground 1h) is calculated using principle of stacking according to the electric leakage flow distribution for the grounding grids tried to achieve,
Potential calculation formula on ground at any point P is：
In formula, UiPFor i-th section of conductor leakage current a p-shaped into surface potential；ρ is soil resistivity；rp,zpFor i-th
The polar coordinate representation of distance between section conductor midpoint and point P；
Calculate the current potential of the leakage current of every section of conductor in each Ground Point formation of grounded screen respectively, then by the calculating of all conductors
As a result it is overlapped, so as to obtain the surface potential distribution result of calculation of grounded screen.
Described step 2 determines echo state network structure and input, output, is specifically：
Echo state network structure described in 2a) includes input layer, reserve pool and output layer, the input of described input layer
Signal is connected to the reserve pool being made up of the neuron largely arranged at random by inputting connection weight matrix, and neuron passes through interior
Portion's connection weight formation reserve pool output, constitutes the internal state vector of network, and be connected to output by exporting connection weight
Layer；
Each parameter of the echo state network, including state reserve pool neuron number, internal connection weight spectrum 2b) are set
Radius etc.；
Input and the output unit number of echo state network 2c) are determined according to the conductor number and mesh count of specific grounded screen
Mesh；
2d) the connection weight matrix W between random initializtion input and deposit pool unitin, it is sparse between reserve pool internal element
Connection weight matrix W.
The method that described step 3 sets up the grounded screen surface potential computation model based on echo state network, be specifically：
3a) according to grounded screen surface potential result of calculation, the input u (k) of training sample needed for determining echo state network
With output y (k), wherein, k=1,2 ..., r, r is number of samples；
3b) the original state x (0) of arbitrarily selected network reserve pool intrinsic nerve member, elects 0 as；
Training input sample 3c) is added into reserve pool through inputting connection weight, reserve pool is sequentially completed by echo state network
The calculating of state and corresponding network outputCalculating and collection；The vectorial calculation formula of described reserve pool internal state
For：
X (k+1)=f1(Winu(k+1)+Wx(k))
In formula, f1For reserve pool neuron activation functions；U (k+1) is the input of+1 iteration of echo state network kth；
The calculation formula of corresponding network output is：
In formula, f2For output function, because output layer is linear, therefore f2Take identity function；WoutFor output connection weight square
Battle array；
It is specific when calculating, echo state network collection system state since the m times iteration, and with vector x (k) (k=m,
M+1 ..., r) constitutes matrix B, while collecting corresponding output sample y (k) constitutes matrix T；
3d) utilize network reality outputDesired output y (k) is approached, that is, calculates and obtains making network mean square error minimum
Output connection weight matrix Wout, the calculating process, which can be converted into, solves following optimization problem：
The optimization problem is solved using linear regression method, calculating obtains Wout, so as to complete the instruction to echo state network
Practice；The WoutExpression formula be：
(Wout)T=B-1T
Linear regression method is mathematical method conventional in the art in this step, therefore no longer progress is detailed herein by inventor
Description.
The workload of on-the-spot test is greatly reduced to the selection mode of measuring point in described step 4, to large-scale grounding network
It is particularly evident.
Region division is carried out in described step 5 to grounded screen and causes the surface potential meter based on echo state network
Calculating model has larger fitness.
The detailed process of calculating grounded screen surface potential distribution is in described step 6：
6a) to a certain conductor or mesh, according to the position coordinates x=[x of its known surface potential point0,x1,…,x6]TAnd
Corresponding surface potentialConstruct orthogonal polynomial { PL(x) }, its recurrence Relation is：
In formula, Pk(x) it is k order polynomials that leading coefficient is 1；ak,βkFor multinomial coefficient；
According to Pk(x) orthogonality draws ak,βkWith Pk(x) relational expression, its expression formula is：
By ak,βkExpression formula substitute into { PL(x) stepping type }, progressively recursion obtain { PL(x) each single item in }, and then
The polynomial construction of complete pairwise-orthogonal；
6b) digital simulation curve coefficientsAnd progressivelyIt is added in matched curve function F (x), is somebody's turn to do
The surface potential of conductor or mesh is distributed, and described coefficient formulas and surface potential expression formula is：
Its surface potential 6c) is calculated all conductors and mesh as stated above, and then superposition obtains whole surface potentials
Distribution, is calculated so as to complete to be distributed the surface potential of grounding net of transformer substation.
That is, the technical program is the surface potential measured value according to limited measuring point of substation field, using returning
Sound state network and least square method, calculate the surface potential distribution for obtaining grounding net of transformer substation.
The further optimization of the present invention is：It is based on not to the theoretical calculation that grounded screen surface potential is distributed in step one
What equipotential grounded screen model was carried out, distributed constant replaced using lumped parameter to ground connection body unit, and by Circuit theory
It is combined with electric field theory, surface potential is calculated.
The further optimization of the present invention is：Echo state network is inputted in step 2 and the selection of output parameter is integrated
Consider computational accuracy and efficiency, it is ensured that under the premise of network training workload is acceptable, obtain accurate entirety
The substantially regularity of distribution of grounded screen surface potential；In addition, being carried out to three weight matrixs after random initializtion, iterating to calculate
Without changing its value again in journey, so that network training need to only determine to export one parameter to be asked of weight matrix.
The further optimization of the present invention is：The work of on-the-spot test is greatly reduced to the selection mode of measuring point in step 4
Measure, it is particularly evident to large-scale grounding network.
The further optimization of the present invention is：Grounded screen progress region division is caused in step 5 described based on echo shape
The surface potential computation model of state network has larger fitness.
The further optimization of the present invention is：The orthogonal polynomial constructed in step 6 can avoid solution surface potential from estimating
Occurs the coefficient matrix of morbid state during evaluation.
Compared with prior art, present invention application echo state network algorithm, which can be trained, obtains ad hoc networks hole number grounded screen
Surface potential distributed computing model, by grounded screen carry out region division, on-the-spot test workload can be greatly decreased
In the case of, the substantially distribution of accurate grounding net of transformer substation surface potential is obtained, meanwhile, docked using least-squares algorithm
The surface potential curve of earth mat is fitted, and can further obtain more accurate grounded screen surface potential distribution.
Brief description of the drawings
Fig. 1 is the grounded screen model schematic in the embodiment of the present invention；
Fig. 2 is the T-shaped isoboles of grounding grids unit of the present invention；
Fig. 3 is echo state network structural model of the present invention；
Fig. 4 is the result of calculation of echo state network of the present invention；
Fig. 5 is a certain conductor surface potential result of calculation of grounded screen of the present invention and fitting result；
Fig. 6 is the overall earth's surface Calculation of Potential Distribution result of grounded screen of the present invention.
Embodiment
The present invention is described in detail with specific embodiment below in conjunction with the accompanying drawings.
Carried out by subjects of certain substation grounding pessimistic concurrency control shown in Fig. 1 in surface potential calculating, Fig. 1, x, y is seat
Direction is marked, the origin of coordinates is O points, and the surface potential for calculating the grounded screen according to the following steps is distributed：
(1) calculate grounded screen surface potential using numerical computation method to be distributed, described grounding net of transformer substation surface potential
Distribution can use following numerical computation method：
Interstitial content is divided into m=25, n=40 in n sections of conductors, the present embodiment by 1a. for m grounded screen, is calculated this n sections and is led
Mutual resistance matrix R between body, wherein, matrix element RijThe mutual impedance between i sections of conductors and j sections of conductors is represented, it calculates public
Formula is：
I=1 ..., n；J=1 ..., n
In formula, σEFor soil conductivity；ε0For permittivity of vacuum；εrFor soil relative dielectric constant；εE=ε0·εrFor
Soil dielectric constant；liWith ljRespectively i-th section and jth section conductor length；li'For the image length of i-th section of conductor；Di,jTo incite somebody to action
The distance between i-th section and jth section conductor；Di',jFor by i-th section of conductor mirror image and jth section the distance between conductor；
1b. represents this n sections of conductor respectively using T-shaped equivalent circuit, i.e., 1 section conductor 1 T-shaped equivalent circuit of correspondence is described
T-shaped equivalent circuit by i-th section of conductor (i=1 ..., self-inductance L, self-resistance Z n)0, i-th section and jth section (j=1 ..., n)
Mutual inductance M between conductor, the direct-to-ground capacitance C of i-th section of conductor and conductance G is constituted over the ground, as shown in Figure 2；Through T-shaped circuit equivalent
Afterwards, the grounded screen has m+n node and 2n sections of conductors, i.e., 65 nodes and 80 sections of conductors；
1c. calculates incidence matrix A of the grounded screen through T-shaped equivalent circuit each section of conductor after equivalent, wherein, incidence matrix A's
Row corresponds to number of branches 2n corresponding to grounded screen the interstitial content m+n through T-shaped equivalent circuit after equivalent, incidence matrix A row,
Arbitrary element a in incidence matrix Ai,jDefinition be：
1d. calculates the impedance matrix Z of the grounded screen after equivalent through T-shaped equivalent circuit with m+n node and 2n bar branch roads,
Its calculation formula is：
In formula, Mi,jFor each branch road of grounded screen through it is T-shaped it is equivalent after mutual inductance matrix；kiFor through it is T-shaped it is equivalent after i-th section of conductor
Length (i=1 ..., 2n)；hi,jFor the distance between i-th section of conductor and jth section conductor；Z0iFor the internal impedance of i-th section of conductor；μ0
For soil magnetic conductivity, and assume that soil is identical with air permeability；μ=μ0μrFor conductor magnetic conductivity；μr
For conductor relative permeability；ρcFor conductor resistance rate；r0For conductor radius；I0(γr0)、I1(γr0) it is respectively zeroth order and single order
Bessel function；
1e., according to incidence matrix A and impedance matrix Z calculate node admittance matrixs, is Yn+m=AZ-1AT；According to impedance matrix
R calculates admittance matrix, is G=R-1；
1f. calculates the midpoint potential of n sections of conductors of grounding gridsAnd node potentialThis can be by solving grounded screen
The fundamental equation of mathematical modeling is obtained, and the fundamental equation of described grounded screen mathematical modeling is：
In formula, G is n × n matrix；For n midpoint potential column vector；For m node column vector；For m node Injection Current column vector；Herein, m=25, n=40；
1g. calculates the leakage current distribution of n sections of conductors of grounding grids, and this can pass through equationTry to achieve.Its
In, mutual resistance matrix R is n × n matrix；It is on every section of conductor for n dimensional vectors
Leak electricity flow vector；For n midpoint potential column vector；Herein, n=40；
1h. calculates the Potential distribution on ground according to the electric leakage flow distribution for the grounding grids tried to achieve using principle of stacking,
Potential calculation formula on ground at any point P is：
In formula, UiPFor i-th section of conductor leakage current a p-shaped into surface potential；ρ is soil resistivity；rp,zpFor i-th
The polar coordinate representation of distance between section conductor midpoint and point P；
Calculate the current potential of the leakage current of every section of conductor in each Ground Point formation of grounded screen respectively, then by the calculating of all conductors
As a result it is overlapped, so as to obtain the surface potential distribution result of calculation of grounded screen；
(2) determine echo state network structure, using grounded screen by boundary's subdivision of node as n sections of conductors after grounded screen node
The surface potential at place, each conductor midpoint and mesh center is input quantity；Output quantity is made up of two parts, and one is led for ground connection
Body portion, it is output quantity to take surface potential at its six Along ent；Secondly being mesh-portion, its parallel conductor six Along ents of correspondence are taken
Surface potential is output quantity at six Along ents of line；Herein, n=40；Described determination echo state network structure and input,
The method of output is：
Echo state network structure described in 2a. includes three layers of input, reserve pool and output, and the input signal of input layer is led to
Cross input connection weight matrix and be connected to the reserve pool being made up of the neuron largely arranged at random, neuron is connected by inside
Power forms reserve pool output, constitutes the internal state vector of network, and is connected to output layer by exporting connection weight, such as schemes
Shown in 3；
2b. sets each parameter of the echo state network, including state reserve pool neuron number, internal connection weight spectrum
Radius etc.；Herein, reserve pool neuron number is 200, and spectral radius is 0.8；
2c. determines input and the output unit number of echo state network according to the conductor number and mesh count of specific grounded screen
Mesh；Herein, input block number is 81, and output unit number is 625；
2d. random initializtions are inputted laying in sparse between the connection weight matrix Win between pool unit, reserve pool internal element
Connection weight matrix W；
(3) echo state network is trained according to grounding net of transformer substation surface potential result of calculation, obtains echo shape
State network exports connection weight matrix, the grounded screen surface potential computation model based on echo state network after being trained；Institute
The method of grounded screen surface potential computation model of the foundation stated based on echo state network is：
3a. is according to grounded screen surface potential result of calculation, training sample input input u needed for composition echo state network
(k) with output y (k), wherein, k=1,2 ..., r, r is number of samples；Herein, r=100；
The original state x (0) of 3b. selected network reserve pools intrinsic nerve member, is usually chosen to 0；
3c. will train input sample to add to reserve pool through inputting connection weight, and reserve pool is sequentially completed by echo state network
The calculating of state and corresponding network outputCalculating and collection；The vectorial calculation formula of described reserve pool internal state
For：
X (k+1)=f1(Winu(k+1)+Wx(k))
In formula, f1For reserve pool neuron activation functions, generally linear, tangent or other S type functions；U (k+1) is back
The input of sound state network+1 iteration of kth；Herein, f1For typical S type functions hyperbolic tangent function, its mathematic(al) representation
For：
The calculation formula of corresponding network output is：
In formula, f2For output function, because output layer is linear, therefore f2Take identity function；WoutFor output connection weight square
Battle array；
It is specific when calculating, echo state network collection system state since the m times iteration, and with vector x (k) (k=m,
M+1 ..., r) constitutes matrix B, while collecting corresponding output sample y (k) constitutes matrix T；Herein, m=20；
3d. utilizes network reality outputDesired output y (k) is approached, that is, calculates and obtains making network mean square error minimum
Output connection weight matrix Wout, the calculating process, which can be converted into, solves following optimization problem：
The optimization problem is solved using linear regression method, calculating obtains Wout, so as to complete the instruction to echo state network
Practice；The WoutExpression formula be：
(Wout)T=B-1T
Linear regression method is mathematical method conventional in the art in this step, therefore no longer progress is detailed herein by inventor
Description；
(4) using AC signal generator by one can and node inject power frequency to the grounding net of transformer substation studied and encourage
Electric current, surface potential is measured by power frequency parameter test instrument along above grounded screen；Grounded screen is divided into n sections by cut-point of node to lead
Body, chooses at node, each conductor midpoint and mesh center are measuring point；Herein, n=40；
(5) echo state network structure carries out region division to studied grounded screen according to obtained by the training, it is ensured that every
The mesh count in individual region is consistent with the mesh count of training network (can have lap between each region).By the survey in each region
Point measured value inputs echo state network respectively as input data, reads the output valve of network, you can obtain grounded screen and respectively lead
Surface potential at surface potential at the Along ent of body six, and six Along ents of mesh parallel conductor six Along ent lines of correspondence, and then
Obtain the substantially earth's surface Potential distribution of grounding net of transformer substation；As shown in Figure 4；
(6) the surface potential curve of grounding grids and mesh is fitted using least square method, thus obtain compared with
It is distributed for accurate grounding net of transformer substation surface potential, described grounding net of transformer substation surface potential distribution calculating process is：
AB sections of conductors in Fig. 1 are divided into six parts by 6a., and wherein A point coordinates is (3.5,3.5), B point coordinates for (5.5,
3.5) it is potential measurement point, wherein each seat of potential measurement point in the x-direction, to choose each Along ent and AB sections of conductor two-end-points
Mark is respectively x=[3.5,3.83,4.17,4.5,4.83,5.17,5.5]T, according to this 7 current potential measuring point coordinates and corresponding
Table potential measurement valueConstruct orthogonal polynomial { PL
(x) }, its recurrence Relation is：
In formula, Pk(x) it is k order polynomials that leading coefficient is 1；ak,βkFor multinomial coefficient；
According to Pk(x) orthogonality draws ak,βkWith Pk(x) relational expression, its expression formula is：
Observe the surface potential distribution curve obtained by theoretical calculation to find, the approximate secondary letter of surface potential distribution of conductor
Number, therefore, takes L=2 herein.By ak,βkExpression formula substitute into { PL(x) stepping type }, progressively recursion obtain { PL(x) in }
Each single item, and then the polynomial construction of complete pairwise-orthogonal；
6b. digital simulation curve coefficientsAnd progressivelyIt is added in matched curve function F (x), and then
Surface potential to the conductor or mesh is distributed, and described coefficient formulas and surface potential expression formula is：
Herein, conductor AB surface potential result of calculation and fitting result are as shown in Figure 5；
6c. calculates all conductors and mesh its surface potential as stated above, and then superposition obtains whole surface potentials
Distribution, is calculated, result of calculation is as shown in Figure 6 so as to complete to be distributed the surface potential of grounding net of transformer substation.
Therefore the present invention can obtain the surface potential distributed computing model of specific mesh count grounded screen, by being connect to studying
Earth mat carry out region division, can on the premise of on-the-spot test workload is greatly decreased, effectively, exactly calculate obtain power transformation
The surface potential distribution for grounded screen of standing, so as to be the Failure Diagnosis of Substation Ground Network and state estimation that are distributed based on surface potential
Theoretical calculation foundation is provided.
It should be noted that listed above is only specific embodiment of the invention, it is clear that implement the invention is not restricted to more than
Example, the similar change for having many therewith.If those skilled in the art directly exports or joined from present disclosure
All deformations expected, all should belong to protection scope of the present invention.
Claims (5)
1. a kind of grounding net of transformer substation surface potential distribution calculation method based on echo state network, it is characterised in that including
Following steps：
Step 1, the surface potential distribution using numerical computation method calculating grounding net of transformer substation；
Step 2, echo state network structure is determined, after by grounded screen by boundary's subdivision of node being n sections of conductors, with grounded screen node
The surface potential at place, each conductor midpoint and mesh center is input quantity；Output quantity is made up of two parts, and one is led for ground connection
Body portion, it is output quantity to take surface potential at its six Along ent；Secondly being mesh-portion, its parallel conductor six Along ents of correspondence are taken
Surface potential is output quantity at six Along ents of line；
Step 3, according to grounding net of transformer substation surface potential result of calculation echo state network is trained, obtains echo state
Network exports weight matrix, the grounded screen surface potential computation model based on echo state network after being trained；
Step 4, using AC signal generator by one can and node to grounding net of transformer substation inject power frequency exciting current, by work
Frequency parameter tester measures surface potential along above grounded screen；Grounded screen is divided into n sections of conductors by cut-point of node, section is chosen
Point place, each conductor midpoint and mesh center are measuring point；
Step 5, according to the echo state network structure after training to grounded screen carry out region division, division principle for ensure it is each
The mesh count in region is consistent with the mesh count of training network；Measuring point measured value in each region is defeated as input data
Enter echo state network, read the output valve of network, you can obtain surface potential at each Along ent of conductor six of grounded screen, and mesh
Surface potential at six Along ents of parallel conductor six Along ent lines of correspondence, and then obtain the substantially earth's surface electricity of grounding net of transformer substation
Bit distribution；
Step 6, using least square method the surface potential curve of grounding grids and mesh is fitted, so as to obtain power transformation
Grounded screen of standing surface potential is distributed.
2. a kind of grounding net of transformer substation surface potential distribution calculating side based on echo state network according to claim 1
Method, it is characterised in that the surface potential that described step 1 calculates grounding net of transformer substation by numerical computation method is distributed, specifically
It is：
Interstitial content 1a) is divided into n sections of conductors for m grounded screen, the mutual resistance matrix R between this n sections of conductor is calculated, wherein,
Matrix element RijThe mutual impedance between i sections of conductors and j sections of conductors is represented, its calculation formula is：
In formula, σEFor soil conductivity；ε0For permittivity of vacuum；εrFor soil relative dielectric constant；εE=ε0·εrFor soil
Dielectric constant；F is frequency；liWith ljRespectively i-th section and jth section conductor length；li'For the mirror of i-th section of conductor
As length；Di,jFor by i-th section and jth section the distance between conductor；Di',jFor by between i-th section of conductor mirror image and jth section conductor
Distance；
This n sections of conductor 1b) is represented respectively using T-shaped equivalent circuit, i.e., 1 section conductor corresponds to 1 T-shaped equivalent circuit, and described is T-shaped
Self-inductance L, self-resistance Z of the equivalent circuit by i-th section of conductor0, i-th section of mutual inductance M between jth section conductor, i-th section of conductor
Direct-to-ground capacitance C and over the ground conductance G are constituted, wherein i=1 ..., n, j=1 ..., n；Through T-shaped equivalent circuit it is equivalent after, the ground connection
Net has m+n node and 2n sections of conductors；
Incidence matrix A of the grounded screen through T-shaped equivalent circuit each section of conductor after equivalent 1c) is calculated, wherein, incidence matrix A row pair
Interstitial content m+n that should be in grounded screen through T-shaped equivalent circuit after equivalent, incidence matrix A row correspond to number of branches 2n, association
Arbitrary element a in matrix Ai,jDefinition be：
The impedance matrix Z of the grounded screen after equivalent through T-shaped equivalent circuit with m+n node and 2n bar branch roads 1d) is calculated, it is counted
Calculating formula is：
In formula, Mi,jMutual inductance matrix for each branch road of grounded screen through T-shaped equivalent circuit after equivalent；kiTo be equivalent through T-shaped equivalent circuit
I-th section of conductor length, wherein i=1 ..., 2n afterwards；hi,jFor the distance between i-th section of conductor and jth section conductor；Z0iFor i-th section
The internal impedance of conductor；μ0For soil magnetic conductivity, and assume that soil is identical with air permeability；μ=μ0μr
For conductor magnetic conductivity；μrFor conductor relative permeability；ρcFor conductor resistance rate；r0For conductor radius；I0(γr0)、I1(γr0) point
Wei not zeroth order and first-order bessel function；
It is Y 1e) according to incidence matrix A and impedance matrix Z calculate node admittance matrixsn+m=AZ-1AT；According to mutual resistance matrix R
Admittance matrix is calculated, is G=R-1；
1f) calculate the midpoint potential of n sections of conductors of grounding gridsAnd node potentialBy solving grounded screen mathematical modeling
Fundamental equation obtain, the fundamental equation of described grounded screen mathematical modeling is：
In formula, G is n × n matrix；For n midpoint potential column vector；For m node column vector；
For m node Injection Current column vector；
The leakage current distribution of n sections of conductors of grounding grids 1g) is calculated, passes through equationTry to achieve, wherein, mutual impedance
Matrix R is n × n matrix；It is the electric leakage flow direction on every section of conductor for n dimensional vectors
Amount；For n midpoint potential column vector；
The Potential distribution on ground, ground 1h) are calculated using principle of stacking according to the electric leakage flow distribution for the grounding grids tried to achieve
Potential calculation formula at upper any point P is：
In formula, UiPFor i-th section of conductor leakage current a p-shaped into surface potential；ρ is soil resistivity；rp,zpFor i-th section of conductor
The polar coordinate representation of distance between midpoint and point P；
Calculate the current potential of the leakage current of every section of conductor in each Ground Point formation of grounded screen respectively, then by the result of calculation of all conductors
It is overlapped, so as to obtain the surface potential distribution result of calculation of grounded screen.
3. a kind of grounding net of transformer substation surface potential distribution calculating side based on echo state network according to claim 1
Method, it is characterised in that described step 2 determines echo state network structure and input, output, is specifically：
Echo state network structure described in 2a) includes input layer, reserve pool and output layer, the input signal of described input layer
The reserve pool being made up of the neuron largely arranged at random is connected to by inputting connection weight matrix, neuron is connected by inside
The power of connecing forms reserve pool output, constitutes the internal state vector of network, and is connected to output layer by exporting connection weight；
Each parameter of the echo state network, including state reserve pool neuron number, internal connection weight spectrum half 2b) are set
Footpath；
Input and the output unit number of echo state network 2c) are determined according to the conductor number and mesh count of specific grounded screen；
2d) the connection weight matrix W between random initializtion input and deposit pool unitin, partially connected between reserve pool internal element
Weight matrix W.
4. a kind of grounding net of transformer substation surface potential distribution calculating side based on echo state network according to claim 3
Method, it is characterised in that the method that described step 3 sets up the grounded screen surface potential computation model based on echo state network,
Specifically：
3a) according to grounded screen surface potential result of calculation, the input u (k) of training sample needed for determining echo state network and defeated
Go out y (k), wherein, k=1,2 ..., r, r is number of samples；
3b) the original state x (0) of arbitrarily selected reserve pool intrinsic nerve member, elects 0 as；
Training input sample 3c) is added into reserve pool through inputting connection weight, reserve pool state is sequentially completed by echo state network
Calculating and corresponding network outputCalculating and collection；The vectorial calculation formula of described reserve pool internal state is：
X (k+1)=f1(Winu(k+1)+Wx(k))
In formula, f1For reserve pool neuron activation functions；U (k+1) is the input of+1 iteration of echo state network kth；
The calculation formula of corresponding network output is：
In formula, f2For output function, because output layer is linear, therefore f2Take identity function；WoutFor output connection weight matrix；
During specific calculating, echo state network collection system state since the m times iteration, and with vector x (k) (k=m, m+
1 ..., matrix B r) is constituted, while collecting corresponding output sample y (k) constitutes matrix T；
3d) utilize network reality outputDesired output y (k) is approached, that is, calculates and obtains making the defeated of network mean square error minimum
Go out connection weight matrix Wout, the calculating process, which can be converted into, solves following optimization problem：
The optimization problem is solved using linear regression method, calculating obtains Wout, so as to complete the training to echo state network；
The WoutExpression formula be：
(Wout)T=B-1T。
5. a kind of grounding net of transformer substation surface potential distribution calculating side based on echo state network according to claim 1
Method, it is characterised in that the detailed process of calculating grounded screen surface potential distribution is in described step 6：
4a) to a certain conductor or mesh, according to the position coordinates x=[x of its known surface potential point0,x1,…,xL-1]TAnd it is corresponding
Surface potential z=[z0,z1,…,zL-1]T, wherein x0,x1,…,xL-1And z0,z1,…,zL-1For L position coordinate value and accordingly
Representative potential value, construction orthogonal polynomial { PL(x) }, its recurrence Relation is：
In formula, Pk(x) it is k order polynomials that leading coefficient is 1；ak,βkFor multinomial coefficient；
According to Pk(x) orthogonality draws ak,βkWith Pk(x) relational expression, its expression formula is：
By ak,βkExpression formula substitute into { PL(x) stepping type }, progressively recursion obtain { PL(x) each single item in }, and then completion pair
The construction of orthogonal polynomial；
4b) digital simulation curve coefficientsAnd progressivelyBe added in matched curve function F (x), obtain the conductor or
The surface potential of mesh is distributed, and described coefficient formulas and surface potential expression formula is：
Its surface potential 4c) is calculated by above-mentioned steps to all conductors and mesh, and then superposition obtains whole earth's surface Potential distributions,
Calculated so as to which the surface potential completed to grounding net of transformer substation is distributed.
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| CN107505536B (en) * | 2017-08-07 | 2020-03-31 | 国网上海市电力公司 | Transformer substation grounding grid earth surface potential distribution calculation method considering multiple metal pipelines |
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| CN108387817B (en) * | 2018-01-23 | 2020-10-27 | 中国科学院电工研究所 | Grounding grid fault diagnosis method and device based on current injection type multi-field coupling |
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