CN115000947A - Power distribution network topological structure and line parameter identification method based on intelligent electric meter measurement - Google Patents
Power distribution network topological structure and line parameter identification method based on intelligent electric meter measurement Download PDFInfo
- Publication number
- CN115000947A CN115000947A CN202210701249.XA CN202210701249A CN115000947A CN 115000947 A CN115000947 A CN 115000947A CN 202210701249 A CN202210701249 A CN 202210701249A CN 115000947 A CN115000947 A CN 115000947A
- Authority
- CN
- China
- Prior art keywords
- equal
- formula
- follows
- line
- admittance
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000009826 distribution Methods 0.000 title claims abstract description 55
- 238000005259 measurement Methods 0.000 title claims abstract description 48
- 238000000034 method Methods 0.000 title claims abstract description 30
- 238000012417 linear regression Methods 0.000 claims abstract description 22
- 238000005457 optimization Methods 0.000 claims abstract description 9
- 239000011159 matrix material Substances 0.000 claims description 69
- 239000013598 vector Substances 0.000 claims description 11
- 238000002347 injection Methods 0.000 claims description 8
- 239000007924 injection Substances 0.000 claims description 8
- 238000004364 calculation method Methods 0.000 claims description 7
- 230000003044 adaptive effect Effects 0.000 claims description 6
- 238000012216 screening Methods 0.000 claims description 4
- 230000017105 transposition Effects 0.000 claims description 4
- NAWXUBYGYWOOIX-SFHVURJKSA-N (2s)-2-[[4-[2-(2,4-diaminoquinazolin-6-yl)ethyl]benzoyl]amino]-4-methylidenepentanedioic acid Chemical compound C1=CC2=NC(N)=NC(N)=C2C=C1CCC1=CC=C(C(=O)N[C@@H](CC(=C)C(O)=O)C(O)=O)C=C1 NAWXUBYGYWOOIX-SFHVURJKSA-N 0.000 claims description 3
- 238000003491 array Methods 0.000 claims 3
- 230000001360 synchronised effect Effects 0.000 description 4
- 230000005540 biological transmission Effects 0.000 description 2
- 238000011156 evaluation Methods 0.000 description 2
- VZSRBBMJRBPUNF-UHFFFAOYSA-N 2-(2,3-dihydro-1H-inden-2-ylamino)-N-[3-oxo-3-(2,4,6,7-tetrahydrotriazolo[4,5-c]pyridin-5-yl)propyl]pyrimidine-5-carboxamide Chemical compound C1C(CC2=CC=CC=C12)NC1=NC=C(C=N1)C(=O)NCCC(N1CC2=C(CC1)NN=N2)=O VZSRBBMJRBPUNF-UHFFFAOYSA-N 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000005206 flow analysis Methods 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000010248 power generation Methods 0.000 description 1
- 238000005070 sampling Methods 0.000 description 1
Images
Classifications
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J3/00—Circuit arrangements for ac mains or ac distribution networks
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
-
- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
- H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
- H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
- Y02T90/10—Technologies relating to charging of electric vehicles
- Y02T90/16—Information or communication technologies improving the operation of electric vehicles
- Y02T90/167—Systems integrating technologies related to power network operation and communication or information technologies for supporting the interoperability of electric or hybrid vehicles, i.e. smartgrids as interface for battery charging of electric vehicles [EV] or hybrid vehicles [HEV]
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Mathematical Physics (AREA)
- Pure & Applied Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Computational Mathematics (AREA)
- Data Mining & Analysis (AREA)
- Theoretical Computer Science (AREA)
- Computing Systems (AREA)
- Algebra (AREA)
- Databases & Information Systems (AREA)
- Software Systems (AREA)
- General Engineering & Computer Science (AREA)
- Power Engineering (AREA)
- Supply And Distribution Of Alternating Current (AREA)
Abstract
The invention discloses a power distribution network topological structure and line parameter identification method based on intelligent electric meter measurement, which comprises the following steps: an active power, reactive power and voltage amplitude measurement sequence is injected into an input node; establishing a linear power flow model according to the operation characteristics of the power distribution network, and solving an admittance estimation array based on linear regression to obtain an initial topological structure and a line parameter estimation initial value; and correcting the estimated value of the line admittance through decoupling iterative optimization among variables, and outputting a final topological structure and a line parameter identification result. The method is based on the measurement of the intelligent ammeter, does not need to obtain the phase angle measurement of the node voltage, and has good applicability in the actual power distribution network; and secondly, admittance parameters of the running line can be effectively estimated while the topological structure is accurately identified, and the limitation that the traditional identification scheme can only carry out topology identification is overcome.
Description
Technical Field
The invention belongs to the field of intelligent power grid power distribution, and particularly relates to a power distribution network topological structure and line parameter identification method based on intelligent electric meter measurement.
Background
The power distribution network is an important link for connecting power generation and transmission with power supply and utilization in a power system, and the premise of ensuring safe and stable operation of the power distribution network is that national economy develops rapidly. Along with novel power supplies and load devices such as distributed photovoltaic, microgrid and electric vehicle charging stations are continuously connected into the power grid, the complexity and flexibility of the power distribution grid are greatly increased, the topological structure changes frequently, and the line parameter updating lags behind. The correct topological structure and line parameter information are the prerequisite condition for the state estimation and the power flow analysis of the power distribution network, and are the basis for realizing accurate regulation and control of the power grid production management system.
The construction of a high-level measurement system enables a large amount of electrical data generated in the operation process of the power distribution network to be effectively collected and uploaded, and currently, measurement equipment applied to the power distribution network is mainly divided into a synchronous vector measurement device and a smart meter. The synchronous vector measurement device simultaneously obtains high-precision node injection power and voltage phasor measurement information through a global positioning system, has the advantages of high data transmission speed and small synchronous time error, but is only installed at key nodes such as important transformer substations and the like at present due to high investment cost, and cannot realize comprehensive coverage in a power distribution network. The intelligent electric meter measuring equipment is widely deployed in a power distribution network due to low physical cost, but can only collect node injection power and voltage amplitude data and cannot measure a node voltage phase angle.
The existing topology identification technology based on the intelligent electric meter measuring equipment mostly searches for adjacent nodes by analyzing the correlation between node voltage amplitudes, or obtains an operation topological structure by solving an optimization model containing line switch state information based on a state estimation thought, but the methods cannot estimate line admittance parameters at the same time, so that the method has certain limit in practical application.
Disclosure of Invention
The invention aims to provide a method for identifying a topological structure and line parameters of a power distribution network based on intelligent electric meter measurement, and aims to solve the problems that the existing topological identification method is poor in applicability in an actual power distribution network and cannot identify the topological structure and the line parameters at the same time.
The technical scheme is as follows: in order to achieve the purpose, the invention discloses a power distribution network topological structure and line parameter identification method based on intelligent electric meter measurement, which comprises the following steps:
s1, inputting the injection active power, the injection reactive power and the voltage amplitude measurement sequence of all the nodes in the power distribution network;
s2, establishing a linear power flow model, and solving an admittance estimation array based on linear regression to obtain an initial topological structure and a line parameter identification result;
and S3, correcting the line admittance estimated value based on decoupling iterative optimization, and outputting a final topological structure and line parameter identification result.
Further, the specific steps of establishing the linear power flow model in S2 include the following:
s2.1.1, active power p is injected into the node, reactive power q is injected, and the classic power flow equation is satisfied between the voltage amplitude v and the voltage phase angle theta, and the formula is as follows:
wherein i is a node number in the power distribution network, i belongs to {1,2, …, N }, N is the total number of nodes in the power distribution network, and G and B are a real part and an imaginary part of a power distribution network admittance matrix respectively;
s2.1.2, the distribution network actually operated has the following characteristics:
the node voltage amplitude is usually stabilized around a per unit value of 1, so that there is a node voltage variation Δ v i Is a small amount, Δ v i The formula of (1) is as follows:
Δv i ＝v i -1 (3)
phase angle difference theta of branch voltage ik Hardly exceeds 10 °, a small amount is also considered, so that:
sinθ ik ≈θ ik (4)
cosθ ik ≈1 (5)
s2.1.3, equation (1), and equation (2) can be written as follows:
s2.1.4, through 1+ Δ v k Replacement node voltage v k In conjunction with equation (4) and equation (5), equation (6) and equation (7) become:
s2.1.5, due to Δ v k And theta ik Both are small, the product terms of both become second order small, and therefore can be omitted, and equation (8) and equation (9) become:
s2.1.6 parallel admittance element value y of nodes in power distribution network i0 Smaller, the diagonal elements of the admittance matrix are approximately equal to the sum of the admittances of the branches connected to the corresponding nodes, and the off-diagonal elements of the admittance matrix are equal to the negative of the admittance of the branches between the corresponding nodes, so that the two values in each of the equations (10) and (11) are zero, and the equations after removing the zero term are respectively as followsThe following:
s2.1.7, writing the formula (12) and the formula (13) into a matrix form to obtain a linear power flow model, wherein the formula is as follows:
wherein, [ p/v ]]＝[p 1 /v 1 …p N /v N ] T ，[q/v]＝[q 1 /v 1 …q N /v N ] T ，[Δv]＝[Δv 1 …Δv N ] T ，[θ]＝[θ 1 …θ N ] T Measuring vectors of information for all nodes of the power distribution network; [] T Representing a matrix transposition;
s2.1.8, the linear power flow model represented by equation (14) can be extended to applications where node voltage phase angle information is unknown, due to the smaller values of voltage phase angle compared to voltage magnitude. Equation (14) is thus further simplified as follows:
further, the specific steps of solving the admittance estimation array based on linear regression in S2 to obtain the initial topological structure and line parameter identification result include the following:
s2.2.1 calculating [ P/V ], [ Q/V ] and [ Δ V ] from the measured sequence, and substituting them into the equations (15) and (16) to obtain the following equations:
wherein, [ P/V]＝[[p/v] 1 …[p/v] M1 ]，[Q/V]＝[[q/v] 1 …[q/v] M1 ]，[ΔV]＝[[Δv] 1 …[Δv] M1 ]；M 1 Obtaining the measured quantity;
s2.2.2 finding admittance estimating array G based on linear regression ^ And B ^ The formulas are respectively as follows:
s2.2.3, order G ^ last Is equal to the current G ^ ；
S2.2.4, pair G ^ And B ^ Carrying out noise reduction treatment;
s2.2.5, pair G ^ And B ^ Carrying out a symmetry treatment to obtain G ^ sym And B ^ sym The formulas are respectively as follows:
s2.2.6, judgment G ^ sym Whether or not it is equal to G ^ last If G is ^ sym Is equal to G ^ last Then G will be ^ sym The line numbers corresponding to all the non-zero elements except the diagonal element in the upper triangular part form an operation line set E ^ And output E ^ ，G ^ sym And B ^ sym As the initial topological structure and line parameter identification result; if G is ^ sym Is not equal to G ^ last Then, the following steps are continuously executed;
s2.2.7, order G ^ last And G ^ Is equal to G ^ sym ，B ^ Is equal to B ^ sym ；
S2.2.8 updating G based on linear regression ^ And B ^ To S2.2.4.
Further, the specific step of S2.2.4 is to traverse G ^ For | G ^ ik |/|G ^ ii |＜ω g And | G ^ ki |/|G ^ kk |＜ω g Of an element of (A) having G ^ ik ＝B ^ ik ＝G ^ ki ＝B ^ ki 0. Wherein, ω is g For the noise reduction threshold, the formula is as follows:
further, the S2.2.8 is updated based on linear regression ^ And B ^ The specific steps of the non-zero element in (1) comprise the following steps:
s2.2.8.1, setting the line number i to 1;
s2.2.8.2 screening G ^ Non-zero element G in row i ik Generating a set K from the column numbers K corresponding to all the non-zero elements i ，K i Radical of (A) is denoted as r i ；
S2.2.8.3, update G ^ Non-zero element G in row i i,Ki The formula is as follows:
wherein [ P ] i /V i ]＝[(p i /v i ) 1 …(p i /v i ) M1 ]，[ΔV Ki ]＝[[ΔV 1 ]；…；[ΔV k ]；…；[ΔV ri ]]，[ΔV k ]＝[Δv k1 …Δv kM1 ]；
S2.2.8.4, update B ^ Non-zero element B in row i i,Ki The formula is as follows:
wherein [ Q ] i /V i ]＝[(q i /v i ) 1 …(q i /v i ) M1 ]，[ΔV Ki ]＝[[ΔV 1 ]；…；[ΔV k ]；…；[ΔV ri ]]，[ΔV k ]＝[Δv k1 …Δv kM1 ]；
S2.2.8.5, i ═ i +1, back to S2.2.8.2 until i ═ N.
Further, the specific steps of S3 include the following:
s3.1, setting the iteration number T to be 1, and changing the parameter variable quantity delta x ^ Select the last M from the measurement sequence as 0 2 Performing the subsequent steps of strip measurement; wherein M is 2 The following formula is required:
wherein M is ^ Is E ^ A group of (a);
s3.2, calculating pseudo load flow to obtain node voltage phase angle information;
s3.3, current line admittance estimated value matrix x ^ The formula of (1) is as follows:
wherein, [ g ]]＝[g 1 …g M^ ] T ，[b]＝[b 1 …b M^ ] T Each represents E ^ A conductivity value and susceptance value matrix of the middle line; let x be ^ last Is equal to x ^ ，Δx ^ last Is equal to Δ x ^ ；
S3.4, judging whether T is an odd number, if T is an odd number, utilizing [ P ]]，[V]，[θ]Calculating a coefficient matrix A 1 ,y 1 And a weight matrix w 1 (ii) a If T is even, then [ Q ] is utilized]，[V]，[θ]Calculating a coefficient matrix A 2 ,y 2 And a weight matrix w 2 (ii) a Wherein A is 1 ＝[a p1 ；…；a pM2 ]，y 1 ＝[p 1 ；…；p M2 ]；A 2 ＝[a q1 ；…；a qM2 ]，y 2 ＝[q 1 ；…；q M2 ]；[a p ]＝[a g a b ]，[p]＝[p 1 …p N ] T ；[a q ]＝[a b -a g ]，[q]＝[q 1 …q N ] T ；a g And a b Are all of NxM ^ The dimension matrix has the following formula of element values:
wherein τ is M ^ X 2 dimensional matrix, first column storing E ^ The second column stores the numbers of the end nodes; w is a 1 And w 2 Are all 2M ^ X 1-dimensional weight coefficient matrix, the formula is as follows:
wherein x is 0_1 And x 0_2 Respectively as follows:
x 0_1 ＝(A 1 T A 1 ) -1 A 1 T y 1 (32)
x 0_2 ＝(A 2 T A 2 ) -1 A 2 T y 2 (33)
s3.5, solving x based on self-adaptive ridge regression model ^ ；
S3.6 according to x ^ Modified admittance estimate array G ^ And B ^ Element value of middle corresponding position, G ^ And B ^ Middle non-diagonal elements are respectively equal to x ^ The conductance value and the susceptance value of the corresponding branch are negative, and the diagonal elements are respectively equal to x ^ The sum of the conductance value and the susceptance value of the branch connected with the corresponding node;
s3.7, go through G ^ If there is | G ^ ij |/|G ^ ii |＜ω g Then x is ^ The admittance estimated value of the corresponding line in the network is set to be zero;
s3.8, calculating x before and after iteration ^ Change Δ x of ^ The formula is as follows:
Δx ^ ＝||x ^ -x ^ last || 2 (34)
wherein | | | purple hair 2 A 2-norm representing a vector;
s3.9, determining Delta x ^ -Δx ^ last Is less than the convergence threshold
If less than, according to x ^ Modified admittance estimate array G ^ And B ^ And obtaining a final operation line set E ^ Output E ^ ，G ^ And B ^ As the final topological structure and line parameter identification result; otherwise T ═ T +1, return to S3.2.
Further, the specific step of the pseudo load flow calculation in S3.2 is based on M 2 Active power measurement, reactive power measurement and G ^ ，B ^ And obtaining a corresponding node voltage phase angle estimation value through load flow calculation.
Further, the specific steps of S3.5 include the following:
s3.5.1, the regularization parameter λ when the function V (λ) takes the minimum value is represented as λ opt The formula of V (λ) is as follows:
wherein, I represents an identity matrix, tr () represents a trace of the matrix, and K has the following formula:
K＝A(A T A+(M 2 ×N)λw·w·I 2M^ ) -1 A T (36)
wherein if T is an odd number, then A equals A 1 Y is equal to y 1 W is equal to w 1 (ii) a Otherwise, A equals A 2 Y is equal to y 2 W is equal to w 2 ；
S3.5.2, obtaining x by solving a minimized adaptive ridge regression model ^ The formula is as follows:
wherein'-' represents a matrix dot product operator; if T is odd, A equals A 1 Y is equal to y 1 W is equal to w 1 (ii) a Otherwise, A equals A 2 Y is equal to y 2 W is equal to w 2 。
Has the beneficial effects that:
1. according to the method for identifying the topological structure and the line parameters of the power distribution network based on the measurement of the intelligent electric meter, the initial identification result of the topological structure and the line parameters can be rapidly obtained by establishing the linear power flow model; and then, the line admittance estimated value is corrected through decoupling optimization iteration among variables, so that the accuracy of the identification result is further improved.
2. The method for identifying the topological structure and the line parameters of the power distribution network based on the measurement of the intelligent electric meter does not need to acquire the phase angle measurement of the node voltage, has good applicability in the actual power distribution network, and has lower physical cost of intelligent electric meter measurement equipment compared with the identification method based on a synchronous vector measurement device.
3. The method for identifying the topological structure and the line parameters of the power distribution network based on the measurement of the intelligent electric meter can accurately identify the topological structure and effectively estimate the admittance parameters of the running line, and overcomes the limitation that the traditional identification scheme can only identify the topology.
Drawings
FIG. 1 is a general flow diagram of the present invention;
FIG. 2 is a flow chart of the present invention for solving initial topology and line parameter identification results based on linear regression;
FIG. 3 is a flowchart of the method for solving the final topology and line parameter identification results based on decoupling iterative optimization.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
As shown in fig. 1, the present invention provides a method for identifying a topology and line parameters of a power distribution network based on smart meter measurement, comprising the following steps:
(1) inputting the injected active power, the injected reactive power and the voltage amplitude measurement sequence of all nodes in the power distribution network;
(2) establishing a linear power flow model, and solving an admittance estimation array based on linear regression to obtain an initial topological structure and a line parameter identification result; the specific steps for establishing the linear power flow model comprise the following steps:
(2.1.1), the node injects active power p, injects reactive power q, satisfies the classic trend equation between voltage amplitude v and voltage phase angle theta, and the formula is as follows:
wherein i is a node number in the power distribution network, i belongs to {1,2, …, N }, N is the total number of nodes in the power distribution network, and G and B are a real part and an imaginary part of a power distribution network admittance matrix respectively;
(2.1.2) the power distribution network in actual operation has the following characteristics:
the node voltage amplitude is usually stabilized around a per unit value of 1, so that there is a node voltage variation Δ v i Is a small quantity, Δ v i The formula (c) is as follows:
Δv i ＝v i -1 (3)
phase angle difference theta of branch voltage ik Hardly exceeds 10 °, a small amount is also considered, so that:
sinθ ik ≈θ ik (4)
cosθ ik ≈1 (5)
(2.1.3), formula (1), and formula (2) can be written as the following formulas, respectively:
(2.1.4), by 1+ Δ v k Alternative node voltage v k Combining equations (4) andequation (5), equation (6) and equation (7) become:
(2.1.5) due to Δ v k And theta ik Both are small quantities, the product terms of both become second order small quantities and therefore can be omitted, and equation (8) and equation (9) become:
(2.1.6) parallel admittance element value y of node in power distribution network i0 Smaller, the diagonal elements of the admittance matrix are approximately equal to the sum of the admittances of the branches connected to the corresponding nodes, and the off-diagonal elements of the admittance matrix are equal to the negative of the admittance of the branches between the corresponding nodes, so that the two values in the formula (10) and the formula (11) are respectively zero, and the formula after removing the zero term is respectively as follows:
(2.1.7), writing the formula (12) and the formula (13) into a matrix form to obtain a linear power flow model, wherein the formula is as follows:
wherein, [ p/v ]]＝[p 1 /v 1 …p N /v N ] T ，[q/v]＝[q 1 /v 1 …q N /v N ] T ，[Δv]＝[Δv 1 …Δv N ] T ，[θ]＝[θ 1 …θ N ] T The vector containing the measurement information of all nodes of the power distribution network is obtained; [] T Representing a matrix transposition;
(2.1.8), since the voltage phase angle is smaller than the voltage magnitude, the linear power flow model represented by equation (14) can be extended to situations where the node voltage phase angle information is unknown. Equation (14) is thus further simplified as follows:
as shown in fig. 2, the specific steps of solving the admittance estimation array based on linear regression to obtain the initial topological structure and line parameter identification result include the following:
(2.2.1), [ P/V ], [ Q/V ] and [ Δ V ] are calculated from the measured sequence, and are substituted into the formula (15) and the formula (16), respectively, to obtain the following formulas:
wherein, [ P/V]＝[[p/v] 1 …[p/v] M1 ]，[Q/V]＝[[q/v] 1 …[q/v] M1 ]，[ΔV]＝[[Δv] 1 …[Δv] M1 ]；M 1 Obtaining the measured quantity;
(2.2.2) obtaining admittance estimation matrix G based on linear regression ^ And B ^ The formulas are respectively as follows:
(2.2.3) order G ^ last Equal to the current G ^ ；
(2.2.4) to G ^ And B ^ Carrying out noise reduction treatment; the specific steps are traversing G ^ For | G ^ ik |/|G ^ ii |＜ω g And | G ^ ki |/|G ^ kk |＜ω g Of an element of (A) having G ^ ik ＝B ^ ik ＝G ^ ki ＝B ^ ki 0. Wherein, ω is g For the noise reduction threshold, the formula is as follows:
(2.2.5) to G ^ And B ^ Carrying out a symmetry treatment to obtain G ^ sym And B ^ sym The formulas are respectively as follows:
(2.2.6) judgment G ^ sym Whether or not equal to G ^ last If G is ^ sym Is equal to G ^ last Then G will be ^ sym The line numbers corresponding to all the non-zero elements except the diagonal element in the upper triangular part form an operation line set E ^ And output E ^ ，G ^ sym And B ^ sym As the initial topological structure and line parameter identification result; if G is ^ sym Is not equal to G ^ last Then, the following steps are continuously executed;
(2.2.7) order G ^ last And G ^ Is equal to G ^ sym ，B ^ Is equal to B ^ sym ；
(2.2.8) updating G based on Linear regression ^ And B ^ Go to (2.2.4). Wherein G is updated based on linear regression ^ And B ^ The specific steps of the non-zero element in (1) include the following:
(2.2.8.1), setting a row number i to 1;
(2.2.8.2) screening G ^ Non-zero element G in row i ik Generating a set K from the column numbers K corresponding to all the non-zero elements i ，K i Radical of (A) is denoted as r i ；
(2.2.8.3) update G ^ Non-zero element G in row i i,Ki The formula is as follows:
wherein [ P ] i /V i ]＝[(p i /v i ) 1 …(p i /v i ) M1 ]，[ΔV Ki ]＝[[ΔV 1 ]；…；[ΔV k ]；…；[ΔV ri ]]，[ΔV k ]＝[Δv k1 …Δv kM1 ]；
(2.2.8.4) update B ^ Non-zero element B in row i i,Ki The formula is as follows:
wherein [ Q ] i /V i ]＝[(q i /v i ) 1 …(q i /v i ) M1 ]，[ΔV Ki ]＝[[ΔV 1 ]；…；[ΔV k ]；…；[ΔV ri ]]，[ΔV k ]＝[Δv k1 …Δv kM1 ]；
And (2.2.8.5), i is equal to i +1, and the step (2.2.8.2) is returned until i is equal to N.
(3) And as shown in fig. 3, correcting the line admittance estimated value based on decoupling iterative optimization, and outputting a final topological structure and line parameter identification result. The method comprises the following specific steps:
(3.1) setting the iteration number T to be 1, and changing the parameter variable quantity delta x ^ Select the last M from the measurement sequence as 0 2 Performing the subsequent steps of strip measurement; wherein, M 2 The following formula is required:
wherein M is ^ Is E ^ A group of (a);
(3.2) calculating pseudo load flow to obtain node voltage phase angle information; wherein the specific steps of the pseudo load flow calculation are based on M 2 Active power measurement, reactive power measurement and G ^ ，B ^ And obtaining a corresponding node voltage phase angle estimation value through load flow calculation.
(3.3) current line admittance estimate matrix x ^ The formula (c) is as follows:
wherein, [ g ]]＝[g 1 …g M^ ] T ，[b]＝[b 1 …b M^ ] T Each represents E ^ A conductivity value and susceptance value matrix of the middle line; let x ^ last Is equal to x ^ ，Δx ^ last Is equal to Δ x ^ ；
(3.4) determining whether T is odd, if T is odd, [ P ] is used]，[V]，[θ]Calculating a coefficient matrix A 1 ,y 1 And a weight matrix w 1 (ii) a If T is even, then [ Q ] is utilized]，[V]，[θ]Calculating a coefficient matrix A 2 ,y 2 And a weight matrix w 2 (ii) a Wherein, A 1 ＝[a p1 ；…；a pM2 ]，y 1 ＝[p 1 ；…；p M2 ]；A 2 ＝[a q1 ；…；a qM2 ]，y 2 ＝[q 1 ；…；q M2 ]；[a p ]＝[a g a b ]，[p]＝[p 1 …p N ] T ；[a q ]＝[a b -a g ]，[q]＝[q 1 …q N ] T ；a g And a b Are all NxM ^ The formula of the element values of the dimensional matrix is as follows:
wherein τ is M ^ X 2 dimensional matrix, first column storing E ^ The second column stores the serial numbers of the end nodes; w is a 1 And w 2 Are all 2M ^ X 1-dimensional weight coefficient matrix, the formula is as follows:
wherein x is 0_1 And x 0_2 Respectively as follows:
x 0_1 ＝(A 1 T A 1 ) -1 A 1 T y 1 (32)
x 0_2 ＝(A 2 T A 2 ) -1 A 2 T y 2 (33)
(3.5) obtaining x based on adaptive ridge regression model ^ (ii) a The method comprises the following specific steps:
(3.5.1) recording the regularization parameter λ as λ when the function V (λ) takes the minimum value opt The formula of V (λ) is as follows:
wherein, I represents an identity matrix, tr () represents a trace of the matrix, and K has the following formula:
K＝A(A T A+(M 2 ×N)λw·w·I 2M^ ) -1 A T (35)
wherein if T is an odd number, then A equals A 1 Y is equal to y 1 W is equal to w 1 (ii) a Otherwise, A equals A 2 Y is equal to y 2 W is equal to w 2 ；
(3.5.2) obtaining x by solving a minimization of adaptive ridge regression model ^ The formula is as follows:
wherein'-' represents a matrix dot product operator; if T is odd, A equals A 1 Y is equal to y 1 W is equal to w 1 (ii) a Otherwise, A equals A 2 Y is equal to y 2 W is equal to w 2 。
(3.6) according to x ^ Modified admittance estimate array G ^ And B ^ Element value of middle corresponding position, G ^ And B ^ Middle non-diagonal elements are respectively equal to x ^ Of conductance and susceptance values of the respective branchesNegative number, diagonal elements equal to x respectively ^ The sum of the conductance value and the susceptance value of the branch connected with the corresponding node;
(3.7) traverse G ^ If there is | G ^ ij |/|G ^ ii |＜ω g Then x is ^ The admittance estimated value of the corresponding line in the network is set to be zero;
(3.8) calculating x before and after iteration ^ Change Δ x of ^ The formula is as follows:
Δx ^ ＝||x ^ -x ^ last || 2 (37)
wherein | | | purple hair 2 A 2-norm representing a vector;
(3.9) determination of Δ x ^ -Δx ^ last Is less than a convergence threshold
If less than, according to x ^ Modified admittance estimate array G ^ And B ^ And obtaining a final operation line set E ^ Output E ^ ，G ^ And B ^ As the final topological structure and line parameter identification result; otherwise, returning to the step (3.2) if T is equal to T + 1.
Example 1
The embodiment is based on a distribution network with 33 nodes in a certain area, and data come from injection active power, injection reactive power and voltage amplitude measurement sequences of all nodes in the distribution network in one day. The sampling interval of the intelligent ammeter is 5 minutes, namely M 1 Equal to 288; the precision grade of the intelligent electric meter is 0.2s, namely the maximum relative percentage error of the measured data is within +/-0.2%. The method for identifying the topological structure and the line parameters of the power distribution network based on the measurement of the intelligent electric meter based on the data comprises the following steps:
(1) inputting the injected active power, the injected reactive power and the voltage amplitude measurement sequence of all nodes in the power distribution network;
(2) establishing a linear power flow model, and solving an admittance estimation array based on linear regression to obtain an initial topological structure and a line parameter identification result; the specific steps for establishing the linear power flow model comprise the following steps:
(2.1.1), the node injects active power p, injects reactive power q, satisfies the classic trend equation between voltage amplitude v and voltage phase angle theta, and the formula is as follows:
wherein i is a node number in the power distribution network, i is epsilon {1,2, …, N }, N is a total number of nodes in the power distribution network, in embodiment 1, N is equal to 33, and G and B are a real part and an imaginary part of an admittance matrix of the power distribution network respectively;
(2.1.2) the power distribution network in actual operation has the following characteristics:
the node voltage amplitude is usually stabilized around a per unit value of 1, so that there is a node voltage variation Δ v i Is a small amount, Δ v i The formula of (1) is as follows:
Δv i ＝v i -1 (3)
phase angle difference theta of branch voltage ik Hardly exceeds 10 °, a small amount is also considered, so that:
sinθ ik ≈θ ik (4)
cosθ ik ≈1 (5)
(2.1.3), formula (1), and formula (2) can be written as the following formulas, respectively:
(2.1.4) by 1+ Δ v k Alternative node voltage v k In conjunction with equations (4) and (5), equations (6) and (7) become:
(2.1.5) due to Δ v k And theta ik Both are small quantities, the product terms of both become second order small quantities and therefore can be omitted, and equation (8) and equation (9) become:
(2.1.6) parallel admittance element value y of node in power distribution network i0 Smaller, the diagonal elements of the admittance matrix are approximately equal to the sum of the admittances of the branches connected to the corresponding nodes, and the off-diagonal elements of the admittance matrix are equal to the negative of the admittance of the branches between the corresponding nodes, so that the two values in the formula (10) and the formula (11) are respectively zero, and the formula after removing the zero term is respectively as follows:
(2.1.7), writing the formula (12) and the formula (13) into a matrix form to obtain a linear power flow model, wherein the formula is as follows:
wherein, [ p/v ]]＝[p 1 /v 1 …p N /v N ] T ，[q/v]＝[q 1 /v 1 …q N /v N ] T ，[Δv]＝[Δv 1 …Δv N ] T ，[θ]＝[θ 1 …θ N ] T Measuring vectors of information for all nodes of the power distribution network; [] T Representing a matrix transposition;
(2.1.8), since the voltage phase angle is smaller than the voltage magnitude, the linear power flow model represented by equation (14) can be extended to situations where the node voltage phase angle information is unknown. Equation (14) is thus further simplified as follows:
as shown in fig. 2, the specific steps of solving the admittance estimation array based on linear regression to obtain the initial topological structure and line parameter identification result include the following:
(2.2.1), [ P/V ], [ Q/V ] and [ Δ V ] are calculated from the measured sequence, and are substituted into the formula (15) and the formula (16), respectively, to obtain the following formulas:
wherein, [ P/V]＝[[p/v] 1 …[p/v] M1 ]，[Q/V]＝[[q/v] 1 …[q/v] M1 ]，[ΔV]＝[[Δv] 1 …[Δv] M1 ]；M 1 For the measured quantities obtained, M in example 1 1 Equal to 288;
(2.2.2) obtaining an admittance estimating array G based on linear regression ^ And B ^ The formulas are respectively as follows:
(2.2.3) order G ^ last Is equal to the current G ^ ；
(2.2.4) to G ^ And B ^ Carrying out noise reduction treatment; the specific steps are traversing G ^ For | G ^ ik |/|G ^ ii |＜ω g And | G ^ ki |/|G ^ kk |＜ω g Of an element of (A) having G ^ ik ＝B ^ ik ＝G ^ ki ＝B ^ ki 0. Wherein, ω is g For the noise reduction threshold, the formula is as follows:
in example 1,. omega. g The value is 0.03;
(2.2.5) to G ^ And B ^ Carrying out a symmetry treatment to obtain G ^ sym And B ^ sym The formulas are respectively as follows:
(2.2.6) judgment G ^ sym Whether or not equal to G ^ last If G is ^ sym Is equal to G ^ last Then G will be ^ sym The line numbers corresponding to all the non-zero elements except the diagonal element in the upper triangular part form an operation line set E ^ And output E ^ ，G ^ sym And B ^ sym As the initial topological structure and line parameter identification result; if G is ^ sym Is not equal to G ^ last Then continuing to execute the following steps;
(2.2.7) order G ^ last And G ^ Is equal to G ^ sym ，B ^ Is equal to B ^ sym ；
(2.2.8) updating G based on Linear regression ^ And B ^ Go to (2.2.4). Wherein G is updated based on linear regression ^ And B ^ The specific steps of the non-zero element in (1) include the following:
(2.2.8.1), setting a row number i to 1;
(2.2.8.2) screening G ^ Non-zero element G in row i ik Generating a set K from the column numbers K corresponding to all the non-zero elements i ，K i Radical of (A) is denoted as r i ；
(2.2.8.3) update G ^ Non-zero element G in row i i,Ki The formula is as follows:
wherein [ P ] i /V i ]＝[(p i /v i ) 1 …(p i /v i ) M1 ]，[ΔV Ki ]＝[[ΔV 1 ]；…；[ΔV k ]；…；[ΔV ri ]]，[ΔV k ]＝[Δv k1 …Δv kM1 ]；
(2.2.8.4) update B ^ Non-zero in row iElement B i,Ki The formula is as follows:
wherein [ Q ] i /V i ]＝[(q i /v i ) 1 …(q i /v i ) M1 ]，[ΔV Ki ]＝[[ΔV 1 ]；…；[ΔV k ]；…；[ΔV ri ]]，[ΔV k ]＝[Δv k1 …Δv kM1 ]；
And (2.2.8.5), i is equal to i +1, and the step (2.2.8.2) is returned until i is equal to N.
(3) And as shown in fig. 3, correcting the line admittance estimated value based on decoupling iterative optimization, and outputting a final topological structure and line parameter identification result. The method comprises the following specific steps:
(3.1) setting the iteration number T to be 1, and changing the parameter by the quantity delta x ^ Select the last M from the measurement sequence as 0 2 Performing the subsequent steps of strip measurement; wherein, M 2 The following formula is required:
wherein M is ^ Is E ^ A group of (b); example 1, E in the initial recognition result ^ Base M of ^ Equal to 33, M taking into account the measurement errors present 2 The value is 10;
(3.2) calculating pseudo load flow to obtain node voltage phase angle information; wherein the specific steps of the pseudo load flow calculation are based on M 2 Active power measurement, reactive power measurement and G ^ ，B ^ And obtaining a corresponding node voltage phase angle estimation value through load flow calculation.
(3.3) current line admittance estimate matrix x ^ The formula of (1) is as follows:
wherein, [ g ]]＝[g 1 …g M^ ] T ，[b]＝[b 1 …b M^ ] T Each represents E ^ A conductivity value and susceptance value matrix of the middle line; let x ^ last Is equal to x ^ ，Δx ^ last Is equal to Δ x ^ ；
(3.4) determining whether T is odd, if T is odd, [ P ] is used]，[V]，[θ]Calculating a coefficient matrix A 1 ,y 1 And a weight matrix w 1 (ii) a If T is even, then [ Q ] is utilized]，[V]，[θ]Calculating a coefficient matrix A 2 ,y 2 And a weight matrix w 2 (ii) a Wherein A is 1 ＝[a p1 ；…；a pM2 ]，y 1 ＝[p 1 ；…；p M2 ]；A 2 ＝[a q1 ；…；a qM2 ]，y 2 ＝[q 1 ；…；q M2 ]；[a p ]＝[a g a b ]，[p]＝[p 1 …p N ] T ；[a q ]＝[a b -a g ]，[q]＝[q 1 …q N ] T ；a g And a b Are all NxM ^ The formula of the element values of the dimensional matrix is as follows:
wherein τ is M ^ X 2 dimensional matrix, first column stores E ^ The second column stores the serial numbers of the end nodes; w is a 1 And w 2 Are all 2M ^ X 1-dimensional weight coefficient matrix, the formula is as follows:
wherein x is 0_1 And x 0_2 Respectively as follows:
x 0_1 ＝(A 1 T A 1 ) -1 A 1 T y 1 (32)
x 0_2 ＝(A 2 T A 2 ) -1 A 2 T y 2 (33)
(3.5) obtaining x based on adaptive ridge regression model ^ (ii) a The method comprises the following specific steps:
(3.5.1) recording the regularization parameter λ as λ when the function V (λ) takes the minimum value opt The formula of V (λ) is as follows:
wherein, I represents an identity matrix, tr () represents a trace of the matrix, and K has the following formula:
K＝A(A T A+(M 2 ×N)λw·w·I 2M^ ) -1 A T (35)
wherein if T is an odd number, then A equals A 1 Y is equal to y 1 W is equal to w 1 (ii) a Otherwise, A equals A 2 Y is equal to y 2 W is equal to w 2 ；
(3.5.2) obtaining x by solving a minimization of adaptive ridge regression model ^ The formula is as follows:
wherein'·' denotes a matrix dot product operator; if T is odd, A equals A 1 Y is equal to y 1 W etc. ofAt w 1 (ii) a Otherwise, A equals A 2 Y is equal to y 2 W is equal to w 2 。
(3.6) according to x ^ Modified admittance estimate array G ^ And B ^ Element value of middle corresponding position, G ^ And B ^ Middle non-diagonal elements are respectively equal to x ^ The negative number of conductance value and susceptance value of corresponding branch, and diagonal elements are respectively equal to x ^ The sum of the conductance value and the susceptance value of the branch connected with the corresponding node;
(3.7) traverse G ^ If there is | G ^ ij |/|G ^ ii |＜ω g Then x is ^ The admittance estimated value of the corresponding line in the network is set to be zero;
(3.8) calculating x before and after iteration ^ Change Δ x of ^ The formula is as follows:
Δx ^ ＝||x ^ -x ^ last || 2 (37)
wherein | | | calving 2 A 2-norm representing a vector;
(3.9) determination of Δ x ^ -Δx ^ last Is less than a convergence threshold
If less than, according to x ^ Modified admittance estimate array G ^ And B ^ And obtaining a final operation line set E ^ Output E ^ ，G ^ And B ^ As the final topological structure and line parameter identification result; otherwise, returning to the step (3.2) when T is T + 1. In example 1, the convergence threshold value
The value was 0.02.
In embodiment 1, the F1 score is selected as an evaluation index for measuring the accuracy of the identification result of the topology. Operating line set E obtained according to topology estimation ^ The matching relation with the actual operation line set E can divide the judgment result into True Positive (TP) and false positive (FalsePosi)Positive, FP), True Negative (TN), False Negative (FN), the classification results can be represented by the confusion matrix in table 1.
TABLE 1 confusion matrix for topological structure identification results
The formula for the F1 score is as follows:
wherein, P and R are accuracy rate and recall rate index respectively, and the formula is as follows:
as can be seen from equations (38) - (40), the larger the value of F1, the higher the accuracy of the topology identification result, and the F1 score is at most equal to 1, indicating that the topology identification result is completely correct.
In example 1, the Mean Absolute Percentage Error (MAPE) is selected as an evaluation index for measuring the accuracy of the line parameter identification result, and MAPE formulas of the line conductance and susceptance estimation values are as follows:
where m is the number of lines actually runningAmount, in example 1, m is equal to 32; g ij And b ij Respectively representing the actual values of conductance and susceptance of the branch ij; g ij ^ And b ij ^ The estimates of conductance and susceptance for branch ij are shown, respectively.
The identification results of example 1 are shown in table 2. It can be known from the table that only one line with identification error exists in the identification result of the initial topological structure, the F1 score reaches more than 0.95, and the estimated value of the line admittance parameter has certain error; after the estimated value of the line admittance is corrected through decoupling iterative optimization, the final F1 score reaches 1, which indicates that the identification of the topological structure is completely correct, and the identification quality of the line parameters is obviously improved compared with the initial identification result, the MAPE of the final line conductance and susceptance are respectively 0.35% and 0.54%, and the identification result of the line parameters of the embodiment 1 is in an effective range in consideration of the existence of 0.2% of measurement error.
Table 2 example 1 identification results
Claims (8)
1. A power distribution network topological structure and line parameter identification method based on intelligent electric meter measurement is characterized by comprising the following steps:
s1, inputting the injection active power, the injection reactive power and the voltage amplitude measurement sequence of all the nodes in the power distribution network;
s2, establishing a linear power flow model, and solving an admittance estimation array based on linear regression to obtain an initial topological structure and a line parameter identification result;
and S3, correcting the line admittance estimated value based on decoupling iterative optimization, and outputting a final topological structure and line parameter identification result.
2. The method of claim 1, wherein the step of establishing the linear power flow model in S2 comprises the following steps:
s2.1.1, active power p is injected into the node, reactive power q is injected, and the classic power flow equation is satisfied between the voltage amplitude v and the voltage phase angle theta, and the formula is as follows:
wherein i is a node number in the power distribution network, i belongs to {1,2, …, N }, N is the total number of nodes in the power distribution network, and G and B are a real part and an imaginary part of a power distribution network admittance matrix respectively;
s2.1.2, the distribution network actually operated has the following characteristics:
the node voltage amplitude is usually stabilized around a per unit value of 1, so that there is a node voltage variation Δ v i Is a small quantity, Δ v i The formula of (1) is as follows:
Δv i ＝v i -1 (3)
phase angle difference theta of branch voltage ik Is not more than 10 °, a small amount is considered, and therefore:
sinθ ik ≈θ ik (4)
cosθ ik ≈1 (5)
s2.1.3, equation (1), and equation (2) can be written as follows:
s2.1.4, by 1+ Δ v k Replacement node voltage v k Knot (c)Combining equations (4) and (5), equations (6) and (7) are changed to:
s2.1.5, due to Δ v k And theta ik Both are small quantities, the product terms of the two are changed into second-order small quantities, which are omitted, and the formula (8) and the formula (9) are respectively changed into:
s2.1.6, parallel admittance element value y of nodes in power distribution network i0 Smaller, the diagonal elements of the admittance matrix are approximately equal to the sum of the admittances of the branches connected to the corresponding nodes, and the off-diagonal elements of the admittance matrix are equal to the negative of the admittance of the branches between the corresponding nodes, so that the two values in the formula (10) and the formula (11) are respectively zero, and the formula after removing the zero term is respectively as follows:
s2.1.7, writing the formula (12) and the formula (13) into a matrix form to obtain a linear power flow model, wherein the formula is as follows:
wherein, [ p/v ]]＝[p 1 /v 1 … p N /v N ] T ，[q/v]＝[q 1 /v 1 … q N /v N ] T ，[Δv]＝[Δv 1 … Δv N ] T ，[θ]＝[θ 1 … θ N ] T The vector containing the measurement information of all nodes of the power distribution network is obtained; [] T Representing a matrix transposition;
s2.1.8, since the voltage phase angle is smaller than the voltage amplitude value, the linear power flow model represented by equation (14) can be extended to be applied to the situation where the node voltage phase angle information is unknown, so equation (14) is further simplified as the following equation:
3. the method of claim 2, wherein the step of solving the admittance estimation array based on linear regression in S2 to obtain the initial topological structure and line parameter identification result comprises:
s2.2.1 calculating [ P/V ], [ Q/V ] and [ Δ V ] from the measured sequence, and substituting them into the equations (15) and (16) to obtain the following equations:
wherein, [ P/V]＝[[p/v] 1 …[p/v] M1 ]，[Q/V]＝[[q/v] 1 …[q/v] M1 ]，[ΔV]＝[[Δv] 1 …[Δv] M1 ]；M 1 Obtaining the measured quantity;
s2.2.2, obtaining admittance estimation arrays G ^ and B ^ based on linear regression, wherein the formulas are respectively as follows:
s2.2.3, letting G ^ a last Equal to the current G ^ a;
s2.2.4, carrying out noise reduction processing on G ^ and B ^;
s2.2.5, and carrying out symmetry processing on G ^ and B ^ to obtain G ^ sym And B ^ a sym The formulas are respectively as follows:
s2.2.6, determining G ^ sym Whether or not to equal G ^ last If G ^ a sym Equal to G ^ last Then G ^ is set sym The line numbers corresponding to all non-zero elements except the diagonal elements in the upper triangular part form an operating line set E ^ and output E ^ and G ^ sym And B ^ a sym As the initial topological structure and line parameter identification result; if G ^ s sym Is not equal to G ^ last Then, the following steps are continuously executed;
s2.2.7, letting G ^ a last And G ^ is equal to G ^ sym B ^ is equal to B ^ sym ；
S2.2.8, updating non-zero elements in G ^ and B ^ based on linear regression, go to S2.2.4.
4. The method of claim 3, wherein the step of S2.2.4 is traversing G ^ for | G ^ for ik |/|G^ ii |＜ω g And G ^ G ki |/|G^ kk |＜ω g The element of (a) has G ^ ik ＝B^ ik ＝G^ ki ＝B^ ki 0, wherein ω g For the noise reduction threshold, the formula is as follows:
5. the method of claim 3, wherein the specific step of updating non-zero elements in G and B based on linear regression in S2.2.8 comprises the following steps:
s2.2.8.1, setting the line number i to 1;
s2.2.8.2 screening non-zero elements G in line G ^ i ik Generating a set K from the column numbers K corresponding to all the non-zero elements i ，K i Radical of (A) is denoted as r i ；
S2.2.8.3, updating non-zero element G in line Gth i,Ki The formula is as follows:
wherein [ P ] i /V i ]＝[(p i /v i ) 1 … (p i /v i ) M1 ]，[ΔV Ki ]＝[[ΔV 1 ]；…；[ΔV k ]；…；[ΔV ri ]]，[ΔV k ]＝[Δv k1 … Δv kM1 ]；
S2.2.8.4 updating non-zero element B in line B ^ ith i,Ki The formula is as follows:
wherein [ Q ] i /V i ]＝[(q i /v i ) 1 … (q i /v i ) M1 ]，[ΔV Ki ]＝[[ΔV 1 ]；…；[ΔV k ]；…；[ΔV ri ]]，[ΔV k ]＝[Δv k1 … Δv kM1 ]；
S2.2.8.5, i ═ i +1, return S2.2.8.2 until i ═ N.
6. The method of claim 1, wherein the step S3 includes the following steps:
s3.1, setting the iteration times T as 1, setting the parameter variation quantity delta x as 0, and selecting the last M from the measurement sequence 2 Performing the subsequent steps of strip measurement; wherein M is 2 The following formula is required:
wherein M ^ is a group of E ^;
s3.2, calculating pseudo load flow to obtain node voltage phase angle information;
s3.3, the formula of the current line admittance estimated value matrix x ^ is as follows:
wherein, [ g ]]＝[g 1 …g M^ ] T ，[b]＝[b 1 …b M^ ] T Respectively representing a matrix of the conductance value and the susceptance value of the line in E ^ a; let x ^ last Is equal to x ^, Δ x ^ last Is equal to Deltax ^;
s3.4, judging whether T is an odd number, if T is an odd number, utilizing [ P ]]，[V]，[θ]Calculating a coefficient matrix A 1 ,y 1 And a weight matrix w 1 (ii) a If T is even, then [ Q ] is utilized]，[V]，[θ]Calculating a coefficient matrix A 2 ,y 2 And a weight matrix w 2 (ii) a Wherein A is 1 ＝[a p1 ；…；a pM2 ]，y 1 ＝[p 1 ；…；p M2 ]；A 2 ＝[a q1 ；…；a qM2 ]，y 2 ＝[q 1 ；…；q M2 ]；[a p ]＝[a g a b ]，[p]＝[p 1 … p N ] T ；[a q ]＝[a b -a g ]，[q]＝[q 1 … q N ] T ；a g And a b Are NxM ^ dimensional matrixes, and the formula of the element values is as follows:
wherein tau is an M ^ x 2-dimensional matrix, the first row stores the initial node numbers corresponding to all lines in the E ^ and the second row stores the terminal node numbers; w is a 1 And w 2 All are 2M ^ x 1-dimensional weight coefficient matrixes, and the formulas are respectively as follows:
wherein x is 0_1 And x 0_2 Respectively as follows:
x 0_1 ＝(A 1 T A 1 ) -1 A 1 T y 1 (32)
x 0_2 ＝(A 2 T A 2 ) -1 A 2 T y 2 (33)
s3.5, solving x ^ based on an adaptive ridge regression model;
s3.6, correcting the element values of corresponding positions in the admittance estimation arrays G ^ and B ^ according to x ^ wherein the non-diagonal elements in G ^ and B ^ are respectively equal to the negative numbers of the conductance value and the susceptance value of corresponding branches in x ^ and the diagonal elements are respectively equal to the sum of the conductance value and the susceptance value of branches connected with corresponding nodes in x ^;
s3.7, traversing G ^ if the L is G ^ ij |/|G^ ii |＜ω g Setting the admittance estimated value of the corresponding line in x ^ to be zero;
s3.8, calculating the change delta x of x ^ before and after iteration, wherein the formula is as follows:
Δx^＝||x^-x^ last || 2 (34)
wherein | | | purple hair 2 A 2-norm representing a vector;
s3.9, determining delta x ^ -delta x ^ last Is less than the convergence threshold
If the current value is less than the threshold value, correcting admittance estimation arrays G ^ and B ^ according to x ^ and obtaining a final operation line set E ^ and outputting E ^ and G ^ and B ^ as a final topological structure and line parameter identification result; otherwise T ═ T +1, return to S3.2.
7. The method of claim 6, wherein the pseudo load flow calculation in S3.2 is based on M 2 Active power measurement, reactive power measurement and G ^ and B ^ through load flow calculationAnd obtaining a corresponding node voltage phase angle estimation value.
8. The method of claim 6, wherein the specific steps of S3.5 include the following:
s3.5.1, the regularization parameter λ when the function V (λ) takes the minimum value is expressed as λ opt The formula of V (λ) is as follows:
wherein, I represents an identity matrix, tr () represents a trace of the matrix, and K has the following formula:
wherein if T is an odd number, then A equals A 1 Y is equal to y 1 W is equal to w 1 (ii) a Otherwise, A equals A 2 Y is equal to y 2 W is equal to w 2 ；
S3.5.2, obtaining x ^ by solving the minimized self-adaptive ridge regression model, wherein the formula is as follows:
wherein'-' represents a matrix dot product operator; if T is odd, A equals A 1 Y is equal to y 1 W is equal to w 1 (ii) a Otherwise, A equals A 2 Y is equal to y 2 W is equal to w 2 。
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210701249.XA CN115000947A (en) | 2022-06-20 | 2022-06-20 | Power distribution network topological structure and line parameter identification method based on intelligent electric meter measurement |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202210701249.XA CN115000947A (en) | 2022-06-20 | 2022-06-20 | Power distribution network topological structure and line parameter identification method based on intelligent electric meter measurement |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN115000947A true CN115000947A (en) | 2022-09-02 |
Family
ID=83036201
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202210701249.XA Pending CN115000947A (en) | 2022-06-20 | 2022-06-20 | Power distribution network topological structure and line parameter identification method based on intelligent electric meter measurement |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115000947A (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116260128A (en) * | 2022-10-31 | 2023-06-13 | 广东电网有限责任公司中山供电局 | Regional power grid analysis method and device |
| CN117117876A (en) * | 2023-10-25 | 2023-11-24 | 国网浙江省电力有限公司宁波供电公司 | Power grid full-element resource coordination control method and system |
| CN117559456A (en) * | 2024-01-11 | 2024-02-13 | 南京信息工程大学 | Method for identifying working state of power distribution network by using power distribution network measuring unit |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112072659A (en) * | 2020-09-17 | 2020-12-11 | 清华大学 | Power distribution network topology and parameter identification method adaptive to measured data quality |
| CN112488874A (en) * | 2020-12-07 | 2021-03-12 | 清华大学 | Data-driven distribution network topology estimation and line parameter identification method |
| US20210397762A1 (en) * | 2018-11-06 | 2021-12-23 | Siemens Aktiengesellschaft | Distribution grid admittance estimation with limited nonsynchronized measurements |
-
2022
- 2022-06-20 CN CN202210701249.XA patent/CN115000947A/en active Pending
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20210397762A1 (en) * | 2018-11-06 | 2021-12-23 | Siemens Aktiengesellschaft | Distribution grid admittance estimation with limited nonsynchronized measurements |
| CN112072659A (en) * | 2020-09-17 | 2020-12-11 | 清华大学 | Power distribution network topology and parameter identification method adaptive to measured data quality |
| CN112488874A (en) * | 2020-12-07 | 2021-03-12 | 清华大学 | Data-driven distribution network topology estimation and line parameter identification method |
Non-Patent Citations (1)
| Title |
|---|
| 周宇 等: "基于数据驱动技术的配电网拓扑结构及线路参数识别方法", 《自动化与仪器仪表》, 25 May 2021 (2021-05-25), pages 193 - 196 * |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116260128A (en) * | 2022-10-31 | 2023-06-13 | 广东电网有限责任公司中山供电局 | Regional power grid analysis method and device |
| CN117117876A (en) * | 2023-10-25 | 2023-11-24 | 国网浙江省电力有限公司宁波供电公司 | Power grid full-element resource coordination control method and system |
| CN117117876B (en) * | 2023-10-25 | 2024-01-09 | 国网浙江省电力有限公司宁波供电公司 | Power grid full-element resource coordination control method and system |
| CN117559456A (en) * | 2024-01-11 | 2024-02-13 | 南京信息工程大学 | Method for identifying working state of power distribution network by using power distribution network measuring unit |
| CN117559456B (en) * | 2024-01-11 | 2024-03-26 | 南京信息工程大学 | Method for identifying working state of power distribution network by using power distribution network measuring unit |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN115000947A (en) | Power distribution network topological structure and line parameter identification method based on intelligent electric meter measurement | |
| CN107658881A (en) | Voltage stability critical point determination methods based on Thevenin's equivalence method | |
| CN104836223B (en) | Power grid parameter error and bad data coordinated identification and estimation method | |
| CN110676940B (en) | Power distribution network PMU configuration method and system for improving parameter identification precision | |
| CN110190600B (en) | Three-phase power distribution network topology identification method based on AMI measurement nearest neighbor regression | |
| CN107453357A (en) | A kind of State Estimation for Distribution Network based on hierarchical solving | |
| CN112600191B (en) | Low-voltage distribution network parameter and topology joint identification method based on nonlinear regression | |
| CN105929340B (en) | A method of battery SOC is estimated based on ARIMA | |
| CN109088407B (en) | Power distribution network state estimation method based on deep belief network pseudo-measurement modeling | |
| CN110308366B (en) | Harmonic source positioning method based on orthogonal matching pursuit algorithm | |
| CN112117763A (en) | Low-voltage distribution network topology identification and parameter estimation method | |
| CN107453484B (en) | SCADA data calibration method based on WAMS information | |
| CN106208050B (en) | A kind of grid branch static parameter detection and identification method based on PMU | |
| CN111797974A (en) | Power system state estimation method combining particle filtering and convolutional neural network | |
| CN115453193B (en) | Power distribution network harmonic state estimation method based on cooperation of PQM, TTU and SM measurement data | |
| CN107749627A (en) | Based on the intelligent distribution network Load Flow Jacobian Matrix method of estimation for improving match tracing | |
| CN106372440B (en) | A kind of adaptive robust state estimation method of the power distribution network of parallel computation and device | |
| CN107505534B (en) | Distribution network fault genetic search positioning method | |
| CN109698505B (en) | Regulation and control quantitative mapping calculation method for large power grid static voltage stability online prevention and control | |
| CN107958120B (en) | System Thevenin equivalent parameter calculation method based on power series expansion | |
| CN109494743A (en) | The estimation method of electric system mains by harmonics state based on matrix reconstruction | |
| CN110907720A (en) | Complete parameter identification method for short-circuit same-tower double-circuit line based on PMU measurement | |
| CN116257973A (en) | Particle swarm optimization-based low-voltage power network line impedance and loss calculation method and system | |
| CN110443358A (en) | A kind of harmonic source identification method based on weighting regularization extreme learning machine | |
| Zhang et al. | Research on power system harmonic state estimation |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |