CN112072659B - Power distribution network topology and parameter identification method adaptive to measured data quality - Google Patents

Power distribution network topology and parameter identification method adaptive to measured data quality Download PDF

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CN112072659B
CN112072659B CN202010977507.8A CN202010977507A CN112072659B CN 112072659 B CN112072659 B CN 112072659B CN 202010977507 A CN202010977507 A CN 202010977507A CN 112072659 B CN112072659 B CN 112072659B
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distribution network
power distribution
topology
measurement
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CN112072659A (en
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刘羽霄
张宁
康重庆
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Tsinghua University
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    • 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
    • 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
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • 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]

Abstract

The invention provides a power distribution network topology and parameter identification method capable of self-adapting to measured data quality, and belongs to the technical field of power distribution network parameter identification and optimization. The method comprises the steps of firstly reading initial data including historical operation measurement data of the power distribution network and the precision of each measurement device. And then, the method obtains a topology initial value of the power distribution network by using a tree topology identification method and obtains a line parameter initial value by using a least square method. The invention provides a conservative radical self-adaptive method iteration parameter combining suboptimal optimization and quadratic optimization. And in the iteration process, updating the system topology by using the line parameter values. Finally, a set of estimated power distribution network topology and line parameters is obtained. The method can identify the topology and the line parameters of the power distribution network, considers the conditions of incomplete measurement data and noise, has higher robustness, and the identification result is favorable for high-order application of the power distribution network, such as state estimation, voltage control, relay protection, demand side management and the like.

Description

Power distribution network topology and parameter identification method adaptive to measured data quality
Technical Field
The invention belongs to the technical field of power distribution network parameter identification and optimization, and particularly relates to a power distribution network topology and parameter identification method adaptive to measured data quality.
Background
Distributed power generation and the wide access of electric automobiles bring great challenges to the economic and safe operation of a power distribution network. State estimation, demand side response management, voltage control, etc. in smart distribution networks will be implemented more and more commonly at the distribution network level. The precise topology and line parameters are the precondition of the applications, but the precise topology and line parameters are usually missing in the medium and low voltage distribution network, so that effective and precise distribution network topology and line parameter identification is very important.
At present, the identification of the topology and parameters of the power distribution network still requires some unreasonable assumptions as a precondition. For example, the topology identification technique of the document Weng, Yang, Yizing Liao, and Ram Rajagopal, "Distributed energy resources topology identification information Systems," IEEE Transactions on Power Systems 32.4(2016): 2682-; the Topology and parameter identification techniques of the documents Moffat, Keith, Mohini Bariya, and Alexandra Von meier. "unsupervied Impedance and Topology Estimation of Distribution Networks-Limitations and tools." IEEE Transactions on Smart Grid 11.1(2019):846 856 requires an assumption that every node of the Distribution network has a phase angle measurement, whereas in practical cases the Distribution network often lacks a phase angle measurement; the document Zhang, Jiawei, et al, "polarity Identification and Line Parameter Estimation for non-PMU Distribution Network a Numerical method," IEEE Transactions on Smart Grid (2020) requires precise voltage amplitude measurements as input, whereas voltage amplitude measurements of power Distribution networks inevitably present noise.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a power distribution network topology and parameter identification method adaptive to measured data quality. The method comprises the steps of firstly reading initial data including historical operation measurement data of the power distribution network and the precision of each measurement device. And then, the method obtains a topology initial value of the power distribution network by using a tree topology identification method and obtains a line parameter initial value by using a least square method. And then, providing iteration parameters of a conservative radical self-adaptive method combining suboptimal optimization and quadratic optimization. And in the iteration process, updating the system topology by using the line parameter values. Finally, a set of estimated power distribution network topology and line parameters is obtained. The method can identify the topology and the line parameters of the power distribution network, considers the conditions of incomplete measurement data and noise, has higher robustness, and the identification result is favorable for high-order application of the power distribution network, such as state estimation, voltage control, relay protection, demand side management and the like.
The invention provides a power distribution network topology and parameter identification method adaptive to measured data quality, which is characterized by comprising the following steps of:
1) reading initial data; the method comprises the following specific steps:
1-1) reading historical measurement data of the power distribution network, wherein the historical measurement data is expressed in a vector z form:
Figure GDA0003360852970000021
wherein, Pi tRepresenting the active power injection measurement of the i-node at time t,
Figure GDA0003360852970000022
represents the reactive power injection measurement, V, of the i node at time ti tRepresenting the voltage magnitude measurement at the i-node at time t,
Figure GDA0003360852970000023
represents the voltage angle measurement of the i-node at time t, MPRepresenting a set of nodes containing active power injection measurements, MQRepresenting a set of nodes containing reactive power injection measurements, MVRepresenting a set of nodes containing a measure of the magnitude of the voltage, MθRepresenting a node set containing voltage phase angle measurements, A representing the total number of time;
1-2) reading the precision of the distribution network measuring equipment, wherein the precision is expressed in a vector sigma, and the sigma represents the standard deviation of measurement:
Figure GDA0003360852970000024
wherein the content of the first and second substances,
Figure GDA0003360852970000025
represents the standard deviation of the i-node active power injection measurement,
Figure GDA0003360852970000026
represents the standard deviation of the i-node reactive power injection measurement,
Figure GDA0003360852970000027
represents the standard deviation of the i-node voltage magnitude measurement,
Figure GDA0003360852970000028
standard deviation representing i-node voltage phase angle measurements;
2) identifying the topology of the power distribution network and the initial values of the parameters; the method comprises the following specific steps:
2-1) setting an initial topology set STIs an empty set;
2-2) calculating the average value of the voltage amplitudes of each node in the power distribution network at all times, and arranging the average values in a descending order, wherein the node sequence number after reordering is as follows: [ d1, d2, …, dN ], wherein di is the number of the ith node after descending order, and i is 1,2, …, N; n is the total number of nodes of the power distribution network;
2-3) setting the unallocated node set B0And an allocated node set B1(ii) a At the beginning, let B0＝[d2,…,dN]And as current B0Set up B1＝[d1]And as current B1；
2-4) from the current B0The first element is selected and marked as di, and the di is deleted from the set, and the current B is updated0(ii) a Calculating the current B1Neutralization of
Figure GDA0003360852970000029
Marking the node with the maximum correlation coefficient as dj, adding di into the current B1Update the current B1(ii) a Adding the node connection relation of di and dj into the topology set S as a node pair (di, dj)T：
Figure GDA0003360852970000031
2-5) judging: if it is currently B0If the set is an empty set, executing the step 2-6); if it is currently B0If not, returning to the step 2-4);
2-6) Pair topology set STFor each node pair (di, dj), the corresponding line parameter is calculated by:
Figure GDA0003360852970000032
Figure GDA0003360852970000033
wherein, gdidjRepresenting the conductance of the line between nodes di and dj, bdidjRepresenting the susceptance of the line between node di and node dj;
2-7) utilizing the results of the step 2-6) to carry out all the g according to the corresponding relation of the node serial numbersdidjIs converted into corresponding gijAll b aredidjConversion to corresponding bijThen entering step 3);
3) updating the topology and the line parameters of the power distribution network; the method comprises the following specific steps:
3-1) setting a power distribution network state vector, and expressing the vector by x;
Figure GDA0003360852970000034
wherein the content of the first and second substances,
Figure GDA0003360852970000035
representing an estimate of the voltage amplitude at node i at time t,
Figure GDA0003360852970000036
representing the voltage phase angle estimated value of the i node at the t moment, and representing the initial values of all the estimated values by using corresponding measured values, wherein for the node without the corresponding measured values, the initial value of the voltage amplitude estimated value at the t moment of the node is 1, and the initial value of the phase angle estimated value at the t moment of the node is 0;
3-2) writing a measurement equation according to the measurement vector and the state vector column:
z＝h(x)+ε (6)
the measurement equation includes: an active measurement equation, a reactive measurement equation, a voltage amplitude measurement equation and a voltage angle measurement equation;
wherein, the active power measurement equation:
Figure GDA0003360852970000037
wherein the content of the first and second substances,
Figure GDA0003360852970000041
injecting measured noise for the active power at the moment t of the i node;
reactive power measurement equation:
Figure GDA0003360852970000042
wherein the content of the first and second substances,
Figure GDA0003360852970000043
the noise measured for the reactive injection at the moment t of the node i;
voltage amplitude measurement equation:
Figure GDA0003360852970000044
wherein the content of the first and second substances,
Figure GDA0003360852970000045
noise measured for the voltage amplitude at the time t of the i node;
voltage phase angle measurement equation:
Figure GDA0003360852970000046
wherein the content of the first and second substances,
Figure GDA0003360852970000047
noise measured for voltage phase angle at inode t;
3-3) let k represent iteration step number, set initial iteration step number k as 0, set last iteration state vectorX k-1And a momentum mk-1Setting a momentum parameter alpha and a line admittance reference value for the initial value in the step 3-1)
Figure GDA0003360852970000048
Setting a voltage amplitude reference value
Figure GDA0003360852970000049
Setting a reference value of a voltage phase angle
Figure GDA00033608529700000410
Wherein the superscript cr represents the reference value; setting an initial coefficient r0Maximum coefficient rmaxA growth coefficient β, a stop coefficient η, a convergence coefficient γ;
3-4) setting the loss function as:
Figure GDA00033608529700000411
calculating the gradient g of the loss function with respect to the state vector of the last iterationk：
Figure GDA00033608529700000412
Wherein, gkDecomposed into parts corresponding to admittance, voltage amplitude, voltage phase angle, respectively:
Figure GDA00033608529700000413
respectively calculate the vector
Figure GDA00033608529700000414
The arithmetic mean of all elements of (a), the result is noted as:
Figure GDA00033608529700000415
3-6) update the momentum for the kth iteration:
Figure GDA00033608529700000416
mk＝αmk-1+(α-1)gk (15)
3-7) mixing0Assigning to r: r ← r0；
3-8) judging: if r is less than or equal to rmaxIf yes, executing step 3-9), otherwise executing step 3-11);
3-9) updating: x is to bek-1+mk/βrIs assigned to xk：xk←xk-1+mk/βr，
Assigning r +1 to r: r ← r + 1;
3-10) judging: if Loss (x)k-1)-Loss(xk)≤η(gk)Tmk/βrThen m isk/βrIs assigned to mk：mk←mk/βrAnd then proceeding to step 3-11), otherwise, returning to step 3-8);
3-11) calculating an information matrix of the kth iteration:
Figure GDA0003360852970000051
wherein diag denotes constructing the vector as a diagonal matrix;
and (3) calculating:
dk＝-gk(Fk)-1. (17)
wherein d iskRepresenting an updated value obtained by a Newton method after the k iteration;
3-12) mixing0Assigning to r: r ← r0；
3-13) judging: if r is less than or equal to rmaxExecuting the step 3-14), otherwise executing the step 3-17);
3-14) calculating w1＝1/(1+βr)，w2＝βr/(1+βr) X is to bek-1+w1mk+w2dkIs assigned to xk：
xk←xk-1+w1mk+w2dk；
3-15) judging: if Loss (x)k-1)-Loss(xk)≤η(gk)T(w1mk+w2dk) Then x iskIs assigned to Xk-1：xk-1←xkM isk/βrIs assigned to mk：mk←mk/βrEntering step 3-16); otherwise, assigning r +1 to r: r ← r +1, then return to step 3-13);
3-16) judging: if max (| x)k-xk-1If the | is less than or equal to gamma, executing the step 3-17), otherwise returning to the step 3-5);
3-17) judging: if STIn which the node pair (i, j) satisfies max (g)ij/gii,gij/gjj) If the number of the node pairs (i, j) meets the condition, g corresponding to all the node pairs (i, j) meeting the condition is less than 0.05, i is not equal to jijAnd bijAre assigned a value of 0: gij←0,bijAnd (e) step of ← 0, converting (di, dj) corresponding to the node pair (i, j) from STThen returning to the step 3-5); otherwise, entering step 4);
4) the topology and the parameter identification of the power distribution network are finished, and a topology set S is outputTAnd corresponding line parameter gij,bij。
The invention has the characteristics and beneficial effects that:
the method applies the unconstrained nonlinear optimization technology to the technical field of subdivision of power distribution network topology and parameter identification, combines the stability of primary optimization and the quick convergence of secondary optimization, and can have excellent performance in the strong non-convex and ill-conditioned optimization problem of power distribution network topology and parameter identification. The identification result of the topology and the parameters of the power distribution network is beneficial to high-order application of the power distribution network, such as state estimation, voltage control, relay protection, demand side management and the like, so that the economy and the safety of the power distribution network are improved.
Detailed Description
The invention provides a power distribution network topology and parameter identification method adaptive to measured data quality, which comprises the following steps:
1) reading initial data; the method comprises the following specific steps:
1-1) reading historical measurement data of the power distribution network, wherein the historical measurement data is expressed in a vector z form:
Figure GDA0003360852970000061
wherein, Pi tRepresenting the active power injection measurement of the i-node at time t,
Figure GDA0003360852970000062
represents the reactive power injection measurement, V, of the i node at time ti tRepresenting the voltage magnitude measurement at the i-node at time t,
Figure GDA0003360852970000063
represents the voltage angle measurement of the i-node at time t, MPRepresenting a set of nodes containing active power injection measurements, MQRepresenting a set of nodes containing reactive power injection measurements, MVRepresenting a set of nodes containing a measure of the magnitude of the voltage, MθThe method comprises the steps that a node set containing voltage phase angle measurement is shown, A represents the total time, and A is generally more than three times of the total number N of nodes of a power distribution network;
1-2) reading the precision of the distribution network measuring equipment, wherein the precision is expressed in a vector sigma, and the sigma represents the standard deviation of measurement:
Figure GDA0003360852970000064
wherein the content of the first and second substances,
Figure GDA0003360852970000065
represents the standard deviation of the i-node active power injection measurement,
Figure GDA0003360852970000066
represents the standard deviation of the i-node reactive power injection measurement,
Figure GDA0003360852970000067
represents the standard deviation of the i-node voltage magnitude measurement,
Figure GDA0003360852970000068
standard deviation representing i-node voltage phase angle measurements;
2) identifying the topology of the power distribution network and the initial values of the parameters; the method comprises the following specific steps:
2-1) setting an initial topology set STIs an empty set;
2-2) calculating the average value of the voltage amplitudes of each node in the power distribution network at all times and arranging the average values in a descending order, wherein the arrangement number sequence of the node voltages is from the original numbering sequence: [1,2, …, N ] becomes descending order: [ d1, d2, …, dN ], wherein di is the number of the ith node after descending order, and i is 1,2, …, N; n is the total number of nodes of the power distribution network;
2-3) setting the unallocated node set B0And an allocated node set B1(ii) a At the beginning, let B0＝[d2,…,dN]And as current B0Set up B1＝[d1]And as current B1；
2-4) from the current set B0The first element is selected and marked as di, and the di is deleted from the set, and the current set B is updated0(ii) a Calculating a currently assigned node set B1Neutralization of
Figure GDA0003360852970000071
The node with the largest correlation coefficient is marked as dj (initially, di is d1), and di is added to the current set B1Update the current set B1Adding the node connection relation of di and dj as a node pair (di, dj) into the topology set ST：
Figure GDA0003360852970000072
2-5) judging: if the current set B0If the set is an empty set, executing the step 2-6); if the current set B0If not, returning to the step 2-4);
2-6) Pair topology set STFor each node pair (di, dj), the corresponding line parameter is calculated by the following formula:
Figure GDA0003360852970000073
Figure GDA0003360852970000074
wherein, gdidjRepresenting the conductance of the line between nodes di and dj, bdidjRepresenting the susceptance of the line between node di and node dj;
2-7) utilizing the results of the step 2-6) to carry out all the g according to the corresponding relation of the node serial numbersdidjIs converted into corresponding gijAll b aredidjConversion to corresponding bijThen entering step 3);
3) updating the topology and the line parameters of the power distribution network by an iteration method for self-adapting the quality of measured data; the method comprises the following specific steps:
3-1) setting a power distribution network state vector, and expressing the vector by x;
Figure GDA0003360852970000081
wherein the content of the first and second substances,
Figure GDA0003360852970000082
representing an estimate of the voltage amplitude at node i at time t,
Figure GDA0003360852970000083
representing the voltage phase angle estimated value of the i node at the t moment, and representing the initial values of all the estimated values by using corresponding measured values, wherein for the node without the corresponding measured values, the initial value of the voltage amplitude estimated value at the t moment of the node is 1, and the initial value of the phase angle estimated value at the t moment of the node is 0;
3-2) writing a measurement equation according to the measurement vector and the state vector column:
z＝h(x)+ε (6)
the measurement equation includes: an active measurement equation, a reactive measurement equation, a voltage amplitude measurement equation and a voltage angle measurement equation;
wherein, the active power measurement equation:
Figure GDA0003360852970000084
wherein the content of the first and second substances,
Figure GDA0003360852970000085
injecting measured noise for the active power at the moment t of the i node;
reactive power measurement equation:
Figure GDA0003360852970000086
wherein the content of the first and second substances,
Figure GDA0003360852970000087
the noise measured for the reactive injection at the moment t of the node i;
voltage amplitude measurement equation:
Figure GDA0003360852970000088
wherein the content of the first and second substances,
Figure GDA0003360852970000089
noise measured for the voltage amplitude at the time t of the i node;
voltage phase angle measurement equation:
Figure GDA00033608529700000810
wherein the content of the first and second substances,
Figure GDA00033608529700000811
noise measured for voltage phase angle at inode t;
3-3) let k represent iteration step number, set initial iteration step number k as 0, and set state vector X of last iterationk-1And a momentum mk-1Setting a momentum parameter alpha and a line admittance reference value for the initial value in the step 3-1)
Figure GDA00033608529700000812
Setting a voltage amplitude reference value
Figure GDA00033608529700000813
Setting a reference value of a voltage phase angle
Figure GDA00033608529700000814
Wherein the superscript cr represents the reference value; setting an initial coefficient r0Maximum coefficient rmaxA growth coefficient β, a stop coefficient η, a convergence coefficient γ; wherein the momentum parameter alpha is 0-1, 0.9 is suggested, and the reference value of line admittance is adopted
Figure GDA0003360852970000091
Take [0,10000 ]]According to the estimated average admittance size of the power distribution network, 1000 is taken when unknown, and the voltage amplitude reference value is taken
Figure GDA0003360852970000092
Take [0.8,1.2 ]]Voltage phase angle reference value
Figure GDA0003360852970000093
Take [0,0.1 ]]Initial coefficient r0Take the value of [ -10,0]An integer of-5 is suggested, and the maximum coefficient rmaxTake [10,30 ]]An integer of 20 is proposed, and the growth coefficient beta is (1, 8)]It is recommended to take 5, and the stopping coefficient eta is taken to be [0.001, 1%]It is proposed to take 0.01 and the convergence factor gamma [10 ]-10,10-2]It is recommended to take 10-6。
3-4) setting the loss function as:
Figure GDA0003360852970000094
3-5) calculating the gradient g of the loss function with respect to the state vector of the last iterationk：
Figure GDA0003360852970000095
Wherein g iskCan be decomposed into parts corresponding to admittance, voltage amplitude and voltage phase angle:
Figure GDA0003360852970000096
respectively calculate the vector
Figure GDA0003360852970000097
The arithmetic mean of all elements of (a), the result is noted as:
Figure GDA0003360852970000098
3-6) update the momentum for the kth iteration:
Figure GDA0003360852970000099
mk＝αmk-1+(α-1)gk (15)
3-7) mixing0Assigning to r: r ← r0；
3-8) judging: if r is less than or equal to rmaxIf yes, executing step 3-9), otherwise executing step 3-11);
3-9) updating: x is to bek-1+mk/βrIs assigned to xk：xk←xk-1+mk/βrAssigning r +1 to r: r ← r + 1;
3-10) judging: if Loss (x)k-1)-Loss(xk)≤η(gk)Tmk/βrThen m isk/βrIs assigned tomk：mk←mk/βrAnd then proceeding to step 3-11), otherwise, returning to step (3-8);
3-11) calculating an information matrix of the kth iteration:
Figure GDA00033608529700000910
wherein diag denotes constructing the vector as a diagonal matrix; then, calculating:
dk＝-gk(Fk)-1. (17)
wherein d iskRepresenting an updated value obtained by a Newton method after the kth iteration;
3-12) mixing0Assigning to r: r ← r0；
3-13) judging: if r is less than or equal to rmaxIf not, executing the step (3-14), otherwise, executing the step (3-17);
3-14) calculating w1＝1/(1+βr)，w2＝βr/(1+βr) X is to bek-1+w1mk+w2dkIs assigned to xk：
xk←xk-1+w1mk+w2dk；
3-15) judging: if Loss (x)k-1)-Loss(xk)≤η(gk)T(w1mk+w2dk) Then x iskIs assigned to Xk-1：xk-1←xkM isk/βrIs assigned to mk：mk←mk/βrEntering step 3-16); otherwise, assigning r +1 to r: r ← r +1, then return to step 3-13);
3-16) judging: if max (| x)k-xk-1If the | is less than or equal to gamma, executing the step 3-17), otherwise returning to the step 3-5);
3-17) judging: if STIn which the node pair (i, j) satisfies max (g)ij/gii,gij/gjj) If the number of the node pairs (i, j) meets the condition, g corresponding to all the node pairs (i, j) meeting the condition is less than 0.05, i is not equal to jijAnd bijAre assigned a value of 0: gij←0,bijAnd (e) step of ← 0, converting (di, dj) corresponding to the node pair (i, j) from STThen returning to the step 3-5); otherwise, entering step 4);
4) the topology and the parameter identification of the power distribution network are finished, and a topology set S is outputTAnd corresponding line parameter gij,bij。

Claims (1)

1. A power distribution network topology and parameter identification method adaptive to measured data quality is characterized by comprising the following steps:
1) reading initial data; the method comprises the following specific steps:
1-1) reading historical measurement data of the power distribution network, wherein the historical measurement data is expressed in a vector z form:
Figure FDA0003360852960000011
wherein, Pi tRepresenting the active power injection measurement of the i-node at time t,
Figure FDA0003360852960000012
represents the reactive power injection measurement, V, of the i node at time ti tRepresenting the voltage magnitude measurement at the i-node at time t,
Figure FDA0003360852960000013
represents the voltage angle measurement of the i-node at time t, MPRepresenting a set of nodes containing active power injection measurements, MQRepresenting a set of nodes containing reactive power injection measurements, MVRepresenting a set of nodes containing a measure of the magnitude of the voltage, MθRepresenting a node set containing voltage phase angle measurements, A representing the total number of time;
1-2) reading the precision of the distribution network measuring equipment, wherein the precision is expressed in a vector sigma, and the sigma represents the standard deviation of measurement:
Figure FDA0003360852960000014
wherein the content of the first and second substances,
Figure FDA0003360852960000015
represents the standard deviation of the i-node active power injection measurement,
Figure FDA0003360852960000016
represents the standard deviation of the i-node reactive power injection measurement,
Figure FDA0003360852960000017
represents the standard deviation of the i-node voltage magnitude measurement,
Figure FDA0003360852960000018
standard deviation representing i-node voltage phase angle measurements;
2) identifying the topology of the power distribution network and the initial values of the parameters; the method comprises the following specific steps:
2-1) setting an initial topology set STIs an empty set;
2-2) calculating the average value of the voltage amplitudes of each node in the power distribution network at all times, and arranging the average values in a descending order, wherein the node sequence number after reordering is as follows: [ d1, d2, …, dN ], wherein di is the number of the ith node after descending order, and i is 1,2, …, N; n is the total number of nodes of the power distribution network;
2-3) setting the unallocated node set B0And an allocated node set B1(ii) a At the beginning, let B0＝[d2,…,dN]And as current B0Set up B1＝[d1]And as current B1；
2-4) from the current B0The first element is selected and marked as di, and the di is deleted from the set, and the current B is updated0(ii) a Calculating the current B1Neutralization of
Figure FDA0003360852960000019
Marking the node with the maximum correlation coefficient as dj, adding di into the current B1Update the current B1(ii) a Adding the node connection relation of di and dj into the topology set S as a node pair (di, dj)T：
Figure FDA0003360852960000021
2-5) judging: if it is currently B0If the set is an empty set, executing the step 2-6); if it is currently B0If not, returning to the step 2-4);
2-6) Pair topology set STFor each node pair (di, dj), the corresponding line parameter is calculated by:
Figure FDA0003360852960000022
Figure FDA0003360852960000023
wherein, gdidjRepresenting the conductance of the line between nodes di and dj, bdidjRepresenting the susceptance of the line between node di and node dj;
2-7) utilizing the results of the step 2-6) to carry out all the g according to the corresponding relation of the node serial numbersdidjIs converted into corresponding gijAll b aredidjConversion to corresponding bijThen entering step 3);
3) updating the topology and the line parameters of the power distribution network; the method comprises the following specific steps:
3-1) setting a power distribution network state vector, and expressing the vector by x;
Figure FDA0003360852960000024
wherein the content of the first and second substances,
Figure FDA0003360852960000025
representing an estimate of the voltage amplitude at node i at time t,
Figure FDA0003360852960000026
representing the voltage phase angle estimated value of the i node at the t moment, and representing the initial values of all the estimated values by using corresponding measured values, wherein for the node without the corresponding measured values, the initial value of the voltage amplitude estimated value at the t moment of the node is 1, and the initial value of the phase angle estimated value at the t moment of the node is 0;
3-2) writing a measurement equation according to the measurement vector and the state vector column:
z＝h(x)+ε (6)
the measurement equation includes: an active measurement equation, a reactive measurement equation, a voltage amplitude measurement equation and a voltage angle measurement equation;
wherein, the active power measurement equation:
Figure FDA0003360852960000027
wherein the content of the first and second substances,
Figure FDA0003360852960000028
injecting measured noise for the active power at the moment t of the i node;
reactive power measurement equation:
Figure FDA0003360852960000031
wherein the content of the first and second substances,
Figure FDA0003360852960000032
the noise measured for the reactive injection at the moment t of the node i;
voltage amplitude measurement equation:
Figure FDA0003360852960000033
wherein the content of the first and second substances,
Figure FDA0003360852960000034
noise measured for the voltage amplitude at the time t of the i node;
voltage phase angle measurement equation:
Figure FDA0003360852960000035
wherein the content of the first and second substances,
Figure FDA0003360852960000036
noise measured for voltage phase angle at inode t;
3-3) let k represent iteration step number, set initial iteration step number k as 0, and set state vector X of last iterationk-1And a momentum mk-1Setting a momentum parameter alpha and a line admittance reference value for the initial value in the step 3-1)
Figure FDA0003360852960000037
Setting a voltage amplitude reference value
Figure FDA0003360852960000038
Setting a reference value of a voltage phase angle
Figure FDA0003360852960000039
Wherein the superscript cr represents the reference value; setting an initial coefficient r0Maximum coefficient rmaxA growth coefficient β, a stop coefficient η, a convergence coefficient γ;
3-4) setting the loss function as:
Figure FDA00033608529600000310
3-5) calculating the gradient g of the loss function with respect to the state vector of the last iterationk：
Figure FDA00033608529600000311
Wherein, gkDecomposed into parts corresponding to admittance, voltage amplitude, voltage phase angle, respectively:
Figure FDA00033608529600000312
respectively calculate the vector
Figure FDA00033608529600000313
The arithmetic mean of all elements of (a), the result is noted as:
Figure FDA00033608529600000314
3-6) update the momentum for the kth iteration:
Figure FDA00033608529600000315
mk＝αmk-1+(α-1)gk (15)
3-7) mixing0Assigning to r: r ← r0；
3-8) judging: if r is less than or equal to rmaxIf yes, executing step 3-9), otherwise executing step 3-11);
3-9) updating: x is to bek-1+mk/βrIs assigned to xk：xk←xk-1+mk/βr，
Assigning r +1 to r: r ← r + 1;
3-10) judging: if Loss (x)k-1)-Loss(xk)≤η(gk)Tmk/βrThen m isk/βrIs assigned to mk：mk←mk/βrThen proceeding to the proceeding step3-11), otherwise, returning to the step 3-8) again;
3-11) calculating an information matrix of the kth iteration:
Figure FDA0003360852960000041
wherein diag denotes constructing the vector as a diagonal matrix;
and (3) calculating:
dk＝-gk(Fk)-1. (17)
wherein d iskRepresenting an updated value obtained by a Newton method after the k iteration;
3-12) mixing0Assigning to r: r ← r0；
3-13) judging: if r is less than or equal to rmaxExecuting the step 3-14), otherwise executing the step 3-17);
3-14) calculating w1＝1/(1+βr)，w2＝βr/(1+βr) X is to bek-1+w1mk+w2dkIs assigned to xk：
xk←xk-1+w1mk+w2dk；
3-15) judging: if Loss (x)k-1)-Loss(xk)≤η(gk)T(w1mk+w2dk) Then x iskIs assigned to Xk-1：xk-1←xkM isk/βrIs assigned to mk：mk←mk/βrEntering step 3-16); otherwise, assigning r +1 to r: r ← r +1, then return to step 3-13);
3-16) judging: if max (| x)k-xk-1If the | is less than or equal to gamma, executing the step 3-17), otherwise returning to the step 3-5);
3-17) judging: if STIn which the node pair (i, j) satisfies max (g)ij/gii,gij/gjj) If the number of node pairs is less than 0.05, i is not equal to j, all node pairs (i, j) meeting the condition are pairedG should beijAnd bijAre assigned a value of 0: gij←0,bijAnd (e) step of ← 0, converting (di, dj) corresponding to the node pair (i, j) from STThen returning to the step 3-5); otherwise, entering step 4);
4) the topology and the parameter identification of the power distribution network are finished, and a topology set S is outputTAnd corresponding line parameter gij,bij。
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