CN112072659A - 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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CN112072659A
CN112072659A CN202010977507.8A CN202010977507A CN112072659A CN 112072659 A CN112072659 A CN 112072659A CN 202010977507 A CN202010977507 A CN 202010977507A CN 112072659 A CN112072659 A CN 112072659A
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distribution network
power distribution
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topology
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CN112072659B (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]

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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 BDA0002686266920000021
wherein, Pi tRepresenting the active power injection measurement of the i-node at time t,
Figure BDA0002686266920000022
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 BDA0002686266920000023
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 BDA0002686266920000024
wherein,
Figure BDA0002686266920000025
indicating i-node active power notesThe standard deviation of the measured quantity is measured,
Figure BDA0002686266920000026
represents the standard deviation of the i-node reactive power injection measurement,
Figure BDA0002686266920000027
represents the standard deviation of the i-node voltage magnitude measurement,
Figure BDA0002686266920000028
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 dk is the number of the kth node in descending order, and k 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 BDA0002686266920000029
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 BDA0002686266920000031
2-5) judging: if it is presentB0If 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 BDA0002686266920000032
Figure BDA0002686266920000033
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 BDA0002686266920000034
wherein,
Figure BDA0002686266920000035
representing an estimate of the voltage amplitude at node i at time t,
Figure BDA0002686266920000036
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)+ (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 BDA0002686266920000041
wherein,
Figure BDA0002686266920000042
injecting measured noise for the active power at the moment t of the i node;
reactive power measurement equation:
Figure BDA0002686266920000043
wherein,
Figure BDA0002686266920000044
the noise measured for the reactive injection at the moment t of the node i;
voltage amplitude measurement equation:
Figure BDA0002686266920000045
wherein,
Figure BDA0002686266920000046
noise measured for the voltage amplitude at the time t of the i node;
voltage phase angle measurement equation:
Figure BDA0002686266920000047
wherein,
Figure BDA0002686266920000048
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 BDA0002686266920000049
Setting a voltage amplitude reference value
Figure BDA00026862669200000410
Setting a reference value of a voltage phase angle
Figure BDA00026862669200000411
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 BDA00026862669200000412
3-5) calculating the gradient g of the loss function with respect to the state vector of the last iterationk：
Figure BDA00026862669200000413
Wherein, gkDecomposed into parts corresponding to admittance, voltage amplitude, voltage phase angle, respectively:
Figure BDA00026862669200000414
respectively calculate the vector
Figure BDA00026862669200000415
The arithmetic mean of all elements of (a), the result is noted as:
Figure BDA00026862669200000416
3-6) update the momentum for the kth iteration:
Figure BDA0002686266920000051
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 BDA0002686266920000052
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) mixing0Is assigned tor：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 BDA0002686266920000061
wherein, Pi tRepresenting the active power injection measurement of the i-node at time t,
Figure BDA0002686266920000062
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 BDA0002686266920000063
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 BDA0002686266920000064
wherein,
Figure BDA0002686266920000065
represents the standard deviation of the i-node active power injection measurement,
Figure BDA0002686266920000066
represents the standard deviation of the i-node reactive power injection measurement,
Figure BDA0002686266920000067
represents the standard deviation of the i-node voltage magnitude measurement,
Figure BDA0002686266920000068
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 dk is the number of the kth node in descending order, and k 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 BDA0002686266920000071
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 BDA0002686266920000072
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 BDA0002686266920000073
Figure BDA0002686266920000074
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 BDA0002686266920000081
wherein,
Figure BDA0002686266920000082
representing the voltage amplitude of the i-node at time tThe value of the estimated value is,
Figure BDA0002686266920000083
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)+ (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 BDA0002686266920000084
wherein,
Figure BDA0002686266920000085
injecting measured noise for the active power at the moment t of the i node;
reactive power measurement equation:
Figure BDA0002686266920000086
wherein,
Figure BDA0002686266920000087
the noise measured for the reactive injection at the moment t of the node i;
voltage amplitude measurement equation:
Figure BDA0002686266920000088
wherein,
Figure BDA0002686266920000089
noise measured for the voltage amplitude at the time t of the i node;
voltage phase angle measurement equation:
Figure BDA00026862669200000810
wherein,
Figure BDA00026862669200000811
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 BDA00026862669200000812
Setting a voltage amplitude reference value
Figure BDA00026862669200000813
Setting a reference value of a voltage phase angle
Figure BDA00026862669200000814
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 BDA0002686266920000091
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 BDA0002686266920000092
Take [0.8,1.2 ]]Voltage phase angle reference value
Figure BDA0002686266920000093
Take [0,0.1 ]]Initial coefficient ofr0Take 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 BDA0002686266920000094
3-5) calculating the gradient g of the loss function with respect to the state vector of the last iterationk：
Figure BDA0002686266920000095
Wherein g iskCan be decomposed into parts corresponding to admittance, voltage amplitude and voltage phase angle:
Figure BDA0002686266920000096
respectively calculate the vector
Figure BDA0002686266920000097
The arithmetic mean of all elements of (a), the result is noted as:
Figure BDA0002686266920000098
3-6) update the momentum for the kth iteration:
Figure BDA0002686266920000099
mk＝αmk-1+(α-1)gk (15)
3-7) mixing0Assigning to r: r ← r0；
3-8) judging: if it isr≤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 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 BDA00026862669200000910
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 FDA0002686266910000011
wherein,
Figure FDA0002686266910000012
representing the active power injection measurement of the i-node at time t,
Figure FDA0002686266910000013
representing the reactive power injection measurement at the i node at time t,
Figure FDA0002686266910000014
representing the voltage magnitude measurement at the i-node at time t,
Figure FDA0002686266910000015
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 FDA0002686266910000016
wherein,
Figure FDA0002686266910000017
represents the standard deviation of the i-node active power injection measurement,
Figure FDA0002686266910000018
represents the standard deviation of the i-node reactive power injection measurement,
Figure FDA0002686266910000019
represents the standard deviation of the i-node voltage magnitude measurement,
Figure FDA00026862669100000110
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 dk is the number of the kth node in descending order, and k 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 FDA00026862669100000111
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 FDA0002686266910000021
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 FDA0002686266910000022
Figure FDA0002686266910000023
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 FDA0002686266910000024
wherein,
Figure FDA0002686266910000025
representing an estimate of the voltage amplitude at node i at time t,
Figure FDA0002686266910000026
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)+ (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 FDA0002686266910000027
wherein,
Figure FDA0002686266910000028
noise measured for active injection at time t of i-node；
Reactive power measurement equation:
Figure FDA0002686266910000031
wherein,
Figure FDA0002686266910000032
the noise measured for the reactive injection at the moment t of the node i;
voltage amplitude measurement equation:
Figure FDA0002686266910000033
wherein,
Figure FDA0002686266910000034
noise measured for the voltage amplitude at the time t of the i node;
voltage phase angle measurement equation:
Figure FDA0002686266910000035
wherein,
Figure FDA0002686266910000036
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 FDA0002686266910000037
Setting a voltage amplitude reference value
Figure FDA0002686266910000038
Setting a reference value of a voltage phase angle
Figure FDA0002686266910000039
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 FDA00026862669100000310
3-5) calculating the gradient g of the loss function with respect to the state vector of the last iterationk：
Figure FDA00026862669100000311
Wherein, gkDecomposed into parts corresponding to admittance, voltage amplitude, voltage phase angle, respectively:
Figure FDA00026862669100000312
respectively calculate the vector
Figure FDA00026862669100000313
The arithmetic mean of all elements of (a), the result is noted as:
Figure FDA00026862669100000314
3-6) update the momentum for the kth iteration:
Figure FDA00026862669100000315
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 FDA0002686266910000041
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。
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