CN108462181A - Sparse-considered robust estimation method for jacobian matrix of power flow of intelligent power distribution network - Google Patents
Sparse-considered robust estimation method for jacobian matrix of power flow of intelligent power distribution network Download PDFInfo
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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
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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
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Abstract
A sparse considered robust estimation method for a power flow Jacobian matrix of an intelligent power distribution network comprises the following steps: 1) acquiring the number of nodes of the power distribution network and numbering the nodes; 2) acquiring measurement data of a synchronous phasor measurement device; 3) constructing a sensing matrix, and enabling a row number m of the tidal current Jacobian matrix to be 1; 4) solving a least square solution as an estimation solution; 5) if the iteration termination condition is judged to be satisfied, the step 8) is carried out; otherwise, entering step 6); 6) solving the minimized correlation entropy model as an estimation solution; 7) if the iteration termination condition is satisfied, entering step 8); otherwise, updating the column number index set of the sensing matrix and returning to the step 6); 8) and judging whether the estimation of all rows of the Jacobian matrix is finished, if so, outputting an estimation result, otherwise, returning to the step 4), if not, taking m as m + 1. The method effectively avoids the bad data in the measurement from influencing the estimation result while utilizing the sparsity of the flow Jacobian matrix, and can still ensure the estimation accuracy under the condition that the bad data is contained in the measurement.
Description
Technical Field
The invention relates to a power flow jacobian matrix estimation method for a power distribution network. In particular to a sparsity-considered robust estimation method for a jacobian matrix of a power flow of an intelligent power distribution network.
Background
The large-scale renewable energy sources are connected into the power distribution network, and the randomness and the fluctuation of the output of the large-scale renewable energy sources provide higher requirements for operation monitoring and control of the power distribution network. In order to improve the level of new energy consumption of the power distribution network, the traditional power distribution network is gradually developed into an intelligent power distribution network. The tidal current jacobian matrix is an important parameter for analyzing the running state of the power distribution network and performing optimization control on the power distribution network, and the accurate acquisition of the tidal current jacobian matrix is an important premise and basis for running situation analysis and decision control on the power distribution network. However, the current method of obtaining the load flow jacobian matrix through offline load flow calculation is influenced by the problems that the parameters of the power distribution network line are difficult to accurately obtain, the topological connection relation is not updated timely, the operation point of the power grid is difficult to track, and the like, and the accuracy and the reliability of the method are greatly restricted.
The development and application of the synchronous phasor measurement technology not only improve the observability of the power system, but also provide new support and means for the operation control of the power distribution network. Particularly, with the development and technical innovation of the micro synchronous phasor measurement device, the requirement of the power distribution network for measurement data is met, the measurement precision is ensured, and the miniaturization and low cost of the synchronous phasor measurement device are gradually realized, so that the device can be applied to the power distribution system in a large range.
By utilizing the real-time measurement data of the synchronous phasor measurement device and the historical measurement data of multiple discontinuous surfaces, the online estimation of the load flow Jacobian matrix can be realized through a least square estimation method, the running state of the power distribution network can be tracked in real time, the dependency of the load flow Jacobian matrix calculation on the information of line parameters, topological connection relations and the like is greatly reduced, and the accuracy of parameter estimation calculation is effectively ensured. Particularly, the dependence of the estimation problem on measurement can be effectively reduced by utilizing the sparsity of the tidal current Jacobian matrix, and meanwhile, the estimation precision of the Jacobian matrix is improved.
The original Jacobian matrix estimation problem is converted into a sparse recovery problem by utilizing a compressed sensing technology, and the high-precision estimation of the Jacobian matrix can be realized by less measurement by utilizing the sparsity of the Jacobian matrix. For the sparse recovery problem, the greedy algorithm is an effective solution. The existing sparse recovery algorithm and core idea are to continuously solve the least square solution by iteration until a solution meeting the set estimation precision is found and is used as the optimal solution for estimation. However, the least square estimation has high sensitivity to bad data, and if the measured data contains bad data, the estimation result will deviate from the true value seriously. Although high-precision measurement data can be obtained through the synchronous phasor measurement device, due to the influence of links such as data acquisition, conversion and communication, bad data may still be contained in the measurement data, so that an estimation result is unavailable, and a more robust sparse recovery algorithm needs to be provided for estimating the tidal current jacobian matrix.
Disclosure of Invention
The invention aims to solve the technical problem of providing a smart distribution network power flow jacobian matrix robust estimation method which realizes the consideration of sparsity of the smart distribution network power flow jacobian matrix by less measurement.
The technical scheme adopted by the invention is as follows: a sparse considered robust estimation method for a power flow jacobian matrix of an intelligent power distribution network comprises the following steps:
1) acquiring the number of nodes of the power distribution network, setting the number of a source node as 0, setting the numbers of other nodes as 1, …, i, … and N in sequence, and inputting a conservative estimated value d of the maximum degree of the networkmaxSetting a residual error threshold epsilon, a maximum iteration number M and a historical measurement data demand group number C;
2) acquiring measurement data of active power, reactive power, voltage amplitude and voltage phase angle at the current moment, which are acquired by a synchronous phasor measurement device installed on each node of the system, and measurement data of C historical moments of each node;
3) respectively subtracting the measurement data of C historical moments of each node from the current measurement value, obtaining C variable quantities of active power, reactive power, voltage amplitude and voltage phase angle by each node, constructing a sensing matrix by using the variable quantities of the voltage and amplitude of the nodes from 1 to N, and initializing the row number m of the power flow jacobian matrix to be 1;
4) initializing residual vector, calculating correlation coefficient vector u of voltage phase angleθVector u of correlation coefficients with voltage amplitudeUInitializing the column index set Lambda of the sensing matrix when the number of initialization iterations n is 1nIs an empty set;
5) respectively selecting the related coefficient vector u of the voltage phase angleθVector u of correlation coefficients with voltage amplitudeUOf the maximum z values, where z is dmax+1, forming the intermediate set omega of the nth iteration by the column number index in the sensing matrix corresponding to the z numerical valuesn；
6) Intermediate set omega using nth iterationnUpdating sensing matrix column number index set LambdanSolving least square as an estimation solution, and updating a residual vector;
7) if the 2 norm R of the updated residual vector is smaller than the residual threshold epsilon, entering step 11); otherwise: if the iteration number n is equal to 1, the iteration number n is equal to n +1, and the correlation coefficient vectors u of the voltage phase angles are respectively selectedθVector u of correlation coefficients with voltage amplitudeUThe maximum 2z values in the n-th iteration are formed by the indexes in the sensing matrix corresponding to the 2z valuesnReturning to the step 6); if the iteration number n is 2, the iteration number n is n +1, and the step 8) is carried out;
8) calculating a residual error correlation coefficient vector u by adopting the sensing matrix and the residual error vector, selecting the maximum 2z column in the residual error correlation coefficient vector u, and forming an intermediate set omega of the nth iteration by indexes in the sensing matrix corresponding to the 2z columnnUpdating the column index set Lambda of the sensing matrixn；
9) Indexing set Lambda by updating column number of sensing matrixnEstablishing a minimum correlation entropy optimization model, solving the minimum correlation entropy model as an estimation solution, selecting a 4z item with the maximum absolute value in the estimation solution, and updating an index in a sensing matrix corresponding to the 4z item to a middle set omega of the nth iterationnReconstructing the column index set Lambda of the sensing matrixnUpdating the residual vector again;
10) if the 2 norm R of the residual vector updated again is smaller than the residual threshold epsilon or the iteration number exceeds the set maximum iteration number M, the step 11) is carried out; otherwise, returning to the step 8) if n is n + 1);
11) outputting an estimation solution, and recovering a 2N-dimensional vector as an estimation result of the mth row of the Jacobian matrix according to a sensing matrix column number index set, wherein m is m + 1; if m is larger than 2N, stopping iteration and outputting the estimation result of the Jacobian matrix, otherwise, returning to the step 4).
Establishing a minimum correlation entropy optimization model in the step 9), wherein an objective function is established as follows:
in the formula, ekThe k-th element of the vector e is represented,r0is the initial residual vector of the image data,index set lambda representing column number of sensing matrixnAnd (3) a matrix formed by each column of the sensing matrix corresponding to the middle element, x represents a decision variable for the solution, epsilon is a set residual threshold, sigma is an auxiliary constant, exp represents an exponential function, and C is the historical measurement data demand group number.
Solving the minimized correlation entropy model in the step 9), which comprises the following steps:
(1) initializing an optimized allowable error δ, initializing an initial solution x0The initialized weight vector w is 1, and 1 represents a constant vector with the value of 1;
(2) and solving a weighted least square solution for the decision variable x of the generation:
in the formula,index set lambda representing column number of sensing matrixnMatrix formed by columns of sensing matrix corresponding to medium elements, r0For the initial residual vector, diag (×) indicates that the diagonal matrix is formed by the elements in the vector "×";
(3) calculating a residual vector:
(4) the value of the auxiliary constant sigma is calculated from the residual vector r,c is the number of historical measurement data demand groups;
(5) the kth element of the weight vector w is calculated using the auxiliary constant σ:wkand rkThe kth elements of vectors w and r, respectively;
(6) judgment ofIf the condition is true, a solution is estimatedOutputting the estimation result, if the condition is not satisfied, making x0And (4) returning to the step (2).
The reconstructed sensing matrix column number index set in the step 9) is as follows:
Λn＝Ωn
in the formula, ΛnSet of sense matrix column index for nth iteration, ΩnRepresenting the updated intermediate set of the nth iteration.
The re-updated residual vector described in step 9) is represented as:
in the formula,set of representations ΛnMatrix formed by columns of sensing matrix corresponding to medium elements, rnIs the residual vector of the nth iteration, r0For the initial residual vector, diag (×) indicates that the diagonal matrix is formed by the elements in the vector "×", and w indicates the weight vector.
According to the intelligent power distribution network power flow jacobian matrix robust estimation method considering sparsity, measurement data of multiple time scales of synchronous phasor measurement are utilized, the sparsity of the power flow jacobian matrix is utilized, bad data possibly contained in the measurement data is considered, the mode of minimizing a related entropy optimization algorithm is provided, the robustness of a sparse recovery algorithm to the bad data is improved, and the robust estimation of the power flow jacobian matrix under the background of the intelligent power distribution network is achieved. The algorithm of the invention can effectively avoid bad data in measurement from influencing the estimation result while considering the sparsity of the Jacobian matrix, and can still ensure the estimation accuracy under the condition that bad data is contained in the measurement.
Drawings
FIG. 1 is a flow chart of a smart distribution network power flow Jacobian matrix robust estimation method considering sparsity;
fig. 2 is a diagram of IEEE33 node calculations.
Detailed Description
The following describes in detail a sparse consideration smart distribution network power flow jacobian matrix robust estimation method according to the present invention with reference to embodiments and drawings.
As shown in fig. 1, the sparse consideration smart distribution network power flow jacobian matrix robust estimation method of the present invention includes the following steps:
1) acquiring the number of nodes of the power distribution network, setting the number of a source node as 0, setting the numbers of other nodes as 1, …, i, … and N in sequence, and inputting a conservative estimated value d of the maximum degree of the networkmaxSetting a residual error threshold epsilon, a maximum iteration number M and a historical measurement data demand group number C;
2) acquiring measurement data of active power, reactive power, voltage amplitude and voltage phase angle at the current moment, which are acquired by a synchronous phasor measurement device installed on each node of the system, and measurement data of C historical moments of each node; wherein,
the C historical measurement data generation method comprises the following steps:
(1) the kth active power measurement of node i is generated in the following manner.
In the formula, Pi(k) Represents the kth active power history measure, P, of node ii(0) Representing the active power measurement of the current node i,the random numbers are normally distributed according to the average value of 0 and are respectively used for simulating the power change and the measurement error of different measurement moments relative to the current moment;
(2) generating a kth reactive power measurement of node i using the following equation
In the formula, Qi(k) Represents the kth reactive power measurement, Q, of node ii(0) Representing the reactive power measurement of the current node i,is a random number that follows a normal distribution with a mean value of 0;
(3) after the kth active power and reactive power of the node i are measured, the corresponding voltage phase angle theta is obtained through load flow calculationi(k) Sum amplitude Vi(k) As the kth voltage phase angle and magnitude measurements for node i.
3) Respectively subtracting the measurement data of C historical moments of each node from the current measurement value, obtaining the variation of C active power, reactive power, voltage amplitude and voltage phase angle by each node, constructing a sensing matrix by using the voltage phase angles of the nodes from 1 to N and the variation measured by the voltage amplitude, and initializing the line number m of the power flow jacobian matrix to be 1; wherein,
(1) the variation of C active power, reactive power, voltage amplitude and voltage phase angle is expressed as:
ΔPi[k]＝Pi(k)-Pi(0)、ΔQi[k]＝Qi(k)-Qi(0)、ΔVi[k]＝Vi(k)-Vi(0) and Δ θi[k]＝ θi(k)-θi(0)，k＝1,2,…,C，Pi(0)、Qi(0)、θi(0)、Vi(0) Respectively show the sectionsMeasuring values of active power, reactive power, voltage phase angle and voltage amplitude at the current moment of the point i; pi(k)、Qi(k)、θi(k)、Vi(k) Respectively representing the k-th historical measurement value of the node i;
(2) the constructed sensing matrix A is as follows:
in the formula,representing a matrix formed by voltage phase angle and voltage amplitude measurement variation vectors, Delta thetai＝[Δθi[1],…,Δθi[C]]TA column vector, Δ V, representing the C voltage angle measurement variations of node ii＝[ΔVi[1],…,ΔVi[C]]TA column vector consisting of C voltage amplitude measurement variations of the node i;to representElement of (1), Ap,qRepresenting the elements of the p-th row and q-th column in the sensing matrix a.
4) Initializing residual vector, calculating correlation coefficient vector u of voltage phase angleθVector u of correlation coefficients with voltage amplitudeU(ii) a Initializing a sensing matrix column number index set ΛnFor empty sets, the number of iterations is initializedn is 1; wherein,
4) initializing residual vector, calculating correlation coefficient vector u of voltage phase angleθVector u of correlation coefficients with voltage amplitudeU(ii) a Initializing the number of iterations n as 1, and initializing the column number index set Lambda of the sensing matrixnIs an empty set; wherein
(1) The calculation mode of the initialization residual error vector is as follows:
if m is more than or equal to 1 and less than or equal to N:
r0＝ΔPi
if N is more than m and less than or equal to 2N:
r0＝ΔQi
in the formula, r0Representing the initial residual vector, Δ Pi＝[ΔPi[1],…,ΔPi[C]]TA column vector consisting of C groups of active power change quantities representing nodes i; in the formula,. DELTA.Qi＝[ΔQi[1],…,ΔQi[C]]TAnd C groups of reactive power variable quantities representing the nodes i form a column vector.
(2) Vector u of correlation coefficients of voltage phase angleθThe calculation method comprises the following steps:
if m is more than or equal to 1 and less than or equal to N:
uθ＝abs(ATAq)
if N is more than m and less than or equal to 2N:
uθ＝abs(ATAq-N)
wherein abs (. circle.) represents an absolute value operation, A is a sensor matrix, and A is aqAnd Aq-NRespectively representing the q-th column and the q-N column of the sensing matrix A;
(3) vector u of correlation coefficients of voltage amplitudesUThe calculation method comprises the following steps:
if m is more than or equal to 1 and less than or equal to N:
uU＝abs(ATAq+N)
if N is more than m and less than or equal to 2N:
uU＝abs(ATAq)。
5) respectively selecting the related coefficient vector u of the voltage phase angleθVector u of correlation coefficients with voltage amplitudeUOf the maximum z values, where z is dmax+1, forming the intermediate set omega of the nth iteration by the column number index in the sensing matrix corresponding to the z numerical valuesn；
6) Intermediate set omega using nth iterationnUpdating sensing matrix column number index set LambdanSolving a least square solution and updating a residual vector; wherein,
(1) the updated sensing matrix column number index set is expressed as:
Λn＝Λn-1∪Ωn
in the formula, ΛnFor the column index set of the sensing matrix of the nth iteration, when n is 1, Λn-1Represents the initial sensing matrix column number index set, ΩnRepresenting an intermediate set of the nth iteration;
(2) the least squares solution is represented as:
in the formula,represents the least squares solution at the nth iteration, r0Is the initial residual vector of the image data,sensing matrix column number index set Lambda representing nth iterationnSensing moment corresponding to medium elementA matrix formed by the array;
(3) the updated residual vector is represented as:
in the formula, rnIs the residual vector of the nth iteration.
7) If the 2 norm R of the updated residual vector is smaller than the residual threshold epsilon, entering step 11); otherwise: if the iteration number n is equal to 1, the iteration number n is equal to n +1, and the correlation coefficient vectors u of the voltage phase angles are respectively selectedθVector u of correlation coefficients with voltage amplitudeUThe maximum 2z values in the n-th iteration are formed by the indexes in the sensing matrix corresponding to the 2z valuesnReturning to the step 6); if the iteration number n is 2, the iteration number n is n +1, and the step 8) is carried out;
8) calculating a residual error correlation coefficient vector u by adopting the sensing matrix and the residual error vector, selecting the maximum 2z column in the residual error correlation coefficient vector u, and forming an intermediate set omega of the nth iteration by indexes in the sensing matrix corresponding to the 2z columnnUpdating the column index set Lambda of the sensing matrixn(ii) a The residual error correlation coefficient vector u is calculated in the following way:
u＝abs(ATrn-1)
where u is a correlation coefficient vector, abs (·) represents an absolute value operation, and r isn-1Denotes the residual vector at the n-1 th iteration, and when n is 1, rn-1Representing the initial residual vector, and a is the sensing matrix.
9) Indexing set Lambda by updating column number of sensing matrixnEstablishing a minimum correlation entropy optimization model, solving the minimum correlation entropy model as an estimation solution, selecting a 4z item with the maximum absolute value in the estimation solution, and updating an index in a sensing matrix corresponding to the 4z item to a middle set omega of the nth iterationnReconstructing the column number of the sensing matrixIndex set ΛnUpdating the residual vector again; wherein
(1) The establishment of the minimum correlation entropy optimization model comprises the following steps of establishing an objective function:
in the formula, ekDenotes the kth element of the vector e, e ═ r0-AΛnx，r0Is the initial residual vector of the image data,index set lambda representing column number of sensing matrixnAnd (3) a matrix formed by each column of the sensing matrix corresponding to the middle element, x represents a decision variable for the solution, epsilon is a set residual threshold, sigma is an auxiliary constant, exp represents an exponential function, and C is the historical measurement data demand group number.
(2) The solving of the minimized correlation entropy model comprises the following steps:
(2.1) initializing the optimal allowable error δ, initializing the initial solution x0The initialized weight vector w is 1, and 1 represents a constant vector with the value of 1;
(2.2) solving a weighted least square solution of the decision variable x of the generation:
in the formula,index set lambda representing column number of sensing matrixnMatrix formed by columns of sensing matrix corresponding to medium elements, r0For the initial residual vector, diag (×) indicates that the diagonal matrix is formed by the elements in the vector "×";
(2.3) calculating a residual vector:
(2.4) calculating the value of the auxiliary constant sigma from the residual vector r,c is the number of historical measurement data demand groups;
(2.5) calculating the kth element of the weight vector w using the auxiliary constant σ:wkand rkThe kth elements of vectors w and r, respectively;
(2.6) judgmentIf the condition is true, a solution is estimatedOutputting the estimation result, if the condition is not satisfied, making x0And returning to the step (2.2).
(3) The reconstructed sensing matrix column number index set is as follows:
Λn＝Ωn
in the formula, ΛnSet of sense matrix column index for nth iteration, ΩnRepresenting the intermediate set of the nth iteration.
(4) The re-updated residual vector is represented as:
in the formula,set of representations ΛnMiddle elementMatrix formed by corresponding sensing matrix columns, rnIs the residual vector of the nth iteration, r0For the initial residual vector, diag (×) indicates that the diagonal matrix is formed by the elements in the vector "×", and w indicates the weight vector.
10) If the 2 norm R of the residual vector updated again is smaller than the residual threshold epsilon or the iteration number exceeds the set maximum iteration number M, the step 11) is carried out; otherwise, returning to the step 8) if n is n + 1);
11) outputting an estimation solution, and recovering a 2N-dimensional vector as an estimation result of the mth row of the Jacobian matrix according to a sensing matrix column number index set, wherein m is m + 1; if m is larger than 2N, stopping iteration and outputting the estimation result of the Jacobian matrix, otherwise, returning to the step 4). The estimation result of recovering the 2N-dimensional vector as the mth row of the Jacobian matrix according to the column number index set of the sensing matrix is expressed as follows:
in the formula,representing the estimated solution at the nth iteration,representing a 2N-dimensional recovery vector,to representThe g-th element of (a),representing sensing momentArray number index set ΛnVector corresponding to each element inOf elements of (2) toOther elements not in the column index set take values of 0;matrix arrayThe 2-norm of the q-th column, represents the estimated solution of the qth element of the mth row of the jacobian matrix Y, where g equals q.
Specific examples are given below:
first, an example network topology connection relation of IEEE33 nodes is shown in fig. 2, where node 0 is a balanced node, other nodes 1 to 32 are PQ nodes, a reference capacity of the system is 1MVA, a reference voltage is 12.66kV, and current power measurement of each PQ node is shown in table 1. The conservative estimate of the maximum degree of the input network is 4, the standard difference of the analog measurement power change and the error random number is set to be 0.01 and 0.025%, respectively, and the measurement group numbers are set to be 30, 35, 40, 45, 50, 55 and 60, respectively. The errors of the jacobian matrix and the voltage power sensitivity matrix are calculated using the following equations.
In the formula,respectively representing estimated values of the elements of the jacobian matrix, Ji,jAre theoretical values of the elements of the jacobian matrix.
And calculating the estimation error of the ith row of the Jacobian matrix by adopting the following formula, and when the estimation error is less than 10, judging that the row estimation is successful.
In order to verify the advancement of the method, the following two scenes are adopted for analysis:
in the scene 1, no bad data is solved by adopting a least square solution in the step 9) of the invention and the minimum correlation entropy model of the invention, and the number of rows and errors of the Jacobian matrix which are successfully estimated are shown in the tables 2 and 3 respectively.
In scenario 2, bad data are added to the 10 th group of active power measurements of the node 24 and the 20 th group of active power measurements of the node 29, the bad data condition is shown in tables 4 and 5, respectively, and the least square solution is adopted in step 9) for solving and the minimum correlation entropy model is adopted for solving, so that the number of rows of successful jacobian matrix estimation and the estimation error are shown in tables 6 and 7, respectively.
The computer hardware environment for executing the optimization calculation is Intel (R) Xeon (R) CPU E5-1620, the main frequency is 3.70GHz, and the memory is 32 GB; the software environment is a Windows 7 operating system, and the fashion flow is calculated by adopting the MATPOWER toolkit of MATLAB.
As can be seen from tables 2 and 3, when there is no bad data, the minimized correlation entropy method of the present invention has the same estimation success rate and estimation accuracy as the minimized two-times method, so that the method of the present invention can realize that the estimation accuracy is not sacrificed when there is no bad data in the measured data; as can be seen from tables 6 and 7, when the measurement contains bad data, the estimation of any row of the jacobian matrix cannot be realized by using the minimum two-times method, while the estimation of all rows of the power flow jacobian matrix can be realized by using the method of the present invention when the number of measurement groups reaches 35 groups, although the estimation accuracy is increased compared with that when no bad data exists, the estimation accuracy is maintained at the same level. Therefore, the method can realize the robustness of bad data while utilizing the sparsity of the jacobian matrix, and finally realize the robust estimation of the tidal current jacobian matrix.
TABLE 1 IEEE33 node example PQ node Current Power measurement
TABLE 2 Scenario 1 number of rows with unsuccessful Jacobian matrix estimation
Table 3 scene 1 jacobian matrix estimation error
TABLE 4 bad data case for node 24
TABLE 5 bad data case for node 29
TABLE 6 Scenario 2 Jacobian matrix estimate unsuccessful number of rows
TABLE 7 Scenario 2 Jacobian matrix estimation error
Claims (5)
1. A sparse considered robust estimation method for a power flow Jacobian matrix of an intelligent power distribution network is characterized by comprising the following steps:
1) acquiring the number of nodes of the power distribution network, setting the number of a source node as 0, setting the numbers of other nodes as 1, …, i, … and N in sequence, and inputting a conservative estimated value d of the maximum degree of the networkmaxSetting a residual error threshold epsilon, a maximum iteration number M and a historical measurement data demand group number C;
2) acquiring measurement data of active power, reactive power, voltage amplitude and voltage phase angle at the current moment, which are acquired by a synchronous phasor measurement device installed on each node of the system, and measurement data of C historical moments of each node;
3) respectively subtracting the measurement data of C historical moments of each node from the current measurement value, obtaining C variable quantities of active power, reactive power, voltage amplitude and voltage phase angle by each node, constructing a sensing matrix by using the variable quantities of the voltage and amplitude of the nodes from 1 to N, and initializing the row number m of the power flow jacobian matrix to be 1;
4) initializing residual vector, calculating correlation coefficient vector u of voltage phase angleθVector u of correlation coefficients with voltage amplitudeUInitializing the column index set Lambda of the sensing matrix when the number of initialization iterations n is 1nIs an empty set;
5) respectively selecting the related coefficient vector u of the voltage phase angleθVector u of correlation coefficients with voltage amplitudeUOf the maximum z values, where z is dmax+1, forming the intermediate set omega of the nth iteration by the column number index in the sensing matrix corresponding to the z numerical valuesn；
6) Intermediate set omega using nth iterationnUpdating sensing matrix column number index set LambdanSolving least square as an estimation solution, and updating a residual vector;
7) if the 2 norm R of the updated residual vector is smaller than the residual threshold epsilon, entering step 11); otherwise: if the iteration number n is equal to 1, the iteration number n is equal to n +1, and the correlation coefficient vectors u of the voltage phase angles are respectively selectedθVector u of correlation coefficients with voltage amplitudeUThe maximum 2z values in the n-th iteration are formed by the indexes in the sensing matrix corresponding to the 2z valuesnReturning to the step 6); if the iteration number n is 2, the iteration number n is n +1, and the step 8) is carried out;
8) calculating a residual error correlation coefficient vector u by adopting the sensing matrix and the residual error vector, selecting the maximum 2z column in the residual error correlation coefficient vector u, and forming an intermediate set omega of the nth iteration by indexes in the sensing matrix corresponding to the 2z columnnUpdating the column index set Lambda of the sensing matrixn；
9) Indexing set Lambda by updating column number of sensing matrixnEstablishingThe minimum correlation entropy optimization model is solved to serve as an estimation solution, a 4z item with the maximum absolute value in the estimation solution is selected, and indexes in the sensing matrix corresponding to the 4z item are updated to a middle set omega of the nth iterationnReconstructing the column index set Lambda of the sensing matrixnUpdating the residual vector again;
10) if the 2 norm R of the residual vector updated again is smaller than the residual threshold epsilon or the iteration number exceeds the set maximum iteration number M, the step 11) is carried out; otherwise, returning to the step 8) if n is n + 1);
11) outputting an estimation solution, and recovering a 2N-dimensional vector as an estimation result of the mth row of the Jacobian matrix according to a sensing matrix column number index set, wherein m is m + 1; if m is larger than 2N, stopping iteration and outputting the estimation result of the Jacobian matrix, otherwise, returning to the step 4).
2. The sparse consideration smart distribution network power flow jacobian matrix robust estimation method according to claim 1, wherein the establishing of the minimized correlation entropy optimization model in the step 9) comprises establishing an objective function as follows:
in the formula, ekThe k-th element of the vector e is represented,r0is the initial residual vector of the image data,index set lambda representing column number of sensing matrixnAnd (3) a matrix formed by each column of the sensing matrix corresponding to the middle element, x represents a decision variable for a substitution, epsilon is a set residual error threshold, sigma is an auxiliary constant, exp represents an exponential function, and C is the historical measurement data demand group number.
3. The sparse consideration smart distribution network power flow jacobian matrix robust estimation method according to claim 1, wherein the solving of the minimized correlation entropy model in the step 9) comprises:
(1) initializing an optimized allowable error δ, initializing an initial solution x0The initialized weight vector w is 1, and 1 represents a constant vector with the value of 1;
(2) and solving a weighted least square solution for the decision variable x of the generation:
in the formula,index set lambda representing column number of sensing matrixnMatrix formed by columns of sensing matrix corresponding to medium elements, r0For the initial residual vector, diag (×) indicates that the diagonal matrix is formed by the elements in the vector "×";
(3) calculating a residual vector:
(4) the value of the auxiliary constant sigma is calculated from the residual vector r,c is the number of historical measurement data demand groups;
(5) the kth element of the weight vector w is calculated using the auxiliary constant σ:wkand rkThe kth elements of vectors w and r, respectively;
(6) judgment ofIf the condition is true, a solution is estimatedOutputting the estimation result, if the condition is not satisfied, making x0And (4) returning to the step (2).
4. The sparsity-considered robust estimation method for the power flow jacobian matrix of the intelligent power distribution network according to claim 1, wherein the column index set of the reconstructed sensing matrix in the step 9) is:
Λn＝Ωn
in the formula, ΛnSet of sense matrix column index for nth iteration, ΩnRepresenting the updated intermediate set of the nth iteration.
5. The sparsity-considered robust estimation method for the power flow jacobian matrix of the intelligent power distribution network according to claim 1, wherein the re-updating residual vector in the step 9) is represented as:
in the formula,set of representations ΛnMatrix formed by columns of sensing matrix corresponding to medium elements, rnIs the residual vector of the nth iteration, r0For the initial residual vector, diag (×) indicates that the diagonal matrix is formed by the elements in the vector "×", and w indicates the weight vector.
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