CN107742885A - Power distribution network voltage power sensitivity estimation method based on regular matching pursuit - Google Patents
Power distribution network voltage power sensitivity estimation method based on regular matching pursuit Download PDFInfo
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Abstract
A power distribution network voltage power sensitivity estimation method based on regular matching pursuit comprises the following steps: acquiring the number of nodes of the power distribution network, inputting a conservative estimated value of the maximum degree of the network, and setting a residual error threshold and the maximum iteration times; acquiring measurement data of current time history of each node of the system; respectively subtracting the historical measurement data of the group from the current measurement value to obtain a plurality of groups of variation vectors to construct a sensing matrix; obtaining a correlation coefficient vector of a voltage phase angle and a voltage amplitude; updating a sensing matrix column number index set; solving a least square solution by using a sensing matrix column number index set, and updating a residual vector; judging whether the 2 norm of the updated residual vector is smaller than a residual threshold value; and outputting a least square estimation result, recovering a 2N-dimensional vector as an estimation result of one element of the Jacobian matrix according to the column number index set of the sensing matrix, outputting the estimation result, inverting the obtained Jacobian matrix, and obtaining an estimation result of the voltage power sensitivity matrix. The invention realizes the accurate estimation of the voltage power sensitivity parameter of the power distribution network.
Description
Technical Field
The invention relates to a voltage power sensitivity estimation method. In particular to a power distribution network voltage power sensitivity estimation method based on regular matching pursuit.
Background
The power distribution network is arranged at the tail end of the power system and is directly connected with the users, and the power distribution network is an important ring for guaranteeing safe and reliable power supply of the users. The distribution network has the characteristics of wide geographical distribution, large system scale, various equipment types and operation modes and the like, and meanwhile, with the access of distributed power supplies such as photovoltaic power supplies, fans, gas turbines and the like, the continuously improved permeability makes the operation control of the distribution network face greater challenges, and especially the problem of voltage out-of-limit and the like becomes an important restriction on the access of new energy. The problem of voltage control of the power distribution network is solved by depending on adjustable equipment and a control strategy thereof in the power distribution network, the relation between power change and voltage change is accurately modeled, and the applicability and the effectiveness of a voltage control scheme are directly determined.
The voltage power sensitivity parameters can be obtained through inversion of the tidal current Jacobian matrix, traditional tidal current Jacobian matrix calculation depends on accurate power distribution network line parameters and network topology information, and the inaccurate line parameters and topology connection relations enable the calculation of the voltage power sensitivity parameters to have large deviation, and the voltage control effect is directly influenced. The synchronous phasor measurement device can realize high-precision synchronous measurement of electric quantities such as active power, reactive power, voltage phase angle, voltage amplitude, system frequency and the like, and enables online estimation of voltage power sensitivity parameters to be possible. Especially, the development and application of the micro synchronous phasor measurement device gradually realize miniaturization and low cost of the synchronous phasor measurement device, and the application of the synchronous phasor measurement device in the level of a power distribution system has wide prospect.
The synchronous phasor measurement can realize the state measurement of dozens of operating points per second, the measurement change vectors of power and voltage can be obtained through the difference between the historical measurement and the current operating point, and the time interval between the measurement points is short, the measurement change quantity is small, and the power change quantity and the voltage change quantity approximately meet the linear relation. When the measured data exceeds the dimension of the power flow Jacobian matrix, the least square estimation method can be adopted to realize the accurate estimation of the Jacobian matrix, and further realize the estimation of the voltage power sensitivity matrix.
Considering the topological connection relationship, the power flow Jacobian matrix has strong sparsity, and the sparsity is considered when the Jacobian matrix is estimated, so that the dependence of the estimation problem on the measured data quantity can be effectively reduced, and higher estimation accuracy can be realized under the condition of the same measurement group number. Therefore, the original problem can be converted into the sparse recovery problem in consideration of the sparsity of the matrix, and the orthogonal matching pursuit algorithm selects a local optimal solution for each iteration through greedy thinking and approaches the original value step by step, so that the method is an effective means for solving the sparse recovery problem.
Disclosure of Invention
The invention aims to solve the technical problem of providing a power distribution network voltage and power sensitivity estimation method based on regular matching pursuit, which can improve the accuracy of voltage and power sensitivity parameter estimation and reduce the iteration times and the solving time.
The technical scheme adopted by the invention is as follows: a power distribution network voltage power sensitivity estimation method based on regular matching pursuit comprises the following steps:
1) acquiring the number of nodes of the power distribution network, numbering a source node as 0, numbering 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 and a maximum iteration number M;
2) acquiring measurement data of active power, reactive power, voltage amplitude and voltage phase angle of each node synchronous phasor measurement device of the system at the current moment and C group historical measurement data, wherein C is an integer greater than 1;
3) respectively subtracting the historical measurement data of the C group from the current measurement value to obtain variation vectors of active power, reactive power, voltage amplitude and voltage phase angle of the C group, constructing a sensing matrix by using the variation vectors measured by the voltages of the nodes 1 to N, and initializing the line number m of the tidal current jacobian matrix to be 1;
4) if m is not larger than N, selecting an active power measurement change vector of a node i to initialize a residual vector, wherein i is m; if m is larger than N, initializing a residual vector by using a reactive power measurement change vector of a node i, wherein i is m-N; initializing a column number index set of a sensing matrix into an empty set, and initializing iteration times n to be 1;
5) respectively calculating the correlation between the residual error vector and each column of the sensing matrix to obtain a residual error correlation coefficient vector u, and selecting the maximum 2z columns in the residual error correlation coefficient vector u, wherein z is dmax+1, the indexes in the sensing matrix corresponding to 2z columns form a set omeganAfter regularization processing, updating a column number index set of the sensing matrix;
6) solving a least square solution by using a sensing matrix column number index set, 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 8); otherwise, returning to the step 5) if n is n + 1);
8) outputting a least square estimation result, 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, outputting a Jacobian matrix estimation result, and entering the step 9), otherwise, returning to the step 4);
9) and 8) inverting the Jacobian matrix obtained in the step 8) to obtain an estimation result of the voltage power sensitivity matrix.
In step 3)
(1) The variation vectors of the C groups of active power, reactive power, voltage amplitude and voltage phase angle are represented as follows:
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 representing the measurement values of active power, reactive power, voltage phase angle and voltage amplitude of the node i at the current moment; pi(k)、Qi(k)、θi(k)、Vi(k) Respectively representing the historical measurement values of the kth group 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-set voltage angle measurement variation of node ii＝[ΔVi[1],…,ΔVi[C]]TA column vector consisting of C groups of voltage amplitude measurement variable quantities representing nodes i;to representElement of (1), Ap,qRepresenting the elements of the p-th row and q-th column in the sensing matrix a.
In step 4)
(1) The active power measurement change vector initialization residual vector of the selected node i is represented as:
r0＝ΔPi
in the formula, r0Representing the initial residual vector, Δ Pi＝[ΔPi[1],…,ΔPi[C]]TA column vector consisting of C groups of active power measurement variable quantities representing nodes i;
(2) initializing a residual vector by using a reactive power measurement change vector of a node i, and expressing the residual vector as follows:
r0＝ΔQi
in the formula,. DELTA.Qi＝[ΔQi[1],…,ΔQi[C]]TAnd C groups of reactive power measurement variable quantities representing the nodes i form a column vector.
In step 5)
(1) The calculation mode of the residual error correlation coefficient vector u is as follows:
u＝abs[ATrn-1]
wherein u is the vector of the correlation coefficient, abs [. sup. ]]Representing an absolute value operation, rn-1Denotes the residual vector at the n-1 th iteration, when n is 1, rn-1Representing the initial residual vector, and a is the sensing matrix.
(2) The regularization process is represented as being set ΩnFind all the requirements in (c) for any i, j ∈ Ω0，ui≤2ujIs given by0And selects the formula sigma calculated in all subsetsjuj,j∈Ω0Maximum subset, update set omegan＝Ω0；
(3) 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 nth iteration, when n is 1, Λn-1Denotes the initial set of column index, ΩnRepresenting the set of newly selected indices.
Step 6) comprises the following steps:
(1) 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,set of column index Λ representing the nth iterationnA matrix formed by all columns of the sensing matrix corresponding to the middle element;
(2) the updated residual vector is represented as:
in the formula, rnIs the residual vector of the nth iteration.
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 in the step 8) is expressed as follows:
in the formula,represents the least squares solution at the nth iteration,representing a 2N-dimensional recovery vector,to representThe g-th element of (a),set of representative column index ΛnVector corresponding to each element inOf elements of (2) toOther elements not in the column index set take values of 0;matrix arrayThe modulus value 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.
According to the power distribution network power sensitivity estimation method based on the regular matching pursuit, accurate estimation of the power distribution network voltage sensitivity parameters is achieved by means of data of a plurality of time period surfaces obtained through synchronous phasor measurement. Meanwhile, the sparse characteristic of the tidal current Jacobian matrix is considered, the original problem is converted into a sparse recovery problem, the sparse recovery problem is solved by utilizing a regularized orthogonal matching pursuit algorithm, and the accuracy of voltage and power sensitivity estimation is improved. Compared with the traditional orthogonal matching tracking algorithm, the regularized orthogonal matching tracking algorithm greatly reduces the iteration times of problem solving by selecting multiple columns and regularizing in each iteration, thereby improving the calculation efficiency of the algorithm.
Drawings
FIG. 1 is a flow chart of a power distribution network voltage power sensitivity estimation method based on regular matching pursuit in accordance with the present invention;
fig. 2 is a diagram of IEEE33 node calculations.
Detailed Description
The following describes the method for estimating the voltage power sensitivity of the power distribution network based on the regular matching pursuit according to the present invention in detail with reference to the following embodiments and the accompanying drawings.
As shown in fig. 1, the method for estimating the voltage power sensitivity of the power distribution network based on the regular matching pursuit of the invention comprises the following steps:
1) acquiring the number of nodes of the power distribution network, numbering a source node as 0, numbering 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 and a maximum iteration number M;
2) acquiring measurement data of active power, reactive power, voltage amplitude and voltage phase angle of each node synchronous phasor measurement device of the system at the current moment and C group historical measurement data, wherein C is an integer greater than 1;
the method for generating the C group historical measurement data comprises the following steps:
(1) generating the kth group of active power measurement data of the node i by adopting the following formula,
in the formula, Pi(k) The k group active power, P, representing node ii(0) Represents 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 the k-th group of reactive power measurement data of the node i by adopting the following formula,
in the formula, Qi(k) The kth group of reactive powers, Q, representing node ii(0) Representing reactive power of the current node iThe measurement of the rate is carried out,are random numbers that follow a normal distribution with a mean of 0.
(3) After the k group of active power and reactive power measurement data of the node i are obtained, the corresponding voltage phase angle theta is obtained through load flow calculationi(k) Sum amplitude Vi(k) The kth set of voltage phase angle and magnitude measurements are taken as node i.
3) Respectively subtracting the historical measurement data of the C group from the current measurement value to obtain variation vectors of active power, reactive power, voltage amplitude and voltage phase angle of the C group, constructing a sensing matrix by using the variation vectors measured by the voltages of the nodes 1 to N, and initializing the line number m of the tidal current jacobian matrix to be 1; wherein,
(1) the variation vectors of the C groups of active power, reactive power, voltage amplitude and voltage phase angle are represented as follows:
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 representing the measurement values of active power, reactive power, voltage phase angle and voltage amplitude of the node i at the current moment; pi(k)、Qi(k)、θi(k)、Vi(k) Respectively representing the historical measurement values of the kth group 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-set voltage angle measurement variation of node ii＝[ΔVi[1],…,ΔVi[C]]TA column vector consisting of C groups of voltage amplitude measurement variable quantities representing nodes i;to representElement of (1), Ap,qRepresenting the elements of the p-th row and q-th column in the sensing matrix a.
4) If m is not larger than N, selecting an active power measurement change vector of a node i to initialize a residual vector, wherein i is m; if m is larger than N, initializing a residual vector by using a reactive power measurement change vector of a node i, wherein i is m-N; initializing a column number index set of a sensing matrix into an empty set, and initializing iteration times n to be 1; wherein,
(1) the active power measurement change vector initialization residual vector of the selected node i is represented as:
r0＝ΔPi
in the formula, r0Representing the initial residual vector, Δ Pi＝[ΔPi[1],…,ΔPi[C]]TA column vector consisting of C groups of active power measurement variable quantities representing nodes i;
(2) initializing a residual vector by using a reactive power measurement change vector of a node i, and expressing the residual vector as follows:
r0＝ΔQi
in the formula,. DELTA.Qi＝[ΔQi[1],…,ΔQi[C]]TAnd C groups of reactive power measurement variable quantities representing the nodes i form a column vector.
5) Respectively calculating the correlation between the residual error vector and each column of the sensing matrix to obtain a residual error correlation coefficient vector u, and selecting the maximum 2z columns in the residual error correlation coefficient vector u, wherein z is dmax+1, the indexes in the sensing matrix corresponding to 2z columns form a set omeganAfter regularization processing, updating a column number index set of the sensing matrix; wherein,
(1) the calculation mode of the residual error correlation coefficient vector u is as follows:
u＝abs[ATrn-1]
wherein u is the vector of the correlation coefficient, abs [. sup. ]]Representing an absolute value operation, rn-1Denotes the residual vector at the n-1 th iteration, when n is 1, rn-1Representing the initial residual vector, and a is the sensing matrix.
(2) The regularization process is represented as being set ΩnFind all the requirements in (c) for any i, j ∈ Ω0，ui≤2ujIs given by0And selects the formula sigma calculated in all subsetsjuj,j∈Ω0Maximum subset, update set omegan＝Ω0；
(3) 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 nth iteration, when n is 1, Λn-1Denotes the initial set of column index, ΩnRepresenting the set of newly selected indices.
6) Solving a least square solution by using a sensing matrix column number index set, and updating a residual vector; the method comprises the following steps:
(1) 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,set of column index Λ representing the nth iterationnA matrix formed by all columns of the sensing matrix corresponding to the middle element;
(2) 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 8); otherwise, returning to the step 5).
8) Outputting a least square estimation result, 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, outputting a Jacobian matrix estimation result, and entering the step 9), 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,represents the least squares solution at the nth iteration,representing a 2N-dimensional recovery vector,to representThe g-th element of (a),set of representative column index ΛnVector corresponding to each element inOf elements of (2) toOther elements not in the column index set take values of 0;matrix arrayThe modulus value 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.
9) And 8) inverting the Jacobian matrix obtained in the step 8) to obtain an estimation result of the voltage power sensitivity matrix.
Specific examples are given below:
for the present embodiment, first, an IEEE33 node arithmetic network topology connection relationship is input as shown in fig. 2, where a node 0 is a balanced node, the remaining nodes 1 to 32 are PQ nodes, a reference capacity of the system is 1MVA, a reference voltage is 12.66kV, and a current power measurement of each PQ node is shown in table 1. The measurement sets are respectively set as 100, 150, 200, 250, 300, 350 and 400 sets, and the standard deviation of the random numbers simulating the power variation and the error of the measurement is respectively set as 0.01 and 0.025 percent. The following two formulas are respectively adopted to calculate the errors of the Jacobian matrix and the voltage power sensitivity matrix.
In the formula,andrespectively representing the estimated values of the parameters of the Jacobian matrix and the parameters of the voltage power sensitivity matrix, Ji，jAnd Si，jTo use the calculated values of the accurate line parameters.
In order to verify the advancement of the method, the method of directly utilizing the least square method, the orthogonal matching pursuit and the method of the invention are respectively adopted to solve the problem of flow Jacobian matrix estimation, and the solving results are shown in tables 2 to 5.
The computer hardware environment for executing the estimation 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 MATPOWER toolkit of MATLAB is adopted to calculate the load flow.
Table 2 and table 3 show the average values of the estimation errors of the jacobian matrix and the voltage power sensitivity matrix for 10 times of calculation for each measurement group number of 100, 150, 200, 250, 300, 350, 400, respectively, and it can be seen from table 2 and table 3 that, compared with the direct least square method, under the same measurement data, the orthogonal matching pursuit algorithm and the algorithm of the present invention can utilize the sparsity of the power flow jacobian matrix, improve the estimation accuracy of the power flow jacobian matrix and the voltage power sensitivity matrix, and the algorithm of the present invention has higher accuracy. As can be seen from tables 4 and 5, compared with the orthogonal matching pursuit algorithm, the method of the present invention greatly reduces the iterative process required by the estimation calculation while ensuring the estimation accuracy, thereby saving a large amount of calculation time, and being more suitable for the online estimation of the voltage power sensitivity.
TABLE 1IEEE 33 node example PQ node Current Power measurement
Table 2 jacobian estimation error (. 10)-3)
Table 3 voltage power sensitivity matrix estimation error (. about.10)-11)
TABLE 4 comparison of iteration number
TABLE 5 calculation of time comparison(s)
Claims (6)
1. A power distribution network voltage power sensitivity estimation method based on regular matching pursuit is characterized by comprising the following steps:
1) acquiring the number of nodes of the power distribution network, numbering a source node as 0, numbering 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 and a maximum iteration number M;
2) acquiring measurement data of active power, reactive power, voltage amplitude and voltage phase angle of each node synchronous phasor measurement device of the system at the current moment and C group historical measurement data, wherein C is an integer greater than 1;
3) respectively subtracting the historical measurement data of the C group from the current measurement value to obtain variation vectors of active power, reactive power, voltage amplitude and voltage phase angle of the C group, constructing a sensing matrix by using the variation vectors measured by the voltages of the nodes 1 to N, and initializing the line number m of the tidal current jacobian matrix to be 1;
4) if m is not larger than N, selecting an active power measurement change vector of a node i to initialize a residual vector, wherein i is m; if m is larger than N, initializing a residual vector by using a reactive power measurement change vector of a node i, wherein i is m-N; initializing a column number index set of a sensing matrix into an empty set, and initializing iteration times n to be 1;
5) respectively calculating the correlation between the residual error vector and each column of the sensing matrix to obtain a residual error correlation coefficient vector u, and selecting the maximum 2z columns in the residual error correlation coefficient vector u, wherein z is dmax+1, the indexes in the sensing matrix corresponding to 2z columns form a set omeganAfter regularization processing, updating a column number index set of the sensing matrix;
6) solving a least square solution by using a sensing matrix column number index set, 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 8); otherwise, returning to the step 5) if n is n + 1);
8) outputting a least square estimation result, 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, outputting a Jacobian matrix estimation result, and entering the step 9), otherwise, returning to the step 4);
9) and 8) inverting the Jacobian matrix obtained in the step 8) to obtain an estimation result of the voltage power sensitivity matrix.
2. The regular matching pursuit based power and voltage sensitivity estimation method for power distribution network according to claim 1, characterized in that in step 3)
(1) The variation vectors of the C groups of active power, reactive power, voltage amplitude and voltage phase angle are represented as follows:
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 representing the measurement values of active power, reactive power, voltage phase angle and voltage amplitude of the node i at the current moment; pi(k)、Qi(k)、θi(k)、Vi(k) Respectively representing the historical measurement values of the kth group of the node i;
(2) the constructed sensing matrix A is as follows:
<mrow> <mover> <mi>A</mi> <mo>~</mo> </mover> <mo>=</mo> <mo>&lsqb;</mo> <msub> <mrow> <mo>(</mo> <msub> <mi>&Delta;&theta;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>N</mi> </mrow> </msub> <msub> <mrow> <mo>(</mo> <msub> <mi>&Delta;V</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>N</mi> </mrow> </msub> <mo>&rsqb;</mo> </mrow>
<mrow> <mo>|</mo> <msub> <mover> <mi>A</mi> <mo>~</mo> </mover> <mi>q</mi> </msub> <mo>|</mo> <mo>=</mo> <msqrt> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>p</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>C</mi> </munderover> <msubsup> <mover> <mi>A</mi> <mo>~</mo> </mover> <mrow> <mi>p</mi> <mo>,</mo> <mi>q</mi> </mrow> <mn>2</mn> </msubsup> </mrow> </msqrt> </mrow>
<mrow> <msub> <mi>A</mi> <mrow> <mi>p</mi> <mo>,</mo> <mi>q</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mover> <mi>A</mi> <mo>~</mo> </mover> <mrow> <mi>p</mi> <mo>,</mo> <mi>q</mi> </mrow> </msub> <mrow> <mo>|</mo> <msub> <mover> <mi>A</mi> <mo>~</mo> </mover> <mi>q</mi> </msub> <mo>|</mo> </mrow> </mfrac> </mrow>
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-set voltage angle measurement variation of node ii＝[ΔVi[1],…,ΔVi[C]]TA column vector consisting of C groups of voltage amplitude measurement variable quantities representing nodes i;to representElement of (1), Ap,qRepresenting the elements of the p-th row and q-th column in the sensing matrix a.
3. The regular matching pursuit based power and voltage sensitivity estimation method for power distribution network according to claim 1, characterized in that in step 4)
(1) The active power measurement change vector initialization residual vector of the selected node i is represented as:
r0＝ΔPi
in the formula, r0Representing the initial residual vector, Δ Pi＝[ΔPi[1],…,ΔPi[C]]TA column vector consisting of C groups of active power measurement variable quantities representing nodes i;
(2) initializing a residual vector by using a reactive power measurement change vector of a node i, and expressing the residual vector as follows:
r0＝ΔQi
in the formula,. DELTA.Qi＝[ΔQi[1],…,ΔQi[C]]TAnd C groups of reactive power measurement variable quantities representing the nodes i form a column vector.
4. The regular matching pursuit based power and voltage sensitivity estimation method for power distribution network according to claim 1, characterized in that in step 5)
(1) The calculation mode of the residual error correlation coefficient vector u is as follows:
u＝abs[ATrn-1]
wherein u is the vector of the correlation coefficient, abs [. sup. ]]Representing an absolute value operation, rn-1Denotes the residual vector at the n-1 th iteration, when n is 1, rn-1Representing the initial residual vector, and a is the sensing matrix.
(2) The regularization process is represented as being set ΩnFind all the requirements in (c) for any i, j ∈ Ω0，ui≤2ujIs given by0And selects the formula sigma calculated in all subsetsjuj,j∈Ω0Maximum subset, update set omegan＝Ω0；
(3) 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 nth iteration, when n is 1, Λn-1Denotes the initial set of column index, ΩnRepresenting the set of newly selected indices.
5. The regular matching pursuit based power and voltage sensitivity estimation method for the power distribution network according to claim 1, wherein the step 6) comprises:
(1) the least squares solution is represented as:
<mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>n</mi> </msub> <mo>=</mo> <msup> <mrow> <mo>(</mo> <msubsup> <mi>A</mi> <msub> <mi>&Lambda;</mi> <mi>n</mi> </msub> <mi>T</mi> </msubsup> <msub> <mi>A</mi> <msub> <mi>&Lambda;</mi> <mi>n</mi> </msub> </msub> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <msubsup> <mi>A</mi> <msub> <mi>&Lambda;</mi> <mi>n</mi> </msub> <mi>T</mi> </msubsup> <msub> <mi>r</mi> <mn>0</mn> </msub> </mrow>
in the formula,represents the least squares solution at the nth iteration, r0Is the initial residual vector of the image data,set of column index Λ representing the nth iterationnA matrix formed by all columns of the sensing matrix corresponding to the middle element;
(2) the updated residual vector is represented as:
<mrow> <msub> <mi>r</mi> <mi>n</mi> </msub> <mo>=</mo> <msub> <mi>r</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mi>A</mi> <msub> <mi>&Lambda;</mi> <mi>n</mi> </msub> </msub> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>n</mi> </msub> </mrow>
in the formula, rnIs the residual vector of the nth iteration.
6. The method for estimating the voltage power sensitivity of the power distribution network based on the regular matching pursuit as claimed in claim 1, wherein the step 8) of recovering the 2N-dimensional vector according to the column number index set of the sensing matrix as the estimation result of the mth row of the jacobian matrix is represented as follows:
<mrow> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <msub> <mi>&Lambda;</mi> <mi>n</mi> </msub> </msub> <mo>=</mo> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>n</mi> </msub> </mrow>
<mrow> <msub> <mover> <mi>Y</mi> <mo>^</mo> </mover> <mrow> <mi>m</mi> <mo>,</mo> <mi>q</mi> </mrow> </msub> <mo>=</mo> <mfrac> <msub> <mover> <mi>x</mi> <mo>^</mo> </mover> <mi>g</mi> </msub> <mrow> <mo>|</mo> <msub> <mover> <mi>A</mi> <mo>~</mo> </mover> <mi>q</mi> </msub> <mo>|</mo> </mrow> </mfrac> </mrow>
in the formula,represents the least squares solution at the nth iteration,representing a 2N-dimensional recovery vector,to representThe g-th element of (a),set of representative column index ΛnVector corresponding to each element inOf elements of (2) toOther elements not in the column index set take values of 0;matrix arrayThe modulus value 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.
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| CN110308366B (en) * | 2019-06-26 | 2021-04-20 | 国网山西省电力公司电力科学研究院 | Harmonic source positioning method based on orthogonal matching pursuit algorithm |
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