CN108462181B - Sparse-considered robust estimation method for jacobian matrix of power flow of intelligent power distribution network - Google Patents

Abstract

A method for robust estimation of a power flow Jacobian matrix of an intelligent distribution network considering sparsity, comprising: 1) obtaining and numbering the number of nodes in a distribution network; 2) obtaining measurement data of a synchrophasor measuring device; 3) constructing Sensing matrix, let the row number m=1 of the power flow Jacobian matrix; 4) find the least squares solution as the estimated solution; 5) judge if the iteration termination condition is satisfied, then go to step 8); otherwise, go to step 6); 6) Solve the minimization related entropy model as the estimated solution; 7) If the iteration termination condition is satisfied, go to step 8); otherwise, update the index set of the column number of the sensing matrix, and return to step 6); 8) Judge whether to complete all rows of the Jacobian matrix If it is estimated, output the estimated result; otherwise, m=m+1, and return to step 4). While utilizing the sparsity of the power flow Jacobian matrix, the present invention effectively avoids the bad influence of the bad data in the measurement on the estimation result, and can still ensure the accuracy of the estimation under the condition that the measurement contains bad data.

Description

Robust estimation method of power flow Jacobian matrix in smart distribution network considering sparsity

technical field

The invention relates to a power flow Jacobian matrix estimation method for a distribution network. In particular, it relates to a robust estimation method of power flow Jacobian matrix in smart distribution network considering sparsity.

Background technique

Large-scale renewable energy is connected to the distribution network, and the randomness and volatility of its output put forward higher requirements for the operation monitoring and control of the distribution network. In order to improve the level of new energy consumption in the distribution network, the traditional distribution network is gradually developed into an intelligent distribution network. The power flow Jacobian matrix is an important parameter for analyzing the operation state of the distribution network and optimizing the control of the distribution network. Accurately obtaining the power flow Jacobian matrix is an important premise and basis for the analysis of the operation situation and the decision-making control of the distribution network. However, the current method of obtaining the power flow Jacobian matrix through offline power flow calculation is affected by the problems such as the difficulty of accurately obtaining the line parameters of the distribution network, the untimely update of the topology connection relationship, and the difficulty in tracking the operation points of the power grid. Its accuracy and reliability are extremely affected. big constraints.

The development and application of synchrophasor measurement technology not only improves the observability of the power system, but also provides a new support and means for the operation control of the distribution network. Especially with the development and technological innovation of miniature synchrophasor measuring devices, facing the demand for measurement data of distribution network, while ensuring the measurement accuracy, the miniaturization and low cost of synchrophasor measuring devices have been gradually realized. The cost makes it possible to apply it in a wide range of power distribution systems.

Using the real-time measurement data of the synchrophasor measurement device and the historical measurement data of multiple time sections, the online estimation of the power flow Jacobian matrix can be realized by the least squares estimation method, and the operation status of the distribution network can be tracked in real time, which greatly reduces the The dependence of power flow Jacobian matrix calculation on line parameters, topological connection relationship and other information effectively ensures the accuracy of parameter estimation calculation. In particular, using the sparsity of the power flow Jacobian matrix can effectively reduce the dependence of the estimation problem on the measurement, and at the same time improve the accuracy of the Jacobian matrix estimation.

Using compressed sensing technology, the original Jacobian matrix estimation problem is transformed into a sparse restoration problem, and the sparseness of the Jacobian matrix can be used to achieve high-precision estimation of the Jacobian matrix with fewer measurements. For the sparse recovery problem, the greedy algorithm is an effective means to solve it. The existing sparse recovery algorithm and core idea are to solve the least squares solution iteratively until a solution that satisfies the set estimation accuracy is found, which is regarded as the optimal solution of the estimation. However, the least squares estimation is highly sensitive to bad data. If the measured data contains bad data, the estimation result will be seriously deviated from the true value. Although high-precision measurement data can be obtained through the synchrophasor measurement device, due to the influence of data acquisition, conversion and communication, the measurement data may still contain bad data, resulting in unusable estimation results. A more robust sparse recovery algorithm estimates the power flow Jacobian.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide a method for robust estimation of the Jacobian matrix of the power flow of the smart distribution network considering the sparsity of the Jacobian matrix of the power flow of the smart distribution network with less measurement.

The technical scheme adopted in the present invention is: a method for robust estimation of power flow Jacobian matrix of smart distribution network considering sparsity, comprising the following steps:

1) Obtain the number of nodes in the distribution network, set the number of the source node to 0, and set the number of other nodes to 1,...,i,...,N in turn, input the conservative estimate d _max of the maximum degree of the network, and set the residual threshold ε and the maximum number of iterations M, the number of historical measurement data demand groups C;

2) Obtain the measurement data of active power, reactive power, voltage amplitude and voltage phase angle at the current moment collected by the synchrophasor measurement device installed at each node of the system, as well as the measurement data at C historical moments of each node;

3) Differentiate the measurement data of each node at C historical moments with the current measurement value, and each node obtains C changes of active power, reactive power, voltage amplitude and voltage phase angle, using node 1 ～Construct the sensing matrix with the variation of node N voltage and amplitude, and initialize the row number m=1 of the power flow Jacobian matrix;

4) Initialize the residual vector, calculate the correlation coefficient vector u _θ of the voltage phase angle and the correlation coefficient vector u _U of the voltage amplitude, initialize the number of iterations n=1, and initialize the sensing matrix column number index set Λ _n to be an empty set;

5) Respectively select the largest z values in the correlation coefficient vector u _θ of the voltage phase angle and the correlation coefficient vector u _U of the voltage amplitude, where z = d _max +1, and set the columns in the sensing matrix corresponding to the z values. The number index constitutes the intermediate set Ω _n of the nth iteration;

6) Using the intermediate set Ω _n of the nth iteration to update the sensor matrix column number index set Λ _n , obtain the least squares as the estimated solution, and update the residual vector;

7) If the 2-norm R of the updated residual vector is less than the residual threshold ε, go to step 11); otherwise: if the number of iterations is n=1, the number of iterations is set to n=n+1, and the voltage phase angles are selected respectively. The largest 2z values in the correlation coefficient vector u _θ of the voltage amplitude and the correlation coefficient vector u _U of the voltage amplitude, the indices in the sensing matrix corresponding to the 2z values constitute the intermediate set Ω _n of the nth iteration, and return to step 6) ; If the number of iterations n=2, then the number of iterations n=n+1, enter step 8);

8) Use the sensing matrix and the residual vector to calculate the residual correlation coefficient vector u, select the largest 2z column in the residual correlation coefficient vector u, and form the index in the sensing matrix corresponding to the 2z column to form the intermediate set of the nth iteration Ω _n , update the sensor matrix column number index set Λ _n ;

9) Using the updated sensing matrix column number index set Λ _n , establish an optimization model of minimizing the correlation entropy, solve the minimum correlation entropy model as the estimated solution, select the 4z item with the largest absolute value in the estimated solution, and set the sensor corresponding to the 4z item. The index in the matrix updates the intermediate set Ω _n of the nth iteration, reconstructs the sensor matrix column number index set Λ _n , and updates the residual vector again;

10) if the 2-norm R of the residual vector updated again is less than the residual threshold ε or the number of iterations exceeds the maximum number of iterations M set, then enter step 11); otherwise n=n+1, return to step 8);

11) Output the estimated solution, and recover the 2N-dimensional vector according to the index set of the column number of the sensing matrix as the estimation result of the mth row of the Jacobian matrix, m=m+1; if m is greater than 2N, stop the iteration and output the Jacobian matrix estimation result , otherwise, go back to step 4).

The establishment of the minimization related entropy optimization model described in step 9) includes establishing the objective function as:

r₀为初始的残差向量，

表示传感 矩阵列号索引集合Λ_n中元素对应的传感矩阵各列构成的矩阵，x表示代求的决策变量，ε为设 定的残差阈值，σ为辅助常量，exp表示指数函数，C为历史量测数据需求组数。In the formula, e _k represents the kth element of the vector e,

r ₀ is the initial residual vector,

Represents the matrix formed by the columns of the sensor matrix corresponding to the elements in the sensor matrix column index set Λ _n , x represents the decision variable to be obtained, ε is the set residual threshold, σ is the auxiliary constant, exp represents the exponential function, C is the number of historical measurement data demand groups.

The solution described in step 9) minimizes the relevant entropy model, including:

(1) Initialize the optimization allowable error δ, initialize the initial solution x ₀ as a zero vector, and initialize the weight vector w=1, where 1 represents a constant vector with a value of 1;

(2) Find the weighted least squares solution for the decision variable x to be obtained:

表示传感矩阵列号索引集合Λ_n中元素对应的传感矩阵各列构成的矩阵，r₀为 初始的残差向量，diag(*)表示由向量“*”中的元素构成对角矩阵；In the formula,

Represents the matrix formed by each column of the sensor matrix corresponding to the elements in the sensor matrix column number index set Λ _n , r ₀ is the initial residual vector, and diag(*) represents the diagonal matrix formed by the elements in the vector "*";

(3) Calculate the residual vector:

C为历史量测数据需求组数；(4) Calculate the value of the auxiliary constant σ according to the residual vector r,

C is the number of historical measurement data demand groups;

w_k和r_k分别表示 向量w和r的第k个元素；(5) Use the auxiliary constant σ to calculate the kth element of the weight vector w:

w _k and r _k represent the kth element of the vectors w and r, respectively;

如果条件成立，则估计解

输出估计结果，如果条件不成立，令x₀＝x，返回第(2)步。(6) Judgment

If the condition holds, estimate the solution

Output the estimation result, if the condition is not satisfied, set x ₀ =x, and return to step (2).

The reconstructed sensing matrix column number index set described in step 9) is:

Λ _n = Ω _n

In the formula, Λ _n is the index set of the sensor matrix column number of the n-th iteration, and Ω _n is the updated intermediate set of the n-th iteration.

The re-updating residual vector described in step 9) is expressed as:

表示集合Λ_n中元素对应的传感矩阵各列构成的矩阵，r_n为第n次迭代的残差 向量，r₀为初始的残差向量，diag(*)表示由向量“*”中的元素构成对角矩阵，w表示权重向量。In the formula,

Represents the matrix formed by the columns of the sensing matrix corresponding to the elements in the set Λ _n , rn is the residual vector of the _nth iteration, r ₀ is the initial residual vector, diag(*) represents the The elements form a diagonal matrix, and w represents the weight vector.

The robust estimation method of the power flow Jacobian matrix of the smart distribution network considering the sparsity of the present invention utilizes the multi-time scale measurement data measured by the synchrophasor, and considers the sparseness of the power flow Jacobian matrix at the same time. The measurement data may contain bad data. An optimization algorithm by minimizing the correlation entropy is proposed to improve the robustness of the sparse recovery algorithm to bad data, and realize the robust estimation of the power flow Jacobian matrix in the context of smart distribution network. While considering the sparsity of the Jacobian matrix, the algorithm of the present invention can effectively avoid the bad influence of the bad data in the measurement on the estimation result, and can still ensure the accuracy of the estimation even when the measurement contains bad data.

Description of drawings

Fig. 1 is the flow chart of the present invention considering the sparseness of the intelligent distribution network power flow Jacobian matrix robust estimation method;

Figure 2 is an example diagram of an IEEE33 node.

Detailed ways

The following describes in detail the method for robust estimation of power flow Jacobian matrix of smart distribution network considering sparsity of the present invention with reference to the embodiments and accompanying drawings.

As shown in Figure 1, the method for robust estimation of the power flow Jacobian matrix of a smart distribution network considering sparsity of the present invention includes the following steps:

1) Obtain the number of nodes in the distribution network, set the number of the source node to 0, and set the number of other nodes to 1,...,i,...,N in turn, input the conservative estimate d _max of the maximum degree of the network, and set the residual threshold ε and the maximum number of iterations M, the number of historical measurement data demand groups C;

2) Obtain the measurement data of active power, reactive power, voltage amplitude and voltage phase angle at the current moment collected by the synchrophasor measurement device installed at each node of the system, as well as measurement data at C historical moments of each node; in,

The C historical measurement data generation methods are as follows:

(1) Generate the kth active power measurement of node i in the following manner.

是服从均值为0正态分布的随机数，分别用来模拟不同量测时刻相对于当前时刻 的功率变化和量测误差；In the formula, P _i (k) represents the k-th active power historical measurement of node i, P _i (0) represents the current active power measurement of node i,

is a random number that obeys a normal distribution with a mean of 0, and is used to simulate the power change and measurement error at different measurement moments relative to the current moment;

(2) Use the following formula to generate the kth reactive power measurement of node i

是服从均值为0正态分布的随机数；In the formula, Q _i (k) represents the kth reactive power measurement of node i, and Q _i (0) represents the current reactive power measurement of node i,

is a random number that obeys a normal distribution with mean 0;

(3) After obtaining the k-th active power and reactive power measurement of node i, the corresponding voltage phase angle θ _i (k) and amplitude V _i (k) are obtained through power flow calculation as the k-th measurement of node i A voltage phase angle and amplitude measurement value.

3) Differentiate the measurement data of each node at C historical moments with the current measurement value, and each node obtains C changes of active power, reactive power, voltage amplitude and voltage phase angle, using node 1 ～Construct the sensing matrix with the measured variation of voltage phase angle and voltage amplitude at node N, and initialize the row number m=1 of the power flow Jacobian matrix; among them,

(1) The variation of the C active power, reactive power, voltage amplitude and voltage phase angle is expressed as:

ΔP _i [k]=P _i (k)-P _i (0), ΔQ _i [k]=Q _i (k)-Q _i (0), ΔV _i [k]=V _i (k)-V _i (0) and Δθ _i [k] = θ _i (k)-θ _i (0), k=1,2,...,C, P _i (0), Q _i (0), θ _i (0), V _i (0) represent the measured values of active power, reactive power, voltage phase angle and voltage amplitude of node i at the current moment; P _i (k), Q _i (k), θ _i (k), V _i (k) respectively represent the historical measurement value of the kth node i;

(2) The construction of the sensing matrix A is as follows:

表示由电压相角和电压幅值量测变化向量构成的矩阵，Δθ_i＝[Δθ_i[1],…,Δθ_i[C]]^T表示节点i的C个电压相角量测变化量组成的列向量，ΔV_i＝[ΔV_i[1],…,ΔV_i[C]]^T表示节点i 的C个电压幅值量测变化量组成的列向量；

表示

中的元素，A_p,q表示传感矩阵A中第p 行第q列的元素。In the formula,

Represents a matrix composed of voltage phase angle and voltage amplitude measurement variation vector, Δθ _i = [Δθ _i [1],...,Δθ _i [C]] ^T represents the C voltage phase angle measurement variation of node i composed of , ΔV _i =[ΔV _i [1],...,ΔV _i [C]] ^T represents a column vector composed of C voltage amplitude measurement changes at node i;

express

The elements in A _p,q represent the elements in the p-th row and the q-th column of the sensing matrix A.

4) Initialize the residual vector, calculate the correlation coefficient vector u _θ of the voltage phase angle and the correlation coefficient vector u _U of the voltage amplitude; Initialize the sensing matrix column number index set Λ _n to be an empty set, and the initialization iteration number n=1; wherein ,

4) Initialize the residual vector, calculate the correlation coefficient vector u _θ of the voltage phase angle and the correlation coefficient vector u _U of the voltage amplitude; Initialize the iteration number n=1, and initialize the sensing matrix column number index set Λ _n is an empty set; wherein

(1) The initialization residual vector calculation method is:

If 1≤m≤N:

r ₀ =ΔP _i

If N<m≤2N:

r ₀ =ΔQ _i

In the formula, r ₀ represents the initial residual vector, ΔP _i = [ΔP _i [1],...,ΔP _i [C]] ^T represents the column vector composed of the active power changes of the C group of node i; in the formula, ΔQ _i =[ΔQ _i [1],...,ΔQ _i [C]] ^T represents a column vector composed of reactive power changes of group C of node i.

(2) The calculation method of the correlation coefficient vector u _θ of the voltage phase angle is:

If 1≤m≤N:

u _θ = abs(A ^T A _q )

If N<m≤2N:

u _θ = abs(A ^T A _qN )

In the formula, abs( ) represents the operation of taking the absolute value, A is the sensing matrix, A _q and A _qN represent the qth column and the qNth column of the sensing matrix A, respectively;

(3) The calculation method of the correlation coefficient vector u _U of the voltage amplitude is:

If 1≤m≤N:

u _U =abs(A ^T A _q+N )

If N<m≤2N:

u _U =abs(A ^T A _q ).

5) Respectively select the largest z values in the correlation coefficient vector u _θ of the voltage phase angle and the correlation coefficient vector u _U of the voltage amplitude, where z = d _max +1, and set the columns in the sensing matrix corresponding to the z values. The number index constitutes the intermediate set Ω _n of the nth iteration;

6) Use the intermediate set Ω _n of the nth iteration to update the sensor matrix column number index set Λ _n , find the least squares solution, and update the residual vector; where,

(1) The described update sensing matrix column number index set is expressed as:

Λ _n =Λ _n-1 ∪Ω _n

In the formula, Λ _n is the index set of the sensor matrix column number of the nth iteration, when n=1, Λ _n-1 represents the initial set of column number index of the sensor matrix, Ω _n represents the intermediate set of the nth iteration ;

(2) The least squares solution is expressed as:

表示第n次迭代时的最小二乘解，r₀为初始的残差向量，

表示第n次迭代 的传感矩阵列号索引集合Λ_n中元素对应的传感矩阵各列构成的矩阵；In the formula,

represents the least squares solution at the nth iteration, r ₀ is the initial residual vector,

represents the matrix formed by each column of the sensing matrix corresponding to the elements in the n-th iteration of the sensing matrix column number index set Λ _n ;

(3) The updated residual vector is expressed as:

In the formula, rn is the residual vector of the _nth iteration.

7) If the 2-norm R of the updated residual vector is less than the residual threshold ε, go to step 11); otherwise: if the number of iterations is n=1, the number of iterations is set to n=n+1, and the voltage phase angles are selected respectively. The largest 2z values in the correlation coefficient vector u _θ of the voltage amplitude and the correlation coefficient vector u _U of the voltage amplitude, the indices in the sensing matrix corresponding to the 2z values constitute the intermediate set Ω _n of the nth iteration, and return to step 6) ; If the number of iterations n=2, then the number of iterations n=n+1, enter step 8);

8) Use the sensing matrix and the residual vector to calculate the residual correlation coefficient vector u, select the largest 2z column in the residual correlation coefficient vector u, and form the index in the sensing matrix corresponding to the 2z column to form the intermediate set of the nth iteration Ω _n , update the sensing matrix column number index set Λ _n ; the calculation method of the residual correlation coefficient vector u is:

u=abs(A ^T r _n-1 )

In the formula, u is the correlation coefficient vector, abs( ) represents the absolute value operation, r _n-1 represents the residual vector at the n-1th iteration, when n=1, r _n-1 represents the initial residual error vector, A is the sensing matrix.

9) Using the updated sensing matrix column number index set Λ _n , establish an optimization model of minimizing the correlation entropy, solve the minimum correlation entropy model as the estimated solution, select the 4z item with the largest absolute value in the estimated solution, and set the sensor corresponding to the 4z item. The index in the matrix updates the intermediate set Ω _n of the nth iteration, reconstructs the sensor matrix column number index set Λ _n , and updates the residual vector again; where

(1) The described establishment minimizes the relevant entropy optimization model, including establishing the objective function as:

表示传感矩阵列号索引集合Λ_n中元素对应的传感矩阵各列构成的矩阵，x表示代求的决策变量，ε为设 定的残差阈值，σ为辅助常量，exp表示指数函数，C为历史量测数据需求组数。In the formula, _ek represents the kth element of vector e, e=r ₀ -A _Λn x, r ₀ is the initial residual vector,

Represents the matrix formed by the columns of the sensor matrix corresponding to the elements in the sensor matrix column index set Λ _n , x represents the decision variable to be obtained, ε is the set residual threshold, σ is the auxiliary constant, exp represents the exponential function, C is the number of historical measurement data demand groups.

(2) the described solution minimizes the relevant entropy model, including:

(2.1) Initialize the optimization allowable error δ, initialize the initial solution x ₀ as a zero vector, and initialize the weight vector w=1, where 1 represents a constant vector whose value is 1;

(2.2) Find the weighted least squares solution for the decision variable x to be obtained:

表示传感矩阵列号索引集合Λ_n中元素对应的传感矩阵各列构成的矩阵，r₀为 初始的残差向量，diag(*)表示由向量“*”中的元素构成对角矩阵；In the formula,

Represents the matrix formed by each column of the sensor matrix corresponding to the elements in the sensor matrix column number index set Λ _n , r ₀ is the initial residual vector, and diag(*) represents the diagonal matrix formed by the elements in the vector "*";

(2.3) Calculate residual vector:

C为历史量测数据需求组数；(2.4) Calculate the value of the auxiliary constant σ according to the residual vector r,

C is the number of historical measurement data demand groups;

w_k和r_k分别表 示向量w和r的第k个元素；(2.5) Use the auxiliary constant σ to calculate the kth element of the weight vector w:

w _k and r _k represent the kth element of the vectors w and r, respectively;

如果条件成立，则估计解

输出估计结果，如果条件 不成立，令x₀＝x，返回第(2.2)步。(2.6) Judgment

If the condition holds, estimate the solution

Output the estimation result, if the condition does not hold, set x ₀ =x, and return to step (2.2).

(3) The described reconstructed sensing matrix column number index set is:

Λ _n = Ω _n

In the formula, Λ _n is the index set of the sensor matrix column numbers of the nth iteration, and Ω _n represents the intermediate set of the nth iteration.

(4) The re-updated residual vector is expressed as:

表示集合Λ_n中元素对应的传感矩阵各列构成的矩阵，r_n为第n次迭代的残差 向量，r₀为初始的残差向量，diag(*)表示由向量“*”中的元素构成对角矩阵，w表示权重向量。In the formula,

Represents the matrix formed by the columns of the sensing matrix corresponding to the elements in the set Λ _n , rn is the residual vector of the _nth iteration, r ₀ is the initial residual vector, diag(*) represents the The elements form a diagonal matrix, and w represents the weight vector.

10) if the 2-norm R of the residual vector updated again is less than the residual threshold ε or the number of iterations exceeds the maximum number of iterations M set, then enter step 11); otherwise n=n+1, return to step 8);

11) Output the estimated solution, and recover the 2N-dimensional vector according to the index set of the column number of the sensing matrix as the estimation result of the mth row of the Jacobian matrix, m=m+1; if m is greater than 2N, stop the iteration and output the Jacobian matrix estimation result , otherwise, go back to step 4). The described estimation result of recovering 2N-dimensional vector as the mth row of Jacobian matrix according to the index set of sensing matrix column number is expressed as:

表示第n次迭代时的估计解，

表示2N维恢复向量，

表示

的第g个元素，

表 示传感矩阵列号索引集合Λ_n中各元素所对应的向量

的元素组成的向量，对于

其他不在列号 索引集合中的元素取值为0；

矩阵

第q列的2范数，

表示雅可比矩阵Y的第m行第q个元素的估计解，其中，g＝q。In the formula,

represents the estimated solution at the nth iteration,

represents a 2N-dimensional recovery vector,

express

the gth element of ,

Represents the vector corresponding to each element in the sensor matrix column number index set Λ _n

A vector of elements of , for

Other elements not in the column index set have the value 0;

matrix

The 2-norm of the qth column,

represents the estimated solution for the qth element of the mth row of the Jacobian matrix Y, where g=q.

Specific examples are given below:

First enter the IEEE33 node calculation example network topology connection relationship as shown in Figure 2, where node 0 is a balanced node, other nodes 1 to 32 are PQ nodes, the reference capacity of the system is 1MVA, and the reference voltage is 12.66kV. The power measurement is shown in Table 1. The conservative estimate of the maximum degree of the input network is 4, the standard deviation of the analog measurement power change and the error random number are set to 0.01 and 0.025%, respectively, and the number of measurement groups is set to 30, 35, 40, 45, 50, 55, respectively. , 60. Calculate the errors of the Jacobian matrix and the voltage power sensitivity matrix using the following equations.

分别表示雅可比矩阵元素的估计值，J_i,j为雅可比矩阵元素的理论值。In the formula,

represent the estimated values of the Jacobian matrix elements, respectively, and J _i,j are the theoretical values of the Jacobian matrix elements.

The following formula is used to calculate the estimation error of the ith row of the Jacobian matrix. When the estimation error is less than 10, the estimation of the row is considered to be successful.

In order to verify the advanced nature of the method of the present invention, the following two scenarios are adopted for analysis:

Scenario 1, there is no bad data, respectively adopt least squares solution to solve and solve the minimum correlation entropy model of the present invention in step 9) of the present invention, the obtained Jacobian matrix estimates the number of successful rows and the estimated error as shown in the table respectively. 2 and Table 3.

Scenario 2, add bad data to the 10th group of active power measurement of node 24 and the 20th group of active power measurement of node 29 respectively. The square solution and the minimum correlation entropy model of the present invention are used to solve, and the number of rows and the estimated error of the obtained Jacobian matrix are shown in Table 6 and Table 7, respectively.

The computer hardware environment for the optimization calculation is Intel(R) Xeon(R) CPU E5-1620, the main frequency is 3.70GHz, and the memory is 32GB; the software environment is Windows 7 operating system, and MATLAB's MATPOWER toolkit is used to calculate the trend.

As can be seen from Table 2 and Table 3, when there is no bad data, the method of minimizing the correlation entropy of the present invention has the same estimation success rate and estimation accuracy as the least squares method, so that the method of the present invention can realize the quantitative When the measurement data has no bad data, the estimation accuracy is not sacrificed; it can be seen from Tables 6 and 7 that when the measurement contains bad data, the least squares method cannot be used to estimate any row of the Jacobian matrix, and this The inventive method can realize the estimation of all rows of the power flow Jacobian matrix when the number of measurement groups reaches 35. Although the estimation accuracy is increased compared with that without bad data, it remains at the same level. Therefore, the method of the present invention can realize the robustness to bad data while utilizing the sparseness of the Jacobian matrix, and finally realize the robust estimation of the power flow Jacobian matrix.

Table 1 Current power measurement value of PQ node in IEEE 33 node calculation example

Table 2 Scenario 1 Jacobian Matrix Estimation Unsuccessful Rows

Table 3 Scenario 1 Jacobian Matrix Estimation Error

Table 4 Bad data situation of node 24

Table 5 Bad data situation of node 29

Table 6 Scenario 2 Jacobian Matrix Estimation Unsuccessful 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, and sequentially setting the numbers of other nodes as 1, a_maxSetting residual error threshold epsilon and maximumIteration times M and historical measurement data requirement 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 phase angles and the amplitude values 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 angle_θVector u of correlation coefficients with voltage amplitude_UInitializing the column index set Lambda of the sensing matrix when the number of initialization iterations n is 1_nIs an empty set;

5) respectively selecting the related coefficient vector u of the voltage phase angle_θVector u of correlation coefficients with voltage amplitude_UOf the maximum z values, where z is d_max+1, the column number indexes in the sensing matrix corresponding to 2z values form the middle set omega of the nth iteration_n；

6) Intermediate set omega using nth iteration_nUpdating sensing matrix column number index set Lambda_nSolving 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 selected_θVector u of correlation coefficients with voltage amplitude_UThe maximum 2z values in the n-th iteration, and the indexes in the sensing matrix corresponding to the 4z values form an intermediate set omega of the n-th iteration_nReturning 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 a sensing matrix and the residual error vector, selecting the largest 2z column in the residual error correlation coefficient vector u, and performing sensing corresponding to the 2z columnThe indices in the matrix form the intermediate set omega for the nth iteration_nUpdating the column index set Lambda of the sensing matrix_n；

9) Indexing set Lambda by updating column number of sensing matrix_nEstablishing 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 iteration_nReconstructing the column index set Lambda of the sensing matrix_nUpdating 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, e_kThe 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 matrix_nThe matrix formed by the columns of the sensing matrix corresponding to the middle element, x represents the decision variable of the generation,epsilon is a set residual error threshold value, sigma is an auxiliary constant, exp represents an exponential function, and C is a historical measurement data demand set 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 matrix_nMatrix 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:

w_kand r_kThe kth elements of vectors w and r, respectively;

(6) judgment of

If the condition is true, a solution is estimated

Outputting 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:

Λ_n＝Ω_n

in the formula, Λ_nSet of sense matrix column index for nth iteration, Ω_nRepresenting 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 Λ_nMatrix formed by columns of sensing matrix corresponding to medium elements, r_nIs 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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