Power distribution network complex number field prediction auxiliary state estimation method based on FPGA large-scale parallel computing

Abstract

The invention discloses a power distribution network complex number domain prediction auxiliary state estimation method based on FPGA large-scale parallel computing. The method comprises the steps that a topological structure, line parameters and real-time measurement data of a power distribution network are acquired; constructing a state prediction model and a complex field equivalent measurement model according to the obtained topological structure, line parameters and real-time measurement data of the power distribution network; constructing a complex field prediction auxiliary state estimation model according to the state prediction model and the complex field equivalent measurement model; and establishing a large-scale parallel computing framework based on the FPGA, and splitting the complex field prediction auxiliary state estimation model into a plurality of computing modules to obtain a state estimation result of the power distribution network. According to the method, the estimation precision and the calculation efficiency of state estimation of the power distribution network are improved, large-scale parallel calculation can be carried out by utilizing the FPGA, the real-time performance of state estimation is further improved, and the estimation performance is more stable.

Description

Technical Field

[0001] The invention relates to a distribution network complex domain prediction auxiliary state estimation method based on FPGA large-scale parallel computing, belonging to the technical field of power system operation and dispatching. Background Art

[0002] State estimation is the data foundation for other advanced applications in the power system and plays a vital role in ensuring the safe, stable, efficient and low-carbon operation of the distribution network. In recent years, the continuous access of distributed generation and flexible loads has increased the randomness and volatility of the distribution network operation, making the demand for accurate and real-time monitoring of each node in the system more urgent than ever before. However, the distribution network has always had problems with low measurement redundancy and poor measurement data quality, and has higher requirements on the estimation performance of the state estimator than the transmission network. In order to better track the state fluctuations of the distribution network, it is necessary to use a prediction-assisted state estimation method instead of the traditional static estimation method to ensure the accuracy of tracking. However, most prediction-assisted state estimation methods are inefficient and cannot meet the needs of real-time tracking of the distribution network state, which increases the demand for high-real-time prediction-assisted state estimation methods.

[0003] At present, the most widely used state estimation algorithm is the static state estimation algorithm, such as the Weighted Least Square (WLS) algorithm. However, the static state estimation algorithm can only use the information of a single time section, and its estimation accuracy is seriously dependent on the redundancy of the measurement, which is not suitable for distribution network scenarios. In order to make up for the problem of insufficient estimation accuracy of the static state estimation algorithm, the prediction-assisted state estimation algorithm uses the information of multiple time sections through the prediction step, which significantly improves the state tracking capability. The most common prediction-assisted state estimation algorithm is the Extended Kalman Filter (EKF) algorithm, which minimizes the computational efficiency of the prediction-assisted state estimator by linearizing the measurement equation. However, since the EKF algorithm uses the first-order Taylor approximation, it often shows low accuracy when facing highly nonlinear systems, and even has the problem of non-convergence of calculation. Iterated Extended Kalman Filter (IEKF) reduces linearization error by continuously linearizing nonlinear equations and achieves a near-optimal solution. However, since IEKF needs to repeatedly solve the Jacobian matrix and Kalman gain matrix in the process of successive linearization, the computational efficiency is greatly reduced compared to EKF. Another way to solve the linearization error is to use a sampling point-based method. Ensemble Kalman Filter (EnKF) and Particle Filter (PF) algorithms approximate the posterior error of random variables through random sampling. However, these methods require a large number of sampling points to achieve high accuracy, resulting in a significant increase in the amount of calculation and a significant decrease in computational efficiency. Unscented Kalman Filter (UKF) and Cubature Kalman Filter (CKF) algorithms use a small number of specific regular sampling points to approximate the probability distribution of the mean and variance, which can significantly reduce the amount of calculation compared to EnKF and PF. However, UKF and CKF have serious numerical stability problems, and the calculation often fails to converge. In addition, due to the reduction of sampling points, the estimation accuracy of UKF and CKF will also decrease accordingly. In general, the current distribution network prediction auxiliary state estimation method is difficult to balance the estimation accuracy and computational efficiency, and cannot be truly applied to the actual distribution network. Therefore, it is of great significance to study a distribution network prediction auxiliary state estimation method with high estimation accuracy and high real-time performance. Summary of the invention

[0004] The purpose of the invention is to solve the problem that the current distribution network prediction auxiliary state estimator is difficult to meet the estimation accuracy and computational efficiency at the same time. The present invention provides a distribution network complex domain prediction auxiliary state estimation method based on FPGA large-scale parallel computing. By constructing the complex domain equivalent measurement of SCADA and AMI, the linearization solution of the real domain distribution network nonlinear state estimation problem in the complex domain is realized, and the high-precision and high-efficiency perception of the distribution network state is realized. At the same time, a large-scale parallel computing framework based on FPGA is established to further improve the real-time performance of the algorithm.

[0005] Technical solution, in order to achieve the above-mentioned invention object, the present invention proposes a distribution network complex domain prediction auxiliary state estimation method based on FPGA large-scale parallel computing, the method comprising the following steps:

[0006] Step 1, obtaining the topological structure, line parameters and real-time measurement data of the distribution network, wherein the measurement data includes SCADA measurement data and AMI measurement data;

[0007] Step 2: construct a state prediction model and a complex domain equivalent measurement model based on the obtained distribution network topology, line parameters and real-time measurement data;

[0008] Step 3, constructing a complex domain prediction-assisted state estimation model based on the state prediction model and the complex domain equivalent measurement model;

[0009] Step 4: Establish a large-scale parallel computing framework based on FPGA, split the complex domain prediction-assisted state estimation model into multiple computing modules to calculate and obtain the distribution network state estimation results.

[0010] Furthermore, in step 1, the obtained distribution network topology structure includes the line number, the head node number and the terminal node number; the obtained distribution network line parameters include the line series impedance, the line parallel admittance, the transformer ratio and the transformer equivalent impedance; and the obtained distribution network real-time measurement data, including the SCADA and AMI measurement data, include the node voltage amplitude, the node injected active power, the node injected reactive power, the branch active power and the branch reactive power.

[0011] Furthermore, in step 2, a state prediction model and a complex domain equivalent measurement model are constructed, and the specific method is as follows:

[0012] In the complex domain, the state prediction model of the distribution network and the complex domain measurement model are constructed as follows:

[0013] x k =f(x k-1 )+ω k

[0014]

[0015] Among them, x k and They represent the state vector and measurement vector at time k, respectively, and x k-1 represents the state vector at time k-1; ω k and ε k They represent the system process noise and measurement noise at time k, and the covariance matrices are Q k and R k ; f(·) and h(·) represent the state prediction equation and the equivalent measurement equation in the complex domain, respectively;

[0016] The Holt method is used to model the state prediction equation as follows:

[0017] x k|k-1 =a k +b k

[0018] a k =α k x k-1 +(1-α k )x k-1|k-2

[0019] b k =β k (a k -a k-1 )+(1-β k )b k-1

[0020] Among them, x k|k-1 and x k-1|k-2 are the predicted values ​​of the state vector at time k and time k-1, α k and β k are two smoothing parameters used to adjust the adaptability of the prediction equation to new trends in the data. Their value range is (0,1). k , b k Represents the two intermediate structural parameters at time k, a k-1 , b k-1 Representing the two intermediate structural parameters at time k-1, the matrix expression of the state prediction equation f(·) is as follows:

[0021] f(x k-1 )=F k x k-1 +u k

[0022] Among them, the state transfer matrix F k and the state transition vector u k It is obtained by the following formula:

[0023] F k =α k (1+β k )I

[0024] u k =(1+β k )(1-α k )x k-1 -β k a k-1 +(1-β k )b k-1

[0025] Where I represents the identity matrix;

[0026] Construct a complex domain equivalent measurement model for SCADA and AMI node voltage amplitude measurement, node injected active power measurement, node injected reactive power measurement, branch active power measurement and branch reactive power measurement. k As follows: Depending on the measurement type, z k Equivalent voltage phasor measurement Equivalent injection current measurement Equivalent branch current measurement There are 3 categories in total, and the equivalent measurement models in the complex domain are constructed as follows:

[0027]

[0028] in, represents the voltage phasor of node f at time k; and They represent the voltage amplitude measurement of node f at time k, the node injection complex power measurement of node f, and the branch complex power measurement of branch ft, respectively, and t represents node t; and They respectively represent the node injected active power measurement of node f at time k, the node injected reactive power measurement of node f, the branch active power measurement of branch ft, and the branch reactive power measurement of branch ft.

[0029] Furthermore, in step 3, a complex domain prediction auxiliary state estimation model is constructed, and the specific method is as follows:

[0030] According to the state prediction model and the complex domain equivalent measurement model, the following complex domain augmented state space model is constructed:

[0031]

[0032] Among them, the augmented state vector at time k is Augmented state transfer matrix Augmented State Transfer Vector Augmented Equivalent Measurement Vector Superscript (·) T , (·) H and(·) * Represents matrix transposition, matrix conjugate transposition and conjugate operation respectively; the augmented state vector at time k-1 and They represent the augmented process noise and augmented measurement noise at time k respectively; is the augmented Jacobian matrix at time k, which is constructed as follows:

[0033]

[0034] in, and denote the constant Jacobian matrix and the conjugate Jacobian matrix respectively; The augmented process covariance matrix is The augmented measurement covariance matrix of

[0035] Define and To take the real part and the imaginary part, we define the complex domain measurement The real number combination measurement vector Its covariance matrix is ​​expressed as and The covariance matrices of and as follows:

[0036]

[0037] in, and They represent the measurement variances corresponding to the voltage amplitude measurement of node f at time k, the node injected active power measurement of node f, the node injected reactive power measurement of node f, the branch active power measurement of branch ft, and the branch reactive power measurement of branch ft, respectively;

[0038] and The matrix expression between is as follows:

[0039]

[0040] Among them, T is the measurement transformation matrix, and the augmented measurement covariance matrix is ​​constructed as follows:

[0041]

[0042] Among them, V k and M k are the real covariance matrix and the complex complementary covariance matrix respectively. In the application of distribution network state estimation, the conjugate Jacobian matrix J is ignored. k , reconstructing the augmented Jacobian matrix and augmented covariance matrix into and The complex domain state space model is established as follows:

[0043]

[0044] The complex domain state space model is further simplified, and the final complex domain state space model is obtained as follows:

[0045] x k =F k x k-1 +u k +ω k

[0046] z k (x k )=H k x k +ε k

[0047] According to the above complex domain state space model, the complex domain prediction auxiliary state estimation model is constructed as follows: Definition is the estimated value of the state vector at time k-1, and its corresponding covariance matrix is ​​P k-1 , the predicted state vector is calculated according to the following formula And its corresponding covariance matrix P k|k-1 :

[0048]

[0049] According to the above formula, P k|k-1 Afterwards, the Kalman gain matrix K is calculated k as follows:

[0050]

[0051] After the calculation is completed, the estimated value of the state vector at time k is iteratively calculated according to the following formula And calculate the corresponding covariance matrix P k as follows:

[0052]

[0053] P k =P k|k-1 -K k Hk P k|k-1

[0054] in, and denote the calculated values ​​of the state vector for the j-th and j-1-th iterations respectively, The initial value is when When it is less than the convergence threshold, update the estimated value of the state vector at time k

[0055] Using Huber function and projection statistics theory, the solution formula of Kalman gain matrix is ​​reconstructed into the following form:

[0056]

[0057] Among them, the diagonal matrix S k represents the covariance scaling matrix, whose i-th diagonal element S k {i,i} is calculated using the following covariance scaling model:

[0058]

[0059] in, and σ k are the measurement prediction value residual vector and the measurement standard deviation vector, respectively, k {i} and σ k {i} represents r k and σ k The i-th element of ; the segmentation parameter c is a positive number used to adjust the robustness of the state estimator and normalize the weight vector ω k The i-th element of is ω k {i}=min{1,(b k {i} / PS k {i}) 2}, where the truncation parameter b k {i} and projection statistical parameter PS k {i} is calculated using the following projection statistics formula:

[0060]

[0061] Among them, d k {i} indicates H k The number of non-zero elements in the i-th row; Denotes the degree of freedom as d k {i}, chi-square test with a confidence level of 97.5%; H{i} k , H{j} k , H{l} k Respectively represent H kThe i-th, j-th and l-th columns of ; lom represents the lower median operation.

[0062] Furthermore, in step 4, a large-scale parallel computing framework based on FPGA is established, and the specific method is as follows:

[0063] The complex domain prediction-assisted state estimation model is divided into 11 computing modules, among which A k , B k , C k , D k and E k There are 5 intermediate parameter matrices:

[0064] Module 1: Computing The module input is u k and F k , the module output is

[0065] Module 2: Computing The module input is F k , P k-1 and Q k , the module output is P k|k-1 ;

[0066] Module 3: First, based on the complex domain equivalent measurement model, Calculate z k ,use and H k Calculate the measurement prediction residual vector Using V k Calculate the measurement standard deviation vector Among them, diag(V k ) is V k The diagonal elements of H k Calculate b k {i} and PS k {i}, according to the formula ω k {i}=min{1,(b k {i} / PS k {i}) 2} Calculate the normalized weight vector ω k ; The most covariance-scaling model uses r k , σ k and ω k Calculate the covariance scaling matrix S k ; That is, the module input is H k and V k , the module output is S k ;

[0067] Module 4: Computing The module input is H k and The module output is D k ;

[0068] Module 5: Computing The module input is P k|k-1 and H k , the module output is A k ;

[0069] Module 6: Calculation B k =C k +S k V k , the module input is C k , S k and V k , the module output is B k ;

[0070] Module 7: Calculation of C k =H k A k , the module input is H k and A k , the module output is C k ;

[0071] Module 8: Calculating E k =H k P k|k-1 , the module input is H k and P k|k-1 , the module output is E k ;

[0072] Module 9: Computing The module input is A k and B k , the module output is K k ;

[0073] Module 10: Utilization of Equivalent Measurement Models Based on Complex Domains Calculate z k ,use K k and D k Iterative Calculation in, The initial value is After iterative convergence, the final state estimation result is obtained That is, the module input is K k and D k , the module output is

[0074] Module 11: Calculating P k =P k|k-1 -K k E k , the module input is P k|k-1 , K k and E k , the module output is P k ;

[0075] According to the 11 modules designed above, the following large-scale parallel processing strategy is designed based on the hardware programmable characteristics of FPGA. The calculation steps are as follows:

[0076] 1. Execute the calculations of module 1 and module 2 in parallel and obtain and P k|k-1 ;

[0077] 2. Execute the calculations of modules 3, 4 and 5 in parallel to obtain S k , D k and A k ;

[0078] 3. Execute the calculations of modules 6, 7 and 8 in parallel to obtain B k , C k and E k ;

[0079] 4. Execute the calculation of module 9 to obtain K k ;

[0080] 5. Execute the calculations of modules 10 and 11 in parallel to obtain the final state vector estimate And its corresponding covariance matrix P k .

[0081] Through the above FPGA-based massively parallel processing strategy, the prediction-assisted state estimator can be executed in massive parallel to provide high real-time distribution network state information.

[0082] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0083] The method of the present invention first constructs a state prediction model and a complex domain equivalent measurement model according to the obtained distribution network topology, line parameters and real-time measurement data; then, a complex domain prediction-assisted state estimation model is constructed according to the state prediction model and the complex domain equivalent measurement model; finally, a large-scale parallel computing framework based on FPGA is established to split the complex domain prediction-assisted state estimation model into multiple computing modules to obtain the distribution network state estimation result. The test results of the IEEE standard system show that since the distribution network prediction-assisted state estimator is subjected to a quasi-linear solution process in the complex domain, the estimation accuracy and computational efficiency of the method proposed in the present invention are higher than the existing state estimation algorithm, and the large-scale parallel computing framework based on FGPA further improves the real-time performance of the state estimator, so that the method proposed in the present invention can complete the state estimation calculation at a faster speed than the existing prediction-assisted state estimator, or even the static state estimator. Therefore, the method of the present invention improves the estimation accuracy and computational efficiency of the state estimator. The proposed large-scale parallel computing framework based on FPGA further improves the real-time performance of the state estimator, making the estimation performance more stable. BRIEF DESCRIPTION OF THE DRAWINGS

[0084] Figure 1 The present invention is a flow chart of the method for assisted state estimation of distribution network complex domain prediction based on FPGA large-scale parallel computing.

[0085] Figure 2 FIG. 4 is a schematic diagram showing a comparison of estimation errors of different algorithms in the present invention in the IEEE 123 system.

[0086] Figure 3 FIG. 4 is a schematic diagram showing a comparison of estimation results using CPU and FPGA in the IEEE 33 system in the present invention. DETAILED DESCRIPTION

[0087] The present invention is further explained below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the present invention by those skilled in the art all fall within the scope defined by the claims attached to this application.

[0088] like Figure 1 As shown, the present invention proposes a distribution network complex domain prediction auxiliary state estimation method based on FPGA large-scale parallel computing, the method comprising the following steps:

[0089] Step 1, obtaining the topological structure, line parameters and real-time measurement data of the distribution network, wherein the measurement data includes SCADA measurement data and AMI measurement data;

[0090] Step 2: construct a state prediction model and a complex domain equivalent measurement model based on the obtained distribution network topology, line parameters and real-time measurement data;

[0091] Step 3, constructing a complex domain prediction-assisted state estimation model based on the state prediction model and the complex domain equivalent measurement model;

[0092] Step 4: Establish a large-scale parallel computing framework based on FPGA, split the complex domain prediction-assisted state estimation model into multiple computing modules to calculate and obtain the distribution network state estimation results.

[0093] Furthermore, in step 1, the obtained distribution network topology structure includes the line number, the head node number and the terminal node number; the obtained distribution network line parameters include the line series impedance, the line parallel admittance, the transformer ratio and the transformer equivalent impedance; and the obtained distribution network real-time measurement data, including the SCADA and AMI measurement data, include the node voltage amplitude, the node injected active power, the node injected reactive power, the branch active power and the branch reactive power.

[0094] Furthermore, in step 2, a state prediction model and a complex domain equivalent measurement model are constructed, and the specific method is as follows:

[0095] In the complex domain, the state prediction model of the distribution network and the complex domain measurement model are constructed as follows:

[0096] x k =f(x k-1 )+ω k

[0097]

[0098] Among them, x k and They represent the state vector and measurement vector at time k, respectively, and x k-1 represents the state vector at time k-1; ω k and ε k They represent the system process noise and measurement noise at time k, and the covariance matrices are Q k and R k ; f(·) and h(·) represent the state prediction equation and the equivalent measurement equation in the complex domain, respectively;

[0099] The Holt method is used to model the state prediction equation as follows:

[0100] x k|k-1 =a k +b k

[0101] a k =α k xk-1 +(1-α k )x k-1|k-2

[0102] b k =β k (a k -a k-1 )+(1-β k )b k-1

[0103] Among them, x k|k-1 and x k-1|k-2 are the predicted values ​​of the state vector at time k and time k-1, α k and β k are two smoothing parameters used to adjust the adaptability of the prediction equation to new trends in the data. Their value range is (0,1). k , b k Represents the two intermediate structural parameters at time k, a k-1 , b k-1 Representing the two intermediate structural parameters at time k-1, the matrix expression of the state prediction equation f(·) is as follows:

[0104] f(x k-1 )=F k x k-1 +u k

[0105] Among them, the state transfer matrix F k and the state transition vector u k It is obtained by the following formula:

[0106] F k =α k (1+β k )I

[0107] u k =(1+β k )(1-α k )x k-1 -β k a k-1 +(1-β k )b k-1

[0108] Where I represents the identity matrix;

[0109] Construct a complex domain equivalent measurement model for SCADA and AMI node voltage amplitude measurement, node injected active power measurement, node injected reactive power measurement, branch active power measurement and branch reactive power measurement. k As follows: Depending on the measurement type, z kEquivalent voltage phasor measurement Equivalent injection current measurement Equivalent branch current measurement There are 3 categories in total, and the equivalent measurement models in the complex domain are constructed as follows:

[0110]

[0111] in, represents the voltage phasor of node f at time k; and They represent the voltage amplitude measurement of node f at time k, the node injection complex power measurement of node f, and the branch complex power measurement of branch ft, respectively, and t represents node t; and They respectively represent the node injected active power measurement of node f at time k, the node injected reactive power measurement of node f, the branch active power measurement of branch ft, and the branch reactive power measurement of branch ft.

[0112] Furthermore, in step 3, a complex domain prediction auxiliary state estimation model is constructed, and the specific method is as follows:

[0113] According to the state prediction model and the complex domain equivalent measurement model, the following complex domain augmented state space model is constructed:

[0114]

[0115] Among them, the augmented state vector at time k is Augmented state transfer matrix Augmented State Transfer Vector Augmented Equivalent Measurement Vector Superscript (·) T , (·) H and(·) * Represents matrix transposition, matrix conjugate transposition and conjugate operation respectively; the augmented state vector at time k-1 and They represent the augmented process noise and augmented measurement noise at time k respectively; is the augmented Jacobian matrix at time k, which is constructed as follows:

[0116]

[0117] in, and denote the constant Jacobian matrix and the conjugate Jacobian matrix respectively; The augmented process covariance matrix is The augmented measurement covariance matrix of

[0118] Define and To take the real part and the imaginary part, we define the complex domain measurement The real number combination measurement vector Its covariance matrix is ​​expressed as and The covariance matrices of and as follows:

[0119]

[0120] in, and They represent the measurement variances corresponding to the voltage amplitude measurement of node f at time k, the node injected active power measurement of node f, the node injected reactive power measurement of node f, the branch active power measurement of branch ft, and the branch reactive power measurement of branch ft, respectively;

[0121] and The matrix expression between is as follows:

[0122]

[0123] Among them, T is the measurement transformation matrix, and the augmented measurement covariance matrix is ​​constructed as follows:

[0124]

[0125] Among them, V k and M k are the real covariance matrix and the complex complementary covariance matrix respectively. In the application of distribution network state estimation, the conjugate Jacobian matrix J is ignored. k , reconstructing the augmented Jacobian matrix and augmented covariance matrix into and The complex domain state space model is established as follows:

[0126]

[0127] The complex domain state space model is further simplified, and the final complex domain state space model is obtained as follows:

[0128] x k =F k x k-1 +u k +ω k

[0129] zk (x k )=H k x k +ε k

[0130] According to the above complex domain state space model, the complex domain prediction auxiliary state estimation model is constructed as follows: Definition is the estimated value of the state vector at time k-1, and its corresponding covariance matrix is ​​P k-1 , the predicted state vector is calculated according to the following formula And its corresponding covariance matrix P k|k-1 :

[0131]

[0132] According to the above formula, P k|k-1 Afterwards, the Kalman gain matrix K is calculated k as follows:

[0133]

[0134] After the calculation is completed, the estimated value of the state vector at time k is iteratively calculated according to the following formula And calculate the corresponding covariance matrix P k as follows:

[0135]

[0136] P k =P k|k-1 -K k H k P k|k-1

[0137] in, and denote the calculated values ​​of the state vector for the j-th and j-1-th iterations respectively, The initial value is when When it is less than the convergence threshold, update the estimated value of the state vector at time k

[0138] Using Huber function and projection statistics theory, the solution formula of Kalman gain matrix is ​​reconstructed into the following form:

[0139]

[0140] Among them, the diagonal matrix S k represents the covariance scaling matrix, whose i-th diagonal element S k {i,i} is calculated using the following covariance scaling model:

[0141]

[0142] in, and σ k are the measurement prediction value residual vector and the measurement standard deviation vector, respectively, k {i} and σ k {i} represents r k and σ k The i-th element of ; the segmentation parameter c is a positive number used to adjust the robustness of the state estimator and normalize the weight vector ω k The i-th element of is ω k {i}=min{1,(b k {i} / PS k {i}) 2}, where the truncation parameter b k {i} and projection statistical parameter PS k {i} is calculated using the following projection statistics formula:

[0143]

[0144] Among them, d k {i} indicates H k The number of non-zero elements in the i-th row; Denotes the degree of freedom as d k {i}, chi-square test with a confidence level of 97.5%; H{i} k , H{j} k , H{l} k Respectively represent H k The i-th, j-th and l-th columns of ; lom represents the lower median operation.

[0145] Furthermore, in step 4, a large-scale parallel computing framework based on FPGA is established, and the specific method is as follows:

[0146] The complex domain prediction-assisted state estimation model is divided into 11 computing modules, among which A k , B k , C k , D k and E k There are 5 intermediate parameter matrices:

[0147] Module 1: Computing The module input is u k and F k , the module output is

[0148] Module 2: Computing The module input is Fk , P k-1 and Q k , the module output is P k|k-1 ;

[0149] Module 3: First, based on the complex domain equivalent measurement model, Calculate z k ,use and H k Calculate the measurement prediction residual vector Using V k Calculate the measurement standard deviation vector Among them, diag(V k ) is V k The diagonal elements of H k Calculate b k {i} and PS k {i}, according to the formula ω k {i}=min{1,(b k {i} / PS k {i}) 2} Calculate the normalized weight vector ω k ; The most covariance-scaling model uses r k , σ k and ω k Calculate the covariance scaling matrix S k ; That is, the module input is H k and V k , the module output is S k ;

[0150] Module 4: Computing The module input is H k and The module output is D k ;

[0151] Module 5: Computing The module input is P k|k-1 and H k , the module output is A k ;

[0152] Module 6: Calculation B k =C k +S k V k , the module input is C k , S k and V k , the module output is B k ;

[0153] Module 7: Calculation of C k =Hk A k , the module input is H k and A k , the module output is C k ;

[0154] Module 8: Calculating E k =H k P k|k-1 , the module input is H k and P k|k-1 , the module output is E k ;

[0155] Module 9: Calculating K k =A k B k -1 , the module input is A k and B k , the module output is K k ;

[0156] Module 10: Utilization of Equivalent Measurement Models Based on Complex Domains Calculate z k ,use K k and D k Iterative Calculation in, The initial value is After iterative convergence, the final state estimation result is obtained That is, the module input is K k and D k , the module output is

[0157] Module 11: Calculating P k =P k|k-1 -K k E k , the module input is P k|k-1 , K k and E k , the module output is P k ;

[0158] According to the 11 modules designed above, the following large-scale parallel processing strategy is designed based on the hardware programmable characteristics of FPGA. The calculation steps are as follows:

[0159] 1. Execute the calculations of module 1 and module 2 in parallel and obtain and P k|k-1 ;

[0160] 2. Execute the calculations of modules 3, 4 and 5 in parallel to obtain S k , Dk and A k ;

[0161] 3. Execute the calculations of modules 6, 7 and 8 in parallel to obtain B k , C k and E k ;

[0162] 4. Execute the calculation of module 9 to obtain K k ;

[0163] 5. Execute the calculations of modules 10 and 11 in parallel to obtain the final state vector estimate And its corresponding covariance matrix P k .

[0164] Through the above FPGA-based massively parallel processing strategy, the prediction-assisted state estimator can be executed in massive parallel to provide high real-time distribution network state information.

[0165] In order to verify the accuracy and real-time performance of the method of the present invention, the IEEE 13, 33, 123 node standard system is used for verification.

[0166] During the test, the measurement data of each standard system is obtained by adding Gaussian noise to the power flow calculation value, the standard deviation of the voltage amplitude measurement is set to 5‰, and the standard deviation of the node injection power and the branch power is set to 1%. The sampling interval of the data is 15 minutes. For comparison, the present invention selects the EKF algorithm, IEKF algorithm, UKF algorithm, the CWLS algorithm proposed in the document "A complexvariable perturbed Gauss-Newton method for tracking mode state estimation", and the RIUKF algorithm proposed in the document "Robust unscented Kalman filter for power system dynamicstate estimation with unknown noise statistics" to compare the performance with the method proposed in the present invention. Except for CWLS, all algorithms are prediction-assisted state estimation algorithms. The estimation error and execution time are obtained by averaging 100 random experiments. MAE is selected as the quantitative indicator of the estimation error, and its calculation formula is as follows:

[0167]

[0168] in, and They represent the estimated state value and the true state value respectively, and n is the length of the state vector.

[0169] Table 1 Estimation error of different algorithms in each test system (pu,)

[0170]

[0171] Table 1 shows the estimation accuracy of different algorithms in IEEE 13, 33, and 123 node systems. Figure 2 The average MAE values ​​of different algorithms in the IEEE 123 system are further shown. It can be seen that the algorithm proposed in the present invention has the highest estimation accuracy in all tests.

[0172] Table 2 Execution time of different algorithms in each test system (seconds)

[0173]

[0174] Table 2 shows the average execution time of different algorithms in IEEE 13, 33, and 123 node systems, where the algorithm of the present invention runs in the CPU like other algorithms. It can be seen that without using FPGA to accelerate the calculation, the proposed algorithm has a higher computational efficiency than all other prediction-assisted state estimation algorithms.

[0175] Furthermore, we used FPGA in an IEEE 33-node system to test the impact of the proposed large-scale parallel computing framework on the estimation accuracy and computational efficiency of the algorithm of the present invention. Figure 3 The state estimation results of the algorithm of the present invention for node 8 in the IEEE 33-node system are shown. It can be seen that the calculation results of the algorithm of the present invention in the CPU and in the FPGA are completely consistent. In addition, for the IEEE 33-node system, the execution time of the algorithm of the present invention in the FPGA is 2.172×10 -5 seconds, compared to the CPU execution time of 1.82×10 -3 It is nearly 2 orders of magnitude faster, even faster than the static state estimator CWLS, which takes 1.11×10 -3 Faster, verifying the significant improvement of real-time performance by the proposed large-scale parallel computing framework.

[0176] The above simulation results verify the effectiveness and practicality of the method of the present invention. Therefore, the method of the present invention improves the estimation accuracy and computational efficiency of the distribution network state estimation. The proposed large-scale parallel computing framework based on FPGA further improves the real-time performance of the method and makes the estimation performance more stable.

[0177] The embodiments of the present invention are described in detail above with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. A distribution network complex domain prediction-assisted state estimation method based on FPGA large-scale parallel computing, characterized in that: The following steps are involved: Step 1, obtaining the topological structure, line parameters and real-time measurement data of the distribution network, wherein the measurement data includes SCADA measurement data and AMI measurement data; Step 2: construct a state prediction model and a complex domain equivalent measurement model based on the obtained distribution network topology, line parameters and real-time measurement data; Step 3, constructing a complex domain prediction-assisted state estimation model based on the state prediction model and the complex domain equivalent measurement model; Step 4: Establish a large-scale parallel computing framework based on FPGA, split the complex domain prediction-assisted state estimation model into multiple computing modules to calculate and obtain the distribution network state estimation results.

2. According to claim 1, a distribution network complex domain prediction auxiliary state estimation method based on FPGA large-scale parallel computing is characterized in that: In step 1, the obtained distribution network topology structure includes the line number, the head node number and the terminal node number; the obtained distribution network line parameters include the line series impedance, the line parallel admittance, the transformer ratio and the transformer equivalent impedance; and the obtained distribution network real-time measurement data SCADA and AMI measurement data include node voltage amplitude, node injected active power, node injected reactive power, branch active power and branch reactive power.

3. According to claim 1, a distribution network complex domain prediction auxiliary state estimation method based on FPGA large-scale parallel computing is characterized in that: In step 2, a state prediction model and a complex domain equivalent measurement model are constructed, and the specific method is as follows: In the complex domain, the state prediction model of the distribution network and the complex domain measurement model are constructed as follows: x k =f(x k-1 )+ω k Among them, x k and They represent the state vector and measurement vector at time k, respectively, and x k-1 represents the state vector at time k-1; ω k and ε k They represent the system process noise and measurement noise at time k, and the covariance matrices are Q k and R k ; f(·) and h(·) represent the state prediction equation and the equivalent measurement equation in the complex domain, respectively; The Holt method is used to model the state prediction equation as follows: x k|k-1 =a k +b k a k =a k x k-1 +(1-a k )x k-1|k-2 b k =b k (a k -a k-1 )+(1-β k )b k-1 Among them, x k|k-1 and x k-1|k-2 are the predicted values ​​of the state vector at time k and time k-1, respectively, k and β k are two smoothing parameters used to adjust the adaptability of the prediction equation to new trends in the data. Their value range is (0,1). k , b k Represents the two intermediate structural parameters at time k, a k-1 , b k-1 Representing the two intermediate structural parameters at time k-1, the matrix expression of the state prediction equation f(·) is as follows: f(x k-1 )=F k x k-1 +u k Among them, the state transfer matrix F k and the state transition vector u k It is obtained by the following formula: F k =a k (1+b k )I you k =(1+β k )(1-a k )x k-1 -b k a k-1 +(1-β k )b k-1 Where I represents the identity matrix; Construct a complex domain equivalent measurement model for SCADA and AMI node voltage amplitude measurement, node injected active power measurement, node injected reactive power measurement, branch active power measurement and branch reactive power measurement. k As follows: Depending on the measurement type, z k Equivalent voltage phasor measurement Equivalent injection current measurement Equivalent branch current measurement There are 3 categories in total, and the equivalent measurement models in the complex domain are constructed as follows: in, represents the voltage phasor of node f at time k; and They represent the voltage amplitude measurement of node f at time k, the node injection complex power measurement of node f, and the branch complex power measurement of branch ft, respectively, and t represents node t; and They respectively represent the node injected active power measurement of node f at time k, the node injected reactive power measurement of node f, the branch active power measurement of branch ft, and the branch reactive power measurement of branch ft.

4. According to claim 3, a distribution network complex domain prediction auxiliary state estimation method based on FPGA large-scale parallel computing is characterized in that: In step 3, a complex domain prediction auxiliary state estimation model is constructed, and the specific method is as follows: According to the state prediction model and the complex domain equivalent measurement model, the following complex domain augmented state space model is constructed: Among them, the augmented state vector at time k is Augmented state transfer matrix Augmented State Transfer Vector Augmented Equivalent Measurement Vector Superscript (·) T , (·) H and(·) * Represents matrix transposition, matrix conjugate transposition and conjugate operation respectively; the augmented state vector at time k-1 and They represent the augmented process noise and augmented measurement noise at time k respectively; is the augmented Jacobian matrix at time k, which is constructed as follows: in, and denote the constant Jacobian matrix and the conjugate Jacobian matrix respectively; The augmented process covariance matrix is The augmented measurement covariance matrix of Define and To take the real part and the imaginary part, we define the complex domain measurement The real number combination measurement vector Its covariance matrix is ​​expressed as and The covariance matrices of and as follows: in, and They represent the measurement variances corresponding to the voltage amplitude measurement of node f at time k, the node injected active power measurement of node f, the node injected reactive power measurement of node f, the branch active power measurement of branch ft, and the branch reactive power measurement of branch ft, respectively; and The matrix expression between is as follows: Among them, T is the measurement transformation matrix, and the augmented measurement covariance matrix is ​​constructed as follows: Among them, V k and M k are the real covariance matrix and the complex complementary covariance matrix respectively. In the application of distribution network state estimation, the conjugate Jacobian matrix J is ignored. k , reconstructing the augmented Jacobian matrix and augmented covariance matrix into and The complex domain state space model is established as follows: The complex domain state space model is further simplified, and the final complex domain state space model is obtained as follows: x k =F k x k-1 +u k +ω k z k (x k )=H k x k +ε k According to the above complex domain state space model, the complex domain prediction auxiliary state estimation model is constructed as follows: Definition is the estimated value of the state vector at time k-1, and its corresponding covariance matrix is ​​P k-1 , the predicted state vector is calculated according to the following formula And its corresponding covariance matrix P k|k-1 : According to the above formula, P k|k-1 Afterwards, the Kalman gain matrix K is calculated k as follows: After the calculation is completed, the estimated value of the state vector at time k is iteratively calculated according to the following formula And calculate the corresponding covariance matrix P k as follows: P k =P k|k-1 -K k H k P k|k-1 in, and denote the calculated values ​​of the state vector for the j-th and j-1-th iterations respectively, The initial value is when When it is less than the convergence threshold, update the estimated value of the state vector at time k Using Huber function and projection statistics theory, the solution formula of Kalman gain matrix is ​​reconstructed into the following form: Among them, the diagonal matrix S k represents the covariance scaling matrix, whose i-th diagonal element S k {i,i} is calculated using the following covariance scaling model: in, and σ k are the measurement prediction value residual vector and the measurement standard deviation vector, r k {i} and σ k {i} represents r k and σ k The i-th element of ; the segmentation parameter c is a positive number used to adjust the robustness of the state estimator and normalize the weight vector ω k The i-th element of is ω k {i}=min{1,(b k {i} / PS k {i}) 2 }, where the truncation parameter b k {i} and projection statistical parameter PS k {i} is calculated using the following projection statistics formula: Among them, d k {i} indicates H k The number of non-zero elements in the i-th row; Denotes the degree of freedom as d k {i}, chi-square test with a confidence level of 97.5%; H{i} k , H{j} k , H{l} k Respectively represent H k The i-th, j-th and l-th columns of ; lom represents the lower median operation.

5. According to claim 4, a distribution network complex domain prediction auxiliary state estimation method based on FPGA large-scale parallel computing is characterized in that: In step 4, a large-scale parallel computing framework based on FPGA is established, and the specific method is as follows: The complex domain prediction-assisted state estimation model is divided into 11 computing modules, among which A k , B k , C k , D k and E k There are 5 intermediate parameter matrices: Module 1: Computing The module input is u k and F k , the module output is Module 2: Computing The module input is F k , P k-1 and Q k , the module output is P k|k-1 ; Module 3: First, based on the complex domain equivalent measurement model, Calculate z k ,use and H k Calculate the measurement prediction residual vector Using V k Calculate the measurement standard deviation vector Among them, diag(V k ) is V k The diagonal elements of H k Calculate b k {i} and PS k {i}, according to the formula ω k {i}=min{1,(b k {i} / PS k {i}) 2 } Calculate the normalized weight vector ω k ; The most covariance-scaling model uses r k , σ k and ω k Calculate the covariance scaling matrix S k ; That is, the module input is H k and V k , the module output is S k ; Module 4: Computing The module input is H k and The module output is D k ; Module 5: Computing The module input is P k|k-1 and H k , the module output is A k ; Module 6: Calculation B k =C k +S k V k , the module input is C k , S k and V k , the module output is B k ; Module 7: Calculation of C k =H k A k , the module input is H k and A k , the module output is C k ; Module 8: Calculating E k =H k P k|k-1 , the module input is H k and P k|k-1 , the module output is E k ; Module 9: Computing The module input is A k and B k , the module output is K k ; Module 10: Utilization of Equivalent Measurement Models Based on Complex Domains Calculate z k ,use K k and D k Iterative Calculation in, The initial value is After iterative convergence, the final state estimation result is obtained That is, the module input is K k and D k , the module output is Module 11: Calculating P k =P k|k-1 -K k E k , the module input is P k|k-1 , K k and E k , the module output is P k ; According to the 11 modules designed above, the following large-scale parallel processing strategy is designed based on the hardware programmable characteristics of FPGA. The calculation steps are as follows:

1. Execute the calculations of module 1 and module 2 in parallel and obtain and P k|k-1 ; 2. Execute the calculations of modules 3, 4 and 5 in parallel to obtain S k , D k and A k ; 3. Execute the calculations of modules 6, 7 and 8 in parallel to obtain B k , C k and E k ; 4. Execute the calculation of module 9 to obtain K k ; 5. Execute the calculations of modules 10 and 11 in parallel to obtain the final state vector estimate And its corresponding covariance matrix P k .

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