A complex domain prediction-assisted state estimation method for distribution network based on FPGA massive parallel computing

Abstract

The present invention discloses a distribution network complex domain prediction auxiliary state estimation method based on FPGA large-scale parallel computing, including: obtaining the topological structure, line parameters and real-time measurement data of the distribution network; constructing a state prediction model and a complex domain equivalent measurement model according to the obtained distribution network topological structure, line parameters and real-time measurement data; constructing a complex domain prediction auxiliary state estimation model according to the state prediction model and the complex domain equivalent measurement model; establishing a large-scale parallel computing framework based on FPGA, splitting the complex domain prediction auxiliary state estimation model into multiple computing modules, and obtaining the distribution network state estimation result. The present invention improves the estimation accuracy and computing efficiency of the distribution network state estimation, and can use FPGA for large-scale parallel computing, further improve the real-time performance of the state estimation, and make the estimation performance more stable.

Description

Technical Field

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

[0002] State estimation is the data basis for other advanced applications in a power system and plays a crucial role in ensuring the safe, stable, efficient, and low-carbon operation of a distribution network. In recent years, the continuous access of distributed generation and flexible loads has increased the randomness and volatility of the operation of the distribution network, making the need for accurately and real-time monitoring of each node of the monitoring system more urgent than ever. However, the distribution network has always suffered from the problems of low measurement redundancy and poor measurement data quality, and has higher requirements for the estimation performance of the state estimator compared with the transmission network. In order to better track the state fluctuations of the distribution network, it is necessary to adopt a prediction-aided state estimation method to replace the traditional static estimation method to ensure the accuracy of tracking. However, most of the prediction-aided state estimation methods have low efficiency and cannot meet the needs of real-time tracking of the distribution network state, increasing the demand for a high-real-time prediction-aided state estimation method.

[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 utilize the information of a single moment section, and its estimation accuracy highly depends on the redundancy of measurements, making it inapplicable to the distribution network scenario. To address the issue of insufficient estimation accuracy of the static state estimation algorithm, the prediction-aided state estimation algorithm utilizes the information of multiple time sections in the prediction step, significantly improving the state tracking ability. The most common prediction-aided state estimation algorithm is the Extended Kalman Filter (EKF) algorithm, which linearizes the measurement equation to minimize the computational efficiency problem of the prediction-aided state estimator as much as possible. However, due to the use of the first-order Taylor approximation in the EKF algorithm, when facing a highly nonlinear system, it often exhibits low accuracy and even problems of computational divergence. The Iterated Extended Kalman Filter (IEKF) reduces the linearization error by continuously linearly approximating the nonlinear equation to achieve a solution close to the optimal one. However, since the IEKF needs to repeatedly solve the Jacobian matrix and the Kalman gain matrix in the successive linearization process, its computational efficiency is greatly reduced compared to the EKF. Another way to solve the linearization error is to adopt a sampling point-based method. The Ensemble Kalman Filter (EnKF) and the 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 computational volume and a significant reduction in computational efficiency. The Unscented Kalman Filter (UKF) and the Cubature Kalman Filter (CKF) algorithms use a small number of sampling points with specific rules to approximate the probability distributions of the mean and variance, which can significantly reduce the computational volume compared to the EnKF and PF. However, the UKF and CKF have relatively serious numerical stability problems, often experiencing problems of computational divergence, and due to the reduction of sampling points, the estimation accuracy of the UKF and CKF will also decrease accordingly. Generally speaking, the current prediction-aided state estimation methods for distribution networks are difficult to balance estimation accuracy and computational efficiency and cannot be truly applied to actual distribution networks. Therefore, it is of great significance to study a prediction-aided state estimation method for distribution networks with high estimation accuracy and high real-time performance. Summary of the Invention

[0004] Object of the invention. To solve the problem that the current prediction-aided state estimator for distribution networks is difficult to simultaneously meet the estimation accuracy and calculation efficiency, the present invention provides a distribution network complex-domain prediction-aided state estimation method based on large-scale parallel computing of FPGA. By constructing complex-domain equivalent measurements of SCADA and AMI, the non-linear state estimation problem of the real-domain distribution network is solved in a quasi-linear manner in the complex domain, realizing high-precision and high-efficiency perception of the distribution network state. 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. To achieve the above object of the invention, the present invention proposes a distribution network complex-domain prediction-aided state estimation method based on large-scale parallel computing of FPGA, 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 data acquisition and monitoring control system (SCADA) measurement data and advanced metering infrastructure (AMI) measurement data;

[0007] Step 2, constructing a state prediction model and a complex-domain equivalent measurement model according to the obtained topological structure, line parameters and real-time measurement data of the distribution network;

[0008] Step 3, constructing a complex-domain prediction-aided state estimation model according to the state prediction model and the complex-domain equivalent measurement model;

[0009] Step 4, establishing a large-scale parallel computing framework based on FPGA, splitting the complex-domain prediction-aided state estimation model into multiple computing modules for calculation to obtain the distribution network state estimation result.

[0010] Further, in step 1, the obtained topological structure of the distribution network includes line numbers, head node numbers and end node numbers; the obtained line parameters of the distribution network include series impedance of the line, shunt admittance of the line, transformer turns ratio and transformer equivalent impedance; and, in the obtained real-time measurement data of the distribution network, both the SCADA and AMI measurement data include node voltage amplitude, node injected active power, node injected reactive power, branch active power and branch reactive power.

[0011] Further, in step 2, the method for constructing the state prediction model and the complex-domain equivalent measurement model is as follows:

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

[0013] x k =f(x k-1 )+ω k

[0014]

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

[0016] The state prediction equation is modeled by the Holt method 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 respectively, and α k and β k are two smoothing parameters used to adjust the adaptability of the prediction equation to new trends in the data, and their value ranges are (0,1). a k , b k represent two intermediate structure parameters at time k, and a k-1 , b k-1 represent two intermediate structure 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 transition matrix F k and the state transition vector u k are obtained through the following formulas:

[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 z for the node voltage magnitude measurement, node injected active power measurement, node injected reactive power measurement, branch active power measurement, and branch reactive power measurement of SCADA and AMI k as follows: According to different measurement types, z k is divided into equivalent voltage phasor measurement equivalent injected current measurement equivalent branch current measurement a total of 3 categories, and the complex - domain equivalent measurement models are constructed as follows respectively:

[0027]

[0028] where represents the voltage phasor of node f at time k; and represent the voltage magnitude measurement of node f at time k, the node - injected complex power measurement of node f, and the branch - complex power measurement of branch f - t respectively, where t represents node t; and represent 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 f - t, and the branch - reactive power measurement of branch f - t at time k respectively.

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

[0030] Construct the following complex - domain augmented state - space model according to the state prediction model and the complex - domain equivalent measurement model:

[0031]

[0032] where the augmented state vector at time k augmented state transition matrix Augmented state transition vector Augmented equivalent measurement vector Superscript (·) T , (·) H and (·) * respectively represent matrix transpose, conjugate transpose of matrix and conjugate operation; the augmented state vector at time k-1 and respectively represent the augmented process noise and augmented measurement noise at time k; is the augmented Jacobian matrix at time k, and its construction method is as follows:

[0033]

[0034] wherein, and respectively represent the constant Jacobian matrix and the conjugate Jacobian matrix; The augmented process covariance matrix of The augmented measurement covariance matrix of

[0035] respectively define and as the real part taking and imaginary part taking operations, and then define the complex domain measurement The real combined measurement vector of Its covariance matrix is expressed as and The covariance matrices of and are respectively expressed as

[0036]

[0037] wherein, and respectively represent the measurement variances corresponding to the voltage amplitude measurement of node f at time k, the active power injection measurement of node f, the reactive power injection measurement of node f, the active power measurement of branch f-t and the reactive power measurement of branch f-t;

[0038] and The matrix expression between

[0039]

[0040] wherein, 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 k is ignored, and the augmented Jacobian matrix and the augmented covariance matrix are reconstructed as and A complex-domain state space model is established as follows:

[0043]

[0044] The complex-domain state space model is further simplified to obtain the final complex-domain state space model 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, a complex-domain prediction-aided state estimation model is constructed as follows: Define as the estimated value of the state vector at time k - 1, and its corresponding covariance matrix is P k-1 . The predicted state vector and its corresponding covariance matrix P k|k-1 are calculated according to the following formula:

[0048]

[0049] After calculating P k|k-1 according to the above formula, the Kalman gain matrix K k is calculated 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 its corresponding covariance matrix P k is calculated as follows:

[0052]

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

[0054] Among them, and respectively represent the calculated values of the state vectors at the j-th and (j - 1)-th iterations, The initial value of When is less than the convergence threshold, update the estimated value of the state vector at time k

[0055] Use the Huber function and projection statistical theory to reconstruct the solution formula of the Kalman gain matrix into the following form:

[0056]

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

[0058]

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

[0060]

[0061] Among them, d k {i} represents the number of non-zero elements in the i-th row of H k ; represents the chi-square test with d k {i} degrees of freedom and a confidence level of 97.5%; H{i} k , H{j} k , H{l} k respectively represent H kThe i-th column, j-th column, and l-th column; lom represents the low 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-aided state estimation model is split into 11 computing modules, where A k , B k , C k , D k and E k are 5 intermediate parameter matrices:

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

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

[0066] Module 3: First, according to the complex domain equivalent measurement model, use to calculate z k , use and H k to calculate the measurement prediction residual vector Use V k to calculate the measurement standard deviation vector where diag(V k ) is the diagonal element of V k ; According to the projection statistical formula, use H k to calculate b k {i} and PS k {i}, and according to the formula ω k {i} = min{1, (b k {i} / PS k {i}) 2} to calculate the normalized weight vector ω k ; Finally, according to the covariance scaling model, use r k , σ k and ω k to calculate the covariance scaling matrix S k ; That is, the module input is H k and V k , and the module output is S k ;

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

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

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

[0070] Module 7: Calculate C k = H k A k The module input is H k and A k and the module output is C k ;

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

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

[0073] Module 10: According to the equivalent measurement model in the complex number field, use to calculate z k , use K k and D k to perform iterative calculation where the initial value of After the iteration converges, the final state estimation result is obtained That is, the module input is K k and D k and the module output is

[0074] Module 11: Calculate 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] Based on the 11 modules designed above, a large-scale parallel processing strategy is designed based on the hardware programmability of FPGA, and the calculation steps are as follows:

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

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

[0078] 3. Execute the calculations of Module 6, Module 7 and Module 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 Module 10 and Module 11 in parallel to obtain the final state vector estimate and its corresponding covariance matrix P k .

[0081] Through the above large-scale parallel processing strategy based on FPGA, the prediction-aided state estimator can be executed in large-scale parallel, providing 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 structure, line parameters, and real-time measurement data; then, constructs a complex-domain prediction-aided state estimation model based on the state prediction model and the complex-domain equivalent measurement model; finally, establishes a large-scale parallel computing framework based on FPGA, splits the complex-domain prediction-aided state estimation model into multiple computing modules, and obtains the distribution network state estimation result. The test results of the IEEE standard system show that, due to the quasi-linearization solution process of the distribution network prediction-aided state estimator in the complex domain, the estimation accuracy and computing efficiency of the method proposed by the present invention are higher than those of the existing state estimation algorithms, and the large-scale parallel computing framework based on FGPA further improves the real-time performance of the state estimator, enabling the method proposed by the present invention to complete the state estimation calculation at a faster speed than the existing prediction-aided state estimator, or even the static state estimator. Therefore, the method of the present invention improves the estimation accuracy and computing 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 FIG. is a flowchart of the distribution network complex-domain prediction-aided state estimation method based on large-scale parallel computing of FPGA according to the present invention.

[0085] Figure 2 FIG. is a schematic diagram comparing the estimation errors of different algorithms in the IEEE 123 system according to the present invention.

[0086] Figure 3 FIG. is a schematic diagram comparing the estimation results of using CPU and FPGA in the IEEE 33 system according to the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

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

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

[0089] Step 1, obtain the topology structure, line parameters, and real-time measurement data of the distribution network, where the measurement data includes data acquisition and monitoring control system (SCADA) measurement data and advanced measurement infrastructure (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 structure, line parameters, and real-time measurement data;

[0091] Step 3: Construct a complex-domain prediction-aided 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-aided state estimation model into multiple computing modules for calculation to obtain the distribution network state estimation result.

[0093] Furthermore, in Step 1, the obtained distribution network topology structure includes line numbers, head node numbers, and end node numbers; the obtained distribution network line parameters include line series impedance, line shunt admittance, transformer turns ratio, and transformer equivalent impedance; and, among the obtained distribution network real-time measurement data, both SCADA and AMI measurement data include node voltage amplitude, node injected active power, node injected reactive power, branch active power, and branch reactive power.

[0094] Furthermore, in Step 2, the specific methods for constructing the state prediction model and the complex-domain equivalent measurement model are as follows:

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

[0096] x k =f(x k-1 )+ω k

[0097]

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

[0099] Model the state prediction equation using the Holt method 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] where 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, α k and β k are two smoothing parameters used to adjust the adaptability of the prediction equation to new trends in the data, and their value ranges are (0, 1). a k , b k represent two intermediate structure parameters at time k, and a k-1 , b k-1 represent two intermediate structure 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] where the state transition matrix F k and the state transition vector u k are obtained through the following formulas:

[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] For the node voltage magnitude measurement, node active power injection measurement, node reactive power injection measurement, branch active power measurement and branch reactive power measurement of SCADA and AMI, construct the complex domain equivalent measurement model z k as follows: According to different measurement types, z kDivided into equivalent voltage phasor measurements Equivalent injected current measurements Equivalent branch current measurements There are a total of 3 categories, and the complex-domain equivalent measurement models are constructed as follows:

[0110]

[0111] Among them, represents the voltage phasor of node f at time k; and respectively represent the voltage magnitude measurement of node f at time k, the complex power injection measurement of node f, and the complex power measurement of branch f-t, where t represents node t; and respectively represent the active power injection measurement of node f, the reactive power injection measurement of node f, the active power measurement of branch f-t, and the reactive power measurement of branch f-t at time k.

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

[0113] Construct the following complex-domain augmented state space model according to the state prediction model and the complex-domain equivalent measurement model:

[0114]

[0115] Among them, the augmented state vector at time k Augmented state transition matrix Augmented state transition vector Augmented equivalent measurement vector Superscript (·) T , (·) H and (·) * respectively represent matrix transpose, matrix conjugate transpose, and conjugate operation; the augmented state vector at time k-1 and respectively represent the augmented process noise and augmented measurement noise at time k; is the augmented Jacobian matrix at time k, and its construction method is as follows:

[0116]

[0117] Among them, and respectively represent the constant Jacobian matrix and the conjugate Jacobian matrix; The augmented process covariance matrix of The augmented measurement covariance matrix is

[0118] Define respectively and as the operations of taking the real part and the imaginary part, and then define the complex-domain measurement The real combined measurement vector of Its covariance matrix is expressed as and The covariance matrices of and are respectively expressed as

[0119]

[0120] Wherein, and respectively represent the measurement variances corresponding to the voltage magnitude measurement of node f at time k, the active power injection measurement of node f, the reactive power injection measurement of node f, the active power measurement of branch f-t, and the reactive power measurement of branch f-t;

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

[0122]

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

[0124]

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

[0126]

[0127] The complex-domain state space model is further simplified to obtain the final complex-domain state space model 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, construct the complex - domain prediction - assisted state - estimation model as follows: Define as the estimated value of the state vector at time k - 1, and its corresponding covariance matrix is P k-1 . Calculate the predicted state vector and its corresponding covariance matrix P k|k-1 :

[0131]

[0132] After calculating P k|k-1 , calculate the Kalman gain matrix K k as follows:

[0133]

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

[0135]

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

[0137] where and represent the calculated values of the state vector at the j - th and (j - 1)-th iterations respectively, the initial value of When is less than the convergence threshold, update the estimated value of the state vector at time k

[0138] Re - construct the solution formula of the Kalman gain matrix using the Huber function and projection statistical theory into the following form:

[0139]

[0140] where the diagonal matrix S k represents the covariance scaling matrix, and its i - th diagonal element S k {i,i} is calculated according to the following covariance scaling model:

[0141]

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

[0143]

[0144] Among them, d k {i} represents the number of non-zero elements in the i-th row of H k ; represents the chi-square test with degrees of freedom d k {i} and a confidence level of 97.5%; H{i} k , H{j} k , H{l} k represent the i-th column, the j-th column, and the l-th column of H k respectively; lom represents the low 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-aided state estimation model is split into 11 computing modules, where A k , B k , C k , D k and E k are 5 intermediate parameter matrices:

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

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

[0149] Module 3: First, calculate z using the equivalent measurement model in the complex number field by Calculate z k , and use and H k to calculate the measurement prediction value residual vector Use V k to calculate the measurement standard deviation vector where, diag(V k ) are the diagonal elements of V k ; calculate b k using H according to the projection statistical formula k {i} and PS k {i}, and calculate the normalized weight vector ω k {i} = min{1, (b k {i} / PS k {i}) 2}; finally, calculate the covariance scaling matrix S using r k , σ k , and ω k ; that is, the module input is k H k and V H k and V k , and the module output is S k ;

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

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

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

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

[0154] Module 8: Calculate 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: Calculate 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: According to the equivalent measurement model in the complex number field, use to calculate z k , use K k and D k to perform iterative calculation where, the initial value of is After iterative convergence, the final state estimation result is obtained That is, the module input is k K k and D

[0157] Module 11: Calculate 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] Based on the 11 modules designed above, a large-scale parallel processing strategy is designed based on the hardware programmability of FPGA, and the calculation steps are as follows:

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

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

[0161] 3. Execute the calculations of Module 6, Module 7, and Module 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 Module 10 and Module 11 in parallel to obtain the final state vector estimate and its corresponding covariance matrix P k .

[0164] Through the above large-scale parallel processing strategy based on FPGA, the predictive-aided state estimator can be executed in large-scale parallel, providing high real-time distribution network state information.

[0165] To verify the accuracy and real-time performance of the method of the present invention, the IEEE 13, 33, and 123-bus standard systems are used for verification and illustration below.

[0166] During the test, the measurement data of each standard system is obtained by adding Gaussian noise to the power flow calculation values. The standard deviation of the voltage magnitude measurement is set to 5‰, and the standard deviations of the node injection power and branch power are set to 1%. The sampling interval of the data is 15 minutes. For comparison, the EKF algorithm, IEKF algorithm, UKF algorithm, the CWLS algorithm proposed in the literature "A complex variable perturbed Gauss-Newton method for tracking mode state estimation", and the RIUKF algorithm proposed in the literature "Robust unscented Kalman filter for power system dynamic state estimation with unknown noise statistics" are selected to compare with the method proposed in the present invention. Among them, except for CWLS, all algorithms are predictive-aided state estimation algorithms. The estimation error and execution time are both obtained by averaging 100 random trials. The MAE is selected as the quantization index of the estimation error, and its calculation formula is as follows:

[0167]

[0168] where and represent the state estimate value and the true state value respectively, and n is the length of the state vector.

[0169] Table 1 Estimation errors of different algorithms in each test system (p.u.)

[0170]

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

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

[0173]

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

[0175] Furthermore, we tested the influence of the proposed large - scale parallel computing framework on the estimation accuracy and computational efficiency of the algorithm of the present invention in the IEEE 33 - bus system using FPGA. Figure 3 Shows the state - estimation results of node 8 in the IEEE 33 - bus system by the algorithm of the present invention. It can be seen that the calculation results of the algorithm of the present invention in the CPU and in the FPGA are exactly the same. In addition, for the IEEE 33 - bus system, the execution time of the algorithm of the present invention in the FPGA is 2.172×10 -5 seconds, which is nearly two orders of magnitude faster than the execution time of 1.82×10 -3 in the CPU, and even faster than the execution time of 1.11×10 -3 of the static state - estimator CWLS, verifying the significant improvement of the proposed large - scale parallel computing framework on real - time performance.

[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 FPGA - based large - scale parallel computing framework further improves the real - time performance of the method, making the estimation performance more stable.

[0177] The above - mentioned embodiments of the present invention have been described in detail in conjunction with the accompanying drawings. However, the present invention is not limited to the above - mentioned embodiments. Within the scope of knowledge possessed by those of ordinary skill in the art, various changes can be made without departing from the gist 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 result; 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; 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 represent 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 at time k respectively; 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.

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, 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.

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, the state prediction equation is modeled as follows using the Holt method: 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, 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: 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.

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, The construction is 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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