A weighted average fast forward-backward robust state estimation method for radiation networks

Abstract

The present invention discloses a method for weighted average fast forward back-generation robust state estimation of a radiation network. The present invention replaces the traditional least square state estimation method by adopting a weighted averaging method, and adopts a forward back-generation idea from local to global. First, node power estimation is performed on the end nodes of the branch, and then a weighted average state estimation is performed on the branch. After the estimation of all nodes and branches is completed from the bottom branch to the top branch, a correction value of the estimated value of the system state quantity is obtained from the top to the bottom, thereby realizing the weighted average fast forward back-generation robust state estimation of the radiation network.

Description

Technical Field

[0001] The invention relates to the technical field of power system state estimation, in particular to a weighted average fast forward-backward robust state estimation method for a radiation network. Background Art

[0002] Power system state estimation is one of the important functions of modern power dispatching system. Power system state estimation can use various types of measurement data provided by the power system to estimate the current state of the power system. Due to various reasons, a certain proportion of bad data will inevitably appear in the measurement data provided by the power system, which will cause the state estimation result to deviate from the true value to a certain extent, and have an adverse impact on the quality of the basic data of the power system. The existing global weighted least squares state estimation has good robustness, but for large power systems, it has high memory usage and slow calculation speed. Due to the interaction between multiple bad data, residual drowning and pollution are prone to occur, resulting in insufficient identification and processing capabilities of the method for bad data once non-convergence occurs. The existing forward-backward robust state estimation method estimates the state of each branch through the localization idea. It has high estimation accuracy and good identification effect on bad data. However, since it is necessary to estimate the state of each branch, its calculation speed is greatly reduced. For this reason, we propose a weighted average fast forward-backward robust state estimation method for radiation network. Summary of the invention

[0003] The purpose of the present invention is to provide a weighted average fast forward-backward robust state estimation method for a radiation network to solve the problems raised in the above-mentioned background technology.

[0004] To achieve the above object, the present invention provides the following technical solution: a weighted average fast forward-backward robust state estimation method for a radiation network, comprising the following steps:

[0005] 1. Obtain the basic data of the power grid, which includes the topological structure of the power grid and the measurement information of the power system, including the injected active power and injected reactive power of the node, the voltage amplitude of the node, and the branch active power and branch reactive power at the beginning and end of each branch;

[0006] 2. Preprocess the basic data of the power grid and replace the obviously wrong data. The purpose of bad data preprocessing is to first identify some obviously wrong bad data before state estimation and replace them with correct estimated values;

[0007] 3. Taking the bottom system branch as the starting point and the top system branch as the end point, perform weighted average state estimation on each branch of each layer to obtain the initial value of the power grid state estimation;

[0008] 4. Taking the top-level system branch as the starting point and the bottom-level system branch as the end point, perform power flow back substitution according to the voltage distribution of the root node and the power distribution of the system, correct the node voltage, and obtain the correction result of the power grid state quantity;

[0009] 5. According to the correction result of the power grid state quantity, the weight of the measured data is corrected through the exponential weight function;

[0010] 6. Determine whether the difference between the current grid state correction result and the previous grid state correction result is less than the set convergence criterion. If converged, end the state estimation, otherwise return to step 3.

[0011] Preferably, the specific steps in step 2 are: A. The power balance of the branch end node is judged. If it is unbalanced, it means that there is bad data at the branch end node. Do not estimate the node power for this node and jump to D, where k h ∈j represents the nodes directly connected to node j, but does not include node j itself; P j , Q j Respectively represent the injected active power and injected reactive power of node j; ε1 represents the upper limit threshold of balance judgment determined according to the measurement type and its reference value; B. Perform node power estimation on the node, and obtain the head-end estimation value derived from the terminal measurement value through the power flow calculation method. The node power estimation process is as follows: B1. Establish the node power balance equation Where: k = k1, k2, ... k l , i; k∈j represents all nodes adjacent to node j, but excluding node j itself; w pjk 、w pj 、w qjk 、w qj They represent the weights corresponding to the four types of measurement data: branch active power, injected active power, branch reactive power, and injected reactive power; P jk , P j , Q jk , Q j It indicates the estimated value after estimation; P mjk , P mj , Q mjk , Q mj Represents the measured value corresponding to the estimated value; B2. Solve the node power balance equation Where: is the estimated value after estimation; C. According to the formula and Determine whether the power and voltage amplitudes at the head and end are consistent. If not, it means that there is bad data in the head measurement. Replace it with the estimated value derived from the end and jump to the single branch state estimation. If consistent, it means that there is no bad data at the head and end, and directly perform single branch state estimation, where: and They are respectively the active power at the beginning of the branch derived from the end of the branch and the measured value of the active power at the beginning of the branch; and They are the reactive power at the beginning of the branch derived from the end of the branch and the measured reactive power at the beginning of the branch; ε2 represents the upper limit threshold of balance judgment determined according to the power measurement type and its reference value. The method for determining the upper limit of the threshold is as follows: Where: ε is the upper threshold of different measurement types; E is the estimated value error rate allowed for different measurement types, which must meet the requirements of active power not exceeding 2%, reactive power not exceeding 3%, voltage of 220kV and above not exceeding 0.5%, voltage below 220kV not exceeding 2%, Z b is the system reference value of voltage or power, Z base is the estimated value error rate reference value determined by the voltage or power system reference value; D. The head-end estimated value derived from the terminal measurement value is obtained by the power flow calculation method; E. According to the formula and Determine whether the power at the head and the terminal is consistent. If they are consistent, and the lower branches of the terminal node have no bad data or have been replaced, it means that the injected power of the terminal node is wrong. After replacing it, perform single branch state estimation.

[0012] Preferably, the specific steps of weighted average state estimation in step 3 are as follows: A. Based on the measured data at the end of the branch, the power flow method is used to calculate the weighted average state of the branch. The calculated value of the branch head end is calculated, where is the measured value or the last estimated value of the complex power at the end of the branch, is the measured value or the last estimated value of the branch terminal voltage, Z j is the branch impedance, are the complex voltage and complex power of the branch head end calculated respectively; B. The calculated value of the head end calculated according to the end and the measured value of the head end are calculated according to the formula Perform weighted averaging to obtain the estimated value of the branch head end, where h f is the estimated value of the point, h mf is the measurement value at the head end, The calculated value of the head end is derived from the end end, w f is the weight of the head-end measurement, w t is the weight of the terminal measurement.

[0013] Preferably, in step 4, according to formula Perform trend back generation.

[0014] Preferably, the step 5 includes A. establishing a model of an exponential weight function, and the model of the exponential weight function is as follows: In the formula is the updated weight, R i -1 is the initial fixed weight, r N is the standardized residual; B. Measurement classification and standardization. According to the measurement type, the residual dz is divided into three types: voltage type measurement residual dz_V, active power type measurement residual dz_P, and reactive power type measurement residual dz_Q. Assuming that the three types of measurement residuals all satisfy the normal distribution, the above three types of residuals are divided by the standard deviation of the corresponding type to obtain the standardized residual r N , and then according to the standardized residual r N , using exponential weight function Get the correction weight of each measurement value.

[0015] Compared with the prior art, the present invention has the following beneficial effects:

[0016] The present invention replaces the traditional least squares state estimation method by adopting a weighted averaging method, and adopts the idea of ​​forward and backward substitution from local to global. First, the node power of the branch end node is estimated, and then the branch state is estimated by weighted averaging. After the estimation of all nodes and branches is completed from the bottom branch to the top branch, the correction value of the system state quantity estimate is obtained from the top to the bottom, thereby completing the weighted average fast forward and backward substitution anti-error state estimation of the radiation network. At the same time, the algorithm does not need to perform least squares state estimation on each branch, which greatly improves the calculation speed of the forward and backward substitution state estimation method while retaining a certain degree of accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a node of IEEE33 node system;

[0018] Figure 2 Schematic diagram of node power estimation;

[0019] Figure 3 It is a schematic diagram of weighted average state estimation;

[0020] Figure 4 Flowchart for weighted average forward-backward robust state estimation. DETAILED DESCRIPTION

[0021] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0022] In order to verify the correctness of the present invention, a simulation analysis is performed through the IEEE33 node system, and the steps are as follows:

[0023] 1. Establish a simulation system, IEEE33 node system such as Figure 1 As shown, the system's reference voltage is 12.66kV, the system's reference capacity is 100MVA, and a threshold of 10-20 times is superimposed on the true value of the flow calculation to generate bad data. When setting bad data at a special location, the bad data at the special location is superimposed with a threshold of 10 on the true value of the flow calculation. The remaining measured data uses the true value of the flow. According to the threshold calculation method mentioned above, since there is no voltage and power reference value corresponding to 12.66kV, the line active or reactive power reference value 37MVA corresponding to 35kV and the bus voltage reference value 42kV are used. According to the linearization ratio, the power reference value of the 12.66kV system is calculated to be 12.66÷35×37≈13MVA, and the voltage reference value is 12.66÷35×42≈15kV, so the threshold value can be obtained as:

[0024] (1)

[0025] (2)

[0026] (3) 2. Perform topological analysis on the system to obtain the network hierarchy matrix LL and the branch head-end matrix MM. The network hierarchy matrix LL is used to describe the hierarchical structure of the network. The number of rows represents the hierarchy of the matrix, and the elements of each row are used to represent the branch number belonging to the layer; the branch head-end matrix MM is used to describe the head-end node number of each branch. Assuming that the number of branches is n, MM is a 2-row n-column matrix, where the elements in the first row of the i-th column represent the head-end node number of the branch numbered i; the elements in the second row represent the end node number of the branch numbered i. After topological analysis of the IEEE33 node, the network hierarchy matrix LL and the branch head-end matrix MM are:

[0027]

[0028]

[0029] 3. Preprocess the bad data of the system measurement data. According to the network hierarchy matrix LL and the branch head and end node matrix MM, start from the end nodes of the bottom 16, 20, 23, and 31 branches, and perform node power estimation and bad data identification and replacement for each branch until the top branch 0. The system state quantity after bad data preprocessing is shown in Table 1. The specific steps of node power estimation are as follows: It can be obtained from Kirchhoff's law that the injected power and outflow power of any node in the power system should be balanced, such as Figure 2 As shown, there should be in Represents the power injected into node j, k∈j represents all nodes adjacent to node j, but does not include node j itself. Since there are certain errors in the measured value and the estimated value after branch state estimation, the measured value or estimated value of the node power can be state estimated according to the principle of WLS to satisfy Kirchhoff's law, so as to participate in the state estimation calculation of the upper-level branch.

[0030] (4)

[0031] (5)

[0032] Where: k = k1, k2, ... k l , i; k∈j represents all nodes adjacent to node j, but excluding node j itself; W pjk , W pj , W qjk , W qj They represent the weights corresponding to the four types of measurement data: branch active power, injected active power, branch reactive power, and injected reactive power; P jk , P j , Q jk , Q j It indicates the estimated value after estimation; P mjk , P mj , Q mjk , Q mj Represents the measured value corresponding to the estimated value, and solving the above formula yields:

[0033] (6)

[0034] (7)

[0035] Where: It is the estimated value after estimation.

[0036] 4. According to the LL and MM matrices, starting from the end nodes of the 16, 20, 23, and 31 branches at the bottom, the weighted average state estimation is performed on each branch until the top branch 0, and the initial value of the system state is obtained. At this time, the system state is shown in Table 1. The weighted average state estimation ( Figure 3 ) are as follows: For a simple branch, assume that it is a complete measurement system, that is, there is a quantity measurement: V im , V jm , P im , P jm , Q im , Q jm , P jm , Q jm , P jim , Q jim , from the end of the branch, measure V jm , P jim , Q jim Based on the forward flow calculation method, the calculated value V at the head end of the branch can be calculated according to the following formula: ic , P jc , Q jc .

[0037] (8) In the formula is the measured value or the last estimated value of the complex power at the end of the branch, is the measured value or the last estimated value of the branch terminal voltage, Z j is the branch impedance, are the calculated complex voltage and complex power at the head end of the branch respectively.

[0038] Each time, the calculated value and the initial branch head end measurement value are weighted averaged according to formula (9) to obtain a new estimated value, which is used in the calculation of the next level branch.

[0039] (9) Where h f is the estimated value of the point, h mf is the measurement value at the head end, The estimated value of the head end is derived from the end, w f is the weight of the head-end measurement, w t is the weight of the terminal measurement.

[0040] 5. According to the LL and MM matrices, starting from the head end node 0 of the top-level branch 0, the voltage amplitude of each node is corrected with the voltage at the head end and the overall power distribution of the system to obtain the state quantity correction value of the system. The specific results are shown in Table 1.

[0041] 6. According to the correction value of the system state quantity, it is classified and standardized into three types: voltage amplitude, active power, and reactive power, and the weight of each type is corrected by an exponential weight function.

[0042] 7. Compare the system state quantity correction value obtained this time with the system state quantity correction value obtained last time to determine whether they converge. If they converge, exit the loop and calculate the index; if they do not converge, jump to step 4 and perform the next forward back-substitution state estimation until the algorithm converges.

[0043] Table 1 Simulation results

[0044]

[0045] 8. Algorithm Effect

[0046] 8.1 Indicator Definition

[0047] When the robustness function is not considered, in order to evaluate the calculation accuracy of the method, the mean of the whole network objective function, the whole network measurement error statistics and the whole network estimation error statistics are defined.

[0048] (10)

[0049] Where: is the mean of the objective function of the entire network; and are the network-wide measurement error statistics and network-wide estimation error statistics respectively; t is the calculation order; T is the total number of calculations; and S i，t are the estimated and true values ​​of the i-th quantity measured at the t-th calculation, respectively.

[0050] When considering the robustness function, in order to evaluate the robustness performance of the method, the average error of the system and the maximum error of the system are defined.

[0051] (11)

[0052] (12)

[0053] Where: S1 is the average error of the system; S2 is the maximum error of the system; and x i are the estimated value and true value of the i-th state variable respectively.

[0054] 8.2 Simulation Scheme

[0055] When comparing the accuracy of the calculation results, the traditional WLS state estimation method, the complete forward back-substitution state estimation method and the incomplete forward back-substitution state estimation method are compared with the present method without the robustness function; when verifying the accuracy of the calculation results, no bad data is set, and only the measurement error is superimposed according to formula (13).

[0056] (13)z=PF_T(1+N(0, std_error))

[0057] Where PF_T is the power flow calculation value; std_error is the standard deviation of the measurement error. According to different measurement types, voltage amplitudes, standard deviations of injected power and branch power are set to 0.004, 0.01, and 0.008, respectively.

[0058] When comparing the robustness of the calculation results, the traditional WLS robust state estimation with exponential weight function, the complete forward back substitution robust state estimation and the present method containing the robustness function are compared. When setting special bad data, the bad data is the true value of the flow with a threshold of 10-20 times superimposed on it, and the rest of the measured data is the true value of the flow. When setting bad data of different proportions, the bad data is the true value of the flow with a threshold of 10-20 times superimposed on it, and the rest of the measured data is the true value of the flow superimposed on the measurement error.

[0059] Table 2 Various simulation schemes

[0060]

[0061] 8.3 Simulation Results and Analysis

[0062] The simulation results of the accuracy of the calculation results are as follows:

[0063] Table 3 Accuracy indicators of various methods

[0064]

[0065] From the accuracy of the calculation results:

[0066] Since the measurement data of the four methods are all based on the true value of the power flow calculation with the same measurement error superimposed, their full-network measurement errors are the same. Compared with the full-network measurement error, the full-network estimation errors of the four methods are all reduced, indicating that the four methods have a certain filtering effect. The full-network estimation error of this method is higher than that of the traditional WLS method, but it is still lower than the incomplete forward-backward method M3, which uses the least squares method for forward-forward and the power flow back-substitution for back-substitution.

[0067] In summary, the estimation accuracy of the global WLS and the complete forward back substitution state estimation method is equivalent in normal measurement. The estimation accuracy of the method of the present invention is slightly worse than the former two, but still higher than the incomplete forward back substitution method.

[0068] Table 4 Computation time and convergence accuracy of various methods

[0069]

[0070] From the perspective of calculation speed and power flow convergence:

[0071] The power flow convergence accuracy of the least squares method and the method of the present invention both reached 10 -15 The power flow accuracy of the complete forward back generation and the incomplete forward back generation is 10 -5 The reason is that the least squares method has the constraint of the injection power equation, and the algorithm of the present invention has the constraint of node power balance. Although the forward and backward methods have node power balance, when estimating the branch state, there is no constraint of the injection equation, which reduces the convergence accuracy of the power flow.

[0072] From the perspective of calculation speed, the algorithm of the present invention is comparable to the global least squares method and is significantly faster than the other algorithms. This is because the algorithm of the present invention uses power flow calculation. Compared with local state estimation, the number of calculations for each branch is greatly reduced. Compared with the complete forward-backward method, the incomplete forward-backward method only uses branch state estimation when forwarding, so its calculation time is also faster than the complete forward-backward method. As the system scale becomes increasingly complex, the calculation time required for the global least squares method will increase significantly, and the advantage of the method of the present invention in calculation efficiency will become more obvious.

[0073] The simulation results of the robustness performance are as follows:

[0074] When setting special bad data at different positions, it can be seen that when a single bad data or multiple measurement errors at the same node are set, the method of the present invention has excellent error tolerance, because weighted averaging can effectively reduce the impact of the situation where bad data only appears on one side of the branch, and the preprocessing link of the bad data has identified and replaced the obvious bad data. Once multiple measurement errors occur in related branches, the method of the present invention has poor error tolerance, because if both the head and the end of the branch are bad data, the bad data preprocessing cannot be identified, and when the weighted averaging method has bad data at both the head and the end, it will still take the average value according to the relative weights of the measurement data at the head and the end.

[0075] Table 5 Simulation results of special location defect data

[0076]

[0077] After setting different proportions of bad data, it can be seen that in terms of robustness, the method of the present invention has poorer robustness than the traditional WLS robust state estimation method and the full forward back-substitution robustness method. From the perspective of computational efficiency, since there is no need to perform the least squares iteration process, the computational efficiency of the method of the present invention is much faster than the full forward back-substitution robustness method, and as the scale of the system continues to increase, its computational efficiency will be more obvious compared to the traditional WLS robust state estimation.

[0078] Table 6 Simulation results of different proportions of bad data

[0079]

[0080] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A weighted average fast forward back-translation robust state estimation method for a radiation network, characterized by: The following steps are involved: (1) Obtaining basic data of the power grid, which includes the topological structure of the power grid and the measurement information of the power system, including the injected active power and injected reactive power of the node, the voltage amplitude of the node, and the branch active power and branch reactive power at the beginning and end of each branch; (2) Preprocess the basic data of the power grid and replace the obviously erroneous data. The purpose of bad data preprocessing is to first identify some obviously erroneous bad data before state estimation and replace them with correct estimated values; (3) Taking the bottom system branch as the starting point and the top system branch as the end point, a weighted average state estimation is performed on each branch of each layer to obtain the initial state estimation value of the power grid; (4) Taking the top-level system branch as the starting point and the bottom-level system branch as the end point, perform power flow back substitution according to the voltage distribution of the root node and the power distribution of the system, correct the node voltage, and obtain the correction result of the power grid state quantity; (5) According to the correction result of the power grid state quantity, the weight of the measured data is corrected by using an exponential weight function; (6) Determine whether the difference between the current grid state correction result and the previous grid state correction result is less than the set convergence criterion. If converged, end the state estimation, otherwise return to step 3; The specific steps in step 2 are: 2A. According to The power balance of the branch end node is judged. If it is unbalanced, it means that there is bad data at the branch end node. Do not estimate the node power for this node and jump to step 2D, where k h ∈j represents the nodes directly connected to node j, but does not include node j itself; P j , Q j They represent the injected active power and injected reactive power of node j respectively; ε1 represents the upper limit threshold of balance judgment determined according to the measurement type and its reference value; 2B. Perform node power estimation on the node and obtain the head-end estimated value derived from the end-end measured value by the power flow calculation method. The node power estimation process is as follows: 2B1. Establish node power balance equation Where: k = k1, k2, ... k l ; k∈j represents all nodes adjacent to node j, excluding node j itself; w pjk , w pj , w qjk , w qj They represent the weights corresponding to the four types of measurement data: branch active power, injected active power, branch reactive power, and injected reactive power; P jk , P j , Q jk , Q j It indicates the estimated value after estimation; P mjk , P mj , Q mjk , Q mj represents the measured value corresponding to the estimated value; 2B2. Solve the node power balance equation Where: is the estimated value after estimation; 2C, according to the formula and Determine whether the power and voltage amplitudes at the head and end are consistent. If not, it means that there is bad data in the head measurement. Replace it with the estimated value derived from the end and jump to the single branch state estimation. If consistent, it means that there is no bad data at the head and end, and directly perform single branch state estimation, where: and P ij They are respectively the active power at the beginning of the branch derived from the end of the branch and the measured value of the active power at the beginning of the branch; and Q ij They are the reactive power at the beginning of the branch derived from the end of the branch and the measured reactive power at the beginning of the branch; ε2 represents the upper limit threshold of balance judgment determined according to the power measurement type and its reference value. The method for determining the upper limit of the threshold is as follows: Where: ε is the upper threshold of different measurement types; E is the estimated value error rate allowed for different measurement types, which must meet the requirements of active power not exceeding 2%, reactive power not exceeding 3%, voltage of 220kV and above not exceeding 0.5%, voltage below 220kV not exceeding 2%, Z B is the system reference value of voltage or power, z base is the estimated value error rate reference value determined by the voltage or power system reference value; 2D, obtain the head-end estimated value derived from the terminal measurement value through the power flow calculation method; 2E, according to the formula and Determine whether the power at the head and the end is consistent. If it is consistent, and the lower branches of the end node have no bad data or have been replaced, it means that the injection power of the end node is wrong. After replacing it, perform single branch state estimation; The specific steps of weighted average state estimation in step 3 are as follows: 3A. Based on the measured data at the end of the branch, the flow method is used Calculate the calculated value of the branch head end, where is the measured value or the last estimated value of the complex power at the end of the branch, is the measured value or the last estimated value of the branch terminal voltage, Z ij is the branch impedance, are the calculated complex voltage and complex power at the head end of the branch respectively; 3B. The calculated value at the end and the measured value at the end are calculated according to the formula Perform weighted averaging to obtain the estimated value of the branch head end, where h f is the estimated value of the point, h mf is the measurement value at the head end, The calculated value of the head end is derived from the end end, w f is the weight of the head-end measurement, w t is the weight of the terminal measurement; In step 4, according to the formula Perform tidal back generation; The step 5 includes: 5A. Model establishment of exponential weight function. The model of exponential weight function is as follows: In the formula is the updated weight, is the initial fixed weight, r N is the standardized residual; 5B. Measurement classification and standardization. According to the measurement type, the residual dz is divided into three types: voltage type measurement residual dz_V, active power type measurement residual dz_P, and reactive power type measurement residual dz_Q. Assuming that the three types of measurement residuals all satisfy the normal distribution, the above three types of residuals are divided by the standard deviation of the corresponding type to obtain the standardized residual rN , and then according to the standardized residual r N , an exponential weight function is used to obtain the correction weight of each measurement value.

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