Fast formation method of state estimation information matrix based on non-sparse matrix technique

Abstract

The application discloses a fast forming method of state estimation information matrix based on non-sparse matrix technology, which does not change the data structure and main method flow of power system state estimation, does not adopt complex sparse matrix technology, only redesigns the flow of multiplication of three matrices of transpose H T , weight matrix R ‑1 and Jacobian matrix H, and adopts appropriate zero elimination operation, greatly improves the speed of calculating information matrix (H T R ‑1 H) of basic weighted least square method state estimation method, and further improves the calculation speed of state estimation. The implementation example shows that the fast forming method of state estimation information matrix based on non-sparse matrix technology provided by the application significantly reduces the calculation time of power system state estimation. The designed information matrix calculation method can be applied to large-scale power systems, and is more suitable for researchers to use due to the fact that the method does not involve sparse matrix technology.

Description

Technical Field

[0001] This invention relates to a state estimation method for power systems, and more particularly to a method for rapidly generating a state estimation information matrix based on non-sparse matrix technology. Background Technology

[0002] State estimation is a crucial component of the energy management system (EMS) used by power system dispatching departments. As the scale of the power grid increases year by year, the level of automation in the power system also rises. To ensure the safe and economical operation of the power system, modern power dispatching systems are required to accurately, rapidly, and comprehensively grasp the actual operating status of the power system. This information is used to analyze the current operating status of the system, predict its operating trends, and promptly propose solutions and formulate subsequent operational plans for various problems that occur during operation.

[0003] To monitor the operating status of the power system, measuring units are installed at various power plants and substations to acquire real-time data on various electrical quantities. This real-time data, known as measurement data, is transmitted to the power grid dispatch center via various communication methods. However, due to some limitations of measurement data, the state of the power system cannot be directly determined based on it. Measurement data has the following two shortcomings:

[0004] (1) Incomplete measurement data. The measurement data does not include all the data of the power grid; only a portion of the power grid data was collected.

[0005] (2) Inaccurate measurement data. The real-time data obtained by the power grid dispatch center is transmitted through remote control devices such as sensors and converters. There are errors in each link of data acquisition, transformation and communication, and there is interference of varying degrees. Therefore, these data are not absolutely reliable, and may even have large errors.

[0006] Due to the aforementioned shortcomings, directly using these measurement data to analyze the state of the power system is clearly unreliable and cannot meet the requirements of power grid dispatching. Measurement data cannot be used directly; it must be processed to supplement missing data, eliminate highly erroneous data, and estimate the best value that most closely approximates the actual system, thus reducing the impact of errors before it can be used. This processing is called state estimation.

[0007] The most basic analytical method for state estimation is the basic weighted least squares method, which uses the least squares criterion to minimize the objective function.

[0008] The principle of basic weighted least squares state estimation is as follows:

[0009] Let the power system measurement equations be:

[0010] z = h(x) + v (1)

[0011] In the formula, z is an m-dimensional measurement vector; x is a 2N-1-dimensional state variable vector (composed of the voltage amplitude and voltage phase angle of each node except the voltage phase angle of the reference node); h(x) is an m-dimensional measurement function vector, and the calculated value of the measurement function is the estimated value of the measurement; v is an m-dimensional measurement error vector; N is the number of nodes in the power system; and m is the number of measurements.

[0012] The measurements include branch active power measurement, branch reactive power measurement, node injected active power measurement, node injected reactive power measurement, and node voltage amplitude measurement.

[0013] Given a measurement z, we need to find a set of state variables x such that the sum of squares of the weighted residuals (the residuals are the differences between the measurement and the measurement estimate) is minimized.

[0014] Let the objective function be:

[0015] J(x)=[zh(x)] T R -1 [zh(x)] (2)

[0016] In the formula, R -1 This is the measurement weight matrix.

[0017] The measurement weight matrix is ​​a diagonal matrix, and its diagonal elements are chosen to be the reciprocals of the measurement variance, i.e.:

[0018]

[0019] In the formula, The weight for measuring the i-th quantity. Let be the variance of the measurement of the i-th quantity.

[0020] The least squares method aims to minimize the objective function J(x). Since h(x) is a set of nonlinear functions, x cannot be calculated directly; therefore, Newton's method can be used for iterative solution.

[0021] According to Newton's method, the obtained state estimate is in the value x. (t) The corrected equation is:

[0022] H T (x (t) )R -1 H(x (t) )Δx=H T (x (t) )R -1 [zh(x (t) (4)

[0023] In the formula, The Jacobian matrix H of the measurement function vector at x = x (t) The value of H has a dimension of m×(2N-1), and the superscript T indicates transpose; T R -1 H is called the information matrix.

[0024] The iterative formula is as follows:

[0025] Δx (t) =[H T (x (t) )R -1 H(x (t) )] -1 H T (x (t) )R -1 [zh(x (t) (5)

[0026] x (t+1) =x (t) +Δx (t) (6)

[0027] In the formula, the superscript (t) indicates the t-th iteration.

[0028] Iterative corrections are made according to equations (5) and (6) until... Until then (ε is the convergence precision), the best estimate is obtained, which makes the objective function J(x) equal to the sum of its parts. (t) (To obtain the minimum value)

[0029] like Figure 1 and Figure 2 As shown, the conventional basic weighted least squares state estimation method includes the following steps:

[0030] A. Read network data and measurement data.

[0031] B. Voltage initialization: Set the voltage amplitude of each node to the initial given value of the reference node voltage amplitude, and the voltage phase angle to 0.

[0032] C. Set the iteration count t = 0.

[0033] D. Forming the Jacobian matrix H(x) (t) ) and measurement function vector h(x) (t) ).

[0034] E. Calculate the vector H on the right-hand side of the corrected equation. T (x (t) )R -1 (zh(x (t) )).

[0035] F. Forming the information matrix H T (x(t) )R -1 H(x (t) ).

[0036] Forming the information matrix H T (x (t) )R -1 H(x (t) The steps are as follows:

[0037] F1. Clear array G;

[0038] F2, Let i = 1;

[0039] F3, Let j = 1;

[0040] F4. Let k = 1;

[0041] F5. Calculate the information matrix element G according to formula (7). ij :

[0042]

[0043] In the formula, H ki The Jacobian matrix H(x) (t) The element in the k-th row and i-th column of ); It is the measurement weight matrix R -1 The element in the kth row and kth column.

[0044] F6. Let k = k + 1;

[0045] F7. Determine if k is greater than the measured number m. If k is not greater than m, proceed to step F5; otherwise, proceed to step F8.

[0046] F8. Let j = j + 1;

[0047] F9. Determine if j is greater than the number of state variables n. If j is not greater than n, proceed to step F4; otherwise, proceed to step F10.

[0048] F10. Let i = i + 1;

[0049] F11. Determine if i is greater than the number of state variables n. If i is not greater than n, proceed to step F3; otherwise, proceed to step G.

[0050] G. Form the state estimation correction equation shown in equation (4), and solve equation (4) to find Δx. (t) And find the maximum correction amount |Δx max |

[0051] H. Determine the maximum correction amount |Δx max |Is it less than the convergence accuracy ε? If it is less than the convergence accuracy ε, go ​​to step J; otherwise, correct the state variables according to equation (8) and go to step I.

[0052] x (t+1) =x (t) +Δx (t) (8)

[0053] In the formula, the superscript (t) indicates the t-th iteration; Δx is the column vector of state variable corrections.

[0054] I. Let t = t + 1, and return to step D for the next iteration;

[0055] J. Output the state estimation results and end.

[0056] The basic weighted least squares (BLS) state estimation method has a long computation time. Therefore, for the state estimation of very large power systems, fast decomposition state estimation methods using sparse matrix techniques are often employed. The BLS method shows better convergence when dealing with power systems with ill-conditioned conditions. To improve the computation speed of the BLS method, sparse matrix techniques can be used. However, sparse matrix techniques are complex, and program modification, debugging, and adding new functions are difficult, making them unsuitable for research purposes. Furthermore, even with sparse matrix techniques, the computation time for state estimation remains long. A major reason for the long computation time of the BLS method is the significant time required to form the information matrix, which consumes the majority of the computation time. Therefore, significantly reducing the information matrix formation time in the BLS method is a crucial measure. Summary of the Invention

[0057] To address the aforementioned problems in existing technologies, this invention proposes a rapid method for forming a state estimation information matrix based on non-sparse matrix technology. This method significantly reduces the time required to form the information matrix, thereby improving the computational speed of the basic weighted least squares state estimation method.

[0058] To achieve the above objectives, the technical solution of the present invention is as follows: a method for rapidly forming a state estimation information matrix based on non-sparse matrix technology, comprising the following steps:

[0059] A. Read network data and measurement data;

[0060] B. Voltage initialization: Set the voltage amplitude of each node to the initial given value of the reference node voltage amplitude, and the voltage phase angle to 0.

[0061] C. Set the iteration count t = 0;

[0062] D. Forming the Jacobian matrix H(x) (t) ) and measurement function vector h(x) (t) );

[0063] E. Calculate the vector H on the right-hand side of the corrected equation. T (x (t) )R -1 (zh(x (t) )).

[0064] z is an m-dimensional measurement vector; h(x) (t) Let be an m-dimensional measurement function vector, where the calculated value of the measurement function is the estimated value of the measurement; the superscript (t) indicates the t-th iteration; The Jacobian matrix H of the measurement function vector at x = x (t) The value of R is m×(2N-1); the superscript T indicates transpose; -1 is the measurement weight matrix; x is a 2N-1 dimensional state variable vector (composed of the voltage magnitude and voltage phase angle of each node except the voltage phase angle of the reference node); N is the number of nodes in the power system; m is the number of measurements;

[0065] F. Forming the information matrix H T (x (t) )R -1 H(x (t) );

[0066] Forming the information matrix H T (x (t) )R -1 H(x (t) The steps are as follows:

[0067] F1. Clear array G;

[0068] F2, Let i = 1;

[0069] F3, Let k = 1;

[0070] F4. Determine the elements H of the Jacobian matrix. ki Is it equal to 0? If H ki If the result is 0, proceed to step F10; otherwise, proceed to step F5.

[0071] F5, Command

[0072]

[0073] In the formula, H ki The Jacobian matrix H(x) (t) The element in the k-th row and i-th column of ); It is the measurement weight matrix R -1 The element in the kth row and kth column.

[0074] F6. Let j = 1;

[0075] F7. Calculate the information matrix element G according to formula (10). ij:

[0076] G ij =G ij +A·H kj (10)

[0077] F8. Let j = j + 1;

[0078] F9. Determine if j is greater than the number of state variables n. If j is not greater than n, go to step F7; otherwise, go to step F10.

[0079] F10, Let k = k + 1;

[0080] F11. Determine if k is greater than the measured number m. If k is not greater than m, proceed to step F4; otherwise, proceed to step F12.

[0081] F12. Let i = i + 1;

[0082] F13. Determine if i is greater than the number of state variables n. If i is not greater than n, proceed to step F3; otherwise, proceed to step G.

[0083] G. Form the state estimation correction equation shown in equation (4), and solve equation (4) to find Δx. (t) And find the maximum correction amount |Δx max |

[0084] H. Determine the maximum correction amount |Δx max |Is it less than the convergence accuracy ε? If it is less than the convergence accuracy ε, go ​​to step J; otherwise, correct the state variables according to equation (11) and go to step I.

[0085] x (t+1) =x (t) +Δx (t) (11)

[0086] In the formula, Δx is the column vector of state variable corrections.

[0087] I. Let t = t + 1, and return to step D for the next iteration;

[0088] J. Output the state estimation results and end.

[0089] Compared with the prior art, the present invention has the following beneficial effects:

[0090] This invention, without altering the data structure and main methodology of power system state estimation, and without employing complex sparse matrix techniques, significantly reduces the time required to form the information matrix simply by redesigning the multiplication process of three matrices and using appropriate zero-removal operations. This, in turn, improves the computational speed of the basic weighted least squares state estimation method. Implementation examples demonstrate that this invention can substantially increase the speed of information matrix formation and significantly reduce the computation time for power system state estimation. Therefore, the basic weighted least squares state estimation method designed in this invention is not only applicable to large-scale power systems, but also, because it does not involve sparse matrix techniques, is more suitable for research use by scientific and technical personnel. Attached Figure Description

[0091] This invention has a total of appendices Figure 3 Zhang, of which:

[0092] Figure 1 This is a flowchart of the basic weighted least squares state estimation method.

[0093] Figure 2 This is a flowchart of how existing technologies form an information matrix.

[0094] Figure 3 This is a flowchart of the information matrix formation process of the present invention. Detailed Implementation

[0095] The invention will now be further described with reference to the accompanying drawings.

[0096] Using existing technologies and this invention, a calculation was performed on a 445-node power system example. The branch power measurement was simulated by adding a certain error to the power flow calculation results of transmission lines and transformers in the 445-node power system example. A voltage measurement was also performed. The active power error for all branches was set to +0.02 (nominal value +2MW), and the reactive power error to +0.05 (nominal value +5Mvar). The convergence accuracy was 0.00001, the unit was per unit, the weight was set to 1.0, the number of state variables was 889, and the number of measurements was 2385. Both methods used the basic weighted least squares state estimation method, achieving convergence after 7 iterations. The total computation time for the existing technology was 92.74 seconds, while the total computation time for this invention was 0.49 seconds. The hardware environment was a Lenovo ThinkPad X390 laptop with an Intel Core i5-10210U 1.60GHz CPU and 8GB of RAM. The code was written in C++, using VC++ 6.0 as the programming environment, and a Release version was generated for execution. Table 1 shows the calculation time and information matrix formation time for each iteration of both methods.

[0097] Table 1 shows the calculation time and information matrix formation time for each iteration of different estimation methods.

[0098]

[0099] As can be seen from Table 1, the calculation time of the information matrix in the prior art is very long, taking up most of the time in each iteration, while the calculation time of the information matrix in this invention is very short, accounting for less than half of the time in each iteration.

[0100] This invention can be implemented using any programming language and environment, such as C, C++, FORTRAN, Delphi, etc. Development environments can include Visual C++, Borland C++Builder, Visual FORTRAN, etc.

[0101] This invention is not limited to this embodiment. Any equivalent concept or modification within the technical scope disclosed in this invention shall be included within the protection scope of this invention.

Claims

1. A method for rapidly generating a state estimation information matrix based on non-sparse matrix techniques, characterized in that: Includes the following steps: A. Read network data and measurement data; B. Voltage initialization: Set the voltage amplitude of each node to the initial given value of the reference node voltage amplitude, and the voltage phase angle to 0. C. Set the iteration count t = 0; D. Forming the Jacobian matrix H(x) (t) ) and measurement function vector h(x) (t) ); E. Calculate the vector H on the right-hand side of the corrected equation. T (x (t) )R -1 (zh(x (t) )); z is an m-dimensional measurement vector; h(x) (t) Let be an m-dimensional measurement function vector, where the calculated value of the measurement function is the estimated value of the measurement; the superscript (t) indicates the t-th iteration; The Jacobian matrix H of the measurement function vector at x = x (t) The value of R is m×(2N-1); the superscript T indicates transpose; -1 is the measurement weight matrix; x is a 2N-1 dimensional state variable vector (composed of the voltage magnitude and voltage phase angle of each node except the voltage phase angle of the reference node); N is the number of nodes in the power system; m is the number of measurements; F. Forming the information matrix H T (x (t) )R -1 H(x (t) ); Forming the information matrix H T (x (t) )R -1 H(x (t) The steps are as follows: F1. Clear array G; F2, Let i = 1; F3, Let k = 1; F4. Determine the elements H of the Jacobian matrix. ki Is it equal to 0? If H ki If the value is 0, proceed to step F10; Otherwise, proceed to step F5; F5, Command In the formula, H ki The Jacobian matrix H(x) (t) The element in the k-th row and i-th column of ); It is the measurement weight matrix R -1 The element in the k-th row and k-th column; F6. Let j = 1; F7. Calculate the information matrix element G according to formula (2). ij G ij =G ij +A·H kj (2) F8. Let j = j + 1; F9. Determine if j is greater than the number of state variables n. If j is not greater than n, go to step F7; otherwise, go to step F10. F10, Let k = k + 1; F11. Determine if k is greater than the measured number m. If k is not greater than m, proceed to step F4; otherwise, proceed to step F12. F12. Let i = i + 1; F13. Determine if i is greater than the number of state variables n. If i is not greater than n, proceed to step F3; otherwise, proceed to step G. G. Form the state estimation correction equation shown in equation (3), and solve equation (3) to find Δx. (t) And find the maximum correction amount |Δx max |; H T (x (t) )R -1 H(x (t) )Δx=H T (x (t) )R -1 [z-h(x (t) )] (3) H. Determine the maximum correction amount |Δx max |Is it less than the convergence accuracy ε? If it is less than the convergence accuracy ε, go ​​to step J; otherwise, correct the state variables according to equation (4) and go to step I. x (t+1) =x (t) +Δx (t) (4) In the formula, Δx is the column vector of state variable corrections; I. Let t = t + 1, and return to step D for the next iteration; J. Output the state estimation results and end.

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