Method for forming elements of line measurement jacobian matrix for fast decoupled state estimation

Abstract

This invention discloses a method for forming the Jacobian matrix elements of line measurements using a fast decomposition method for state estimation. When the p-th measurement is a reactive power measurement at the line's starting node i, if the line-to-ground susceptance b... c =0, Q-U type constant Jacobian matrix B r element B in row p and column i r.pi The traditional method is multiplied by a correction factor α, where α is related to the scale and structure of the power system and ranges from [1.001, 1.100]. If b c B is not 0 r Element B r.pi Add a correction factor of 3b to the traditional method. c This invention measures reactive power at the line start-up end by multiplying the Jacobian matrix elements by a correction factor α or adding a correction amount 3b. c This invention improves the calculation method of the Jacobian matrix for line reactive power measurement in fast decomposition state estimation, effectively improving the convergence of state estimation. Implementation examples demonstrate that this invention significantly improves convergence and substantially reduces the number of iterations in power system state estimation.

Description

Technical Field

[0001] This invention relates to a state estimation method for power systems, and more particularly to a method for forming the Jacobian matrix elements for reactive power measurement of transmission lines in a fast decomposition state estimation. Background Technology

[0002] State estimation is a crucial component of the energy management system (EMS) used by power system dispatching departments. To ensure the safe and economical operation of the power system, modern power dispatching systems must accurately, rapidly, and comprehensively grasp the actual operating status of the power system. This information is used to analyze the current system operating status, predict system 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 the following problems with measurement data, the state of the power system cannot be directly determined based on it:

[0004] (1) Incomplete measurement data. The measurement data does not include all the data of the power grid; some data was not 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 system's state 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 closest to the actual system, thus reducing the impact of errors before it can be used. This processing is called state estimation.

[0007] The most commonly used algorithms for power system state estimation are the basic weighted least squares method and the fast decomposition state estimation method. Because the basic weighted least squares method requires a large amount of memory and has a long computation time, the fast decomposition state estimation method is often used in practical systems.

[0008] Let the power system measurement equations be:

[0009] z = h(x) + v (1)

[0010] 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.

[0011] 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.

[0012] Power system branches include transmission lines and transformers. Figure 2 This is the equivalent circuit of a transmission line, with parameters including resistance r, reactance x, and susceptance to ground b. c . Figure 3 This is the equivalent circuit of a transformer, with parameters including resistance r, reactance x, and a non-standard turns ratio k. Resistance r and reactance x are located on the first node i side, and the non-standard turns ratio k is located on the last node j side. The impedance of the branch is r + jx.

[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 represents the measurement weight matrix.

[0017] The principle of solving equation (2) using the fast decomposition state estimation method is as follows:

[0018] The state variables are divided into two categories: voltage phase angle and voltage magnitude, as follows:

[0019]

[0020] In the formula, δ is n a 1D node voltage phase angle column vector; U is an n-dimensional node voltage phase angle column vector; r n-dimensional column vector of node voltage magnitudes; a n is the number of voltage phase angle state variables; r This represents the number of state variables for voltage amplitude.

[0021] Measurement vectors are classified into the following two categories:

[0022]

[0023] In the formula, z a For m a The active power quantity measurement column vector includes branch active power measurements and node injected active power measurements for transmission lines and transformers; z r For m r The reactive power measurement column vector includes measurements of branch reactive power of transmission lines and transformers, measurements of node injected reactive power, and measurements of node voltage amplitude; m a The number of active power quantities measured; m r The number of reactive power quantities measured.

[0024] The measurement weight matrix R -1 They are also classified into active and reactive categories as follows:

[0025]

[0026] In the formula, For the corresponding z a m a A weighted diagonal matrix; For the corresponding z r m r A diagonal matrix of order weights.

[0027] Similarly, measurement functions are divided into the following two categories:

[0028]

[0029] In the formula, h a For the corresponding z a The measurement function; h r For the corresponding z r The measurement function.

[0030] Since h(x) is a set of nonlinear functions, x cannot be directly calculated. We linearize h(x) and consider the characteristics of the power system, performing P-Q decoupling to obtain two sets of corrected equations: P-δ iteration and QU iteration. These are the iterative corrected equations for the fast decomposition state estimation shown below:

[0031] AΔδ (t) =a (t) (7)

[0032] CΔU (t) =c (t) (8)

[0033] In the formula, A is n a ×n a The active information matrix of order n; a is an n-order matrix. a dimensional active free vector; C is an n-dimensional free vector. r ×n r The reactive power information matrix is ​​of order n; c is an n-order matrix.r The reactive free vector is given by the following formula:

[0034]

[0035]

[0036]

[0037]

[0038] In the formula, B a For m a ×n a B-δ type constant Jacobian matrix; r For m r ×n r A QU-type constant Jacobian matrix; U0 is the initial given value of the reference node voltage magnitude.

[0039] For the measurement of active power injected into nodes, B a B is the imaginary part of the nodal admittance matrix; for branch active power measurement, B a This represents the imaginary part of the nodal admittance matrix for this branch. For the measurement of nodal injected reactive power, B... r B is the imaginary part of the nodal admittance matrix; for branch reactive power measurement, B r Take the imaginary part of the node admittance matrix of this branch; if the p-th quantity is a measurement of the node voltage magnitude of node i, then B r The element in the p-th row and i-th column is -1 / U0, B r All other elements in row p are 0.

[0040] In traditional fast decomposition state estimation, in order to improve convergence, B a This is the imaginary part of the node admittance matrix formed using only branch reactances, ignoring the non-standard transformer ratio, transmission line-to-ground capacitance, and branch resistance, which have little impact on the active power distribution.

[0041] like Figure 1 As shown, the traditional fast decomposition state estimation method includes the following steps:

[0042] A. Read network data and measurement data.

[0043] B. Forming a QU-type constant Jacobian matrix B r .

[0044] For branch reactive power measurement and node injected reactive power measurement, B r Take the imaginary part of the admittance matrix; if the p-th quantity is a measurement of the node voltage magnitude at node i, then B rThe element in the p-th row and i-th column is -1 / U0, B r All other elements in row p are 0.

[0045] C. Forming P-δ type constant Jacobian matrices B a .

[0046] B a This is the imaginary part of the admittance matrix formed using only branch reactances, neglecting the non-standard transformer ratio, transmission line-to-ground capacitance, and branch resistance, which have little impact on the active power distribution.

[0047] D. 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.

[0048] E. Form information matrices A and C of the fast decomposition state estimation correction equation and perform triangular decomposition.

[0049] F. Set the iteration count t = 0, and set Δδ max =5ε δ ΔU max =5ε U .

[0050] G. Determine whether the maximum voltage amplitude correction value |ΔU is satisfied. max | Less than the convergence accuracy ε U And the maximum correction amount of voltage phase angle |Δδ max | Less than the convergence accuracy ε δ If the condition is met, proceed to step M; otherwise, proceed to step H.

[0051] H. Calculate the active free vector a (t) Solve equation (7) to find Δδ (t) And find the maximum correction amount of voltage phase angle |Δδ max |

[0052] I. Correct the voltage phase angle according to formula (13);

[0053] δ (t+1) =δ (t) +Δδ (t) (13)

[0054] In the formula, the superscript (t) indicates the t-th iteration; Δδ is the column vector of node voltage phase angle correction.

[0055] J. Calculate the reactive free vector c (t) Solve equation (8) to find ΔU (t) And find the maximum correction amount of voltage amplitude |ΔU max |

[0056] K. Correct the voltage amplitude according to formula (14);

[0057] U (t+1) =U (t) +ΔU (t) (14)

[0058] In the formula, the superscript (t) indicates the t-th iteration; ΔU is the column vector of node voltage magnitude correction.

[0059] L. Let t = t + 1, and return to step G for the next iteration;

[0060] M, Output the state estimation result, then end.

[0061] While the fast decomposition state estimation method (FDSE) significantly reduces computation time compared to the basic weighted least squares (BLS) method in most cases, it may diverge when only branch power measurements are available in the power system. To improve convergence performance, the reference node voltage magnitude is typically excluded from the estimation process. This is because the initial value of the reference node voltage magnitude may be merely an initial value or a measurement with some error, making it unsuitable as a known quantity. Therefore, the convergence of the FDSE method still needs further improvement.

[0062] To address this issue, Chinese Patent 202111657954.6 (A Method for Forming the Jacobian Matrix of Transmission Line Measurements in Fast Decomposition State Estimation) proposes a method for forming the Jacobian matrix of transmission line measurements in fast decomposition state estimation. This method adds the partial derivative of the reactive power measurement of the transmission line with respect to the voltage on the power inflow side to the ground susceptance b of the π-shaped equivalent circuit of the transmission line. c Using three times the value of the corresponding Jacobian matrix element improves the convergence performance and computation speed of power system state estimation.

[0063] Although the method in Chinese Patent 202111657954.6 improves the method for forming the Jacobian matrix of transmission line measurements and enhances the convergence performance of power system state estimation, it still has limitations when the transmission line's ground susceptance b... c When the value is 0, the improved method has no effect on these transmission lines, affecting the convergence performance improvement of power system state estimation. Summary of the Invention

[0064] To address this problem, this invention proposes a method for forming the Jacobian matrix elements of line measurements using a fast decomposition method for state estimation, regardless of the transmission line's susceptance to ground (b). c Whether the value is 0 or not, it can improve the convergence performance of power system state estimation.

[0065] To achieve the above objectives, the technical solution of the present invention is as follows: a method for forming the Jacobian matrix elements of line measurement for state estimation using the fast decomposition method, comprising the following steps:

[0066] A. Read network data and measurement data;

[0067] B. Forming a QU-type constant Jacobian matrix B r ;

[0068] Formation B r The steps are as follows:

[0069] B1. Formed using traditional methods r ;

[0070] For the measurement of reactive power injected at nodes, B r Take the imaginary part of the nodal admittance matrix; for branch reactive power measurement, B r Take the imaginary part of the node admittance matrix of this branch; if the l-th quantity is a measurement of the node voltage magnitude of node i, then B r The element in the l-th row and i-th column is -1 / U0, B r All other elements in the l-th row are 0;

[0071] B2. Set the quantity measurement count p = 1;

[0072] B3. Take the type T of the measurement for the p-th quantity;

[0073] B4. Determine whether the measurement type T is the reactive power measurement type at the beginning of the transmission line. If it is not the reactive power measurement type at the beginning of the transmission line, proceed to step B9.

[0074] B5. Take the p-th quantity and measure the first node number i and the ground susceptance b of the corresponding transmission line. c ;

[0075] B6. Determine the susceptance to ground (b) c Is it 0? If b c If the value is 0, proceed to step B8;

[0076] B7. Correct matrix B according to equation (15). r element B in row p and column i r.pi Proceed to step B9;

[0077] B r.pi =B r.pi +3b c (15)

[0078] In the formula, b c The susceptance to ground of the π-shaped equivalent circuit of the transmission line;

[0079] B8. Correct matrix B according to equation (16). r element B in row p and column i r.pi ;

[0080] B r.pi =αB r.pi (16)

[0081] In the formula, α is a correction coefficient, which is related to the scale and structure of the power system, and its value ranges from [1.001, 1.100].

[0082] B9. Let p = p + 1;

[0083] B10. Determine if p is greater than the number of measurements m. If p is greater than the number of measurements m, proceed to step C; otherwise, return to step B3 for the next iteration.

[0084] C. Forming P-δ type constant Jacobian matrices B a ;

[0085] For the measurement of active power injected into nodes, B a The imaginary part of the nodal admittance matrix is ​​formed using only branch reactances, neglecting the non-standard transformer ratios, transmission line-to-ground capacitance, and branch resistance, which have little impact on active power distribution; for branch active power measurement, B a This is the imaginary part of the node admittance matrix formed using only the reactance of this branch, ignoring the non-standard transformer ratio, transmission line-to-ground capacitance, and branch resistance, which have little impact on the active power distribution.

[0086] D. Voltage initialization: Set the voltage amplitude of each node to the initial given value U0 of the reference node voltage amplitude, and the voltage phase angle to 0.

[0087] E. Form information matrices A and C of the fast decomposition state estimation correction equation and perform triangular decomposition;

[0088]

[0089] In the formula, A is n a ×n a n-order active information matrix; a The number of node voltage phase angle state variables;

[0090]

[0091] In the formula, C is n r ×n r n-order reactive power information matrix; r The number of state variables representing the node voltage magnitude;

[0092] F. Set the iteration count t = 0, and set Δδ max=5ε δ ΔU max =5ε U ;

[0093] G. Determine whether the maximum voltage amplitude correction value |ΔU is satisfied. max | Less than the convergence accuracy ε U And the maximum correction amount of voltage phase angle |Δδ max | Less than the convergence accuracy ε δ If the condition is met, proceed to step M; otherwise, proceed to step H.

[0094] H. Calculate the active free vector a (t) Solve equation (19) to find Δδ (t) And find the maximum correction amount of voltage phase angle |Δδ max |;

[0095] AΔδ (t) =a (t) (19)

[0096] In the formula, a is n a 1. Active free vector; Δδ is the column vector of node voltage phase angle correction; the superscript (t) indicates the t-th iteration;

[0097]

[0098] In the formula, B a For m a ×n a A P-δ type constant Jacobian matrix; z a For m a The active power quantity measurement column vector includes active power quantity measurements of transmission lines and transformer branches, and active power quantity measurements injected into nodes; h a For the corresponding z a Measurement function; For the corresponding z a m a The weight diagonal matrix of order n; δ is an n-order weighted matrix. a 1D node voltage phase angle column vector; U is an n-dimensional node voltage phase angle column vector; r dimensional column vector of node voltage magnitudes; m a The number of active quantity measurements;

[0099] I. Correct the voltage phase angle according to formula (21);

[0100] δ (t+1) =δ (t) +Δδ (t) (twenty one)

[0101] J. Calculate the reactive free vector c (t) Solve equation (22) to find ΔU(t) And calculate the maximum correction amount of voltage amplitude |ΔUmax|;

[0102] CΔU (t) =c (t) (twenty two)

[0103] In the formula, ΔU is the column vector of node voltage magnitude correction; c is the n r The reactive free vector is calculated using the following formula:

[0104] c (t) =U0(-B r ) T R r -1 [z r -h r (δ (t) U (t) )] (twenty three)

[0105] In the formula, B r For m r ×n r QU-class constant Jacobian matrix; z r For m r The reactive power measurement column vector includes measurements of branch reactive power of transmission lines and transformers, measurements of node injected reactive power, and measurements of node voltage amplitude; h r For the corresponding z r Measurement function; For the corresponding z r m r Order-order weight diagonal matrix; m r Number of reactive power quantities measured;

[0106] K. Correct the voltage amplitude according to formula (24);

[0107] U (t+1) =U (t) +ΔU (t) (twenty four)

[0108] L. Let t = t + 1, and return to step G for the next iteration;

[0109] M, Output the state estimation result, then end.

[0110] The following analysis examines the divergence mechanism of the existing rapid decomposition state estimation method and the convergence of the invented method.

[0111] In the existing rapid decomposition state estimation technology, when the ground susceptance of the transmission line is b c When the value is 0, the several measurement equations formed by the reactive power measurement of the transmission line are linearly correlated, which may lead to divergence in the state estimation. The analysis is as follows:

[0112] The state estimation is performed by solving the measurement equations using the least squares method. The least squares method can ensure that the residuals of each measurement equation are not large. Therefore, the convergence performance of the state estimation can be qualitatively analyzed using the solution obtained by directly solving the measurement equations.

[0113] In equation (1), neglecting error, the measurement equation is:

[0114] z = h(x) (25)

[0115] h(x) is a nonlinear function. Let h(x) be initialized to x. (0) After performing a Taylor series expansion at the given point and ignoring terms of second degree and above, we obtain equation (26):

[0116] h(x)=h(x (0) )+H(x (0) )Δx (0) (26)

[0117] In the formula, the value of the Jacobian matrix is... The partial derivative of the measurement function h(x) with respect to the state variable x is given by... (0) The value at that location.

[0118] Substituting equation (26) into equation (25), we get:

[0119] H(x (0) )Δx (0) =zh(x (0) )=μ(x (0) (27)

[0120] In the formula, μ is the residual.

[0121] The following analysis, based on equation (27), examines the impact of the magnitude of the state variable correction on the convergence of the state estimation during the first iteration. For ease of explanation, equation (27) is simplified as follows:

[0122] HΔx=μ (28)

[0123] For transmission lines, refer to Figure 2 The equivalent circuit shown illustrates the measurement of reactive power Q at the beginning of the transmission line. ij and terminal reactive power measurement Q ji The corresponding Jacobian matrix elements are:

[0124]

[0125] In the formula, b ij =-x / (r 2 +x 2 () represents the branch susceptance of the transmission line.

[0126] When the equivalent measurement is of the reactive power measurement type at the head end of the transmission line, the measurement equation for state estimation is:

[0127] -U0(b ij +b c )ΔU i +U0b ij ΔU j =μ i (30)

[0128] When the equivalent measurement is of the reactive power measurement type at the end of the transmission line, the measurement equation for state estimation is:

[0129] U0b ij ΔU i -U0(b ij +b c )ΔU j =μ j (31)

[0130] When the ground susceptance of the transmission line is b c When =0, equations (30) and (31) are:

[0131] -U0b ij ΔU i +U0b ij ΔU j =μ i (32)

[0132] U0b ij ΔU i -U0b ij ΔU j =μ j (33)

[0133] It can be seen that equations (32) and (33) are linearly related, with only one independent equation. The residual μ in equation (32) i The residual μ in equation (33) j Smaller, U0 is approximately equal to 1, |b ij |If it is relatively large, then:

[0134] ΔU i ≈ΔU j (34)

[0135] Therefore, as long as equation (34) holds, equations (32) and (33) will also hold, and ΔU i and ΔU j The value of needs to be solved by combining equation (32) or equation (33) with other equations, which may be very large, leading to divergence in state estimation.

[0136] Chinese Patent 202111657954.6 adds a correction factor 3b to the deflection of the reactive power measurement of transmission lines to the voltage on the power inflow side. c As corresponding Jacobian matrix elements, this avoids the linear correlation of the measurement equations corresponding to reactive power measurements in transmission line branches. However, when b c When = 0, since the added correction is 0, it can be seen that the measurement equation corresponding to the reactive power measurement of the transmission line branch is still linearly related. Therefore, the ground susceptance b of the transmission line is... c When =0, Chinese Patent 202111657954.6 cannot improve the convergence of state estimation.

[0137] b c When = 0, for the reactive power measurement type at the beginning of the transmission line, the measurement equation for state estimation in this invention is:

[0138] -αU0b ij ΔU i +U0b ij ΔU j =μ i (35)

[0139] For reactive power measurement types at the end of transmission lines, the measurement equation for state estimation is:

[0140] U0b ij ΔU i -U0b ij ΔU j =μ j (36)

[0141] It can be seen that equations (35) and (36) are no longer linearly related. Multiplying equation (36) by α and adding it to equation (35) yields:

[0142] (1-α)U0b ij ΔU j =μ i +αμ j (37)

[0143]

[0144] In equation (38), U0 is approximately equal to 1, and the residual μ i and residual μ j Smaller, |b ij | Relatively large. If α is very close to 1.0, then ΔU j A large α is detrimental to convergence; if α is very small or very large, it causes the elements of the Jacobian matrix to deviate significantly from their partial derivatives, which is also detrimental to convergence; if α is chosen appropriately, with a value range of [1.001, 1.100], then the obtained ΔU jThe smaller the partial derivatives of the Jacobian matrix elements, the better the convergence.

[0145] Compared with the prior art, the present invention has the following beneficial effects:

[0146] When forming the Jacobian matrix elements for reactive power measurement at the head end of a transmission line using the fast decomposition method for state estimation, if the transmission line's susceptance to ground is b... c ≠0, add a modification amount of 3b to the partial derivative of reactive power measurement with respect to the head-end voltage. c As the corresponding Jacobian matrix element; if the transmission line's susceptance to ground b c =0, multiply the partial derivative of the reactive power measurement with respect to the head-end voltage by the modification factor α to obtain the corresponding Jacobian matrix element. Thus, regardless of the transmission line's susceptance to ground b... c Whether the result is 0 or not, the convergence of the fast decomposition method for state estimation can be improved by refining the method of forming the Jacobian matrix elements of transmission line measurements, which can better improve the convergence performance of state estimation. Attached Figure Description

[0147] This invention has a total of appendices Figure 4 Zhang, of which:

[0148] Figure 1 This is a flowchart of the existing technology for rapid decomposition state estimation.

[0149] Figure 2 It is the equivalent circuit diagram of a power transmission line.

[0150] Figure 3 This is the equivalent circuit diagram of a transformer.

[0151] Figure 4 This is a flowchart of the Jacobian matrix formation process for reactive power measurement of transmission lines according to the present invention. Detailed Implementation

[0152] The invention will now be further described with reference to the accompanying drawings.

[0153] This invention was used to calculate the IEEE 30 power flow calculation example. The invention simulates branch power measurement by adding a certain error to the branch power results of the transmission lines and transformers calculated in the example. All branch active power errors are assumed to be -0.005 (nominal value -0.5MW), reactive power errors are assumed to be -0.005 (nominal value -0.5Mvar), all measurement weights are set to 1.0, node 1 is the reference node with an initial reference voltage setpoint of 1.0, and the convergence accuracy is 0.00001 (unit: per unit). The correction coefficient α of this invention is set to 1.004. Traditional fast decomposition state estimation methods do not converge. The method in Chinese Patent 202111657954.6 converges after 8 iterations, while this invention converges after 6 iterations. The maximum correction of state variables in each iteration for the three methods is shown in Table 1 (unit: per unit).

[0154] Table 1. Maximum correction amount of state variables in each iteration of different state estimation methods.

[0155] Iteration number Traditional methods Invention No. 202111657954.6 Method Method of the present invention 1 0.241899 -0.239385 -0.239385 2 -0.312568 0.031367 0.025969 3 0.454649 0.004345 0.007172 4 -0.800997 0.000465 -0.000334 5 0.771265 0.000184 0.000063 6 -0.666321 -0.000038 -0.000008 7 0.719446 0.000010 8 -0.869745 -0.000002 9 0.794893 10 -0.582897 11 0.675594 12 -0.923661

[0156] As shown in Table 1, the maximum correction amount of the state variables in the first iteration of all three methods is relatively large. After the first iteration, the maximum correction amount of the state variables of the method in Chinese Patent 202111657954.6 and the present invention is significantly reduced. The method in Chinese Patent 202111657954.6 converges after 8 iterations, and the present invention converges after 6 iterations. However, the absolute value of the maximum correction amount of the state variables of the traditional method remains large and eventually diverges.

[0157] To verify the correctness of this invention, the branch power results of the power flow calculations for transmission lines and transformers in the example were used to simulate the measurement of branch power, with a measurement error of 0 and other conditions remaining unchanged. This invention underwent 6 iterations. The comparison results between the estimated node voltage amplitude values ​​from the state estimation and the calculated power flow values ​​are shown in Table 2, in per-unit values.

[0158] Table 2. Estimated voltage amplitude and error at each node in this invention.

[0159]

[0160]

[0161] As shown in Table 2, the node voltage estimates obtained by the state estimation method of this invention have a very small error compared with the calculated power flow values, with a maximum error of 0.0000105, which is slightly greater than the convergence accuracy. This indicates that the state estimation calculation results of this invention are accurate and reliable.

[0162] 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.

[0163] 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 forming the elements of the Jacobian matrix for line measurement in fast decomposition state estimation, characterized in that: Includes the following steps: A. Read network data and measurement data; B. Forming a QU-type constant Jacobian matrix B r ; Formation B r The steps are as follows: B1. Formed using traditional methods r ; For the measurement of reactive power injected at nodes, B r Take the imaginary part of the nodal admittance matrix; for branch reactive power measurement, B r Take the imaginary part of the nodal admittance matrix of this branch; If the l-th measurement is the node voltage magnitude measurement at node i, then B r The element in the l-th row and i-th column is -1 / U0, B r All other elements in the l-th row are 0; B2. Set the quantity measurement counter p = 1; B3. Take the type T of the measurement for the p-th quantity; B4. Determine whether the measurement type T is the reactive power measurement type at the beginning of the transmission line. If it is not the reactive power measurement type at the beginning of the transmission line, proceed to step B9. B5. Take the p-th quantity and measure the first node number i and the ground susceptance b of the corresponding transmission line. c ; B6. Determine the susceptance to ground (b) c Is it 0? If b c If the value is 0, proceed to step B8; B7. Correct matrix B according to equation (1) r element B in row p and column i r.pi Proceed to step B9; B r.pi =B r.pi +3b c (1) In the formula, b c The susceptance to ground of the π-shaped equivalent circuit of the transmission line; B8. Correct matrix B according to equation (2) r element B in row p and column i r.pi ; B r.pi =αB r.pi (2) In the formula, α is a correction coefficient, which is related to the scale and structure of the power system, and its value ranges from [1.001, 1.100]. B9. Let p = p + 1; B10. Determine if p is greater than the number of measurements m. If p is greater than the number of measurements m, proceed to step C; otherwise, return to step B3 for the next iteration. C. Forming P-δ type constant Jacobian matrices B a ; For the measurement of active power injected into nodes, B a This is the imaginary part of the nodal admittance matrix formed using only branch reactances, ignoring the non-standard transformer ratio, transmission line-to-ground capacitance, and branch resistance, which have little impact on the active power distribution. For the measurement of active power in branch circuits, B a This is the imaginary part of the node admittance matrix formed using only the reactance of this branch, ignoring the non-standard transformer ratio, transmission line-to-ground capacitance, and branch resistance, which have little impact on the active power distribution. D. Voltage initialization: Set the voltage amplitude of each node to the initial given value U0 of the reference node voltage amplitude, and the voltage phase angle to 0. E. Form information matrices A and C of the fast decomposition state estimation correction equation and perform triangular decomposition; In the formula, A is n a ×n a n-order active information matrix; a The number of node voltage phase angle state variables; In the formula, C is n r ×n r n-order reactive power information matrix; r The number of state variables representing the node voltage magnitude; F. Set the iteration count t = 0, and set Δδ max =5ε δ ΔU max =5ε U ; G. Determine whether the maximum voltage amplitude correction value |ΔU is satisfied. max | Less than the convergence accuracy ε U And the maximum correction amount of voltage phase angle |Δδ max | Less than the convergence accuracy ε δ If the conditions are met, proceed to step M; Otherwise, proceed to step H; H. Calculate the active free vector a (t) Solve equation (5) to find Δδ (t) And find the maximum correction amount of voltage phase angle |Δδ max |; AΔD (t) =a (t) (5) In the formula, a is n a 1. Active free vector; Δδ is the column vector of node voltage phase angle correction; the superscript (t) indicates the t-th iteration; In the formula, B a For m a ×n a A P-δ type constant Jacobian matrix; z a For m a The active power quantity measurement column vector includes active power quantity measurements of transmission lines and transformer branches, and active power quantity measurements injected into nodes; h a For the corresponding z a Measurement function; For the corresponding z a m a The weight diagonal matrix of order n; δ is an n-order weighted matrix. a 1D node voltage phase angle column vector; U is an n-dimensional node voltage phase angle column vector; r m-dimensional column vector of node voltage magnitudes; a The number of active quantity measurements; I. Correct the voltage phase angle according to formula (7); d (t+1) =d (t) +Dd (t) (7) J. Calculate the reactive free vector c (t) Solve equation (8) to find ΔU (t) And find the maximum correction amount of voltage amplitude |ΔU max |; CΔU (t) =c (t) (8) In the formula, ΔU is the column vector of node voltage magnitude correction; c is the n r The reactive free vector is calculated using the following formula: In the formula, B r For m r ×n r QU-class constant Jacobian matrix; z r For m r The reactive power measurement column vector includes measurements of branch reactive power of transmission lines and transformers, measurements of node injected reactive power, and measurements of node voltage amplitude; h r For the corresponding z r Measurement function; For the corresponding z r m r Order-order weight diagonal matrix; m r Number of reactive power quantities measured; K. Correct the voltage amplitude according to formula (10); U (t+1) = U (t) +ΔU (t) (10) L. Let t = t + 1, and return to step G for the next iteration; M, Output the state estimation result, then end.

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