Electric power system load flow calculation method based on rigid accurate Rosenbrock format

Abstract

The invention discloses an electric power system load flow calculation method based on a rigid accurate Rosenbrock format, and relates to the field of electric power system load flow analysis. The method comprises the following steps: converting an alternating current load flow calculation model of a power system into a group of differential algebraic equations; according to a given voltage phase angle and an amplitude iteration initial value, calculating a differential algebraic equation state variable and an algebraic variable initial value; solving the differential algebraic equation set according to the obtained initial values of the state variable and the algebraic variable by using a rigid accurate Rosenbrock format until the error of the original power system load flow calculation model is smaller than a given error limit; and finally deriving a voltage phase angle and amplitude calculation result. According to the method, the characteristics of non-iteration, high efficiency and high numerical stability of the rigid accurate Rosenbrock format are combined, and the convergence performance of power flow calculation of the power system is improved. The method is suitable for secondary checking of a non-convergent scene of a traditional load flow calculation method, and fast robust convergence of load flow calculation in an ill-conditioned load flow initial value scene is guaranteed.

Description

Technical Field

[0001] The invention relates to the field of power system flow analysis, in particular to a power system flow calculation method based on a rigid and precise Rosenbrock format. Background Art

[0002] Obtaining the power system flow distribution is the basis for power system calculation and analysis. The power system flow distribution depends on the power system flow calculation. Generally, the power system operation and dispatching personnel solve the output of each generator through the power system flow calculation according to the user load, so as to determine the power system operation and dispatching plan. Before performing the power system flow calculation, a set of predicted values ​​of the voltage phase angle and amplitude are generally given first, and then the Newton-Raphson power flow calculation method and the Gauss-Seidel power flow calculation method are used to iteratively solve until convergence. However, the traditional Newton-Raphson power flow calculation method and the Gauss-Seidel power flow calculation method are not easy to converge in the scenario where the predicted values ​​of the given voltage phase angle and amplitude deviate from the true values, and it is impossible to obtain feasible results. This brings difficulties to the power system calculation and analysis. Therefore, it is necessary to develop a more robust power system flow calculation method. Summary of the invention

[0003] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a power system flow calculation method based on the rigid and precise Rosenbrock format, which is an efficient and robust numerical method for power system flow analysis in ill-conditioned initial value scenarios and can be used for secondary verification of scenarios where the traditional Newton-Raphson power flow method does not converge.

[0004] The present invention adopts the following technical solutions to solve the above technical problems:

[0005] A method for calculating power system flow based on a rigid and precise Rosenbrock format according to the present invention comprises the following steps:

[0006] Step S1, converting the original power system AC power flow calculation model into a set of differential algebraic equations about voltage phase angle and amplitude;

[0007] Step S2, calculating the initial values ​​of the state variables and algebraic variables of the differential algebraic equation in step S1 according to the predetermined voltage phase angle and amplitude iteration initial values;

[0008] Step S3, using the rigid precise Rosenbrock format, according to the state variables and initial values ​​of algebraic variables obtained in step S2, solve the differential algebraic equations of step S1 until the error of the original power system flow calculation model is less than the given error limit, and obtain the voltage phase angle and amplitude calculation results.

[0009] As a further optimization scheme of the power system flow calculation method based on the rigid accurate Rosenbrock format described in the present invention, in step S1, a set of differential algebraic equations

[0010]

[0011] Where y represents the vector consisting of the voltage phase angle and amplitude to be determined; g(y) represents the complex power balance equation of the power system node; represents the derivative of y; z is the derivative of the voltage phase angle and amplitude; J(y) represents the derivative of the complex power balance equation of the power system node with respect to y.

[0012] As a further optimization scheme of the power system flow calculation method based on the rigid accurate Rosenbrock format described in the present invention,

[0013]

[0014] As a further optimization scheme of the power system flow calculation method based on the rigid accurate Rosenbrock format described in the present invention, in step S2, the initial value y is iterated according to the given voltage phase angle and amplitude (0) , calculate the initial value y0 of y and the initial value z0 of z:

[0015] y0=y (0) ,z0=-J(y (0) ) -1 g(y (0) )

[0016] Among them, J(y (0) ) is to convert y (0) Substituting into J(y) we get the matrix g(y (0) ) is to convert y (0) Substitute the resulting vector into g(y).

[0017] As a further optimization scheme of the power system flow calculation method based on the rigid and accurate Rosenbrock format described in the present invention, in step S3, the rigid and accurate Rosenbrock format is used to solve the differential algebraic equations of step S1 according to the state variables and the initial values ​​of the algebraic variables obtained in step S2; after each time step of the differential algebraic equations is calculated, the state variable calculation result y of the current step is converted into * Substituting into the complex power balance equation g(y) of the power system node, we get the result g(y * ), if g(y * ) is less than the given convergence error limit, the calculation is terminated and the voltage phase angle and amplitude calculation results are obtained. Otherwise, y *As the initial value, the rigid exact Rosenbrock scheme is used to start the calculation of the next time step of the differential algebraic equation system.

[0018] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0019] The present invention transforms the original power system power flow calculation problem into the solution of a differential algebraic equation system, and solves it non-iteratively and efficiently by combining the rigid and precise Rosenbrock format with ultra-stability, thereby ensuring the rapid and robust convergence of the power flow calculation in the scenario where the given voltage phase angle and amplitude prediction value deviate from the true value. Therefore, the power flow calculation results can be secondary checked in the scenario where the traditional Newton-Raphson power flow method does not converge, thereby ensuring the accuracy and reliability of the power grid operation analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0021] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is described in detail below in conjunction with the accompanying drawings and implementation examples. It should be understood that the specific implementation examples described herein are only used to explain the present invention and are not used to limit the invention.

[0022] like Figure 1 It is a flow chart of the present invention, considering the following power system AC power flow model:

[0023]

[0024] Where, θ is the voltage phase angle vector; is the voltage magnitude vector; I is the busbar injection current vector; S d is the bus load vector; S g is the generator power vector; C g is the generator association matrix. If generator j is connected to bus i, the value of the (i, j)th element of the matrix is ​​1, otherwise it is 0. The subscript D indicates that the vector is converted into the corresponding diagonal matrix, and the superscript * indicates the complex conjugate operation.

[0025] The AC power flow model of the power system described in equation (1) is rewritten as a differential algebraic equation system:

[0026]

[0027] Among them, the Jacobian matrix Given the initial value y of the voltage phase angle and amplitude (0) , the initial value y0 of the state variable y and the initial value z0 of the algebraic variable z can be calculated by the following formula:

[0028] y0=y (0) ,z0=-J(y (0) ) -1 g(y (0) )

[0029] Among them, J(y) represents the derivative of the complex power balance equation of the power system node with respect to the vector y, that is,

[0030]

[0031] The initial value problem of the differential algebraic equation described in equation (2) is solved using an s-level rigid and exact Rosenbrock format. The rigid and exact Rosenbrock format has the following form:

[0032]

[0033] Wherein, M is the singular mass matrix corresponding to the differential algebraic equation system described in claim 1, h is the simulation step length, γ ij , α ij , b i For the given calculation parameters, γ 11 =γ 22 =γ 33 =…γ ii =γ,

[0034]

[0035] represents the Kronecker product, represents the gradient operator,

[0036] At each step in solving the differential-algebraic equation described in Eq. (2) using the class-s rigid exact Rosenbrock scheme, the matrix Perform partial LU decomposition. Specifically, the matrix Rewrite as

[0037]

[0038] At each step, the matrix Perform LU decomposition and get

[0039]

[0040] Thus we can get LU decomposition of

[0041]

[0042] This reduces the dimension of matrix decomposition and improves computational efficiency.

[0043] An embedded format is used to control the computational step size h. Using the formula

[0044]

[0045] The truncation error is estimated. Further, using the formula

[0046]

[0047] The solution step size is adjusted, where q is the order of the rigid exact Rosenbrock format, Atol and Rtol are the set absolute and relative error limits, respectively, and |·| ∞ Represents the infinity norm of a vector.

[0048] A four-level third-order embedded second-order, strongly damped, ultra-stable format Rodas3d is constructed to solve equation (2). Specifically, its parameters are

[0049] α 41 =0.3263,α 42 =0.1009,α 43 =0.5728,

[0050] α 31 =1.0000,α 32 =0.0000,

[0051] α 21 =1.2451,

[0052]

[0053] b1=0.6978, b2=0.0565, b3=-0.3271, b4=0.5728

[0054] γ=0.5728

[0055] After each step of solving the differential algebraic equation described in equation (2) using the s-level rigid exact Rosenbrock format is completed, the state variable calculation result y of the current step is * Substitute into the complex power balance equation g(y) of the power system node. If g(y * ) is less than the given convergence error limit, the calculation is terminated and the voltage phase angle and amplitude calculation results are derived; otherwise, y * As the initial value, continue to calculate the differential algebraic equation system described in formula (2) using the rigid exact Rosenbrock format.

[0056] Two embodiments are given below.

[0057] The present invention was compared with the following methods.

[0058] M1: Newton-Raphson method

[0059] M2: Iwamoto robust method

[0060] M3: Continuous Newton method based on explicit Runge-Kutta

[0061] M4: Robust method based on Romberg integral

[0062] M5: Improved continuous Newton method based on second-order fourth-order explicit Runge–Kutta

[0063] M6: Mann Iteration Method

[0064] M7: Implicit continuous Newton method with adaptive step size, including ICNM-JH, ICNM-J, ICNM-J1, ICNM-J0

[0065] M8: Method provided by the present invention

[0066] The programming environment of the embodiment is MATLAB R2024A. All methods are programmed based on the open source power system power flow analysis software MATPOWER. The error limit of power flow calculation is set to 1e-5. The relevant example parameters and program codes are open source at the website https: / / github.com / rzyu45 / MATPOWER-SICNM.

[0067] Example 1 takes three typical power system pathological initial value scenarios as examples. Use M1 to M8 to solve the scenario. Record the number of iterations and calculation time, as shown in Table 1 below:

[0068] Table 1 Comparison of iterative calculation times and calculation time in Example 1

[0069]

[0070] The number of iterative calculations and the calculation time from M1 to M8 are shown in Table 1. The method provided by the present invention can effectively guarantee and accelerate the convergence of power flow calculation.

[0071] Example 2 Based on Example 9241pegase, one-half of the unbalanced bus nodes are randomly selected, and a random perturbation with normal distribution in the interval [-0.005, 0.005] is added to the initial value of the voltage phase angle, and 1000 sets of such scenarios are solved using M1 to M8. The number of times that M1 to M8 can converge within 40 iterations is counted, and the results are shown in Table 2. The method provided by the present invention is far superior to M1 to M7, and can achieve fast convergence in nearly 60% of the scenarios.

[0072] Table 2 Convergence rate of Example 2

[0073]

[0074] It can be seen from the above two embodiments that the present invention can realize fast and robust calculation of power flow in scenarios where the Newton-Raphson power flow method diverges, and can be used for secondary verification of scenarios where the traditional Newton-Raphson power flow method does not converge.

[0075] The above description is only a specific implementation of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by a technician familiar with the technical field within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention.

Claims

1. A method for calculating power flow in a power system based on a rigid and accurate Rosenbrock format, characterized in that: The following steps are involved: Step S1, converting the original power system AC power flow calculation model into a set of differential algebraic equations about voltage phase angle and amplitude; Step S2, calculating the initial values ​​of the state variables and algebraic variables of the differential algebraic equation in step S1 according to the predetermined voltage phase angle and amplitude iteration initial values; Step S3, using the rigid precise Rosenbrock format, according to the state variables and initial values ​​of algebraic variables obtained in step S2, solve the differential algebraic equations of step S1 until the error of the original power system flow calculation model is less than the given error limit, and obtain the voltage phase angle and amplitude calculation results.

2. A method for calculating power flow in a power system based on a rigid and accurate Rosenbrock format according to claim 1, characterized in that: In step S1, a set of differential algebraic equations Where y represents the vector consisting of the voltage phase angle and amplitude to be determined; g(y) represents the complex power balance equation of the power system node; represents the derivative of y; z is the derivative of the voltage phase angle and amplitude; J(y) represents the derivative of the complex power balance equation of the power system node with respect to y.

3. The method for calculating power flow in a power system based on a rigid and accurate Rosenbrock format according to claim 2, characterized in that:

4. The method for calculating power flow in a power system based on a rigid and accurate Rosenbrock format according to claim 2, characterized in that: In step S2, the initial value y is iterated according to the given voltage phase angle and amplitude (0) , calculate the initial value y0 of y and the initial value z0 of z: y0=y (0) ,z0=-J(y (0) ) -1 g(y (0) ) Among them, J(y (0) ) is to convert y (0) Substituting into J(y) we get the matrix g(y (0) ) is to convert y (0) Substitute the resulting vector into g(y).

5. The method for calculating power flow in a power system based on a rigid and accurate Rosenbrock format according to claim 2, characterized in that: In step S3, the rigid exact Rosenbrock format is used to solve the differential algebraic equations of step S1 according to the state variables and initial values ​​of algebraic variables obtained in step S2; after each time step of the differential algebraic equations is calculated, the state variable calculation result y of the current step is converted into * Substituting into the complex power balance equation g(y) of the power system node, we get the result g(y * ), if g(y * ) is less than the given convergence error limit, the calculation is terminated and the voltage phase angle and amplitude calculation results are obtained. Otherwise, y * As the initial value, the rigid exact Rosenbrock scheme is used to start the calculation of the next time step of the differential algebraic equation system.

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