Power flow iterative calculation method and system based on hybrid preprocessing

Abstract

The invention discloses a hybrid preprocessing-based power flow iterative calculation method and system, and mainly relates to the technical field of data calculation of a power system. Comprising the following steps: constructing a linear system corresponding to a Jacobian matrix based on a Newton-Krayrov subspace load flow calculation basic framework; performing norm scaling, row and column rearrangement and incomplete decomposition on the Jacobian matrix in sequence to generate a preprocessing operator; a preprocessing operator is embedded into a biconjugate gradient stabilization algorithm, and a nonlinear solution is updated by dynamically adjusting a residual control strategy; and according to the condition that the residual error meets Newton-Kraylov space load flow calculation convergence conditions, judging that calculation is terminated, and outputting a load flow result or continuing iteration. The method has the beneficial effects that the combination of the physical characteristics of the power grid and the numerical precondition technology is realized, and a reliable solution is provided for the simulation of a large-scale node power system.

Description

Technical Field

[0001] The present invention relates to the technical field of data calculation of power systems, and in particular to a method and system for iterative calculation of power flow based on hybrid preprocessing. Background Art

[0002] The continued growth in load demands on existing infrastructure, coupled with the widespread integration of renewable energy sources (RES) such as solar, wind, and energy storage, as well as dynamic loads such as electric vehicles and data centers, has profoundly changed the operational characteristics of modern power systems. This integration exacerbates the challenges of large-scale ill-conditioned power flow calculations, stemming from the inherent characteristics of distribution networks, such as high R / X ratios, weak grid connections, voltage instability, and network congestion. These factors have been widely demonstrated to be the primary cause of ill-conditioned Jacobian matrices in the Newton-Raphson (NR) algorithm, leading to decreased numerical stability and hindered convergence. Although the intermittent nature and load fluctuations of RES can indirectly increase the risk of ill-conditioning by pushing the system to operational limits such as voltage collapse, the fundamental cause of numerical instability lies in the grid parameters themselves, rather than random fluctuations in RES.

[0003] The published patent documents involve a "hybrid multi-layer preprocessing method for pathological power flow systems" and a "pathological assessment method for power flow systems based on power network parameters". The urgent problem of how to solve the power system power flow based on the above methods is to be solved.

[0004] Therefore, a power flow iterative calculation method and system based on hybrid preprocessing are proposed to solve the above problems. Summary of the Invention

[0005] The purpose of the present invention is to provide a method and system for iterative calculation of power flow based on hybrid preprocessing, which combines the physical characteristics of the power grid with numerical preconditioning technology and provides a reliable solution for power system simulation at the billion-node scale.

[0006] To achieve the above-mentioned purpose, the present invention is implemented through the following technical solutions:

[0007] On the one hand, a power flow iterative calculation method based on hybrid preprocessing is proposed, which includes the following steps:

[0008] S1: Based on the basic framework of Newton-Krylov subspace power flow calculation, construct the linear system corresponding to the Jacobian matrix;

[0009] S2: Perform norm scaling, row and column rearrangement, and incomplete decomposition on the Jacobian matrix to generate preprocessing operators;

[0010] S3: Embed the preprocessing operator into the biconjugate gradient stabilization algorithm and update the nonlinear solution by dynamically adjusting the residual control strategy;

[0011] S4: Determine the convergence based on the residual norm or solution correction. If the conditions are met, terminate the calculation and output the power flow results; otherwise, continue the iteration.

[0012] Preferably, the initial state vector is The power flow residual is F(x0), and the linear system corresponding to the Jacobian matrix is ​​J (k) ΔX (k) =-G(X (k) ), where k represents the number of iterations, J (k) is the Jacobian matrix, ΔX (k) is the correction vector.

[0013] Preferably, the step S2 is specifically as follows: performing l1-norm scaling, approximate minimum degree sorting, and incomplete LU decomposition with a threshold on the Jacobian matrix in sequence to generate a preprocessing matrix LU.

[0014] Preferably, including:

[0015] l1-norm scaling: The rows and columns of the Jacobian matrix are scaled by and Perform scaling to generate a normalized matrix J′;

[0016] Approximate minimum degree sorting: Apply the approximate minimum degree sorting algorithm to the scaled matrix J′ to produce the row and column permutation matrix P and obtain the rearranged matrix J′ amd =PJ′P T ;

[0017] Incomplete LU decomposition: for J′ amd Perform incomplete LU decomposition with threshold, retaining the filler threshold droptol=10 -8 , generate preprocessing factors L and U.

[0018] Preferably, in step S3, the preprocessing operator is embedded in the biconjugate gradient stabilization algorithm, including:

[0019] S31: Set the linear system residual r0 = -F(x0) and the initial search direction p0 = r0;

[0020] S32: Based on the initial search direction, establish the biorthogonalization process:

[0021] Calculate the intermediate vector

[0022] Calculating scalar parameters

[0023] Update intermediate solution

[0024] Calculate correction step

[0025] S33: Based on the biorthogonalization process, the solution and residual updates are performed:

[0026] The solution is updated to:

[0027] Δx=Δx+α j p j +w j s j ;

[0028] Residual update:

[0029]

[0030] Preferably, in step S3, the nonlinear solution is updated by dynamically adjusting the residual control strategy, including:

[0031] Nonlinear solution update:

[0032] x k+1 =x k +Δx

[0033] Recalculate the power flow residual F(x k+1 );

[0034] Dynamic control strategy:

[0035] Adjust the number of iterations in the biconjugate gradient stabilization algorithm according to the residual norm; when ‖F(x k )‖ is large, the solution accuracy is relaxed.

[0036] Preferably, the step S4 is specifically as follows:

[0037] If ‖F(x k+1 )‖2<∈or‖Δx‖ ∞ <δ, terminate the calculation; otherwise, return to step S1 and iterate again.

[0038] In another aspect, a power flow iterative calculation system based on hybrid preprocessing is provided, comprising:

[0039] Data acquisition module: used to obtain grid topology parameters, branch impedance and node power data;

[0040] Morbidity assessment module: real-time calculation of multi-dimensional morbidity indicators, output of risk level and pre-processing parameters;

[0041] Preprocessing operator generation module: performs regularization, rearrangement and ILU decomposition to generate a preprocessing matrix that adapts to the current pathological state;

[0042] Newton-BICGSTAB solver: Iterative solution core with integrated pre-processing matrix and support for dynamic convergence condition adjustment;

[0043] Optimization feedback module: updates the threshold and preprocessing strategy according to the convergence results to form a closed-loop optimization.

[0044] Compared with the prior art, the beneficial effects of the present invention are:

[0045] 1. Pathological perception preprocessing: Dynamically adjust preprocessing parameters through multi-dimensional indicators to solve the lack of adaptability of traditional fixed strategies;

[0046] 2. Hybrid operator design: Regularization enhances numerical stability, rearrangement optimizes sparsity, and ILU decomposition balances accuracy and efficiency. The three work together to reduce the condition number.

[0047] 3. Risk-driven solution: Modify the initial guess value and iteration parameters according to the pathological level to improve the robustness of the Newton method;

[0048] 4. System-level closed-loop optimization: The feedback module realizes real-time matching of algorithm parameters and grid status, which is suitable for large-scale time-varying power grids. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 This is a flow chart of a method for iterative calculation of power flow based on hybrid preprocessing of the present invention;

[0050] Figure 2 This is a schematic diagram of the structure of a power flow iterative calculation system based on hybrid preprocessing of the present invention;

[0051] Figure 3 This is a test result analysis diagram of a power flow iterative calculation method based on hybrid preprocessing of the present invention. DETAILED DESCRIPTION

[0052] Below in conjunction with specific embodiment, further set forth the present invention.Should be understood that these embodiments are only used to illustrate the present invention and are not used in limiting the scope of the present invention.In addition, should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms fall within the scope limited by the application equally.

[0053] In the present invention, terms such as "upper", "lower", "left", "right", "front", "back", "vertical", "horizontal", "side", "bottom", etc. indicating directions or positional relationships are based on the directions or positional relationships shown in the accompanying drawings. They are relational words determined only for the convenience of describing the structural relationships of the various parts or elements of the present invention, and do not specifically refer to any part or element in the present invention, and should not be understood as limiting the present invention.

[0054] In the present invention, terms such as "fixed connection," "connected," and "connection" should be interpreted broadly to mean a fixed connection, an integral connection, or a detachable connection; a direct connection or an indirect connection through an intermediary. Relevant researchers or technicians in this field may determine the specific meanings of these terms in the present invention based on specific circumstances, and they should not be construed as limitations of the present invention.

[0055] Example:

[0056] like Figure 1 As shown, this embodiment provides a method for iterative calculation of power flow based on hybrid preprocessing, comprising the following steps:

[0057] S1: Based on the basic framework of Newton-Krylov subspace power flow calculation, construct the linear system corresponding to the Jacobian matrix;

[0058] S2: Perform norm scaling, row and column rearrangement, and incomplete decomposition on the Jacobian matrix to generate preprocessing operators;

[0059] S3: Embed the preprocessing operator into the biconjugate gradient stabilization algorithm and update the nonlinear solution by dynamically adjusting the residual control strategy;

[0060] S4: Determine the convergence based on the residual norm or solution correction. If the conditions are met, terminate the calculation and output the power flow results; otherwise, continue the iteration.

[0061] Among them, in step S1, the initial state vector is The power flow residual is F(x0), and the linear system corresponding to the Jacobian matrix is ​​J (k) ΔX (k) =-G9X (k) ), where k represents the number of iterations, J (k) is the Jacobian matrix, ΔX (k) is the correction vector.

[0062] Step S2 specifically includes: performing l1-norm scaling, approximate minimum degree sorting, and incomplete LU decomposition with threshold on the Jacobian matrix in sequence to generate a preprocessing matrix LU, including:

[0063] l1-norm scaling: The rows and columns of the Jacobian matrix are scaled by and Perform scaling to generate a normalized matrix J′;

[0064] Approximate minimum degree sorting: Apply the approximate minimum degree sorting algorithm to the scaled matrix J′ to produce the row and column permutation matrix P and obtain the rearranged matrix J′ amd =PJ′P T ;

[0065] Incomplete LU decomposition: for J′ amd Perform incomplete LU decomposition with threshold, retaining the filler threshold droptol=10 -8 , generate preprocessing factors L and U.

[0066] In step S3, the preprocessing operator is embedded in the biconjugate gradient stabilization algorithm, including:

[0067] S31: Set the linear system residual r0 = -F(x0) and the initial search direction p0 = r0;

[0068] S32: Based on the initial search direction, establish the biorthogonalization process:

[0069] Calculate the intermediate vector

[0070] Calculating scalar parameters

[0071] Update intermediate solution

[0072] Calculate correction step

[0073] S33: Based on the biorthogonalization process, the solution and residual updates are performed:

[0074] The solution is updated to:

[0075] Δx=Δx+α j p j +w j s j ;

[0076] Residual update:

[0077]

[0078] The nonlinear solution is updated by dynamically adjusting the residual control strategy, including:

[0079] Nonlinear solution update:

[0080] x k+1 =x k +Δx

[0081] Recalculate the power flow residual F(x k+1 );

[0082] Dynamic control strategy:

[0083] Adjust the number of iterations in the biconjugate gradient stabilization algorithm according to the residual norm; when ‖F(x k )‖ is large, the solution accuracy is relaxed.

[0084] Step S4 is specifically as follows:

[0085] If ‖F(x k+1 )‖2<∈or‖Δx‖ ∞ <δ, terminate the calculation; otherwise, return to step S1 and iterate again.

[0086] like Figure 2 As shown, this embodiment further provides a system based on the above-mentioned hybrid preprocessing-based power flow iterative calculation method, including:

[0087] Data acquisition module: used to obtain grid topology parameters, branch impedance and node power data;

[0088] Morbidity assessment module: real-time calculation of multi-dimensional morbidity indicators, output of risk level and pre-processing parameters;

[0089] Preprocessing operator generation module: performs regularization, rearrangement and ILU decomposition to generate a preprocessing matrix that adapts to the current pathological state;

[0090] Solver module: It integrates the iterative solution core of the pre-processing matrix and supports dynamic convergence condition adjustment;

[0091] Optimization feedback module: updates the threshold and preprocessing strategy according to the convergence results to form a closed-loop optimization.

[0092] like Figure 3 As shown, the performance calculation annotations are as follows:

[0093]

[0094] Negative values ​​indicate that BICGSTAB is slower than the direct solver, with a flat start initial condition. Applying the method in this example, the hybrid preconditioned BiCGSTAB algorithm exhibits the following advantages over the Newton-AMD-Direct method in a power system model containing 82,000 buses:

[0095] By introducing C1-norm scaling combined with AMD sorting and ILU preconditioning (21-norm scaling-AMD-ILU preconditioning), the BiCGSTAB algorithm maintained stable convergence performance (2-7 iterations) in all test scenarios, remaining robust even under extreme pathological conditions with extremely high matrix condition numbers. This method achieved a solution time of 13.88 seconds in the case syntheticUSA large-scale system simulation, a 64%-69% improvement in time compared to the 45.28 seconds achieved by the Newton method-AMD sorting direct solver. Direct solvers, however, consume exponentially more computational resources due to the high-order memory requirements of the matrix decomposition process.

[0096] The BiCGSTAB algorithm's relative performance advantage increases significantly with system scale. Its computational efficiency is particularly pronounced when the grid node scale exceeds 10,000. This scalability stems from the algorithm's effective avoidance of the memory bottlenecks inherent in direct solvers due to dense matrix storage, demonstrating unique engineering application value in the field of ultra-large-scale power grid analysis.

[0097] This preprocessing method, combined with the BiCGSTAB algorithm, maintains numerical stability even for condition numbers as high as (J)~10, and the number of iterations is still controlled to <10 in the most severe pathological systems. This robustness ensures that the method can maintain consistent performance even under extreme pathological conditions.

[0098] The embodiments are described in detail, but the present invention is not limited to the embodiments. Those skilled in the art can make various equivalent modifications or substitutions to the transaction features between nodes without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. A method for iterative calculation of power flow based on hybrid preprocessing, characterized in that: The following steps are involved: S1: Based on the basic framework of Newton-Krylov subspace power flow calculation, construct the linear system corresponding to the Jacobian matrix; S2: Perform norm scaling, row and column rearrangement, and incomplete decomposition on the Jacobian matrix to generate preprocessing operators; S3: Embed the preprocessing operator into the biconjugate gradient stabilization algorithm and update the nonlinear solution by dynamically adjusting the residual control strategy; S4: Determine the convergence based on the residual norm or solution correction. If the conditions are met, terminate the calculation and output the power flow results; otherwise, continue the iteration.

2. The method for iterative calculation of power flow based on hybrid preprocessing according to claim 1, characterized in that: The initial state vector is The power flow residual is F(x0), and the linear system corresponding to the Jacobian matrix is ​​J (k) ΔX (k) =-G(X (k) ), where k represents the number of iterations, J (k) is the Jacobian matrix, ΔX (k) is the correction vector.

3. The method for iterative calculation of power flow based on hybrid preprocessing according to claim 1, characterized in that: The step S2 specifically comprises: performing l1-norm scaling, approximate minimum degree sorting, and incomplete LU decomposition with a threshold on the Jacobian matrix in sequence to generate a preprocessing matrix LU.

4. The method for iterative calculation of power flow based on hybrid preprocessing according to claim 3, characterized in that: include: l1-norm scaling: The rows and columns of the Jacobian matrix are scaled by and Perform scaling to generate a normalized matrix J′; Approximate minimum degree sorting: Apply the approximate minimum degree sorting algorithm to the scaled matrix J′ to produce the row and column permutation matrix P and obtain the rearranged matrix J′ amd =PJ′P T ; Incomplete LU decomposition: for J′ amd Perform incomplete LU decomposition with threshold, retaining the filler threshold droptol=10 -8 , generate preprocessing factors L and U.

5. The method for iterative calculation of power flow based on hybrid preprocessing according to claim 1, characterized in that: In step S3, the preprocessing operator is embedded in the biconjugate gradient stabilization algorithm, including: S31: Set the linear system residual r0 = -F(x0) and the initial search direction p0 = r0; S32: Based on the initial search direction, establish the biorthogonalization process: Calculate the intermediate vector Calculating scalar parameters Update intermediate solution s j =r j -α j A pj ; Calculate correction step S33: Based on the biorthogonalization process, the solution and residual updates are performed: The solution is updated to: Δx=Δx+α j p j +w j s j ; Residual update: r j+1 =s j -w j A sj 。 6. The method for iterative calculation of power flow based on hybrid preprocessing according to claim 5, characterized in that: In step S3, the nonlinear solution is updated by dynamically adjusting the residual control strategy, including: Nonlinear solution update: x k+1 =x k +Δx Recalculate the power flow residual F(x k+1 ); Dynamic control strategy: Adjust the number of iterations in the biconjugate gradient stabilization algorithm according to the residual norm; when ‖F(x k )‖ is large, the solution accuracy is relaxed.

7. The method for iterative calculation of power flow based on hybrid preprocessing according to claim 1, characterized in that: The step S4 is specifically as follows: If ‖F(x k+1 )‖2<∈or‖Δx‖ ∞ <δ, terminate the calculation; otherwise, return to step S1 and iterate again.

8. A system based on the hybrid preprocessing-based power flow iterative calculation method according to claim 1, characterized in that: include: Data acquisition module: used to obtain grid topology parameters, branch impedance and node power data; Morbidity assessment module: real-time calculation of multi-dimensional morbidity indicators, output of risk level and pre-processing parameters; Preprocessing operator generation module: performs regularization, rearrangement and ILU decomposition to generate a preprocessing matrix that adapts to the current pathological state; Solver module: It integrates the iterative solution core of the pre-processing matrix and supports dynamic convergence condition adjustment; Optimization feedback module: updates the threshold and preprocessing strategy according to the convergence results to form a closed-loop optimization.

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