Power flow calculation method and device for AC-DC hybrid power distribution network considering incomplete LU decomposition preconditioning
By improving the Jacobian matrix through incomplete LU decomposition preprocessing and the stable biconjugate gradient method, the sensitivity of the unified iterative method to initial conditions is solved, and fast, stable convergence and efficient solution of power flow calculation in AC/DC hybrid distribution networks are achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- STATE GRID HUBEI ELECTRIC POWER RES INST
- Filing Date
- 2026-03-06
- Publication Date
- 2026-05-29
AI Technical Summary
Among the existing methods for calculating power flow in AC/DC hybrid distribution networks, the unified iterative method is sensitive to initial values, which can easily lead to singular Jacobian matrices. Furthermore, it has low computational efficiency and is difficult to adapt to complex systems.
An incomplete LU decomposition preprocessing method combined with a stable biconjugate gradient method is adopted. By establishing a unified AC/DC power flow calculation model, the Jacobian matrix is modified to reduce the dependence on the initial value. The ILU(0) method is used for preprocessing to maintain the sparsity of the matrix. The stable biconjugate gradient method is then used for iterative solution.
It significantly improves the robustness and efficiency of power flow calculation, enables rapid convergence in complex systems, reduces sensitivity to initial conditions, and is suitable for AC/DC hybrid distribution networks with multiple VSCs.
Smart Images
Figure CN122118772A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of power flow calculation in AC / DC hybrid distribution networks, specifically a method and apparatus for calculating power flow in AC / DC hybrid distribution networks that considers incomplete LU decomposition preprocessing. Background Technology
[0002] With the high proportion of renewable energy grid connection and the widespread application of power electronic equipment, traditional power supply and consumption patterns and distribution network structures have undergone tremendous changes, with AC / DC hybrid distribution networks becoming an important form of new power systems. Simultaneously, advancements in power electronics technology, particularly the maturity of fully controlled devices, have made voltage source converters (VSCs) the core equipment in AC / DC hybrid distribution networks. Applying VSC technology to the distribution network field can effectively address the challenges faced by urban distribution networks. Power flow analysis, as a crucial foundation for the planning and design, operation and control, distributed generation grid connection planning, and fault analysis of AC / DC hybrid distribution networks, is therefore essential for research. Current power flow calculations for AC / DC hybrid systems mainly employ alternating iterative methods and unified iterative methods. Alternating iterative methods are difficult to apply to complex AC / DC hybrid systems, and this method obscures the coupling relationship between the AC and DC systems, resulting in low accuracy of power flow calculation results. The unified iterative method has a broader application prospect. This method extends AC power flow calculation to include converters and DC modules, offering speed and stability. However, it is sensitive to initial values in power flow calculation, and the singularity of the Jacobian matrix can lead to non-convergence. Furthermore, its computational efficiency drops significantly as the number of VSCs connected to the system increases. In summary, reducing the dependence of the unified iterative method on initial values, controlling the operating mode of VSCs, and improving the robustness of power flow calculation in complex AC / DC hybrid distribution systems are urgent problems to be solved in AC / DC hybrid distribution network power flow calculation. Summary of the Invention
[0003] To address the shortcomings of the existing technologies, this invention provides a method and apparatus for calculating power flow in AC / DC hybrid distribution networks that considers incomplete LU decomposition preprocessing. A unified AC / DC power flow calculation model is established. By modifying and preprocessing the Jacobian matrix with incomplete LU decomposition, the power flow calculation converges rapidly, effectively reducing the dependence of the unified iterative method on initial calculation values. Simultaneously, it can quickly solve complex AC / DC hybrid distribution network power flow problems. The stable biconjugate gradient algorithm proposed in this invention can solve the problem of sensitivity to initial calculation values in the traditional unified iterative method.
[0004] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:
[0005] A method for calculating power flow in a hybrid AC / DC distribution network considering incomplete LU decomposition preprocessing includes the following steps:
[0006] Step 1: Based on the steady-state voltage and power equations of the voltage source converter (VSC), establish the active power control equations and reactive power control equations for the VSC.
[0007] Step 2: Based on Kirchhoff's current law, establish the power imbalance equations for AC nodes and DC nodes;
[0008] Step 3: Perform Taylor expansion on the VSC active power control equations and VSC reactive power control equations established in Step 1, as well as the AC node power imbalance equations and DC node power imbalance equations established in Step 2, and ignore higher-order terms to obtain the linearized unified power flow equations of the AC / DC hybrid distribution network. Then, transform the linearized unified power flow equations into a Jacobian matrix in matrix form.
[0009] Step 4: Perform incomplete LU decomposition preprocessing on the Jacobian matrix in matrix form obtained in Step 3, and use the stable biconjugate gradient method to solve the preprocessed Jacobian matrix to obtain the power flow solution.
[0010] Furthermore, in step one, the active power control mode of the VSC includes the DC side voltage of the stator converter, the active power of the DC side of the stator converter, and the active power of the AC side of the stator converter; the reactive power control mode of the VSC includes the AC voltage of the stator converter and the reactive power of the AC side of the stator converter.
[0011] Furthermore, in step two, based on whether the nodes are connected to the VSC, AC nodes are divided into pure AC nodes and non-pure AC nodes, and DC nodes are divided into pure DC nodes and non-pure DC nodes, and their power imbalance equations are established respectively.
[0012] For non-pure AC nodes, the power imbalance equation is the power imbalance equation of a pure AC node minus the power term injected into the converter.
[0013] For non-pure DC nodes, the power imbalance equation is based on the power imbalance equation of pure DC nodes, minus the active power term injected into the converter.
[0014] Meanwhile, based on the principle that the AC side power of the converter is equal to the DC side power, the VSC power balance equation is established.
[0015] Furthermore, in step three, the linearized unified power flow equation set includes the linearized forms of the AC node power imbalance equation, the DC node power imbalance equation, the VSC power balance equation, and the VSC control equation.
[0016] The Jacobian matrix in matrix form is constructed based on the above linearized equations, and its elements include modules corresponding to the AC system power imbalance equation, the DC system power imbalance equation, the converter power balance equation, and the converter control equation.
[0017] Furthermore, in step four, the incomplete LU decomposition preprocessing adopts the incomplete LU decomposition ILU(0) method without filling, and preprocesses it while maintaining the sparsity of the Jacobian matrix to obtain the preprocessed matrix;
[0018] The stable biconjugate gradient method iteratively solves the linearized unified power flow equations based on the preprocessing matrix. When the maximum unbalanced power is less than the preset convergence accuracy, the power flow solution is obtained.
[0019] A power flow calculation device for AC / DC hybrid distribution networks considering incomplete LU decomposition preprocessing includes:
[0020] The VSC control equation establishment module is used to establish the active power control equation and reactive power control equation of the VSC based on the steady-state voltage and power equation of the voltage source converter VSC.
[0021] The power imbalance equation establishment module is used to establish AC node power imbalance equations and DC node power imbalance equations based on Kirchhoff's current law.
[0022] The power flow equation linearization module is used to perform Taylor expansion on the VSC active power control equation, VSC reactive power control equation output by the VSC control equation establishment module, and the AC node power imbalance equation and DC node power imbalance equation output by the power imbalance equation establishment module, respectively, and ignore higher-order terms to obtain a linearized unified power flow equation set for the AC / DC hybrid distribution network, and transform the linearized unified power flow equation set into a matrix form of Jacobian matrix.
[0023] The preprocessing solution module is used to perform incomplete LU decomposition preprocessing on the matrix form Jacobian matrix output by the linearization module of the power flow equations, and to solve the preprocessed Jacobian matrix using the stable biconjugate gradient method to obtain the power flow solution.
[0024] Furthermore, in the VSC control equation establishment module, the active power control mode of the VSC includes the DC side voltage of the stator converter, the active power of the DC side of the stator converter, and the active power of the AC side of the stator converter; the reactive power control mode of the VSC includes the AC voltage of the stator converter and the reactive power of the AC side of the stator converter.
[0025] Furthermore, the power imbalance equation establishment module divides AC nodes into pure AC nodes and non-pure AC nodes, and DC nodes into pure DC nodes and non-pure DC nodes, based on whether the nodes are connected to the VSC, and establishes their respective power imbalance equations.
[0026] For non-pure AC nodes, the power imbalance equation is the power imbalance equation of a pure AC node minus the power term injected into the converter.
[0027] For non-pure DC nodes, the power imbalance equation is based on the power imbalance equation of pure DC nodes, minus the active power term injected into the converter.
[0028] Meanwhile, based on the principle that the AC side power of the converter is equal to the DC side power, the VSC power balance equation is established.
[0029] Furthermore, the linearized unified power flow equation set constructed by the power flow equation set linearization module includes the linearized forms of AC node power imbalance equations, DC node power imbalance equations, VSC power balance equations, and VSC control equations.
[0030] The Jacobian matrix in matrix form is constructed based on the above linearized equations, and its elements include modules corresponding to the AC system power imbalance equation, the DC system power imbalance equation, the converter power balance equation, and the converter control equation.
[0031] Furthermore, the preprocessing solution module uses the unfilled incomplete LU decomposition ILU(0) method to preprocess the Jacobian matrix to obtain the preprocessed matrix;
[0032] The preprocessing solution module uses the stable biconjugate gradient method to iteratively solve the linearized unified power flow equations based on the preprocessing matrix. When the maximum unbalanced power is less than the preset convergence accuracy, the power flow solution is output.
[0033] This invention proposes a method and apparatus for calculating power flow in AC / DC hybrid distribution networks, considering incomplete LU decomposition preprocessing. It establishes the VSC control equations and AC / DC node power imbalance equations, constructs a linearized unified power flow equation set and Jacobian matrix through Taylor expansion, and then solves the equations using incomplete LU decomposition preprocessing combined with the stable biconjugate gradient method. Based on the above innovations, this invention has the following beneficial effects:
[0034] 1. Reduce initial value sensitivity and improve computational robustness: Traditional unified iterative methods are sensitive to the selection of initial values and are prone to non-convergence due to singular Jacobian matrices. This invention adopts a stable biconjugate gradient method combined with incomplete LU decomposition preprocessing, which can effectively overcome the initial value dependence problem and still achieve stable convergence when the initial value is inappropriate or the matrix is sparse, significantly improving the robustness of power flow calculation.
[0035] 2. Accelerate iterative convergence and improve computational efficiency: The Jacobian matrix is preprocessed by incomplete LU decomposition without filling (ILU(0)), which improves its condition number while maintaining the sparsity of the matrix. Combined with the stable biconjugate gradient method, the number of iterations is greatly reduced, and the convergence speed of power flow calculation is accelerated. It is especially suitable for complex AC / DC hybrid systems with multiple VSCs.
[0036] 3. Adaptable to complex systems and highly scalable: The established unified power flow model fully considers various VSC control modes (constant DC voltage, constant active power, constant AC voltage, constant reactive power, etc.) and distinguishes between pure nodes and non-pure nodes to establish power imbalance equations, which can flexibly adapt to AC / DC hybrid distribution networks with different topologies and control requirements.
[0037] 4. Balancing sparsity and computational accuracy: The ILU(0) preprocessing method is used to avoid the injection of non-zero elements, thus maintaining the sparsity of the Jacobian matrix and avoiding a sharp increase in computation time due to the increase of non-elements, while ensuring the accuracy of the power flow solution. Attached Figure Description
[0038] Figure 1 This is a schematic diagram of the equivalent circuit of a voltage source converter.
[0039] Figure 2 This is a schematic diagram of the IEEE 33 AC / DC hybrid system.
[0040] Figure 3 These are the voltage calculation results under different VSC control modes.
[0041] Figure 4 These are the phase angle calculation results under different VSC control modes.
[0042] Figure 5 This is a flowchart of a power flow calculation method for AC / DC hybrid distribution networks that considers incomplete LU decomposition preprocessing, according to an embodiment of the present invention. Detailed Implementation
[0043] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0044] like Figure 5 As shown in the figure, this embodiment of the invention provides a method for calculating the power flow of an AC / DC hybrid distribution network considering incomplete LU decomposition preprocessing, including the following steps:
[0045] Step 1: Based on the steady-state voltage and power equations of the voltage source converter (VSC), establish the active power control equations and reactive power control equations for the VSC.
[0046] Voltage source converters (VSCs) are key components in AC / DC hybrid distribution networks. They enable independent and rapid decoupling control of active and reactive power, and can reverse power flow by changing the current direction. Their physical structure is as follows: Figure 1 As shown in the figure: and These represent the active and reactive power injected into the converter of the AC system, respectively. The active power injected into the converter from the DC system. and These represent the voltage amplitude and phase angle of the AC node directly connected to the converter, respectively. and These represent the AC side voltage amplitude and phase angle of the converter, respectively. and These are the equivalent loss voltage and reactance of the converter, respectively. This indicates the node where the converter is connected to AC. This indicates the node where the converter is connected to DC.
[0047] When space pulse width vector modulation is used, the voltage and voltage Satisfying Relationship:
[0048] (1)
[0049] In the formula: The converter modulation ratio, This represents the amplitude of the AC side voltage of the converter.
[0050] Active power injected into VSC from the AC system reactive power As shown in the following formula:
[0051] (2)
[0052] In the formula: For converter control angle; θ is the equivalent impedance angle of the converter; Y is the equivalent impedance of the converter.
[0053] Active power injected into VSC by DC system As shown in the following formula:
[0054] (3)
[0055] In power flow calculations for AC / DC hybrid systems, the control equations of the converter are mainly divided into two categories: active power control equations and reactive power control equations.
[0056] Active power control methods include:
[0057] (1) DC side voltage of the constant converter
[0058] (4)
[0059] In the formula: U dcref This is the reference DC voltage value on the DC side of the VSC.
[0060] (2) Active power on the DC side of the constant converter
[0061] (5)
[0062] In the formula: P dcref This is the reference active power value on the DC side of the VSC.
[0063] (3) Active power on the AC side of the constant converter
[0064] (6)
[0065] In the formula: P asref It is the reference active power value on the AC side of VSC.
[0066] Reactive power control methods include:
[0067] (1) AC voltage of the constant converter
[0068] (7)
[0069] In the formula: P asref It is the reference active power value on the AC side of VSC.
[0070] (2) Reactive power on the AC side of the constant converter
[0071] (8)
[0072] In the formula: Q asref It is the reference active power value on the AC side of VSC.
[0073] Step 2: Based on Kirchhoff's current law, establish the power imbalance equations for AC nodes and DC nodes;
[0074] In AC / DC hybrid systems, the types of nodes are complex. Based on whether AC nodes and DC nodes are directly connected to the converter, nodes can be roughly divided into four categories: (1) AC nodes directly connected to the converter; (2) other AC nodes; (3) DC nodes directly connected to the converter; and (4) other DC nodes.
[0075] In a communication system, nodes can be classified into pure communication nodes and non-pure communication nodes based on whether they are connected to the VSC.
[0076] For a purely AC node, the active and reactive power imbalance equations are as follows:
[0077] (9)
[0078] In the formula: n is the number of communication nodes; Let i be the voltage amplitude at node i in the AC system. The phase angle difference between node i and node j; and Let be the conductance and susceptance between node i and node j; and These represent the injected active and reactive power of node i in the AC system, respectively.
[0079] For the active and reactive power imbalance equations of non-pure AC nodes, a power term to be injected into the converter needs to be extracted from equation (9), as shown in the following equation:
[0080] (10)
[0081] In DC systems, nodes can be classified as pure DC nodes and non-pure DC nodes based on whether they are connected to the VSC.
[0082] For a pure DC node, the active power imbalance equation is as follows:
[0083] (11)
[0084] In the formula: m is the number of DC nodes; It is the voltage amplitude at DC node i; It is the admittance between DC node i and DC node j; It is the injected active power at DC node i.
[0085] For non-pure DC nodes, an active power term needs to be extracted from equation (11) and injected into the converter. The specific equation is as follows:
[0086] (12)
[0087] Since the converter losses are equivalent to the loss impedance, the AC side power and DC side power of the converter are equal. Based on the power balance principle, the VSC balance equation can be established, as shown in the following equation:
[0088] (13)
[0089] Step 3: Perform Taylor expansion on the VSC active power control equations and VSC reactive power control equations established in Step 1, as well as the AC node power imbalance equations and DC node power imbalance equations established in Step 2, and ignore higher-order terms to obtain the linearized unified power flow equations of the AC / DC hybrid distribution network. Then, transform the linearized unified power flow equations into a Jacobian matrix in matrix form.
[0090] In step three, the VSC control equations, AC node and DC node power imbalance equations are expanded using Taylor expansion, and higher-order terms are ignored to obtain a linear unified power flow equation set for the AC / DC hybrid distribution network. The linear equation set is then transformed into matrix form. Based on equations (4) to (13), the power flow calculation equations are established. For the AC / DC node power imbalance equations not directly connected to the converter, the linearized result is as follows:
[0091] (14)
[0092] The above system of equations can be expressed in matrix form as follows:
[0093] (15)
[0094] The off-diagonal elements of the Jacobian matrix satisfy the following:
[0095] (16)
[0096] Diagonal elements satisfy:
[0097] (17)
[0098] The power imbalance equations for AC and DC nodes directly connected to the converter can be linearized as follows:
[0099] (18)
[0100] The converter power balance equation is linearized as follows:
[0101] (19)
[0102] Combining equations (15) to (19), we can obtain the following iterative equations for calculating the power flow of AC hybrid distribution networks.
[0103] (20)
[0104]
[0105] The elements corresponding to the extended module of the AC system power imbalance equation satisfy:
[0106] (twenty one)
[0107] In the formula: The number of VSCs connected in the hybrid system.
[0108] The corresponding elements of the extended module of the DC system power imbalance equation satisfy:
[0109] (twenty two)
[0110] The elements in the Jacobian matrix corresponding to the newly added converter power balance equation satisfy:
[0111] (twenty three)
[0112] The elements of the converter control equations will change depending on the control method.
[0113] Step 4: Perform incomplete LU decomposition preprocessing on the Jacobian matrix in matrix form obtained in Step 3, and use the stable biconjugate gradient method to solve the preprocessed Jacobian matrix to obtain the power flow solution.
[0114] This invention preprocesses the Jacobian matrix before solving the power flow problem, which accelerates the convergence of the power flow calculation. Incomplete LU decomposition is mainly divided into three categories: ILU(0), ILU(1), and ILU(2). This invention uses ILU(0) preprocessing, also known as unfilled incomplete LU decomposition. This preprocessing method decomposes the iteration matrix into L and U, where L and U have the same non-zero structure as the lower and upper triangular parts of the iteration matrix, respectively. Before solving the power flow equations of the AC / DC hybrid distribution network, using ILU(0) to preprocess the iteration matrix can accelerate the convergence of the calculation while maintaining the sparsity of the iteration matrix.
[0115] Because the unified solution method for AC / DC hybrid distribution network power flow extends the DC model and converter module, the dimension of the Jacobian matrix increases and it becomes more sparse. The stable biconjugate gradient algorithm is suitable for solving asymmetric sparse linear equation systems, and it is insensitive to initial iteration values, exhibiting better robustness. Furthermore, preprocessing the Jacobian matrix using incomplete LU decomposition can significantly improve the algorithm's convergence speed. The specific solution steps are as follows:
[0116] 1) Input basic data, including power generation, load, branch impedance, and VSC control mode;
[0117] 2) Generate the node admittance matrix based on the branch data, thereby obtaining the branch conductance and susceptance;
[0118] 3) Set variables , , , and Initial value;
[0119] 4) Based on the basic power flow equations, the modified equations for power flow calculation in AC / DC hybrid distribution networks are obtained, generating power imbalance and iteration matrices;
[0120] (twenty four)
[0121] In the formula:
[0122] (25)
[0123] (26)
[0124] (27)
[0125] Considering the asymmetry and sparsity of the Jacobian matrix, this invention employs the BICGSTAB algorithm.
[20] The linear equations are solved by preprocessing the Jacobian matrix using incomplete LU decomposition, and the specific steps are as follows:
[0126] Step 1: First, given the iteration matrix J, vector b, and initial values... and the maximum number of iterations Maximum tolerance The preprocessing matrix W is obtained by preprocessing the Jacobian matrix using incomplete LU decomposition, and then the calculation is performed. and order ,
[0127] Step 2: If and If the result is positive, proceed to step 3; otherwise, stop the calculation and output the result. .
[0128] Step 3: .like or If the result is not found, the algorithm terminates and the calculation fails; otherwise, proceed to step 4.
[0129] Step 4: If ,but Otherwise, calculate
[0130]
[0131] Step 5: Solve the equation ,calculate , , .
[0132] Step 6: ,like ,but Otherwise, stop output. .
[0133] Step 7: Solve , , , , , Let k = k + 1, then go to step 2.
[0134] 5) Calculate equation (25) to obtain the correction amount. The algorithm determines if the maximum unbalanced power is less than the convergence accuracy. If the convergence accuracy is met, the algorithm converges; otherwise, the correction value is updated. .
[0135] 6) Number of update iterations If the number of iterations is greater than or equal to the maximum number of iterations, the algorithm exits and power flow calculation is not completed; otherwise, go to step 4.
[0136] by Figure 2 The IEEE33 AC / DC hybrid system shown is used as a test platform. The power flow calculation of the system under different VSC control modes is performed using the method of this invention. Figure 3 and Figure 4The calculated results for the voltage amplitude and phase angle of each node are presented, and all results are within a reasonable range. The method proposed in this invention can stably converge to an accurate power flow solution in AC / DC hybrid distribution network power flow calculation scenarios, effectively overcoming the problems of traditional models easily diverging and having insufficient convergence accuracy under complex conditions such as multi-voltage level interaction and nonlinear characteristics of DC converter stations. Under different operating conditions and control strategies, the algorithm exhibits good adaptability and robustness, and has strong tolerance to network topology changes, parameter perturbations, and load fluctuations. Through system testing in multiple AC / DC hybrid distribution network examples, the proposed linearized unified power flow model can achieve integrated modeling of AC networks, DC networks, converter devices, and distribution points, significantly reducing the nonlinearity of the power flow equations while ensuring model accuracy. The proposed preprocessing solution strategy further improves solution efficiency and numerical stability through equation regularization, coefficient matrix optimization, and adaptive selection of iterative initial values. The calculation results show that the proposed method outperforms conventional power flow algorithms in terms of convergence speed, solution accuracy, and numerical robustness, fully verifying the correctness, effectiveness, and engineering practical value of the proposed linearized unified power flow model and preprocessing solution method in power flow analysis of AC / DC hybrid distribution networks.
[0137] Embodiments of the present invention also provide a power flow calculation device for AC / DC hybrid distribution networks that considers incomplete LU decomposition preprocessing, comprising:
[0138] The VSC control equation establishment module is used to establish the active power control equation and reactive power control equation of the VSC based on the steady-state voltage and power equation of the voltage source converter VSC.
[0139] The power imbalance equation establishment module is used to establish AC node power imbalance equations and DC node power imbalance equations based on Kirchhoff's current law.
[0140] The power flow equation linearization module is used to perform Taylor expansion on the VSC active power control equation, VSC reactive power control equation output by the VSC control equation establishment module, and the AC node power imbalance equation and DC node power imbalance equation output by the power imbalance equation establishment module, respectively, and ignore higher-order terms to obtain a linearized unified power flow equation set for the AC / DC hybrid distribution network, and transform the linearized unified power flow equation set into a matrix form of Jacobian matrix.
[0141] The preprocessing solution module is used to perform incomplete LU decomposition preprocessing on the matrix form Jacobian matrix output by the linearization module of the power flow equations, and to solve the preprocessed Jacobian matrix using the stable biconjugate gradient method to obtain the power flow solution.
[0142] The following specific embodiment further illustrates the implementation effect of the AC / DC hybrid distribution network considering incomplete LU decomposition preprocessing provided by the present invention.
[0143] by Figure 2 Taking the distribution network shown as an example, this distribution network contains 33 nodes, with a rated AC voltage of 12.66kV, a VSC unit capacity of 1MVA, and an equivalent impedance of the converter. , Convergence accuracy is taken The maximum number of iterations is set to 50. Based on the power output and load demand data of the distribution network, the power flow of the AC / DC hybrid distribution network is solved using the method provided in this invention. The effectiveness of the preprocessing method proposed in this invention is verified, and the robustness of the algorithm is verified by comparison with other algorithms.
[0144] 1) Proof of the effectiveness of preprocessing
[0145] As can be seen from Table 1, the preprocessing method of the present invention significantly reduces the number of iterations and accelerates iterative convergence under most VSC control strategies.
[0146] Table 1 Comparison of iteration counts before and after preprocessing
[0147]
[0148] The incomplete LU decomposition preprocessing methods are divided into three types: ILU(0), ILU(1), and ILU(2). As shown in Table 2, under different VSC control modes, the number of non-zero elements injected by the ILU(1) and ILU(2) preprocessing methods is relatively large, which leads to a significant increase in computation time. The preprocessing method of this invention does not inject any non-zero elements, maintains the sparsity of the matrix, and can accelerate convergence.
[0149] Table 2 Comparison of non-zero element injection using different pretreatment methods
[0150]
[0151] 2) Robustness verification of the method proposed in this invention
[0152] When the convergence accuracy is 1e-5, the power flow calculation convergence times are 30 times under the first VSC control mode, 9 times under the second VSC control mode, and 4 times under the third and fourth VSC control modes. Table 4 lists the power flow calculation times of Newton's iteration method, the Generalized Minimal Residual Algorithm (GMRES), and the algorithm of this invention.
[0153] Table 3 Comparison of computation time between the algorithm of this invention and other algorithms
[0154]
[0155] As can be seen from the table, the GMRES algorithm takes the longest to compute for the same number of iterations. The algorithm of this invention is slightly slower than Newton's method in terms of computation speed.
[0156] To verify that the convergence of the algorithm of this invention is less affected by the initial value, this chapter appropriately changes the VSC modulation ratio and the initial value of the control angle iteration. The calculation results are shown in Table 4.
[0157] Table 4. Comparison of convergence results between the algorithm of this invention and other algorithms.
[0158]
[0159] In summary, among the three algorithms, Newton's iteration method has the shortest computation time, but it is highly sensitive to initial conditions. If the initial conditions are not chosen appropriately or the iteration matrix has high sparsity, singularities in the iteration matrix may occur, leading to non-convergence. The GMRES algorithm is a more conservative algorithm; although its sensitivity to initial conditions in power flow calculation is relatively low, its computation time is relatively long. The algorithm presented in this invention combines stability and speed.
[0160] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.
Claims
1. A method for calculating power flow in AC / DC hybrid distribution networks considering incomplete LU decomposition preprocessing, characterized in that, Includes the following steps: Step 1: Based on the steady-state voltage and power equations of the voltage source converter (VSC), establish the active power control equations and reactive power control equations for the VSC. Step 2: Based on Kirchhoff's current law, establish the power imbalance equations for AC nodes and DC nodes; Step 3: Perform Taylor expansion on the VSC active power control equations and VSC reactive power control equations established in Step 1, as well as the AC node power imbalance equations and DC node power imbalance equations established in Step 2, and ignore higher-order terms to obtain the linearized unified power flow equations of the AC / DC hybrid distribution network. Then, transform the linearized unified power flow equations into a Jacobian matrix in matrix form. Step 4: Perform incomplete LU decomposition preprocessing on the Jacobian matrix in matrix form obtained in Step 3, and use the stable biconjugate gradient method to solve the preprocessed Jacobian matrix to obtain the power flow solution.
2. The AC / DC hybrid distribution network power flow calculation method considering incomplete LU decomposition preprocessing as described in claim 1, characterized in that: In step one, the active power control mode of the VSC includes the DC side voltage of the stator converter, the active power of the DC side of the stator converter, and the active power of the AC side of the stator converter; the reactive power control mode of the VSC includes the AC voltage of the stator converter and the reactive power of the AC side of the stator converter.
3. The AC / DC hybrid distribution network power flow calculation method considering incomplete LU decomposition preprocessing as described in claim 1, characterized in that: In step two, based on whether the nodes are connected to the VSC, AC nodes are divided into pure AC nodes and non-pure AC nodes, and DC nodes are divided into pure DC nodes and non-pure DC nodes, and their power imbalance equations are established respectively. For non-pure AC nodes, the power imbalance equation is the power imbalance equation of a pure AC node minus the power term injected into the converter. For non-pure DC nodes, the power imbalance equation is based on the power imbalance equation of pure DC nodes, minus the active power term injected into the converter. Meanwhile, based on the principle that the AC side power of the converter is equal to the DC side power, the VSC power balance equation is established.
4. The AC / DC hybrid distribution network power flow calculation method considering incomplete LU decomposition preprocessing as described in claim 1, characterized in that, In step three, the linearized unified power flow equation set includes the linearized forms of the AC node power imbalance equation, the DC node power imbalance equation, the VSC power balance equation, and the VSC control equation. The Jacobian matrix in matrix form is constructed based on the above linearized equations, and its elements include modules corresponding to the AC system power imbalance equation, the DC system power imbalance equation, the converter power balance equation, and the converter control equation.
5. The AC / DC hybrid distribution network power flow calculation method considering incomplete LU decomposition preprocessing as described in claim 1, characterized in that, In step four, the incomplete LU decomposition preprocessing adopts the incomplete LU decomposition ILU(0) method without filling, and preprocesses it while maintaining the sparsity of the Jacobian matrix to obtain the preprocessed matrix; The stable biconjugate gradient method iteratively solves the linearized unified power flow equations based on the preprocessing matrix. When the maximum unbalanced power is less than the preset convergence accuracy, the power flow solution is obtained.
6. A power flow calculation device for AC / DC hybrid distribution networks considering incomplete LU decomposition preprocessing, characterized in that it comprises: The VSC control equation establishment module is used to establish the active power control equation and reactive power control equation of the VSC based on the steady-state voltage and power equations of the voltage source converter VSC. The power imbalance equation establishment module is used to establish AC node power imbalance equations and DC node power imbalance equations based on Kirchhoff's current law. The power flow equation linearization module is used to perform Taylor expansion on the VSC active power control equation, VSC reactive power control equation output by the VSC control equation establishment module, and the AC node power imbalance equation and DC node power imbalance equation output by the power imbalance equation establishment module, respectively, and ignore higher-order terms to obtain a linearized unified power flow equation set for the AC / DC hybrid distribution network, and transform the linearized unified power flow equation set into a matrix form of Jacobian matrix. The preprocessing solution module is used to perform incomplete LU decomposition preprocessing on the matrix form Jacobian matrix output by the linearization module of the power flow equations, and to solve the preprocessed Jacobian matrix using the stable biconjugate gradient method to obtain the power flow solution.
7. The AC / DC hybrid distribution network power flow calculation device considering incomplete LU decomposition preprocessing according to claim 6, characterized in that, In the VSC control equation establishment module, the active power control mode of the VSC includes the DC side voltage of the stator converter, the active power of the DC side of the stator converter, and the active power of the AC side of the stator converter; the reactive power control mode of the VSC includes the AC voltage of the stator converter and the reactive power of the AC side of the stator converter.
8. The AC / DC hybrid distribution network power flow calculation device considering incomplete LU decomposition preprocessing according to claim 6, characterized in that, The power imbalance equation establishment module classifies AC nodes into pure AC nodes and non-pure AC nodes, and DC nodes into pure DC nodes and non-pure DC nodes, based on whether the nodes are connected to VSC, and establishes their respective power imbalance equations. For non-pure AC nodes, the power imbalance equation is the power imbalance equation of a pure AC node minus the power term injected into the converter. For non-pure DC nodes, the power imbalance equation is based on the power imbalance equation of pure DC nodes, minus the active power term injected into the converter. Meanwhile, based on the principle that the AC side power of the converter is equal to the DC side power, the VSC power balance equation is established.
9. The AC / DC hybrid distribution network power flow calculation device considering incomplete LU decomposition preprocessing according to claim 6, characterized in that, The linearized unified power flow equation set constructed by the power flow equation set linearization module includes the linearized forms of AC node power imbalance equations, DC node power imbalance equations, VSC power balance equations, and VSC control equations. The Jacobian matrix in matrix form is constructed based on the above linearized equations, and its elements include modules corresponding to the AC system power imbalance equation, the DC system power imbalance equation, the converter power balance equation, and the converter control equation.
10. The AC / DC hybrid distribution network power flow calculation device considering incomplete LU decomposition preprocessing according to claim 6, characterized in that, The preprocessing solution module uses the incomplete LU decomposition ILU(0) method without filling to preprocess the Jacobian matrix and obtain the preprocessed matrix; The preprocessing solution module uses the stable biconjugate gradient method to iteratively solve the linearized unified power flow equations based on the preprocessing matrix. When the maximum unbalanced power is less than the preset convergence accuracy, the power flow solution is output.