A power flow calculation method and system for alternating current and direct current power systems based on quasi-newton method

Abstract

The application discloses a power flow calculation method and system of AC / DC power system based on quasi-Newton method, establishes a power flow calculation model of conventional DC converter station and flexible DC converter station based on input and output characteristics of AC side and DC side; extends the rectangular coordinate equation of only considering node voltage in traditional power flow calculation to the augmented rectangular coordinate system considering node voltage and current, and establishes a unified power flow calculation model of AC / DC power flow calculation; establishes the direction and step length of the first iteration through Newton method, and obtains the initial value of quasi-Newton iteration; continuously updates the quasi-Newton iteration matrix in the iteration process, so that the calculation of Jacobian matrix and inversion is not required repeatedly; when the power flow solution iteration meets the requirements, the solution of power flow calculation is output. Through the calculation method, the unified iteration of AC / DC power flow can be realized by using the unified power flow model of AC / DC, meanwhile, the quasi-Newton method is adopted to save the time required by each iteration, and has the characteristics of super-linear convergence.

Description

Technical Field

[0001] This invention belongs to the field of power technology, specifically relating to a method and system for calculating AC / DC power flow based on the quasi-Newton method. Background Technology

[0002] With the widespread grid connection of new energy sources and the commissioning of DC projects, the future power system will be a large-scale AC / DC hybrid power grid. Therefore, based on traditional AC power system flow calculations, future power grid flow calculations will need to further calculate the flow of the DC network. Existing methods for AC / DC power system flow calculations can be divided into alternating iterative methods and unified iterative methods. The alternating iterative method calculates the flow of the AC and DC systems separately, using the AC system solution as the initial value for the DC system and vice versa, iterating repeatedly until a satisfactory solution is found. However, when the number of converters in the system is large, the number of nodes to be calculated increases, making convergence difficult. Furthermore, the repeated alternating iterative calculations on both the AC and DC sides can lead to a huge computational burden and low efficiency in AC / DC power system flow calculations. The unified iterative method aims to establish unified equations for the AC and DC network equations, performing unified iterative calculations on both AC and DC power systems, thus solving the problems of poor convergence and large computational burden caused by repeated calculations in the alternating iterative method. However, the unified iterative method requires a unified iterative model for AC / DC power system flow.

[0003] Newton's method is a classic algorithm for power flow calculation, achieving good convergence speed in engineering calculations due to its quadratic convergence property. However, Newton's method is highly sensitive to initial conditions. After a large number of renewable energy sources are connected to the grid, the system's operating mode changes significantly, and traditional flat-start strategies may not converge to a suitable operating point. Furthermore, Newton's method determines the step size and direction of each iteration by solving the Jacobian matrix. However, in power flow problems with large variations, this can easily lead to ill-conditioned problems, i.e., the Jacobian matrix becomes singular near the iteration point, at which point Newton's method cannot function properly. In addition, because the Jacobian matrix needs to be recalculated in each iteration, although Newton's method has a fast convergence speed, the computational load of each iteration is large, resulting in a practically unsatisfactory computational speed.

[0004] Therefore, there is an urgent need for a unified power flow model for AC / DC power systems for unified iteration, and to find an iterative method that can improve computational performance. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a power flow calculation method and system for AC / DC power systems based on the quasi-Newton method, which addresses the shortcomings of the prior art. This method solves the problems that it is difficult to give a unified power flow equation under new power systems, that ill-conditioned problems exist in the calculation process of Newton method and are difficult to solve, and that repeated differentiation and inversion lead to a large amount of computation.

[0006] The present invention adopts the following technical solution:

[0007] A method for calculating AC / DC power flow based on the quasi-Newton method includes the following steps:

[0008] Based on the input, output, and control characteristics of AC / DC converter stations, a power flow calculation model for AC / DC power systems, including conventional DC transmission and flexible DC transmission, is constructed.

[0009] Based on the AC / DC power flow calculation model, a unified power flow calculation model for AC / DC power systems is established in the augmented rectangular coordinate system.

[0010] Based on the unified power flow calculation model of the system, at the flat start point, the direction and step size of the first iteration are determined by Newton's method, and the initial value of the quasi-Newton method iteration is obtained.

[0011] Based on the obtained initial values ​​of the quasi-Newton method, the power flow equations are solved iteratively using the quasi-Newton method, and the iterative matrix is ​​updated based on the Broyden rank-1 correction scheme.

[0012] Power flow iteration is performed based on a unified iterative scheme for AC / DC hybrid power flow and an iterative matrix based on the quasi-Newton method with Broyden rank-1 correction. After each iteration, when , Let be the iteration value for the kth iteration. To account for the error, the power flow solution is obtained.

[0013] Preferably, the power flow calculation model for AC / DC power systems using conventional DC transmission is as follows:

[0014]

[0015]

[0016]

[0017]

[0018] in, , These are DC voltage and current, respectively. , , These represent the complex power, reactive power, and active power flowing from the AC side to the DC side, respectively. , , These are the converter transformer turns ratio, converter control angle, and equivalent commutation reactance, respectively. The commutation angle coefficient, The voltage amplitude of the AC node connected to the LCC;

[0019] Power flow calculation model for AC / DC power systems using flexible DC transmission:

[0020]

[0021]

[0022]

[0023] in, and These are the reference values ​​for reactive power and voltage on the AC side, respectively.

[0024] Preferably, in power flow calculations, for the sending-end DC station:

[0025]

[0026] For the receiving end system:

[0027]

[0028] in, For losses.

[0029] Preferably, the unified power flow calculation model for AC / DC power systems established in the augmented rectangular coordinate system is as follows:

[0030] For AC nodes, the following can be obtained from the node voltage equations:

[0031]

[0032] PQ node:

[0033]

[0034] PV nodes:

[0035]

[0036] Balance node:

[0037]

[0038] The node voltage equation for a DC node is given:

[0039]

[0040] in, Define the real part of the node voltage on the AC side. The virtual part, Inject the real part of the current into the node. The virtual part, Define the node voltage amplitude for the DC side. Inject current amplitude into the node, The node voltage amplitude given for the AC node. The active power given to the AC node. Reactive power Provide active power to the DC node. The imaginary part of the admittance matrix is... Let be the real part of the admittance matrix. For the admittance at this point, This represents the node voltage amplitude at that point.

[0041] Preferably, the AC / DC power system contains n One communication node, d DC nodes, and k One AC / DC converter station; the system in augmented rectangular coordinates has One unknown variable.

[0042] Preferably, before writing the power flow equations, the per-unit values ​​of the AC and DC networks are uniformly processed and selected. , , These are the AC and DC side voltage reference values, respectively. , These are the AC and DC power reference values, respectively. This is the system's rated power.

[0043] Preferably, the direction and step size of the first iteration are determined using Newton's method as follows:

[0044]

[0045] in, As the initial value, This is the value from the first iteration. This is the Jacobian matrix from the first iteration. This is the function value from the first iteration.

[0046] Preferably, the matrix updated iteratively based on the Broyden rank-1 correction scheme is as follows:

[0047]

[0048] in, Let be the quasi-Newton matrix for the k-th iteration. Let be the gradient of the i-th search direction in the k-th iteration. Let be the iteration value for the kth iteration. Let be the i-th unit vector.

[0049] Preferably, the power flow equations are solved iteratively using the quasi-Newton method as follows:

[0050]

[0051] in, Let this be the initial value for the k-th iteration. This is the initial value for the (k+1)th iteration. Let be the quasi-Newton matrix for the k-th iteration. This is the function value in the k-th iteration.

[0052] Secondly, embodiments of the present invention provide a power flow calculation system for AC / DC power systems based on the quasi-Newton method, comprising:

[0053] The first generation module constructs a power flow calculation model of the AC / DC power system, including conventional DC transmission and flexible DC transmission, based on the input, output and control characteristics of the AC / DC converter station.

[0054] The second generation module establishes a unified power flow calculation model for AC / DC power systems in an augmented rectangular coordinate system, based on the AC / DC power system power flow calculation model.

[0055] The calculation module, based on the system's unified power flow calculation model, establishes the direction and step size of the first iteration at the flat start-up point using Newton's method, obtaining the initial value for the quasi-Newton method iteration. Based on the obtained initial value for the quasi-Newton method iteration, it iteratively solves the power flow equations using the quasi-Newton method, updating the iteration matrix based on the Broyden rank-1 correction scheme. Power flow iteration is performed based on the unified iteration scheme for AC / DC hybrid power flow and the iteration matrix based on the Broyden rank-1 correction quasi-Newton method. After each iteration, when... , Let be the iteration value for the kth iteration. To account for the error, the power flow solution is obtained.

[0056] Thirdly, a computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described AC / DC power flow calculation method based on the quasi-Newton method.

[0057] Fourthly, embodiments of the present invention provide a computer-readable storage medium including a computer program, which, when executed by a processor, implements the steps of the above-described AC / DC power flow calculation method based on the quasi-Newton method.

[0058] Fifthly, a chip includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described AC / DC power flow calculation method based on the quasi-Newton method.

[0059] In a sixth aspect, embodiments of the present invention provide an electronic device, including a computer program, which, when executed by the electronic device, implements the steps of the above-described AC / DC power flow calculation method based on the quasi-Newton method.

[0060] Compared with the prior art, the present invention has at least the following beneficial effects:

[0061] A power flow calculation method for AC / DC power systems based on the quasi-Newton method is proposed. Based on the input-output characteristics of the AC and DC sides, power flow calculation models for conventional and flexible DC converter stations are established. The rectangular coordinate equations in traditional power flow calculations, which only consider node voltages, are extended to an augmented rectangular coordinate system that considers both node voltages and currents, establishing a unified power flow calculation model for AC / DC power flow. At the flat-start operation point of traditional power flow calculations, the direction and step size of the first iteration are determined using the Newton method, obtaining the initial values ​​for the quasi-Newton method iteration. According to the Broyden rank-1 corrected quasi-Newton iteration scheme, the quasi-Newton iteration matrix is ​​continuously updated during the iteration process, thus eliminating the need for repeated differentiation, calculation of the Jacobian matrix, and inversion. When the power flow solution iterates to a point that meets the requirements, the power flow calculation solution is output. The calculation method provided by this invention enables unified iteration of AC / DC power flow using a unified AC / DC power flow model. Furthermore, compared to the Newton method, the quasi-Newton method significantly reduces the time required for each iteration while still maintaining superlinear convergence.

[0062] Furthermore, due to the continuous increase in the scale of new energy grid connection and the development of DC transmission technology, the future power grid will exhibit AC / DC hybrid characteristics. By studying the input-output characteristics of conventional DC and flexible DC converter stations, a unified iterative power flow model for AC / DC systems is established. By extending the voltage variables in the Cartesian coordinate system in traditional power flow calculations to voltage and current variables in the augmented Cartesian coordinate system, a unified power flow model for AC / DC systems capable of iterative calculations is constructed to address the problems of poor convergence and high computational complexity caused by the alternating iterative method in AC / DC power flow calculations.

[0063] Furthermore, the quasi-Newton method reduces the computational cost of each step in the Newton method iteration by replacing the Jacobian matrix in the Newton method with an easily obtainable matrix. It can be proven that the quasi-Newton method exhibits superlinear convergence under certain conditions. For nonlinear equations, the quasi-Newton method involves replacing the tangent line in the previous iteration with the secant line from the previous two iterations. For systems of nonlinear equations, to reduce computational cost, a correction scheme is typically adopted, using information from the previous iteration to update the quasi-Newton matrix.

[0064] Furthermore, the correction equations for quasi-Newton matrices mainly employ rank-1 and rank-2 corrections, that is, adding or subtracting a lower-rank matrix from the previous iteration's quasi-Newton matrix to obtain the next iteration's quasi-Newton matrix. Although the convergence speed of rank-1 correction is slower, rank-2 correction is often used for symmetric problems. Power flow problems in power systems, especially AC / DC hybrid power flows, exhibit strong asymmetry; therefore, the Broyden form of rank-1 correction is used.

[0065] Furthermore, based on the traditional Broyden rank-1 algorithm, a correction scheme that does not require inversion is obtained through the Sherman-Morrison formula.

[0066] Furthermore, at the flat start point, the direction and step size of the first iteration are determined by Newton's method, thus obtaining the initial values ​​for the quasi-Newton method iteration.

[0067] It is understandable that the beneficial effects of the second aspect mentioned above can be found in the relevant descriptions in the first aspect mentioned above, and will not be repeated here.

[0068] In summary, this invention constructs a unified power flow calculation model for AC / DC systems, which can realize unified iteration of AC / DC power flow using the unified AC / DC power flow model. At the same time, the use of the quasi-Newton method saves the time required for each iteration and has the characteristic of superlinear convergence.

[0069] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0070] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0071] Figure 2 This is a simplified topology diagram of a conventional DC transmission converter station.

[0072] Figure 3 A simplified topology model diagram of a flexible DC transmission converter station;

[0073] Figure 4 The flowchart shows the quasi-Newton algorithm using Broyden rank-1 correction.

[0074] Figure 5 A schematic diagram of a modified 39-node example used for power flow calculation;

[0075] Figure 6 A schematic diagram comparing the convergence of Newton's method and quasi-Newton's method;

[0076] Figure 7 This is a schematic diagram of the AC / DC power flow calculation system based on the quasi-Newton method of the present invention.

[0077] Figure 8 A schematic diagram of a computer device provided in an embodiment of the present invention;

[0078] Figure 9 This is a block diagram of a chip provided according to an embodiment of the present invention. Detailed Implementation

[0079] 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, not all, of the embodiments of the present invention. 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.

[0080] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0081] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0082] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this invention generally indicates that the preceding and following objects have an "or" relationship.

[0083] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0084] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0085] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0086] This invention provides a power flow calculation method for AC / DC power systems based on the quasi-Newton method. Based on the input-output characteristics of the AC and DC sides, power flow calculation models for conventional and flexible DC converter stations are established. The rectangular coordinate equations in traditional power flow calculations, which only consider node voltages, are extended to an augmented rectangular coordinate system that considers both node voltages and currents, establishing a unified power flow calculation model for AC / DC power flow. At the flat-start operation point of traditional power flow calculations, the direction and step size of the first iteration are determined using the Newton method, obtaining the initial values ​​for the quasi-Newton method iteration. According to the Broyden rank-1 corrected quasi-Newton iteration scheme, the quasi-Newton iteration matrix is ​​continuously updated during the iteration process, thus eliminating the need for repeated differentiation, calculation of the Jacobian matrix, and inversion. When the power flow solution iterates to a point that meets the requirements, the power flow calculation solution is output. Through the calculation method provided by this invention, unified iteration of AC / DC power flow can be achieved using the unified AC / DC power flow model. Furthermore, compared to the Newton method, the quasi-Newton method significantly saves the time required for each iteration while still maintaining superlinear convergence.

[0087] Please see Figure 1 This invention provides a method for calculating the power flow of AC / DC power systems based on the quasi-Newton method, comprising the following steps:

[0088] S1. The conventional DC-DC converter is a current-source converter (LCC), with the following topology: Figure 2 If the filtering and reactive power compensation devices are equivalent to AC nodes, then the rectifier station and inverter station (hereinafter referred to as...) R and I The steady-state equations for all (represented by) are:

[0089]

[0090]

[0091]

[0092]

[0093] in, , These are DC voltage and current, respectively. , , These represent the complex power, reactive power, and active power flowing from the AC side to the DC side, respectively. , , These are the converter transformer turns ratio, converter control angle, and equivalent commutation reactance, respectively. The commutation angle coefficient, This refers to the voltage amplitude of the AC node connected to the LCC.

[0094] For a DC transmission line with resistance of For a conventional DC transmission system at both ends, the DC network equation, i.e., the DC line equation, is as follows:

[0095]

[0096] Ignoring the converter transformer turns ratio For switching, the control method of the rectifier station is usually constant current control, constant power control, or constant firing angle control, and the equations are respectively...

[0097]

[0098]

[0099]

[0100] Inverter stations typically employ either constant voltage control or constant turn-off angle control, with the following equations:

[0101]

[0102]

[0103] Each of the LCC converter stations at both ends of a DC transmission line has one governing equation.

[0104] In a Cartesian coordinate system, an AC / DC power flow model containing conventional DC current is established. The power flow equations for pure AC nodes remain unchanged, while for AC nodes connected to the LCC, the equations are as follows:

[0105]

[0106]

[0107]

[0108] Among them, the rectifier side is the addition of DC active power. The inverter side is to subtract the DC active power. The AC nodes connected to the LCC converter station are treated as special PQ nodes.

[0109] In a power system containing a conventional DC transmission line, the DC network equations, LCC steady-state equations, and control equations, at the converter transformer turns ratio... There are 13 equations and unknown variables when the condition is fixed. These are combined with the AC node power flow equations to obtain the power flow solution model.

[0110] When using a flexible DC-DC converter station (VSC), multi-terminal DC networks can be connected to AC networks. The VSC topology is shown in the attached figure. Figure 3 As shown, since the VSC controls the input and output of the converter through a given voltage signal, its control is more flexible than that of the LCC, and it has two control quantities: active and reactive power.

[0111] At the active power control level, it is divided into constant active power control. Hehe DC voltage control :

[0112]

[0113] Constant DC voltage control :

[0114]

[0115] At the reactive power control level, it is divided into constant reactive power control. and constant AC voltage control :

[0116]

[0117] Constant AC voltage control :

[0118]

[0119] in, and These represent the active and reactive power values ​​on the AC side, respectively.

[0120] Since reactance does not affect the steady-state characteristics of a DC line, the DC network model is a purely resistive linear model. For any DC transmission line, we have:

[0121]

[0122] in, For the series branch i Node flow j The current at the node, , They are respectively i Nodes and j Node voltage, The conductance of the series branch.

[0123] Since VSC-based flexible DC transmission is suitable for forming multi-terminal DC transmission networks, the entire DC network can be described as a node conductance matrix. Then, the relationship between node injection current and node voltage can be obtained from the node voltage equation, where the node injection current is positive in the direction of flowing into the DC network.

[0124] Assume there is a DC network d There are several DC nodes, and the injected current at each DC node forms the injected current vector. The voltages at the branch nodes form a voltage vector. The nodal conductance matrix is Then the linear node voltage equation is

[0125]

[0126] Nodal conductance matrix elements Satisfy: When hour, For mutual conductance; when hour, It is self-conductive.

[0127] DC power sources and DC loads are not included in the DC linear network and are treated as constant power models.

[0128] If the direction of power injected into the DC network is considered positive, then the relationship between the injected power and the injected current and voltage at the node is as follows:

[0129]

[0130] In a multi-terminal flexible DC transmission system, the control methods of each converter station need to be coordinated. Common inter-station coordinated control mainly includes single-point DC voltage control and multi-point DC voltage control.

[0131] In the master-slave control mode, a typical single-point DC voltage control method, only one master station controls the DC node voltage, ensuring the DC voltage equals a specified reference value; the rest are slave stations, controlling the active power of the DC nodes, also ensuring the active power equals a specified reference value. The master station maintains the voltage stability of the DC system and ensures the system's power balance, meaning the active power input to the DC network equals the sum of the output and losses, acting as a balancing node.

[0132] In multi-point DC voltage control, multiple converter station nodes simultaneously control the DC voltage. One implementation method is voltage droop control. When power imbalance occurs or any VSC converter station goes out of operation, voltage droop control can achieve active power distribution among DC nodes without relying on communication and stabilize the DC voltage.

[0133] For those n A multi-point DC voltage control DC network with multiple nodes, including m The DC node is controlled by voltage droop, and its control equation is as follows:

[0134]

[0135] in, This refers to the active power output at the DC side of the VSC converter station. This represents the DC voltage amplitude. and These are the corresponding given reference values. Let be the coefficient; rewrite this formula as:

[0136]

[0137] in, , .

[0138] In other words, both DC power and DC voltage are controlled simultaneously. Therefore, each converter station using the voltage droop control method participates in stabilizing the DC voltage and directly allocates DC power based on the DC voltage at the converter station outlet.

[0139] the remaining A DC node can either function as a power station with active power control or be a pure DC node that is not connected to the AC network via VSC.

[0140] Both LCC and VSC experience losses of only 1% to 3% during normal operation. To simplify calculations, this portion of the loss is ignored in power flow calculations. When considering losses, we have:

[0141]

[0142] in, , , These are the loss coefficients, The AC side voltage amplitude is typically used.

[0143] Losses are related to the direction of power flow. For the sending-end DC station, the following applies:

[0144]

[0145] For the receiving end system, we have:

[0146]

[0147] S2. Based on the original power flow equations which only include power flow voltage equations, current variables are introduced in the rectangular coordinate system. In addition to the node voltage, the node injection current is retained as an unknown variable. That is, the power flow equations in the augmented rectangular coordinate system are established, including linear node voltage equations, node power equations with the highest order being second, and VSC control equations, ensuring that the number of power flow equations is equal to the number of unknown variables.

[0148] Assume that the AC / DC power system contains n One communication node, d DC nodes, and k One VSC converter station.

[0149] Based on the aforementioned VSC steady-state model, we obtain the following: An expanded communication network of individual communication nodes.

[0150] In power flow calculations, all physical quantities are expressed in per-unit values. Before writing the power flow equations, the per-unit values ​​of the AC and DC networks are first processed uniformly. Let the reference values ​​of the AC and DC voltages be respectively... , The AC and DC power reference values ​​are respectively , The system's rated power is Select:

[0151] The AC nodes in the expanded AC network are divided into two main categories: AC-side exit nodes of the VSC converter station and pure AC nodes. In addition to the three node types, pure AC nodes also handle zero-injection nodes separately.

[0152] For all AC nodes, the node voltage equations can be obtained, consisting of two equations concerning the real and imaginary parts of the injected current:

[0153]

[0154] Similar to traditional power flow calculations, AC nodes are categorized into three types: PQ, PV, and slack nodes. Specifically, for PQ nodes:

[0155]

[0156] For PV nodes:

[0157]

[0158] For the equilibrium node, we have:

[0159]

[0160] For DC nodes, a pure DC node can be given by the DC node voltage equation:

[0161]

[0162] And there is the nodal injection power equation:

[0163]

[0164] Furthermore, when considering converter losses, a new variable is introduced. Therefore:

[0165]

[0166] By retaining the injected current at nodes as an unknown variable, and to ensure that the number of unknowns equals the number of equations, linear node voltage equations are retained. Furthermore, for nodes with zero injection, their constraint equations are rewritten to be linear as well. This results in a high degree of linearization of the power flow equations, which greatly improves the convergence properties of iterative solutions. Because the number of unknowns and equations is expanded compared to the traditional power flow model in Cartesian coordinates, it is called the power flow model in augmented Cartesian coordinates.

[0167] S3. The mathematical essence of power flow problem solving is solving a system of nonlinear equations. For problems involving power flow, it is virtually impossible to solve analytically; therefore, numerical solutions are generally obtained through iterative methods. Newton's method is an effective method for solving nonlinear equation systems.

[0168] The iterative formula for the traditional Newton's method is:

[0169]

[0170] in, Let be the Jacobian matrix of the k-th iteration, which is a function about exist The derivative value at that point, The function value for the kth iteration is... .

[0171] Since Newton's method requires recalculating and inverting the Jacobian matrix in each iteration, the computational cost of each iteration is high. Therefore, quasi-Newton methods consider using matrix... Approaching And through a certain iterative update This eliminates the need to calculate the Jacobian matrix every time.

[0172] make , The tangent direction of Newton's method is replaced by the secant direction between adjacent iteration points, i.e.:

[0173]

[0174] Thus, the iterative formula for the quasi-Newton method is obtained:

[0175]

[0176] Suppose that the iterative formula obtained by the quasi-Newton method eventually converges to Then we have:

[0177]

[0178] Depend on ,set up If it is not singular, then it must exist. , so that:

[0179]

[0180] set up Therefore:

[0181]

[0182] If:

[0183]

[0184] If the quasi-Newtonian step asymptotically approximates the Newtonian step in both magnitude and direction, then:

[0185]

[0186] Right now , Superlinear convergence to Thus, the quasi-Newton method also has superlinear convergence characteristics.

[0187] As can be seen from the iterative formula, the quasi-Newton method requires initial values ​​at the start of the iteration. Compared to the value of the first iteration Therefore, in addition to the traditional flat-start strategy, the format of the first iteration also needs to be provided. In the first iteration, Newton's method is used to provide the initial values. In traditional AC systems, Newton's method can converge quickly, requiring only 4-5 iterations to obtain a satisfactory solution. However, in the unified iteration of AC / DC power systems, due to the complexity of the variables, Newton's method does not converge as quickly. Therefore, using Newton's method to provide the initial values ​​for the iteration does not reduce the overall computational speed of the algorithm.

[0188] S4. To avoid the repeated inversion of the Jacobian matrix in Newton's method, the iteration process directly uses... Perform iterations and record... Consider correcting iteratively. ,Right now ,in for The function formed.

[0189] Generally, correction is achieved by adding or subtracting a low-order matrix (such as a rank-1 or rank-2 matrix). Rank-1 correction is the simplest method, correcting the quasi-Newton matrix using a rank-1 matrix. The Broyden rank-1 algorithm is the most widely used quasi-Newton algorithm, applicable to both symmetric and asymmetric cases of the quasi-Newton matrix. Although existing research indicates that the iterative method using Broyden rank-1 correction converges slowly for symmetric problems, power flow problems, especially AC / DC hybrid power flow problems, are highly asymmetric. Therefore, the iterative algorithm using the Broyden rank-1 correction scheme is generally slightly faster than the symmetric forms of rank-1 and rank-2 correction. Subsequent examples also verify this.

[0190] Rank-1 correction is used, that is:

[0191]

[0192] According to the equations of the quasi-Newton method, we obtain:

[0193]

[0194] Therefore:

[0195]

[0196] That is, vector and In the same direction, we get:

[0197]

[0198] Further The correction formula for Broyden's rank-1 method is obtained as follows:

[0199]

[0200] Applying the Sherman-Morrison formula

[0201]

[0202] Regarding The correction formula is converted to ,get

[0203]

[0204] Furthermore, to demonstrate the comparison between the traditional Newton's method and different quasi-Newton methods in the embodiments of this invention, two correction schemes based on rank-2 correction are provided:

[0205] DFP format:

[0206]

[0207] BFGS format:

[0208]

[0209] For large-scale power flow problems, the Jacobian matrix in the iteration process of Newton's method is usually sparse, thus greatly reducing memory consumption during iteration. Although the quasi-Newton method eliminates the need for differentiation, significantly improving computational speed, the matrix corrected by Broyden's rank-1 correction, while having a rank of only 1, results in a quasi-Newton matrix. The sparsity is violated during iteration, meaning that the original zero elements become non-zero elements. Therefore, we consider using a certain transformation to convert the correction matrix into a sparse format, so as not to destroy the sparsity of the quasi-Newton matrix.

[0210] Let matrix H k In satisfying H k The set of elements (i,j) = 0 is (i,j)∈K, defined as:

[0211]

[0212] The Broyden rank-1 correction formula for the sparse scheme is obtained as follows:

[0213]

[0214] Indicates if Then guarantee .

[0215] S5. Power flow iteration is performed using a unified iterative scheme based on AC / DC hybrid power flow and an iterative scheme based on the quasi-Newton method with Broyden rank-1 correction. After each iteration, it is determined whether the iterative solution meets the requirements. ,in To allow for error, if the requirements are met, the power flow solution will be output.

[0216] In another embodiment of the present invention, a power flow calculation system for AC / DC power systems based on the quasi-Newton method is provided. This system can be used to implement the above-mentioned power flow calculation method for AC / DC power systems based on the quasi-Newton method. Specifically, the power flow calculation system for AC / DC power systems based on the quasi-Newton method includes a first generation module, a second generation module, and a calculation module.

[0217] The first generation module constructs a power flow calculation model of AC / DC power system, including conventional DC transmission and flexible DC transmission, based on the input, output and control characteristics of the AC / DC converter station.

[0218] The second generation module establishes a unified power flow calculation model for AC / DC power systems in an augmented rectangular coordinate system, based on the AC / DC power system power flow calculation model.

[0219] The calculation module, based on the system's unified power flow calculation model, establishes the direction and step size of the first iteration at the flat start-up point using Newton's method, obtaining the initial value for the quasi-Newton method iteration. Based on the obtained initial value for the quasi-Newton method iteration, it iteratively solves the power flow equations using the quasi-Newton method, updating the iteration matrix based on the Broyden rank-1 correction scheme. Power flow iteration is performed based on the unified iteration scheme for AC / DC hybrid power flow and the iteration matrix based on the quasi-Newton method using Broyden rank-1 correction. After each iteration, when... , Let be the iteration value for the kth iteration. To account for the error, the power flow solution is obtained.

[0220] In another embodiment of the present invention, a terminal device is provided, comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to achieve a corresponding method flow or corresponding function. The processor described in this embodiment can be used for operating a power flow calculation method for AC / DC power systems based on the quasi-Newton method, including:

[0221] Based on the input-output and control characteristics of AC / DC converter stations, a power flow calculation model for AC / DC power systems, including conventional DC transmission and flexible DC transmission, is constructed. Based on this model, a unified power flow calculation model for the AC / DC power system is established in an augmented rectangular coordinate system. Using this unified model, at the initial start-up point, the direction and step size of the first iteration are determined using Newton's method, yielding the initial values ​​for the quasi-Newton method iteration. Based on these initial values, the power flow equations are solved iteratively using the quasi-Newton method, and the iteration matrix is ​​updated using the Broyden rank-1 correction scheme. Power flow iteration is performed using the unified iteration scheme for AC / DC hybrid power flow and the iteration matrix based on the Broyden rank-1 correction quasi-Newton method. After each iteration, when… , Let be the iteration value for the kth iteration. To account for the error, the power flow solution is obtained.

[0222] Please see Figure 8The terminal device is a computer device. In this embodiment, the computer device 60 includes a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When executed by the processor 61, the computer program 63 implements the AC / DC power flow calculation method based on the quasi-Newton method in this embodiment. To avoid repetition, details are omitted here. Alternatively, when executed by the processor 61, the computer program 63 implements the functions of each model / unit in the AC / DC power flow calculation system based on the quasi-Newton method in this embodiment. To avoid repetition, details are omitted here.

[0223] Computer device 60 can be a desktop computer, laptop, handheld computer, cloud server, or other computing device. Computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will understand that... Figure 8 This is merely an example of computer device 60 and does not constitute a limitation on computer device 60. It may include more or fewer components than shown, or combine certain components, or different components. For example, computer device may also include input / output devices, network access devices, buses, etc.

[0224] The processor 61 may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0225] The memory 62 can be an internal storage unit of the computer device 60, such as a hard disk or RAM of the computer device 60. The memory 62 can also be an external storage device of the computer device 60, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. equipped on the computer device 60.

[0226] Furthermore, the memory 62 may include both internal storage units of the computer device 60 and external storage devices. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 can also be used to temporarily store data that has been output or will be output.

[0227] Please see Figure 9 The terminal device is a chip. In this embodiment, the chip 600 includes a processor 622, which may be one or more, and a memory 632 for storing computer programs executable by the processor 622. The computer program stored in the memory 632 may include one or more modules, each corresponding to a set of instructions. Furthermore, the processor 622 may be configured to execute the computer program to perform the aforementioned AC / DC power flow calculation method based on the quasi-Newton method.

[0228] Additionally, chip 600 may also include a power supply component 626 and a communication component 650. The power supply component 626 can be configured to perform power management of chip 600, and the communication component 650 can be configured to enable communication of chip 600, such as wired or wireless communication. Furthermore, chip 600 may also include an input / output interface 658. Chip 600 can operate on an operating system stored in memory 632.

[0229] In another embodiment of the present invention, a storage medium is provided, specifically a computer-readable storage medium, which is a memory device in a terminal device for storing programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and extended storage media supported by the terminal device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, the storage space also stores one or more instructions suitable for loading and execution by a processor; these instructions can be one or more computer programs. It should be noted that the computer-readable storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device.

[0230] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the AC / DC power flow calculation method based on the quasi-Newton method in the above embodiments; one or more instructions in the computer-readable storage medium are loaded and executed by the processor in the following steps:

[0231] Based on the input-output and control characteristics of AC / DC converter stations, a power flow calculation model for AC / DC power systems, including conventional DC transmission and flexible DC transmission, is constructed. Based on this model, a unified power flow calculation model for the AC / DC power system is established in an augmented rectangular coordinate system. Using this unified model, at the initial start-up point, the direction and step size of the first iteration are determined using Newton's method, yielding the initial values ​​for the quasi-Newton method iteration. Based on these initial values, the power flow equations are solved iteratively using the quasi-Newton method, and the iteration matrix is ​​updated using the Broyden rank-1 correction scheme. Power flow iteration is performed using the unified iteration scheme for AC / DC hybrid power flow and the iteration matrix based on the Broyden rank-1 correction quasi-Newton method. After each iteration, when… , Let be the iteration value for the kth iteration. To account for the error, the power flow solution is obtained.

[0232] 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, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0233] Based on the standard IEEE 39-node example, a 5-node DC network consisting of a four-terminal VSC flexible DC line and two LCC DC lines are added. The specific topology diagram is attached. Figure 5 As shown, power flow calculations for this system were performed using MATLAB, and the computational performance differences between Newton's method and the quasi-Newton method were compared.

[0234] Table 1 compares the convergence speed and computation time of several algorithms in the ensemble algorithm. The two quasi-Newton methods using rank-2 correction fail to converge. This is because, when applied to asymmetric problems, the step size and direction of rank-2 correction deviate from those of Newton's step size and direction, resulting in poor convergence. The quasi-Newton method using Broyden rank-1 correction and the traditional Newton method both converge. Although the quadratic convergence characteristic of the traditional Newton method makes its convergence speed faster, achieving the required accuracy with fewer iterations, compared to the rank-1 correction algorithm, the computation time is significantly increased because it requires solving the Jacobian matrix and its inverse matrix in each iteration.

[0235] Table 1: Comparison of convergence speed and computation time of several algorithms

[0236]

[0237] Please see Figure 5 The graph shows the relationship between the mismatch and the number of iterations for several algorithms, which more clearly illustrates the differences in convergence speed among them. In the first few iterations, the quasi-Newton method using Broyden rank-1 correction converges even faster than the traditional Newton method.

[0238] The above process verifies the outstanding advantages of the present invention in AC / DC hybrid power flow calculation. Compared with traditional AC / DC power flow calculation methods, the present invention has obvious superiority.

[0239] This invention provides a method for constructing a unified AC / DC power flow model. In this embodiment, a unified power flow calculation model is first established in an augmented rectangular coordinate system by constructing models of the converter station and the DC system.

[0240] This invention also presents a method for improving power flow calculation performance using a quasi-Newton method. In this embodiment, the quasi-Newton iterative scheme with Broyden rank-1 correction, although having a slower convergence speed than the traditional Newton method, significantly improves the calculation speed.

[0241] In summary, this invention provides a power flow calculation method and system for AC / DC power systems based on the quasi-Newton method. From a modeling perspective, it establishes a unified power flow model for AC / DC hybrid systems. Algorithmically, it approximates the Newton step in terms of direction and step size using the quasi-Newton method, simplifying the iterative differentiation and inversion operations, greatly simplifying the calculation process, improving the calculation speed, and demonstrating significant effectiveness in actual simulation results.

[0242] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0243] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0244] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0245] In the embodiments provided by this invention, it should be understood that the disclosed devices / terminals and methods can be implemented in other ways. For example, the device / terminal embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0246] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0247] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0248] If the integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random-access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0249] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus, and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0250] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0251] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0252] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A method for calculating power flow in AC / DC power systems based on the quasi-Newton method, comprising the following steps: Based on the input-output and control characteristics of AC / DC converter stations, a power flow calculation model for AC / DC power systems, including conventional DC transmission and flexible DC transmission, is constructed. The power flow calculation model for AC / DC power systems with conventional DC transmission is as follows: in, , These are DC voltage and current, respectively. , , These represent the complex power, reactive power, and active power flowing from the AC side to the DC side, respectively. , , These are the converter transformer turns ratio, converter control angle, and equivalent commutation reactance, respectively. The commutation angle coefficient, The voltage amplitude of the AC node connected to the LCC; Power flow calculation model for AC / DC power systems using flexible DC transmission: in, and These are the reference values ​​for reactive power and voltage on the AC side, respectively. Based on the AC / DC power flow calculation model, a unified power flow calculation model for AC / DC power systems is established in an augmented rectangular coordinate system. Specifically, the unified power flow calculation model for AC / DC power systems in the augmented rectangular coordinate system is established as follows: For AC nodes, the following can be obtained from the node voltage equations: PQ node: PV nodes: Balanced node: The node voltage equation for a DC node is given: in, Define the real part of the node voltage on the AC side. The virtual part, Inject the real part of the current into the node. The virtual part, Inject current amplitude into the node, The active power given to the AC node. Reactive power Provide active power to the DC node. The imaginary part of the admittance matrix is... Let be the real part of the admittance matrix. For the admittance at this point, This represents the node voltage amplitude at that point; Based on the unified power flow calculation model of the system, at the flat start point, the direction and step size of the first iteration are determined by Newton's method, and the initial value of the quasi-Newton method iteration is obtained. Based on the obtained initial values ​​of the quasi-Newton method, the power flow equations are solved iteratively using the quasi-Newton method, and the iterative matrix is ​​updated based on the Broyden rank-1 correction scheme. Power flow iteration is performed based on a unified iterative scheme for AC / DC hybrid power flow and an iterative matrix based on the quasi-Newton method with Broyden rank-1 correction. After each iteration, when , Let be the iteration value for the kth iteration. To account for the error, the power flow solution is obtained.

2. The AC / DC power flow calculation method based on the quasi-Newton method according to claim 1, characterized in that, In power flow calculations, for the sending-end DC station: For the receiving end system: in, This is due to losses.

3. The AC / DC power flow calculation method based on the quasi-Newton method according to claim 1, characterized in that, AC and DC power systems contain n One communication node, d DC nodes, and k One AC / DC converter station; the system in augmented rectangular coordinates has One unknown variable.

4. The AC / DC power flow calculation method based on the quasi-Newton method according to claim 1, characterized in that, Before writing the power flow equations, the per-unit values ​​of the AC and DC networks are processed uniformly, and selected... , , These are the AC and DC side voltage reference values, respectively. , These are the AC and DC power reference values, respectively. This is the system's rated power.

5. The AC / DC power flow calculation method based on the quasi-Newton method according to claim 1, characterized in that, The direction and step size for the first iteration are determined using Newton's method as follows: in, As the initial value, This is the value from the first iteration. This is the Jacobian matrix from the first iteration. This is the function value from the first iteration.

6. The AC / DC power flow calculation method based on the quasi-Newton method according to claim 1, characterized in that, The matrix updated based on the Broyden rank-1 correction scheme is as follows: in, Let be the quasi-Newton matrix for the k-th iteration. Let be the gradient of the i-th search direction in the k-th iteration. Let be the iteration value for the kth iteration. Let be the i-th unit vector.

7. The AC / DC power flow calculation method based on the quasi-Newton method according to claim 1, characterized in that, The power flow equations are solved iteratively using the quasi-Newton method as follows: in, This is the initial value for the k-th iteration. Let be the initial value for the (k+1)th iteration. Let be the quasi-Newton matrix for the k-th iteration. This is the function value for the k-th iteration.

8. A power flow calculation system for AC / DC power systems based on the quasi-Newton method, characterized in that, include: The first generation module constructs a power flow calculation model for the AC / DC power system, including both conventional and flexible DC transmission, based on the input / output and control characteristics of the AC / DC converter station. The power flow calculation model for the AC / DC power system with conventional DC transmission is as follows: in, , These are DC voltage and current, respectively. , , These represent the complex power, reactive power, and active power flowing from the AC side to the DC side, respectively. , , These are the converter transformer turns ratio, converter control angle, and equivalent commutation reactance, respectively. The commutation angle coefficient, The voltage amplitude of the AC node connected to the LCC; Power flow calculation model for AC / DC power systems using flexible DC transmission: in, and These are the reference values ​​for reactive power and voltage on the AC side, respectively. The second generation module, based on the AC / DC power system power flow calculation model, establishes a unified power flow calculation model for the AC / DC power system in an augmented rectangular coordinate system. Specifically, the establishment of this unified power flow calculation model in the augmented rectangular coordinate system is as follows: For AC nodes, the following can be obtained from the node voltage equations: PQ node: PV nodes: Balanced node: The node voltage equation for a DC node is given: in, Define the real part of the node voltage on the AC side. The virtual part, Inject the real part of the current into the node. The virtual part, Inject current amplitude into the node, The active power given to the AC node. Reactive power Provide active power to the DC node. The imaginary part of the admittance matrix is... Let be the real part of the admittance matrix. For the admittance at this point, This represents the node voltage amplitude at that point; The calculation module, based on the system's unified power flow calculation model, establishes the direction and step size of the first iteration at the flat start-up point using Newton's method, obtaining the initial value for the quasi-Newton method iteration. Based on the obtained initial value for the quasi-Newton method iteration, it iteratively solves the power flow equations using the quasi-Newton method, updating the iteration matrix based on the Broyden rank-1 correction scheme. Power flow iteration is performed based on the unified iteration scheme for AC / DC hybrid power flow and the iteration matrix based on the quasi-Newton method using Broyden rank-1 correction. After each iteration, when... , To account for the error, the power flow solution is obtained.

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