AC / DC power system load flow calculation method and system based on quasi-Newton method

Abstract

The invention discloses an AC / DC power system load flow calculation method and system based on a quasi-Newton method, and the method comprises the steps: building load flow calculation models of a conventional DC converter station and a flexible DC converter station based on the input and output characteristics of an AC side and a DC side; a rectangular coordinate equation which only considers node voltage in traditional load flow calculation is expanded to an augmented rectangular coordinate system which considers node voltage and current, and a unified load flow calculation model of AC-DC load flow calculation is established; determining the direction and step length of the first iteration through a Newton method, and obtaining an iteration initial value of the quasi-Newton method; the quasi-Newton iteration matrix is continuously updated in the iteration process, so that repeated derivation calculation of the Jacobian matrix and inversion are not needed; and when the power flow solution is iterated to meet the requirement, outputting a power flow calculation solution. Through the calculation method provided by the invention, the unified iteration of the alternating current and direct current power flow can be realized by utilizing the alternating current and direct current unified power flow model, meanwhile, the time required by each iteration is saved by adopting the quasi-Newton method, and the method has the characteristic of super-linear convergence.

Description

Technical Field

[0001] The present invention belongs to the field of electric power technology, and in particular relates to a method and system for calculating power flow of an AC or DC power system based on a quasi-Newton method. Background Art

[0002] With the large-scale grid connection of new energy and the commissioning of DC projects, the future power system will be a large AC / DC hybrid power grid. Therefore, based on the traditional AC power system power flow calculation, the power flow calculation of the future power grid needs to further calculate the power flow of the DC grid. The existing methods for AC / DC power system power flow calculation can be divided into alternating iteration method and unified iteration method. The alternating iteration method calculates the power flow of the AC system and the DC system respectively during the calculation process, and uses the solution of the AC system as the initial value of the DC system, and uses the solution of the DC system as the initial value of the AC system, and iterates repeatedly until a solution that meets the requirements is found. However, when the number of converters in the system is large, the number of nodes to be calculated increases, and the calculation results are difficult to converge. In addition, due to multiple alternating iterative calculations on the AC and DC sides, the calculation amount of the AC / DC power system power flow calculation may be huge and inefficient. The unified iteration method aims to establish a unified equation for the AC network equation and the DC network equation, and iterate the AC / DC power system in a unified manner, solving the problem of poor convergence and large amount of calculation caused by repeated calculations in the alternating iteration method. However, the unified iteration method requires a unified iteration model for the power flow of AC / DC power systems.

[0003] Newton's method is a classic algorithm for power flow calculation. Due to its quadratic convergence characteristics, it has achieved a good convergence speed in engineering calculations. However, on the one hand, Newton's method is very sensitive to initial values. After a large number of new energy sources are connected to the grid, the operation mode of the system changes greatly, and the traditional flat start strategy may not converge to a suitable operating point; on the other hand, Newton's method determines the step size and direction of the iteration by solving the Jacobian matrix in each iteration process. However, in power flow problems with large changes, it is easy to cause ill-conditioned problems, that is, the Jacobian matrix is ​​singular near the iteration point, and the Newton method cannot operate normally at this time. In addition, since the Jacobian matrix needs to be recalculated in each iteration, although the Newton method converges quickly, the amount of calculation for each iteration is large, resulting in the actual calculation speed may not be very ideal.

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

[0005] The technical problem to be solved by the present invention is to provide a method and system for calculating the power flow of an AC or DC power system based on the quasi-Newton method in view of the deficiencies in the above-mentioned prior art, so as to solve the technical problems that the unified power flow equation is difficult to give in a new power system, there are ill-conditioned problems in the calculation process of the Newton method that are difficult to solve, and repeated derivation and inversion result in a large amount of calculation.

[0006] The present invention adopts the following technical solutions: A method for calculating power flow of an AC / DC power system based on a quasi-Newton method comprises the following steps: According to the input, output and control characteristics of the AC / DC converter station, a power flow calculation model for the AC / DC power system including conventional DC transmission and flexible DC transmission is constructed; Based on the AC / DC power system power flow calculation model, a unified power flow calculation model for AC / DC power systems is established in an augmented rectangular coordinate system. Based on the unified power flow calculation model of the system, at the flat start operation point, the direction and step size of the first iteration are determined by the Newton method, and the initial value of the iteration of the quasi-Newton method is obtained; Based on the obtained iterative initial value of the quasi-Newton method, the power flow equation is iteratively solved by the quasi-Newton method, and the iterative matrix is ​​updated based on the Broyden rank 1 correction format; The power flow iteration is performed based on the unified iteration format of the AC / DC hybrid power flow and the iterative matrix of the quasi-Newton method based on Broyden rank 1 correction. After each iteration, when , is the k-th iteration amount, For the allowable error, the power flow solution is obtained.

[0007] Preferably, the AC / DC power system flow calculation model for conventional DC transmission is:

[0008]

[0009]

[0010]

[0011] in, , are the DC voltage and current, , , are the complex power, reactive power, and active power flowing from the AC side to the DC side, , , They are the converter transformer ratio, converter control angle, and equivalent commutation reactance. is the commutation angle coefficient, is the voltage amplitude of the AC node connected to the LCC; AC / DC power system flow calculation model for flexible DC transmission:

[0012]

[0013]

[0014] in, and They are the reference values ​​of reactive power and voltage on the AC side respectively.

[0015] Preferably, in the power flow calculation, for the sending-end DC station:

[0016] To the receiving system:

[0017] in, For loss.

[0018] Preferably, the unified power flow calculation model of the AC / DC power system is established in the augmented rectangular coordinate system as follows:

[0019] For AC nodes, the node voltage equation is:

[0020]

[0021] PQ Node: PV Node: Balance Node:

[0022] The DC nodes are given by the DC node voltage equation:

[0023] in, Define the real part of the node voltage for the AC side, is the imaginary part, Inject the real part of the current into the node, is the imaginary part, Define the node voltage amplitude for the DC side, The magnitude of the current injected into the node, is the node voltage amplitude given by the AC node, is the active power given by the AC node, is the reactive power, Given the active power at the DC node, is the imaginary part of the admittance matrix, is the real part of the admittance matrix, is the point admittance, is the node voltage amplitude at this point.

[0024] Preferably, the AC and DC power systems contain n Communication nodes, d DC nodes, and k AC / DC converter stations; the system in augmented rectangular coordinates has unknown variable.

[0025] Preferably, before writing the power flow equation, the per-unit values ​​of the AC and DC networks are uniformly processed and selected. , , are the voltage reference values ​​of the AC side and the DC side respectively. , are the power reference values ​​of the AC side and the DC side respectively. is the rated power of the system.

[0026] Preferably, the direction and step size of the first iteration are established by Newton's method as follows:

[0027] in, is the initial value, is the value of the first iteration, is the Jacobian matrix of the first iteration, is the function value at the first iteration.

[0028] Preferably, the matrix of the update iteration based on the Broyden rank 1 correction format is as follows:

[0029] in, is the quasi-Newton matrix of the kth iteration, is the gradient of the ith search direction in the kth iteration, is the number of iterations for the kth time, is the i-th unit vector.

[0030] Preferably, the tidal current equation is iteratively solved by the quasi-Newton method as follows:

[0031] in, is the initial value of the kth iteration, is the initial value of the k+1th iteration, is the quasi-Newton matrix of the kth iteration, is the function value at the kth iteration.

[0032] In a second aspect, an embodiment of the present invention provides an AC / DC power system flow calculation system based on a quasi-Newton method, comprising: The first generation module constructs an AC / DC power system power flow calculation model including conventional DC transmission and flexible DC transmission according to the input, output and control characteristics of the AC / DC converter station; The second generation module establishes a unified power flow calculation model of the AC and DC power systems in an augmented rectangular coordinate system based on the power flow calculation model of the AC and DC power systems; The calculation module is based on the unified power flow calculation model of the system. At the flat start operation point, the direction and step size of the first iteration are determined by the Newton method to obtain the initial iteration value of the quasi-Newton method. Based on the obtained initial iteration value of the quasi-Newton method, the power flow equation is iteratively solved by the quasi-Newton method, and the iterative matrix is ​​updated based on the Broyden rank 1 correction format. The power flow is iterated based on the unified iteration format of the AC / DC hybrid power flow and the iterative matrix of the quasi-Newton method based on the Broyden rank 1 correction. After each iteration, when , is the number of iterations for the kth time, For the allowable error, the power flow solution is obtained.

[0033] In a third aspect, a computer device comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above-mentioned method for calculating the flow of an AC or DC power system based on the quasi-Newton method when executing the computer program.

[0034] In a fourth aspect, an embodiment of the present invention provides a computer-readable storage medium, including a computer program, which, when executed by a processor, implements the steps of the above-mentioned method for calculating the power flow of an AC or DC power system based on the quasi-Newton method.

[0035] In a fifth aspect, a chip comprises a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the steps of the above-mentioned method for calculating the flow of AC and DC power systems based on the quasi-Newton method are implemented.

[0036] In a sixth aspect, an embodiment of the present invention provides an electronic device, including a computer program, which, when executed by the electronic device, implements the steps of the above-mentioned method for calculating the power flow of an AC or DC power system based on the quasi-Newton method.

[0037] Compared with the prior art, the present invention has at least the following beneficial effects: A method for calculating the flow of AC and DC power systems based on the quasi-Newton method, based on the input-output characteristics of the AC side and the DC side, establishes a flow calculation model for a conventional DC converter station and a flexible DC converter station; the rectangular coordinate equation that only considers the node voltage in the traditional flow calculation is extended to an augmented rectangular coordinate system that considers the node voltage and current, and a unified flow calculation model for AC and DC flow calculation is established; the direction and step size of the first iteration are established by the Newton method at the flat start operation point of the traditional flow calculation, and the initial value of the iteration of the quasi-Newton method is obtained; according to the Broyden rank 1 corrected quasi-Newton iteration format, the quasi-Newton iteration matrix is ​​continuously updated during the iteration process, so that there is no need to repeatedly derive and calculate the Jacobian matrix and invert it; when the flow solution is iterated to meet the requirements, the solution of the flow calculation is output. Through the calculation method provided by the present invention, the unified iteration of AC and DC flow can be realized by using the AC and DC unified flow model, and at the same time, the quasi-Newton method greatly saves the time required for each iteration compared with the Newton method, and still has the characteristics of superlinear convergence.

[0038] 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 show AC / DC hybrid characteristics. By studying the input and output characteristics of conventional DC and flexible DC converter stations, a unified iterative power flow model for AC / DC systems is established. By expanding the voltage variables in the rectangular coordinate system in the traditional power flow calculation to the voltage and current variables in the augmented rectangular coordinate system, a unified power flow model for AC / DC systems that can be used for iterative calculations is constructed to solve the problems of poor convergence and large amount of calculation caused by the use of alternating iteration methods in AC / DC power flow calculations.

[0039] Furthermore, the quasi-Newton method replaces the Jacobian matrix in the Newton method calculation with an easily obtained matrix, thereby reducing the amount of calculation in each step of the Newton method iteration. It can be proved that when certain requirements are met, the quasi-Newton method has superlinear convergence characteristics. For nonlinear equations, the use of the quasi-Newton method is to replace the tangent line in the previous iteration process with the secant line in the previous two iterations. For nonlinear equations, in order to reduce the amount of calculation, a certain correction format is usually adopted to update the quasi-Newton matrix using the information of the previous iteration.

[0040] Furthermore, the correction equation of the quasi-Newton matrix mainly adopts rank 1 correction and rank 2 correction, that is, the quasi-Newton matrix of the previous iteration is added or subtracted by a low-rank matrix to obtain the quasi-Newton matrix of the next iteration. Although the convergence speed of rank 1 correction is slow, rank 2 correction is often used for symmetric problems. The power flow problem of the power system, especially the AC / DC hybrid power flow, shows strong asymmetry, so the Broyden form of rank 1 correction is used.

[0041] Furthermore, based on the traditional Broyden rank 1 algorithm, a correction format without inversion is obtained through the Sherman-Morrison formula.

[0042] Furthermore, the direction and step size of the first iteration are determined by the Newton method at the flat start operation point, and the initial value of the iteration of the quasi-Newton method is obtained.

[0043] It can be understood that the beneficial effects of the second aspect mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here.

[0044] In summary, the present invention constructs a unified power flow calculation model for AC / DC systems, which can realize unified iteration of AC / DC power flows using the AC / DC unified power flow model. At the same time, the quasi-Newton method is used to save the time required for each iteration and has the characteristics of superlinear convergence.

[0045] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a schematic diagram of the process of the present invention; Figure 2 It is a simplified topological model schematic diagram of a conventional DC transmission converter station; Figure 3 This is a simplified topology model diagram of a flexible DC transmission converter station; Figure 4 This is the flow chart of the quasi-Newton algorithm using Broyden rank 1 correction; Figure 5 This is a schematic diagram of the modified 39-node calculation example for power flow calculation; Figure 6 This is a schematic diagram comparing the convergence of Newton's method and quasi-Newton's method; Figure 7 It is a schematic diagram of the structure of the AC / DC power system power flow calculation system based on the quasi-Newton method of the present invention; Figure 8 A schematic diagram of a computer device provided by an embodiment of the present invention; Fig. 9 The block diagram of a chip provided according to an embodiment of the present invention. DETAILED DESCRIPTION

[0047] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0048] In the description of the present invention, it should be understood that the terms “include” and “comprises” indicate the presence of described features, wholes, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, wholes, steps, operations, elements, components and / or collections thereof.

[0049] It should also be understood that the terms used in the present specification are only for the purpose of describing specific embodiments and are not intended to limit the present invention. As used in the present specification and the appended claims, unless the context clearly indicates otherwise, the singular forms "a", "an" and "the" are intended to include plural forms.

[0050] It should be further understood that the term "and / or" used in the present specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes these combinations. For example, A and / or B can represent: A exists alone, A and B exist at the same time, and B exists alone. In addition, the character " / " in the present invention generally indicates that the associated objects are in an "or" relationship.

[0051] It should be understood that, although the terms first, second, third, etc. may be used to describe preset ranges, etc. in the embodiments of the present invention, these preset ranges should not be limited to these terms. These terms are only used to distinguish preset ranges from each other. 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.

[0052] The word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining" or "in response to detecting", depending on the context. Similarly, the phrases "if it is determined" or "if (stated condition or event) is detected" may be interpreted as "when it is determined" or "in response to determining" or "when detecting (stated condition or event)" or "in response to detecting (stated condition or event)", depending on the context.

[0053] Various structural schematic diagrams of the embodiments disclosed in the present invention are shown in the accompanying drawings. These figures are not drawn to scale, and some details are magnified and some details may be omitted for the purpose of clear expression. The shapes of various regions and layers shown in the figures and the relative sizes and positional relationships therebetween are only exemplary, and may deviate in practice due to manufacturing tolerances or technical limitations, and those skilled in the art may additionally design regions / layers with different shapes, sizes, and relative positions according to actual needs.

[0054] The present invention provides an AC / DC power system power flow calculation method based on the quasi-Newton method. Based on the input-output characteristics of the AC side and the DC side, a power flow calculation model of a conventional DC converter station and a flexible DC converter station is established; the rectangular coordinate equation that only considers the node voltage in the traditional power flow calculation is extended to an augmented rectangular coordinate system that considers the node voltage and current, and a unified power flow calculation model for AC / DC power flow calculation is established; the direction and step size of the first iteration are established by the Newton method at the flat start operation point of the traditional power flow calculation, and the initial value of the iteration of the quasi-Newton method is obtained; according to the Broyden rank 1 corrected quasi-Newton iteration format, the quasi-Newton iteration matrix is ​​continuously updated during the iteration process, so that there is no need to repeatedly derive and calculate the Jacobian matrix and inverse it; when the power flow solution is iterated to meet the requirements, the solution of the power flow calculation is output. Through the calculation method provided by the present invention, the unified iteration of AC / DC power flow can be realized by using the AC / DC unified power flow model. At the same time, the quasi-Newton method greatly saves the time required for each iteration compared with the Newton method, and still has the characteristics of superlinear convergence.

[0055] See also Figure 1 The present invention provides a method for calculating power flow of an AC / DC power system based on a quasi-Newton method, comprising the following steps: S1. The converter in conventional DC is a current source converter LCC, and the topology is as follows Figure 2 , the filtering and reactive power compensation devices are equivalent to the AC nodes, then the rectifier station and the inverter station (hereinafter referred to as R and I The steady-state equations are:

[0056]

[0057]

[0058]

[0059] in, , are the DC voltage and current, , , are the complex power, reactive power, and active power flowing from the AC side to the DC side, , , They are the converter transformer ratio, converter control angle, and equivalent commutation reactance. is the commutation angle coefficient, is the voltage amplitude of the AC node connected to the LCC.

[0060] For a DC transmission line resistance The DC network equation, that is, the DC line equation, of the conventional DC transmission system at both ends is:

[0061] The transformer ratio is not considered. The control mode of the rectifier station is usually constant current control, constant power control or constant firing angle control. The equations are

[0062]

[0063]

[0064] The control mode of the inverter station is usually constant voltage control or constant shutdown angle control, and the equations are

[0065]

[0066] The LCC converter stations at both ends of the DC transmission line each have one control equation.

[0067] In the rectangular coordinate system, an AC / DC power flow model with conventional DC is established. The power flow equation of the pure AC node remains unchanged, while for the AC node connected to the LCC:

[0068]

[0069]

[0070] Among them, the rectifier side is added with DC active , the inverter side is minus the DC active power , the AC nodes connected to the LCC converter station are treated as special PQ nodes.

[0071] In a power system with a conventional DC transmission line, the DC network equations, LCC steady-state equations and control equations are When fixed, there are 13 equations and unknown variables, which are combined with the AC node flow equation to obtain the model for flow solution.

[0072] When a flexible DC transmission converter station VSC is used, the connection between a multi-terminal DC network and an AC network can be realized. The topology of the VSC is shown in the following figure. Figure 3 As shown, since VSC controls the input and output of the converter through a given voltage signal, its control is more flexible than that of LCC, and it has two control quantities: active and reactive.

[0073] At the active power control level, it is divided into fixed active power control Hehe constant DC voltage control :

[0074] Constant DC voltage control :

[0075] At the reactive power control level, it is divided into fixed reactive power control Constant AC voltage control :

[0076] Constant AC voltage control :

[0077] in, and are the active and reactive values ​​on the AC side respectively.

[0078] Since the reactance does not affect the steady-state characteristics of the DC line, the DC network model is a pure resistance linear model. For any DC transmission line, we have:

[0079] in, For the series branch i Node flow j The current at the node, , They are i Node and j The voltage at the node, is the conductance of the series branch.

[0080] Since VSC-based flexible DC transmission is suitable for forming a multi-terminal DC transmission network, the entire DC network is described as a node conductance matrix. The relationship between the node injection current and the 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.

[0081] Assume that there is a DC network d DC nodes, the DC node injection current constitutes the injection current vector , the branch node voltages form a voltage vector , the node conductance matrix is , then the linear node voltage equation is

[0082] Nodal conductance matrix elements Satisfied: When hour, is mutual conductance; when hour, For self-conductance.

[0083] The DC power supply and DC load are not included in the DC linear network and are treated as a constant power model.

[0084] The DC node injection power is positive when it is injected into the DC network. The relationship between the node injection power, node injection current, and node voltage is:

[0085] The control methods of each converter station in a multi-terminal flexible DC transmission system need to be coordinated. Common coordinated control between converter stations mainly includes single-point DC voltage control and multi-point DC voltage control.

[0086] The master-slave control mode is a typical single-point DC voltage control mode. There is only one master station for DC node voltage control, and the DC voltage is equal to the specified reference value; the rest are slave stations, which control the active power of the DC nodes, and the active power is equal to the specified reference value. The master station is used to maintain the voltage stability of the DC system and ensure the power balance of the system, that is, the active power input to the DC network is equal to the sum of the active power output and loss, which is equivalent to a balanced node.

[0087] In the multi-point DC voltage control mode, multiple converter station nodes control the DC voltage simultaneously. One implementation method is to use voltage droop control. When power imbalance occurs or any VSC converter station is out of operation, the voltage droop control method can achieve active power distribution between DC nodes without relying on communication and stabilize the DC voltage.

[0088] For n A multi-point DC voltage control DC network with nodes, where m The DC nodes are voltage droop controlled, and the control equation is:

[0089] in, is the active power at the DC side of the VSC converter station, is the DC voltage amplitude, and are the corresponding given reference values, is the coefficient; rewrite this formula as:

[0090] in, , .

[0091] That is, DC power and DC voltage are controlled at the same time. Therefore, each converter station using voltage droop control method participates in stabilizing the DC voltage and directly distributes DC power according to the DC voltage at the converter station outlet.

[0092] the remaining Each DC node can either be used as a power station with active power control, or as a pure DC node that is not connected to the AC network through a VSC.

[0093] Whether it is LCC or VSC, the loss in normal operation is only 1%~3%. In order to simplify the calculation, the influence of this part of loss is ignored in the power flow calculation. When the loss is considered, there are:

[0094] in, , , are the loss coefficients, Generally, the voltage amplitude on the AC side is taken.

[0095] The loss is related to the power flow direction. For the sending-end DC station, there are:

[0096] For the receiving system, there are:

[0097] S2. On the basis of the original power flow equation which only contains the power flow voltage equation, the current variable is introduced in the rectangular coordinate system, and the node injection current is retained as an unknown variable except the node voltage. That is, the power flow equation in the augmented rectangular coordinate system is established, including the linear node voltage equation, the node power equation with the highest order being quadratic, and the VSC control equation, to ensure that the number of power flow equations is equal to the number of unknown variables.

[0098] Assume that the AC and DC power systems contain n Communication nodes, d DC nodes, and k VSC converter stations.

[0099] Based on the above VSC steady-state model, we get An extended communication network with 10 communication nodes.

[0100] All physical quantities in the power flow calculation adopt per unit values. Before writing the power flow equation, the per unit values ​​of the AC and DC networks are first processed uniformly. The voltage reference values ​​of the AC and DC sides are assumed to be , , the power reference values ​​of the AC side and DC side are , , the system rated power is . Select: The AC nodes in the extended AC network are divided into two categories: VSC converter station AC side exit nodes and pure AC nodes. In addition to the three types of nodes in the pure AC nodes, zero injection nodes are also processed separately.

[0101] For all AC nodes, the node voltage equations can be obtained, which are two equations about the real and imaginary parts of the injected current:

[0102]

[0103] Similar to traditional power flow calculation, AC nodes are divided into three categories: PQ, PV and balance nodes. For PQ nodes:

[0104] For PV nodes: For the balancing node:

[0105] For DC nodes, pure DC nodes can be given by the DC node voltage equation:

[0106] And there is a node injection power equation:

[0107] Furthermore, when considering the converter losses, a new variable is introduced: , and then we have:

[0108] The node injection current is retained as an unknown variable. In order to make the unknown quantity equal to the number of equations, the linear node voltage equation is retained, and for the zero injection node, its constraint equation is also rewritten as linear. The power flow equation has a high degree of linearization, which can greatly improve the convergence properties of the iterative solution. Compared with the power flow model in the traditional rectangular coordinate system, the number of unknown quantities and equations is expanded, so it is called the power flow model in the augmented rectangular coordinate system.

[0109] S3. The essence of solving the problem of power flow is to solve the nonlinear equations in mathematics. For the problem of tidal current, it is basically impossible to solve it by analytical solution, so it is generally solved numerically by iteration. Newton's method is an effective method for solving nonlinear equations; The iterative formula of the traditional Newton method is:

[0110] in, is the Jacobian matrix of the kth iteration, which is the function about exist The derivative value at is the function value of the kth iteration, that is .

[0111] Since the Newton method needs to recalculate the Jacobian matrix and invert it for each iteration, the amount of calculation for each iteration is large. Therefore, the quasi-Newton method considers using the matrix Come closer , and through certain iterative updates , thus eliminating the need to calculate the Jacobian matrix each time.

[0112] make , , replace the tangent direction of Newton's method by the secant direction between adjacent iteration points, that is:

[0113] Thus, the iterative formula of the quasi-Newton method is obtained:

[0114] Assume that the iterative formula obtained by the quasi-Newton method eventually converges to , then:

[0115] Depend on ,set up If it is not strange, it must exist , so that:

[0116] set up , and then we have:

[0117] If yes:

[0118] That is, the quasi-Newton step asymptotically approaches the Newton step in both size and direction, so:

[0119] Right now , Superlinear convergence to , so the quasi-Newton method also has superlinear convergence characteristics.

[0120] It can be seen from the iterative formula that when the quasi-Newton method is iterated, an initial value is required at the start of the iteration. With the value of the first iteration Therefore, on the basis of the traditional flat start strategy, the format of the first iteration needs to be given. In the first iteration, the Newton method is used to give the initial value. In the traditional AC system, the Newton method can converge quickly, and only 4-5 iterations are required to obtain a solution that meets the requirements. However, in the unified iteration of AC and DC power systems, due to the complexity of the variables, the Newton method will not converge so quickly, so using the Newton method to give the initial value of the iteration will not reduce the calculation speed of the algorithm as a whole.

[0121] S4. In order to avoid the repeated inversion of the Jacobian matrix in the Newton method, the iterative process directly adopts Iterate and remember , consider correcting by iterative method ,Right now ,in for The constructed function.

[0122] 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 correction method, which implements the correction of the quasi-Newton matrix through a rank 1 matrix. Broyden rank 1 algorithm is the most widely used quasi-Newton algorithm, which can be used for both symmetric and asymmetric quasi-Newton matrices. Although existing studies have shown that the iterative method using Broyden rank 1 correction converges slowly for symmetric problems. However, power flow problems, especially AC / DC hybrid power flow problems, are highly asymmetric problems. Therefore, the iterative algorithm using Broyden rank 1 correction format is generally slightly faster than the symmetric rank 1 correction and rank 2 correction. The subsequent examples also verified this point.

[0123] The rank 1 correction is adopted, that is:

[0124] According to the equation of the quasi-Newton method, we get:

[0125] So we have:

[0126] That is, vector and In the same direction, we get:

[0127] Further order , we get the correction formula of Broyden rank 1 method:

[0128] Apply the Sherman-Morrison formula

[0129] About The correction formula is converted to ,get

[0130] In addition, in order to reflect the comparison between the traditional Newton method and the quasi-Newton methods of different formats in the embodiments of the present invention, two correction formats based on rank 2 correction are provided: DFP Format:

[0131] BFGS format:

[0132] For large-scale power flow problems, the Jacobian matrix in the Newton method iteration process is usually sparse, so the memory consumption in the iteration can be greatly reduced. Although the quasi-Newton method does not require derivative operations, which greatly improves the calculation speed, the matrix corrected by Broyden rank 1 has a rank of only 1, but it leads to a quasi-Newton matrix The sparsity is destroyed in the iteration, that is, the original 0 elements become non-0 elements. Therefore, it is considered to adopt a certain transformation to convert the correction matrix into a sparse format, so as not to destroy the sparsity of the quasi-Newton matrix.

[0133] Let matrix H k Satisfy H k The set of elements where (i,j)=0 is (i,j)∈K, defined as:

[0134] The Broyden rank 1 correction formula in sparse format is obtained:

[0135] Indicates that if , then guarantee .

[0136] S5, based on the unified iteration format of AC / DC hybrid power flow and the iteration format of the quasi-Newton method based on Broyden rank 1 correction, the power flow iteration is performed, and after each iteration, it is determined whether the iterative solution meets the requirements, that is, ,in is the allowable error. If the requirements are met, the power flow solution is output.

[0137] In another embodiment of the present invention, an AC / DC power system flow calculation system based on the quasi-Newton method is provided. The system can be used to implement the above-mentioned AC / DC power system flow calculation method based on the quasi-Newton method. Specifically, the AC / DC power system flow calculation system based on the quasi-Newton method includes a first generation module, a second generation module and a calculation module.

[0138] Among them, the first generation module constructs an AC / DC power system power flow calculation model including conventional DC transmission and flexible DC transmission according to the input, output and control characteristics of the AC / DC converter station; The second generation module establishes a unified power flow calculation model of the AC and DC power systems in an augmented rectangular coordinate system based on the power flow calculation model of the AC and DC power systems; The calculation module is based on the unified power flow calculation model of the system. At the flat start operation point, the direction and step size of the first iteration are determined by the Newton method to obtain the initial iteration value of the quasi-Newton method. Based on the obtained initial iteration value of the quasi-Newton method, the power flow equation is iteratively solved by the quasi-Newton method, and the iterative matrix is ​​updated based on the Broyden rank 1 correction format. The power flow is iterated based on the unified iteration format of the AC / DC hybrid power flow and the iterative matrix of the quasi-Newton method based on the Broyden rank 1 correction. After each iteration, when , is the number of iterations for the kth time, For the allowable error, the power flow solution is obtained.

[0139] In another embodiment of the present invention, a terminal device is provided, which includes a processor and a memory, wherein the memory is used to store a computer program, the computer program includes program instructions, and the processor is used to execute 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 (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, which is suitable for implementing one or more instructions, and is specifically suitable for loading and executing one or more instructions to implement the corresponding method flow or corresponding function; the processor described in the embodiment of the present invention can be used for the operation of the AC / DC power system flow calculation method based on the quasi-Newton method, including: According to the input, output and control characteristics of the AC / DC converter station, an AC / DC power system power flow calculation model including conventional DC transmission and flexible DC transmission is constructed; based on the AC / DC power system power flow calculation model, a unified power flow calculation model of the AC / DC power system is established in the augmented rectangular coordinate system; based on the unified power flow calculation model of the system, at the level start operation point, the direction and step size of the first iteration are determined by the Newton method, and the initial iteration value of the quasi-Newton method is obtained; based on the obtained initial iteration value of the quasi-Newton method, the power flow equation is iteratively solved by the quasi-Newton method, and the iterative matrix is ​​updated based on the Broyden rank 1 correction format; power flow iteration is performed based on the unified iteration format of the AC / DC hybrid power flow and the iterative matrix of the quasi-Newton method based on the Broyden rank 1 correction. After each iteration, when , is the k-th iteration amount, For the allowable error, the power flow solution is obtained.

[0140] See also Figure 8 , the terminal device is a computer device, and the computer device 60 of this embodiment includes: a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When the computer program 63 is executed by the processor 61, the AC / DC power system flow calculation method based on the quasi-Newton method in the embodiment is implemented. To avoid repetition, it is not described one by one here. Alternatively, when the computer program 63 is executed by the processor 61, the functions of each model / unit in the AC / DC power system flow calculation system based on the quasi-Newton method in the embodiment are implemented. To avoid repetition, it is not described one by one here.

[0141] The computer device 60 may be a computing device such as a desktop computer, a notebook, a PDA, or a cloud server. The computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will appreciate that Figure 8 This is only an example of the computer device 60 and does not constitute a limitation of the computer device 60. It may include more or fewer components than shown in the figure, or a combination of certain components, or different components. For example, the computer device may also include input and output devices, network access devices, buses, etc.

[0142] The processor 61 may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) 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, etc.

[0143] The memory 62 may be an internal storage unit of the computer device 60, such as a hard disk or memory of the computer device 60. The memory 62 may also be an external storage device of the computer device 60, such as a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, etc., equipped on the computer device 60.

[0144] Furthermore, the memory 62 may include both an internal storage unit of the computer device 60 and an external storage device. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 may also be used to temporarily store data that has been output or is to be output.

[0145] See also Fig. 9 , the terminal device is a chip, and the chip 600 of this embodiment includes a processor 622, which may be one or more, and a memory 632 for storing a computer program 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. In addition, the processor 622 may be configured to execute the computer program to execute the above-mentioned AC / DC power system power flow calculation method based on the quasi-Newton method.

[0146] In addition, the chip 600 may further include a power supply component 626 and a communication component 650, wherein the power supply component 626 may be configured to perform power management of the chip 600, and the communication component 650 may be configured to implement communication, for example, wired or wireless communication, of the chip 600. In addition, the chip 600 may further include an input / output interface 658. The chip 600 may operate based on an operating system stored in the memory 632.

[0147] In another embodiment of the present invention, the present invention also provides a storage medium, specifically a computer-readable storage medium, which is a memory device in a terminal device for storing programs and data. It can be understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and the extended storage medium supported by the terminal device. The computer-readable storage medium provides a storage space, which stores the operating system of the terminal. In addition, one or more instructions suitable for being loaded and executed by the processor are also stored in the storage space, and these instructions can be one or more computer programs. It should be noted that the computer-readable storage medium here can be a high-speed RAM memory, or a non-volatile memory (Non-VolatileMemory), such as at least one disk memory.

[0148] The processor may load and execute one or more instructions stored in a computer-readable storage medium to implement the corresponding steps of the AC / DC power system power flow calculation method based on the quasi-Newton method in the above embodiment; the processor may load and execute the following steps: According to the input, output and control characteristics of the AC / DC converter station, an AC / DC power system power flow calculation model including conventional DC transmission and flexible DC transmission is constructed; based on the AC / DC power system power flow calculation model, a unified power flow calculation model of the AC / DC power system is established in the augmented rectangular coordinate system; based on the unified power flow calculation model of the system, at the level start operation point, the direction and step size of the first iteration are determined by the Newton method, and the initial iteration value of the quasi-Newton method is obtained; based on the obtained initial iteration value of the quasi-Newton method, the power flow equation is iteratively solved by the quasi-Newton method, and the iterative matrix is ​​updated based on the Broyden rank 1 correction format; power flow iteration is performed based on the unified iteration format of the AC / DC hybrid power flow and the iterative matrix of the quasi-Newton method based on the Broyden rank 1 correction. After each iteration, when , is the number of iterations for the kth time, For the allowable error, the power flow solution is obtained.

[0149] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention described and shown in the drawings here can usually be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0150] Based on the IEEE 39-node standard example, a 5-node DC network consisting of a four-terminal VSC flexible DC and two LCC DC lines are added. The specific topology diagram is shown in the attached figure. Figure 5 The power flow calculation of the system is carried out using MATLAB, and the calculation performance differences between the Newton method and the quasi-Newton method are compared.

[0151] Table 1 shows the convergence speed and calculation time comparison of several algorithms in the centralized algorithm. The two quasi-Newton methods using rank 2 correction cannot converge. This is because when used for asymmetric problems, the step size and direction of the rank 2 correction will deviate from the Newton step size and direction, resulting in poor convergence of the algorithm. Both the quasi-Newton method using Broyden rank 1 correction and the traditional Newton method can converge. Although the quadratic convergence characteristics of the traditional Newton method make it converge faster and achieve the required accuracy with fewer iterations, compared with the rank 1 correction algorithm, the calculation time used is greatly increased because the Jacobian matrix and its inverse matrix need to be solved in each iteration.

[0152] Table 1: Convergence speed and calculation time comparison of several algorithms

[0153] See also Figure 5 , which is the relationship between the mismatch and the number of iterations of several algorithms, can more clearly show the difference in convergence speed of several algorithms. In the first few steps of the iteration, the quasi-Newton method using Broyden rank 1 correction converges faster than the traditional Newton method.

[0154] The above process verifies the outstanding advantages of the present invention in AC / DC hybrid power flow calculation. Compared with the traditional AC / DC power flow calculation method, the present invention has obvious superiority.

[0155] The present invention provides a method for constructing an AC / DC unified power flow model. In this embodiment, firstly, by constructing models of a converter station and a DC system, a unified power flow calculation model is established in an augmented rectangular coordinate system.

[0156] The present invention also provides a method for improving the performance of power flow calculation by using the quasi-Newton method. In this embodiment, the quasi-Newton iteration format corrected by Broyden rank 1, although the convergence speed is slower than that of the traditional Newton method, greatly improves the calculation speed.

[0157] In summary, the present invention provides an AC / DC power system power flow calculation method and system based on the quasi-Newton method, which establishes a unified power flow model of the AC / DC hybrid system from a modeling perspective, and algorithmically approximates the Newton step in direction and step size through the quasi-Newton method, thereby simplifying the repeated derivation and inversion operations in the iterative process, greatly simplifying the calculation process, and improving the calculation speed, which has obvious effects in actual simulation results.

[0158] The technicians in the relevant field can clearly understand that for the convenience and simplicity of description, only the division of the above-mentioned functional units and modules is used as an example for illustration. In practical applications, the above-mentioned function allocation can be completed by 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 embodiment can be integrated in a processing unit, or each unit can exist physically separately, or two or more units can be integrated in one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of software functional units. In addition, the specific names of the functional units and modules are only for the convenience of distinguishing each other, and are not used to limit the scope of protection of this application. The specific working process of the units and modules in the above-mentioned system can refer to the corresponding process in the aforementioned method embodiment, which will not be repeated here.

[0159] In the above embodiments, the description of each embodiment has its own emphasis. For parts that are not described or recorded in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0160] Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed in the present invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention.

[0161] In the embodiments provided by the present 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 only schematic. For example, the division of the modules or units is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0162] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0163] In addition, each functional unit in each embodiment of the present invention may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0164] If the integrated module / unit is implemented in the form of 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, the present invention implements all or part of the processes in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium, and the computer program can implement the steps of the above-mentioned various method embodiments when executed by the processor. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electric carrier signal, telecommunication signal and software distribution medium, etc. It should be noted that the content contained in the computer-readable medium can be appropriately increased or decreased 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 electric carrier signals and telecommunication signals.

[0165] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices, and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of the processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0166] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0167] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0168] The above contents are only for explaining the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A method for calculating power flow of an AC / DC power system based on a quasi-Newton method, comprising the following steps: According to the input, output and control characteristics of the AC / DC converter station, a power flow calculation model for the AC / DC power system including conventional DC transmission and flexible DC transmission is constructed; Based on the AC / DC power system power flow calculation model, a unified power flow calculation model for AC / DC power systems is established in an augmented rectangular coordinate system. Based on the unified power flow calculation model of the system, at the flat start operation point, the direction and step size of the first iteration are determined by the Newton method, and the initial value of the iteration of the quasi-Newton method is obtained; Based on the obtained iterative initial value of the quasi-Newton method, the power flow equation is iteratively solved by the quasi-Newton method, and the iterative matrix is ​​updated based on the Broyden rank 1 correction format; The power flow iteration is performed based on the unified iteration format of the AC / DC hybrid power flow and the iterative matrix of the quasi-Newton method based on Broyden rank 1 correction. After each iteration, when , is the number of iterations for the kth time, For the allowable error, the power flow solution is obtained.

2. The method for calculating power flow of AC and DC power systems based on the quasi-Newton method according to claim 1, characterized in that: AC / DC power system flow calculation model for conventional DC transmission: in, , are the DC voltage and current, , , are the complex power, reactive power, and active power flowing from the AC side to the DC side, , , They are the converter transformer ratio, converter control angle, and equivalent commutation reactance. is the commutation angle coefficient, is the voltage amplitude of the AC node connected to the LCC; AC / DC power system flow calculation model for flexible DC transmission: in, and They are the reference values ​​of reactive power and voltage on the AC side respectively.

3. The method for calculating power flow of AC and DC power systems based on the quasi-Newton method according to claim 2, characterized in that: In the power flow calculation, for the sending-end DC station: To the receiving system: in, For loss.

4. The method for calculating power flow of AC and DC power systems based on the quasi-Newton method according to claim 1, characterized in that: The unified power flow calculation model of AC / DC power system is established in the augmented rectangular coordinate system as follows: For AC nodes, the node voltage equation is: PQ Node: PV Node: Balance Node: The DC nodes are given by the DC node voltage equation: in, Define the real part of the node voltage for the AC side, is the imaginary part, Inject the real part of the current into the node, is the imaginary part, Define the node voltage amplitude for the DC side, The magnitude of the current injected into the node, is the node voltage amplitude given by the AC node, is the active power given by the AC node, is the reactive power, Given the active power at the DC node, is the imaginary part of the admittance matrix, is the real part of the admittance matrix, is the point admittance, is the node voltage amplitude at this point.

5. The method for calculating power flow of AC and DC power systems based on the quasi-Newton method according to claim 4, characterized in that: AC and DC power systems contain n Communication nodes, d DC nodes, and k AC / DC converter stations; the system in augmented rectangular coordinates has unknown variable.

6. The method for calculating power flow of AC and DC power systems based on the quasi-Newton method according to claim 4, characterized in that: Before writing the power flow equation, the AC and DC network standard values ​​are processed uniformly and the , , are the voltage reference values ​​of the AC side and the DC side respectively. , are the power reference values ​​of the AC side and the DC side respectively. is the rated power of the system.

7. The method for calculating power flow of AC and DC power systems based on the quasi-Newton method according to claim 1, characterized in that: The direction and step size of the first iteration are established by Newton's method as follows: in, is the initial value, is the value of the first iteration, is the Jacobian matrix of the first iteration, is the function value at the first iteration.

8. The method for calculating power flow of AC and DC power systems based on the quasi-Newton method according to claim 1, characterized in that: The matrix of the update iteration based on Broyden rank 1 correction format is as follows: in, is the quasi-Newton matrix of the kth iteration, is the gradient of the ith search direction in the kth iteration, is the number of iterations for the kth time, is the i-th unit vector.

9. The method for calculating power flow of AC and DC power systems based on the quasi-Newton method according to claim 1, characterized in that: The tidal flow equation is solved iteratively by the quasi-Newton method as follows: in, is the initial value of the kth iteration, is the initial value of the k+1th iteration, is the quasi-Newton matrix of the kth iteration, is the function value at the kth iteration.

10. An AC / DC power system flow calculation system based on the quasi-Newton method, characterized in that: include: The first generation module constructs an AC / DC power system power flow calculation model including conventional DC transmission and flexible DC transmission according to the input, output and control characteristics of the AC / DC converter station; The second generation module establishes a unified power flow calculation model of the AC and DC power systems in an augmented rectangular coordinate system based on the power flow calculation model of the AC and DC power systems; The calculation module is based on the unified power flow calculation model of the system. At the flat start operation point, the direction and step size of the first iteration are determined by the Newton method to obtain the initial iteration value of the quasi-Newton method. Based on the obtained initial iteration value of the quasi-Newton method, the power flow equation is iteratively solved by the quasi-Newton method, and the iterative matrix is ​​updated based on the Broyden rank 1 correction format. The power flow is iterated based on the unified iteration format of the AC / DC hybrid power flow and the iterative matrix of the quasi-Newton method based on the Broyden rank 1 correction. After each iteration, when , For the allowable error, the power flow solution is obtained.

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