Harmonic power flow calculation method and system considering harmonic network external network static equivalence

Abstract

The present application relates to power system harmonic analysis technology, specifically relates to a harmonic power flow calculation method and system considering harmonic network external network static equivalence, the method comprises the internal network, the external network and a plurality of boundary nodes by dividing the power grid to be analyzed;Obtain a plurality of boundary node harmonic voltage phasor and harmonic current phasor measurement data;Establish a harmonic network external network static equivalence model for a plurality of boundary nodes, and identify external network static equivalence parameters according to boundary node harmonic current balance constraint;Construct the equivalent harmonic admittance matrix of the boundary node and the extended harmonic node admittance matrix, and establish the extended harmonic network node voltage equation which can be used for harmonic power flow calculation;Finally, the harmonic power flow distribution of the internal network node and a plurality of boundary nodes is obtained. The method can reduce the dependence on the complete topology and detailed parameters of the external network under the condition of ensuring the calculation accuracy, and improve the harmonic power flow solving efficiency.

Description

Technical Field

[0001] This invention belongs to the field of power system harmonic analysis technology, and particularly relates to a method and system for calculating harmonic power flow considering the static equivalent of the external network of the harmonic network. Background Technology

[0002] With the widespread integration of harmonic source devices such as grid-connected inverters from new energy sources and industrial rectifier loads into power systems, the problem of power grid harmonics has become increasingly prominent. Harmonics not only increase the additional losses of electrical equipment but may also cause problems such as relay protection malfunctions and interference with precision industrial control equipment. Therefore, accurately calculating the harmonic power flow distribution in the power grid is of great significance for the design of harmonic mitigation schemes and the planning and operation of the power grid.

[0003] Traditional harmonic power flow calculations typically require obtaining the entire network's topology, line parameters, transformer parameters, and load parameters. For large-scale real-world power grids, obtaining complete and detailed parameters for the entire network presents significant challenges. Furthermore, in regional power grid harmonic analysis, researchers often focus on the harmonic source access area and its vicinity, while areas far from the harmonic sources and with lower harmonic levels generally do not require detailed modeling. Establishing a complete harmonic network model for the entire network would increase the difficulty of parameter collection and the computational burden. Therefore, how to perform reasonable external network static equivalence for unknown harmonic networks and thereby achieve accurate harmonic power flow calculations has become a pressing technical problem in the field of power system harmonic analysis. Summary of the Invention

[0004] This invention provides a harmonic power flow calculation method and system that considers the static equivalence of the external harmonic network, in order to solve the shortcomings of the existing technology in traditional harmonic power flow calculation for large-scale power grids, which increases the difficulty of parameter collection and computational burden by establishing a complete harmonic network model for the entire network, thereby reducing the dependence of large-scale power grid harmonic power flow calculation on detailed data of the external network.

[0005] This invention provides a method for calculating harmonic power flow considering the static equivalent values ​​of the external network of a harmonic network, comprising the following steps: Step 1. Divide the harmonic network to be analyzed into regions and obtain the network topology and component parameters; Step 2. Obtain harmonic measurement data for multiple boundary nodes; Step 3. Construct the theoretical form of the harmonic network node voltage equations after the external network is equivalent; Step 4. Establish the static equivalent model of the harmonic network external network and identify its parameters; Step 5. Establish the extended harmonic network node voltage equations for harmonic power flow calculation; Step 6. Iteratively solve the harmonic power flow by simultaneously establishing the node voltage equations of the extended harmonic network and the equivalent injection model of the harmonic source.

[0006] According to the harmonic power flow calculation method considering the static equivalent of the external network of the harmonic network provided by the present invention, step 1 includes the following steps: The power grid to be analyzed is divided into an internal network, an external network, and multiple boundary nodes. The area containing the grid connection point of harmonic source equipment, the nodes around the harmonic source equipment, and the target node area for harmonic power flow calculation is divided into the internal network. The network area without connected harmonic source equipment or with a total harmonic voltage distortion rate of nodes below a preset threshold is divided into the external network. The connection nodes between the internal network and the external network are used as boundary nodes. The network topology, transmission line parameters, transformer parameters, and load parameters of the internal network and multiple boundary nodes are obtained.

[0007] According to the present invention, a harmonic power flow calculation method considering the static equivalence of the external network of a harmonic network is provided. The harmonic measurement data in step 2 includes the harmonic voltage phasor of each boundary node and the harmonic current phasor flowing to each boundary node. The harmonic source equipment includes at least one of the following: industrial rectifier load, electric arc furnace, power electronic converter, new energy grid-connected inverter, and flexible DC converter station. The measured boundary node harmonic voltage phasor is:

[0008] The measured harmonic current phasor flowing towards the boundary node is represented as follows:

[0009] in, k =1, 2, , ; Indicates the number of boundary nodes; No. t The measurement time of the first measurement moment k boundary nodes h Second harmonic voltage phasor; Indicates the first t The flow direction at the measurement moment is the first k boundary nodes h Second harmonic current phasor; t =1, 2, , N ; N Indicates the number of measurement samples.

[0010] According to the harmonic power flow calculation method considering the static equivalence of the external network of the present invention, step 3, which involves constructing the harmonic network node equations in theoretical form after external network equivalence, includes: For the analysis h The first harmonic frequency, the admittance matrix of the entire network harmonic network nodes is denoted as... The node harmonic voltage is denoted as The harmonic current injected into the node is denoted as The voltage equations at the nodes of the harmonic network are then:

[0011] Theoretically, the harmonic network node voltage equations after the external network is equivalent are as follows:

[0012] in, Let be the equivalent harmonic admittance matrix of the boundary nodes. and This represents the harmonic mutual admittance matrix between boundary nodes and internal network nodes. The harmonic admittance matrix of the internal network nodes. and These represent the harmonic voltage phasors of the boundary nodes and the internal network nodes, respectively. and These represent the injected harmonic current phasors of the boundary nodes and the internal network nodes, respectively. Calculate the internal components in the area to be analyzed h The harmonic admittance at the second harmonic frequency is used to construct the harmonic admittance matrix of the internal network nodes. and the harmonic mutual admittance matrix between boundary nodes and internal network nodes. and .

[0013] According to the harmonic power flow calculation method considering the static equivalent of the external network of the harmonic network provided by the present invention, the implementation of step 4 includes: The equivalent harmonic admittance matrix of the boundary node The equivalent model is a static equivalent model of the harmonic network external network; the static equivalent model of the harmonic network external network consists of the equivalent ground branches of each boundary node and the equivalent coupling branches between any two boundary nodes; specifically: The equivalent harmonic admittance matrix of the boundary nodes corresponding to the static equivalent model of the harmonic network external network. for An ordinal matrix, the elements of which satisfy the following correspondence: matrix The diagonal element is the first k The equivalent ground admittance of each boundary node, and the sum of the equivalent coupling branch admittances between that node and all other boundary nodes; matrix Off-diagonal elements are the negative values ​​of the admittance of the equivalent coupling branches between corresponding nodes, specifically expressed as:

[0014]

[0015] in, For the first k Equivalent ground admittance of each boundary node For the first k The boundary node and the first m The equivalent coupling branch admittance between boundary nodes, when m < k hour, ; The parameters to be identified in the equivalent model of the harmonic external network are:

[0016] in, and They represent the first k Conductivity and susceptance of the equivalent ground admittance at each boundary node. and They represent the first k The boundary node and the first m Conductance and susceptance of the equivalent coupling branch admittance between boundary nodes. Indicates to be identified h Subharmonic external network static equivalent parameter vector; The harmonic current balance constraint equations for the multiple boundary nodes are as follows:

[0017] in, Indicates the first t The measurement time of the first measurement moment k boundary nodes h Second harmonic voltage phasor; Indicates the first t The measurement time of the first measurement moment m boundary nodes h Second harmonic voltage phasor; Indicates the first t The flow direction at the measurement moment is the first k boundary nodes h Second harmonic current phasor; The boundary node harmonic current balance constraint equation is a complex equation. Constraints are established on the real and imaginary parts of the complex equation, respectively, in the form of:

[0018] in, r =1, 2; when r When =1, Indicates the first t The measurement time of the first measurement moment k The real part constraint function of the harmonic current balance equation at each boundary node; when r When =2, Indicates the first t The measurement time of the first measurement moment k The imaginary part constraint function of the harmonic current balance equation at each boundary node; The equivalent parameters of the harmonic external network are identified based on the harmonic current balance constraint equations of multiple boundary nodes, using the following least squares estimation method:

[0019] in, The target function for identifying the equivalent parameters of the harmonic external network is represented; the target function is made to... When the minimum value is obtained, the corresponding These are the estimated values ​​of the equivalent parameters of the harmonic external network.

[0020] According to the harmonic power flow calculation method considering the static equivalence of the external network of the harmonic network provided by the present invention, the specific steps of establishing the extended harmonic network node voltage equations for harmonic power flow calculation in step 5 are as follows: Based on the parameter estimates of the equivalent ground admittance of the boundary nodes and the equivalent coupling branch admittance between boundary nodes obtained in step 4, the actual equivalent harmonic admittance matrix of the boundary nodes is constructed; this matrix is ​​then combined in blocks with the self-admittance matrix of the internal network and the mutual admittance matrix between the internal network and the boundary nodes to construct an extended harmonic node admittance matrix containing the internal network nodes and the boundary nodes; for h The extended harmonic nodal admittance matrix is ​​constructed for each of the second harmonics. ; The extended harmonic network node voltage equations used for harmonic power flow calculations are expressed as follows:

[0021] in, express h Extended harmonic node admittance matrix of equivalent network under subharmonics; This represents the extended harmonic node voltage vector to be solved; This represents the extended harmonic node injected current vector.

[0022] According to the harmonic power flow calculation method considering the static equivalent of the external network of the harmonic network provided by the present invention, step 6, which iteratively solves the harmonic power flow by simultaneously solving the extended harmonic network node voltage equations and the equivalent injection model of the harmonic source, includes the following steps: Step 6.1. Based on the fundamental power flow calculation results, substitute the fundamental voltage phasor of each harmonic source device's grid-connected node and the fundamental current phasor of the grid-connected branch into the equivalent injection model of each harmonic source, solve for the initial harmonic current phasors injected by each harmonic source, and construct the extended node injection current vector accordingly. ; Step 6.2. Using the extended harmonic network node voltage equations formed after static equivalence of the outer harmonic network corresponding to each harmonic, solve for the harmonic voltage phasors of each node in the internal network and the boundary nodes. Step 6.3. Substitute the updated harmonic voltage phasors at the grid connection point of the harmonic source back into the equivalent injection model of the harmonic source, and update the injected harmonic current phasors. Step 6.4. Repeat the alternating solution process of Step 6.2 and Step 6.3 until the difference between the amplitudes of each harmonic voltage of each node in two adjacent iterations is less than the preset convergence threshold, or the preset maximum number of iterations is reached. Then, end the iteration and output the phasor of each harmonic voltage of each node and the phasor of each harmonic current of each branch.

[0023] The present invention also provides a harmonic power flow calculation system considering the static equivalence of the harmonic network external network, used to implement the harmonic power flow calculation method considering the static equivalence of the harmonic network external network. The system includes: a data acquisition module, a network partitioning and data processing module, a harmonic network external network static equivalence module, and a harmonic power flow calculation module. The data acquisition module is used to acquire the access information of harmonic source equipment of the power grid to be analyzed, the total harmonic voltage distortion rate data of each node, the network topology of the internal network and multiple boundary nodes, line parameters and transformer parameters; and to acquire the harmonic measurement data of multiple boundary nodes at the harmonic frequency to be analyzed. The network partitioning and data processing module is used to divide the power grid to be analyzed into an internal network, an external network, and multiple boundary nodes based on the access information of harmonic source devices and the total harmonic voltage distortion rate data of each node; calculate the harmonic admittance at the harmonic frequency to be analyzed based on the network topology, line parameters, and transformer parameters of the internal network and multiple boundary nodes; and construct the self-admittance matrix of the internal network and the mutual admittance matrix between the internal network and multiple boundary nodes. The harmonic network external static equivalent module is used to establish a static equivalent model of the harmonic network external network for multiple boundary nodes. Based on the harmonic voltage phasors and harmonic current phasors of multiple boundary nodes, it establishes the harmonic current balance constraint equations of the boundary nodes and identifies the parameters of the harmonic network external static equivalent model through the least squares estimation method. According to the identified equivalent ground admittance and equivalent coupling branch admittance between boundary nodes, the equivalent harmonic admittance matrix of the boundary nodes is constructed. The equivalent harmonic admittance matrix of the boundary nodes is combined with the self-admittance matrix of the internal network and the mutual admittance matrix between the internal network and multiple boundary nodes to form the extended harmonic node admittance matrix. The harmonic power flow calculation module is used to obtain the fundamental operating status information of the internal network and multiple boundary nodes, calculate the phasors of each harmonic current injected by the harmonic source using the equivalent injection model of the harmonic source, and establish the voltage equations of the extended harmonic network nodes based on the extended harmonic node admittance matrix. By iteratively solving the extended harmonic network node voltage equations and the equivalent injection model of the harmonic source, the phasors of each harmonic voltage of the internal network nodes and multiple boundary nodes and the phasors of each harmonic current of each branch are obtained, thus completing the harmonic power flow calculation.

[0024] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the harmonic power flow calculation method considering the static equivalence of the external harmonic network as described above.

[0025] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the harmonic power flow calculation method considering the static equivalence of the external harmonic network as described above.

[0026] Compared with the prior art, the beneficial effects of the present invention are: 1) This invention does not require obtaining the complete topology and detailed component parameters of the external network. It can construct a static equivalent model of the external network of the harmonic network at the harmonic frequency to be analyzed by using only the harmonic voltage phasors and harmonic current phasors of multiple boundary nodes, and identify the equivalent admittance parameters of the model, thereby reducing the dependence of large-scale power grid harmonic power flow calculation on detailed data of the external network.

[0027] 2) This invention constructs an actual boundary node equivalent harmonic admittance matrix based on the identified harmonic network external static equivalent model, and combines it with the internal network self-admittance matrix and the mutual admittance matrix between the internal network and boundary nodes in blocks to form an extended harmonic node admittance matrix. Furthermore, by jointly iteratively solving the extended harmonic node admittance matrix with the equivalent injection model of harmonic sources, the harmonic power flow distribution under multi-harmonic frequency scenarios can be obtained, improving the computational efficiency and engineering applicability of regional power grid harmonic analysis. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0029] Figure 1This is an overall flowchart of a harmonic power flow calculation method considering the static equivalent of the external network of a harmonic network, provided by an embodiment of the present invention. Figure 2 This is a schematic diagram of the harmonic network partitioning of the modified IEEE 39-node system provided in an embodiment of the present invention; Figure 3 This is a comparison chart of the calculated and simulated values ​​of harmonic power flow at two harmonic frequencies provided in this embodiment of the invention; Figure 4 This is a schematic diagram of the structure of the electronic device provided in an embodiment of the present invention. Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this 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 this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0031] This embodiment presents a harmonic power flow calculation method considering the static equivalent of the external network of a harmonic network. Based on the access information of the harmonic source equipment in the power grid to be analyzed and the historical total harmonic voltage distortion rate data of each node, the power grid to be analyzed is divided into an internal network, an external network, and multiple boundary nodes. Measurement data of harmonic voltage phasors and harmonic current phasors at multiple boundary nodes at the harmonic frequencies to be analyzed are obtained. Based on the topology and parameters of the internal network and boundary nodes, the self-admittance matrix of the internal network and the mutual admittance matrix of the boundaries are constructed. A static equivalent model of the external network of the harmonic network oriented towards multiple boundary nodes is established, and the static equivalent parameters of the external network are identified according to the harmonic current balance constraints of the boundary nodes. Then, the equivalent harmonic admittance matrix of the boundary nodes and the extended harmonic node admittance matrix are constructed, and an extended harmonic network node voltage equation that can be used for harmonic power flow calculation is established. Finally, the extended harmonic network node equation and the equivalent injection model of the harmonic source are solved iteratively to obtain the harmonic power flow distribution of the internal network nodes and multiple boundary nodes. This invention can reduce the dependence on the complete topology and detailed parameters of the external network while ensuring computational accuracy, thereby improving the efficiency of harmonic power flow solution and providing strong support for power grid harmonic analysis and mitigation.

[0032] like Figure 1 As shown in the figure, this embodiment presents a harmonic power flow calculation method considering the static equivalent of the external network of a harmonic network, which is implemented through the following steps: S1. Based on the harmonic source equipment access information of the power grid to be analyzed and the historical total harmonic voltage distortion rate data of each node, the power grid to be analyzed is divided into an internal network, an external network and multiple boundary nodes, and the network topology, transmission line parameters, transformer parameters and load parameters of the internal network and multiple boundary nodes are obtained. S2, acquire the harmonic measurement data of the multiple boundary nodes at the harmonic frequency to be analyzed, the harmonic measurement data includes the harmonic voltage phasor of each boundary node and the harmonic current phasor flowing to each boundary node; S3. For the harmonic frequency to be analyzed, the internal network self-admittance matrix and the mutual admittance matrix between the internal network and the boundary nodes are constructed using the network topology and component parameters of the internal network and multiple boundary nodes. The influence of the unknown external network on multiple boundary nodes is equivalent to an abstract boundary node admittance correction term, thereby constructing the theoretical form of the external network equivalent harmonic network node equation. S4. Establish a static equivalent model of the harmonic network external network. Based on the harmonic measurement data of the multiple boundary nodes, establish multiple boundary node harmonic current balance constraint equations and identify the parameters of the static equivalent model of the harmonic network external network. S5. Using the identified harmonic network external static equivalent model parameters, construct the actual boundary node equivalent harmonic admittance matrix, establish the extended harmonic node admittance matrix including internal network nodes and multiple boundary nodes, and establish the extended harmonic network node voltage equation that can be used for harmonic power flow calculation. S6: Obtain the fundamental operating status information of the grid-connected node of the harmonic source device, and iteratively solve the extended harmonic node equation and the equivalent injection model of the harmonic source to complete the harmonic power flow calculation.

[0033] In S1, the network area division based on the power grid to be analyzed includes: The region containing the grid connection point of the harmonic source equipment, the surrounding nodes of the harmonic source equipment, and the target node for harmonic power flow calculation is divided into an internal network; the network region without connected harmonic source equipment or with a total harmonic voltage distortion rate below a preset threshold is divided into an external network; and the connecting nodes between the internal and external networks are designated as boundary nodes. The total harmonic voltage distortion rate threshold can be set according to power quality standards, operational experience, or engineering requirements.

[0034] The harmonic source equipment includes at least one of the following: industrial rectifier load, electric arc furnace, power electronic converter, new energy grid-connected inverter, and flexible DC converter station.

[0035] In S2, the measured boundary node harmonic voltage phasor is represented as follows: (1) The measured harmonic current phasor flowing towards the boundary node is represented as follows: (2) in, k =1, 2, , ; Indicates the number of boundary nodes; No. t The measurement time of the first measurement moment k boundary nodes h Second harmonic voltage phasor; Indicates the first t The flow direction at the measurement moment is the first k boundary nodes h Second harmonic current phasor; t =1, 2, , N ; N Indicates the number of measurement samples.

[0036] In S3, the harmonic network node equations after constructing the theoretical form of the external network equivalent are as follows: For the analysis h The first harmonic frequency, the admittance matrix of the entire network harmonic network nodes is denoted as... The node harmonic voltage is denoted as The harmonic current injected into the node is denoted as The voltage equations at the nodes of the harmonic network are then: (3) All nodes in the harmonic network are divided into three sets, where set 1 Includes all internal network nodes; set Includes all boundary nodes; set It includes all external network nodes. Based on this division method, equation (3) can be expressed in block form as follows: (4) in, The harmonic admittance matrix of the external network nodes; The harmonic admittance matrix of the boundary nodes; The harmonic admittance matrix of the internal network nodes; and This represents the harmonic mutual admittance matrix between external network nodes and boundary nodes; and This represents the harmonic mutual admittance matrix between boundary nodes and internal network nodes; , and These represent the harmonic voltage phasors of external network nodes, boundary nodes, and internal network nodes, respectively. , and These represent the injected harmonic current phasors of external network nodes, boundary nodes, and internal network nodes, respectively.

[0037] Due to the external network node set The nodes in the analysis are not connected to harmonic source devices or their harmonic injection current is negligible, therefore, in the nodes to be analyzed... h At the second harmonic frequency, the harmonic current injected into the external network node satisfies: (5) The block equation corresponding to the external network nodes: (6) The equivalent admittance correction term of the external network for the boundary nodes is obtained: (7) Will Substituting the corresponding block equations for the boundary nodes, we obtain the equivalent harmonic admittance matrix of the boundary nodes after eliminating the external network nodes. : (8) The harmonic admittance matrix of the boundary node is changed from Replace with Harmonic currents injected at boundary nodes The values ​​remain unchanged. The theoretical form of the harmonic network node voltage equations after external network equivalent is: (9) Based on the obtained network topology of the internal network and boundary nodes, transmission line parameters, transformer parameters, and load parameters, calculate the performance of each internal component under analysis. h The harmonic admittance at the second harmonic frequency is used to construct the harmonic admittance matrix of the internal network nodes. and the harmonic mutual admittance matrix between boundary nodes and internal network nodes. and For unknown external networks Its actual equivalent form is obtained through S4 modeling and identification.

[0038] In S4, the equivalent harmonic admittance matrix of the boundary node in the theoretical form The equivalent model is a static equivalent model of the harmonic network external network; the static equivalent model of the harmonic network external network consists of the equivalent ground branches of each boundary node and the equivalent coupling branches between any two boundary nodes.

[0039] For the set of boundary nodes B The first in k For each boundary node, its equivalent ground admittance is set as follows: (10) In the formula, and They represent the first k Conductivity and susceptance of the equivalent ground admittance at each boundary node.

[0040] For the set of boundary nodes B The first in k The boundary node and the first m The equivalent coupling branch between the boundary nodes is set with the following admittance: (11) In the formula, and They represent the first k The boundary node and the first m Conductance and susceptance of the equivalent coupling branch admittance between boundary nodes.

[0041] The equivalent harmonic admittance matrix of the boundary nodes corresponding to the static equivalent model of the harmonic network external network. for An ordinal matrix, the elements of which satisfy the following correspondence: matrix The diagonal element is the first k The equivalent ground admittance of each boundary node, and the sum of the equivalent coupling branch admittances between that node and all other boundary nodes; matrix Off-diagonal elements are the negative values ​​of the admittance of the equivalent coupling branches between corresponding nodes, specifically expressed as: (12) (13) Among them, when m < k hour, .

[0042] The parameters to be identified in the equivalent model of the harmonic external network are: (14) in, Indicates to be identified h Subharmonic external network static equivalent parameter vector.

[0043] In S4, the harmonic current balance constraint equations for the multiple boundary nodes are as follows: (15) in, Indicates the first t The measurement time of the first measurement moment k boundary nodes h Second harmonic voltage phasor; Indicates the firstt The measurement time of the first measurement moment m boundary nodes h Second harmonic voltage phasor; Indicates the first t The flow direction at the measurement moment is the first k boundary nodes h Secondary harmonic current phasor.

[0044] The boundary node harmonic current balance constraint equation is a complex equation. Constraints are established on the real and imaginary parts of the complex equation, and its general form is as follows: (16) in, r =1, 2; when r When =1, Indicates the first t The measurement time of the first measurement moment k The real part constraint function of the harmonic current balance equation at each boundary node; when r When =2, Indicates the first t The measurement time of the first measurement moment k The imaginary constraint function of the harmonic current balance equation at each boundary node.

[0045] The equivalent parameters of the harmonic external network are identified based on the harmonic current balance constraint equations of multiple boundary nodes, using the following least squares estimation method: (17) in, The target function for identifying the equivalent parameters of the harmonic external network is represented; the target function is made to... When the minimum value is obtained, the corresponding These are the estimated values ​​of the equivalent parameters of the harmonic external network.

[0046] The harmonic frequencies to be analyzed include one or more harmonic frequencies. When there are multiple harmonic frequencies to be analyzed, a corresponding harmonic network external static equivalent model is established for each harmonic frequency to be analyzed, and the external static equivalent parameters under the corresponding harmonic frequency are identified respectively.

[0047] In S5, the extended harmonic network node voltage equation that can be used for harmonic power flow calculation is expressed as: (18) in, express h Extended harmonic node admittance matrix of equivalent network under subharmonics; This represents the extended harmonic node voltage vector to be solved; This represents the extended harmonic node injected current vector.

[0048] In S6, the equivalent injection model of the harmonic source can be provided by the equipment manufacturer or obtained through statistical analysis of historical operating data. The equivalent injection model of the harmonic source adopts a functional form to describe the relationship between the fundamental voltage phasor, the phasors of each harmonic voltage, and the phasors of each harmonic current injected by the harmonic source at the grid-connected node of the harmonic source equipment. Its expression is: (19) in, Represents the fundamental voltage phasor, the voltage phasors of each harmonic, and the... h Correspondence between phasors of subharmonic currents; H The highest frequency of the harmonics under consideration; Indicates the first i The first harmonic source injected the first h Second harmonic current phasor; Indicates the first i The fundamental voltage phasor of a harmonic source device grid-connected node; Indicates the first i The first harmonic source device grid connection node h Second harmonic voltage phasor; For the first i The fundamental current phasor of a harmonic source device connected to the grid.

[0049] For each harmonic source node, the corresponding harmonic injection current is taken, while the harmonic injection current of non-harmonic source nodes is set to zero. The harmonic injection currents of all nodes are combined to form an extended harmonic node injection current vector. .

[0050] In S6, the fundamental operating status information of the grid-connected node of the harmonic source device is the fundamental voltage phasor of the grid-connected node of the harmonic source device and the fundamental current phasor of the grid-connected branch; the fundamental operating status information of the grid-connected node of the harmonic source device is obtained through on-site fundamental measurement data, or through fundamental equivalent network and fundamental power flow calculation.

[0051] In S6, the iterative solution specifically includes the following steps: S61. Based on the fundamental power flow calculation results, substitute the fundamental voltage phasor of each harmonic source device's grid-connected node and the fundamental current phasor of the grid-connected branch into the equivalent injection model of each harmonic source, solve for the initial harmonic current phasors injected by each harmonic source, and construct the extended node injection current vector accordingly. ; S62. Using the extended harmonic network node voltage equations formed after static equivalence of the outer harmonic network corresponding to each harmonic, the harmonic voltage phasors of each node in the internal network and the boundary nodes are solved to obtain the harmonic voltage phasors of each node in the internal network and the boundary nodes. S63. Substitute the updated harmonic voltage phasors at the grid connection point of the harmonic source back into the equivalent injection model of the harmonic source, and update the injected harmonic current phasors. S64. Repeat the alternating solution process of steps S62 and S63 until the difference between the amplitudes of each harmonic voltage of each node in two adjacent iterations is less than the preset convergence threshold, or the preset maximum number of iterations is reached. Then, end the iteration and output the phasor of each harmonic voltage of each node and the phasor of each harmonic current of each branch.

[0052] The following describes a harmonic power flow calculation system that considers the static equivalence of the external network of a harmonic network, provided by the present invention. The harmonic power flow calculation system that considers the static equivalence of the external network of a harmonic network described below can be referred to in correspondence with the harmonic power flow calculation method that considers the static equivalence of the external network of a harmonic network described above.

[0053] The system includes: a data acquisition module, a network partitioning and data processing module, a harmonic network external static equivalent module, and a harmonic power flow calculation module; The data acquisition module is used to acquire the access information of harmonic source equipment of the power grid to be analyzed, the total harmonic voltage distortion rate data of each node, the network topology of the internal network and multiple boundary nodes, line parameters and transformer parameters; and to acquire the harmonic measurement data of multiple boundary nodes at the harmonic frequency to be analyzed. The network partitioning and data processing module is used to divide the power grid to be analyzed into an internal network, an external network, and multiple boundary nodes based on the access information of harmonic source devices and the total harmonic voltage distortion rate data of each node; calculate the harmonic admittance at the harmonic frequency to be analyzed based on the network topology, line parameters, and transformer parameters of the internal network and multiple boundary nodes; and construct the self-admittance matrix of the internal network and the mutual admittance matrix between the internal network and multiple boundary nodes. The harmonic network external static equivalent module is used to establish a static equivalent model of the harmonic network external network for multiple boundary nodes. Based on the harmonic voltage phasors and harmonic current phasors of multiple boundary nodes, it establishes the harmonic current balance constraint equations of the boundary nodes and identifies the parameters of the harmonic network external static equivalent model through the least squares estimation method. According to the identified equivalent ground admittance and equivalent coupling branch admittance between boundary nodes, the equivalent harmonic admittance matrix of the boundary nodes is constructed. The equivalent harmonic admittance matrix of the boundary nodes is combined with the self-admittance matrix of the internal network and the mutual admittance matrix between the internal network and multiple boundary nodes to form the extended harmonic node admittance matrix. The harmonic power flow calculation module is used to obtain the fundamental operating status information of the internal network and multiple boundary nodes, calculate the phasors of each harmonic current injected by the harmonic source using the equivalent injection model of the harmonic source, and establish the voltage equations of the extended harmonic network nodes based on the extended harmonic node admittance matrix. By iteratively solving the extended harmonic network node voltage equations and the equivalent injection model of the harmonic source, the phasors of each harmonic voltage of the internal network nodes and multiple boundary nodes and the phasors of each harmonic current of each branch are obtained, thus completing the harmonic power flow calculation. Specific implementation examples: In the IEEE 39 standard node example system, the linear load of access node 21 is replaced with a 24-pulse industrial electrolytic aluminum rectifier load (harmonic source equipment), which emits characteristic harmonics of the 23rd, 25th, 47th, and 49th orders. Branches 9-39 are disconnected, and the modified IEEE 39 node network is used as the initial network.

[0055] Step S1: Harmonic network region division, topology and component parameter collection.

[0056] First, based on the access information of the harmonic source devices in the power grid to be analyzed, the maintenance personnel divide the power grid into network regions, namely, an internal network, an external network, and two boundary nodes. The network division results are as follows: Figure 2 As shown in the diagram. In this embodiment, nodes 3 and 17 are used as boundary nodes to divide the initial network, with node 3 being the first boundary node and node 17 being the second boundary node. Nodes 1, 2, 18, 25-30, and 37-39 are external network nodes, none of which have nonlinear harmonic source devices connected. Nodes 4-16, 19-24, and 31-36 are internal network nodes, which constitute the target node region for harmonic power flow calculation.

[0057] After the partitioning is completed, it is only necessary to collect and obtain the network topology, transformer parameters, transmission line parameters, and load operation parameters of the internal network and each boundary node. The internal topology and detailed component parameters of the external network do not need to be collected.

[0058] Step S2: Acquire harmonic measurement data from multiple boundary nodes In this embodiment, the harmonic frequencies to be analyzed are... h For the 23rd and 25th harmonics, the harmonic voltage phasors at the two boundary nodes and the harmonic current phasors flowing to each boundary node are obtained at 100 measurement times by using synchronous phasor measurement units or power quality monitoring devices deployed at the boundary nodes that support harmonic measurement data.

[0059] Step S3: Construct the theoretical form of the harmonic network node voltage equations after the external network is equivalent. For the analysis hFor the second harmonic frequency, the harmonic network node voltage equations after constructing the theoretical form of the external network equivalent are as follows:

[0060] Since the internal network topology is known, the harmonic admittance matrix of the internal network nodes can be directly calculated based on the network topology of the internal network and boundary nodes, transmission line parameters, transformer parameters, and load parameters. and the mutual admittance matrix between boundary nodes and internal network nodes and .

[0061] Step S4: Establishment and parameter identification of the static equivalent model of the harmonic network external network.

[0062] Since the external network topology and detailed parameters are unknown, the theoretical form of the harmonic network node voltage equations after the external network is equivalent is as follows: The theoretical value cannot be obtained. This invention equivalently models it as a static equivalent model of the harmonic network external network. This model consists of equivalent ground-to-ground branches of the first and second boundary nodes and equivalent coupling branches between the two boundary nodes, including the equivalent ground-to-ground admittance of the first boundary node. Second boundary node equivalent earth admittance Admittance of the equivalent coupling branch between the two boundary nodes ,in:

[0063]

[0064]

[0065] The equivalent harmonic admittance matrix of the boundary nodes corresponding to the static equivalent model of the harmonic network external network. for An ordinal matrix, with each element as follows:

[0066]

[0067]

[0068] Therefore, for the two boundary nodes in this embodiment, the parameters to be identified include two equivalent ground branch admittance parameters and one equivalent coupling branch admittance. The parameter vector to be identified for the static equivalent model of the harmonic external network is represented as follows:

[0069] Based on Kirchhoff's current law, establish the harmonic current balance constraint equation:

[0070]

[0071] Since the above equation is a complex equation, this embodiment expands its real and imaginary parts into real constraint equations respectively:

[0072] in, r =1, 2; when r When =1, Indicates the first t The measurement time of the first measurement moment k The real part constraint function of the harmonic current balance equation at each boundary node; when r When =2, Indicates the first t The measurement time of the first measurement moment k The imaginary constraint function of the harmonic current balance equation at each boundary node.

[0073] Using the harmonic current balance constraints of all boundary nodes at 100 measurement times, the following least-squares parameter identification model can be established:

[0074] in, The target function for identifying the equivalent parameters of the harmonic external network is represented; the target function is made to... When the minimum value is obtained, the corresponding These are the estimated values ​​of the equivalent parameters of the harmonic external network.

[0075] In this embodiment, the harmonic frequencies to be analyzed are the 23rd and 25th harmonic frequencies. For each harmonic frequency to be analyzed, the above steps are repeated to establish the static equivalent model of the harmonic network external network under the corresponding frequency, and to identify the static equivalent parameters of the external network under that frequency.

[0076] Step S5: Establish extended harmonic node voltage equations that can be used for harmonic power flow calculations.

[0077] After completing the identification of static equivalent parameters of the external network, the actual equivalent harmonic admittance matrix of the boundary nodes is constructed based on the identified equivalent ground admittance and equivalent coupling branch admittance between boundary nodes. .

[0078] Eliminate all nodes and branches of the original external network, and retain only the internal network nodes, multiple boundary nodes, and the connection relationships between the internal network and multiple boundary nodes.

[0079] Combine it with the internal network self-admittance matrix The mutual admittance matrix between the internal network and the boundary nodes and By combining the blocks, an extended harmonic node admittance matrix is ​​constructed:

[0080] The corresponding extended harmonic node voltage vector is:

[0081] The extended harmonic node injected current vector is:

[0082] Therefore, the extended harmonic network node voltage equations that can be used for harmonic power flow calculations are:

[0083] Step S6: Iteratively solve the harmonic power flow by simultaneously establishing the node voltage equations of the extended harmonic network and the equivalent injection model of the harmonic source.

[0084] In this embodiment, the equivalent injection model of the harmonic source is obtained based on historical operational statistics. This model describes the relationship between the fundamental voltage phasor, the phasors of each harmonic voltage, and the phasors of each harmonic current injected by the harmonic source at the grid-connected node. Its expression is:

[0085] The harmonic source nodes are set to their corresponding harmonic injection currents, the harmonic injection currents of non-harmonic source nodes are set to zero, and the harmonic injection currents of all nodes are combined to form an extended harmonic node injection current vector. .

[0086] Under normal circumstances, the impact of harmonic power flow on fundamental power flow is much smaller than the impact of fundamental power flow on harmonic power flow. Therefore, from an engineering application perspective, for ease of calculation, the influence of harmonic power flow on fundamental operating state information can usually be ignored in harmonic power flow calculations. Furthermore, since the harmonic source injection current is related to the harmonic voltage at the grid connection point, there is a coupling relationship between the harmonic source injection current and the node harmonic voltage. This embodiment uses an iterative method to solve for harmonic power flow, and the specific process is as follows: S61 Based on the fundamental power flow calculation results, the fundamental voltage phasor of the grid-connected node of the harmonic source equipment and the fundamental current phasor of the grid-connected branch are substituted into the equivalent injection model of the harmonic source to solve for the initial harmonic current phasors injected by the harmonic source, and the extended node injection current vector is constructed accordingly. ; S62. Using the extended harmonic network node voltage equations formed after static equivalence of the outer harmonic network corresponding to each harmonic, the harmonic voltage phasors of each node in the internal network and the boundary nodes are solved to obtain the harmonic voltage phasors of each node in the internal network and the boundary nodes. S63. Substitute the updated harmonic voltage phasors at the grid connection point of the harmonic source back into the equivalent injection model of the harmonic source to update the harmonic current phasors injected by the harmonic source. S64. Repeat the alternating solution process of steps S62 and S63 until the difference between the amplitudes of each harmonic voltage at each node obtained in two adjacent iterations is less than the preset convergence threshold (e.g., 10). -5 The maximum number of iterations (e.g., 50) is reached, or the maximum number of iterations is reached. Once the convergence condition is met, the harmonic voltages of the internal network nodes and multiple boundary nodes, as well as the harmonic currents of each branch, are output.

[0087] This embodiment uses the calculated harmonic voltage amplitudes of the internal network and boundary nodes as the demonstration object. To verify the effectiveness of the method of the present invention, the calculated values ​​of the 23rd and 25th harmonic voltage amplitudes obtained by the method of the present invention are compared with the simulated values ​​obtained by the simulation model based on the complete harmonic network. The comparison results are as follows. Figure 3 As shown. By Figure 3 It can be seen that at the 23rd and 25th harmonic frequencies, the calculated values ​​of the method of the present invention are basically consistent with the simulated values, and the deviation between the two is small, indicating that the method of the present invention has high calculation accuracy and good engineering applicability.

[0088] Figure 4 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 4 As shown, the electronic device may include a processor, a communications interface, a memory, and a communication bus, wherein the processor, communications interface, and memory communicate with each other via the communication bus. The processor can call logical instructions in the memory to execute a harmonic power flow calculation method that considers the static equivalent values ​​of the external harmonic network.

[0089] Furthermore, the logical instructions in the aforementioned memory can be implemented as software functional units and sold or used as independent products, and can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0090] In another aspect, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the harmonic power flow calculation method considering the static equivalence of the external harmonic network provided by the methods described above.

[0091] The device embodiments described above are merely illustrative. 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 modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0092] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0093] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating harmonic power flow considering the static equivalent values ​​of the external network of a harmonic network, characterized in that, Includes the following steps: Step 1. Divide the harmonic network to be analyzed into regions and obtain the network topology and component parameters; Step 2. Obtain harmonic measurement data for multiple boundary nodes; Step 3. Construct the theoretical form of the harmonic network node voltage equations after the external network is equivalent; Step 4. Establish the static equivalent model of the harmonic network external network and identify its parameters; Step 5. Establish the extended harmonic network node voltage equations for harmonic power flow calculation; Step 6. Iteratively solve the harmonic power flow by simultaneously establishing the node voltage equations of the extended harmonic network and the equivalent injection model of the harmonic source.

2. The harmonic power flow calculation method considering the static equivalent of the external network of the harmonic network according to claim 1, characterized in that, Step 1 includes the following steps: The power grid to be analyzed is divided into an internal network, an external network, and multiple boundary nodes. The area containing the grid connection point of harmonic source equipment, the nodes around the harmonic source equipment, and the target node area for harmonic power flow calculation is divided into the internal network. The network area without connected harmonic source equipment or with a total harmonic voltage distortion rate of nodes below a preset threshold is divided into the external network. The connection nodes between the internal network and the external network are used as boundary nodes. The network topology, transmission line parameters, transformer parameters, and load parameters of the internal network and multiple boundary nodes are obtained.

3. The harmonic power flow calculation method considering the static equivalent of the external network of the harmonic network according to claim 2, characterized in that, The harmonic measurement data in step 2 includes harmonic voltage phasors at each boundary node and harmonic current phasors flowing to each boundary node; the harmonic source equipment includes at least one of industrial rectifier loads, electric arc furnaces, power electronic converters, new energy grid-connected inverters, and flexible DC converter stations. The measured boundary node harmonic voltage phasor is: The measured harmonic current phasor flowing towards the boundary node is represented as follows: in, k =1, 2, , ; Indicates the number of boundary nodes; No. t The measurement time of the first measurement moment k boundary nodes h Second harmonic voltage phasor; Indicates the first t The flow direction at the measurement moment is the first k boundary nodes h Second harmonic current phasor; t =1, 2, , N ; N Indicates the number of measurement samples.

4. The harmonic power flow calculation method considering the static equivalent of the external network of the harmonic network according to claim 3, characterized in that, Step 3, which involves constructing the theoretical form of the external network equivalent harmonic network node equations, includes: For the analysis h The first harmonic frequency, the admittance matrix of the entire network harmonic network nodes is denoted as... The node harmonic voltage is denoted as The harmonic current injected into the node is denoted as The voltage equations at the nodes of the harmonic network are then: Theoretically, the harmonic network node voltage equations after the external network is equivalent are as follows: in, Let be the equivalent harmonic admittance matrix of the boundary nodes. and This represents the harmonic mutual admittance matrix between boundary nodes and internal network nodes. The harmonic admittance matrix of the internal network nodes. and These represent the harmonic voltage phasors of the boundary nodes and the internal network nodes, respectively. and These represent the injected harmonic current phasors of the boundary nodes and the internal network nodes, respectively. Calculate the internal components in the area to be analyzed h The harmonic admittance at the second harmonic frequency is used to construct the harmonic admittance matrix of the internal network nodes. and the harmonic mutual admittance matrix between boundary nodes and internal network nodes. and .

5. The harmonic power flow calculation method considering the static equivalent of the external network of the harmonic network according to claim 4, characterized in that, The implementation of step 4 includes: The equivalent harmonic admittance matrix of the boundary node The equivalent model is a static equivalent model of the harmonic network external network; the static equivalent model of the harmonic network external network consists of the equivalent ground branches of each boundary node and the equivalent coupling branches between any two boundary nodes; specifically: The equivalent harmonic admittance matrix of the boundary nodes corresponding to the static equivalent model of the harmonic network external network. for An ordinal matrix, the elements of which satisfy the following correspondence: matrix The diagonal element is the first k The equivalent ground admittance of each boundary node, and the sum of the equivalent coupling branch admittances between that node and all other boundary nodes; matrix Off-diagonal elements are the negative values ​​of the admittance of the equivalent coupling branches between corresponding nodes, specifically expressed as: in, For the first k Equivalent ground admittance of each boundary node For the first k The boundary node and the first m The equivalent coupling branch admittance between boundary nodes, when m < k hour, ; The parameters to be identified in the equivalent model of the harmonic external network are: in, and They represent the first k Conductivity and susceptance of the equivalent ground admittance at each boundary node. and They represent the first k The boundary node and the first m Conductance and susceptance of the equivalent coupling branch admittance between boundary nodes. Indicates to be identified h Subharmonic external network static equivalent parameter vector; The harmonic current balance constraint equations for the multiple boundary nodes are as follows: in, Indicates the first t The measurement time of the first measurement moment k boundary nodes h Second harmonic voltage phasor; Indicates the first t The measurement time of the first measurement moment m boundary nodes h Second harmonic voltage phasor; Indicates the first t The flow direction at the measurement moment is the first k boundary nodes h Second harmonic current phasor; The boundary node harmonic current balance constraint equation is a complex equation. Constraints are established on the real and imaginary parts of the complex equation, and its general form is as follows: in, r =1, 2; when r When =1, Indicates the first t The measurement time of the first measurement moment k The real part constraint function of the harmonic current balance equation at each boundary node; when r When =2, Indicates the first t The measurement time of the first measurement moment k The imaginary part constraint function of the harmonic current balance equation at each boundary node; The equivalent parameters of the harmonic external network are identified based on the harmonic current balance constraint equations of multiple boundary nodes, using the following least squares estimation method: in, The target function for identifying the equivalent parameters of the harmonic external network is represented; the target function is made to... When the minimum value is obtained, the corresponding These are the estimated values ​​of the equivalent parameters of the harmonic external network.

6. The harmonic power flow calculation method considering the static equivalent of the external network of the harmonic network according to claim 5, characterized in that, The specific steps for establishing the extended harmonic network node voltage equations for harmonic power flow calculation, as described in step 5, are as follows: Based on the parameter estimates of the equivalent ground admittance of the boundary nodes and the equivalent coupling branch admittance between boundary nodes obtained in step 4, the actual equivalent harmonic admittance matrix of the boundary nodes is constructed; this matrix is ​​then combined in blocks with the self-admittance matrix of the internal network and the mutual admittance matrix between the internal network and the boundary nodes to construct an extended harmonic node admittance matrix containing the internal network nodes and the boundary nodes; for h The extended harmonic nodal admittance matrix is ​​constructed for each of the second harmonics. ; The extended harmonic network node voltage equations used for harmonic power flow calculations are expressed as follows: in, express h Extended harmonic node admittance matrix of equivalent network under subharmonics; This represents the extended harmonic node voltage vector to be solved; This represents the extended harmonic node injected current vector.

7. The harmonic power flow calculation method considering the static equivalent of the external network of the harmonic network according to claim 1, characterized in that, Step 6, which involves iteratively solving the harmonic power flow by simultaneously establishing the extended harmonic network node voltage equations and the equivalent injection model of the harmonic source, includes the following steps: Step 6.

1. Based on the fundamental power flow calculation results, substitute the fundamental voltage phasor of each harmonic source device's grid-connected node and the fundamental current phasor of the grid-connected branch into the equivalent injection model of each harmonic source, solve for the initial harmonic current phasors injected by each harmonic source, and construct the extended node injection current vector accordingly. ; Step 6.

2. Using the extended harmonic network node voltage equations formed after static equivalence of the outer harmonic network corresponding to each harmonic, solve for the harmonic voltage phasors of each node in the internal network and the boundary nodes. Step 6.

3. Substitute the updated harmonic voltage phasors at the grid connection point of the harmonic source back into the equivalent injection model of the harmonic source, and update the injected harmonic current phasors. Step 6.

4. Repeat the alternating solution process of Step 6.2 and Step 6.3 until the difference between the amplitudes of each harmonic voltage of each node in two adjacent iterations is less than the preset convergence threshold, or the preset maximum number of iterations is reached. Then, end the iteration and output the phasor of each harmonic voltage of each node and the phasor of each harmonic current of each branch.

8. A harmonic power flow calculation system considering the static equivalent of the external network of a harmonic network, characterized in that, The system for the harmonic power flow calculation method considering the static equivalence of the harmonic network external network as described in any one of claims 1-7 includes: a data acquisition module, a network partitioning and data processing module, a harmonic network external network static equivalence module, and a harmonic power flow calculation module. The data acquisition module is used to acquire the access information of harmonic source equipment of the power grid to be analyzed, the total harmonic voltage distortion rate data of each node, the network topology of the internal network and multiple boundary nodes, line parameters and transformer parameters; and to acquire the harmonic measurement data of multiple boundary nodes at the harmonic frequency to be analyzed. The network partitioning and data processing module is used to divide the power grid to be analyzed into an internal network, an external network, and multiple boundary nodes based on the access information of harmonic source devices and the total harmonic voltage distortion rate data of each node; calculate the harmonic admittance at the harmonic frequency to be analyzed based on the network topology, line parameters, and transformer parameters of the internal network and multiple boundary nodes; and construct the self-admittance matrix of the internal network and the mutual admittance matrix between the internal network and multiple boundary nodes. The harmonic network external static equivalent module is used to establish a static equivalent model of the harmonic network external network for multiple boundary nodes. Based on the harmonic voltage phasors and harmonic current phasors of multiple boundary nodes, it establishes the harmonic current balance constraint equations of the boundary nodes and identifies the parameters of the harmonic network external static equivalent model through the least squares estimation method. According to the identified equivalent ground admittance and equivalent coupling branch admittance between boundary nodes, the equivalent harmonic admittance matrix of the boundary nodes is constructed. The equivalent harmonic admittance matrix of the boundary nodes is combined with the self-admittance matrix of the internal network and the mutual admittance matrix between the internal network and multiple boundary nodes to form the extended harmonic node admittance matrix. The harmonic power flow calculation module is used to obtain the fundamental operating status information of the internal network and multiple boundary nodes, calculate the phasors of each harmonic current injected by the harmonic source using the equivalent injection model of the harmonic source, and establish the voltage equations of the extended harmonic network nodes based on the extended harmonic node admittance matrix. By iteratively solving the extended harmonic network node voltage equations and the equivalent injection model of the harmonic source, the phasors of each harmonic voltage of the internal network nodes and multiple boundary nodes and the phasors of each harmonic current of each branch are obtained, thus completing the harmonic power flow calculation.

9. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the harmonic power flow calculation method considering the static equivalence of the external harmonic network as described in any one of claims 1-7.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the harmonic power flow calculation method considering the static equivalence of the external network of the harmonic network as described in any one of claims 1-7.

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