Method and device for determining position of harmonic source of power distribution network, electronic equipment and medium

Abstract

Disclosed are a method and device for determining the location of a harmonic source in a power distribution network, electronic equipment and a medium. The method for determining the location of the harmonic source comprises: obtaining harmonic current information of a plurality of initial nodes in a power distribution system, wherein the plurality of initial nodes are nodes provided with a measurement device; determining a target section based on the harmonic current information, wherein the target section comprises a plurality of target links; and determining location information of a target harmonic source from the plurality of target links based on a target measurement matrix set, wherein the target measurement matrix set comprises a first-dimensional measurement matrix, a second-dimensional measurement matrix and a state variable matrix. The present application solves the technical problem of low accuracy in locating the harmonic source in the power distribution system in the prior art.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of automation, in particular to a method and device for determining the location of a harmonic source in a power distribution network, an electronic device and a medium. BACKGROUND

[0002] In modern society, with the widespread use of power electronic devices, higher requirements are put forward for harmonic pollution control of power systems. In the process of connecting power electronic devices to power systems, nonlinear loads distort the voltage and current waveforms of the power grid, generating a large amount of harmonics. High harmonic content not only causes electromagnetic interference to the power grid, but also affects the normal operation of power electronic devices, even causing overheating, aging and shortening of the service life of power electronic devices, affecting the stable operation and economic operation of the power grid, and even causing damage to equipment and power line accidents. Therefore, the problem of harmonic control in the power distribution network has attracted much attention in recent years, and mastering the harmonic distribution of the power grid and accurately locating the harmonic source are the premise and foundation.

[0003] Harmonic state estimation based on the principle of complete observability of the system is the most commonly used method for locating harmonic sources at the present stage, that is, according to the harmonic voltage and current data of a limited number of measurement points, combined with the topology and parameters of the power grid, a linear measurement model is established through network analysis to estimate the harmonic state of the power grid. However, harmonic state estimation of the power distribution network cannot be based on the complete observability condition, and it is essentially a state estimation problem of a low-observable complex system. The main difficulty brought by low observability is that the measurement equation established is underdetermined, the model has a non-unique solution, and it is difficult to locate the harmonic source.

[0004] At present, there are two ways to deal with underdetermined equations, the first is to convert the underdetermined equation into a well-determined or overdetermined equation for solving, common methods include reducing the number of states to be estimated, converting the unobservable region into an equivalent observable region, etc., but this method has a high harmonic state estimation error, and as the number of nodes increases, the calculation dimension and complexity increase exponentially.

[0005] The second method is to directly solve the underdetermined equation from a mathematical point of view, using singular value decomposition, independent component analysis, linear programming, etc., but this method may have incorrect solutions due to the infinite number of solutions of the underdetermined equation, and is easily affected by factors such as measurement point location, measurement noise and non-synchronous measurement of measurement points, leading to positioning failure.

[0006] At present, there is no corresponding solution to the above problems. SUMMARY

[0007] The embodiments of the present application provide a method and device for determining the location of a harmonic source in a power distribution network, an electronic device and a medium, to at least solve the technical problem of low positioning accuracy of harmonic sources in the power distribution system in the prior art.

[0008] According to one of the embodiments of the present application, a method for determining the location of a harmonic source in a power distribution network is provided, comprising: obtaining harmonic current information of a plurality of initial nodes in a power distribution system, wherein the plurality of initial nodes are nodes equipped with measurement devices; determining a target section according to the harmonic current information, wherein the target section comprises a plurality of target links; determining location information of a target harmonic source from the plurality of target links according to a target measurement matrix set, wherein the target measurement matrix set comprises a first dimension measurement matrix, a second dimension measurement matrix, and a state variable matrix.

[0009] Optionally, the method for determining the location of a harmonic source in a power distribution network further comprises: obtaining a plurality of circuit nodes of the power distribution system; determining a plurality of initial nodes from the plurality of circuit nodes, wherein the plurality of initial nodes at least include boundary nodes, branch nodes, and link nodes.

[0010] Optionally, the method for determining the location of a harmonic source in a power distribution network further comprises: obtaining a plurality of initial sections of the power distribution system based on the plurality of initial nodes; determining a plurality of balanced nodes from the plurality of initial sections; measuring current information of the plurality of balanced nodes to obtain the harmonic current information.

[0011] Optionally, the method for determining the location of a harmonic source in a power distribution network further comprises: classifying the plurality of circuit nodes based on the initial nodes to obtain a plurality of node sets; performing a clustering topology operation on the plurality of node sets to obtain the plurality of initial sections.

[0012] Optionally, the method for determining the location of a harmonic source in a power distribution network further comprises: obtaining the target measurement matrix set according to the harmonic current information; generating an initial harmonic state estimation model according to the target measurement matrix set; determining a target node based on the initial harmonic state estimation model; determining the target section according to the target node.

[0013] Optionally, the method for determining the location of a harmonic source in a power distribution network further comprises: determining a first initial node and a second initial node of the target section; obtaining first harmonic current information of the first initial node and second harmonic current information of the second initial node; determining location information of the target harmonic source from the plurality of target links based on the first harmonic current information, the second harmonic current information, and the target measurement matrix set.

[0014] Optionally, the method for determining the location of a harmonic source in a power distribution network further comprises: establishing a state relationship matrix according to the first harmonic current information and the second harmonic current information; generating a target harmonic state estimation model according to the state relationship matrix and the target measurement matrix set; determining the location information of the target harmonic source based on the target harmonic state estimation model.

[0015] According to an embodiment of the present application, a device for determining a harmonic source position in a power distribution network is provided. The device comprises a first obtaining module configured to obtain harmonic current information of a plurality of initial nodes in a power distribution system, wherein the plurality of initial nodes are nodes equipped with a measurement device; a first determining module configured to determine a target section according to the harmonic current information, wherein the target section comprises a plurality of target links; and a second determining module configured to determine position information of a target harmonic source from the plurality of target links according to a target measurement matrix set, wherein the target measurement matrix set comprises a first dimension measurement matrix, a second dimension measurement matrix and a state variable matrix.

[0016] Optionally, the device for determining the harmonic source position in the power distribution network further comprises a second obtaining module configured to obtain a plurality of circuit nodes of the power distribution system; and a third determining module configured to determine the plurality of initial nodes from the plurality of circuit nodes, wherein the plurality of initial nodes at least comprise a boundary node, a branch node and a link node.

[0017] Optionally, the first obtaining module comprises a first obtaining unit configured to obtain a plurality of initial sections of the power distribution system based on the plurality of initial nodes; a first determining unit configured to determine a plurality of balancing nodes from the plurality of initial sections; and a measuring unit configured to measure current information of the plurality of balancing nodes to obtain the harmonic current information.

[0018] Optionally, the first obtaining unit comprises a classification sub-unit configured to classify the plurality of circuit nodes based on the initial nodes to obtain a plurality of node sets; and an execution sub-unit configured to execute a clustering topology operation on the plurality of node sets to obtain the plurality of initial sections.

[0019] Optionally, the first determining module comprises a second obtaining unit configured to obtain the target measurement matrix set according to the harmonic current information; a generating unit configured to generate an initial harmonic state estimation model according to the target measurement matrix set; a second determining unit configured to determine a target node based on the initial harmonic state estimation model; and a third determining unit configured to determine the target section according to the target node.

[0020] Optionally, the second determining module comprises a fourth determining unit configured to determine a first initial node and a second initial node of the target section; a third obtaining unit configured to obtain first harmonic current information of the first initial node and second harmonic current information of the second initial node; and a fifth determining unit configured to determine the position information of the target harmonic source from the plurality of target links based on the first harmonic current information, the second harmonic current information and the target measurement matrix set.

[0021] Optionally, the fifth determining unit comprises: a establishing subunit, configured to establish a state relation matrix according to the first harmonic current information and the second harmonic current information; a generating subunit, configured to generate a target harmonic state estimation model according to the state relation matrix and the target measurement matrix set; and a determining subunit, configured to determine the position information of the target harmonic source based on the target harmonic state estimation model.

[0022] According to an embodiment of the present application, an electronic device is also provided, comprising a memory and a processor, the memory storing a computer program, and the processor being configured to run the computer program to perform the method for determining the position of the harmonic source of the power distribution network in any of the above.

[0023] According to an embodiment of the present application, a computer readable storage medium is also provided, the computer readable storage medium storing a computer program, and the computer program being configured to perform the method for determining the position of the harmonic source of the power distribution network in any of the above when running.

[0024] In the embodiment of the present application, the harmonic current information of a plurality of initial nodes in the power distribution system is acquired, wherein the plurality of initial nodes are nodes configured with measurement devices, the purpose of determining a target section according to the harmonic current information is achieved, wherein the target section comprises a plurality of target links, the technical effect of determining the position information of the target harmonic source from the plurality of target links according to the target measurement matrix set is achieved, wherein the target measurement matrix set comprises a first dimension measurement matrix, a second dimension measurement matrix and a state variable matrix, and thus the technical problem of low positioning accuracy of the harmonic source in the power distribution system in the prior art can be solved. BRIEF DESCRIPTION OF DRAWINGS

[0025] The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiments of the present application and serve to explain the present application. In the drawings:

[0026] Figure 1 is a flow chart of the method for determining the position of the harmonic source of the power distribution network according to an embodiment of the present application;

[0027] Figure 2 is a schematic diagram of three types of nodes on a radial feeder according to an embodiment of the present application;

[0028] Figure 3 is a schematic diagram of a hierarchical estimation algorithm system division method according to an embodiment of the present application;

[0029] Figure 4 is a structural block diagram of the device for determining the position of the harmonic source of the power distribution network according to an embodiment of the present application. DETAILED DESCRIPTION

[0030] In order to make the person skilled in the art better understand the technical scheme of the present application, the technical scheme in the embodiments of the present application will be described clearly and completely below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by the person skilled in the art without creative work should belong to the protection scope of the present application.

[0031] It should be noted that the terms "first", "second" and the like in the description and claims of the present application and the above-mentioned drawings are used to distinguish similar objects, and do not necessarily indicate a specific order or sequence. It should be understood that the terms thus used can be interchanged under appropriate circumstances, so that the embodiments of the present application described herein can be implemented in other than the order illustrated or described herein. In addition, the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusion, for example, a process, method, system, product or device including a series of steps or units need not be limited to those steps or units clearly listed, but can include other steps or units not clearly listed or inherent to these processes, methods, products or devices.

[0032] According to the embodiments of the present application, an embodiment of a method for determining the location of a harmonic source in a power distribution network is provided. It should be noted that the steps shown in the flowchart of the drawings can be executed in a computer system comprising at least one set of computer executable instructions, and although a logical order is shown in the flowchart, in some cases, the steps shown or described herein can be executed in an order different from that shown herein.

[0033] The method embodiment can also be executed in an electronic device comprising a memory and a processor, a similar control device or electronic equipment. Taking the electronic equipment as an example, the electronic equipment can include one or more processors and a memory for storing data. Optionally, the above-mentioned electronic equipment can also include a communication device for communication function and a display device. Those skilled in the art can understand that the above-mentioned structural description is only illustrative, which does not limit the structure of the above-mentioned electronic equipment. For example, the electronic equipment can include more or less components than the above-mentioned structural description, or have a different configuration from the above-mentioned structural description.

[0034] The processor can include one or more processing units. For example, the processor can include a central processing unit (CPU), a graphics processing unit (GPU), a digital signal processing (DSP) chip, a microcontroller unit (MCU), a field-programmable gate array (FPGA), a neural-network processing unit (NPU), a tensor processing unit (TPU), an artificial intelligent (AI) type processor, or the like. Different processing units can be independent components or integrated in one or more processors. In some examples, the electronic device can also include one or more processors.

[0035] The memory can be used to store a computer program, for example, a computer program corresponding to the method for determining the location of a harmonic source in a power distribution network in the embodiments of the present application. The processor implements the above-mentioned method for determining the location of a harmonic source by running the computer program stored in the memory. The memory can include a high-speed random access memory, and can also include a non-volatile memory, such as one or more magnetic storage devices, flash memories, or other non-volatile solid-state memories. In some examples, the memory can further include a memory remotely disposed relative to the processor, which can be connected to the electronic device through a network. Examples of the network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0036] The communication device is used to receive or send data via a network. Specific examples of the network can include a wireless network provided by a communication provider of a mobile terminal. In one example, the communication device includes a network interface controller (NIC) that can be connected to other network devices through a base station so as to communicate with the Internet. In one example, the communication device can be a radio frequency (RF) module used to communicate with the Internet in a wireless manner. In some embodiments of the present application, the communication device is used to connect with a mobile device such as a mobile phone or a tablet, and can send instructions to the vehicle terminal through the mobile device.

[0037] The display device can be a touch screen type liquid crystal display (LCD) and a touch display (also referred to as a "touch screen" or "touch display screen"). The liquid crystal display can enable a user to interact with a user interface of the in-vehicle terminal. In some embodiments, the in-vehicle terminal described above has a graphical user interface (GUI) with which a user can interact with the GUI through finger contacts and / or gestures on a touch-sensitive surface, where the human-machine interaction function can include a vehicle gear shifting function, and executable instructions for performing the human-machine interaction function are configured / stored in one or more computer program products or readable storage media executable by a processor.

[0038] Figure 1 is a flowchart of a method for determining a harmonic source position of a power distribution network according to an embodiment of the present application, as shown in Figure 1 The method comprises the following steps:

[0039] In step S102, harmonic current information of a plurality of initial nodes in the power distribution system is acquired, wherein the plurality of initial nodes are nodes configured with a measurement device.

[0040] Optionally, the execution subject of the present embodiment is a harmonic source position determination system, and it should be noted that other electronic devices and processors can also serve as the execution subject, which is not limited herein.

[0041] Specifically, in the power distribution system, the initial node refers to a node installed with a measurement device. The measurement device can directly provide real-time voltage and current phasor data of these nodes, including amplitude and phase information of voltage and current, and these information is the basis for system state estimation and monitoring.

[0042] The measurement device can be exemplarily a phasor measurement unit (PMU), which is a device used for synchronous measurement of voltage and current phasors in a power system. The PMU can capture amplitude and phase information of voltage and current of each node in the power system in real time, and ensure that these measurement values are performed under the same time reference through a global positioning system or other synchronous signals, thereby realizing wide-area synchronous phasor measurement.

[0043] For example, the acquisition of the harmonic current information of the plurality of initial nodes in the power distribution system by the PMU includes the following steps: synchronous sampling, the PMU uses the global positioning system to realize high-speed and accurate sampling of the current waveform of each initial node, and ensures that all measurement data is acquired under the same time reference; harmonic analysis, the original current data collected by the PMU needs to be analyzed by Fourier transform (usually fast Fourier transform) to convert the time domain signal into the frequency domain signal, so as to extract the amplitude and phase information of each harmonic current. For the harmonic analysis in the power distribution system, the integer multiple frequency of the fundamental frequency, i.e. the 2nd, 3rd, 5th, 7th and other harmonics, needs to be concerned; data packaging and transmission: the analyzed harmonic current information is packaged by the PMU into a standard data format, such as CIM (Common Information Model), SVG (Scalable Vector Graphics) or a special data transmission protocol of the PMU, and then transmitted in real time to the central control center or data analysis platform through the communication network.

[0044] In step S104, the target section is determined according to the harmonic current information, wherein the target section includes a plurality of target links.

[0045] Specifically, the power distribution system is divided into a plurality of initial sections defined by different types of nodes (such as head-end nodes, end nodes and branch nodes) as initial sections, and each initial section includes a plurality of links.

[0046] Based on the divided initial sections, the current measurement data of the downstream endpoint (i.e. the balanced node) of each section represents the branch current of the section. Since the flow direction of the harmonic current is always from the injection node to the balanced node, the direction towards the balanced node is defined as the downstream of the harmonic transmission path, and the direction away from the balanced node is defined as the upstream. If there is a harmonic source in the section, the harmonic current will only flow through the downstream endpoint measurement point, so only the measurement result of the downstream endpoint contains the harmonic current information in the section, and therefore the measurement result of the downstream endpoint is selected.

[0047] Based on the obtained downstream endpoint current measurement data of each section, a first layer harmonic state estimation model is constructed, which is a mixed integer quadratic programming problem model. By solving the first layer harmonic state estimation model, the flow path of the harmonic current is identified, and the section in which the harmonic source is possibly located, i.e. the target section, is determined. Each target section is composed of a plurality of target links, which are the paths through which the harmonic current flows.

[0048] In step S106, the position information of the target harmonic source is determined from the plurality of target links according to the target measurement matrix set, wherein the target measurement matrix set includes a first dimension measurement matrix, a second dimension measurement matrix and a state variable matrix.

[0049] Specifically, the target measurement matrix set is composed of a first dimension measurement matrix, a second dimension measurement matrix and a state variable matrix. These matrices reflect the relationship between the measurement data and the system state, and are the basis for harmonic state estimation. Among them, the first dimension measurement matrix is used to distinguish which nodes or branches of current and voltage are actually measured, and the second dimension measurement matrix is used to describe the relationship between the harmonic voltage and current of the nodes and branches without measurement devices, that is, even without direct measurement at these locations, state information can be indirectly obtained through the association with the measured nodes and branches.

[0050] Specifically, after determining the target section where the harmonic source is located, the target link of the section where the harmonic source is located is determined according to the determined harmonic current path, and then a second layer harmonic state estimation model is constructed, which is also a mixed integer quadratic programming problem model. By solving the above constructed mixed integer quadratic programming problem, the specific position information of the harmonic source in the target section can be further determined.

[0051] The above steps S102 to S106 can be known that in the present application, the harmonic current information of a plurality of initial nodes in the power distribution system is obtained, wherein the plurality of initial nodes are nodes provided with measurement devices, thereby achieving the purpose of determining the target section according to the harmonic current information, wherein the target section includes a plurality of target links, thereby achieving the technical effect of determining the position information of the target harmonic source from the plurality of target links according to the target measurement matrix set, wherein the target measurement matrix set includes a first dimension measurement matrix, a second dimension measurement matrix and a state variable matrix, thereby solving the technical problem of low positioning accuracy of the harmonic source in the power distribution system in the prior art.

[0052] The above method of the embodiment will be further described in detail.

[0053] As an optional implementation, the method for determining the position of the harmonic source of the power distribution network further includes: obtaining a plurality of circuit nodes of the power distribution system; determining a plurality of initial nodes from the plurality of circuit nodes, wherein the plurality of initial nodes at least include boundary nodes, branch nodes and link nodes.

[0054] Specifically, the network structure of the power distribution system is comprehensively analyzed, and all circuit nodes in the system are identified. These nodes can be load nodes, power supply nodes, or any connection points that can affect current and voltage distribution.

[0055] Based on the identified all circuit nodes, a plurality of initial nodes are determined from the plurality of circuit nodes, the selection of the initial nodes is based on their special location in the network and the potential influence on the harmonic current path. The plurality of initial nodes at least includes boundary nodes, branch nodes and link nodes, wherein the boundary nodes are located at the edge of the power distribution network, they act as the interface of the harmonic current entering and exiting the power distribution network, and are important for the optimization of the measurement range; the branch nodes are located at the branch points of the network, they can help analyze the distribution path of the current and provide information on the possible flow direction of the harmonic current; the link nodes are located on the chain-like structure divided by the boundary nodes and branch nodes, although their measurement information is of low value under low observable conditions (i.e. the measurement data of the power distribution system is insufficient to fully describe or determine the state of the power distribution system), they act as connection nodes and can assist in building a complete network model, which indirectly contributes to the accuracy and comprehensiveness of the harmonic source positioning.

[0056] Exemplarily, Figure 2 is a schematic diagram of three types of nodes on a radial feeder according to an embodiment of the present application. As shown, Figure 2 the node position distribution in the IEEE33 node system (a widely used power distribution system model proposed by IEEE (Institute of Electrical and Electronics Engineers)) is shown. The nodes in the system are divided into the following three types according to their locations: boundary nodes, such as node 1, node 18, node 22, node 25, node 33; branch nodes, such as node 2, node 3, node 6; link nodes, i.e. other nodes in the node system except boundary nodes and branch nodes, such as node 4, node 5, node 7, node 8, node 9, etc. The boundary nodes are located at the network boundary, and due to the one-way transmission characteristics of the radial topology, installing PMUs is beneficial to maximizing the measurement range; the branch nodes are located at the branches, and installing PMUs is beneficial to mastering the specific path of the harmonic current; the link nodes are located on the chain-like structure divided by the boundary nodes and branch nodes, and the measurement information is of low value and is easily associated with the measurement information of the upstream and downstream boundary nodes and branch nodes, and for the link nodes, PMUs can be selectively configured, such as being installed at the bus with critical load or harmonic source.

[0057] As an optional implementation, obtaining the harmonic current information of the plurality of initial nodes includes: based on the plurality of initial nodes, obtaining a plurality of initial sections of the power distribution system; determining a plurality of balance nodes from the plurality of initial sections; and measuring the current information of the plurality of balance nodes to obtain the harmonic current information.

[0058] Specifically, the initial sections are obtained by positioning the plurality of initial nodes, and the boundary nodes and the branch nodes divide the entire power distribution system into a plurality of chain-like or branch-like initial sections.

[0059] Exemplarily, Figure 3is a schematic diagram of a hierarchical estimation algorithm system partition method according to an embodiment of the present application. As shown in Figure 3 As shown in (a) of FIG. 1, the entire system is divided into 7 initial sections, namely, section I, section II, section III, section IV, section V, section VI and section VII, by the boundary nodes 1, 18, 22, 25 and the branch nodes 2, 3, 6.

[0060] In addition, the balancing node is a special node in power system analysis, which is used to provide the voltage reference value of the system, and to provide the power balance condition in the calculation. In each initial section, one or more nodes are selected as the balancing node, and usually this node is the node connected to the power supply of the system, or has a higher voltage or power level in the section. For example, in (a) of FIG. 1, node 1 is designated as the balancing node in the IEEE 33-node system because it provides the reference for the system voltage. Figure 3

[0061] Specifically, on the basis of determining the balancing node, the current information of the multiple balancing nodes is measured by a measuring device such as a PMU to obtain the harmonic current information.

[0062] It should be noted that the flow path of the harmonic current in the system starts from the balancing node and propagates to other nodes along the branches, so by measuring the harmonic current information of the balancing node, the position of the harmonic current and its possible propagation path can be preliminarily judged.

[0063] As an optional implementation, the obtaining of the multiple initial sections of the power distribution system based on the multiple initial nodes comprises: classifying the multiple circuit nodes based on the initial nodes to obtain multiple node sets; and performing a clustering topology operation on the multiple node sets to obtain the multiple initial sections.

[0064] Specifically, based on the determined initial nodes, the multiple circuit nodes in the power distribution system are classified to obtain multiple node sets. For example, the multiple circuit nodes are divided into three categories, namely, boundary nodes, branch nodes and link nodes.

[0065] Specifically, all branches belonging to the same link are aggregated into an equivalent branch and renumbered to simplify the network model, reduce the number of nodes and branches, and improve the calculation efficiency of the state estimation.

[0066] For example, as shown in (a) of FIG. 1, the boundary nodes in the system are renumbered, and the correspondence between the new node numbers and the old node numbers is shown in Table 1. Figure 3

[0067] Table 1 Correspondence between new and old node numbers

[0068] ​​

[0069] As an example, as shown in (b) of FIG. 1, Figure 3 (b) of FIG. 1, Figure 3 (b) of FIG. 1 is to perform a clustering topology operation on the plurality of node sets to obtain a plurality of initial sections.

[0070] As an optional implementation, determining the target section according to the harmonic current information comprises: obtaining a target measurement matrix set according to the harmonic current information; generating an initial harmonic state estimation model according to the target measurement matrix set; determining a target node based on the initial harmonic state estimation model; and determining the target section according to the target node.

[0071] Specifically, according to the collected harmonic current information, a target measurement matrix set is constructed. The measurement matrix reflects the mathematical relationship between the measurement equipment (such as PMU) and the system state variable (the harmonic current and the harmonic voltage of the node and the branch), and is the basis for state estimation.

[0072] It should be noted that, under low observability conditions, in order to construct a more effective and easier to solve model, the data in the measurement matrix needs to be screened. As an example, the branch current measurement data of the initial section balanced node is selected, because these data can more directly reflect the position of the harmonic current path and the potential harmonic source.

[0073] An initial harmonic state estimation model is generated using the screened measurement matrix set and the power grid topology structure information. The model describes the harmonic state of the system through the relationship between the measurement matrix, the measurement equation matrix established by network analysis, and the state variable matrix.

[0074] When constructing the model, the physical characteristics of the power grid, such as node current constraints, branch current constraints, and node voltage constraints, also need to be combined to ensure the reasonableness and accuracy of the model. These constraints reflect the physical laws of power system operation and help the model accurately estimate the harmonic state.

[0075] Specifically, the construction of the basic model of the harmonic state estimation of the distribution system under low observability is as follows:

[0076] For a power grid containing n nodes and I branches, the basic mathematical model for h-th harmonic state estimation is:

[0077] Z(h) = H(h)X(h) + ε (1)

[0078] In the formula, Z(h) represents a p x I dimensional measurement matrix; H(h) represents a p x q dimensional measurement matrix; the matrix X(h) represents a q x I dimensional state variable matrix; ε represents a p x I dimensional measurement error; p represents the number of measurements, and q represents the number of state variables to be solved.

[0079] The harmonic state estimation can be solved by the following optimization problem, with the state that minimizes the measurement error as the estimation result:

[0080]

[0081] The state variable matrix X(h) contains the harmonic currents of each node and branch, and the harmonic voltages of each node, and its expression is:

[0082] x(h) = [(I N (h)) T (V(h)) T (I L (h)) T ] T (3)

[0083] In the formula, I N (h), I L (h) are the hth harmonic current vectors of all nodes and branches respectively; V(h) is the hth harmonic voltage vector of all nodes.

[0084] The expression of the measurement matrix Z(h) is:

[0085]

[0086] In the formula, the superscript m represents the measured value, and is used to distinguish the state and the measurement. If a PMU device is installed at a node, the node voltage and the current of the connected branch are measured.

[0087] According to the expressions of X(h) and Z(h), the measurement matrix H(h) can also be expressed in the form of a block matrix, and the specific expression is as follows:

[0088]

[0089] In the formula, and are 01 matrices, and the corresponding position elements are 1 when the branch current / node voltage is measured, otherwise 0; Y(h) is the hth harmonic admittance matrix between the node current and the node voltage; Y prime (h) represents the hth harmonic admittance matrix between the branch current and the node voltage.

[0090] If H(h) is full rank, equation (2) has a unique solution, and the system is fully observable (the state of a system can be uniquely determined from its measurements, either directly or indirectly); otherwise, the system is not fully observable (the measurements do not cover all state variables). Under the condition of incomplete observability, the measurement data cannot cover all nodes, and it is insufficient to establish a well-posed or overdetermined equation. In this regard, the matrix G(h) can be introduced in combination with the topological information of the system to establish the relationship between the harmonic state of the unobserved node / branch and the measurement. For branches without PMU, the relationship between the harmonic node voltage and the branch harmonic current can be captured by the following equation:

[0091]

[0092] where I is an lxl dimensional identity matrix, and the coupling between the state variables can be effectively increased by equation (6), and the arrangement can obtain:

[0093] 0 = G(h)X(h) (7)

[0094] where the matrix G(h) represents the relationship between the harmonic voltage V(h) of the node without PMU and the harmonic current I L (h) of the branch, and the relationship between the state variables is established through G(h), and the unobservable variables are included in the analysis.

[0095] Further, the augmented mathematical model of harmonic state estimation under the condition of low observability can be established as follows:

[0096]

[0097] Harmonic voltage / current distribution characteristic constraints:

[0098] (a) The constraint condition of the node current is represented as follows:

[0099] -Md≤I N (h)≤Md (9)

[0100] where M is a maximum number, which can be taken as the maximum harmonic current amplitude that can occur in the system; d is used to represent whether the node is assumed to be a harmonic source, and its value is as follows:

[0101]

[0102] For nodes not on the harmonic transmission path, M and d form an upper bound of 0 and a lower bound of 0; for harmonic injection nodes, M can effectively constrain the upper and lower bounds of the harmonic current, reducing the optimization range.

[0103] (b) The constraint condition of the branch current is represented as follows:

[0104] -MΨ(1-d)≤AI L(h)≤MΨ(1-d) (11)

[0105] where A is a u x l 01 matrix for extracting the branch currents of {L\L k}, u represents the branches not in the harmonic transmission path; and Ψ is a u x n 01 matrix with only one element being 1 in each row for imposing the constraint on the branch currents of {L\L k}. Equation (11) limits the harmonic currents of the branches not in the harmonic transmission path to 0 without affecting the values of the harmonic currents of the branches on the harmonic transmission path.

[0106] (c) The constraint condition of the node voltage is expressed as follows:

[0107] -MΦ(1-d)≤BV(h)≤MΦ(1-d) (12)

[0108] where B is a w x n matrix for extracting the nodes of {N\Nk}, with only one corresponding element of ±1 in each row of the adjacent nodes to calculate the voltage drop between the nodes, and w represents the total number of nodes not in the harmonic transmission path; and Φ is a w x n 01 matrix with only one element being 1 in each row for imposing the constraint on the adjacent node pairs of {N\N k}.

[0109] In summary, the problem of harmonic state estimation of the power distribution system under low observability can be expressed as the solution of the following mixed integer programming problem:

[0110]

[0111] subject to equations (3), (9), (10), (11), and (12).

[0112] Iterate through the possible values of d, sequentially solve the above optimization problem, and take the value of d when the objective value is optimal as the harmonic source position. The corresponding X(h) is the harmonic state estimation result.

[0113] Based on the above analysis, the initial harmonic state estimation model is established as follows:

[0114]

[0115] subject to equations (3), (9), (10), (11), and (12).

[0116] where

[0117] Z1(h)=[I L1 (h),I L2 (h),…,I L7 (h)] T (15)

[0118]

[0119]

[0120] The harmonic current path and the target section where the harmonic source is located can be determined by solving the mixed integer quadratic programming problem described by equation (14).

[0121] It should be noted that, since the initial harmonic state estimation model focuses on the identification of the harmonic current path, all voltage measurements are discarded.

[0122] As an optional implementation, the method for determining the location information of the target harmonic source from the plurality of target links according to the target measurement matrix set comprises: determining a first initial node and a second initial node of the target section; obtaining first harmonic current information of the first initial node and second harmonic current information of the second initial node; and determining the location information of the target harmonic source from the plurality of target links based on the first harmonic current information, the second harmonic current information and the target measurement matrix set.

[0123] Specifically, for each target section, the nodes at both ends are determined as the first initial node and the second initial node, which are usually the starting point and the ending point of the section and are equipped with PMUs or corresponding measurement devices.

[0124] After the first and second initial nodes are determined, the harmonic current information is collected by the PMUs or other measurement devices installed on the nodes. For example, the harmonic current phasor of the first initial node and the harmonic current phasor of the second initial node are obtained.

[0125] The first harmonic current information of the first initial node and the second harmonic current information of the second initial node are combined with the target measurement matrix set constructed before to form a more detailed measurement data set. These data will be used to construct a second layer harmonic state estimation model (target harmonic state estimation model) to determine the specific location of the harmonic source.

[0126] For example, Figure 3 is a schematic diagram of the hierarchical estimation algorithm system division method according to an embodiment of the present application. As shown in Figure 3 (b) of FIG. 1, Figure 3 (c) of FIG. 1, the initial harmonic state estimation model is used to determine in which section (i.e., target section) of (b) of FIG. 1 the harmonic source is located, and on this basis, the second layer harmonic state estimation model is used to further determine the specific location of the harmonic source in the target section. Figure 3

[0127] ​As an optional implementation, determining the location information of the target harmonic source based on the first harmonic current information, the second harmonic current information and the target measurement matrix set includes: establishing a state relationship matrix based on the first harmonic current information and the second harmonic current information; generating a target harmonic state estimation model based on the state relationship matrix and the target measurement matrix set; and determining the location information of the target harmonic source based on the target harmonic state estimation model.

[0128] Specifically, the target harmonic state estimation model can be expressed as Equation (13). Solve the mixed integer programming problem described in Equation (13), traverse all possible values ​​of d, and take the d value when the target value is optimal as the position of the target harmonic source.

[0129] Another specific embodiment of this solution is as follows:

[0130] Under low observable conditions, the harmonic current injected by the node is estimated and the harmonic source in the distribution network is located. The simulation software is used to simulate the Figure 2 The IEEE 33-node harmonic power flow program shown in Figure 1 simulates the operation of the distribution network and solves the harmonic state estimation problem based on mixed integer quadratic programming. Figure 2 As shown in the figure, node 1 is a balancing node, and nodes 2-33 are load nodes. A current source model is used to simulate the harmonic currents injected into the nodes by a harmonic source. Nodes 1-4 are connected to current sources as harmonic source nodes in the system. Low observability is achieved by reducing the number of measurement devices. Assume that eight PMUs are installed in the system, located at nodes 1, 2, 3, 6, 18, 22, 25, and 33, to measure node harmonic voltage phasors and branch harmonic current phasors. A harmonic power flow program is used to calculate the harmonic voltage and branch harmonic current values ​​at each node. Gaussian noise signals are added to create a measurement value database. Based on the PMU installation situation, a subset of measurement values ​​are selected from the database to construct the measurement matrix for the harmonic state estimation problem.

[0131] The root mean square error (RMSE) is used as a measure of the accuracy of harmonic source location. The estimated value of the node harmonic current obtained by the harmonic state estimation is compared with the actual value of the node harmonic current. The smaller the RMSE, the smaller the difference between the estimated value and the actual value, that is, the more accurate the harmonic state estimation result. The RMSE formula is as follows:

[0132]

[0133] Where, I N (h) is the true value of the node harmonic current, is the estimated value of the node harmonic current, i is the node number, and n is the total number of nodes.

[0134] Under the same simulation environment, the harmonic state estimation simulation is respectively carried out by using the method and the prior art. The simulation result shows that the root mean square error corresponding to the method is smaller than the root mean square error corresponding to the prior art, that is, the method for determining the harmonic source position is more accurate in the harmonic state estimation than the prior art.

[0135] Through the above description of the embodiments, those skilled in the art can clearly understand that the method according to the above embodiments can be realized by means of software and the necessary general hardware platform, and of course, it can also be realized by hardware, but in many cases, the former is a better embodiment. Based on such understanding, the technical solutions of the present application or the part that contributes to the prior art can be embodied in the form of a software product, which is stored in a storage medium (such as a ROM / RAM, a magnetic disk, or an optical disk) and includes a plurality of instructions for causing a terminal device (which can be a mobile phone, a computer, a server, or a grid device) to execute the method of each embodiment of the present application.

[0136] In the embodiment, a device for determining the position of a harmonic source of a power distribution network is also provided, which is used to implement the above embodiments and preferred embodiments, and will not be described again. As used below, the term "module" can be a combination of software and / or hardware that implements a predetermined function. Although the device described in the following embodiments is preferably implemented in software, hardware or a combination of software and hardware is also possible and is contemplated.

[0137] Figure 4 is a structural block diagram of a device 400 for determining the position of a harmonic source of a power distribution network according to one embodiment of the present application, as shown in Figure 4 The device includes a first acquisition module 401, a first determination module 402, and a second determination module 403.

[0138] The first acquisition module 401 is configured to acquire harmonic current information of a plurality of initial nodes in a power distribution system, wherein the plurality of initial nodes are nodes configured with a measurement device.

[0139] The first determination module 402 is configured to determine a target section according to the harmonic current information, wherein the target section includes a plurality of target links.

[0140] The second determination module 403 is configured to determine position information of a target harmonic source from the plurality of target links according to a target measurement matrix set, wherein the target measurement matrix set includes a first dimension measurement matrix, a second dimension measurement matrix, and a state variable matrix.

[0141] Optionally, the harmonic source position determination apparatus 400 further comprises a second acquisition module configured to acquire a plurality of circuit nodes of the power distribution system; and a third determination module configured to determine a plurality of initial nodes from the plurality of circuit nodes, wherein the plurality of initial nodes comprises at least a boundary node, a branch node and a link node.

[0142] Optionally, the first acquisition module 401 comprises a first acquisition unit configured to acquire a plurality of initial sections of the power distribution system based on the plurality of initial nodes; a first determination unit configured to determine a plurality of balancing nodes from the plurality of initial sections; and a measurement unit configured to measure current information of the plurality of balancing nodes to obtain harmonic current information.

[0143] Optionally, the first acquisition unit comprises a classification sub-unit configured to classify the plurality of circuit nodes based on the initial nodes to obtain a plurality of node sets; and an execution sub-unit configured to execute a clustering topology operation on the plurality of node sets to obtain the plurality of initial sections.

[0144] Optionally, the first determination module 402 comprises a second acquisition unit configured to acquire a target measurement matrix set according to the harmonic current information; a generation unit configured to generate an initial harmonic state estimation model according to the target measurement matrix set; a second determination unit configured to determine a target node based on the initial harmonic state estimation model; and a third determination unit configured to determine a target section according to the target node.

[0145] Optionally, the second determination module 403 comprises a fourth determination unit configured to determine a first initial node and a second initial node of the target section; a third acquisition unit configured to acquire first harmonic current information of the first initial node and second harmonic current information of the second initial node; and a fifth determination unit configured to determine position information of a target harmonic source from a plurality of target links based on the first harmonic current information, the second harmonic current information and the target measurement matrix set.

[0146] Optionally, the fifth determination unit comprises an establishment sub-unit configured to establish a state relationship matrix according to the first harmonic current information and the second harmonic current information; a generation sub-unit configured to generate a target harmonic state estimation model according to the state relationship matrix and the target measurement matrix set; and a determination sub-unit configured to determine the position information of the target harmonic source based on the target harmonic state estimation model.

[0147] Embodiments of the present application also provide an electronic device comprising a memory and a processor, wherein the memory stores a computer program, and the processor is configured to run the computer program to perform the power distribution network harmonic source position determination method described above.

[0148] Optionally, in the present embodiment, the electronic device described above can be configured to store a computer program for performing the following steps:

[0149] In step S102, harmonic current information of a plurality of initial nodes in the power distribution system is obtained, wherein the plurality of initial nodes are nodes provided with a measuring device.

[0150] In step S104, a target section is determined according to the harmonic current information, wherein the target section includes a plurality of target links.

[0151] In step S106, position information of a target harmonic source is determined from the plurality of target links according to a target measurement matrix set, wherein the target measurement matrix set includes a first dimension measurement matrix, a second dimension measurement matrix and a state variable matrix.

[0152] Optionally, when the processor executes the program, the following steps are further implemented: a plurality of circuit nodes of the power distribution system are obtained; and the plurality of initial nodes are determined from the plurality of circuit nodes, wherein the plurality of initial nodes at least include a boundary node, a branch node and a link node.

[0153] Optionally, when the processor executes the program, the following steps are further implemented: a plurality of initial sections of the power distribution system are obtained based on the plurality of initial nodes; a plurality of balance nodes are determined from the plurality of initial sections; and current information of the plurality of balance nodes is measured to obtain the harmonic current information.

[0154] Optionally, when the processor executes the program, the following steps are further implemented: the plurality of circuit nodes are classified based on the initial nodes to obtain a plurality of node sets; and a clustering topology operation is performed on the plurality of node sets to obtain the plurality of initial sections.

[0155] Optionally, when the processor executes the program, the following steps are further implemented: a target measurement matrix set is obtained according to the harmonic current information; an initial harmonic state estimation model is generated according to the target measurement matrix set; a target node is determined based on the initial harmonic state estimation model; and the target section is determined according to the target node.

[0156] Optionally, when the processor executes the program, the following steps are further implemented: a first initial node and a second initial node of the target section are determined; first harmonic current information of the first initial node and second harmonic current information of the second initial node are obtained; and position information of the target harmonic source is determined from the plurality of target links based on the first harmonic current information, the second harmonic current information and the target measurement matrix set.

[0157] Optionally, when the processor executes the program, the following steps are further implemented: a state relationship matrix is established according to the first harmonic current information and the second harmonic current information; a target harmonic state estimation model is generated according to the state relationship matrix and the target measurement matrix set; and the position information of the target harmonic source is determined based on the target harmonic state estimation model.

[0158] The embodiment of the present application also provides a computer readable storage medium, wherein the computer readable storage medium stores a computer program, and the computer program is configured to execute the above-mentioned method for determining the position of the harmonic source of the power distribution network when running on a computer or a processor.

[0159] Optionally, in the embodiment, the computer readable storage medium is configured to store a computer program for executing the following steps:

[0160] In step S102, harmonic current information of a plurality of initial nodes in the power distribution system is acquired, wherein the plurality of initial nodes are nodes provided with a measuring device.

[0161] In step S104, a target section is determined according to the harmonic current information, wherein the target section comprises a plurality of target links.

[0162] In step S106, position information of a target harmonic source is determined from the plurality of target links according to a target measurement matrix set, wherein the target measurement matrix set comprises a first dimension measurement matrix, a second dimension measurement matrix and a state variable matrix.

[0163] Optionally, the storage medium is configured to store program code for executing the following steps: acquiring a plurality of circuit nodes of the power distribution system; determining a plurality of initial nodes from the plurality of circuit nodes, wherein the plurality of initial nodes at least comprise a boundary node, a branch node and a link node.

[0164] Optionally, the storage medium is configured to store program code for executing the following steps: acquiring a plurality of initial sections of the power distribution system based on the plurality of initial nodes; determining a plurality of balance nodes from the plurality of initial sections; measuring current information of the plurality of balance nodes to obtain harmonic current information.

[0165] Optionally, the storage medium is configured to store program code for executing the following steps: classifying the plurality of circuit nodes based on the initial nodes to obtain a plurality of node sets; performing a clustering topology operation on the plurality of node sets to obtain the plurality of initial sections.

[0166] Optionally, the storage medium is configured to store program code for executing the following steps: acquiring a target measurement matrix set according to the harmonic current information; generating an initial harmonic state estimation model according to the target measurement matrix set; determining a target node based on the initial harmonic state estimation model; determining a target section according to the target node.

[0167] Optionally, the storage medium is configured to store program code for performing the following steps: determining the first initial node and the second initial node of the target section; obtaining the first harmonic current information of the first initial node and the second harmonic current information of the second initial node; determining the position information of the target harmonic source from the plurality of target links based on the first harmonic current information, the second harmonic current information, and the target measurement matrix set.

[0168] Optionally, the storage medium is configured to store program code for performing the following steps: establishing a state relationship matrix according to the first harmonic current information and the second harmonic current information; generating a target harmonic state estimation model according to the state relationship matrix and the target measurement matrix set; and determining the position information of the target harmonic source based on the target harmonic state estimation model.

[0169] Optionally, the specific examples in the embodiments can refer to the examples described in the above embodiments and optional implementation manners, which will not be described herein again.

[0170] In the above embodiments of the present application, the description of each embodiment has its own focus, and the parts not described in detail in a certain embodiment can be referred to the relevant description of other embodiments.

[0171] In some embodiments provided in the present application, it should be understood that the disclosed technology can be implemented in other ways. Among them, the above-described device embodiments are only schematic, for example, the division of units can be a logical function division, and actual implementation can have another division manner, for example, a plurality of units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between the displayed or discussed each other can be through some interface, indirect coupling or communication connection between units or modules, which can be electrical or other forms.

[0172] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, that is, they can be located in one place, or they can be distributed to multiple units. Part or all of the units can be selected according to actual needs to achieve the purpose of the present embodiment.

[0173] In addition, each functional unit in each embodiment of the present application can be integrated in one processing unit, or each unit can exist physically, or two or more units can be integrated in one unit. The above integrated unit can be realized in the form of hardware or in the form of software functional unit.

[0174] If the integrated unit is implemented in the form of a software function unit and sold or used as an independent product, it can be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the present application essentially or the part that contributes to the prior art or the whole or part of the technical solutions can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a plurality of instructions for causing a computer device (which can be a personal computer, a server or a grid device, etc.) to execute all or part of the steps of the embodiments of the present application. The aforementioned storage medium includes a U disk, a read-only memory (ROM), a random access memory (RAM), a mobile hard disk, a magnetic disk or an optical disk, and various media that can store program codes.

[0175] The above is only the preferred embodiment of the present application, and it should be pointed out that for those skilled in the art, without departing from the principles of the present application, a number of improvements and refinements can be made, and these improvements and refinements should be considered as the protection scope of the present application.

Claims

1. A method for determining the location of a harmonic source in a power distribution network, characterized by, The method is applied to a power distribution system, and the method comprises: Obtaining harmonic current information of a plurality of initial nodes in the power distribution system, wherein the plurality of initial nodes are nodes configured with a measuring device; Determining a target section according to the harmonic current information, wherein the target section comprises a plurality of target links, and the target links are paths through which harmonic currents flow; Determining position information of a target harmonic source from the plurality of target links according to a target measurement matrix set, wherein the target measurement matrix set comprises a first dimension measurement matrix, a second dimension measurement matrix, and a state variable matrix, the first dimension measurement matrix is used to distinguish which currents and voltages of nodes or branches are actually measured, the second dimension measurement matrix is used to describe the relationship between harmonic voltages and currents of nodes and branches without a measuring device, and the state variable matrix comprises harmonic currents of the nodes and branches and harmonic voltages of the nodes.

2. The method of claim 1, wherein, The method for determining the position of the harmonic source of the power distribution network further comprises: Obtaining a plurality of circuit nodes of the power distribution system; Determining the plurality of initial nodes from the plurality of circuit nodes, wherein the plurality of initial nodes comprise boundary nodes, branch nodes, and link nodes.

3. The method of claim 2, wherein, Obtaining the harmonic current information of the plurality of initial nodes comprises: Obtaining a plurality of initial sections of the power distribution system based on the plurality of initial nodes; Determining a plurality of balance nodes from the plurality of initial sections; Measuring current information of the plurality of balance nodes to obtain the harmonic current information; Wherein, determining a plurality of balance nodes from the plurality of initial sections comprises: in each initial section, selecting one or more initial nodes as balance nodes, wherein the balance nodes are initial nodes connected to a system power supply or initial nodes with a higher voltage or power level in the section.

4. The method of claim 3, wherein, Obtaining the plurality of initial sections of the power distribution system based on the plurality of initial nodes comprises: Classifying the plurality of circuit nodes based on the initial nodes to obtain a plurality of node sets; Performing a clustering topology operation on the plurality of node sets to obtain the plurality of initial sections.

5. The method of claim 1, wherein, Determining the target section according to the harmonic current information comprises: Obtaining the target measurement matrix set according to the harmonic current information; Generating an initial harmonic state estimation model according to the target measurement matrix set; Determining a target node based on the initial harmonic state estimation model; Determining the target section according to the target node.

6. The method of claim 1, wherein, Determining the position information of the target harmonic source from the plurality of target links according to the target measurement matrix set comprises: Taking initial nodes at two ends of the target section as a first initial node and a second initial node; Obtaining first harmonic current information of the first initial node and second harmonic current information of the second initial node; Determining the position information of the target harmonic source from the plurality of target links based on the first harmonic current information, the second harmonic current information, and the target measurement matrix set.

7. The method of claim 6, wherein, Determining the position information of the target harmonic source based on the first harmonic current information, the second harmonic current information, and the target measurement matrix set comprises: establish a state relationship matrix according to the first harmonic current information and the second harmonic current information; generate a target harmonic state estimation model according to the state relationship matrix and the target measurement matrix set; determine the position information of the target harmonic source based on the target harmonic state estimation model.

8. An apparatus for determining the location of a harmonic source in a power distribution network, characterized by The device is applied to a power distribution system, and the device comprises: a first obtaining module configured to obtain harmonic current information of a plurality of initial nodes in the power distribution system, wherein the plurality of initial nodes are nodes configured with a measurement device; a first determining module configured to determine a target section according to the harmonic current information, wherein the target section comprises a plurality of target links, and the target links are paths through which harmonic current flows; a second determining module configured to determine position information of a target harmonic source from the plurality of target links according to a target measurement matrix set, wherein the target measurement matrix set comprises a first dimension measurement matrix, a second dimension measurement matrix, and a state variable matrix, the first dimension measurement matrix is used to distinguish which currents and voltages of nodes or branches are actually measured, the second dimension measurement matrix is used to describe a relationship between harmonic voltages and currents of nodes and branches that are not equipped with a measurement device, and the state variable matrix contains harmonic currents of each node and branch, and harmonic voltages of each node.

9. An electronic device comprising a memory and a processor, characterized in that The memory stores a computer program, and the processor is configured to run the computer program to perform the method for determining the position of a harmonic source of a power distribution network in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer readable storage medium stores a computer program, wherein the computer program is configured to perform the method for determining the position of a harmonic source of a power distribution network in any one of claims 1 to 7 when running on a computer or a processor.

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