Harmonic traceability method based on harmonic power direction of power system

Abstract

The invention discloses a harmonic traceability method based on a harmonic power direction of an electric power system, which belongs to the technical field of electric power quality of the electric power system and comprises the following steps of: constructing matrixes of fundamental waves and harmonic signals, initializing active and reactive power deviation values of nodes, and adopting a decoupling algorithm combined with a Jacobian matrix iteration method to carry out harmonic traceability. And sequentially calculating the fundamental wave voltage and each harmonic current, and finally obtaining the power flow direction and judging the harmonic source attribute. When harmonic power flows from a load to a power grid, the node is identified as a harmonic source; and when the harmonic power flows to the load from the power grid, identifying the node as a harmonic receiving point. An equivalent circuit model is used for separating harmonic influences of a linear load and a non-linear load, and a real-time monitoring technology is combined to realize dynamic tracking and accurate positioning of a harmonic source. The method is low in calculation complexity, excellent in convergence performance and suitable for a modern power distribution network scene where distributed energy and power electronic equipment are widely connected, the harmonic suppression efficiency is remarkably improved, and the safety and stability of power grid operation are ensured.

Description

Technical Field

[0001] The present invention relates to the field of power quality and harmonic source identification of power systems, and in particular to a harmonic source tracing method based on the harmonic power direction of a power system, which is used for locating and identifying harmonic sources in a power distribution system. Background Art

[0002] With the large-scale access of distributed energy (such as photovoltaic power generation, wind power, etc.) and power electronic equipment, the harmonic problem in the power system has become increasingly serious and has become one of the main factors threatening the quality of power. Harmonics not only have an adverse effect on the operational stability of the power system, but also cause equipment failures, energy loss and other problems, posing a threat to the safety and reliability of users' electrical equipment. Therefore, how to accurately locate the source of harmonics has become an important topic in power system research.

[0003] There are two main methods for tracing harmonic sources in the prior art:

[0004] The harmonic source tracing method based on the equivalent circuit model divides the user side and the system side at the common connection point and identifies the harmonic source based on the measurement results of parameters such as current and voltage. However, this method has the following shortcomings:

[0005] Limited recognition capability: Only a single harmonic source can be identified. For scenarios where multiple harmonic sources coexist in complex distribution networks, the recognition accuracy is low. Lack of dynamic adaptability: Due to the assumption that the system is stable and the parameters do not change over time, it is difficult to effectively cope with the dynamic changes of harmonic sources in the power system.

[0006] The source tracing method based on harmonic state estimation builds a harmonic model for the entire network and analyzes the harmonic source based on the relationship between harmonic current and voltage. This method has high theoretical accuracy. However, this method has the following problems:

[0007] High computational complexity: It requires data support from the entire network, and the amount of computation is huge, especially in the case of multiple harmonic sources, which can easily lead to non-convergence of the solution process. Difficulty in practical application: It is difficult to promote and apply in actual complex power grids because it requires a large amount of real-time data and relies on accurate network topology information. Summary of the invention

[0008] In order to solve the problems in the prior art that the existing technology cannot cope with complex scenarios with multiple harmonic sources, lacks dynamic monitoring capabilities, and is difficult to balance efficiency and accuracy, the present invention proposes a harmonic source tracing method based on the harmonic power direction of the power system. Combined with harmonic power flow analysis and dynamic monitoring technology, it can efficiently locate the harmonic source and adapt to the dynamic operation characteristics of modern power grids.

[0009] In order to achieve the above object, the present invention is implemented by the following technical solutions:

[0010] A harmonic source tracing method based on the harmonic power direction of an electric power system comprises the following steps:

[0011] S1: Based on the principle of harmonic power flow calculation, the harmonics in the power system are analyzed and the harmonic power flow equation is established;

[0012] S2: Based on the decoupling algorithm, the harmonic power flow equation is solved by using a simplified alternating iteration method to separate the influence of the fundamental wave and the harmonics;

[0013] S3: Construct equivalent circuit models of linear and nonlinear loads to distinguish the impact of different load types on harmonics;

[0014] S4: Determine the harmonic source properties of the load in combination with the harmonic power flow direction, dynamically monitor the changes in the harmonic power flow direction, and realize dynamic identification and distributed monitoring of the harmonic source location by judging the power flow direction.

[0015] Preferably, in S1, the harmonic power flow calculation adopts a Jacobian matrix solution method to construct the Jacobian matrix of the fundamental power flow and the harmonic power flow, specifically including:

[0016] The Jacobian matrix J of the fundamental power flow equation is constructed. The elements of the matrix J include the partial derivative relationship between the node voltage V and the phase angle θ to the node active power P and reactive power Q, which can be specifically expressed as:

[0017]

[0018] Among them, P represents the active power of the node; Q represents the reactive power of the node; θ represents the phase angle of the node; V represents the voltage amplitude of the node; is the partial derivative of the node active power with respect to the phase angle; is the partial derivative of node active power with respect to voltage; is the partial derivative of the node reactive power with respect to the phase angle; is the partial derivative of node reactive power with respect to voltage;

[0019] For each harmonic frequency k, construct the Jacobian matrix J of the harmonic power flow k , matrix J k Indicates the harmonic current I of the node at the kth harmonic frequency k With harmonic voltage V k The partial derivative relationship is specifically expressed as:

[0020]

[0021] Among them, I k Represents the current of the node at the kth harmonic frequency; V k It represents the voltage of the node at the kth harmonic frequency;

[0022] Based on the constructed Jacobian matrix, the deviation ΔX of the node voltage and phase angle is iteratively calculated by the following formula:

[0023] ΔX=J -1 ×ΔW

[0024] Among them, J -1 It is expressed as the inverse matrix of the Jacobian matrix; ΔW represents the deviation of the active power and reactive power of the node. ΔX is corrected iteratively until the convergence condition is met to ensure the calculation accuracy.

[0025] Preferably, the establishment of the harmonic power flow equation includes the following contents:

[0026] Based on the fundamental power flow analysis of the power system, an equation describing the relationship between the node active power and reactive power and the node voltage amplitude and phase angle is constructed to calculate the fundamental power flow distribution of each node in the system;

[0027] Based on the current and voltage relationship of each harmonic frequency, the power flow equation at each harmonic frequency is constructed to describe the distribution relationship between node harmonic voltage and harmonic current at a specific harmonic frequency.

[0028] Preferably, in S2, the decoupling algorithm uses a simplified alternating iteration method to solve the harmonic power flow equation, including the following steps:

[0029] The deviation of the fundamental power flow is solved based on the constructed Jacobian matrix. The calculation formula is:

[0030] ΔX=J -1 ×ΔW

[0031] Where ΔX represents the adjustment of the node voltage phase angle and amplitude; J -1 represents the inverse matrix of the Jacobian matrix J, which contains the partial derivatives of the node voltage and phase angle with respect to the node active power and reactive power; ΔW represents the deviation of the node active power and reactive power;

[0032] After each iteration of the fundamental power flow, the deviation of each harmonic power flow is calculated based on the determined fundamental voltage and phase angle. The calculation formula is:

[0033]

[0034] Among them, ΔI k Indicates the deviation of the kth harmonic current; Represents the Jacobian matrix J at the kth harmonic frequency k The inverse matrix of k The partial derivative relationship between the harmonic current and voltage of the node is included; ΔV k Indicates the deviation of the kth harmonic voltage;

[0035] Deviations ΔX and ΔI in fundamental and harmonic power flow calculations k The optimization is repeated repeatedly until it converges to the set accuracy range.

[0036] Preferably, in S3, in the equivalent circuit model, the linear load is represented as a harmonic current source, and the linear load adopts a pure resistance model.

[0037] Preferably, the equivalent circuit model specifically includes:

[0038] The nth harmonic active power PL absorbed by the linear load n The expression is as follows:

[0039]

[0040] Among them, V n Indicates the nth harmonic voltage amplitude; IL n Indicates the nth harmonic current absorbed by the linear load; represents the phase angle of the current;

[0041] The nth harmonic active power PL of nonlinear load n The expression is as follows:

[0042]

[0043] Among them, V n Indicates the nth harmonic voltage amplitude; IL n Indicates the current of nonlinear load at the nth harmonic frequency; Indicates the phase angle of the current; the negative sign indicates that the harmonic power flows from the load side to the grid;

[0044] Linear load is equivalent to pure resistance model Z L ,The nonlinear load is represented as a harmonic current source model. Through this equivalent model construction, the ,effects of various types of loads on the grid harmonics are separated.

[0045] Preferably, in S4, the flow direction calculation formula of the harmonic power is:

[0046]

[0047] Among them, P 方向 Indicates the direction of harmonic power flow; V n Indicates the amplitude of the nth harmonic voltage; I n Indicates the nth harmonic current; ψ n Represents the phase angle of the current.

[0048] Preferably, the harmonic source state of the node is determined by the flow direction of the harmonic power, and the specific determination criteria are:

[0049] If P 方向 <0, the load is a harmonic source;

[0050] If P 方向 >0, the node is a harmonic receiving point and is not considered a harmonic source.

[0051] Preferably, the identifying of the location of the harmonic source includes locating the harmonic source at a specific load node of the distribution network, and determining the dynamic changes of the harmonic source location and its impact on the power system by dynamically monitoring the changes in the harmonic power flow direction.

[0052] Compared with the prior art, the beneficial effects of the present invention are as follows: the present invention realizes efficient identification of multiple harmonic sources in complex distribution networks by analyzing the flow of harmonic power, without relying on the topological information of the entire network or global state estimation, and can quickly determine the harmonic source properties of the node. The introduction of a dynamic monitoring mechanism, combined with real-time data calculation and power direction analysis, can accurately track and dynamically respond to the location of the harmonic source, adapt to changes in the operating conditions of the power system, and make the identification results more reliable. The decoupling algorithm and the Jacobian matrix iteration method are used to reduce the computational complexity of the harmonic power flow solution, while improving the iterative convergence performance to meet the real-time requirements. The present invention also effectively separates the harmonic effects of linear loads and nonlinear loads by constructing an equivalent circuit model of the fundamental wave and harmonics, avoiding the identification errors caused by the complex load characteristics in the traditional method, and has high accuracy and stability, which is suitable for modern distribution network scenarios with distributed energy access. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative labor.

[0054] in:

[0055] Figure 1 It is a schematic diagram of the method flow of the present invention;

[0056] Figure 2 Schematic diagram of calculating harmonic power flow using the decoupling method in an embodiment of the present invention;

[0057] Figure 3 It is a network equivalent model of linear load and nonlinear load in the embodiment of the present invention;

[0058] Figure 4 This is a flow chart of harmonic source identification in an embodiment of the present invention;

[0059] Figure 5This is a schematic diagram of a 33-node distribution network in an embodiment of the present invention;

[0060] Figure 6 Schematic diagram of harmonic tracing results of the 5th harmonic active power distribution of each node in an embodiment of the present invention. DETAILED DESCRIPTION

[0061] In order to make the purpose, technical solution and advantages of the embodiment of the present invention clearer, the technical solution of the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings of the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all of the embodiments. Based on the described embodiment of the present invention, all other embodiments obtained by ordinary technicians in this field belong to the scope of protection of the present invention.

[0062] Example 1

[0063] like Figure 1 , Figure 2 As shown, this is an embodiment of the present invention. This embodiment uses a decoupling algorithm to separate the mutual influence of the fundamental wave and the harmonic wave, and iteratively solves the voltage and phase angle of each node by constructing a Jacobian matrix to quickly converge to a stable state of the power flow calculation. The figure shows how to use the decoupling method to simplify the calculation process of the harmonic power flow, avoiding the problem of solving the fundamental wave and the harmonic power flow simultaneously, thereby improving the calculation speed and accuracy. This embodiment provides a harmonic source tracing method based on the harmonic power direction of the power system, including:

[0064] Step S1: Based on the principle of harmonic power flow calculation, the harmonics in the power system are analyzed and the harmonic power flow equation is established;

[0065] Specifically, in step S1, the harmonic power flow calculation adopts the Jacobian matrix solution method to construct the Jacobian matrix of the fundamental power flow and the harmonic power flow, which specifically includes:

[0066] The Jacobian matrix J of the fundamental power flow equation is constructed. The elements of the matrix J include the partial derivative relationship between the node voltage V and the phase angle θ to the node active power P and reactive power Q, which can be specifically expressed as:

[0067]

[0068] Among them, P represents the active power of the node; Q represents the reactive power of the node; θ represents the phase angle of the node; V represents the voltage amplitude of the node; is the partial derivative of the node active power with respect to the phase angle; is the partial derivative of node active power with respect to voltage; is the partial derivative of the node reactive power with respect to the phase angle; is the partial derivative of node reactive power with respect to voltage;

[0069] For each harmonic frequency k, construct the Jacobian matrix J of the harmonic power flow k , matrix J k Represents the harmonic current I of the node at the kth harmonic frequency k With harmonic voltage V k The partial derivative relationship is specifically expressed as:

[0070]

[0071] Among them, I k represents the current of the node at the kth harmonic frequency; V k It represents the voltage of the node at the kth harmonic frequency;

[0072] Based on the constructed Jacobian matrix, the deviation ΔX of the node voltage and phase angle is iteratively calculated by the following formula:

[0073] ΔX=J -1 ×ΔW

[0074] Among them, J -1 It is expressed as the inverse matrix of the Jacobian matrix; ΔW represents the deviation of the active power and reactive power of the node. ΔX is corrected iteratively until the convergence condition is met to ensure the calculation accuracy.

[0075] Specifically, the establishment of the harmonic power flow equation includes the following contents:

[0076] Based on the fundamental power flow analysis of the power system, an equation describing the relationship between the node active power and reactive power and the node voltage amplitude and phase angle is constructed to calculate the fundamental power flow distribution of each node in the system;

[0077] Based on the current and voltage relationship of each harmonic frequency, the power flow equation at each harmonic frequency is constructed to describe the distribution relationship between node harmonic voltage and harmonic current at a specific harmonic frequency.

[0078] Further, step S2: based on the decoupling algorithm, a simplified alternating iteration method is used to solve the harmonic power flow equation to separate the influence of the fundamental wave and the harmonics;

[0079] Specifically, in step S2, the decoupling algorithm uses a simplified alternating iteration method to solve the harmonic power flow equation, including the following steps:

[0080] The deviation of the fundamental power flow is solved based on the constructed Jacobian matrix. The calculation formula is:

[0081] ΔX=J -1 ×ΔW

[0082] Where ΔX represents the adjustment of the node voltage phase angle and amplitude; J -1represents the inverse matrix of the Jacobian matrix J, which contains the partial derivatives of the node voltage and phase angle with respect to the node active power and reactive power; ΔW represents the deviation of the node active power and reactive power;

[0083] After each iteration of the fundamental power flow, the deviation of each harmonic power flow is calculated based on the determined fundamental voltage and phase angle. The calculation formula is:

[0084]

[0085] Among them, ΔI k Indicates the deviation of the kth harmonic current; Represents the Jacobian matrix J at the kth harmonic frequency k The inverse matrix of k The partial derivative relationship between the harmonic current and voltage of the node is included; ΔV k Indicates the deviation of the kth harmonic voltage;

[0086] Deviations ΔX and ΔI in fundamental and harmonic power flow calculations k The optimization is repeated repeatedly until it converges to the set accuracy range.

[0087] Further, step S3: constructing equivalent circuit models of linear loads and nonlinear loads to distinguish the impact of different load types on harmonics;

[0088] Specifically, in step S3, in the equivalent circuit model, the linear load is represented as a harmonic current source, and the linear load adopts a pure resistance model.

[0089] Further, step S4: determine the harmonic source properties of the load in combination with the harmonic power flow direction, dynamically monitor the change of the harmonic power flow direction, and realize dynamic identification and distributed monitoring of the harmonic source position by determining the power flow direction.

[0090] Specifically, the equivalent circuit model specifically includes:

[0091] The nth harmonic active power PL absorbed by the linear load n The expression is as follows:

[0092]

[0093] Among them, V n Indicates the nth harmonic voltage amplitude; IL n Indicates the nth harmonic current absorbed by the linear load; represents the phase angle of the current;

[0094] The nth harmonic active power PL of nonlinear load n The expression is as follows:

[0095]

[0096] Among them, V n Indicates the nth harmonic voltage amplitude; IL n Indicates the current of nonlinear load at the nth harmonic frequency; Indicates the phase angle of the current; the negative sign indicates that the harmonic power flows from the load side to the grid;

[0097] Linear load is equivalent to pure resistance model Z L ,The nonlinear load is represented as a harmonic current source model. Through this equivalent model construction, the ,effects of various types of loads on the grid harmonics are separated.

[0098] The flow calculation formula of the harmonic power is:

[0099]

[0100] Among them, P 方向 Indicates the direction of harmonic power flow; V n Indicates the amplitude of the nth harmonic voltage; I n Indicates the nth harmonic current; ψ n Represents the phase angle of the current.

[0101] Specifically, the harmonic source state of the node is determined by the flow direction of the harmonic power, and the specific determination criteria are:

[0102] If P 方向 <0, the load is a harmonic source;

[0103] If P 方向 >0, the node is a harmonic receiving point and is not considered a harmonic source.

[0104] Specifically, the identifying of the location of the harmonic source includes locating the harmonic source at a specific load node of the distribution network, and determining the dynamic changes of the harmonic source location and its impact on the power system by dynamically monitoring the changes in the harmonic power flow direction.

[0105] Example 2

[0106] This embodiment combines the attached Figure 3 To Attachment Figure 6 The modeling, process and verification process of the harmonic source tracing method based on power direction are described in detail. The attached figures correspond to load modeling, harmonic source tracing process, verification network structure and result distribution, showing the advantages and application effects of this method in complex power grid harmonic analysis from multiple perspectives. Figure 3 As shown, the linear load is equivalent to a pure resistance model Z L , and the nonlinear load is equivalent to a harmonic current source in the form of Z NL, the input end of the power grid is a voltage source U(t), and the equivalent passive network of the power grid is decomposed through harmonic flow analysis. The modeling method of harmonic current source and pure resistance load can effectively separate the influence of various loads on harmonics, which is convenient for the subsequent location and identification of harmonic sources. This model solves the problem of difficulty in separating the contribution of complex loads in traditional tracing methods by distinguishing the characteristics of linear loads and nonlinear loads.

[0107] As attached Figure 4 As shown, the present invention adopts a harmonic source tracing process based on power flow, and the specific steps are as follows:

[0108] Input grid information and data to form a matrix of fundamental wave and harmonic signals;

[0109] Initialize the active power and reactive power deviation values ​​of each node:

[0110] P i * =0,

[0111] Based on the Jacobian matrix, the deviation of the fundamental voltage and phase angle is iteratively calculated using the following formula:

[0112] ΔX=J -1 ×ΔW

[0113] Among them, J -1 It is expressed as the inverse matrix of the Jacobian matrix; ΔW represents the deviation of the active power and reactive power of the node. ΔX is corrected by iteration until the convergence condition is met to ensure the calculation accuracy;

[0114] According to the solved fundamental voltage and phase angle, calculate each harmonic current:

[0115] I k =Y k V k

[0116] Among them, I k is the harmonic current, V k is the harmonic voltage, Y k is the admittance matrix;

[0117] Compare V k Is it equal to V ki .

[0118] Among them, V ki is the measured value of harmonic voltage.

[0119] Calculate the harmonic power:

[0120] P k =V k I k cosψk

[0121] Among them, ψ k is the phase difference between harmonic voltage and current;

[0122] Determine whether the load is a harmonic source based on the power sign:

[0123] If P k >0, the load is a harmonic source;

[0124] If P k ≤0, the load is a harmonic receiving point.

[0125] As attached Figure 5 As shown in FIG. 1 , a 33-node distribution network model is used to verify the applicability of the method of the present invention. The figure includes multiple harmonic source nodes and load nodes, simulating the actual operating environment of a typical complex power grid.

[0126] Each node corresponds to the location of a different load or power supply. By constructing the actual network topology, the actual distribution of distributed harmonic sources is simulated.

[0127] During the verification process, the present invention can quickly locate the harmonic source position of a specific node according to the harmonic power flow direction of the node.

[0128] As attached Figure 6 As shown in the figure, the active power distribution of each node in the 33-node distribution network under the 5th harmonic.

[0129] The horizontal axis represents the node number, and the vertical axis represents the 5th harmonic active power of the corresponding node.

[0130] A positive value indicates that harmonic power flows from the node to the grid, and a negative value indicates that harmonic power flows from the grid to the node.

[0131] The harmonic characteristics of each node can be intuitively analyzed through this figure:

[0132] Nodes with positive power are identified as harmonic sources;

[0133] Nodes with negative power are identified as harmonic reception points.

[0134] The analysis results verify the accuracy and efficiency of the method of the present invention, which can quickly determine the location distribution of harmonic source nodes and provide a reference for harmonic control of power systems.

[0135] In summary, the present invention realizes efficient identification of multiple harmonic sources in complex distribution networks by analyzing the flow of harmonic power, without relying on the whole network topology information or global state estimation, and can quickly determine the harmonic source properties of the node. The introduction of a dynamic monitoring mechanism, combined with real-time data calculation and power direction analysis, can accurately track and dynamically respond to the harmonic source position, adapt to changes in the operating conditions of the power system, and make the identification results more reliable. The decoupling algorithm and the Jacobian matrix iteration method are adopted to reduce the computational complexity of the harmonic power flow solution, while improving the iterative convergence performance and meeting the real-time requirements. The present invention also effectively separates the harmonic effects of linear loads and nonlinear loads by constructing an equivalent circuit model of fundamental and harmonic waves, avoiding the identification errors caused by the complex load characteristics in the traditional method, and has high accuracy and stability, which is suitable for modern distribution network scenarios with distributed energy access. In summary, the present invention realizes efficient, accurate and dynamic harmonic source identification in the harmonic source tracing method, which can significantly improve the effect of power grid harmonic governance and provide important technical support for the safe operation of complex power grids.

[0136] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present application. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine different embodiments or examples described in this specification and the features of different embodiments or examples, unless they are contradictory.

[0137] Any process or method description in the flow chart or otherwise described herein can be understood to represent a module, fragment or portion of a code including one or more executable instructions for implementing the steps of a specific logical function or process. And the scope of the preferred embodiment of the present application includes other implementations, in which the functions may not be performed in the order shown or discussed, including in a substantially simultaneous manner or in a reverse order according to the functions involved.

[0138] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any technician familiar with the technical field can easily think of various changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A harmonic source tracing method based on the harmonic power direction of the power system, characterized in that: The following steps are involved: S1: Based on the principle of harmonic power flow calculation, the harmonics in the power system are analyzed and the harmonic power flow equation is established; S2: Based on the decoupling algorithm, the harmonic power flow equation is solved by using a simplified alternating iteration method to separate the influence of the fundamental wave and the harmonics; S3: Construct equivalent circuit models of linear and nonlinear loads to distinguish the impact of different load types on harmonics; S4: Determine the harmonic source properties of the load in combination with the harmonic power flow direction, dynamically monitor the changes in the harmonic power flow direction through the μpmu device, and dynamically identify and distribute the harmonic source location by judging the power flow direction.

2. The harmonic source tracing method based on the harmonic power direction of the power system according to claim 1 is characterized in that: In S1, the harmonic power flow calculation adopts the Jacobian matrix solution method to construct the Jacobian matrix of the fundamental power flow and the harmonic power flow, which specifically includes: The Jacobian matrix J of the fundamental power flow equation is constructed. The elements of the matrix J include the partial derivative relationship between the node voltage V and the phase angle θ to the node active power P and reactive power Q, which can be specifically expressed as: Among them, P represents the active power of the node; Q represents the reactive power of the node; θ represents the phase angle of the node; V represents the voltage amplitude of the node; is the partial derivative of the node active power with respect to the phase angle; is the partial derivative of node active power with respect to voltage; is the partial derivative of node reactive power with respect to phase angle; is the partial derivative of node reactive power with respect to voltage; For each harmonic frequency k, construct the Jacobian matrix J of the harmonic power flow k , matrix J k Indicates the harmonic current I of the node at the kth harmonic frequency k With harmonic voltage V k The partial derivative relationship is specifically expressed as: Among them, I k represents the current of the node at the kth harmonic frequency; V k It represents the voltage of the node at the kth harmonic frequency; Based on the constructed Jacobian matrix, the deviation ΔX of the node voltage and phase angle is iteratively calculated by the following formula: ΔX=J -1 ×ΔW Among them, J -1 It is expressed as the inverse matrix of the Jacobian matrix; ΔW represents the deviation of the active power and reactive power of the node, and ΔX is corrected iteratively until the convergence condition is met.

3. The harmonic source tracing method based on the harmonic power direction of the power system according to claim 2 is characterized in that: The establishment of the harmonic power flow equation includes the following contents: Based on the fundamental power flow analysis of the power system, an equation describing the relationship between the node active power and reactive power and the node voltage amplitude and phase angle is constructed to calculate the fundamental power flow distribution of each node in the system; Based on the current and voltage relationship of each harmonic frequency, the power flow equation at each harmonic frequency is constructed to describe the distribution relationship between node harmonic voltage and harmonic current at a specific harmonic frequency.

4. The harmonic source tracing method based on the harmonic power direction of the power system according to claim 1 is characterized in that: In S2, the decoupling algorithm uses a simplified alternating iteration method to solve the harmonic power flow equation, including the following steps: The deviation of the fundamental power flow is solved based on the constructed Jacobian matrix. The calculation formula is: ΔX=J -1 ×ΔW Where ΔX represents the adjustment of the node voltage phase angle and amplitude; J -1 represents the inverse matrix of the Jacobian matrix J, which contains the partial derivatives of the node voltage and phase angle with respect to the node active power and reactive power; ΔW represents the deviation of the node active power and reactive power; After each iteration of the fundamental power flow, the deviation of each harmonic power flow is calculated based on the determined fundamental voltage and phase angle. The calculation formula is: Among them, ΔI k Indicates the deviation of the kth harmonic current; Represents the Jacobian matrix J at the kth harmonic frequency k The inverse matrix of k The partial derivative relationship between the harmonic current and voltage of the node is included; ΔV k Indicates the deviation of the kth harmonic voltage; Deviations ΔX and ΔI in fundamental and harmonic power flow calculations k The optimization is repeated repeatedly until it converges to the set accuracy range.

5. The harmonic source tracing method based on the harmonic power direction of the power system according to claim 1 is characterized in that: In S3, in the equivalent circuit model, the linear load is represented as a harmonic current source, and the linear load adopts a pure resistance model.

6. The harmonic source tracing method based on the harmonic power direction of the power system according to claim 5 is characterized in that: The equivalent circuit model specifically includes: The nth harmonic active power PL absorbed by the linear load n The expression is as follows: PL n =V n ×IL n ×cos(ψ Ln ) Among them, V n Indicates the nth harmonic voltage amplitude; IL n Indicates the nth harmonic current absorbed by the linear load; ψ Ln represents the phase angle of the current; The nth harmonic active power PL of nonlinear load n The expression is as follows: PL n =V n ×IL n ×cos(ψ Nn ) Among them, V n Indicates the nth harmonic voltage amplitude; IL n Represents the current of nonlinear load at the nth harmonic frequency; ψ Nn Indicates the phase angle of the current; the negative sign indicates that the harmonic power flows from the load side to the grid; Linear load is equivalent to pure resistance model Z L ,The nonlinear load is represented as a harmonic current source model. Through this equivalent model construction, the ,effects of various types of loads on the grid harmonics are separated.

7. The harmonic source tracing method based on the harmonic power direction of the power system according to claim 1 is characterized in that: In S4, the flow direction calculation formula of the harmonic power is: Among them, P 方向 Indicates the direction of harmonic power flow; V n Indicates the amplitude of the nth harmonic voltage; I n Indicates the nth harmonic current; ψ n Represents the phase angle of the current.

8. The harmonic source tracing method based on the harmonic power direction of the power system according to claim 7 is characterized in that: The harmonic source state of the node is determined by the flow direction of the harmonic power, and the specific determination criteria are: If P 方向 <0, the load is a harmonic source; If P 方向 >0, the node is a harmonic receiving point and is not considered a harmonic source.

9. The harmonic source tracing method based on the harmonic power direction of the power system according to claim 8 is characterized in that: The identifying of the location of the harmonic source includes locating the harmonic source at a specific load node of the distribution network, and determining the dynamic change of the harmonic source location and its impact on the power system by dynamically monitoring the change of the harmonic power flow direction.

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