Method for evaluating resonance severity of power transmission line based on harmonic circular arc model

Abstract

This invention discloses a method for assessing the severity of transmission line resonance based on a harmonic circular arc model, relating to the field of power system technology. The method includes the following steps: single-end harmonic data acquisition, construction of a harmonic circular arc model, calculation of three major assessment indicators, risk level classification of the indicators, resonance severity rating, and resonance point location. This invention only requires single-end harmonic measurement to construct full-line harmonic constraints, eliminating the need for multi-point monitoring and complex impedance modeling, significantly reducing costs and enhancing engineering operability. The design of three major assessment indicators enables multi-dimensional quantification of resonance state, aligning with national and enterprise standards, and solving the problem of traditional methods' difficulty in accurately quantifying resonance severity. A risk matrix is ​​used to classify seven risk levels and accurately locate resonance points, overcoming the limitations of traditional methods that cannot locate them. The method integrates assessment, identification, and location, significantly improving the efficiency and accuracy of resonance assessment, and providing reliable technical support for line operation and maintenance and suppression measures.

Description

Technical Field

[0001] This invention relates to the field of power system technology, specifically to a method for assessing the severity of transmission line resonance based on a harmonic circular arc model. Background Technology

[0002] With the continuous expansion of ultra-high voltage AC / DC hybrid power grids, a large number of power electronic converters and nonlinear loads are being connected to the system, making the harmonic resonance problem of transmission lines increasingly prominent and a significant factor threatening the safe and stable operation of the power grid. Resonance can cause a significant amplification of harmonic voltage and current, leading to equipment insulation aging, relay protection malfunctions, and even serious accidents such as line tripping. Therefore, there is an urgent need for accurate and efficient methods to assess the severity of transmission line resonance, providing technical support for resonance risk management.

[0003] Existing methods for assessing transmission line resonance mainly rely on the harmonic transfer coefficient method, impedance sweep frequency method, or multi-point monitoring modeling method, but all have significant limitations: the harmonic transfer coefficient method can only calculate the harmonic amplification factor at the sending and receiving ends of the line, and cannot reflect the harmonic energy distribution and resonance point location along the line, making it difficult to quantify the severity of resonance; the impedance sweep frequency method requires offline impedance testing of the line, making online real-time assessment impossible, and is also complex and costly to operate; the multi-point monitoring modeling method requires the deployment of multiple monitoring points along the transmission line, resulting in high data acquisition costs, and also relies on an accurate grid impedance model, where model errors directly affect the accuracy of the assessment results.

[0004] In addition, existing assessment methods focus on harmonic amplitude amplification analysis and lack effective means to identify resonance types (series / parallel resonance). They also fail to incorporate key dimensions such as the degree of harmonic energy exceeding limits and the duration of exceeding limits into a unified assessment system. As a result, the assessment results cannot fully reflect the actual state of line resonance risk and are difficult to guide maintenance personnel in formulating targeted resonance suppression measures.

[0005] To address the aforementioned issues, this invention proposes a method for assessing the severity of transmission line resonance based on a harmonic circular arc model. This method can identify the resonance type, locate the resonance point, and comprehensively assess the severity using single-end monitoring data. It overcomes the shortcomings of existing technologies in terms of engineering applicability, comprehensiveness of assessment, and accuracy of results, providing a new technical approach for early warning and efficient management of transmission line resonance risks. Summary of the Invention

[0006] (a) Technical problems to be solved To address the shortcomings of existing technologies, this invention provides a method for assessing the severity of transmission line resonance based on a harmonic circular arc model, thus solving the problems mentioned in the background section.

[0007] (II) Technical Solution To achieve the above objectives, the present invention provides the following technical solution: a method for assessing the severity of transmission line resonance based on a harmonic circular arc model, comprising the following steps: Step 1: Acquire harmonic data at one end: Select the transmission line to be evaluated and obtain its Subharmonic characteristic impedance Phase constant ; in, The equivalent inductance per unit length, The equivalent capacitance per unit length; Simultaneously, data is collected at either the sending or receiving end of the transmission line. Monitoring data of the effective values ​​of subharmonic voltage and current; Step 2: Construct the harmonic circular arc model: Based on the distributed parameter model of lossless transmission lines and the principle of energy conservation, a model is constructed for any location along the transmission line. The harmonic circular arc model at the location satisfies the following circular arc constraint relationships:

[0008] In the formula, and The total harmonic energy coefficient, , for Location RMS values ​​of second harmonic voltage and current; pass:

[0009] Determine the arc The angle corresponding to the location point is the argument. Step 3: Calculate the three major evaluation indicators: Calculation of harmonic energy exceedance index based on harmonic circular arc model Resonance type index And statistically analyze the probability of harmonic energy exceeding the limit time. ; Step 4: Risk Level Classification of Indicators Will , , They are divided into three risk levels: Level 1 is low risk, Level 2 is medium risk, and Level 3 is high risk. Step 5: Resonance Severity Classification: An equal-weighted risk level matrix is ​​established to couple the risk levels of the three indicators. For each indicator whose risk level increases by 1 level, the resonance severity index is increased by 1, and the resonance severity of transmission lines is divided into 7 levels. Step 6: Resonance point location: Argument based on harmonic circular arc model and frequency factor Find the point where the amplitude is the largest or smallest, and calculate the actual distance between that point and the single-end measurement point. This is the resonance point along the transmission line.

[0010] As a further aspect of the present invention: the harmonic energy exceedance index mentioned in the third step The calculation method is as follows: pass:

[0011] Calculate the reference harmonic electric field energy coefficient ; In the formula, For selected The limit for the subharmonic voltage content is determined by referring to the national standard GB / T51200-2016. This refers to the fundamental phase voltage of the line. Then calculate the total harmonic energy coefficient based on the harmonic arc radius. ; Then passed:

[0012] Determine the harmonic energy exceedance index .

[0013] As a further aspect of the present invention: when ≥1 indicates that the line has a risk of harmonic voltage exceeding the limit; when <1 indicates no risk of exceeding the limit.

[0014] As a further aspect of the present invention: in the third step, the resonance type index The calculation method is as follows: Firstly, through:

[0015] calculate Electromagnetic energy ratio at location ; Passed again:

[0016] Define the resonance type index .

[0017] As a further aspect of the present invention: wherein, <0 indicates a series resonance characteristic. >0 indicates a parallel resonance characteristic.

[0018] As a further aspect of the present invention: in the third step, the probability of harmonic energy exceeding the limit time... The calculation method is as follows:

[0019] in, Within the monitoring period Total duration ≥1 This represents the total monitoring duration.

[0020] As a further aspect of the present invention: In the fourth step, the criteria for classifying the risk levels of the indicators are as follows: Level of violation severity classification: Level 1 is <1, 2 levels are 1≤ < Level 3 is ≥ ; in, for The 95% probability is a large value. The ratio of the h-th harmonic assessment limit in the State Grid enterprise standard to that in the national standard; The probability level of exceeding the time limit is divided into levels: Level 1 is... <10%, Level 2 is 10%≤ <50%, Level 3 ≥50%; Resonance type index classification: Level 1 is −0.5 < <0.5, Level 2 ≤−0.5, Level 3 is ≥0.5.

[0021] As a further aspect of the present invention: In the sixth step, the actual distance between the position point with the largest or smallest argument and the single-end measurement point is calculated as follows: For the point with the largest argument: find The maximum value of the harmonic circular arc model along the transmission line under the second harmonic is denoted as . and its corresponding frequency factor The actual distance ; For the point with the smallest argument: find The minimum value of the harmonic circular arc model along the transmission line under the second harmonic is denoted as . and its corresponding frequency factor The actual distance .

[0022] As a further aspect of the present invention: In the first step, the transmission line to be evaluated is a transmission line with a voltage level of 220kV or above, and the sampling frequency of the monitoring data collected at one end is not less than 12.8kHz.

[0023] As a further aspect of the present invention: the harmonic arc model is a lossless transmission line model, and the attenuation rate of line loss on the arc radius is ≤8%.

[0024] (III) Beneficial Effects This invention provides a method for assessing the severity of transmission line resonance based on a harmonic circular arc model. Compared with existing technologies, it has the following advantages: This invention constructs a harmonic circular arc model based on a lossless transmission line distributed parameter model and the principle of energy conservation. Harmonic constraint relationships at any location on the line can be established by collecting the effective values ​​of harmonic voltage and current from a single end. This eliminates the need for multi-point monitoring of the entire transmission line and the construction of complex grid impedance models, significantly reducing the cost of data acquisition and modeling. At the same time, the clear requirements for sampling frequency and analysis interval ensure the accuracy of monitoring data, making the evaluation method highly operable in engineering practice. It is applicable to the resonance evaluation of various long-distance transmission lines of 220kV and above.

[0025] This invention designs three core evaluation indicators: harmonic energy exceedance, resonance type index, and harmonic energy exceedance time probability. It achieves comprehensive quantification of the resonance state of transmission lines from three dimensions: the degree of harmonic energy exceedance, resonance type identification, and exceedance duration. Moreover, the calculation logic of each indicator is closely linked to national standards and State Grid enterprise standards, and the risk level classification standard is clear and explicit. It solves the problem that traditional evaluation methods can only reflect the harmonic amplification factor and cannot accurately quantify the severity of resonance, making the resonance evaluation results more valuable for engineering reference.

[0026] This invention uses an equal-weighted risk level matrix to couple the risk levels of three major indicators, classifying the severity of transmission line resonance into seven levels. This achieves a refined and comprehensive assessment of resonance risk, accurately distinguishing the line status of different resonance risk levels. Furthermore, by combining the amplitude and frequency factor, it can accurately locate resonance points along the line and pinpoint the specific location where resonance occurs. This overcomes the limitations of traditional methods, which cannot locate resonance points and are difficult to formulate targeted control measures, providing precise technical basis for maintenance personnel to take resonance suppression measures.

[0027] The harmonic circular arc model of this invention fully considers the actual loss characteristics of transmission lines. It clarifies that when the attenuation rate of line loss to the arc radius is ≤8%, no additional correction is needed. This ensures the model's adaptability to actual lines and simplifies the evaluation calculation process, avoiding complex calculations caused by loss correction. Simultaneously, the evaluation method enables integrated operation of the entire process, including resonance severity assessment, resonance type identification, and resonance point location. The evaluation results comprehensively reflect the overall state of line resonance, significantly improving the efficiency and accuracy of transmission line resonance evaluation. Attached Figure Description

[0028] Figure 1 This is a flowchart illustrating the transmission line resonance severity assessment method based on the harmonic circular arc model of this invention.

[0029] Figure 2 This is a schematic diagram of the harmonic amplitude circular arc constraint relationship of the transmission line resonance severity assessment method based on the harmonic circular arc model of the present invention.

[0030] Figure 3 This is a schematic diagram of the resonance severity rating matrix of the transmission line resonance severity assessment method based on the harmonic circular arc model of this invention. Detailed Implementation

[0031] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0032] Please see Figures 1 to 3 As shown, the embodiments of the present invention provide the following technical solutions: As an embodiment of the present invention: This invention provides a method for assessing the severity of transmission line resonance based on a harmonic circular arc model, comprising the following steps: The first step is to select the long-distance transmission line to be evaluated and obtain its... Subharmonic characteristic impedance Phase constant ; in, The equivalent inductance per unit length, The equivalent capacitance per unit length. for Subharmonic wavelength; The h-th harmonic voltage phasor is collected at the sending or receiving end of the transmission line using a power quality analyzer. Harmonic current phasor The effective value; In this embodiment, the sampling frequency is not less than 12.8 kHz, the FFT analysis interval is not greater than 0.2 s, and multiple sets of sampling data are obtained within the continuous monitoring period.

[0033] In this embodiment, the line to be evaluated is a 500kV transmission line with a resistance of 0.0256Ω / km and an inductance of 0.856×10⁻⁶. −3 H / km, capacitance 1.392×10 −8 F / km, line length 126.8km, selected the 5th dominant harmonic as the evaluation object, and collected 10 hours of harmonic voltage and current data at the receiving end as the basic data for single-end measurement; For the characteristic impedance of the 5th harmonic:

[0034] The second step involves using a lossless transmission line distributed parameter model and the principle of energy conservation at any location along the transmission line. h-th harmonic voltage at point Harmonic current Satisfy the circular arc constraint relationship:

[0035] In the formula, and The total harmonic energy coefficient is related to the location. Irrelevant , for Location RMS values ​​of second harmonic voltage and current; In this embodiment, for Normalized harmonic electric field energy amplitude at location, for The conservation of the sum of squares of the normalized harmonic magnetic field energy amplitude at the location is the core of the harmonic circular arc model. Define the arc The angle corresponding to the position point is the argument. ; In this embodiment, the argument angle It reflects the magnitude of the normalized load harmonic impedance at this location and is used to identify the resonance type; The larger the angle, The larger the value, the higher the load harmonic impedance exhibits. The smaller the angle, The smaller the value, the lower the load harmonic impedance exhibits low impedance characteristics; In actual transmission lines, when the line length is ≤400km and the dominant harmonic order is ≤13, considering the extreme reflection coefficient condition, the attenuation rate of line loss on the harmonic arc radius is ≤8%. Within the allowable range of the project, the harmonic arc model of the lossless line can be directly adopted without additional correction.

[0036] Step 3: Calculate the harmonic energy exceedance index based on the harmonic circular arc model. Resonance type index And statistically analyze the probability of harmonic energy exceeding the limit time. ; Harmonic energy exceeding limit index The calculation method is as follows: pass:

[0037] Calculate the reference harmonic electric field energy coefficient ; In the formula, For selected The limit for the subharmonic voltage content is determined by referring to the national standard GB / T51200-2016. This refers to the fundamental phase voltage of the line. Then, based on the harmonic arc radius:

[0038] Calculate the total harmonic energy coefficient ; in, , The effective values ​​of the h-th harmonic voltage and current are collected at the sending / receiving end by a single end. Then passed:

[0039] Determine the harmonic energy exceedance index ; when ≥1 indicates that the line has a risk of exceeding harmonic voltage limits; when <1 indicates no risk of exceeding the limit; In this embodiment, the fifth harmonic voltage content limit is taken. =1.25%, fundamental phase voltage =290.5kV, via:

[0040] Calculated As the baseline value;

[0041] The maximum value of the harmonic energy exceeding the limit (95% probability) calculated from the receiving end measurement data is 1.99, indicating a significant risk of exceeding the limit. Resonance type index The calculation method is as follows: Firstly, through:

[0042] calculate Electromagnetic energy ratio at location ; Right now It is equal to the square of the argument tangent at the corresponding point on the harmonic arc, and its value increases monotonically as it increases, which intuitively reflects the relative strength of the harmonic electric field energy. Passed again:

[0043] Define the resonance type index ; because ≥0, therefore The value ranges from -1 to 1; in, <0, that is <1, At angles less than 45°, the harmonic electric field energy is less than the magnetic field energy, resulting in low-resistance characteristics of the load harmonic impedance, exhibiting series resonance features. The closer to -1, the more pronounced the series resonance; >0, that is >1, When the angle is greater than 45°, the harmonic electric field energy is greater than the magnetic field energy, and the load harmonic impedance exhibits high impedance characteristics, demonstrating parallel resonance features. The closer to 1, the more significant the parallel resonance; KRT≈0, that is ≈1, ≈45°, the harmonic electric field energy is close to the magnetic field energy, and it is located at the boundary between parallel resonance and series resonance; In this embodiment: If it is identified as a parallel resonance: take the maximum value of the argument angle along the line. ,but ; If it is identified as a series resonance: take the minimum value of the argument angle along the line. ,but ; The harmonic circular arc model intuitively reflects the conservation and transformation characteristics of harmonic energy. The radius of the circular arc represents the harmonic energy intensity, the harmonic energy limit exceedance index comprehensively quantifies the risk of harmonic energy and harmonic voltage exceeding limits, and the resonance type index reflects the resonance type and state. It clearly describes the distribution of harmonic energy and resonance state in the transmission line from multiple dimensions. In this embodiment, the line is located 5% of the distance from the receiving end. =0.837, exhibiting strong parallel resonance characteristics, that is, from the 5% position of the receiving end. Calculated.

[0044] Harmonic energy exceeding time limit probability The calculation method is as follows: Within the statistically continuous monitoring period, the harmonic energy exceeds the limit Total duration ≥1 ; Subsequently passed:

[0045] Calculate the probability of harmonic energy exceeding the limit time. : in, Total monitoring duration; In this embodiment, =97.8%, indicating that the line harmonic energy exceeds the limit for an extremely long period of time, and the resonance risk has strong persistence; Step 4: , , They are divided into three risk levels; Among them, Level 1 is low risk, Level 2 is medium risk, and Level 3 is high risk. The classification criteria are shown in Table 1. Table 1:

[0046] in, This represents the maximum probability value of harmonic energy exceeding the limit index (95%). For State Grid's enterprise standards and national standards The ratio of the subharmonic test limit; In this embodiment, ; In the formula, For State Grid enterprise standards (Q / GDW11938-2018) Limits on the content of subharmonic voltage; For the national standard (GB / T51200-2016) Limits on the content of subharmonic voltage; Among them, because the national standard limit is stricter than the enterprise standard, A value greater than 1 provides a quantitative basis for risk level classification; In this embodiment, =1.99≥ , =97.8%≥50%, =0.837≥0.5, all three indicators are at level 3, corresponding to high risk; The fifth step is to establish an equal-weight risk level matrix, which couples the three risk levels of harmonic energy exceedance index, resonance type index, and harmonic energy exceedance time probability. For each level increase in the risk level of any index, the resonance severity index is increased by 1, and finally the resonance severity of the transmission line is divided into 7 levels. Among them, level 1 is the lowest and level 7 is the highest; when all three indicators are level 3 (high risk), the resonance severity is level 7, which is the highest risk level, and resonance suppression measures must be taken immediately. In this embodiment, all three indicators are at level 3, and the overall assessment of the resonance severity is level 7. It is determined that the line has a serious parallel resonance problem, and the harmonic voltage continues to exceed the limit. It is necessary to configure a harmonic filter to suppress the resonance. This embodiment focuses on a 500kV long-distance transmission line, constructing a harmonic circular arc model using single-end measurement data, and innovatively proposes... , , Three core indicators enable quantitative assessment of harmonic energy exceedance risk, resonance type, and duration probability. Combining national and enterprise standards to determine grading criteria, and coupling indicator levels through an equal-weighted matrix, a precise seven-level resonance severity classification is achieved, solving the problem of traditional methods' inability to comprehensively quantify resonance risk. This implementation is simple to operate, requires minimal data, and has strong engineering applicability. It can quickly determine whether a line has severe resonance and exceedance risk, providing a direct basis for resonance suppression.

[0047] As a second embodiment of the present invention: In its specific implementation, compared to Embodiment 1, the technical solution of this embodiment differs only in that it further includes: Step 6, the argument based on the harmonic circular arc model. And the characteristics of harmonic voltage distribution, find the position point with the maximum or minimum amplitude on the harmonic arc; Among them, the position point with the largest argument refers to the position point with parallel resonance characteristics, and the position point with the largest argument refers to the position point with series resonance characteristics. This is then combined with the frequency factor of the transmission line. Calculate the actual distance between this location and the single-end measurement point, which is the resonance point along the line; Among them, frequency length factor yes The phase constant of the subharmonic is the product of the distance from a certain position on the transmission line to the reference end; For the location of the parallel resonance characteristic: find the point along the line Corresponding frequency factor The actual distance ; yes The maximum value of the harmonic circular arc model argument along the transmission line under the second harmonic; For the location of the series resonance characteristic: find the point along the line Corresponding frequency factor The actual distance ; yes Minimum value of the harmonic circular arc model argument along the transmission line under subharmonics; In this embodiment, the point where the maximum amplitude is 5% of the line length from the receiving end (6.34km) is the parallel resonance point, which is consistent with the actual location of the harmonic voltage antinode.

[0048] This embodiment adds a resonant point location function to the first embodiment. Utilizing the argument characteristics and frequency factor of the harmonic arc model, it accurately locates the actual distance to parallel or series resonant points along the line. The actual location is calculated by using the frequency factor corresponding to the maximum / minimum argument values. The location result closely matches the harmonic voltage antinodes, solving the problem that traditional methods cannot identify potential resonant locations along the line. This function extends the assessment from "risk determination" to "precise location," providing spatial location data for targeted configuration of harmonic filters and optimization of suppression schemes, further enhancing the engineering application value of the method.

[0049] As an embodiment of the present invention: In specific implementation, compared with Embodiment 1 and Embodiment 2, the technical solution of this embodiment is to combine the solutions of Embodiment 1 and Embodiment 2. The difference between the technical solution of this embodiment and Embodiment 1 and Embodiment 2 is only in this embodiment. This embodiment constructs a 500kV local transmission network simulation model to verify the batch evaluation capability of this method in multi-line and multi-harmonic source scenarios, and compares it with the traditional harmonic transmission coefficient method to verify the superiority of this method.

[0050] A simulation model of a 500kV local power transmission network with 18 nodes and 21 transmission lines was established. The resistance per unit length of the line is 0.027 Ω / km, and the inductance is 0.859 × 10⁻⁶. −3 H / km, capacitance 1.388×10 −8 The simulation was conducted at F / km, with dynamic loads, power plants, harmonic sources, and converter station filters connected, and a total of 1440 sampling points were used for 24 hours.

[0051] The severity of resonance was assessed using this method on 21 lines. The core steps are as follows: Single-ended harmonic data acquisition → construction of harmonic circular arc model → calculation of three major assessment indicators → classification of indicator risk levels → determination of resonance severity level → location of resonance point; The evaluation results are as follows: Line 1 and Line 2 have a resonance severity level of 7; both exhibit strong parallel resonance characteristics, with the highest harmonic voltage content and an over-limit time probability of ≥90%. The resonance severity of line 4 is level 6, with obvious parallel resonance characteristics, and the maximum probability of harmonic energy exceeding the limit is 95%, with a value of 1.82. The resonance severity of lines 3, 7, and 12 is level 5. Among them, lines 3, 7, and 12 exhibit series resonance characteristics, with significant amplification of harmonic current. The remaining 15 lines had a resonance severity level ≤ 3, no obvious resonance characteristics, and the harmonic energy did not exceed the limit.

[0052] Compared with the traditional harmonic transfer coefficient method, which can only reflect the harmonic amplification factor at both ends of the line and cannot identify the resonance point and the actual resonance severity along the line, this method can achieve full-process evaluation through single-end measurement, and the evaluation results are more in line with the actual line resonance state.

[0053] This embodiment constructs a 500kV local transmission network simulation model with multiple nodes and multiple lines, and verifies the method's batch evaluation capability in scenarios with multiple harmonic sources and complex power grids.

[0054] By conducting a centralized assessment of 21 lines, this method efficiently distinguishes different severity levels and resonance types. Compared to the traditional harmonic transfer coefficient method, it not only quantifies the risk but also identifies resonance points along the line, resulting in assessment results that are more realistic. This embodiment demonstrates the method's potential for large-scale application, meeting the needs of batch line resonance assessment in power grid operation and maintenance, and significantly improving the efficiency and accuracy of harmonic mitigation.

[0055] As an embodiment of the present invention: In specific implementation, compared with Embodiment 1, Embodiment 2 and Embodiment 3, the technical solution of this embodiment is to combine the solutions of Embodiment 1, Embodiment 2 and Embodiment 3.

[0056] This embodiment integrates the core functions of the previous three embodiments to achieve a complete solution encompassing "risk quantification assessment + resonance type identification + limit exceedance probability statistics + resonance point location + batch scenario adaptation." It retains the convenience of single-end measurement and the comprehensiveness of multi-indicator coupling, while also possessing the capability for batch assessment and precise location of complex power grids, solving the problems of limited functionality and applicable scenarios in traditional methods. This embodiment covers all needs from single lines to local power grids, from risk assessment to precise governance, providing an integrated and efficient technical means for power grid harmonic resonance assessment, with wider application scenarios and stronger practicality.

[0057] It should be stated that all user data collected in this application was collected with the user's consent and authorization, and the use of user data is legal and compliant, and the use and processing of user data comply with the relevant laws, regulations and standards of the relevant regions.

[0058] Furthermore, any content not described in detail in this specification is existing technology known to those skilled in the art.

[0059] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0060] The above formulas are all dimensionless calculations. Dimensionless calculation involves introducing a reference benchmark, such as the maximum, minimum, standard deviation, or theoretical extreme value of a physical quantity, to transform the original physical quantity into a dimensionless relative value. This value is usually mapped to a specific interval, such as [0,1] or [-1,1], which eliminates the influence of units while preserving the relative size relationship of the physical quantities. The formula is derived from software simulation based on a large amount of collected data to obtain the most recent real-world results. The preset parameters and thresholds in the formulas are set by those skilled in the art according to the actual situation.

[0061] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

[0062] The various embodiments of this application have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or improvement of the technology in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A method for assessing the severity of transmission line resonance based on a harmonic circular arc model, characterized in that, Includes the following steps: Step 1: Select the transmission line to be evaluated and obtain its... Subharmonic characteristic impedance Phase constant ; in, The equivalent inductance per unit length, The equivalent capacitance per unit length; Simultaneously, data is collected at either the sending or receiving end of the transmission line. Monitoring data of the effective values ​​of subharmonic voltage and current; The second step involves constructing a model of the distributed parameters of the lossless transmission line and the principle of energy conservation at any location along the transmission line. The harmonic circular arc model at the location satisfies the following circular arc constraint relationships: In the formula, and The total harmonic energy coefficient, , for Location RMS values ​​of second harmonic voltage and current; pass: Determine the arc The angle corresponding to the location point is the argument. Step 3: Calculate the harmonic energy exceedance index based on the harmonic circular arc model. Resonance type index And statistically analyze the probability of harmonic energy exceeding the limit time. ; Step 4: , , They are divided into three risk levels: Level 1 is low risk, Level 2 is medium risk, and Level 3 is high risk. Step 5: Establish an equal-weighted risk level matrix, coupling the risk levels of the three indicators. For each indicator whose risk level increases by 1 level, the resonance severity index increases by 1, thus dividing the transmission line resonance severity into 7 levels.

2. The method for assessing the severity of transmission line resonance based on a harmonic circular arc model according to claim 1, characterized in that: The harmonic energy exceedance index mentioned in step three The calculation method is as follows: pass: Calculate the reference harmonic electric field energy coefficient ; In the formula, For selected Limits on the content of subharmonic voltage. This refers to the fundamental phase voltage of the line. Then calculate the total harmonic energy coefficient based on the harmonic arc radius. ; Then passed: Determine the harmonic energy exceedance index .

3. The method for assessing the severity of transmission line resonance based on a harmonic circular arc model according to claim 2, characterized in that: when ≥1 indicates that the line has a risk of harmonic voltage exceeding the limit; when <1 indicates no risk of exceeding the limit.

4. The method for assessing the severity of transmission line resonance based on a harmonic circular arc model according to claim 1, characterized in that: In the third step, the resonance type index The calculation method is as follows: Firstly, through: calculate Electromagnetic energy ratio at location ; Passed again: Define the resonance type index .

5. The method for assessing the severity of transmission line resonance based on a harmonic circular arc model according to claim 4, characterized in that: in, <0 indicates a series resonance characteristic. >0 indicates a parallel resonance characteristic.

6. The method for assessing the severity of transmission line resonance based on a harmonic circular arc model according to claim 1, characterized in that: In the third step, the harmonic energy exceeding the time limit probability... The calculation method is as follows: in, Within the monitoring period Total duration ≥1 This represents the total monitoring duration.

7. The method for assessing the severity of transmission line resonance based on a harmonic circular arc model according to claim 1, characterized in that: In the fourth step, the criteria for classifying the risk levels of the indicators are as follows: Level of violation severity classification: Level 1 is <1, 2 levels are 1≤ < Level 3 is ≥ ; in, for The 95% probability is a large value. The ratio of the h-th harmonic assessment limit in the State Grid enterprise standard to that in the national standard; The probability level of exceeding the time limit is divided into levels: Level 1 is... <10%, Level 2 is 10%≤ <50%, Level 3 ≥50%; Resonance type index classification: Level 1 is −0.5 < <0.5, Level 2 ≤−0.5, Level 3 is ≥0.

5.

8. The method for assessing the severity of transmission line resonance based on a harmonic circular arc model according to claim 1, characterized in that: In the first step, the transmission line to be evaluated is a transmission line with a voltage level of 220kV or above, and the sampling frequency of the monitoring data collected at one end is not less than 12.8kHz.

9. The method for assessing the severity of transmission line resonance based on a harmonic circular arc model according to claim 1, characterized in that: It also includes a sixth step: the argument based on the harmonic circular arc model. and frequency factor Find the point where the amplitude is the largest or smallest, and calculate the actual distance between that point and the single-end measurement point. This is the resonance point along the transmission line.

10. The method for assessing the severity of transmission line resonance based on a harmonic circular arc model according to claim 1, characterized in that: The harmonic arc model is a lossless transmission line model, and the attenuation rate of line loss on the arc radius is ≤8%.

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