A large-current ice-melting time prediction model for power transmission line rime icing

Abstract

The application discloses a large-current ice-melting time prediction model for power transmission line rime icing, and mainly establishes an ice-melting estimation model suitable for low-density soft rime. The design of the mathematical model includes some influences ignored in existing researches, a complex variable formula of ice-melting stage time is established, and a control equation is solved by using a mass conservation equation and other some relational expressions. The large-current ice-melting time of power transmission line rime icing is predicted based on a large number of icing samples with different densities and appearances, so that the large-current ice-melting time of power transmission line rime icing can be predicted more accurately. The power loss and power equipment failure caused by soft rime are effectively solved, and the stability and safety of the power system under extreme conditions are improved.

Description

Technical Field

[0001] This invention relates to a high-current de-icing time prediction model for rime ice on transmission lines, belonging to the field of transmission line condition monitoring and diagnosis technology. Background Technology

[0002] Atmospheric icing is a natural phenomenon that poses a high risk to overhead power transmission lines. Severe icing disasters on overhead power transmission lines can cause widespread and serious damage, such as conductor galloping, insulator flashover, structural failure, and even power grid collapse.

[0003] Atmospheric icing is a general term describing specific icing phenomena caused by supercooled water droplets or wet snow. Based on density and other physical properties, atmospheric icing on overhead transmission lines can be classified into several types: glaze ice, hard rime, soft rime, wet snow, and dry snow. Due to their high density and strong adhesion, hard rime and glaze ice are major causes of power equipment failure. Therefore, the growth models and melting methods of high-density icing have been extensively studied. Conversely, the typical density range of soft rime is 300 to 600 kg / m³. This usually does not cause serious load problems for overhead transmission lines. However, soft rime is a significant factor leading to some faults.

[0004] First, corona discharge and the resulting power loss may be caused by soft frost, which is increasingly attracting the attention of power companies. Second, influenced by meteorological parameters and Joule heating of current, soft frost may iculate into denser hard frost, caused by ice crystal melting and refreezing. Worse still, low-density soft frost may continue to grow, forming a very large ice shell under some extreme weather conditions. It is well known that extensive research has been conducted on icing melting models for overhead transmission lines, and these models have been used to address serious safety issues for power companies.

[0005] However, these research findings cannot be directly applied to solving the problem of soft frost, because the melting process of soft frost has many different characteristics. On the one hand, soft frost has a loose and porous structure, with a typical roughness element height of 3-5 mm. Furthermore, this unique structure can lead to significant differences in thermal parameters such as heat transfer coefficient and icing thermal conductivity.

[0006] On the other hand, due to the sponge-like structure of soft frost, the molten liquid caused by Joule heating will not flow down, but will be absorbed by the sponge-like structure to form a layer of ice-water mixture. Summary of the Invention

[0007] The purpose of this invention is to provide a prediction model for the high-current de-icing time of rime ice on transmission lines. The prediction of the high-current de-icing time is achieved by studying the numerical simulation results in an artificial climate chamber.

[0008] The technical solution adopted in this invention is a high-current de-icing time prediction model for rime ice formation on transmission lines, comprising the following steps: Step 1: For an approximately circular cross-section, which is more common in excessive icing disasters, this patent establishes a circular model. If the load current is greater than the minimum melting current, the inner ice shell will gradually melt, and an air gap will appear between the ice shell and the conductor. Since the heat in the natural melting of rime originates from natural conditions, the uncontrollability of melting energy leads to slow melting of rime, and the meltwater is absorbed by the ice tree structure, resulting in a freeze-thaw cycle. After each freeze-thaw cycle, the ice layer density needs to be re-estimated based on the ice layer's water-holding capacity.

[0009] Therefore, the material region of the ice melt is divided into four parts: residual soft frost layer, ice-water mixture layer, air gap layer, and conductor layer. The ice melting process of the glaze can be divided into three stages: heating stage, ice melting stage, and ice removal stage.

[0010] Step 2, Heating Stage: The duration of the heating stage can be determined by applying the thermal energy conservation equation and the typical problem of heat conduction through a cylindrical wall.

[0011] Step 3: The time of the ice melting stage can be obtained by using the heat energy conservation equation, the mass conservation equation, the typical problem of heat conduction in a cylindrical wall, and the volume conservation equation.

[0012] Step 4: Since the icing off of the conductor is a transient phenomenon, the time of the third stage can be ignored. Therefore, the total time for melting ice can be obtained by adding the time of the heating stage and the time of the melting stage.

[0013] The invention is further characterized in that, Step 2 is implemented in the following steps: The total time for the soft frost to melt is expressed as: (1) in Indicates the duration of the warming phase. This indicates the timeframe for the ice-melting phase.

[0014] Step 3: The melting stage can be determined using the heat energy conservation equation, the mass conservation equation, typical problems of heat conduction in a cylindrical wall, and the volume conservation equation. According to the energy conservation equation, the heat conservation equation for the temperature rise stage can be written as: (2) in Joule heating during the heating phase can be represented as: (3) in This represents the de-icing current flowing through the conductor. Represents the resistivity of a conductor. The time of the heating phase. The heat dissipated into the airflow can be represented as: (4) It represents radiative heat flux. This represents the heat flux of convective heat transfer. This represents the heat flux of sublimation or evaporation; (5) in Indicates the heat transfer coefficient. This represents the Stefan-Boltzmann constant. Represents the radiation linearization constant. It is the ratio of the molecular weights of water vapor and dry air. It is the linearization constant for vaporization and evaporation. It is the ambient temperature. The average temperature of the ice surface during the heating phase is expressed as... (6) This represents the instantaneous surface temperature at the end of this stage. Considering that heat conduction within the icy shell is a quasi-steady state, the calculation is performed using the typical problem of heat conduction through a cylindrical wall. (7) in For the temperature of the conductor, Let the radius be the conductor. The thermal conductivity of soft frost is expressed as follows; the expression for the thermal conductivity of icing on transmission lines is as follows: (8) Indicates the thermal conductivity of ice. This indicates the density of the frost layer. This indicates the density of ice. This represents the equivalent coefficient of convective heat transfer. It is a combined coefficient relating to convection, radiation, and sublimation, and is written as... (9) in It is the static pressure of air. It is the specific heat of air; Indicates the use of raising the conductor temperature to Joule heating, expressed as (10) in Indicates the radius of the conductor. The density of a conductor. Indicates the specific heat of a conductor. Joule heating, used to heat the icy outer shell, is denoted as... (11) in This represents the initial density of the soft frost. This indicates the specific heat of ice. The temperature of the icing layer is a key unknown parameter in this calculation formula; the average value of the conductor and the iced surface is defined as the icing temperature. (12) in This indicates the average temperature of the ice-water mixture layer. Therefore, the heating phase lasts for [duration]. (13); The heat conservation equation for the ice melting stage in step 4 can be written as: (14) in The second stage of Joule heating is represented as... (15) The amount of heat used for melting ice is expressed as... (16) in This indicates the density of water. This represents the latent heat of freezing of water. This indicates the volume of the ice-water mixture layer. This indicates the volume percentage of water in the ice-water mixture layer. This represents the heat dissipated into the airflow during the ice melting stage, denoted as... (17) in This indicates the final instantaneous temperature of the icing surface in the second stage. The amount of heat used to heat the ice is expressed as... (18) in This indicates the amount of heat used to heat the ice-water mixture layer. This parameter represents the amount of heat used to heat the remaining soft frost layer. (19) in This represents the air gap volume caused by ice melting and shedding. Extensive ice-melting experiments have shown that the air gap induced by the ice-melting current has an elliptical cross-section, and the lengths of its semi-major and semi-minor axes can be estimated as follows: and , (20) Therefore, the time for the ice melting stage is obtained through a complex formula. (twenty one) The formula contains , , , Since there are four unknowns, the solution cannot be obtained directly; several additional equations are required. 1) The melting process of rime ice follows the law of conservation of mass, therefore: (twenty two); 2) The cross-section of the ice-water mixture layer cannot be accurately defined. Based on experimental observations, the applicant believes the mixture layer is roughly an eccentric ellipse, thinner at the top and wider at the bottom. To simplify the model, the cross-sectional shape is assumed to be a regular ring, such as... Figure 2-4 As shown, heat conduction within the ice shell can be simplified to a typical problem of heat conduction through the wall of a cylinder: (twenty three) in The effective radius of the remaining rime layer; 3) The total volume of the rime ice remains unchanged during the melting stage, therefore the following formula holds true: (twenty four).

[0015] Compared with the prior art, the beneficial effects of the present invention are: This invention is a high-current de-icing time prediction model for frost accretion on power transmission lines. Based on a large number of ice samples with different densities and appearances, the high-current de-icing time of frost accretion on power transmission lines can be predicted with relatively high accuracy.

[0016] This invention is a high-current de-icing time prediction model for rime ice on power transmission lines. It can be combined with weather forecasts to predict the high-current de-icing time for rime ice on power transmission lines, which is beneficial to ensuring power grid safety, improving power supply reliability, optimizing operation plans, and reducing power losses. Attached Figure Description

[0017] Figure 1 This is a flowchart of a high-current de-icing time prediction model for rime ice accretion on power transmission lines according to the present invention; Figure 2Schematic diagram of rime melting and water retention of ice layer on insulator; Figure 3 This is a schematic diagram of the melting process of ice on overhead power lines; Figure 4 It is a simplified structural model of heat conduction on the cylindrical wall. Detailed Implementation

[0018] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0019] This invention provides a high-current de-icing time prediction model for rime ice formation on power transmission lines, such as... Figure 1 As shown, it includes the following steps:

[0020] Step 1: For an approximately circular cross-section, which is more common in excessive icing disasters, this patent establishes the model as circular. If the load current is greater than the minimum melting current, the inner ice shell will gradually melt, and an air gap will appear between the ice shell and the conductor. Therefore, the melting material area is divided into four parts: residual soft frost layer, ice-water mixture layer, air gap layer, and conductor layer, as follows. Figure 2 As shown, the glaze melting process can be divided into three stages: the heating stage, the melting stage, and the de-icing stage, as follows: Figure 3 As shown.

[0021] Step 2, Heating Stage: Using the heat energy conservation equation and the typical problem of heat conduction through a cylindrical wall, the time for the heating stage can be obtained. The total time for the soft frost to melt can be expressed as... (1) in Indicates the duration of the warming phase. This indicates the timeframe for the ice-melting phase.

[0022] Step 3, the melting stage: The time for the melting stage can be obtained using the heat energy conservation equation, the mass conservation equation, typical problems of heat conduction in a cylindrical wall, and the volume conservation equation. The heat conservation equation for the temperature rise stage can be written as: (2) in Joule heating during the heating phase is represented as... (3) in This represents the de-icing current flowing through the conductor. Represents the resistivity of a conductor. Indicates the duration of the warming phase. The heat dissipated into the airflow is represented as... (4) It represents radiative heat flux. This represents the heat flux of convective heat transfer. This represents the heat flux of sublimation or evaporation; (5) in Indicates the heat transfer coefficient. This represents the Stefan-Boltzmann constant. Represents the radiation linearization constant. It is the ratio of the molecular weights of water vapor and dry air. It is the linearization constant for vaporization and evaporation. It is the ambient temperature. The average temperature of the ice surface during the heating phase is expressed as... (6) This represents the instantaneous surface temperature at the end of this stage. Considering that heat conduction within the icy shell is a quasi-steady state, the calculation is performed using the typical problem of heat conduction through a cylindrical wall. (7) in For the temperature of the conductor, Let the radius be the conductor. The thermal conductivity of soft frost is expressed as follows; the expression for the thermal conductivity of icing on transmission lines is as follows: (8) Indicates the thermal conductivity of ice. This indicates the density of the frost layer. This indicates the density of ice. This represents the equivalent coefficient of convective heat transfer. It is a combined coefficient relating to convection, radiation, and sublimation, and is written as... (9) in It is the static pressure of air. It is the specific heat of air; Indicates the use of raising the conductor temperature to Joule heating, expressed as (10) in Indicates the radius of the conductor. The density of a conductor. Indicates the specific heat of a conductor. Joule heating, used to heat the icy outer shell, is denoted as... (11) in This represents the initial density of the soft frost. This indicates the specific heat of ice. The temperature of the icing layer is a key unknown parameter in this calculation formula; the average value of the conductor and the iced surface is defined as the icing temperature. (12) in This indicates the average temperature of the ice-water mixture layer. Therefore, the heating phase lasts for [duration]. (13); Step 4: Since the detachment of ice from the conductor is a transient phenomenon, the time of the third stage can be ignored. Therefore, the total melting time can be obtained by adding the times of the heating stage and the melting stage. The heat conservation equation for the melting stage can be written as: (14) in The second stage of Joule heating is represented as... (15) The amount of heat used for melting ice is expressed as... (16) in This indicates the density of water. This represents the latent heat of freezing of water. This indicates the volume of the ice-water mixture layer. This indicates the volume percentage of water in the ice-water mixture layer. This represents the heat dissipated into the airflow during the ice melting stage, denoted as... (17) in This indicates the final instantaneous temperature of the icing surface in the second stage. The amount of heat used to heat the ice is expressed as... (18) in This indicates the amount of heat used to heat the ice-water mixture layer. This parameter represents the amount of heat used to heat the remaining soft frost layer. (19) in This represents the air gap volume caused by ice melting and shedding. Extensive ice-melting experiments have shown that the air gap induced by the ice-melting current has an elliptical cross-section, and the lengths of its semi-major and semi-minor axes can be estimated as follows: and , (20) Therefore, the time for the ice melting stage is obtained through a complex formula. (twenty one) The formula contains , , , Since there are four unknowns, the solution cannot be obtained directly; several additional equations are required. 1) The melting process of rime ice follows the law of conservation of mass, therefore: (twenty two); 2) The cross-section of the ice-water mixture layer cannot be accurately defined. Based on experimental observations, the applicant believes the mixture layer is roughly an eccentric ellipse, thinner at the top and wider at the bottom. To simplify the model, the cross-sectional shape is assumed to be a regular ring, such as... Figure 4 As shown, heat conduction within the ice shell can be simplified to a typical problem of heat conduction through the wall of a cylinder: (twenty three) in The effective radius of the remaining rime layer; 3) The total volume of the rime ice remains unchanged during the melting stage, therefore the following formula holds true: (twenty four).

Claims

1. A high-current de-icing time prediction model for rime ice accumulation on transmission lines, characterized in that: Includes the following steps, Step 1: Based on on-site observations, simplify the ice-melting model and establish a circular structure model; Step 2: Establish a melting time model for soft frost, dividing the glaze melting process into three stages: heating stage, melting stage, and de-icing stage; Step 3: Based on the law of conservation of energy and thermodynamic equations, expand the thermal energy conservation equation for the heating stage to calculate the heating time for the rime ice to melt. The heat conservation equation is: （2） in Joule heating during the heating phase is represented as... （3） in This represents the de-icing current flowing through the conductor. Represents the resistivity of a conductor. Indicates the duration of the warming phase. The heat dissipated into the airflow is represented as （4） It represents radiative heat flux. This represents the heat flux of convective heat transfer. This represents the heat flux of sublimation or evaporation; （5） in Indicates the heat transfer coefficient. This represents the Stefan-Boltzmann constant. Represents the radiation linearization constant. It is the ratio of the molecular weights of water vapor and dry air. It is the linearization constant for vaporization and evaporation. It is the ambient temperature. The average temperature of the ice surface during the heating phase is expressed as... (6) This represents the instantaneous surface temperature at the end of this stage. Considering that heat conduction within the icy shell is a quasi-steady state, the calculation is performed using the typical problem of heat conduction through a cylindrical wall. （7） in For the temperature of the conductor, Let the radius be the conductor. The thermal conductivity of soft frost is expressed as follows; the expression for the thermal conductivity of icing on transmission lines is as follows: （8） Indicates the thermal conductivity of ice. This indicates the density of the frost layer. This indicates the density of ice. This represents the equivalent coefficient of convective heat transfer. It is a combined coefficient relating to convection, radiation, and sublimation, and is written as... （9） in It is the static pressure of air. It is the specific heat of air; Indicates the use of raising the conductor temperature to Joule heating, expressed as （10） in Indicates the radius of the conductor. The density of a conductor. Indicates the specific heat of a conductor. Joule heating, used to heat the icy outer shell, is denoted as... （11） in This represents the initial density of the soft frost. This indicates the specific heat of ice. The temperature of the icing layer is a key unknown parameter in this calculation formula; the average value of the conductor and the iced surface is defined as the icing temperature. （12） in This indicates the average temperature of the ice-water mixture layer. Therefore, the heating phase lasts for [duration]. （13）； Step 4: Based on the law of conservation of energy and thermodynamic equations, expand the thermal energy conservation equation for the melting stage to calculate the rime ice melting time; The heat conservation equation is: （14） in The second stage of Joule heating is represented as... （15） The amount of heat used for melting ice is expressed as... （16） in This indicates the density of water. This represents the latent heat of freezing of water. This indicates the volume of the ice-water mixture layer. This indicates the volume percentage of water in the ice-water mixture layer. This represents the heat dissipated into the airflow during the ice melting stage, denoted as... （17） in This indicates the final instantaneous temperature of the icing surface in the second stage. The amount of heat used to heat the ice is expressed as... （18） in This indicates the amount of heat used to heat the ice-water mixture layer. This parameter represents the amount of heat used to heat the remaining soft frost layer. （19） in This represents the air gap volume caused by ice melting and shedding. Extensive ice-melting experiments have shown that the air gap induced by the ice-melting current has an elliptical cross-section, and the lengths of its semi-major and semi-minor axes can be estimated as follows: and , （20） Therefore, the time for the ice melting stage is obtained through a complex formula. （21） The formula contains , , , Since there are four unknowns, the solution cannot be obtained directly; several additional equations are required. 1) The melting process of rime ice follows the law of conservation of mass, therefore: (22)； 2) The cross-section of the ice-water mixture layer cannot be accurately defined. Experimental observations suggest that the mixture layer is an eccentric ellipse, thinner at the top and wider at the bottom. To simplify the model, we assume that the cross-sectional shape is a regular ring, and the heat conduction within the ice shell is simplified to a typical cylindrical wall heat conduction problem: (23) in The effective radius of the remaining rime layer; 3) The total volume of the rime ice remains unchanged during the melting stage, therefore the following formula holds true: (24)。 2. The high-current de-icing time prediction model for rime ice on transmission lines according to claim 1, characterized in that: The total time for the soft frost to melt in step 2 is expressed as follows: （1） in Indicates the duration of the warming phase. This indicates the timeframe for the ice-melting phase.

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