GIL temperature rise rapid calculation method based on lumped parameter thermal network model

Abstract

The invention discloses a GIL temperature rise rapid calculation method based on a lumped parameter thermal network model, and belongs to the technical field of line simulation, and the method comprises the steps: constructing a lumped parameter thermal network model according to a gas insulated transmission line; wherein the lumped parameter thermal network is a model of a heat transfer process analogy circuit in the gas insulated transmission line; constructing a model control equation of the lumped parameter thermal network model, wherein the model control equation is used for performing iterative temperature rise calculation on the gas insulated transmission line; initial parameters of the gas insulated transmission line are obtained, the initial parameters comprise geometric parameters, electromagnetic parameters and thermal parameters, iterative calculation is carried out on the initial parameters through the model control equation, a temperature rise calculation result of the gas insulated transmission line is obtained, and rapid and effective temperature rise calculation is carried out on the gas insulated transmission line.

Description

Technical Field

[0001] The invention belongs to the technical field of circuit simulation, and in particular relates to a GIL temperature rise fast calculation method based on a lumped parameter thermal network model. Background Art

[0002] Gas-insulated transmission lines (GIL) have become a powerful alternative to traditional overhead lines and cables in certain situations due to their high reliability, low electromagnetic field interference, and large-capacity transmission.

[0003] In order to ensure the safe and stable operation of the power system, the temperature rise characteristics of the transmission line need to be deeply analyzed before commissioning, so as to reasonably adjust the current carrying capacity of the conductor, maximize the utilization of the conductor cross section, and provide feedback guidance for the design link. The temperature rise characteristics directly affect the load capacity, thermal stability, insulation performance and equipment service life of the transmission line. Compared with traditional overhead lines and cables, GIL faces more challenges in temperature rise calculation due to its special structure and working principle. The temperature rise of GIL is not only affected by factors such as load size, material loss and insulation medium characteristics, but also closely related to heat dissipation conditions, ambient temperature and conductor layout. The calculation process is particularly complicated. Therefore, in-depth research on the temperature rise characteristics of GIL is of great significance for ensuring the maximum utilization of GIL cross section, ensuring the safe and stable operation of the power system, improving transmission efficiency, reducing costs and promoting technological progress.

[0004] The mainstream research methods for temperature rise characteristics in existing technologies include experimental measurement, analytical calculation and numerical simulation. Among them, the experimental measurement method simulates the temperature rise effect of GIL under actual operation by building a GIL transmission model, but this method has strong limitations, high cost and is not widely used. The analytical calculation method is mainly based on the thermal circuit characteristics of GIL, constructs an equivalent thermal circuit model, and estimates the temperature rise of GIL by calculating the resistance of the conductor and the shell, and the thermal resistance of the insulating gas, but there is currently no specification for the analytical calculation of thermal characteristics.

[0005] Numerical simulation techniques include thermal network models (TNM) and computational fluid dynamics (CFD) methods.

[0006] The thermal network method establishes thermodynamic differential equations with a small number of node temperature rises as the solution object, simplifies the cables and the surrounding environment into a circuit network model, and determines the temperature rise of each node of the GIL by constructing a thermal balance equation. CFD simulation uses finite element method, finite volume method or time-domain finite difference method to solve the electromagnetic-fluid-heat coupling partial differential equation, establishes a GIL multi-field coupling model through simulation software such as ANSYS and COMSOL, and simulates the thermal field and electric field of the GIL. In comparison, this method has a large amount of calculation, takes a long time, and requires multidisciplinary knowledge reserves. However, the analytical calculation method is simple but the calculation accuracy is not enough. CFD uses multidisciplinary cross-coupling to make the calculation process complicated. The calculation results are highly accurate but the required computing resources are too many, making it difficult to apply in engineering. In the prior art, COMSOL simulation results are often used to simulate heat sources, and the gas convection parameters, skin effect factors and other key variables of the GIL system are not uniformly integrated, and the advantages of the thermal network method in saving computing time and resources are not truly utilized. Summary of the invention

[0007] In order to solve the above technical problems, the present invention proposes a GIL temperature rise fast calculation method based on a lumped parameter thermal network model to solve the above problems existing in the prior art.

[0008] To achieve the above object, the present invention provides a method for quickly calculating the temperature rise of a GIL based on a lumped parameter thermal network model, comprising:

[0009] According to the gas-insulated transmission line, a lumped parameter thermal network model is constructed; wherein the lumped parameter thermal network model is a model of a circuit analogous to the heat transfer process in the gas-insulated transmission line;

[0010] Constructing a model control equation of the lumped parameter thermal network model, wherein the model control equation is used to perform iterative temperature rise calculation on the gas-insulated transmission line;

[0011] Initial parameters of the gas-insulated transmission line are obtained, wherein the initial parameters include geometric parameters, electromagnetic parameters and thermal parameters, and the initial parameters are iteratively calculated through the model control equation to obtain the temperature rise calculation result of the gas-insulated transmission line.

[0012] Optionally, the construction process of the lumped parameter thermal network model includes:

[0013] The basic structure of the gas-insulated transmission line is obtained, the physical properties in the basic structure are converted to the body nodes of the cross section, and the heat transfer path on the body nodes is obtained, the heat transfer path is visualized through thermal resistance, heat capacity and heat flux source to obtain a visualized structure, the visualized structure is equivalent and reduced to obtain a lumped parameter thermal network model; wherein the convection in the gas domain and the radiation between the solids are equivalent to thermal resistance, the temperature hysteresis of the metal endothermic process is equivalent to heat capacity, and the loss is equivalent to a heat flux source.

[0014] Optionally, the model control equations include: a calculation equation for the skin effect coefficient of the conductor and the shell in the gas-insulated transmission line, a calculation equation for the DC resistance of the conductor and the shell at the operating temperature, a calculation equation for the loss of the shell and the conductor, and a differential equation of the lumped parameter thermal network model.

[0015] Optionally, the process of iteratively calculating the initial parameters through the model control equation includes:

[0016] The initial parameters are calculated by the skin effect coefficient calculation equation to obtain the skin effect coefficients of the conductor and the shell;

[0017] According to the skin effect coefficient and initial parameters of the conductor and the shell, the DC resistance of the conductor and the shell at the operating temperature is calculated by the DC resistance calculation equation;

[0018] According to the DC resistance and skin effect coefficient of the conductor and shell at the operating temperature, the loss of the shell and conductor is obtained through the loss calculation equation;

[0019] According to the losses of the shell and the conductor, the node temperature information of the conductor and the shell at the next moment is calculated by the differential equation of the lumped parameter thermal network model;

[0020] The above calculation process is repeated according to the node temperature information of the conductor and the shell at the next moment to obtain the temperature rise calculation result of the gas-insulated transmission line.

[0021] Optionally, the skin effect coefficient calculation equation is:

[0022]

[0023] in, is the conductor skin effect coefficient, is the skin effect coefficient of the shell, and are the inner and outer radii of the conductor, and are the inner radius and outer radius of the shell respectively.

[0024] Optionally, the DC resistance calculation equation is:

[0025]

[0026] in, and are the DC resistance of the conductor and shell at operating temperature, and are the conductor and shell ambient temperatures respectively The DC resistance under , is calculated from the reference resistivity, and are the resistivity temperature coefficients of the conductor and shell, respectively.

[0027] Optionally, the loss calculation equation is:

[0028]

[0029] Where I is the effective value of the alternating current flowing through the conductor.

[0030] Alternatively, the difference equation for the lumped parameter thermal network model is:

[0031]

[0032] Among them, i-1 is the previous moment, i is the current moment, is the conductor temperature node, is the characteristic temperature of the insulating gas domain above the GIL, is the GIL top case temperature, is the ambient temperature, is the conductor heat capacity, is the heat capacity of the shell, is the conductor loss, is the loss in the upper part of the shell, represents the thermal convection resistance of the upper part of the insulating gas, It represents the heat radiation resistance between the upper conductor and the shell. represents the thermal convection resistance of the air domain above the shell, Represents the thermal radiation resistance of the upper part of the shell to the air domain.

[0033] Optionally, before calculating the node temperature information of the conductor and the shell at the next moment, the following steps are also included:

[0034] The calculation parameters include: convection thermal resistance between the conductor and the shell, radiation thermal resistance between the conductor and the shell, convection thermal resistance between the shell and the external environment, radiation heat transfer between the shell and the outside world, and heat capacity between the conductor and the shell; and the differential equation of the lumped parameter thermal network model is calculated by the calculation parameters.

[0035] Optionally, obtaining the initial parameters of the gas-insulated transmission line includes:

[0036] The multi-field coupling modeling of the gas-insulated transmission line is performed by using the finite element method to obtain a multi-field coupling model, and the gas-insulated transmission line is simulated by using the multi-field coupling model.

[0037] Compared with the prior art, the present invention has the following advantages and technical effects:

[0038] In order to solve the problem of balancing the calculation accuracy and complexity of the temperature rise characteristics of GIL, a lumped-parameter thermal network (LPTN) model is proposed. This model takes into account the distributed thermal convection of insulating gas under the combined influence of gravity and buoyancy. By integrating convection parameters, skin effect factors and other key variables, the gas convection effect under the influence of gravity and buoyancy is simplified to an equivalent heat conduction term. The body nodes are defined by analyzing the heat transfer mechanism and heat path, forming a structural framework based on thermoelectric analogy for the LPTN model. Then, based on basic physical principles, the model control equations are derived through time domain analysis. The feasibility of the model is verified by comparing the calculation results of the LPTN model with the experimental data of the prototype, and the temperature rise characteristics of GIL are studied at different current levels, providing a theoretical basis and technical support for its heat evaluation and optimization design. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0040] Figure 1 A schematic diagram of the structure and simplified mechanism of the LPTN model according to an embodiment of the present invention;

[0041] Figure 2 This is the analysis and solution process of the LPTN model of the embodiment of the present invention. DETAILED DESCRIPTION

[0042] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0043] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0044] Gas-insulated transmission lines (GIL) have become a powerful alternative to traditional overhead lines and cables in certain situations due to their advantages such as high reliability, low electromagnetic field interference, and large-capacity transmission. The temperature rise during the operation of the transmission line directly affects the reliability, safety, and service life of the system. The growing transmission demand of the power system puts forward higher requirements on the accuracy and efficiency of the GIL temperature rise calculation. Aiming at the problem that it is difficult to balance the accuracy and complexity of the calculation of the GIL temperature rise characteristics, the present invention proposes a lumped-parameter thermal network (LPTN) model based on the electrothermal analogy theory. The model considers the distributed thermal convection of the insulating gas under the influence of gravity and buoyancy. By integrating the convection parameters, skin effect factors, and other key variables, the gas convection effect under the influence of gravity and buoyancy is simplified to an equivalent heat conduction term. The body nodes are defined by analyzing the heat transfer mechanism and the heat path, forming a structural framework based on the thermoelectric analogy of the LPTN model. Then, based on the basic physical principles, the model control equations are derived through time domain analysis. Using the experimental data of the prototype as a reference standard, the error of the temperature rise calculation results of the LPTN model is kept within 10%, which is more accurate than the computational fluid dynamics (CFD) simulation and can save about 3,000 times the calculation time. The results show that the LPTN model proposed in this invention significantly reduces the calculation complexity while ensuring the accuracy of the GIL temperature rise calculation, providing an effective tool for the thermal management of GIL.

[0045] 1 Modeling of lumped parameter thermal network

[0046] 1.1 Thermal network model construction

[0047] From the perspective of system modeling, if two systems are similar in some aspects, they can be modeled by transfer analogy to solve similar problems between different disciplines. By analogy with Fourier's thermal conductivity theorem and Ohm's law, it can be seen that the conduction of heat and electricity are similar. In the heat conduction system, the temperature difference is similar to the voltage difference in the circuit, the heat flow is similar to the current, the thermal resistance is similar to the resistor, and the thermal capacitance is similar to the capacitor. Therefore, it is feasible to simplify the temperature rise study of the GIL heat conduction system by constructing a thermal network model.

[0048] The heat transfer excitation of GIL is introduced: the basic structure of GIL includes conductors, shells, insulators and insulating gases. During the operation of GIL, heat transfer includes three types: contact heat conduction between the conductor part, the shell part and the insulator, convection heat exchange between the conductor and the insulating gas, the shell and the external air, and radiation heat transfer between the conductor surface and the shell surface. In addition to the local temperature rise near the connection area of ​​the two unit structures, the temperature gradient along the axial direction of GIL is generally very small and can be ignored. Therefore, the present invention only considers radial heat transfer in the linear unit. The thickness of the GIL conductor and the shell are very small, so the heat conduction of the conductor part and the shell part is not considered. For different laying methods, the temperature rise characteristics of GIL are different. The present invention considers the temperature rise calculation under horizontal laying. It is assumed that the power transmission system is in a closed environment, there is no wind and no solar radiation, and the external air is naturally convective. The heat transfer analysis of the LPTN model is based on the thermal equilibrium state of GIL. When the GIL is in a thermal equilibrium state, the loss of the conductor is transferred to the shell by radiation and natural convection, and the overall loss of GIL is transferred to the surrounding air by radiation and natural convection. The thermal balance equation is as follows. shown.

[0049] ( )

[0050] In the formula, is the power loss per unit length of the conductor; is the power loss per unit length of the shell, generated by the induced current; and is the convection heat transfer and radiation heat transfer per unit length on the conductor; and It is the convective heat transfer and radiation heat transfer per unit length of the shell.

[0051] In the conceptual design stage of GIL, people often do not pay attention to the temperature distribution of a certain component, but pay more attention to the energy transfer relationship and the maximum and minimum temperature of the entire system and components under a certain operating state. Therefore, it is particularly important to simplify the system and calculate quickly while ensuring the accuracy of the calculation. Based on the above concept, the present invention proposes a LPTN modeling strategy for fast calculation of GIL temperature rise, which aggregates the physical properties of the GIL per unit length to several body nodes to reflect the overall temperature of the object, and forms a thermal network model with the heat transfer path. The heat transfer form is analyzed and the heat transfer process is visualized in the form of thermal resistance and heat capacity. The convection in the gas domain and the radiation between the solids are equivalent to thermal resistance, respectively, the temperature lag of the metal endothermic process is equivalent to heat capacity, and the loss is equivalent to a heat flux source. Its equivalent structure and simplified process are as follows: Figure 1 shown.

[0052] Figure 1(a) is a distributed thermal convection model of GIL, wherein the corresponding distributed thermal convection model is constructed by analyzing the cross-sectional physical structure of the gas-insulated transmission line, and the inner and outer rings respectively represent the conductor structure and the shell structure in the cross-sectional physical structure of the gas-insulated transmission line, and the ring structure and the pore structure between the rings correspond to the equivalent circuit structure in shape, and the mapping relationship between the physical structure and the equivalent circuit structure can be intuitively seen, which can more clearly reflect the location of each temperature node. Due to the influence of gravity, the buoyancy of the insulating gas heat makes the upper temperature of the GIL higher than the lower part as a whole, so the LPTN model established by the present invention is divided into two parts to represent the temperature difference between the upper and lower parts of the GIL. Figure 1 (b) Equivalent structure of GIL temperature rise characteristic modeling, where and Respectively represent the thermal convection resistance of the upper and lower parts of the insulating gas, and Respectively represent the thermal radiation resistance between the upper and lower conductors and the shell, and They represent the thermal convection resistance of the air domain in the upper and lower parts of the shell, and They represent the thermal radiation resistance of the upper and lower parts of the shell to the air domain, is the conductor heat capacity, is the heat capacity of the shell, is the heat capacity of the lower part of the shell, is the conductor loss, is the loss in the upper part of the shell, is the loss in the lower part of the shell, is a constant temperature air domain represented by a constant pressure source.

[0053] According to previous research results, the influence of gas gravity and buoyancy causes the GIL temperature to be unevenly distributed along the gravity direction, resulting in a higher temperature at the top of the shell than at the bottom. The insulating gas domain inside the conductor is smaller, and the influence on the temperature distribution becomes smaller, so the conductor can be regarded as a single temperature node. The direct impact of excessive temperature is the damage of the insulator. If the temperature of the shell top and the conductor is within the allowable range, the attention to the temperature of other parts of the GIL can be reduced. Therefore, Figure 1 The LPTN model in (b) is reduced to the following order: Figure 1 As shown in (c), is the conductor temperature node, is the GIL top case temperature, is the ambient temperature. Figure 1 (a) is the characteristic temperature of the insulating gas domain above the GIL.

[0054] 1.2 Model control equations in time domain analysis

[0055] The loss calculation of GIL is the basis of thermal characteristic modeling, and its loss mainly comes from the Joule loss in the conductor and the eddy current loss in the shell. When a large industrial frequency current is passed through the conductor, the alternating electric field generated by the conductor will cause induced eddy current and circulating current to appear in the shell. In engineering applications, GIL is a fully connected structure, and the circulating current loss is generally very small and can be ignored. However, in actual engineering, the length of GIL is relatively long. In theory, the induced current in the shell is equal to the conductor current in magnitude and opposite in direction. When calculating the Joule loss of the conductor, due to the grounding shielding effect of the shell, the proximity effect coefficient of the conductor is 1, and the impedance is small, so the influence of the unbalanced current can be ignored. The alternating magnetic field generated by alternating current will cause the current to concentrate on the surface of the conductor, which is the skin effect. The skin effect will increase the AC resistance of the conductor and the shell, thereby affecting the transmission efficiency of the line. Therefore, it cannot be ignored. The skin effect coefficient of the conductor and the shell is as shown in the formula shown.

[0056] ( )

[0057] In the formula, is the conductor skin effect coefficient, is the skin effect coefficient of the shell, and are the inner and outer radii of the conductor, and are the inner radius and outer radius of the shell respectively. In practical applications, the DC resistance of metal increases with increasing temperature, as shown in the formula shown.

[0058] ( )

[0059] In the formula, and are the DC resistance of the conductor and shell at operating temperature, and are the conductor and shell ambient temperatures respectively The DC resistance under the condition can be calculated from the reference resistivity. and are the resistivity temperature coefficients of the conductor and the shell, respectively. The AC resistance of the conductor and the shell is the product of the DC resistance and the skin effect coefficient. Therefore, the loss of the shell and the conductor can be expressed by Calculated.

[0060] ( )

[0061] Where I is the effective value of the alternating current passing through the conductor. After clarifying the heat loss of the conductor and the shell, the time-domain state-space equation of the LPTN model can be established by using Kirchhoff's law and migration analogy. The heat of the GIL conductor is transferred to the shell by convection and radiation. The convective heat transfer involves complex non-isothermal flow calculations. If the internal temperature distribution of the GIL is ignored, the characteristic temperature of the insulating gas is the average temperature of the conductor and the shell, and the convection of the concentric tube sandwich can be equivalent to a heat conduction phenomenon to greatly simplify the calculation. Among them, the radiation heat transfer depends on the fourth power of the temperature, and the state differential equation of the LPTN model is derived as follows: shown.

[0062] ( )

[0063] When programming and solving, discrete time is used to calculate the temperature change of the node, and then the change of loss and temperature over time is observed. The finite difference method is used to solve the equation After discretization, we can get the difference equation as follows: shown.

[0064] ( )

[0065] In the formula, i-1 is the previous moment, and i is the current moment. The initial temperature is set according to the ambient temperature. The change in temperature will affect the physical parameters of the material, so the convection thermal resistance Thermal resistance are all functions of temperature. It can be seen that after clarifying the thermal resistance and heat capacity in the heat transfer process, the curve of the temperature change of the conductor and the upper part of the shell over time can be obtained. In the solution process, the convergence condition is 0.02, where is the temperature at the current moment, is the temperature of the previous moment. When the temperature at the current moment is less than the preset temperature convergence threshold of 0.02, it is considered that the convergence condition is met and the iteration process is stopped. Otherwise, the skin effect coefficient is recalculated to calculate the temperature change in the next time step.

[0066] 1.3 Model heat transfer process analysis and theoretical derivation

[0067] The model constructed in this invention is based on the structural parameters of 550 kV GIL, whose conductor material is A6063-T5, inner diameter is 140 mm, thickness is 10 mm, and shell material is A5005-O, inner diameter is 480 mm, thickness is 5 mm. Figure 1From the LPTN model in (c), it can be seen that the calculation of node temperature requires the determination of thermal circuit component parameters. Therefore, the theoretical derivation of LPTN model parameters based on the internal characteristics and structural configuration of GIL is a prerequisite for accurately evaluating the temperature rise.

[0068] (1) Convective heat transfer between conductor and shell

[0069] GIL is a coaxial cylindrical structure. When it is laid horizontally, the convection heat transfer between the conductor and the shell is a typical natural convection heat transfer problem in a limited space. The convection heat transfer between the outer surface of the conductor and the inner surface of the shell is achieved through natural convection of the insulating gas in the GIL. Therefore, the convection heat transfer depends on the physical properties of the insulating gas and the shape and size of the internal space of the GIL. The convection thermal resistance between the conductor and the shell is given by the formula - It can be calculated.

[0070] ( )

[0071] ( )

[0072] ( )

[0073] ( )

[0074] ( )

[0075] Mode middle, is the insulating gas Grashof number, which is used to characterize the ratio of buoyancy to viscous force in natural convection heat transfer. is the acceleration due to gravity, is the insulating gas density, is the dynamic viscosity of the insulating gas. middle, is the insulating gas Prandtl number, is the constant-pressure heat capacity of the insulating gas, is the thermal conductivity of insulating gas. middle, is the equivalent thermal conductivity of convection from conductor to shell. middle, is the convective heat transfer between the conductor and the shell per unit length. As shown, according to Kirchhoff's law, thermal resistance is equal to the ratio of temperature difference to heat transfer. In the effective space, the buoyancy generated by gravity and temperature has a greater impact on the physical properties of the gas. Therefore, in the calculation process, , , and All are temperature related parameters.

[0076] (2) Radiative heat transfer between conductor and shell

[0077] Since the insulating gas between the GIL conductor and the shell is thin and has almost no ability to reflect heat, the radiation heat transfer in the GIL cavity mainly occurs between the outer surface of the conductor and the inner surface of the shell. The radiation heat transfer between the GIL conductor and the shell can be calculated according to the Stefan-Boltzmann law. The radiation thermal resistance between two concentric cylinders of the same length is calculated as follows: - shown.

[0078] ( )

[0079] ( )

[0080] ( )

[0081] Mode middle, is the system equivalent blackness, is the surface blackness of the conductor and the shell, both are taken as 0.8. middle, is the radiation heat transfer between the conductor and the shell per unit length, is the blackbody radiation coefficient, take . By formula It can be seen that when the material and shape of the GIL are determined, the radiation thermal resistance is a constant during operation.

[0082] (3) Convective heat transfer between the shell and the external environment

[0083] Considering the environment without wind and solar radiation, the convection heat transfer between the shell and the air belongs to the natural convection heat transfer in a large space, and the flow of the surrounding thermal boundary layer is unimpeded. The heat transfer can be calculated by the Newton cooling formula, as shown in the formula - shown.

[0084] ( )

[0085] ( )

[0086] ( )

[0087] ( )

[0088] ( )

[0089] ( )

[0090] Mode middle, is the volume expansion coefficient of air. middle, is the Grashof number of air, is the dynamic viscosity of air. middle, is the Nusselt number of air. middle, is the natural convection heat transfer coefficient, is the thermal conductivity of air, which characterizes the heat transfer capacity between the fluid and the solid surface. middle, is the convective heat transfer between the shell and the air per unit length. Similar to the convective heat transfer between the conductor and the shell, the physical parameters of the air are and It is also a temperature-dependent parameter. It can be seen that the convection thermal resistance between the shell and the external environment is determined by the physical properties of the air and the outer radius of the shell.

[0091] (4) Heat exchange between the shell and the outside world

[0092] The radiation of the GIL shell to the surrounding air can be equivalent to the radiation heat dissipation of the long cylinder to the outside. For a horizontally laid single-phase GIL, the shell radiation thermal resistance is calculated as follows: and shown.

[0093] ( )

[0094] ( )

[0095] Mode middle, is the radiation heat transfer per unit length of the shell. It can be seen that the radiation thermal resistance of the shell depends on its material and radius.

[0096] (5) Heat capacity of conductor and shell

[0097] By analogy with the calculation formula of current in Kirchhoff's law, the calculation formula of heat capacity of conductor and shell can be obtained as follows: shown.

[0098] ( )

[0099] In the formula is the volume of the conductor and shell per unit length, is the density, is the constant pressure heat capacity. Within the GIL temperature range, the density and constant pressure heat capacity of the aluminum alloy material change very little, so it is considered to be a constant value. The material parameters involved in the above solution process are shown in Table 1, which is the basic parameters of the model material (293 K).

[0100] Table 1

[0101]

[0102] Table 1 only shows the physical parameters required for the solution process, among which the thermal conductivity, constant pressure heat capacity, dynamic viscosity and density of the gas are all functions of temperature. Combining the LPTN model constructed in Section 2.1, the model control equations in Section 2.2 and the heat transfer calculation process in this section, the model is solved using the ODE solver. The analysis and calculation process is as follows: Figure 2 shown.

[0103] 2 Verification of lumped parameter thermal network model based on numerical simulation

[0104] In this section, the finite element method will be used to solve the temperature field distribution of GIL, and an electric-magnetic-thermal-fluid multi-field coupling model will be established for the 550kV single-phase GIL. Under experimental conditions, the accuracy of the LPTN model in calculating the temperature rise of GIL will be verified under current loads of 2600A, 4400A and 5600A respectively.

[0105] 2.1 Numerical simulation theory and CFD simulation calculation

[0106] Numerical simulation involves multidisciplinary cross-coupling, and has strict requirements on boundary conditions. The accuracy of the calculation results is highly dependent on the setting of initial conditions and boundary conditions. The finite element method is used to establish the GIL multi-field coupling model. The boundary conditions and initial conditions are consistent with the experimental conditions. The initial temperatures corresponding to 2600A, 4400A and 5600A are 299K, 289K and 297K respectively. The radius of the external air domain is set to 1m. The accuracy of the LPTN model proposed in this invention is verified by comparing the experimental results, finite element simulation results and thermal network model calculation results.

[0107] The assumptions for establishing the finite element model are the same as those for the LPTN model in Section 1. Starting from the Maxwell equations, the vector magnetic potential is introduced to solve the electromagnetic field distribution in the entire model area, and the eddy current field control equation is established as follows: and shown.

[0108] ( )

[0109] ( )

[0110] In the formula, is the magnetic permeability, which is a constant of 1 for both the conductor and the shell; is the vector magnetic potential; is the angular frequency; is the conductivity; is the source current density, represents the Hamiltonian operator.

[0111] Considering the change of conductivity with temperature, the loss per unit length of the conductor and the shell is Calculate as and shown.

[0112] ( )

[0113] ( )

[0114] In the formula, is the element area per unit length; and are the current density and conjugate current density, respectively; is the conductivity of the material at absolute temperature T, is the material conductivity at 293K, The finite element modeling of the present invention adopts a two-dimensional model for temperature verification, so the axial heat conduction of the GIL is not considered, but the radial heat conduction needs to be considered. The heat conduction control equation is as follows: shown.

[0115] ( )

[0116] In the formula, , , are the nominal density, constant pressure heat capacity and thermal conductivity of the shell conductive material respectively. For the thermal convection of the gas part, the present invention does not consider the ventilation conditions, so the laminar flow model is used to simulate the natural convection of the gas. Considering the coupling relationship between the flow field and the temperature field, the thermal convection needs to consider the three control equations of mass conservation, momentum conservation and energy conservation, as shown in the formula shown.

[0117] ( )

[0118] in, is the gas density; is the gas flow rate; is the gas dynamic viscosity; is the thermal conductivity of gas; is the generalized source term. It should be noted that the gas pressure inside the shell is different from the external air pressure, and its laminar model needs to be expressed separately. The finite element calculation also does not consider gas radiation, so the radiation heat transfer calculation between the conductor and the shell is the same as The radiation heat transfer calculation between the shell and the air is consistent with Consistent.

[0119] After clarifying the finite element calculation theory, a two-dimensional model of GIL is established and meshed. For the GIL temperature rise calculation, the magnetic field-temperature field and the flow field-temperature field are both bidirectionally coupled, that is, the electromagnetic field excitation causes the GIL temperature to rise, and the material properties change due to the influence of temperature, which further affects the loss calculation and heat flow transfer.

[0120] After determining the initial conditions and building the geometric model, the steady-state temperature field can be solved and compared and verified using relevant experimental results as reference values.

[0121] Taking 5600 A current at 297 K as an example, the magnetic flux density is the largest at the GIL conductor, and gradually decreases between the conductor and the shell, and drops to almost 0 outside the shell, which proves that the shell has a good electromagnetic shielding effect and can effectively reduce the electromagnetic interference of the GIL system.

[0122] The current distribution of GIL is related to the transmission loss. Affected by electromagnetic induction, the conductor and the shell will induce eddy currents under large currents or high frequencies, resulting in skin effect. The conductor current is concentrated on the outer surface, and the shell induced current is concentrated on the inner surface. In addition, there is no external current in the shell, and the current flowing through the conductor generates electromagnetic induction, which causes the shell to induce induced currents of equal magnitude and opposite directions. The corresponding loss can be calculated by obtaining the current density, and then the steady-state thermal flow coupling field under the initial temperature of 297 K and the current of 5600 A is solved to obtain the flow rate and temperature distribution diagram of the insulating gas in the GIL shell.

[0123] In the diagram of the flow rate and temperature distribution of the insulating gas in the GIL shell, the gas flow rate is small around the outer wall of the conductor and directly above it, the gas flow rate is the largest at the horizontal center close to the inner wall of the shell, and the gas flow rate in the rest of the part is almost 0. This is because the heat generated by the conductor makes the density of the upper gas lower and generates buoyancy to flow upward, and the rest of the gas flows downward along the inner wall of the shell due to gravity, thus forming natural convection. The temperature field shows obvious axisymmetric distribution characteristics. The maximum temperature value of the GIL is 352.30 K, located directly above the conductor, and the minimum temperature value is 325.59 K, located directly below the shell, which further verifies that the thermal convection of the insulating gas inside the GIL forms a radial temperature gradient, and the temperature of the upper part is significantly higher than that of the lower part.

[0124] 2.2 Analysis of LPTN model verification results

[0125] The relevant experimental initial conditions are used as the input of the LPTN model, and the experimental results are used as reference values ​​to compare the accuracy of the LPTN model calculation results and CFD simulation results. In order to more intuitively observe the GIL temperature rise process, the solution time is set to 26000s, and the finite volume method (FVM) is used to solve the transient thermal fluid field. The ODE solver is used to solve the equation Solve the state equation shown.

[0126] The loss calculation of GIL is the core of the temperature rise solution and verification of the entire system. In the system loss when the temperature tends to be stable, the loss calculation results of the LPTN model are almost equal to the CFD simulation results, with a deviation of no more than 1.10%, indicating that the LPTN model can accurately characterize the current distribution and ohmic loss of GIL.

[0127] During the temperature rise of GIL under load currents of 2600 A, 4400 A and 5600 A, the temperature rise of the LPTN model and CFD simulation has stabilized, proving that 26000 s is enough for the temperature of the GIL to reach a stable state. From the temperature rise process, it can be seen that compared with the CFD simulation of the GIL temperature rise process, the LPTN model can track the temperature change of the GIL more accurately, and the temperature in the stable state is close to the experimental value. In the initial stage, the temperature rise curve of the CFD simulation fluctuates slightly. This is due to the poor convergence effect of the finite element simulation under multi-field coupling. It can also be observed from the simulation process that the convergence time of the temperature rise calculation under the CFD simulation is about 200 s, while the LPTN model is a finite difference calculation and there is no convergence problem. During the whole simulation process, the conductor temperature calculated by the LPTN model was higher than that of the CFD simulation, while the shell temperature was lower than that of the CFD simulation. One possible reason is that the LPTN only uses equivalent thermal resistance to represent the heat dissipation, while the heat dissipation of the insulating gas under CFD simulation is more ideal and comprehensive, which can better dissipate the temperature of the conductor in the form of heat flow, making the conductor temperature lower than that of the LPTN model calculation result and the shell temperature higher than that of the LPTN calculation result.

[0128] In order to more intuitively show the comparison of GIL temperature and its error under different calculation methods, the temperature rise values ​​of GIL conductor and shell under experimental conditions are used as reference, and the steady-state temperature rise values ​​under LPTN model and CFD simulation calculation are quantitatively analyzed to verify the adaptability of LPTN model at different initial temperatures. The GIL temperature and its relative error under different current levels are shown in Table 2. Table 2 shows the temperature rise results and errors of the three methods under different current levels.

[0129] Table 2

[0130]

[0131] As can be seen from Table 2, under the three current levels, the LPTN model calculated the conductor temperature rise results of 14.96 K, 38.24 K and 58.77 K, respectively, which differed from the experimental values ​​by 0.04 K, 2.76 K and 1.23 K, respectively, with a maximum error of 6.73%, while the maximum error of CFD simulation was 12.05%. Under the three current levels, the LPTN model calculated the shell temperature rise results of 7.35 K, 19.26 K and 29.96 K, respectively, which differed from the experimental values ​​by 0.65 K, 1.74 K and 2.04 K, respectively, with a maximum error of 8.29%, while the maximum error of CFD simulation was 9.38%. Under the three current levels, the maximum prediction error of the LPTN model was 8.29%, which differed from the experimental value by only 1.74 K, indicating the adaptability of the LPTN model to the prediction of GIL temperature at different initial temperatures. In addition, compared with similar literature, under the same error calculation method, the maximum prediction error of the thermal network model established in the prior art is 12.81%, that is, the difference with the experimental value is 4.1 K under a load current of 5600 A, indicating that the LPTN model established in the present invention has certain prediction advantages.

[0132] In general, the temperature prediction error of the LPTN model for conductors is generally lower than that of the CFD simulation results, and the temperature prediction error for the shell is not much different from the CFD simulation results. Running time is also an important indicator for evaluating thermal network models and CFD simulation calculations. In the early verification and later operation and maintenance of GIL, improving computing efficiency and saving computing resources are crucial for the state estimation of GIL. Under the same computer configuration, the average time required for LPTN model calculation is 0.65s, while the average time required for CFD simulation under multi-field coupling is 1290s, saving about three thousand times the computing time. It can be seen that the LPTN model provided by the present invention has great reference value in the rapid temperature rise calculation in the GIL verification stage.

[0133] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application 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 method for rapid calculation of GIL temperature rise based on a lumped parameter thermal network model, characterized in that: include: Based on the gas-insulated transmission line, a lumped parameter thermal network model is constructed; The lumped parameter thermal network model is a model of a circuit analogous to the heat transfer process in a gas-insulated transmission line; Constructing a model control equation of the lumped parameter thermal network model, wherein the model control equation is used to perform iterative temperature rise calculation on the gas-insulated transmission line; Initial parameters of the gas-insulated transmission line are obtained, wherein the initial parameters include geometric parameters, electromagnetic parameters and thermal parameters, and the initial parameters are iteratively calculated through the model control equation to obtain the temperature rise calculation result of the gas-insulated transmission line.

2. The method according to claim 1, characterized in that The construction process of the lumped parameter thermal network model includes: The basic structure of the gas-insulated transmission line is obtained, the physical properties in the basic structure are converted to the body nodes of the cross section, and the heat transfer path on the body nodes is obtained, the heat transfer path is visualized through thermal resistance, heat capacity and heat flux source to obtain a visualized structure, the visualized structure is equivalent and reduced to obtain a lumped parameter thermal network model; wherein the convection in the gas domain and the radiation between the solids are equivalent to thermal resistance, the temperature hysteresis of the metal endothermic process is equivalent to heat capacity, and the loss is equivalent to a heat flux source.

3. The method according to claim 1, characterized in that The model control equations include: a calculation equation for the skin effect coefficient of the conductor and the shell in the gas-insulated transmission line, a calculation equation for the DC resistance of the conductor and the shell at the operating temperature, a calculation equation for the loss of the shell and the conductor, and a differential equation for the lumped parameter thermal network model.

4. The method according to claim 3, characterized in that The process of iteratively calculating the initial parameters through the model control equation includes: The initial parameters are calculated by the skin effect coefficient calculation equation to obtain the skin effect coefficients of the conductor and the shell; According to the skin effect coefficient and initial parameters of the conductor and the shell, the DC resistance of the conductor and the shell at the operating temperature is calculated by the DC resistance calculation equation; According to the DC resistance and skin effect coefficient of the conductor and shell at the operating temperature, the loss of the shell and conductor is obtained through the loss calculation equation; According to the losses of the shell and the conductor, the node temperature information of the conductor and the shell at the next moment is calculated by the differential equation of the lumped parameter thermal network model; The above calculation process is repeated according to the node temperature information of the conductor and the shell at the next moment to obtain the temperature rise calculation result of the gas-insulated transmission line.

5. The method according to claim 4, characterized in that The calculation equation of the skin effect coefficient is: in, is the conductor skin effect coefficient, is the skin effect coefficient of the shell, and are the inner and outer radii of the conductor respectively, and are the inner radius and outer radius of the shell respectively.

6. The method according to claim 4, characterized in that The DC resistance calculation equation is: in, and are the DC resistance of the conductor and shell at operating temperature, and are the conductor and shell ambient temperatures respectively The DC resistance under , is calculated from the reference resistivity, and are the resistivity temperature coefficients of the conductor and shell, respectively.

7. The method according to claim 4, characterized in that The loss calculation equation is: Where I is the effective value of the alternating current flowing through the conductor.

8. The method according to claim 4, characterized in that The difference equation of the lumped parameter thermal network model is: Among them, i-1 is the previous moment, i is the current moment, is the conductor temperature node, is the characteristic temperature of the insulating gas domain above the GIL, is the GIL top case temperature, is the ambient temperature, is the conductor heat capacity, is the heat capacity of the shell, is the conductor loss, is the loss in the upper part of the shell, represents the thermal convection resistance of the upper part of the insulating gas, It represents the heat radiation resistance between the upper conductor and the shell. represents the thermal convection resistance of the air domain above the shell, Represents the thermal radiation resistance of the upper part of the shell to the air domain.

9. The method according to claim 8, characterized in that Before calculating the node temperature information of the conductor and the shell at the next moment, it also includes: The calculation parameters include: convection thermal resistance between the conductor and the shell, radiation thermal resistance between the conductor and the shell, convection thermal resistance between the shell and the external environment, radiation heat transfer between the shell and the outside world, and heat capacity between the conductor and the shell; and the differential equation of the lumped parameter thermal network model is calculated by the calculation parameters.

10. The method according to claim 1, characterized in that After obtaining the initial parameters of the gas-insulated transmission line, it includes: The multi-field coupling modeling of the gas-insulated transmission line is performed by using the finite element method to obtain a multi-field coupling model, and the gas-insulated transmission line is simulated by using the multi-field coupling model.

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