阅读说明：本技术 一种用于电缆热循环试验加热电流的计算方法 (Calculation method for heating current of cable thermal cycle test ) 是由 李红雷 马爱清 张杨欢 于 2020-11-13 设计创作，主要内容包括：本发明涉及一种用于电缆热循环试验加热电流的计算方法,包括步骤：获取电缆分布参数热路模型,根据电缆分布参数热路模型获取电缆本体热阻、周围环境热阻、导体损耗和绝缘损耗；对电缆分布参数模型建立电缆集中参数热路模型,获取电缆绝缘层和电缆外护层热容的比例因数；对电缆集中参数热路模型进行简化处理,建立节点热流平衡方程；对建立的节点热流平衡方程进行导体温度限定,获取电缆导体加热电流随时间变化的函数,所述电缆导体加热电流为电缆热循环试验加热电流。与现有技术相比,本发明具有准确、快速确定导体加热电流,减少试验周期以降低试验成本等优点。(The invention relates to a method for calculating heating current for a cable thermal cycle test, which comprises the following steps: acquiring a cable distribution parameter thermal circuit model, and acquiring cable body thermal resistance, ambient environment thermal resistance, conductor loss and insulation loss according to the cable distribution parameter thermal circuit model; establishing a cable centralized parameter heat path model for the cable distribution parameter model, and acquiring a proportional factor of heat capacities of a cable insulating layer and a cable outer protective layer; simplifying a cable centralized parameter heat path model, and establishing a node heat flow balance equation; and limiting the conductor temperature of the established node heat flow balance equation, and obtaining a function of the heating current of the cable conductor along with the change of time, wherein the heating current of the cable conductor is the heating current of the cable thermal cycle test. Compared with the prior art, the method has the advantages of accurately and quickly determining the heating current of the conductor, reducing the test period to reduce the test cost and the like.)

1. A method for calculating heating current for a cable thermal cycle test is characterized by comprising the following steps:

establishing a cable distribution parameter thermal circuit model, and acquiring cable insulation layer thermal resistance, cable outer protective layer thermal resistance, ambient environment thermal resistance, conductor loss and insulation loss according to the cable distribution parameter thermal circuit model;

establishing a cable centralized parameter heat circuit model for the cable distribution parameter model, and acquiring a proportional factor of the heat capacity of the cable insulating layer and the heat capacity of the cable outer protective layer;

simplifying a cable centralized parameter heat path model, and establishing a node heat flow balance equation;

and limiting the conductor temperature of the established node heat flow balance equation, and obtaining a function of the heating current of the cable conductor along with the change of time, wherein the heating current of the cable conductor is the heating current of the cable thermal cycle test.

2. The method for calculating the heating current for the cable thermal cycle test according to claim 1, wherein the specific contents for establishing the cable distribution parameter thermal circuit model are as follows:

and the heat exchange is carried out on the conductor loss and the insulation loss generated by the cable along the radial path of the cable through the cable insulation layer, the cable metal sheath layer and the cable outer protection layer with the external environment.

3. The method for calculating the heating current for the cable thermal cycle test according to claim 2, wherein the specific contents of the cable body thermal resistance and the ambient thermal resistance are obtained as follows:

the method comprises the following steps of obtaining the outer diameters of a cable conductor layer, a cable insulating layer, a cable metal sheath layer or a cable outer sheath layer and the surface temperature of the cable above the environmental temperature, and calculating the thermal resistance of the cable insulating layer, the thermal resistance of the cable outer sheath layer and the thermal resistance of the surrounding environment according to a cable distribution parameter thermal path model, wherein the calculation formulas of the thermal resistance of the cable insulating layer and the thermal resistance of the cable outer sheath layer are as follows:

the ambient thermal resistance T₃The calculation formula of (2) is as follows:

where ρ is the thermal resistivity of the cable material and D_eIs the outer diameter of the cable, h is the heat dissipation coefficient, Delta theta_sTo a surface temperature of the cable above ambient temperature, d_out、d_inRespectively the outer diameter and the inner diameter of the cable insulation layer or the cable outer sheath.

4. Method for calculating a heating current for a cable thermal cycle test according to claim 1, characterized in that said conductor loss W_cThe calculation formula of (A) is as follows:

W_c＝I²R_ac

in which I is the conductor current and R_acIs the ac resistance per unit length of the conductor.

5. Method for calculating a heating current for a cable thermal cycle test according to claim 1, characterized in that said insulation loss W_dThe calculation formula of (A) is as follows:

where ω is 2 π f, f is the system frequency, c is the unit length cable capacitance, U₀For voltage to ground, tan δ is the insulation loss factor.

6. The method for calculating the heating current for the cable thermal cycle test according to claim 1, wherein the specific contents of the cable lumped parameter thermal circuit model established for the cable distribution parameter model are as follows:

the heat capacity of the cable insulation layer and the heat capacity of the cable outer sheath are applied to the heat capacity of the conductor and the heat capacity of the cable metal sheath layer by the distribution factors p and p'.

7. The method for calculating the heating current for the cable thermal cycle test according to claim 6, wherein the calculation formula of the proportional factor p of the heat capacity of the cable insulation layer and the proportional factor p' of the heat capacity of the cable outer sheath after distribution is as follows:

in the formula: d_i、D_e、D_s、d_cThe diameter of the cable insulation layer, the outer diameter of the cable outer sheath, the inner diameter of the cable outer sheath and the diameter of the cable conductor are respectively.

8. The method for calculating the heating current for the cable thermal cycle test according to claim 1, wherein the simplified processing is performed on the cable lumped parameter thermal circuit model by Thevenin's theorem.

9. The method for calculating the heating current for the cable thermal cycle test according to claim 8, wherein the expression of the node heat flow balance equation is as follows:

in the formula, Q_cFor simplified equivalent heat flow, C is simplified equivalent heat capacity, R is simplified equivalent heat resistance, theta_cIs the conductor temperature of the cable, theta₀Is the outside ambient temperature.

10. The method of claim 1, wherein the function of the cable conductor heating current as a function of time is expressed as:

in the formula, theta_CIs the conductor temperature of the cable, theta₀Is the external ambient temperature, W_dFor insulation loss, R is equivalent thermal resistance after simplification, and C isSimplified equivalent heat capacity, R_acIs a conductor AC resistance.

Technical Field

The invention relates to the technical field of cable delivery tests, in particular to a method for calculating heating current for a cable thermal cycle test.

Background

With the continuous increase of the power load, the extra-high voltage large-section long-distance power transmission project will enter various big cities in the future, and once the extra-high voltage cable fails, economic loss and even major accidents which are difficult to estimate are caused. The cable therefore requires rigorous factory testing before installation and commissioning. The cable thermal cycle test belongs to the most critical loop of a cable type test and a pre-identification test, wherein the pre-identification test requires that the thermal cycle test time is 8760h, and the test is cycled for at least 180 times. The test takes a long time, has many influencing factors and consumes a lot of energy. The thermal cycle test is generally carried out according to IEC 62067:2011 or the national standard GB/T22078-. The cable thermal cycle test adopts a conductor through-flow heating mode, the heating time is at least 8 hours, the temperature of the conductor is 5-10 ℃ higher than that of the conductor in normal operation, and the conductor is heated to the specified temperature and is kept for 2 hours; then naturally cooling for at least 16 hours. Because the environmental temperature changes constantly during the test, need constantly to adjust heating current control conductor temperature at the temperature range of regulation. Accurate and fast determination of the heating current is therefore a very important step. However, in the current test, the conductor is heated by inducing short-circuit current through a plurality of parallel feed-through transformers, the heating power is difficult to control, the test period is prolonged, and the test cost and the load of test equipment are increased. In addition, in the analysis calculation, the dielectric loss is mostly ignored in the prior art and research, and the dielectric loss of the ultra-high voltage cable is not negligible; and environmental temperature change is not considered, the calculation result is conservative, and the accuracy is not high.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provide a method for calculating the heating current of the cable thermal cycle test, which can accurately and quickly determine the heating current of a conductor, effectively reduce the test period, reduce the test cost and improve the calculation accuracy of the heating current of the conductor of the thermal cycle test.

The purpose of the invention can be realized by the following technical scheme:

a method for calculating heating current for a cable thermal cycle test comprises the following steps:

establishing a cable distribution parameter thermal circuit model, and acquiring cable insulation layer thermal resistance, cable outer protective layer thermal resistance, ambient environment thermal resistance, conductor loss and insulation loss according to the cable distribution parameter thermal circuit model;

establishing a cable centralized parameter heat circuit model for the cable distribution parameter model, and acquiring a proportional factor of the heat capacity of the cable insulating layer and the heat capacity of the cable outer protective layer;

simplifying a cable centralized parameter heat path model, and establishing a node heat flow balance equation;

and limiting the conductor temperature of the established node heat flow balance equation, and obtaining a function of the heating current of the cable conductor along with the change of time, wherein the heating current of the cable conductor is the heating current of the cable thermal cycle test.

The specific contents of establishing the cable distribution parameter hot circuit model are as follows:

and the heat exchange is carried out on the conductor loss and the insulation loss generated by the cable along the radial path of the cable through the cable insulation layer, the cable metal sheath layer and the cable outer protection layer with the external environment.

The specific contents of obtaining the thermal resistance of the cable body and the thermal resistance of the surrounding environment are as follows:

the method comprises the following steps of obtaining the outer diameter of each layer of the cable and the surface temperature of the cable which exceeds the environmental temperature, calculating the thermal resistance of a cable insulating layer, the thermal resistance of a cable outer protective layer and the thermal resistance of the surrounding environment according to a cable distribution parameter thermal circuit model, wherein the calculation formulas of the thermal resistance of the cable insulating layer and the thermal resistance of the cable outer protective layer are as follows:

the ambient thermal resistance T₃The calculation formula of (2) is as follows:

where ρ is the thermal resistivity of the cable material and D_eIs the outer diameter of the cable, h is the heat dissipation coefficient, Delta theta_sTo a surface temperature of the cable above ambient temperature, d_out、d_inRespectively being cable insulationOr the outer and inner diameters of the outer cable jacket.

The conductor loss W_cThe calculation formula of (A) is as follows:

W_c＝I²R_ac

in which I is the conductor current and R_acIs the ac resistance per unit length of the conductor.

The insulation loss W_dThe calculation formula of (A) is as follows:

where ω is 2 π f, f is the system frequency, c is the unit length cable capacitance, U₀For voltage to ground, tan δ is the insulation loss factor.

The specific contents of establishing the cable centralized parameter hot-circuit model for the cable distribution parameter model are as follows:

the heat capacity of the cable insulation layer and the heat capacity of the cable outer sheath are applied to the heat capacity of the conductor and the heat capacity of the cable metal sheath layer by the distribution factors p and p'.

The calculation formula of the proportional factor p of the heat capacity of the cable insulating layer and the proportional factor p' of the heat capacity of the cable outer protective layer after distribution is as follows:

in the formula: d_i、D_e、D_s、d_cThe diameter of the cable insulation layer, the outer diameter of the cable outer sheath, the inner diameter of the cable outer sheath and the diameter of the cable conductor are respectively.

And further, simplifying the cable lumped parameter thermal circuit model by adopting thevenin theorem to obtain a node heat flow balance equation. The expression of the node heat flow balance equation is as follows:

in the formula, Q_cFor simplified equivalent heat flow, C is simplified equivalent heat capacity, R is simplified equivalent heat resistance, theta_cIs the conductor temperature of the cable, theta₀Is the outside ambient temperature.

The expression of the function of the cable conductor heating current along with the change of time is as follows:

in the formula, theta_CIs the conductor temperature of the cable, theta₀Is the external ambient temperature, W_dFor insulation loss, C is the equivalent heat capacity after simplification, R is the equivalent heat resistance after simplification, R is_acIs a conductor AC resistance.

Compared with the prior art, the method for calculating the heating current for the cable thermal cycle test provided by the invention at least has the following beneficial effects:

1) the invention takes the medium loss of the ultra-high voltage cable and the change of the environmental temperature into consideration to obtain the heating current of the conductor in the thermal cycle test, and can accurately and quickly determine the heating current of the conductor.

2) If the temperature meteorological data of the test base is available, the heating current value of the cable conductor with similar meteorological temperature in months can be estimated by the method, so that the test period can be greatly reduced, the test cost can be reduced, and the accuracy of the heating current calculation of the thermal cycle test conductor can be improved.

Drawings

FIG. 1 is a schematic structural diagram of a cable distribution parameter thermal circuit model in an embodiment;

FIG. 2 is a schematic structural diagram of a cable lumped parameter thermal circuit model in an embodiment;

FIG. 3 is a schematic structural diagram of a simplified model of a cable thermal circuit in an embodiment;

FIG. 4 is a graph showing a curve fitted to the change in temperature and time of a certain day according to the embodiment;

FIG. 5 is a graph of the thermal cycling heating current versus time for the example;

FIG. 6 is the internal temperature field of the cable of the simulation result in the embodiment, wherein FIG. 6a) is the temperature field at 6 hours, and FIG. 6b) is the temperature field at 8 hours;

FIG. 7 is a schematic flow chart of a method for calculating a heating current for a cable thermal cycle test according to an embodiment.

Detailed Description

The invention is described in detail below with reference to the figures and specific embodiments. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, shall fall within the scope of protection of the present invention.

Examples

The invention relates to a method for calculating heating current for a cable thermal cycle test, which takes medium loss W of an extra-high voltage cable into consideration_dAnd ambient temperature theta₀The variation calculates the heating current for the cable thermal cycling test. The method comprises the following steps:

the method comprises the steps of firstly, obtaining a cable distribution parameter thermal circuit model, and obtaining the thermal resistance of a cable body, the thermal resistance of the surrounding environment, conductor loss and insulation loss according to the cable distribution parameter thermal circuit model.

And secondly, establishing a cable centralized parameter heat circuit model for the cable distribution parameter model to obtain a proportional factor of the heat capacities of the cable insulating layer and the cable outer protective layer.

And step three, simplifying the cable centralized parameter heat circuit model and establishing a node heat flow balance equation.

And step four, conducting conductor temperature limitation on the established node heat flow balance equation, and obtaining a function of the change of the heating current of the cable conductor along with time, wherein the heating current of the cable conductor is the heating current of the cable thermal cycle test.

The specific contents are as follows:

according to the IEC 60853-2 standard, the cable reaches a steady-state temperature after a certain period of time after the cable is supplied with current due to the presence of internal heat capacity. The cable is a concentric cylinder structure, and heat flow generated by loss can be diffused only through heat resistance and heat capacity of each layer. Super highThe voltage cable grounding mode is a cross interconnection grounding mode, and the metal sleeve loss can be ignored. When the cable is laid in the air, only the thermal resistance of the surrounding environment is considered, and the thermal capacity is ignored. The cable distribution parameter hot-path model is shown in fig. 1. As can be seen from fig. 1: loss W generated by cable_c、W_dAnd the heat exchange is carried out with the external environment through the insulating layer, the metal sheath layer and the outer protective layer along the radial direction of the cable.

In fig. 1: theta_c、θ₀Is the conductor temperature and the external ambient temperature (deg.C). Q_c、Q_i、Q_s、Q_jRespectively, the heat capacity of conductor, insulating layer, metal sheath layer and outer sheath layer^-1·m^-1). The heat capacity calculation formula is as follows:

in the formula (1), d_out、d_inThe outer diameter and the inner diameter (mm) of the conductor layer, the insulating layer, the metal sheath layer or the outer protective layer, and C is the volume specific heat capacity (J.m)^-3·K^-1)。

T₁、T₂、T₃Respectively thermal insulation layer, outer protective layer and external environment^-1) Metal is a good thermal conductor and the thermal resistance is negligible. The cable body thermal resistance and the ambient thermal resistance are given by IEC 60287 calculation formulas (2) and (3):

equation (2) is the thermal resistance T of the insulating layer₁Thermal resistance T of outer protective layer₂The calculation formula of (2). In the formula: d_out、d_inIs the outer diameter and the inner diameter of the insulating layer and the outer protective layer, rho is the thermal resistance coefficient of the cable material, (K.m.W)^-1)，D_eOuter diameter of cable, h heat dissipation coefficient, Delta theta_sOver a cable surface temperature (K) above ambient temperature.

W_c、W_dFor conductor loss and insulation loss, they are given by equations (4), (5), respectively:

W_c＝I²R_ac (4)

in the formula: i is the conductor current (A), R_acAc resistance per unit length of conductor (omega. m)^-1). ω is power system angular frequency, ω is 2 pi F, F is system frequency (50Hz), c is unit length cable capacitance (F · m)^-1)，U₀Tan δ is the insulation loss factor for voltage (V) to ground.

The parameters in FIG. 1 are all distribution parameters and cannot be used to solve for conductor temperature θ_cIt is converted into lumped parameters by the following principle: the heat capacity of the metal part is a centralized parameter of an actual position in the cable, and the heat capacity of the non-metal material is distributed to two sides through a distribution factor. The cable lumped parameter hot-circuit model is shown in fig. 2. As can be seen from fig. 2: the insulation layer heat capacity and the outer sheath heat capacity are imposed on the conductor heat capacity and the metal sheath heat capacity by the division factors p, p'.

R in FIG. 2_i(i＝1,2,3)、C_i(i ═ 1,2,3) for lumped parameter thermal resistance and capacity, q_sTo account for the ratio of the metal sheath losses, q is grounded due to the cable cross-connect_s1. p, p' are the proportional factors of the heat capacities of the distributed insulating layer and the outer protective layer, and are given by the formula (6):

in the formula: d_i、D_e、D_s、d_cThe diameter of the insulating layer of the cable, the outer diameter of the outer sheath of the cable, the inner diameter of the outer sheath of the cable and the diameter of the conductor of the cable are respectively.

The temperature of the cable conductor cannot be quickly obtained from fig. 2, and the simplification of fig. 2 into a first-order RC circuit is carried out by thevenin's theorem in circuit theory, as shown in fig. 3. Simplified equivalent heat flow Q_cThe thermal resistance R and the thermal capacity C are given by the equations (7), (8), (9).

Q_c＝W_c+W_d (7)

R＝R₁+R₂+R₃ (8)

The heat flow balance equation of the node is established from fig. 3 as follows:

according to the initial condition t being 0, theta_c＝θ₀The equation can be solved as:

θ_C＝θ₀+Q_CR(1-e^-t/RC) (11)

due to the external ambient temperature θ₀The method is changed seasonally, the thermal cycle test is carried out by heating conductor current to a specified temperature range, the specified temperature range is set by the highest operation temperature of the material used by the cable, the temperature capable of bearing reheating can be increased on the basis of the highest operation temperature, the performance is not influenced, and the method is not repeated (for example, the highest operation temperature of the crosslinked polyethylene cable is 90 ℃, the conductor temperature is limited to 95 ℃) so that the heating current of the conductor of the cable can be reversely deduced according to the change rule of the environmental temperature, the cable loss principle and the conductor temperature range limited by the thermal cycle test. The conductor current is given by equation (12):

in the formula: r is the equivalent thermal resistance (K.m.W) of FIG. 3^-1) And C is the equivalent heat capacity (J.K) of FIG. 3^-1·m^-1)，R_acAc resistance per unit length of conductor (omega. m)^-1)。

This example uses YJLW 02290/500 kV 1X 2500mm²The power cable is subjected to thermal cycle conductor current calculation verification. The cable construction and the calculation data of the parameters of the materials used are shown in table 1.

TABLE 1 Cable construction and Material parameter calculation data used

Corresponding to the parameters in equation (12), R can be found to be 1.03K · m · W^-1、C＝22163J·K^-1·m^-1Therefore, the time constant τ is RC 22828s is 6.3 h. The most critical issue is the ambient temperature θ₀How to deal with the problem is to adjust the heating current according to the change of the ambient temperature. Taking the thermal cycling heating phase test in one day as an example, the heating conductor temperature is limited to 90 ℃. If the cable is heated in a through-flow mode at 7 a.m., the heating stage is 7-13 a.13 a.c. conductor temperature is 90 ℃; and the temperature is maintained at 90 ℃ for 13-15 hours. The outdoor ambient temperature at 7-15 hours a day is shown in Table 2. And (3) carrying out Fourier function fitting processing on the measured temperature data, wherein an external environment temperature expression after fitting is given by a formula (13), and an actual temperature and fitting temperature curve is shown in figure 4.

θ₀＝21.58-6.688cos(0.491·t)+0.7366sin(0.491·t) (13)

TABLE 2 temperature data of a day

Substituting the above data into equation (12) can obtain the thermal cycle conductor heating current:

the temperature required for the thermal cycle test at 6 was 90 ℃ and a current of 2983A was obtained. The temperature of the conductor is kept at 90 ℃ within 6-8 hours, and the current of the conductor applied at the corresponding moment is shown in Table 3. The heating current is shown in fig. 5 throughout the thermal cycle.

Conductor current in 36-8 hours of table

t/h	6	6.2	6.4	6.6	6.8	7	7.2	7.4	7.6	7.8	8
												I/A	2983	2952	2924	2900	2879	2860	2844	2831	2820	2810	2803

As can be seen from FIG. 5, the cable thermal cycle heating current is about 2800-3000A at a certain ambient temperature.

In order to verify the accuracy of the calculation method, a cable finite element model is established for simulation calculation, and the internal temperature field of the cable is shown in FIG. 6. The conductor temperature was 90.089 ℃ at 6 ℃ and 88.976 ℃ at 8 ℃ which is closer to the thermal cycle specification of 90 ℃. Therefore, the effective method for quickly calculating the thermal cycle heating current has certain reference value for estimating the thermal cycle heating current.

While the invention has been described with reference to specific embodiments, the invention is not limited thereto, and those skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope of the invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.