Method for calculating ampacity of multi-core magnesia cable using a simplified model

Abstract

The application discloses a method for calculating the allowable current-carrying capacity of a multi-core magnesium oxide cable by using a simplified model, the method uses a laser thermal conductivity instrument to measure the thermal conductivity of compacted magnesium oxide powder, and recommends that the thermal conductivity of the magnesium oxide insulation of the cable be 1.28 W / (m*K), and the structure of the multi-core cable is simplified to determine the thermal resistance of the insulation layer in an equivalent single-core coaxial structure; meanwhile, the highest allowable temperature of the wire core is used to replace the highest allowable temperature of the sheath, and based on the recommended technology of IEC60287, a simplified analytical algorithm for the allowable current-carrying capacity of the multi-core magnesium oxide cable is established. The method is clear in theory and easy to apply, the result is accurate and meets the engineering precision requirement, and provides technical support for the structure design and operation parameter selection of the magnesium oxide cable, and has important significance for guaranteeing the safe and economic operation of the cable.

Description

Technical Field

[0001] This invention relates to the field of magnesium oxide cable technology, specifically to a method for calculating the allowable current carrying capacity of multi-core magnesium oxide cables using a simplified model. It is an analytical method that performs structural equivalence calculations on multi-core magnesium oxide cables, simplifies them under specified temperature conditions, and substitutes the measured thermal conductivity of magnesium oxide material to calculate the allowable current carrying capacity. Background Technology

[0002] In real life, fires caused by substandard cable products and unreasonable circuit design occur frequently. If the cable is flammable, the fire will spread along the cable line, causing the accident to expand and seriously threatening people's lives and property, causing serious losses to the national economy. Fire-resistant cables, on the other hand, are non-flammable and can maintain continuous power supply for tens of minutes during a fire. Therefore, they are widely used in high-rise buildings, airports, subways, and other places with high human activity.

[0003] Fire-resistant cables, also known as magnesium oxide cables or mineral-insulated cables, offer several advantages over traditional flame-retardant and fire-resistant cables. Magnesium oxide cables are heat-resistant, fireproof, explosion-proof, non-combustible (can operate continuously at 250℃ for extended periods and at least 30 minutes at 1000℃), corrosion-resistant, have high mechanical strength, and a long service life. They are widely used in power distribution lines in industrial and civil buildings, especially in hazardous and harsh high-temperature environments such as nuclear power plants, metallurgical plants, chemical plants, mines, and kilns, or in locations requiring high power supply reliability. Furthermore, because the insulation material used is magnesium oxide powder, which has a high thermal conductivity and excellent heat dissipation, magnesium oxide cables can carry a larger current under the same conditions compared to conventional solid-insulated cables of the same cross-section.

[0004] Magnesium oxide cables typically use a copper core, compacted magnesium oxide powder insulation, and a copper sheath structure, such as... Figure 1 As shown; when cables are used in locations susceptible to chemical corrosion or severe industrial pollution, a polyolefin outer sheath can be extruded over the copper sheath. The magnesium oxide powder used as insulation in fire-resistant cables has a purity of over 90%, a particle size between 80 and 325 mesh, and a density of approximately 2.8–3 g / cm³ after compression. 3 .

[0005] The permissible long-term operating temperature of conventional cables is usually specified based on the highest temperature of the conductor. For example, XLPE cables specify a maximum permissible core temperature of 90°C, while IEC 60364-5-52 specifies a maximum permissible temperature of 105°C for the copper sheath of magnesium oxide cables. Furthermore, the insulation layer of multi-core magnesium oxide cables is not a regular coaxial columnar structure, such as... Figure 2As shown, the current-carrying capacity calculation method for this type of cable structure is not recommended or specified in IEC 60287. This results in the lack of applicable analytical methods and formulas for calculating the current-carrying capacity of multi-core magnesium oxide cables, requiring reliance on numerical modeling and iterative solutions based on thermal field calculations, which presents significant challenges for engineering applications. Although there have been studies on nano-magnesium oxide particles, magnesium oxide additives, or sintered magnesium oxide, there is still no actual measured data or recommended values ​​for the thermal conductivity of magnesium oxide powder materials used as insulation in fire-resistant cables. Therefore, the calculation of cable current-carrying capacity lacks an important parameter. Summary of the Invention

[0006] To overcome the problems existing in the prior art, the present invention aims to provide a method for calculating the allowable current carrying capacity of multi-core magnesium oxide cables using a simplified model. This method is based on the measurement data of the thermal conductivity of compacted magnesium oxide powder and a simplified model of the multi-core magnesium oxide cable. It uses the highest allowable operating temperature of the conductor to replace the highest allowable operating temperature of the sheath, thus providing an accurate and convenient analytical method for evaluating the allowable current carrying capacity of multi-core magnesium oxide cables. This method uses a laser thermal conductivity meter to measure the thermal conductivity of compacted magnesium oxide powder and simplifies the multi-core cable structure, determining the thermal resistance of the insulation layer using an equivalent single-core coaxial structure. Simultaneously, it uses the highest allowable temperature of the conductor to replace the highest allowable temperature of the sheath, establishing a simplified analytical algorithm for the allowable current carrying capacity of multi-core magnesium oxide cables based on the IEC 60287 recommended technology. This method is theoretically clear, easy to apply, and yields accurate results that meet engineering precision requirements. It provides technical support for the structural design and operating parameter selection of magnesium oxide cables, and is of great significance for ensuring the safe and economical operation of cables.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] The method for calculating the allowable current carrying capacity of multi-core magnesium oxide cables using a simplified model includes the following steps:

[0009] Step 1: Measure the thermal conductivity of the compacted magnesium oxide powder.

[0010] 1) First, place the magnesium oxide powder in an oven for drying;

[0011] 2) Place the dried magnesium oxide powder in a circular mold and press it into a circular sheet with a preset thickness and density consistent with the compaction density in the magnesium oxide cable using a powder press.

[0012] 3) The thermal conductivity λ of the compressed magnesium oxide circular sheet sample was measured using a laser thermal conductivity meter, and the measured data was obtained in W / (m·K).

[0013] 4) For compacted densities of 2.8–3 g / cm³ 3Magnesium oxide powder material for cable insulation was tested and found to have a constant thermal conductivity within the temperature range of 25–280℃. The average thermal conductivity was taken as 1.28 W / (m·K). The insulation thermal resistance coefficient ρ was used in the calculation of the allowable current carrying capacity of magnesium oxide cables. T It is 0.78 K·m / W;

[0014] Step 2: Establish an equivalent simplified model of a multi-core magnesium oxide cable and calculate the thermal resistance of the insulation layer.

[0015] 1) For multi-core magnesium oxide cables with two or more cores, a simplified model is established. The simplified model is a single-core coaxial structure, in which the cross-sectional area of ​​a single copper core is the sum of the cross-sectional areas of all current-carrying copper cores in the original cable, and it is placed at the center of the structure; the thickness of the copper sheath remains unchanged; the space between the copper core and the copper sheath is filled with magnesium oxide powder insulation; thus, the inner diameter D of the insulation layer in the simplified structure is determined. c (If there are n current-carrying conductors in the cable, and the cross-sectional area of ​​each conductor is A, then) ) and thickness t i (If the inner diameter of the copper sheath is D) s ,but (All units are mm)

[0016] 2) Based on the equivalent simplified model, the thermal resistance T1 of the insulation layer of the multi-core magnesium oxide cable is calculated using formula (1), with the unit being K·m / W;

[0017]

[0018] Step 3: Calculation of other parameters for multi-core magnesium oxide cables

[0019] 1) Calculation of resistance of copper conductor

[0020] The DC resistance R′ of a unit length of copper conductor at the highest temperature is:

[0021] R′=R0×[1+α 20 (θ c -20)] (2)

[0022] In the formula, R0 is the DC resistance of the copper conductor at 20℃, in Ω / m;

[0023] α 20 —Temperature coefficient of copper conductor at 20℃, 1 / K;

[0024] θ c —Maximum permissible temperature of copper conductor, °C; here, substitute the maximum permissible temperature of copper sheath of magnesium oxide cable as specified in the standard, such as 105 °C as specified in IEC 60364-5-52.

[0025] The AC resistance R per unit length of copper conductor at the highest operating temperature is:

[0026] R = R′(1 + Y) s +Y p (3)

[0027] In the formula, Y s —Skin effect factor;

[0028] Y p — Proximity effect factor.

[0029] 2) Calculation of copper sheath loss coefficient

[0030] The formula for calculating the loss coefficient λ1 of the copper sheath of a two-core magnesium oxide cable is:

[0031]

[0032] The formula for calculating the copper sheath loss coefficient λ1 of three-core and above magnesium oxide cables is:

[0033]

[0034] In the formula, c is the distance between the center of the current-carrying conductor and the center of the cable, in mm;

[0035] d—Average diameter of the copper sheath, mm;

[0036] R s —Copper sheath resistance, Ω / m;

[0037] ω——The angular frequency of the power frequency current, 100π.

[0038] 4) The formula for calculating the thermal resistance T4 of the air surrounding a multi-core magnesium oxide cable is as follows:

[0039]

[0040]

[0041] In the formula, h is the heat dissipation coefficient;

[0042] D e —Outer diameter of multi-core magnesium oxide cable, in meters;

[0043] Δθ s —The temperature difference between the surface of a multi-core magnesium oxide cable and the ambient temperature;

[0044] z, E, and g are constants, where z = 0.21, E = 3.94, and g = 0.6.

[0045] Step 4: Calculate the allowable current carrying capacity of the multi-core magnesium oxide cable.

[0046] Combine the thermal resistance T1 of the multi-core magnesium oxide cable insulation layer, the AC resistance R of the copper conductor per unit length at the highest operating temperature, the copper sheath loss coefficient λ1 of the multi-core magnesium oxide cable, the thermal resistance T4 of the air surrounding the multi-core magnesium oxide cable, and the known ambient temperature θ0 and the maximum allowable temperature θ of the copper conductor (i.e., the core) calculated in steps 1 to 3. c Substituting the number of current-carrying conductor cores n in the cable into equation (8), the current-carrying capacity of the multi-core magnesium oxide cable can be calculated:

[0047]

[0048] This invention proposes a simplified model of multi-core magnesium oxide cables based on measurement data of the thermal conductivity of compressed magnesium oxide powder. It uses the highest allowable operating temperature of the conductors instead of the highest operating temperature of the sheath, thus providing a simple and accurate analytical method for evaluating the allowable current carrying capacity of multi-core magnesium oxide cables. This method has the following advantages:

[0049] 1) The insulation thermal resistance coefficient in the calculation of allowable current carrying capacity of magnesium oxide cables is given for the first time, and a method for measuring the thermal conductivity of compressed magnesium oxide powder is recommended.

[0050] 2) The multi-core magnesium oxide cable is simplified into an equivalent single-core coaxial structure, which facilitates the calculation of the thermal resistance of the insulation layer;

[0051] 3) The maximum allowable temperature of the conductor is used instead of the maximum allowable temperature of the sheath, which simplifies the calculation process, establishes an analytical calculation method, and has good engineering applicability;

[0052] 4) The allowable current carrying capacity of magnesium oxide cable calculated based on the method of this invention has an error of no more than 5%, which meets the accuracy requirements for engineering applications; the calculation results are on the safe side, which is conducive to ensuring the safe operation of the line. Attached Figure Description

[0053] Figure 1 This is a schematic diagram of the cross-sectional structure of a magnesium oxide cable.

[0054] Figure 2 This is a picture of a multi-core magnesium oxide cable.

[0055] Figure 3 The thermal conductivity measurement data are for the compressed magnesium oxide powder insulating sample.

[0056] Figure 4 A simplified cross-sectional structural diagram of a multi-core magnesium oxide cable. Detailed Implementation

[0057] The present invention will now be described in more detail with reference to the accompanying drawings and specific embodiments.

[0058] The method proposed in this invention is used for multi-core (two-core, three-core, four-core) systems, with each core having a cross-sectional area of ​​25 mm².2 The allowable current carrying capacity of a 750V magnesium oxide cable laid in air at 30°C (with a maximum permissible sheath temperature of 105°C, i.e., in a location not touched by people) is calculated, including the following steps:

[0059] Step 1: Measure and determine the thermal conductivity of the compacted magnesium oxide powder.

[0060] 1) Place the magnesium oxide powder in an oven at 110℃ for 24 hours to dry it;

[0061] 2) Place the dried magnesium oxide powder into a circular mold with a diameter of 12.7 mm, and press it into tablets with a thickness of 1.9 mm and a density of approximately 2.8–3.0 g / cm³ using a powder press. 3 Circular thin slices;

[0062] 3) The thermal conductivity λ of the circular thin-film sample was measured using a laser thermal conductivity meter, and the results are as follows: Figure 3 As shown, it can be seen that the thermal conductivity λ of the magnesium oxide sample is basically constant in the temperature range of 25 to 280℃, and the average thermal conductivity is taken as 1.28 W / (m·K); that is, the thermal resistance coefficient is 0.78 K·m / W.

[0063] Step 2: Establish a simplified model of the multi-core magnesium oxide cable and calculate the thermal resistance of the insulation layer.

[0064] 1) The structure of 2-4 core magnesium oxide cables is simplified to obtain an equivalent single-core coaxial structure as a simplified model, such as... Figure 4 As shown. Determine the inner diameter D of the insulation layer. c (If there are n current-carrying conductors in the cable, and the cross-sectional area of ​​each conductor is A, then) Insulation layer thickness t i (If the inner diameter of the copper sheath is D) s ,but Substituting into formula (1), the thermal resistance T1 of the insulation layer is calculated, as shown in Table 1.

[0065] Table 1

[0066]

[0067] This method is also applicable to multi-core magnesium oxide cables with other cross-sectional areas and numbers of wires.

[0068] Step 3: Calculation of other parameters for multi-core magnesium oxide cables

[0069] For 25mm 2 The copper conductor has the following parameters: R0 = 7.27 × 10⁻⁶ -4 Ω / m, α 20 =3.93×10 -3 / K; The AC resistance R of the multi-core magnesium oxide cable conductor at the highest operating temperature is determined by formulas (2) and (3), the copper sheath loss coefficient λ1 is determined by formulas (4) and (5), and the ambient air thermal resistance T4 is determined by formula (6). The results are shown in Table 2.

[0070] Table 2

[0071]

[0072] Step 4: Calculate the allowable current carrying capacity of the multi-core magnesium oxide cable.

[0073] Substitute the parameters obtained in steps 1 to 3 into equation (8), and take the maximum allowable temperature of the wire core as 105℃, to calculate the allowable current carrying capacity I of two-core, three-core, and four-core magnesium oxide cables. The results are shown in Table 3.

[0074] Table 3

[0075]

[0076] To verify the accuracy of the calculation results of this method, simulation models of the same two-core, three-core, and four-core magnesium oxide cables were established using Comsol software to calculate the allowable current carrying capacity and compare it with the analytical calculation results of the method of this invention.

[0077] First, a two-dimensional simulation model of a multi-core magnesium oxide cable is established, and its structure and thermodynamic parameters are shown in Table 4.

[0078] Table 4

[0079]

[0080] The surface thermal radiation coefficient of the multi-core magnesium oxide cable is set to 0.65, and the heat transfer coefficient between the multi-core magnesium oxide cable and the surrounding air is 10 W / (m²). 2 Given an ambient temperature θ0 of 30℃, the calculated load current in the multi-core magnesium oxide cable core when the copper sheath temperature reaches 105℃ is the allowable current carrying capacity, as shown in Table 5. Table 5 also lists the allowable current carrying capacity obtained using a simplified analytical algorithm with a maximum allowable core temperature of 105℃, and calculates the relative deviation between the two.

[0081] Table 5

[0082]

[0083] As shown in Table 5, the deviation between the analytical method and the numerical method of this invention does not exceed 5%, meeting the accuracy requirements for engineering calculations. Furthermore, the calculation results of the analytical method of this invention are relatively safe, which is beneficial to the reliable operation of cable lines. Compared with the numerical method, the analytical method of this invention has a clear concept, simple steps, and is easy for engineering technicians to understand and master.

Claims

1. A method for calculating the allowable current carrying capacity of multi-core magnesium oxide cables using a simplified model, characterized in that: Includes the following steps: Step 1: Measure the thermal conductivity of the compacted magnesium oxide powder. 1) First, place the magnesium oxide powder in an oven for drying; 2) Place the dried magnesium oxide powder in a circular mold and press it into a circular sheet of a preset thickness with a density consistent with the compaction density in the magnesium oxide cable using a powder press. 3) The thermal conductivity of the compressed magnesium oxide circular sheet sample was measured using a laser thermal conductivity meter. λ Measurements were taken to obtain actual data, in units of W / (m·K); 4) For compacted densities of 2.8~3 g / cm³ 3 Magnesium oxide powder material for cable insulation was tested and found to have a constant thermal conductivity within the temperature range of 25~280℃. The average thermal conductivity was taken as 1.28 W / (m·K). The insulation thermal resistance coefficient was used in the calculation of the allowable current carrying capacity of magnesium oxide cables. ρ T It is 0.78 K·m / W; Step 2: Establish an equivalent simplified model of a multi-core magnesium oxide cable and calculate the thermal resistance of the insulation layer. 1) For multi-core magnesium oxide cables with two or more cores, a simplified model is established. The simplified model is a single-core coaxial structure, in which the cross-sectional area of ​​a single copper core is the sum of the cross-sectional areas of all current-carrying copper cores in the original cable, and it is placed at the center of the structure; the thickness of the copper sheath remains unchanged; the space between the copper core and the copper sheath is filled with magnesium oxide powder insulation; thus, the inner diameter of the insulation layer in the simplified structure is determined. D c and thickness t i All units are in mm; 2) Based on the equivalent simplified model, the thermal resistance of the insulation layer of the multi-core magnesium oxide cable is calculated using formula (1). T 1. The unit is K·m / W; （1） Step 3: Calculation of other parameters for multi-core magnesium oxide cables 1) Calculation of resistance of copper conductor DC resistance per unit length of copper conductor at the highest temperature R 'for （2） In the formula, R DC resistance of copper conductor at 0–20℃, Ω / m; α 20 —Temperature coefficient of copper conductor at 20℃, 1 / K; θ c —Maximum permissible temperature for copper conductors, °C; AC resistance per unit length of copper conductor at the highest operating temperature R for （3） In the formula, Y s —Skin effect factor; Y p —Proximity effect factor; 2) Calculation of copper sheath loss coefficient Loss coefficient of copper sheath in two-core magnesium oxide cable λ The calculation formula is as follows: （4） Three-core and above magnesium oxide cables copper sheath loss coefficient λ The calculation formula is as follows: （5） In the formula, c — The distance between the conductor core axis and the cable core axis, in mm; d —Average diameter of copper sheath, mm; R s —Copper sheath resistance, Ω / m; ω —Power frequency current angular frequency; 4) Thermal resistance of the air surrounding the multi-core magnesium oxide cable T 4. The calculation formula is: （6） （7） In the formula, h —Heat dissipation coefficient; D e —Outer diameter of multi-core magnesium oxide cable, in meters; Δ θ s —The temperature difference between the surface of a multi-core magnesium oxide cable and the ambient temperature; z , E , g It is a constant; Step 4: Calculate the allowable current carrying capacity of the multi-core magnesium oxide cable. The thermal resistance of the multi-core magnesium oxide cable insulation layer calculated in steps 1-3 is used as the basis for... T 1. AC resistance per unit length of copper conductor at the highest operating temperature R Loss coefficient of copper sheath in multi-core magnesium oxide cable λ 1. Thermal resistance of air surrounding multi-core magnesium oxide cable T 4 and known ambient temperature θ 0. Maximum permissible temperature of copper conductor, i.e., wire core θ c Number of current-carrying conductor cores in the cable n Substituting into equation (8), calculate the current carrying capacity of the multi-core magnesium oxide cable: （8）。 2. The method for calculating the allowable current carrying capacity of a multi-core magnesium oxide cable using a simplified model according to claim 1, characterized in that: The power frequency current angular frequency ω It is 100π.

3. The method for calculating the allowable current carrying capacity of a multi-core magnesium oxide cable using a simplified model according to claim 1, characterized in that: The constant z , E , g The value can be: z =0.21, E =3.94, g =0.6.

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