Submarine cable temperature rise and current-carrying capacity prediction method based on thermal circuit analysis method

Abstract

The invention discloses a submarine cable temperature rise and current-carrying capacity prediction method based on a thermal circuit analysis method. The method comprises the following steps: obtaining related loss data, related thermal resistance data and related thermal capacity data of a submarine cable; constructing an initial submarine cable thermal circuit model based on the related loss data, the related thermal resistance data and the related thermal capacity data; simplifying the initial submarine cable thermal circuit model to obtain a final simplified submarine cable thermal circuit model; constructing a submarine cable internal temperature rise prediction model based on the final simplified submarine cable thermal circuit model; building submarine cable temperature rise prediction models in different laying environments based on the submarine cable internal temperature rise prediction model to predict the temperature of the submarine cable; and constructing a submarine cable current-carrying capacity prediction model in different laying environments based on the related loss data and the related thermal resistance data to predict the current-carrying capacity of the submarine cable. The prediction accuracy can be improved.

Description

Technical Field

[0001] The present invention relates to the technical field of submarine cables, and more particularly to a method for predicting the temperature rise and current carrying capacity of submarine cables based on a thermal path analysis method. Background Art

[0002] Submarine cables are the only carrier for the transmission of offshore wind farm power, offshore oil and gas field platform power supply, and cross-sea communication. Once a failure occurs, it will affect the offshore wind power transmission power and offshore oil and gas field platform exploitation, or directly interrupt the functional supply and information transmission of various marine projects, causing significant economic losses. Under the influence of external factors such as ocean current scouring, human activities, and geological movements, the environment of submarine cables continues to change, resulting in changes in the external environmental thermal resistance of submarine cables, affecting the transmission efficiency and transmission capacity. Only when working at its rated current carrying capacity can long-term safe and stable operation be guaranteed. When submarine cables transmit power and data, the temperature will directly affect their performance. Excessive temperature will reduce the transmission efficiency of the cable, cause aging of the insulation material, lead to line short circuits, and affect the natural environment. Therefore, it is of great significance to accurately predict the temperature and current carrying capacity of submarine cables under different laying environments. However, the existing prediction methods all have the problem of low accuracy.

[0003] Therefore, how to provide a method for predicting the temperature rise and current carrying capacity of submarine cables with higher prediction accuracy is an urgent problem to be solved by those skilled in the art. Summary of the invention

[0004] In view of this, an object of the present invention is to provide a method for predicting the temperature rise and current carrying capacity of a submarine cable based on a thermal circuit analysis method.

[0005] In order to achieve the above object, the present invention adopts the following technical solution:

[0006] A method for predicting the temperature rise and current carrying capacity of a submarine cable based on a thermal path analysis method comprises the following steps:

[0007] Obtain relevant loss data, relevant thermal resistance data and relevant thermal capacity data of submarine cables;

[0008] Constructing an initial submarine cable thermal circuit model based on the relevant loss data, the relevant thermal resistance data and the relevant thermal capacity data;

[0009] Simplifying the initial submarine cable thermal circuit model to obtain a final simplified submarine cable thermal circuit model;

[0010] Constructing a submarine cable internal temperature rise prediction model based on the final simplified submarine cable thermal circuit model;

[0011] Based on the internal temperature rise prediction model of the submarine cable, a submarine cable temperature rise prediction model under different laying environments is constructed to predict the temperature of the submarine cable;

[0012] Based on the relevant loss data and the relevant thermal resistance data, a submarine cable current carrying capacity prediction model under different laying environments is constructed to predict the current carrying capacity of the submarine cable.

[0013] Preferably, the relevant loss data includes the core loss W c , XLPE insulation layer loss W d , alloy lead jacket loss W l and armor layer loss W a ;

[0014] The relevant thermal resistance data include the thermal resistance of the XLPE insulation layer T1, the thermal resistance of the filling layer and the inner cushion layer T2, and the thermal resistance of the PP outer sheath layer T3;

[0015] The relevant heat capacity data include the heat capacity of the water-blocking copper conductor layer Q1, the heat capacity of the XLPE insulation layer Q2, the heat capacity of the alloy lead sheath layer and the PE sheath layer Q3, the heat capacity of the filling layer and the inner cushion layer Q4, the heat capacity of the armor layer Q5, and the heat capacity of the PP outer sheath layer Q6.

[0016] Preferably, the core loss W c Based on the following:

[0017] W c =I 2 R(1)

[0018] R=R′(1+Y s +Y p )(2)

[0019]

[0020] ρ θ =ρ 20 +0.68×10 -4 (θ-20)(4)

[0021] A=πr 2 (5)

[0022]

[0023] In the formula, I represents the current flowing into the submarine cable; R represents the AC resistance of the core per unit length at the operating temperature; R′ represents the DC resistance of the core per unit length at the operating temperature; Y s represents the skin effect coefficient; Y p represents the proximity effect coefficient; ρ θIt represents the resistivity of the wire core at the working temperature; A represents the cross-sectional area of ​​the wire core; l represents the length of the wire core; θ represents the working temperature of the wire core; ρ 20 represents the resistivity of the core at 20°C; r represents the radius of the core; f represents the frequency of I; d c Indicates the outer diameter of the wire core; s indicates the distance between the center axes of the wire core; k s and k p is a constant;

[0024] The XLPE insulation layer loss W d Based on the following formula:

[0025] W d =ω·C(U0) 2 ·tgδ'(8)

[0026]

[0027] Where, ε represents the dielectric constant; D2 represents the outer diameter of the XLPE insulation layer; d c represents the outer diameter of the wire core; ω represents the angular frequency corresponding to f, that is, ω = 2πf; U0 represents the voltage of the XLPE insulation layer to ground; tgδ' represents the tangent of the loss angle δ' of the XLPE insulation layer;

[0028] The alloy lead jacket loss W l Based on the following formula:

[0029] W l =λ1W c (9)

[0030] λ1=λ′1+λ1″≈λ′1 (10)

[0031]

[0032] In the formula, λ1′ represents the circulation loss; λ1″ represents the eddy current loss; R s represents the resistance of the alloy lead sheath at the working temperature; X represents the impedance of the alloy lead sheath at the working temperature; R c Indicates the resistance of the wire core at operating temperature; ρ s Indicates the resistivity of the alloy lead sheath at 20°C; A s Represents the cross-sectional area of ​​the alloy lead sheath; α s Indicates the resistance temperature coefficient of the alloy lead sheath material; θ s represents the working temperature of the alloy lead sheath; η represents the temperature ratio of the alloy lead sheath to the wire core; s represents the center axis distance of the wire core; d l Indicates the outer diameter of the alloy lead sheath;

[0033] The armor layer loss W aBased on the following formula:

[0034] W a =λ2W c (14)

[0035]

[0036] In the formula, R sa Indicates the resistance of the armor layer at operating temperature; R c It represents the resistance of the core at the working temperature; c represents the distance from the core to the axis of the submarine cable; d a The outer diameter of the armor layer.

[0037] Preferably, the initial submarine cable thermal circuit model is simplified for the first time to obtain an intermediate simplified submarine cable thermal circuit model;

[0038] The intermediate simplified submarine cable thermal circuit model is simplified for the second time to obtain a final simplified submarine cable thermal circuit model.

[0039] Preferably, the internal temperature rise prediction model θ of the submarine cable c The expression of (t) is:

[0040] θ c (t) = W c [T a (1-e -at )+T b (1-e -bt )] (39)

[0041]

[0042] T b =(T A1 +T B1 )-T a (41)

[0043]

[0044] N0=Q A1 T A1 Q B1 T B1 (43)

[0045] M0=0.5[Q A1 (T A1 +T B1 )+Q B1 T B1 ] (44)

[0046] Where W c Indicates the core loss; T A1 and TB1 represents the thermal resistance of the final simplified submarine cable thermal circuit model; Q A1 and Q B1 Represents the heat capacity of the final simplified submarine cable thermal circuit model.

[0047] Preferably, T A1 、T B1 , Q A1 and Q B1 The expression is:

[0048] Q A1 =Q a (35)

[0049]

[0050] T A1 =T A (37)

[0051] T B1 =T B +q s T C (38)

[0052]

[0053] Where, T A 、T B and T C is the thermal resistance of the simplified submarine cable thermal circuit model; Q a , Q b and Q c is the heat capacity of the simplified submarine cable thermal circuit model in the middle.

[0054] Preferably, T A 、T B 、T C , Q a , Q b and Q c The expression is:

[0055] T A =T1 / 3(18)

[0056] T B =T2(19)

[0057] T C =q s T3(20)

[0058] Q a =Q A (25)

[0059] Q b =Q B / q s (26)

[0060] Q c =Q C / q s (27)

[0061] Q A =Q1+pQ2(21)

[0062] Q B =(1-p)Q1+Q3+p′Q4(22)

[0063] Q C =(1-p′)Q4+(Q5+p″Q6) / q s (twenty three)

[0064]

[0065] Where D2 represents the outer diameter of the XLPE insulation layer; d c Indicates the outer diameter of the wire core; D3 indicates the outer diameter of the inner cushion layer; D5 indicates the outer diameter of the PP outer sheath layer; d a Indicates the outer diameter of the armor layer.

[0066] Preferably, the temperature rise prediction models of submarine cables under different laying environments include a temperature rise prediction model of a submarine cable exposed to the air and a temperature rise prediction model of a submarine cable buried under the seabed;

[0067] The temperature rise prediction model of submarine cables exposed to air converts T in the temperature rise prediction model of submarine cables into B1 Replace with T B1 +T air ; Among them, T air It represents the thermal resistance of the outside air;

[0068] The expression of the temperature rise prediction model θ(t) of the submarine cable buried under the seabed is:

[0069] θ(t)=θ c (t)+α(t)θ e (t)(49)

[0070]

[0071]

[0072] W t =W c +W d +W l +W a (48)

[0073] In the formula, δ represents the heat dissipation factor of the soil; ρ s Indicates the thermal resistance coefficient of soil; D e Indicates the outer diameter of the submarine cable; L indicates the buried depth of the submarine cable; W t Represents the total loss of the submarine cable.

[0074] Preferably, the current carrying capacity prediction models of submarine cables under different laying environments include a current carrying capacity prediction model of submarine cables exposed to the air and a current carrying capacity prediction model of submarine cables buried under the seabed;

[0075] The expression of the current-carrying capacity prediction model I' of the submarine cable exposed to the air is:

[0076]

[0077] In the formula, is the core temperature rise relative to the ambient temperature; n is the number of load conductors in the submarine cable; T air is the thermal resistance of the outside air; λ1”’ is the ratio of the XLPE insulation loss to the core loss; λ2’ is the ratio of the alloy lead sheath loss to the core loss; R represents the AC resistance of the core per unit length at the operating temperature;

[0078] The expression of the current carrying capacity prediction model I" of submarine cables buried under the seabed is:

[0079]

[0080] In the formula, is the core temperature rise relative to the ambient temperature; n is the number of load conductors in the submarine cable; T 4solid is the external soil thermal resistance of the submarine cable; λ1”’ is the ratio of XLPE insulation loss to core loss; λ2’ is the ratio of alloy lead sheath loss to core loss; R represents the AC resistance of the core per unit length at operating temperature.

[0081] Preferably, if the submarine cable is buried under the seabed in a pipe arrangement, D e Indicates the outer diameter of the outer surface of the tube.

[0082] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a method for predicting the temperature rise and current carrying capacity of a submarine cable based on a thermal path analysis method, which can improve the prediction accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0084] Figure 1 This is a schematic structural diagram of the initial submarine cable thermal circuit model provided by the present invention.

[0085] Figure 2 A schematic diagram of the structure of the intermediate simplified submarine cable thermal circuit model provided by the present invention;

[0086] Figure 3 Schematic diagram of the structure of the final simplified submarine cable thermal circuit model provided by the present invention

[0087] Figure 4 A schematic diagram of the temperature rise results of the finite element simulation provided by the present invention when the current magnitudes are 128A, 228A, 328A, 428A, 528A, and 628A;

[0088] Figure 5 The present invention is a flowchart of a method for predicting the temperature rise and current carrying capacity of a submarine cable based on a thermal circuit analysis method provided in one embodiment of the present invention. DETAILED DESCRIPTION

[0089] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0090] The embodiment of the present invention discloses a method for predicting the temperature rise and current carrying capacity of a submarine cable based on a thermal path analysis method, comprising the following steps:

[0091] S1: Obtain relevant loss data, relevant thermal resistance data and relevant heat capacity data of submarine cables;

[0092] In one embodiment, the relevant loss data includes the core loss W c , XLPE insulation layer loss W d , alloy lead jacket loss W l and armor layer loss W a ;

[0093] The relevant thermal resistance data include the thermal resistance of the XLPE insulation layer T1, the thermal resistance of the filling layer and the inner cushion layer T2, and the thermal resistance of the PP outer sheath layer T3;

[0094] The relevant heat capacity data include the heat capacity of the water-blocking copper conductor layer Q1, the heat capacity of the XLPE insulation layer Q2, the heat capacity of the alloy lead sheath layer and the PE sheath layer Q3, the heat capacity of the filling layer and the inner cushion layer Q4, the heat capacity of the armor layer Q5, and the heat capacity of the PP outer sheath layer Q6.

[0095] In one embodiment, the core loss W c Based on the following:

[0096] W c =I 2 R(1)

[0097] R=R′(1+Y s +Y p )(2)

[0098]

[0099] ρ θ =ρ 20 +0.68×10 -4 (θ-20)(4)

[0100] A=πr 2 (5)

[0101]

[0102] In the formula, I represents the current flowing into the submarine cable; R represents the AC resistance of the core per unit length at the operating temperature; R′ represents the DC resistance of the core per unit length at the operating temperature; Y s represents the skin effect coefficient; Y p represents the proximity effect coefficient; ρ θ It represents the resistivity of the wire core at the working temperature; A represents the cross-sectional area of ​​the wire core; l represents the length of the wire core, which is 1m; θ represents the working temperature of the wire core, in °C; ρ 20 Indicates the resistivity of the wire core at 20°C. r represents the radius of the wire core; f represents the frequency of I, which is 50HZ; d c Indicates the outer diameter of the wire core; s indicates the distance between the center axes of the wire core; k s and k p is a constant;

[0103] The XLPE insulation layer loss W d Based on the following formula:

[0104] W d =ω·C(U0) 2 ·tgδ'(8)

[0105]

[0106] Where, ε represents the dielectric constant; D2 represents the outer diameter of the XLPE insulation layer; d c represents the outer diameter of the wire core; ω represents the angular frequency corresponding to f, that is, ω = 2πf; U0 represents the voltage of the XLPE insulation layer to the ground; tgδ' represents the tangent of the loss angle δ' of the XLPE insulation layer, and its value is 0.001;

[0107] The alloy lead jacket loss W l Based on the following formula:

[0108] W l =λ1W c (9)

[0109] λ1=λ′1+λ1″≈λ′1 (10)

[0110]

[0111] Where, λ1′ represents the circulation loss; λ1″ represents the eddy current loss (the present invention does not consider the eddy current loss, so λ1″ is taken as 0); R s represents the resistance of the alloy lead sheath at the working temperature; X represents the impedance of the alloy lead sheath at the working temperature; R c Indicates the resistance of the wire core at operating temperature; ρ s Indicates the resistivity of the alloy lead sheath at 20°C; A s Represents the cross-sectional area of ​​the alloy lead sheath; α s Indicates the resistance temperature coefficient of the alloy lead sheath material; θ s It indicates the working temperature of the alloy lead sheath; η indicates the temperature ratio of the alloy lead sheath to the wire core, which is generally taken as 0.7-0.8; s indicates the center axis distance of the wire core; d l Indicates the outer diameter of the alloy lead sheath;

[0112] The armor layer loss W a Based on the following formula:

[0113] W a =λ2W c (14)

[0114]

[0115] In the formula, R sa Indicates the resistance of the armor layer at operating temperature; R c It represents the resistance of the core at the working temperature; c represents the distance from the core to the axis of the submarine cable; d a The outer diameter of the armor layer.

[0116] In this embodiment, a 35 kV three-core DC submarine XLPE cable is taken as an example, and the structural parameters of each layer are shown in Table 1 below.

[0117] Table 1

[0118]

[0119]

[0120] According to formulas (1)-(6), the core loss W can be calculated c , where k s Take 1,k p Take 0.8;

[0121] According to formulas (7)-(8), the XLPE insulation loss W can be calculated: d , where the dielectric constant ε is taken as 2.35 to obtain the XLPE insulation layer loss W when the voltage to ground U0 is 35kV d =0.0643W / m.

[0122] In one embodiment, the calculation formulas for the thermal resistance T1 of the XLPE insulation layer, the thermal resistance T2 of the filling layer and the inner cushion layer, and the thermal resistance T3 of the PP outer sheath layer are:

[0123]

[0124] Where T represents the thermal resistance of the corresponding layer; D i Indicates the outer diameter of the corresponding layer; D i-1 represents the inner diameter of the corresponding layer; ρ represents the thermal resistance coefficient of the corresponding layer material;

[0125] It should be noted that:

[0126] When calculating the thermal resistance T2 between the filling layer and the inner cushion layer, D i is the outer diameter of the inner cushion layer, D i-1 is the inner diameter of the filling layer;

[0127] In this embodiment, according to the data in Table 1 and formulas (16)-(17), it is calculated that:

[0128] T1=0.455K·m / W, T2=0.007K·m / W, T3=0.020K·m / W;

[0129] In one embodiment, the calculation formulas for the heat capacity Q1 of the water-blocking copper conductor layer, the heat capacity Q2 of the XLPE insulation layer, the heat capacity Q3 of the alloy lead jacket layer and the PE jacket layer, the heat capacity Q4 of the filling layer and the inner cushion layer, the heat capacity Q5 of the armor layer, and the heat capacity Q6 of the PP outer jacket layer are:

[0130]

[0131] Where Q represents the heat capacity of the corresponding layer; D j Indicates the outer diameter of the corresponding layer; D j-1 represents the inner diameter of the corresponding layer; c' represents the thermal characteristic coefficient of the corresponding layer material;

[0132] It should be noted that when calculating the heat capacity Q3 of the alloy lead sheath and the PE sheath, D j Indicates the outer diameter of the PE sheath layer; D j-1 Indicates the inner diameter of the alloy lead sheath;

[0133] When calculating the heat capacity Q4 of the filling layer and the inner cushion layer, D j Indicates the outer diameter of the inner cushion layer; D j-1 Indicates the inner diameter of the filling layer.

[0134] In this embodiment, according to the data in Table 1 and formulas (16)-(17), it is calculated that: Q1=1138.719 J / K, Q2=4870.184 J / K, Q3=2178.049 J / K, Q4=11035.740 J / K, Q5=5171.846 J / K, Q6=3279.803 J / K.

[0135] S2: constructing an initial submarine cable thermal circuit model based on the relevant loss data, the relevant thermal resistance data and the relevant thermal capacity data;

[0136] The structural schematic diagram of the initial submarine cable thermal circuit model is as follows: Figure 1 As shown;

[0137] S3: simplifying the initial submarine cable thermal circuit model to obtain a final simplified submarine cable thermal circuit model;

[0138] In one embodiment, the initial submarine cable thermal circuit model is simplified for the first time to obtain an intermediate simplified submarine cable thermal circuit model;

[0139] The intermediate simplified submarine cable thermal circuit model is simplified for the second time to obtain a final simplified submarine cable thermal circuit model.

[0140] The structural schematic diagram of the intermediate simplified submarine cable thermal circuit model is as follows: Figure 2 As shown;

[0141] The structural schematic diagram of the final simplified submarine cable thermal circuit model is as follows: Figure 3 As shown;

[0142] S4: constructing a submarine cable internal temperature rise prediction model based on the final simplified submarine cable thermal circuit model;

[0143] In one embodiment, the internal temperature rise prediction model θ of the submarine cable cThe expression of (t) is:

[0144] θ c (t) = W c [T a (1-e -at )+T b (1-e -bt )](39)

[0145]

[0146] T b =(T A1 +T B1 )-T a (41)

[0147]

[0148] N0=Q A1 T A1 Q B1 T B1 (43)

[0149] M0=0.5[Q A1 (T A1 +T B1 )+Q B1 T B1 ](44)

[0150] Where W c Indicates the core loss; T A1 and T B1 represents the thermal resistance of the final simplified submarine cable thermal circuit model; Q A1 and Q B1 Represents the heat capacity of the final simplified submarine cable thermal circuit model.

[0151] In one embodiment, T A1 、T B1 , Q A1 and Q B1 The expression is:

[0152] Q A1 =Q a (35)

[0153]

[0154] T A1 =T A (37)

[0155] T B1 =T B +q s T C (38)

[0156]

[0157] Where, T A 、T B and T C is the thermal resistance of the simplified submarine cable thermal circuit model; Q a , Q b and Q c is the heat capacity of the simplified submarine cable thermal circuit model in the middle.

[0158] In one embodiment, T A 、T B 、T C , Q a , Q b and Q c The expression is:

[0159] T A =T1 / 3(18)

[0160] T B =T2(19)

[0161] T C =q s T3(20)

[0162] Q a =Q A (25)

[0163] Q b =Q B / q s (26)

[0164] Q c =Q C / q s (27)

[0165] Q A =Q1+pQ2(21)

[0166] Q B =(1-p)Q1+Q3+p′Q4(22)

[0167] Q C =(1-p′)Q4+(Q5+p″Q6) / q s (twenty three)

[0168]

[0169] Where D2 represents the outer diameter of the XLPE insulation layer; d c Indicates the outer diameter of the wire core; D3 indicates the outer diameter of the inner cushion layer; D5 indicates the outer diameter of the PP outer sheath layer; da Indicates the outer diameter of the armor layer.

[0170] In this embodiment, T is obtained according to formulas (18)-(38): A1 =0.152K·m / W, T B1 =0.096K·m / W, Q A1 =2965.290K·m / W, Q B1 =8857.88K·m / W.

[0171] S5: Based on the internal temperature rise prediction model of the submarine cable, a submarine cable temperature rise prediction model under different laying environments is constructed to predict the temperature of the submarine cable;

[0172] In one embodiment, the temperature rise prediction models of submarine cables under different laying environments include a temperature rise prediction model of a submarine cable exposed to the air and a temperature rise prediction model of a submarine cable buried under the seabed;

[0173] The temperature rise prediction model of submarine cables exposed to air converts T in the temperature rise prediction model of submarine cables into B1 Replace with T B1 +T air ; Among them, T air Represents the thermal resistance of the outside air (the thermal resistance of the outside air is calculated using an empirical formula, with a value of 0.245);

[0174] The expression of the temperature rise prediction model θ(t) of the submarine cable buried under the seabed is:

[0175] θ(t)=θ c (t)+α(t)θ e (t)(49)

[0176]

[0177] W t =W c +W d +W l +W a (48)

[0178] In the formula, δ represents the heat dissipation factor of the soil, and the unit is m 2 / S;ρ s Indicates the thermal resistance of soil, in K·m / W; D e Indicates the outer diameter of the submarine cable (if the submarine cable is buried under the seabed in a pipe, D e represents the outer diameter of the outer surface of the pipe, in meters; L represents the buried depth of the submarine cable, in meters; W t Represents the total loss of the submarine cable.

[0179] S6: Based on the relevant loss data and the relevant thermal resistance data, a submarine cable current carrying capacity prediction model under different laying environments is constructed to predict the current carrying capacity of the submarine cable.

[0180] In one embodiment, the current carrying capacity prediction models of submarine cables under different laying environments include a current carrying capacity prediction model of submarine cables exposed to the air and a current carrying capacity prediction model of submarine cables buried under the seabed;

[0181] The expression of the current-carrying capacity prediction model I' of the submarine cable exposed to the air is:

[0182]

[0183] In the formula, is the core temperature rise relative to the ambient temperature; n is the number of load conductors in the submarine cable; T air is the thermal resistance of the outside air; λ1”’ is the ratio of the XLPE insulation loss to the core loss; λ2’ is the ratio of the alloy lead sheath loss to the core loss; R represents the AC resistance of the core per unit length at the working temperature (this resistance value varies with the temperature of the conductor core, and can be roughly selected as the AC resistance at the highest temperature of the core in engineering);

[0184] The expression of the current carrying capacity prediction model I" of submarine cables buried under the seabed is:

[0185]

[0186] In the formula, is the core temperature rise relative to the ambient temperature; n is the number of load conductors in the submarine cable; T 4solid is the external soil thermal resistance of the submarine cable; λ1”’ is the ratio of XLPE insulation loss to core loss; λ2’ is the ratio of alloy lead sheath loss to core loss; R represents the AC resistance of the core per unit length at operating temperature (this resistance value varies with the conductor core temperature and can be roughly selected as the AC resistance at the highest core temperature in engineering).

[0187] In one embodiment, relevant environmental parameters for a submarine cable buried under the seabed and a submarine cable buried under the seabed in a casing are shown in Table 2.

[0188] Table 2

[0189]

[0190] As shown in Table 3, the relevant environmental parameters of the submarine cable at the landing section are substituted into formula (45) to calculate the external soil thermal resistance T of the submarine cable. 4solid =0.678K·m / W;

[0191] Substitute the relevant environmental parameters of the shallow water submarine cable into formula (45) to calculate the external soil thermal resistance T of the submarine cable: 4solid =0.422K·m / W;

[0192] Substitute the relevant environmental parameters of the deep-water submarine cable into formula (45) to calculate the external soil thermal resistance T of the submarine cable: 4solid =0.542K·m / W;

[0193] Table 3

[0194] parameter Login segment Shallow water section Deepwater section <![CDATA[T 4solid ]]> 0.678 0.422 0.542

[0195] Finally, taking the case where the current I is 128A, 228A, 328A, 428A, 528A, and 628A and the power-on time is 24h, the temperature prediction value and current carrying capacity prediction value (assuming the initial ambient temperature is 20℃) of the 35kV three-core DC submarine XLPE cable laid in shallow water are shown in Table 4.

[0196] Table 4

[0197]

[0198] It can be seen from Table 4 that when the submarine cable is laid in shallow water, the error between its original current carrying capacity I (i.e., the current I flowing into the submarine cable) and the predicted current carrying capacity I" is about 2A, indicating that the current carrying capacity prediction of the present invention has a certain accuracy.

[0199] Then, the COMSOL finite element simulation software was used to model and simulate the above-mentioned submarine cables according to the same current size (for 35kV three-core DC submarine XLPE cables, the finite element simulation temperature rise results (20℃ is the initial temperature) under the conditions of energized currents of 128A, 228A, 328A, 428A, 528A, and 628A are shown as follows: Figure 4 The simulated cable core temperature and predicted temperature are shown in Table 5.

[0200] Table 5

[0201]

[0202]

[0203] It can be seen from Table 5 that when the submarine cable is laid in shallow water, the error between the simulated cable core temperature and the predicted temperature is about 0.1-1.3°C, indicating that the temperature prediction of the present invention has a certain accuracy.

[0204] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0205] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for predicting temperature rise and current carrying capacity of submarine cables based on thermal circuit analysis, characterized in that: The following steps are involved: Obtain relevant loss data, relevant thermal resistance data and relevant thermal capacity data of submarine cables; Constructing an initial submarine cable thermal circuit model based on the relevant loss data, the relevant thermal resistance data and the relevant thermal capacity data; Simplifying the initial submarine cable thermal circuit model to obtain a final simplified submarine cable thermal circuit model; Constructing a submarine cable internal temperature rise prediction model based on the final simplified submarine cable thermal circuit model; Based on the internal temperature rise prediction model of the submarine cable, a submarine cable temperature rise prediction model under different laying environments is constructed to predict the temperature of the submarine cable; Based on the relevant loss data and the relevant thermal resistance data, a submarine cable current carrying capacity prediction model under different laying environments is constructed to predict the current carrying capacity of the submarine cable.

2. The method for predicting temperature rise and current carrying capacity of a submarine cable based on thermal circuit analysis according to claim 1, characterized in that: The relevant loss data includes the core loss W c , XLPE insulation layer loss W d , alloy lead jacket loss W l and armor layer loss W a ; The relevant thermal resistance data include the thermal resistance of the XLPE insulation layer T1, the thermal resistance of the filling layer and the inner cushion layer T2, and the thermal resistance of the PP outer sheath layer T3; The relevant heat capacity data include the heat capacity of the water-blocking copper conductor layer Q1, the heat capacity of the XLPE insulation layer Q2, the heat capacity of the alloy lead sheath layer and the PE sheath layer Q3, the heat capacity of the filling layer and the inner cushion layer Q4, the heat capacity of the armor layer Q5, and the heat capacity of the PP outer sheath layer Q6.

3. The method for predicting temperature rise and current carrying capacity of a submarine cable based on thermal circuit analysis according to claim 2, characterized in that: The core loss W c Based on the following: W c =I 2 R(1) R=R′(1+Y s +Y p )(2) r θ =ρ 20 +0.68×10 -4 (i-20)(4) A＝πr 2 (5) In the formula, I represents the current flowing into the submarine cable; R represents the AC resistance of the core per unit length at the operating temperature; R′ represents the DC resistance of the core per unit length at the operating temperature; Y s represents the skin effect coefficient; Y p represents the proximity effect coefficient; ρ θ It represents the resistivity of the wire core at the working temperature; A represents the cross-sectional area of ​​the wire core; l represents the length of the wire core; θ represents the working temperature of the wire core; ρ 20 represents the resistivity of the core at 20°C; r represents the radius of the core; f represents the frequency of I; d c Indicates the outer diameter of the wire core; s indicates the distance between the center axes of the wire core; k s and k p is a constant; The XLPE insulation layer loss W d Based on the following formula: W d =ω·C(U0) 2 ·tgδ'(8) Where, ε represents the dielectric constant; D2 represents the outer diameter of the XLPE insulation layer; d c represents the outer diameter of the wire core; ω represents the angular frequency corresponding to f, that is, ω = 2πf; U0 represents the voltage of the XLPE insulation layer to ground; tgδ' represents the tangent of the loss angle δ' of the XLPE insulation layer; The alloy lead jacket loss W l Based on the following formula: W l =λ1W c (9) λ1=λ′1+λ1″≈λ′1 (10) In the formula, λ1′ represents the circulation loss; λ1″ represents the eddy current loss; R s represents the resistance of the alloy lead sheath at the working temperature; X represents the impedance of the alloy lead sheath at the working temperature; R c Indicates the resistance of the wire core at operating temperature; ρ s Indicates the resistivity of the alloy lead sheath at 20°C; A s Represents the cross-sectional area of ​​the alloy lead sheath; α s Indicates the resistance temperature coefficient of the alloy lead sheath material; θ s represents the working temperature of the alloy lead sheath; η represents the temperature ratio of the alloy lead sheath to the wire core; s represents the distance between the center axes of the wire core; d l Indicates the outer diameter of the alloy lead sheath; The armor layer loss W a Based on the following formula: IN a =λ2W c (14) In the formula, R sa Indicates the resistance of the armor layer at operating temperature; R c It represents the resistance of the core at the working temperature; c represents the distance from the core to the axis of the submarine cable; d a The outer diameter of the armor layer.

4. A method for predicting temperature rise and current carrying capacity of a submarine cable based on thermal circuit analysis according to claim 2 or 3, characterized in that: Simplifying the initial submarine cable thermal circuit model for the first time to obtain an intermediate simplified submarine cable thermal circuit model; The intermediate simplified submarine cable thermal circuit model is simplified for the second time to obtain a final simplified submarine cable thermal circuit model.

5. The method for predicting temperature rise and current carrying capacity of submarine cables based on thermal circuit analysis according to claim 4, characterized in that: The internal temperature rise prediction model of the submarine cable θ c The expression of (t) is: θ c (t)=W c [T a (1-e -at )+T b (1-e -bt )] (39) T b =(T A1 +T B1 )-T a (41) N0=Q A1 T A1 Q B1 T B1 (43) M0=0.5[Q A1 (T A1 +T B1 )+Q B1 T B1 ] (44) Where W c Indicates the core loss; T A1 and T B1 represents the thermal resistance of the final simplified submarine cable thermal circuit model; Q A1 and Q B1 Represents the heat capacity of the final simplified submarine cable thermal circuit model.

6. A method for predicting temperature rise and current carrying capacity of submarine cables based on thermal circuit analysis according to claim 5, characterized in that: T A1 , T B1 , Q A1 and Q B1 The expression is: Q A1 =Q a (35) T A1 =T A (37) T B1 =T B +q s T C (38) Where, T A , T B and T C is the thermal resistance of the simplified submarine cable thermal circuit model; Q a , Q b and Q c is the heat capacity of the simplified submarine cable thermal circuit model in the middle.

7. A method for predicting temperature rise and current carrying capacity of a submarine cable based on thermal circuit analysis according to claim 6, characterized in that: T A , T B , T C , Q a , Q b and Q c The expression is: T A =T1 / 3 (18) T B =T2 (19) T C =q s T3 (20) Q a =Q A (25) Q b =Q B / q s (26) Q c =Q C / q s (27) Q A =Q1+pQ2 (21) Q B =(1-p)Q1+Q3+p′Q4 (22) Q C =(1-p′)Q4+(Q5+p″Q6) / q s (23) Where D2 represents the outer diameter of the XLPE insulation layer; d c Indicates the outer diameter of the wire core; D3 indicates the outer diameter of the inner cushion layer; D5 indicates the outer diameter of the PP outer sheath layer; d a Indicates the outer diameter of the armor layer.

8. The method for predicting temperature rise and current carrying capacity of submarine cables based on thermal circuit analysis according to claim 7, characterized in that: The submarine cable temperature rise prediction models under different laying environments include the submarine cable temperature rise prediction model exposed to the air and the submarine cable temperature rise prediction model buried under the seabed; The temperature rise prediction model of submarine cables exposed to air converts T in the temperature rise prediction model of submarine cables into B1 Replace with T B1 +T air ; Among them, T air It represents the thermal resistance of the outside air; The expression of the temperature rise prediction model θ(t) of the submarine cable buried under the seabed is: θ(t)=θ c (t)+α(t)θ e (t) (49) IN t =In c +W d +W l +W a (48) In the formula, δ represents the heat dissipation factor of the soil; ρ s Indicates the thermal resistance coefficient of soil; D e Indicates the outer diameter of the submarine cable; L indicates the buried depth of the submarine cable; W t Represents the total loss of the submarine cable.

9. A method for predicting temperature rise and current carrying capacity of submarine cables based on thermal circuit analysis according to claim 8, characterized in that: The current carrying capacity prediction models of submarine cables under different laying environments include the current carrying capacity prediction model of submarine cables exposed to the air and the current carrying capacity prediction model of submarine cables buried under the seabed; The expression of the current-carrying capacity prediction model I' of the submarine cable exposed to the air is: In the formula, is the core temperature rise relative to the ambient temperature; n is the number of load conductors in the submarine cable; T air is the thermal resistance of the outside air; λ1”’ is the ratio of the XLPE insulation loss to the core loss; λ2’ is the ratio of the alloy lead sheath loss to the core loss; R represents the AC resistance of the core per unit length at the operating temperature; The expression of the current carrying capacity prediction model I" of submarine cables buried under the seabed is: In the formula, is the core temperature rise relative to the ambient temperature; n is the number of load conductors in the submarine cable; T 4solid is the external soil thermal resistance of the submarine cable; λ1”’ is the ratio of XLPE insulation loss to core loss; λ2’ is the ratio of alloy lead sheath loss to core loss; R represents the AC resistance of the core per unit length at operating temperature.

10. The method for predicting temperature rise and current carrying capacity of submarine cables based on thermal circuit analysis method according to claim 8, characterized in that: If the submarine cable is buried under the seabed in a pipe arrangement, then D e Indicates the outer diameter of the outer surface of the tube.

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