A single-core cable ampacity solving algorithm based on distributed optical fiber sensing technology

Abstract

This invention provides an algorithm for calculating the current carrying capacity of a single-core cable based on distributed optical fiber sensing technology. The algorithm includes: establishing mathematical models for calculating the core temperature and current carrying capacity of the single-core cable; calculating the thermal resistance of each cable layer and the environment, the loss of each cable layer, the average heat generation power of each cable layer, and the heat transfer rate at the outer surface; substituting the cable outer sheath temperature measured by the sensor into the aforementioned temperature mathematical model to obtain the cable conductor temperature; substituting the cable outer sheath temperature detected by the sensor into the aforementioned current carrying capacity mathematical model to calculate the theoretical operating current, and solving for the current correction coefficient with the actual detected current cable operating current; assuming the cable conductor temperature is 90 degrees Celsius, solving for the theoretical outer sheath temperature of the cable from the aforementioned temperature mathematical model, substituting it into the aforementioned current carrying capacity mathematical model to calculate the theoretical cable current carrying capacity, and multiplying the theoretical cable current carrying capacity by the current correction coefficient to obtain the final cable current carrying capacity.

Description

Technical Field

[0001] This invention specifically relates to an algorithm for calculating the current carrying capacity of a single-core cable based on distributed optical fiber sensing technology, belonging to the field of algorithm technology. Background Technology

[0002] Cables play a vital role in national energy and power transmission infrastructure, characterized by long transmission distances and difficulties in inspection and maintenance. Furthermore, cable conductor temperature and current-carrying capacity are crucial parameters. When a cable operates at its maximum safe load current, the conductor temperature may have already reached its maximum permissible temperature. Because conductor temperature is difficult to detect, distributed fiber optic sensing technology is typically used for cable condition monitoring; this involves embedding optical fibers in the cable sheath and other components during the cable manufacturing process. Secondly, cable current-carrying capacity represents the safe load current of the cable when the conductor reaches 90 degrees Celsius. If the load current exceeds the current-carrying capacity, the conductor temperature will rise sharply, exceeding the safe temperature and causing permanent damage such as insulation aging and thermal breakdown.

[0003] For cables laid in complex environments, the temperature of the cable conductor is significantly affected by the environment, which in turn affects the current carrying capacity and increases the difficulty of calculating the current carrying capacity in complex environments. Furthermore, the temperature of the cable conductor is difficult to measure directly; therefore, distributed fiber optic temperature sensors are typically used to measure the temperature of the cable's outer sheath to detect the cable's condition. Current methods for calculating cable current carrying capacity mainly include analytical calculation methods and numerical calculation methods.

[0004] The analytical calculation method based on IEC-60287 and the finite element method are both applicable. However, the analytical calculation method cannot be used without considering the cable core temperature. The finite element method, which mostly uses Comsol software, iterates through a given current-carrying capacity range until the cable core temperature reaches 90 degrees Celsius, which has limited practical value.

[0005] Firstly, the analytical calculation method is mainly based on the IEC-60287 standard. It allows for easy substitution of cable type parameters and environmental conditions into the calculation formula, facilitating calculations for designers and making it the most common calculation method in engineering. However, this method makes simple, uniform, and unchanging assumptions about the cable's environmental conditions, directly assuming a conductor temperature of 90 degrees Celsius. It does not consider the errors between the actual operating current and the theoretical operating current under real-world conditions. Therefore, the theoretical current-carrying capacity obtained by this method has a significant error compared to the current-carrying capacity under complex environmental conditions, such as a large error in marine environments.

[0006] Secondly, the finite element method (FEM) is a commonly used numerical calculation method, applied to the calculation of cable current carrying capacity and temperature field, and has gradually become the main calculation method. This method simulates the cable's temperature field based on the cable's laying environment and conditions, arrangement conditions, and load conditions to determine the cable's current carrying capacity. However, this method mostly uses simulation software such as Comsol, requiring extensive model drawing and iterative calculations until the cable conductor temperature reaches 90 degrees Celsius, resulting in a long solution time and limited practical application value.

[0007] Both of the above methods have some drawbacks. Therefore, an algorithm is needed that can reduce the error in cable current carrying capacity calculation, be easy to apply, and be fast in calculation, while taking into account the actual environment. Summary of the Invention

[0008] The purpose of this invention is to solve the problems in the background art mentioned above, so as to reduce the error in cable current carrying capacity calculation in actual environment, facilitate application and fast calculation, and provide a single-core cable current carrying capacity calculation algorithm based on distributed optical fiber sensing technology.

[0009] To achieve the above objectives, the present invention adopts the following technical solution: an algorithm for solving the current carrying capacity of a single-core cable based on distributed optical fiber sensing technology, the algorithm comprising the following steps:

[0010] Step S1: Calculate the cable insulation layer, water-blocking tape, outer sheath, and ambient thermal resistance;

[0011] Step S2: Calculate the losses of the cable conductor, insulation layer, and metal layer;

[0012] Step S3: Calculate the average heat generation power and heat transfer rate at the outer surface of the cable's outer sheath, metal layer, water-blocking tape, and insulation layer.

[0013] Step S4: Substitute the parameters calculated in steps S1, S2, and S3 and the cable outer sheath temperature measured by the distributed optical fiber temperature sensor into the mathematical model for calculating the cable core temperature, and solve in reverse to obtain the current theoretical cable conductor temperature.

[0014] Step S5: Substitute the theoretical cable conductor temperature obtained in step S6 and the cable outer sheath temperature detected by the sensor into the mathematical model for calculating the current carrying capacity of a single-core cable to calculate the theoretical cable operating current, and subtract it from the actual current operating current of the cable to solve for the current correction coefficient.

[0015] Step S6: Based on the mathematical model for calculating the core temperature, calculate the theoretical outer sheath temperature of the cable in the forward direction. Calculate the AC resistance of the conductor and the loss coefficient of the metal layer when the conductor temperature is 90 degrees. Substitute these values ​​into the mathematical model for calculating the current carrying capacity of a single-core cable to calculate the theoretical cable current carrying capacity. Multiply the theoretical cable current carrying capacity by the current correction factor to obtain the final cable current carrying capacity.

[0016] Furthermore, the mathematical model for calculating the cable core temperature is as follows:

[0017]

[0018] Among them, T core T1 is the temperature of the cable conductor, and T2 is the temperature of the cable outer sheath measured by a distributed fiber optic temperature sensor. i and r i+1 These represent the outer and inner radii of each layer of the cable, respectively, Q. 1i Q is the ratio of the average heat generation power of each layer of the cable to four times its thermal conductivity. 2o It is the ratio of the heat transfer rate at the outer surface of each layer of the cable to twice the thermal conductivity and π.

[0019] Furthermore, the mathematical model for calculating the current-carrying capacity of a single-core cable is as follows:

[0020]

[0021] Among them, when T core When the angle is 90 degrees, I is the current carrying capacity, and when T... core When the angle is less than 90 degrees, I is the operating current of the cable, and T is the operating current of the cable. O R is the temperature of the cable's outer sheath detected by the sensor. s R is the AC resistance of a conductor. d For the thermal resistance of the insulation layer, R w To prevent water from flowing and to reduce thermal resistance, R O For the thermal resistance of the outer sheath, R E Where W is the environmental thermal resistance, λ1 is the loss coefficient of the metal layer, λ2 is the ratio of insulation loss to cable conductor loss, and W is the thermal resistance of the environment. d This is insulation layer loss.

[0022] Furthermore, in step S1, the calculation formulas for the thermal resistance of each layer of the cable insulation layer, water-blocking tape, and outer sheath are as follows:

[0023]

[0024] Where R is the thermal resistance, ρ is the thermal resistance coefficient of the insulating layer, the water-blocking strip, and the outer sheath, t is the thickness of the layer, and d is the diameter of the adjacent layer inside the layer.

[0025] If located in a soil environment, the formula for calculating the environmental thermal resistance is:

[0026]

[0027] Among them, R E For environmental thermal resistance, ρR E D is the thermal resistivity of the environment in which the cable is laid. a The overall outer diameter of the cable;

[0028] If located in a marine environment, the formula for calculating environmental thermal resistance is:

[0029]

[0030] Where h is the depth of the cable laid in the environment, h f Where A is the convective heat transfer coefficient and A is the unit area.

[0031] Furthermore, in step S2, the formula for calculating cable conductor loss is:

[0032] W c =I 2 R s

[0033] Among them, W c R represents the cable conductor loss, I represents the cable's current carrying capacity, and R represents the current carrying capacity. s The AC resistance of the cable core conductor;

[0034] The formula for calculating insulation layer loss is:

[0035]

[0036] Among them, W d For insulation layer loss, ω=2πf, f is the system operating frequency, c is the capacitance per unit length of cable, U0 is the voltage relative to ground, and tanδ is the insulation loss factor;

[0037] The formula for calculating metal layer loss is:

[0038] W m =λ1·W c

[0039] Among them W m λ represents the metal layer loss, and λ1 is the metal layer loss coefficient.

[0040] Furthermore, in step S3, regarding the outer sheath, if the cable is placed in a soil environment, then:

[0041]

[0042] Q 11 Q represents the ratio of the average heat generation power of the outer sheath to four times its thermal conductivity. 21q represents the ratio of the heat transfer rate at the outer surface of the outer sheath to twice the thermal conductivity and π. v Where is the heat transfer rate at the outer surface, k is the thermal conductivity, and T is the heat transfer rate at the outer surface. E Where ε is the ambient temperature, σ is the surface emissivity, σ is the Boltzmann constant, and r1 is the outer radius of the outer sheath.

[0043] If the cable is placed in a marine environment, then:

[0044]

[0045] Where, q f This represents convective heat transfer, where D is the cable diameter, k is the thermal conductivity, and P... r Let R be the Prandtl number. e Let N be the Reynolds number. u For Nusselt number, t w t represents the outer surface temperature of the cable. f The values ​​of C1 and m represent the fluid temperature. They need to be obtained from a table based on the ratio of the cable axis distance to the cable diameter and the Reynolds number. C2 is a correction factor.

[0046] For the metal layer, then:

[0047]

[0048] in, Q is the average heating power. 13 Q represents the ratio of the average heat generation power of the metal layer to four times its thermal conductivity. 23 R3 represents the ratio of the heat transfer rate at the outer surface of the metal layer to twice the thermal conductivity and π, R3 represents the temperature at the outer surface of the metal layer, R3 is the outer radius of the metal layer, and R4 is the inner radius of the metal layer.

[0049] For the water-blocking strip, then:

[0050]

[0051] Q 15 Q represents the ratio of the average heating power of the water-blocking strip to four times its thermal conductivity. 25 T3 represents the ratio of the heat transfer rate at the outer surface of the water-blocking strip to twice the thermal conductivity and π, and r5 represents the outer surface temperature of the water-blocking strip.

[0052] For the insulating layer, then:

[0053]

[0054] Q 17 Q represents the ratio of the average heat generation power of the insulation layer to four times its thermal conductivity. 27T7 represents the ratio of the heat transfer rate at the outer surface of the insulation layer to twice the thermal conductivity and π, r7 represents the temperature of the outer surface of the insulation layer, r7 is the outer radius of the insulation layer, and r8 is the inner radius of the insulation layer.

[0055] Further, in step S5, the thermal resistance, loss, average heating power, heat transfer rate at the outer surface, cable outer sheath temperature measured by the distributed optical fiber temperature sensor, and the theoretical cable conductor temperature obtained in step S4 are substituted into the mathematical model for calculating the current carrying capacity of a single-core cable to solve for the theoretical cable operating current and current correction coefficient. The mathematical model for the current correction coefficient is as follows:

[0056] θ=(I′-I) / I

[0057] Where θ is the correction factor, I' is the measured value of the cable operating current, and I is the current when T core The theoretical value of the operating current calculated by the S2 mathematical model when the temperature is less than 90 degrees.

[0058] Further, in step S6, the theoretical outer sheath temperature of the cable is calculated by forward solving the mathematical model for calculating the core temperature. The conductor AC resistance and metal layer loss coefficient at a conductor temperature of 90 degrees Celsius are calculated, substituted into the mathematical model for calculating the current carrying capacity of a single-core cable to calculate the theoretical cable current carrying capacity, and multiplied by the current correction factor to obtain the final current carrying capacity. The calculation formula is as follows:

[0059] i′=(1+θ)I.

[0060] Where i' is the final carrying capacity, and I is the current carrying capacity when T... core The theoretical cable current carrying capacity calculated by the S2 mathematical model when the angle is 90 degrees.

[0061] Beneficial effects: Addressing the current challenge of directly measuring the conductor temperature of single-core cables, a mathematical model for calculating cable core temperature is established based on distributed fiber optic temperature sensors. The conductor temperature is derived by inversely using the detected temperature of the cable's outer sheath, heat conduction, and parameters of each cable layer. Furthermore, to address the issue of significant calculation errors in current-carrying capacity calculations in complex marine environments, the theoretical operating current of the cable is calculated using the calculated conductor temperature. This is then compared with the actual detected operating current to determine a current correction factor. Furthermore, assuming a conductor temperature of 90 degrees Celsius, the theoretical current-carrying capacity is calculated by forward deriving the outer sheath temperature at this temperature. Finally, a more accurate current-carrying capacity is obtained through the correction factor. Attached Figure Description

[0062] Figure 1 This is a flowchart of the algorithm for calculating the current carrying capacity of a single-core cable in the method of this invention;

[0063] Figure 2This is a cable structure diagram of an embodiment of the method of the present invention. Detailed Implementation

[0064] The invention will now be further explained with reference to the accompanying drawings.

[0065] Please refer to Figure 1 The algorithm of the present invention, in this embodiment, is an algorithm for solving the current carrying capacity of a single-core cable based on distributed optical fiber sensing technology, including the following steps:

[0066] Step S1: Calculate the cable insulation layer, water-blocking tape, outer sheath, and environmental thermal resistance.

[0067] Step S2: Calculate the losses of the cable conductor, insulation layer, and metal layer.

[0068] Step S3: Calculate the average heat generation power and heat transfer rate at the outer surface of the cable's outer sheath, metal layer, water-blocking tape, and insulation layer.

[0069] Step S4: Substitute the parameters calculated in steps S1, S2, and S3, and the cable outer sheath temperature measured by the distributed optical fiber temperature sensor, into the mathematical model for calculating the cable core temperature, and solve in reverse to obtain the current theoretical cable conductor temperature.

[0070] Step S5: Substitute the theoretical cable conductor temperature obtained in step S6 and the cable outer sheath temperature detected by the sensor into the mathematical model for calculating the current carrying capacity of a single-core cable to calculate the theoretical cable operating current, and subtract it from the actual current operating current of the cable to solve for the current correction coefficient.

[0071] Step S6: Based on the mathematical model for calculating the core temperature, calculate the theoretical outer sheath temperature of the cable in the forward direction. Calculate the AC resistance of the conductor and the loss coefficient of the metal layer when the conductor temperature is 90 degrees. Substitute these values ​​into the mathematical model for calculating the current carrying capacity of a single-core cable to calculate the theoretical cable current carrying capacity. Multiply the theoretical cable current carrying capacity by the current correction factor to obtain the final cable current carrying capacity.

[0072] In steps S4 and S5, a mathematical model for calculating the cable core temperature is established based on a distributed optical fiber temperature sensor. This model is used to inversely calculate the cable core temperature. The mathematical model is as follows:

[0073]

[0074] Among them, T core T1 is the temperature of the cable conductor, and T2 is the temperature of the cable outer sheath measured by a distributed fiber optic temperature sensor. i and r i+1 These represent the outer and inner radii of each layer of the cable, respectively, Q. 1i Q is the ratio of the average heat generation power of each layer of the cable to four times its thermal conductivity.2i It is the ratio of the heat transfer rate at the outer surface of each layer of the cable to twice the thermal conductivity and π.

[0075] The cable structure in this embodiment is: conductor, insulation layer, water-blocking tape, metal layer, and outer sheath, with the following parameters:

[0076] T1: Temperature measured on the outer sheath

[0077] T2: Temperature of the inner surface of the outer sheath

[0078] T3: Temperature of the outer surface of the metal layer

[0079] T4: Inner surface temperature of the metal layer

[0080] T5: Outer surface temperature of the water-blocking strip

[0081] T6: Inner surface temperature of the water-blocking strip

[0082] T7: Temperature of the outer surface of the insulation layer

[0083] T8: Inner surface temperature of the insulation layer

[0084] r1: Outer radius of the outer sheath

[0085] r2: Inner radius of the outer sheath

[0086] r3: Outer radius of the metal layer

[0087] r4: Inner radius of the metal layer

[0088] r5: Outer radius of the water-blocking strip

[0089] r6: Inner radius of the water-blocking strip

[0090] r7: Outer radius of the insulation layer

[0091] r8: Inner radius of the insulation layer

[0092] Q 11 The ratio of the average heating power of the outer sheath to 4 times its thermal conductivity.

[0093] Q 21 The ratio of the heat transfer rate at the outer surface of the outer sheath to twice the thermal conductivity and π.

[0094] Q 13 The ratio of the average heat generation power of the metal layer to four times its thermal conductivity.

[0095] Q 23 The ratio of the heat transfer rate at the outer surface of the metal layer to twice the thermal conductivity and π.

[0096] Q 15 The ratio of the average heating power of the water-blocking strip to 4 times its thermal conductivity.

[0097] Q 25 The ratio of the heat transfer rate at the outer surface of the water-blocking strip to twice the thermal conductivity and π.

[0098] Q 17 The ratio of the average heating power of the insulation layer to four times its thermal conductivity.

[0099] Q 27 The ratio of the heat transfer rate at the outer surface of the insulation layer to twice the thermal conductivity and π.

[0100] In steps S5 and S6, based on the mathematical model for calculating the cable core temperature, a mathematical model for calculating the current carrying capacity of a single-core cable is determined. The mathematical model is as follows: Among them, when T core When the angle is 90 degrees, I is the current carrying capacity, and when T... core When the angle is less than 90 degrees, I is the operating current of the cable, and T is the operating current of the cable. O R is the temperature of the cable's outer sheath detected by the sensor. s R is the AC resistance of a conductor. d For the thermal resistance of the insulation layer, R w To prevent water from flowing and to reduce thermal resistance, R O For the thermal resistance of the outer sheath, R E Where W is the environmental thermal resistance, λ1 is the loss coefficient of the metal layer, λ2 is the ratio of insulation loss to cable conductor loss, and W is the thermal resistance of the environment. d This is insulation layer loss.

[0101] The formulas for calculating the thermal resistance of each layer of the cable insulation layer, water-blocking tape, and outer sheath in step S1 are as follows: Where R is the thermal resistance, ρ is the thermal resistance coefficient of the insulation layer, water-blocking tape, and outer sheath, t is the thickness of the layer, and d is the diameter of the adjacent layer on the inner side of the layer; the formula for calculating the ambient thermal resistance is: If located in a marine environment, the calculation method for the convective heat transfer resistance between the cable and seawater is as follows: Among them, R E For environmental thermal resistance, D is the thermal resistivity of the environment in which the cable is laid. a Where h is the overall outer diameter of the cable, and h is the depth at which the cable is laid in the environment. f Where A is the convective heat transfer coefficient and A is the unit area.

[0102] The formula for calculating cable conductor loss in step S2 is: W c =I 2 R s Among them, W c R represents the cable conductor loss, I represents the cable's current carrying capacity (or operating current), and R represents the current carrying capacity (or operating current). sThis represents the AC resistance of the cable core conductor. The formula for calculating insulation loss is: Among them, W d For insulation layer loss, ω = 2πf, where f is the system operating frequency, c is the capacitance per unit length of cable, U0 is the voltage relative to ground, and tanδ is the insulation loss factor. The formula for calculating metal layer loss is: W m =λ1·W c Among them, W m λ represents the metal layer loss, and λ1 is the metal layer loss coefficient.

[0103] In step S3, the average heat generation power of the cable's outer sheath, metal layer, water-blocking tape, and insulation layer, as well as the heat transfer rate at the outer surface, are calculated; that is, Q of the mathematical model in S1 is calculated. 1i and Q 2i The calculation results differ for different layers within the cable.

[0104] For the outer sheath, if the cable is placed in a soil environment: Among them, Q 11 Q represents the ratio of the average heat generation power of the outer sheath to four times its thermal conductivity. 21 q represents the ratio of the heat transfer rate at the outer surface of the outer sheath to twice the thermal conductivity and π. v Where is the heat transfer rate at the outer surface, k is the thermal conductivity, and T is the heat transfer rate at the outer surface. E ε is the ambient temperature, ε is the surface emissivity, and σ is the Boltzmann constant.

[0105] If the cable is placed in a marine environment, then: Where, q f This represents convective heat transfer, where D is the cable diameter, k is the thermal conductivity, and P... r Let R be the Prandtl number. e Let N be the Reynolds number. u For Nusselt number, t w t represents the outer surface temperature of the cable. f The values ​​of C1 and m represent the fluid temperature. The values ​​of C1 and m need to be obtained by looking up the corresponding parameter values ​​in the table based on the ratio of the cable axis distance to the cable diameter and the Reynolds number. C2 is a correction factor.

[0106] For metal layers: in, Q is the average heating power. 13 Q represents the ratio of the average heat generation power of the metal layer to four times its thermal conductivity. 23 T3 represents the ratio of the heat transfer rate at the outer surface of the metal layer to twice the thermal conductivity and π, r3 represents the outer surface temperature of the metal layer, r3 is the outer radius of the metal layer, and r4 is the inner radius of the metal layer.

[0107] For water-blocking strips: Q15 Q represents the ratio of the average heating power of the water-blocking strip to four times its thermal conductivity. 25 T3 represents the ratio of the heat transfer rate at the outer surface of the water-blocking strip to twice the thermal conductivity and π, and r5 represents the outer surface temperature of the water-blocking strip.

[0108] For the insulating layer: Q 17 Q represents the ratio of the average heat generation power of the insulation layer to four times its thermal conductivity. 27 T7 represents the ratio of the heat transfer rate at the outer surface of the insulation layer to twice the thermal conductivity and π, r7 represents the temperature of the outer surface of the insulation layer, r7 is the outer radius of the insulation layer, and r8 is the inner radius of the insulation layer.

[0109] In step S4, the thermal resistance, loss, average heat generation power, heat transfer rate at the outer surface calculated in S1, S2, and S3, and the cable outer sheath temperature measured by the distributed optical fiber temperature sensor are substituted into the mathematical model for calculating the cable core temperature, and the theoretical cable conductor temperature T is solved in reverse. core .

[0110] In step S5, the thermal resistance, loss, average heat generation power, heat transfer rate at the outer surface of the cable calculated in S1, S2, S3, and S4, the temperature of the cable outer sheath measured by the distributed fiber optic temperature sensor, and the theoretical cable conductor temperature T solved in S4 are combined. core Substituting this into the mathematical model for calculating the current carrying capacity of a single-core cable, we solve for the theoretical operating current and the current correction coefficient. The mathematical model for the current correction coefficient is: θ = (I' - I) / I. Where θ is the correction coefficient, I' is the measured value of the cable's operating current, and I is the current carrying capacity when T... core The theoretical value of the operating current calculated by the S2 mathematical model when the temperature is less than 90 degrees.

[0111] In step S6, the cable conductor temperature is set to 90 degrees Celsius. The theoretical outer sheath temperature of the cable is then calculated forward using the mathematical model for calculating the cable core temperature. Therefore, it is necessary to derive the cable outer sheath temperature step by step from the conductor temperature outwards. The derivation process is as follows:

[0112] Derive the outer layer temperature of the insulation layer from the known conductor temperature:

[0113] Q 17 This represents the ratio of the average heat generation power of the insulation layer to four times its thermal conductivity; T7 represents the outer surface temperature of the insulation layer; r7 is the outer radius of the insulation layer; r8 is the inner radius of the insulation layer; R... w To prevent water from flowing and to reduce thermal resistance, R O For the thermal resistance of the outer sheath, R E For environmental thermal resistance, T E ε is the ambient temperature, ε is the surface emissivity, and σ is the Boltzmann constant.

[0114] The outer layer temperature of the insulating layer is used to deduce the outer layer temperature of the water-blocking tape: Where T5 represents the outer surface temperature of the water-blocking tape, T7 represents the outer surface temperature of the insulation layer, r5 is the outer radius of the water-blocking tape, r6 is the inner radius of the water-blocking tape, and R... O For the thermal resistance of the outer sheath, R E For environmental thermal resistance, T E ε is the ambient temperature, ε is the surface emissivity, and σ is the Boltzmann constant.

[0115] The outer temperature of the water-blocking band is used to deduce the outer temperature of the metal layer:

[0116] Q 13 This represents the ratio of the average heat generation power of the metal layer to four times its thermal conductivity; T3 represents the outer surface temperature of the metal layer; T5 represents the outer surface temperature of the water-blocking strip; r3 is the outer radius of the metal layer; r4 is the inner radius of the metal layer; R... O For the thermal resistance of the outer sheath, R E For environmental thermal resistance, T E ε is the ambient temperature, ε is the surface emissivity, and σ is the Boltzmann constant.

[0117] The temperature of the outer metal layer was derived from the temperature measured on the outer protective layer placed in a soil environment. Where T1 represents the temperature measured on the outer sheath, T3 represents the temperature of the outer surface of the metal layer, r1 is the outer radius of the outer sheath, r2 is the outer radius of the outer sheath, and R... e For environmental thermal resistance, T E ε is the ambient temperature, ε is the surface emissivity, and σ is the Boltzmann constant.

[0118] In a marine environment, the temperature measured on the outer protective layer is: Among them, h f The convective heat transfer coefficient is given by T1, where T1 represents the temperature measured on the outer sheath, T3 represents the temperature of the outer surface of the metal layer, r1 is the outer radius of the outer sheath, r2 is the outer radius of the outer sheath, and R... E For environmental thermal resistance, T E ε is the ambient temperature, ε is the surface emissivity, and σ is the Boltzmann constant.

[0119] The mathematical models for deriving temperature layer by layer described above are all solved using the following method:

[0120]

[0121] After obtaining the measured temperature of the cable outer sheath, it is substituted along with parameters such as the cable conductor temperature of 90 degrees Celsius into the mathematical model for calculating the current carrying capacity of a single-core cable. The AC resistance of the conductor and the loss coefficient of the metal layer at a conductor temperature of 90 degrees Celsius are calculated and substituted into the theoretical cable current carrying capacity. This is then multiplied by the current correction factor to obtain the final current carrying capacity, calculated using the formula: i'=(1+θ)I. Where i' is the final current carrying capacity, and I is the current carrying capacity when T... core The theoretical cable current carrying capacity calculated by the S2 mathematical model when the angle is 90 degrees.

[0122] This method addresses the challenge of directly measuring the conductor temperature of single-core cables. It establishes a mathematical model for calculating the cable core temperature based on distributed fiber optic temperature sensors. The conductor temperature is derived by inversely from the detected temperature of the cable's outer sheath, heat conduction, and parameters of each layer. To address the issue of significant calculation errors in current-carrying capacity calculations in complex marine environments, the theoretical operating current of the cable is calculated using the calculated conductor temperature. A current correction coefficient is then determined by comparing this with the actual detected operating current. Furthermore, assuming a conductor temperature of 90 degrees Celsius, the theoretical current-carrying capacity is calculated by forward derivation of the outer sheath temperature. Finally, a more accurate current-carrying capacity is obtained through the correction coefficient.

[0123] This invention provides a method for calculating the current carrying capacity of single-core cables in soil and marine environments. Based on the temperature of the cable's outer sheath measured by a distributed optical fiber temperature sensor, the current carrying capacity of single-core cables can be calculated.

[0124] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A single core cable ampacity solution method based on distributed fiber optic sensing technology, characterized in that, The method includes the following steps: Step S1: Calculate the cable insulation layer, water-blocking tape, outer sheath, and ambient thermal resistance; Step S2: Calculate the losses of the cable conductor, insulation layer, and metal layer; Step S3: Calculate the average heat generation power and heat transfer rate at the outer surface of the cable's outer sheath, metal layer, water-blocking tape, and insulation layer. Step S4: Substitute the parameters calculated in steps S1, S2, and S3 and the cable outer sheath temperature measured by the distributed optical fiber temperature sensor into the mathematical model for calculating the cable core temperature, and solve in reverse to obtain the current theoretical cable conductor temperature. The mathematical model for calculating the cable core temperature is as follows: in, For the temperature of the cable conductor, The temperature of the cable's outer sheath is measured by a distributed fiber optic temperature sensor. and These are the outer and inner radii of each layer of the cable, respectively. This is the ratio of the average heat generation power of each layer of the cable to four times its thermal conductivity. The heat transfer rate at the outer surface of each layer of the cable and twice the thermal conductivity. The ratio; Step S5: Substitute the theoretical cable conductor temperature obtained in step S4 and the cable outer sheath temperature detected by the sensor into the mathematical model for calculating the current carrying capacity of a single-core cable to calculate the theoretical cable operating current, and subtract it from the actual current operating current of the cable to solve for the current correction coefficient. Step S6: Based on the mathematical model for calculating the core temperature, calculate the theoretical outer sheath temperature of the cable in the forward direction. Calculate the AC resistance of the conductor and the loss coefficient of the metal layer when the conductor temperature is 90 degrees. Substitute these values ​​into the mathematical model for calculating the current carrying capacity of a single-core cable to calculate the theoretical cable current carrying capacity. Multiply the theoretical cable current carrying capacity by the current correction factor to obtain the final cable current carrying capacity.

2. The method for solving the current-carrying capacity of a single-core cable based on distributed optical fiber sensing technology according to claim 1, characterized in that, The mathematical model for calculating the current carrying capacity of a single-core cable is as follows: Among them, when When it is 90 degrees, For carrying capacity, when When the temperature is less than 90 degrees, This refers to the operating current of the cable. The temperature of the cable's outer sheath as detected by the sensor. For conductor AC resistance, For the thermal resistance of the insulation layer, To prevent water from flowing and to prevent thermal resistance, For the thermal resistance of the outer sheath, For environmental thermal resistance, The loss coefficient of the metal layer, This is the ratio of insulation loss to cable conductor loss. This is insulation layer loss.

3. The method for solving the current-carrying capacity of a single-core cable based on distributed optical fiber sensing technology according to claim 2, characterized in that, In step S1, the calculation formulas for the thermal resistance of each layer of the cable insulation layer, water-blocking tape, and outer sheath are as follows: in For thermal resistance, The thermal resistance coefficients of the insulation layer, water-blocking tape, and outer sheath are given. The thickness of this layer, The diameter of the adjacent layer inside this layer; If located in a soil environment, the formula for calculating the environmental thermal resistance is: in, For environmental thermal resistance, The thermal resistivity of the environment in which the cable is laid. The overall outer diameter of the cable; If located in a marine environment, the formula for calculating environmental thermal resistance is: Where h is the depth of the cable laid in the environment. Here, A is the convective heat transfer coefficient, and A is the area per unit area.

4. The method for solving the current-carrying capacity of a single-core cable based on distributed optical fiber sensing technology according to claim 3, characterized in that, In step S2, the formula for calculating cable conductor loss is: in, For cable conductor loss, The current carrying capacity of the cable. The AC resistance of the cable core conductor; The formula for calculating insulation layer loss is: in, For insulation layer loss, , Where c is the system operating frequency, and c is the capacitance per unit length of the cable. The voltage relative to ground. This is the insulation loss factor; The formula for calculating metal layer loss is: in For metal layer loss, This represents the loss coefficient of the metal layer.

5. The method for solving the current-carrying capacity of a single-core cable based on distributed optical fiber sensing technology according to claim 4, characterized in that, In step S3, regarding the outer sheath, if the cable is placed in a soil environment, then: in This represents the ratio of the average heat generation power of the outer sheath to four times its thermal conductivity. This indicates the heat transfer rate at the outer surface of the outer sheath and twice the thermal conductivity. The ratio, The heat transfer rate at the outer surface, Thermal conductivity, For ambient temperature, For surface emissivity, Boltzmann's constant, The outer radius of the outer protective layer; If the cable is placed in a marine environment, then: in, Indicates convective heat transfer. The diameter of the cable. Thermal conductivity, For Prandtl numbers, Let Reynolds number be 1. For Nusel number, The outer surface temperature of the cable. Indicates fluid temperature. The values ​​of and m need to be obtained by looking up the corresponding parameter values ​​in a table based on the ratio of the cable axis distance to the cable diameter and the Reynolds number. As a correction factor; For the metal layer, then: in, This represents the average heating power. This represents the ratio of the average heat generation power of the metal layer to four times its thermal conductivity. This represents the heat transfer rate at the outer surface of the metal layer and twice the thermal conductivity. The ratio, Indicates the temperature of the outer surface of the metal layer. The outer radius of the metal layer, The inner radius of the metal layer; For the water-blocking strip, then: in This indicates the ratio of the average heating power of the water-blocking strip to four times its thermal conductivity. This indicates the heat transfer rate at the outer surface of the water-blocking strip and twice the thermal conductivity. The ratio, T5 represents the outer surface temperature of the water-blocking strip. The outer radius of the water-blocking strip; For the insulating layer, then: in This represents the ratio of the average heat generation power of the insulation layer to four times its thermal conductivity. This represents the heat transfer rate at the outer surface of the insulating layer and twice the thermal conductivity. The ratio, Indicates the temperature of the outer surface of the insulation layer. The outer radius of the insulation layer, The inner radius of the insulation layer.

6. The method for solving the current-carrying capacity of a single-core cable based on distributed optical fiber sensing technology according to claim 2, characterized in that, In step S5, the thermal resistance, loss, average heating power, heat transfer rate at the outer surface, cable outer sheath temperature measured by the distributed optical fiber temperature sensor, and the theoretical cable conductor temperature calculated in steps S1, S2, S3, and S4 are substituted into the mathematical model for calculating the current carrying capacity of a single-core cable to solve for the theoretical cable operating current. The current correction coefficient is then calculated based on the following mathematical model: in, For correction factor, This is a measured value of the cable's operating current. For when When the temperature is less than 90 degrees, the theoretical value of the operating current is obtained by the mathematical model for calculating the current carrying capacity of a single-core cable.

7. The method for solving the current-carrying capacity of a single-core cable based on distributed optical fiber sensing technology according to claim 6, characterized in that, In step S6, the theoretical outer sheath temperature of the cable is calculated forward using the mathematical model for calculating the cable core temperature. The conductor AC resistance and metal layer loss coefficient at a conductor temperature of 90 degrees Celsius are calculated, and these are substituted into the mathematical model for calculating the current carrying capacity of a single-core cable to calculate the theoretical cable current carrying capacity. This is then multiplied by the current correction factor to obtain the final current carrying capacity. The calculation formula is as follows: in For the final carrying capacity, For when When the angle is 90 degrees, the theoretical cable current carrying capacity is calculated by the mathematical model for calculating the current carrying capacity of a single-core cable.

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