Method for predicting steady-state temperature of three-phase multi-circuit tunnel cable core, and electronic device

Abstract

The present invention relates to a method for predicting the steady-state temperature of a three-phase multi-circuit tunnel cable core, and an electronic device. The method comprises: establishing a single-phase single-circuit tunnel cable steady-state thermal circuit model, and using the constructed single-phase single-circuit tunnel cable steady-state thermal circuit model to obtain the steady-state temperature of a core of a single-phase single-circuit cable; using a correction method to obtain the steady-state temperature of a cable core arranged in a three-phase single circuit; for a single-phase four-circuit arrangement situation, incorporating the influence of a mutual thermal effect between circuit cables on the temperature of the cable core into equivalent mutual-heating thermal resistance, and introducing the equivalent mutual-heating thermal resistance into the single-phase single-circuit tunnel cable steady-state thermal circuit model, so as to form an improved thermal circuit model to predict the steady-state temperature of a cable core of a single-phase multi-circuit cable; and using a three-phase multi-circuit cable as the combination of single-phase single-circuit, three-phase single-circuit and single-phase multi-circuit, and predicting the temperature of a cable core of the three-phase multi-circuit cable. Compared with the prior art, the present invention has advantages such as quickly and accurately predicting the steady-state temperature of a three-phase multi-circuit tunnel cable core.

Description

Steady-state temperature prediction method and electronic equipment for three-phase multi-circuit tunnel cable cores Technical Field

[0001] This invention relates to the field of steady-state temperature rise prediction technology for cables, and in particular to a method and electronic device for predicting the steady-state temperature of a three-phase multi-circuit tunnel cable core. Background Technology

[0002] Tunnel cables are widely used in power transmission and distribution lines in large power plants and urban roads due to their advantages such as large transmission capacity, effective protection against external forces, resistance to external climate and environmental influences, and ease of inspection and maintenance. However, tunnel cables have poor heat dissipation, making them prone to overheating and accelerated insulation aging during operation. For example, for cross-linked polyethylene (XLPE) insulated cables, XLPE ages rapidly when the core temperature exceeds 90°C, thus affecting power transmission safety. Therefore, accurate prediction of the core temperature is crucial for ensuring the safe operation of the cable.

[0003] Tunnel cables can accommodate a large number of transmission lines, so they are usually laid in clusters. During operation, the mutual heating effect between cables in clustered installations increases the cable temperature, which needs to be considered when predicting the cable core temperature. Currently, the prediction of cable core temperature under mutual heating effect mainly adopts three common methods for predicting hot spot temperature in power equipment: numerical calculation method, IEC standard-based thermal circuit method, and machine learning algorithm. The numerical calculation method directly solves the field variables of the cable based on numerical calculation methods such as finite element method. When laid in clusters, no additional method is needed to calculate the mutual heating effect. It has a wide range of applications and high calculation accuracy, but the calculation time is long, which limits its application in engineering. The thermal circuit method establishes a thermal circuit model of the cable heat transfer process based on thermoelectric analogy theory, and considers the influence of mutual heating effect between cables by correcting thermal circuit parameters and introducing new thermal circuit structures. The thermal circuit method has a fast calculation speed and is mostly used for directly buried cables laid in clusters. However, for tunnel cables where the medium between cables is air, the heat transfer between cables includes convective heat transfer and radiative heat transfer, which makes it difficult to establish the thermal circuit for mutual heating effect, and corresponding thermal circuit research is also relatively limited. Machine learning algorithms require sample data obtained through experiments or numerical calculations to construct the relationship between load current and cable core temperature. The influence of mutual heating effect is included in the sample data; therefore, the handling of mutual heating effect is essentially accomplished through experiments or numerical calculations. In summary, current methods for predicting the cable core temperature of tunnel cables in clustered installations are still immature. A new, universal, and rapid method for predicting cable core temperature is needed, specifically for the common clustered installation configurations in tunnel cables.

[0004] For cables laid in clusters within tunnels, the cables in the circuit are usually arranged in a triangular pattern with close spacing between them. Therefore, the mutual heating effect exists both between and within the circuit, making it particularly difficult to handle the mutual heating effect when predicting the cable core temperature.

[0005] A search revealed Chinese invention patent publication number CN112380669A, which discloses a method for rapidly obtaining the steady-state maximum core temperature of a four-circuit trench cable. The method includes the following steps: 1) constructing a calculation model for the maximum core temperature of the four-circuit cable; 2) estimating parameters based on the physical model of the trench cable under different heat flows and ambient temperatures to obtain the thermal radiation coefficient and various constant parameters in the calculation model; 3) obtaining the maximum core temperature of the trench cable based on the four-circuit cable core maximum temperature calculation model after parameter fitting. This existing patent has the problem of not being applicable to predicting the steady-state temperature of cables laid in clusters within tunnels.

[0006] How to predict the steady-state temperature of the core of a three-phase multi-circuit tunnel cable has become a technical problem that needs to be solved. Summary of the Invention

[0007] The purpose of this invention is to overcome the defects of the prior art by providing a method and electronic device for predicting the steady-state temperature of the core of a three-phase multi-circuit tunnel cable.

[0008] The objective of this invention can be achieved through the following technical solutions:

[0009] According to one aspect of the present invention, a method for predicting the steady-state temperature of a three-phase multi-circuit tunnel cable core is provided, the method comprising the following steps:

[0010] Step S1: Establish a steady-state thermal circuit model of a single-phase, single-circuit tunnel cable, and use the established model to solve for the steady-state temperature T of the cable core in a single phase and single circuit. c0 ;

[0011] Step S2: Based on step S1, the steady-state temperature T of the cable core under three-phase single-circuit laying is calculated using a correction method. c0 ';

[0012] Step S3: For single-phase four-circuit laying, the influence of mutual heating effect between loop cables on the core temperature is attributed to the mutual heating effect thermal resistance, and it is introduced into the steady-state thermal circuit model of single-phase single-circuit tunnel cable to form an improved thermal circuit model to predict the steady-state core temperature T of single-phase multi-circuit cable. c1 ;

[0013] Step S4: Treat the three-phase multi-circuit cable as a combination of single-phase single-circuit, three-phase single-circuit, and single-phase multi-circuit, and use the T obtained in steps S1 to S3. c0 Tc0 'and T c1 Predicting the core temperature T of a three-phase multi-circuit cable c .

[0014] Preferably, the steady-state thermal circuit model of the single-phase single-circuit tunnel cable considers the complete flow and heat transfer process within the tunnel cable. In terms of flow, the model includes natural convection between the cable surface and the air inside the tunnel; in terms of heat transfer, the model includes conduction, convection, and radiation.

[0015] Preferably, the steady-state thermal circuit model of the single-phase single-circuit tunnel cable includes multiple heat sources and thermal resistances, wherein the heat sources include the cable core conductor loss when the cable is subjected to alternating current, and the thermal resistances include the thermal resistance of the cable body, the thermal resistance of the air layer inside the tunnel, the thermal resistance of the tunnel layer, and the thermal resistance of the soil layer.

[0016] The thermal resistance of the air layer inside the tunnel is determined by the convective thermal resistance R. cov With radiation thermal resistance R rad Composed of parallel connections.

[0017] Preferably, step S2 includes the following process:

[0018] Step S2-1: Under a given cable load current I, calculate the single-phase, single-circuit cable core temperature T using finite element simulation software. c0 and the core temperature T of a three-phase single-circuit cable c0 ', and thus the cable core temperature correction factor C1 is obtained at this time: C1=T c0 ' / T c0

[0019] Step S2-2, at different currents I i For (i = 1, 2, ..., N), repeat step S2-1 above to obtain C under different currents. i , where N is the number of different currents;

[0020] Steps S2-3, at different currents I i Lower cable core temperature correction factor C i Based on the value, the correction factor C is fitted as a function of the load current I: C = f(I)

[0021] Step S2-4: Given the cable load current I, the core temperature T of the three-phase single-circuit cable is... c0 The solution can be found by: T c0 '=CT c0

[0022] Where T c0 The steady-state temperature of the single-phase, single-circuit cable core is obtained in step S1.

[0023] Preferably, the improved thermal path model construction process in step S3 includes:

[0024] Step S3-1: The loop cable with the core temperature to be determined is called the target cable, and the cables of the other three loops are called adjacent cables. The effect of the heating of the adjacent cables on the increase of the core temperature of the target cable is constructed as an additional thermal resistance R in the air layer thermal path of the target cable. m And called R m To determine the thermal resistance due to mutual heating effect, the finite element method was used to calculate the air temperature rise inside the tunnel under different working conditions, and then the value of R was determined. m value;

[0025] Step S3-2: Change the current I of each adjacent loop cable individually. j All other circuit cables were unloaded, and the finite element method was used to calculate the I values ​​for different circuits. j Average temperature rise ΔT of air inside the lower tunnel aj and ΔT aj Fitted to I j The function: ΔT aj =f j (I j )

[0026] Where j is the j-th neighboring loop, and if loop 1 is the target cable, then j = 2, 3, ..., n;

[0027] Step S3-3: The increase in air temperature ΔT when current is applied to all adjacent circuits simultaneously. a It equals the sum of the increases in air temperature caused by each adjacent loop operating individually:

[0028] Step S3-4: Apply current I to the target cable, calculate the cable loss Q according to IEC standards, and then determine the mutual heating effect R in the steady-state thermal circuit of the target cable. m Calculate using the following formula: R m =C2ΔT a / Q

[0029] Where, ΔT a The temperature rise of the air inside the tunnel is caused by the heating of adjacent loops 2 to n; Q is the heat generated by loop 1 under current I; C2 is a correction factor.

[0030] Step S3-5: Calculate the mutual heating effect thermal resistance R obtained in step S3-4. m Substitute the expression into the thermal circuit model constructed in step S1 to form an improved thermal circuit model.

[0031] More preferably, in step S3, the steady-state temperature T of the cable core of the single-phase multi-loop cable is predicted. c1 Specifically: when n loop currents I1~I are givenn At that time, the cable loss Q is determined based on the target cable current, and ΔT is determined using step S3-3 based on the current of the adjacent cables. a The value is then used in step S3-4 to obtain the thermal resistance R of the mutual heating effect at this time. m Then, substituting this into the improved thermal circuit model, the steady-state temperature T of the cable core under single-phase four-circuit conditions is obtained by solving the improved thermal circuit model. c1 .

[0032] Preferably, in step S4, the core temperature T of the three-phase multi-loop cable is predicted. c The process includes:

[0033] 1) Combine single-phase single-circuit cables into single-phase multi-circuit cables, with the core temperature determined by the steady-state core temperature T of the single-phase single-circuit cable. c0 The steady-state temperature T of the cable core when converted to a single-phase multi-circuit cable c1 T c1 Solved using an improved thermal circuit model;

[0034] 2) In single-phase multi-circuit laying, each adjacent circuit of circuit 1 adds one phase, and the core temperature of circuit 1 is increased from T c1 Transform into T c1 +(T c1 -T c0 );

[0035] 3) Add one phase to each adjacent circuit of circuit 1. At this time, all adjacent circuits are complete three-phase circuits. The core temperature of circuit 1 is T c1 +(T c1 -T c0 ) becomes T c1 +2(T c1 -T c0 );

[0036] 4) Circuit 1 is changed from single-phase to three-phase, and the core temperature of Circuit 1 is changed from T c1 +2(T c1 -T c0 ) becomes C1[T c1 +2(T c1 -T c0 )], where C1 is the correction factor between single-phase and three-phase cables;

[0037] Therefore, the core temperature T of loop 1 in a three-phase multi-loop circuit is... c The expression is as follows:

[0038] T c =C1[T c1 +2(T c1 -T c0 )], that is: T c =C1[Tc0 +3(T c1 -T c0 )).

[0039] More preferably, the convective thermal resistance R cov The calculation is as follows:

[0040] Where A is the cable surface area; h(I) is the convective heat transfer coefficient of the cable surface, a function of the load current I. More preferably, the radiative thermal resistance R... rad The calculation is as follows:

[0041] Where π is the mathematical constant Pi, and T s and T t These are the average temperatures of the cable surface and the tunnel inner wall, respectively; D is the cable outer diameter; ε c Let σ be the surface emissivity of the cable, and σ be the blackbody radiation constant.

[0042] In another aspect, an electronic device is provided, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the program to implement the method described thereon.

[0043] Compared with the prior art, the present invention has the following beneficial effects:

[0044] 1) This invention treats three-phase multi-circuit cables as a combination of simple laying methods. First, the thermal circuit model is used to solve the steady-state temperature of the cable core of a single-phase single-circuit tunnel cable. Then, the steady-state temperature of the cable core under three-phase single-circuit and single-phase multi-circuit conditions is solved respectively. Finally, based on the combination of cable core temperatures, the invention extends from single-phase single-circuit to three-phase multi-circuit, realizing the application of the thermal circuit model to predict the steady-state temperature of the cable core of tunnel cables. The prediction is fast and highly accurate.

[0045] 2) This invention assumes that the heating of adjacent circuits is independent of each other. Since the steady-state thermal path of the cable is composed of linear components, the heating effect of adjacent circuits on the air temperature increases satisfies the superposition principle. The contribution of each circuit to the air temperature rise when it is running alone is calculated using the finite element method. Then, the contribution expression of each circuit to the air temperature rise when it is running alone is obtained by polynomial fitting. Finally, the mutual heating effect resistance is quickly obtained based on the accumulation of the total air temperature rise, which solves the problem of difficulty in establishing the thermal path.

[0046] 3) This invention adds mutual heating effect resistance to the thermal circuit model to represent the effect of adjacent cable heating on the target cable core temperature, forming an improved thermal circuit model. Based on the improved thermal circuit model, the steady-state temperature of the single-phase multi-circuit tunnel cable core is solved, thereby realizing the accurate and rapid solution of the steady-state temperature of the cable core under cluster laying.

[0047] 4) The method of the present invention has a certain degree of universality and can be further applied to the steady-state temperature prediction of tunnel cables with more loops, and has a wide range of applications. Attached Figure Description

[0048] Figure 1 is a schematic diagram of the calculation process of the method in Embodiment 1 of the present invention;

[0049] Figure 2 is a flowchart illustrating the method in Embodiment 1 of the present invention;

[0050] Figure 3 is a schematic diagram of the physical model of a three-phase four-circuit tunnel cable according to an embodiment of the method of the present invention;

[0051] Figure 4 is a schematic diagram of the cable body in one embodiment of the present invention;

[0052] Figure 5 is a schematic diagram of the thermal circuit model for solving the steady-state temperature of the core of a single-phase single-circuit tunnel cable in this invention.

[0053] Figure 6 is a schematic diagram of the improved thermal circuit model for solving the steady-state temperature of the core of a single-phase four-circuit tunnel cable in this invention.

[0054] Figure 7 is a schematic diagram of the steady-state temperature prediction process of a three-phase four-circuit cable core based on the combination method in this invention.

[0055] Figure 8 shows the deviation and relative deviation between the solution result of the highest steady-state temperature of the cable core of loop 1 in the three-phase four-loop cable in this invention and the finite element calculation result. Detailed Implementation

[0056] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0057] Example 1

[0058] This embodiment relates to a method for predicting the steady-state temperature of the cable core of a three-phase four-circuit tunnel cable. This method, specifically for three-phase four-circuit tunnel cables laid in clusters, proposes a combined method for predicting the steady-state temperature of the cable core based on the spatial arrangement of the cables. The three-phase four-circuit cable is considered as a combination of simple laying methods. First, the solution for the cable core temperature of the three-phase four-circuit cable is transformed into solving the cable core temperatures of single-phase single-circuit, three-phase single-circuit, and single-phase four-circuit cables separately. During the solution process, the influence of inter-cable heat exchange effects is handled through correction and improvement of the thermal circuit model. Then, the solution results are combined to finally obtain the steady-state temperature of the cable core under the three-phase four-circuit laying configuration.

[0059] The method of this invention enables accurate prediction of the steady-state temperature of the core of a three-phase four-circuit tunnel cable, and the method has strong universality and can be further extended to tunnel laying scenarios with more circuits.

[0060] To achieve the above objectives, the technical solution adopted by the present invention includes the following steps, as shown in Figure 2:

[0061] Step S1: Establish a steady-state thermal circuit model for a single-phase, single-circuit (single-core) tunnel cable. Determine the thermal circuit parameters based on IEC standards and finite element calculation results. Under a given load current, use the thermal circuit model to solve for the steady-state temperature T of the cable core in a single-phase, single-circuit (i.e., single-core) cable. c0 ;

[0062] Step S2: Based on the steady-state temperature of a single cable core, use a correction method to solve for the steady-state temperature T of the cable core under three-phase single-circuit laying. c0 ';

[0063] Step S3: For single-phase four-circuit cable laying, the influence of mutual heating between loop cables on the cable core temperature is attributed to the mutual heating effect thermal resistance, and introduced into the steady-state thermal circuit model of a single cable to form an improved thermal circuit model for predicting the steady-state temperature T of the cable core of a single-phase four-circuit cable. c1 ;

[0064] Step S4: Treat the three-phase four-circuit cable as a combination of single-phase single-circuit, three-phase single-circuit, and single-phase four-circuit, and use the T obtained in steps S1 to S3. c0 T c0 'and T c1 Determine the core temperature T of a three-phase four-circuit cable c ;

[0065] Finally, the core temperature of the three-phase four-circuit cable was calculated using the finite element method and the method of this invention under different operating conditions, and the results were compared to verify the correctness of the proposed method for predicting the steady-state core temperature of the three-phase four-circuit tunnel cable.

[0066] The steady-state thermal circuit model of the tunnel cable in step S1 includes multiple heat sources and thermal resistances. Heat sources include conductor losses in the cable core when an alternating current is applied, calculated according to IEC standards. Thermal resistances include the cable body thermal resistance, the air layer thermal resistance within the tunnel, the tunnel layer thermal resistance, and the soil layer thermal resistance, determined according to IEC standards combined with finite element simulation. Given a current I, the steady-state thermal circuit model of the tunnel cable is used to predict the core temperature T of a single-phase, single-circuit (single cable). c0 .

[0067] Step S2 uses a correction method to solve for the steady-state temperature T of the three-phase single-circuit cable core. c0 The specific steps are as follows:

[0068] Step S2.1: Under a given cable load current I, calculate the single-phase, single-circuit cable core temperature T using finite element simulation software. c0 and the core temperature T of a three-phase single-circuit cable c0 ', and thus the cable core temperature correction factor C1 is obtained at this time: C1=T c0 ' / T c0

[0069] Step S2.2: At different currents I i For (i = 1, 2, ..., N), repeat step S2.1 above to obtain the cable core temperature correction coefficient C under different currents. i ;

[0070] Step S2.3: At different currents I i C i Based on the value, the correction factor C is fitted as a function of the load current I: C = f(I)

[0071] Step S2.4: Given a load current I, use step S1 to calculate the steady-state temperature T of the cable core of a single cable under current I. c0 And using step S2.3 to calculate the core temperature correction factor C, the core temperature T of the three-phase single-circuit cable is then determined. c0 The solution can be found by: T c0 '=CT c0

[0072] The specific steps for constructing the improved thermal circuit model for solving the core temperature of a single-phase four-circuit cable in step S3 are as follows:

[0073] Step S3.1: The loop cable from which the core temperature is to be determined is referred to as the target cable, and the cables of the other three loops are referred to as adjacent cables. The increase in core temperature of the target cable due to the heating of the adjacent cables is considered as an additional thermal resistance R in the air layer thermal path of the target cable. m And called R m To determine the thermal resistance due to mutual heating, the finite element method is used to calculate the air temperature rise inside the tunnel under different working conditions, and then the R value is determined. m value;

[0074] Step S3.2: Change the current I of each adjacent loop cable individually. j (j represents the j-th adjacent loop. For a four-loop installation, if loop 1 is the target cable, then j = 2, 3, 4). All other loop cables are unloaded (current is zero). The finite element method is used to calculate different I values. j Average temperature rise ΔT of air inside the lower tunnel aj and ΔT aj Fitted to I j The function: ΔT aj =fj (I j (j=2,3,4)

[0075] Step S3.3: The increase in air temperature ΔT when current is applied to all adjacent circuits simultaneously. a It equals the sum of the increases in air temperature caused by each adjacent loop operating individually:

[0076] Step S3.4: Apply current I to the target cable, calculate the cable loss Q according to IEC standards, and then determine the mutual heating effect R in the steady-state thermal circuit of the target cable. m Calculate using the following formula: R m =C2ΔT a / Q

[0077] Where, ΔT a Ri is the temperature rise of the air inside the tunnel caused by the heating of adjacent circuits 2-4; Q is the heat generated by circuit 1 under current I; C2 is a correction factor used to adjust Ri. m The solution is more accurate, determined through model calibration.

[0078] Step S3.5: Calculate the mutual heating effect thermal resistance R obtained in step S3.4. m Substituting the expression into the target cable thermal circuit model (i.e., the thermal circuit model constructed in step S1, as shown in Figure 5), an improved thermal circuit model is formed as shown in Figure 6. Given four loop currents I1 to I4, the cable loss Q is determined based on the target cable current, and ΔT is determined using step S3.3 based on the currents of adjacent cables. a The value is then used in step S3.4 to obtain the thermal resistance R of the mutual heating effect at this time. m Then, substituting this into the improved thermal circuit model, the steady-state temperature T of the cable core under single-phase four-circuit conditions is obtained by solving the improved thermal circuit model. c1 .

[0079] In step S4, the three-phase four-circuit laying is considered as a combination of three simple laying methods: single-phase single-circuit, three-phase single-circuit, and single-phase four-circuit. Based on T obtained in steps S1 to S3... c0 T c0 'and T c1 The core temperature T of a three-phase four-circuit cable is determined by combined calculations. c .

[0080] Within the actual engineering scope, four circuit load currents I1 to I4 are randomly given. The steady-state temperature of the three-phase four-circuit cable core is solved using the finite element method and the method of the present invention, respectively. The calculation results of the two methods are compared, and the deviation and relative deviation between the two are calculated to verify the correctness of the method of the present invention in predicting the steady-state temperature of the three-phase four-circuit tunnel cable core.

[0081] Example 2

[0082] This embodiment relates to a method for predicting the steady-state temperature of the core of a three-phase four-circuit tunnel cable. The steady-state temperature of the cable core is calculated under three laying methods: single-phase single-circuit, three-phase single-circuit, and single-phase four-circuit. Then, the steady-state temperature of the core of the three-phase four-circuit cable is calculated.

[0083] Specifically, the following steps are included:

[0084] Figure 3 is a schematic diagram of a three-phase four-circuit tunnel cable, and the cable structure is shown in Figure 4. A physical model of the tunnel cable is established, which considers the complete flow and heat transfer process within the tunnel cable. In terms of flow, the model includes natural convection between the cable surface and the air inside the tunnel; in terms of heat transfer, the model includes conduction, convection, and radiation.

[0085] Figure 5 shows the steady-state thermal circuit model of a single-phase, single-loop (i.e., single-strand) tunnel cable. The thermal circuit elements include multiple heat sources and thermal resistances, whose parameters are determined based on IEC standards and finite element calculation results. Table 1 shows the solution results or expressions for each thermal resistance in the thermal circuit model:

[0086] Table 1

[0087] In Table 1, R i R p R a and R e These are the thermal resistances of the cable insulation layer, water-blocking layer, air gap, and outer sheath, respectively. R air The thermal resistance of the air layer inside the tunnel is determined by the convective thermal resistance R. cov With radiation thermal resistance R rad Composed of parallel connections, R t and R s These are the thermal resistance of the tunnel layer and the thermal resistance of the soil layer. Among them, the thermal resistance of the cable insulation layer, the thermal resistance of the water-blocking layer, the thermal resistance of the air gap, and the thermal resistance of the outer sheath belong to the thermal resistance of the cable body.

[0088] The above-mentioned convection thermal resistance R cov and radiation thermal resistance R rad The calculation method is as follows:

[0089] In the formula, A is the cable surface area / m² 2 π is the mathematical constant Pi, and T s and T t The average temperatures of the cable surface and the tunnel wall are respectively (K), D is the cable outer diameter (m), and ε is the average temperature of the cable surface and the tunnel wall. c The surface emissivity of the cable is σ = 5.67 × 10⁻⁶. -8 W·m -2 ·K-4 Let I be the blackbody radiation constant, and h(I) be the convective heat transfer coefficient of the cable surface (W·m). -2 ·K -1 , is a function of the load current I.

[0090] The surface heat transfer coefficient was determined by fitting the finite element calculation results under different load currents I. The fitting result is as follows: h(I)=kI+b=0.001224I+2.785

[0091] Where k and b are the slope and intercept of the fitted line, respectively.

[0092] Compared to single-phase single-circuit laying, three-phase single-circuit laying results in mutual heating between phases, leading to higher core temperatures. The steady-state core temperature T of the single-phase single-circuit tunnel cable is obtained using the thermal circuit model shown in Figure 5. c0 Based on this, the steady-state temperature T of the cable core of a three-phase single-circuit cable is solved using a correction method. c0 ', as shown in the following formula: T′ c0 =C1T c0

[0093] The method for solving the correction coefficient C1 is as follows:

[0094] 1) Calculate the temperature T of the single-phase, single-circuit cable core under current I using finite element simulation software. c0 and the core temperature T of a three-phase single-circuit cable c0 ', using C1=T c0 ' / T c0 The correction factor C1 was calculated, and the finite element calculation results for the working conditions and C1 are shown in Table 2.

[0095] Table 2

[0096] 2) Fit the coefficients C1 under different currents I shown in Table 2 to a function C1 = f(I);

[0097] 3) Given a load current I, on the one hand, the temperature T of the single-phase single-circuit cable core is solved using a thermal circuit model. c0 On the other hand, the correction coefficient C1 is solved using the fitting result C1=f(I), and the product of the two is the three-phase single-circuit cable core temperature T. c0 '.

[0098] Compared to single-phase single-circuit laying, single-phase multi-circuit laying results in mutual heating effects between circuits, leading to higher cable core temperatures. For four-circuit laying (as shown in Figure 1), when calculating the cable core temperature of circuit 1, it is necessary to consider the influence of the heating of the three adjacent circuits (circuit 2-4) on the cable core temperature of circuit 1. Therefore, an improved thermal circuit model based on the thermal resistance of mutual heating effect is proposed to solve the steady-state temperature of single-phase four-circuit cable cores. The following only gives the solution method for the cable core temperature of circuit 1 when all four circuits are running simultaneously (i.e., circuit 1 is the target cable, and circuits 2-4 are adjacent cables). The solution for the cable core temperatures of other circuits can be deduced by analogy.

[0099] The thermal influence of adjacent loops 2-4 on loop 1 is represented by a thermal resistance R in the air layer. air Thermal resistance R of tunnel layer t Additional thermal resistance R between m And called R m The thermal resistance is due to mutual heating, as shown in Figure 6. Thermal resistance R m This demonstrates the effect of adjacent circuits heating up the air temperature. It is precisely because the heating of adjacent circuit cables increases the air temperature between the cables that the core temperature of circuit 1 cable is higher than when it is laid alone. Mutual heating effect thermal resistance R m Calculate using the following formula:

[0100] In the formula, ΔT a R1 is the temperature rise in the tunnel air caused by the heating of adjacent circuits 2-4 (K); Q1 is the heat generated by circuit 1 under current I1 (W); C2 is a correction factor used to adjust R1. m The solution is more accurate, determined through model calibration.

[0101] The specific values ​​need to be determined by comparing the predicted results with the finite element calculation results. The purpose is to make minor corrections to the predicted results so that they are closer to the finite element calculation results.

[0102] The following is about the air temperature rise ΔT a Solve the following:

[0103] air temperature rise ΔT a This is caused by the combined heating effect of adjacent circuits 2-4, therefore ΔT a Let I2 be a ternary function of the currents I2 to I4 in loops 2 to 4. Assuming that the heat generation in adjacent loops 2 to 4 is independent, and since the steady-state thermal path of the cable is composed of linear components, the effect of heat generation in adjacent loops on the increase in air temperature satisfies the superposition principle, i.e.: ΔT a =ΔT a2 (I2)+ΔT a3 (I3)+ΔT a4 (I4)

[0104] In the formula, ΔTa2 (I2), ΔT a3 (I3), ΔT a4 (I4) represents the increase in air temperature (or air temperature rise ΔT) when loops 2, 3, and 4 are run individually. a (Contribution amount). To obtain ΔT a2 (I2), ΔT a3 (I3), ΔT a4 The specific expression for (I4) is calculated using finite element simulation software for the effect of ΔT when loops 2 to 4 are run individually. a The contributions are shown in Table 3:

[0105] Table 3

[0106] By performing a polynomial fit on the data in Table 3, ΔT can be obtained. a2 (I2), ΔT a3 (I3), ΔT a4 Substituting the expression for (I4) into ΔT a =ΔT a2 (I2)+ΔT a3 (I3)+ΔT a4 (I4) Obtain the air temperature rise ΔT a This leads to the mutual heating effect thermal resistance R. m The expression is as follows: When four loop currents I1 to I4 are given, on the one hand, the heat generation Q1 of loop 1 (target cable) is solved based on the current I1; on the other hand, the air temperature rise ΔT is solved based on the currents I2 to I4 of loops 2 to 4 (adjacent cables). a Then R m =ΔT a / Q1.

[0107] The R obtained from the above solution m Substituting the values ​​into the improved thermal circuit model shown in Figure 6, the core temperature T of loop 1 under a given operating condition can be determined by solving the thermal circuit. c1 .

[0108] Temperature T of a single cable core c0 Three-phase single-circuit cable core temperature T c0 'and the core temperature T of a single-phase four-circuit cable c1 Based on the solution results, the core temperature T of a three-phase four-circuit cable is solved using a combination method. c The assembly process consists of the following four steps, as shown in Figure 7:

[0109] 1) A single cable assembly is a single-phase four-circuit cable, and the core temperature is T c0 Transform into T c1 T c1The solution is obtained using the improved thermal circuit model based on the mutual heating effect thermal resistance described above;

[0110] 2) In a single-phase four-circuit installation, each adjacent circuit of circuit 1 adds one phase, and the core temperature of circuit 1 is increased from T... c1 Transform into T c1 +(T c1 -T c0 );

[0111] 3) Add one phase to each adjacent circuit of circuit 1. At this time, all adjacent circuits are complete three-phase circuits. The core temperature of circuit 1 is T c1 +(T c1 -T c0 ) becomes T c1 +2(T c1 -T c0 );

[0112] 4) Circuit 1 is changed from single-phase to three-phase, and the core temperature of Circuit 1 is changed from T c1 +2(T c1 -T c0 ) becomes C1[T c1 +2(T c1 -T c0 C1 is the correction factor between single-phase and three-phase cables.

[0113] In summary, the core temperature T of the lower circuit 1 of the three-phase four-circuit cable is... c The expression is as follows:

[0114] T c =C1[T c1 +2(T c1 -T c0 )], that is: T c =C1[T c0 +3(T c1 -T c0 )]

[0115] The accuracy of the above-mentioned method for predicting the steady-state temperature of three-phase four-circuit tunnel cables was verified. Independent and random currents I1 to I4 were applied to each of the four circuits to obtain the required operating conditions for the test. Some operating condition data are shown in Table 4:

[0116] Table 4

[0117] Under the 20 operating conditions listed in Table 4, the steady-state temperature rise of the cable core in loop 1 of the three-phase four-loop cable was calculated using the method of this invention and finite element simulation software. The deviations and relative deviations between the two methods under different operating conditions are shown in Figure 8. As can be seen from Figure 8, within the considered operating conditions, the maximum deviation between the steady-state temperature rise of the cable core predicted by the method of this invention and the finite element calculation result is within 2K, and the maximum relative deviation is within 2.5%, verifying the accuracy of the steady-state temperature prediction method for three-phase four-loop tunnel cables proposed in this invention.

[0118] This invention, based on a combination of cable core temperatures, extends the application of thermal circuit models to predict the steady-state temperature of tunnel cable cores from single-phase, single-circuit to three-phase, four-circuit models, achieving high prediction accuracy. Furthermore, this invention has broad applicability and can be further applied to predicting the steady-state temperature of tunnel cables with an even greater number of circuits, thus having a wide range of applications.

[0119] Example 3

[0120] This embodiment also relates to a method for predicting the steady-state temperature of the core of a three-phase multi-circuit tunnel cable. This method differs from Embodiments 1 and 2 in that it can be extended to three-phase multi-circuit tunnel cables, wherein the number of circuits is not limited to 4 circuits, but can be 5, 6 or even more circuits.

[0121] The difference lies in how the air temperature rise is calculated, specifically the air temperature rise ΔT. a It equals the sum of the increases in air temperature caused by each adjacent loop operating individually, calculated as follows: ΔT aj =f j (I j (j = 2, 3, ..., n)

[0122] Where n is the number of loops.

[0123] Example 4

[0124] The electronic device of this invention includes a central processing unit (CPU), which can perform various appropriate actions and processes according to computer program instructions stored in read-only memory (ROM) or loaded from a storage unit into random access memory (RAM). The RAM may also store various programs and data required for device operation. The CPU, ROM, and RAM are interconnected via a bus. Input / output (I / O) interfaces are also connected to the bus.

[0125] Multiple components in the device are connected to the I / O interface, including: input units such as keyboards and mice; output units such as various types of displays and speakers; storage units such as disks and optical discs; and communication units such as network interface cards (NICs), modems, and wireless transceivers. The communication unit allows the device to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0126] The processing unit executes the various methods and processes described above, such as methods S1 to S4. For example, in some embodiments, methods S1 to S4 may be implemented as computer software programs tangibly contained in a machine-readable medium, such as a storage unit. In some embodiments, part or all of the computer program may be loaded and / or installed on the device via ROM and / or a communication unit. When the computer program is loaded into RAM and executed by the CPU, one or more steps of methods S1 to S4 described above may be performed. Alternatively, in other embodiments, the CPU may be configured to execute methods S1 to S4 by any other suitable means (e.g., by means of firmware).

[0127] The functions described above in this document can be performed, at least in part, by one or more hardware logic components. For example, exemplary types of hardware logic components that can be used, without limitation, include: Field Programmable Gate Arrays (FPGAs), Application-Specific Integrated Circuits (ASICs), Application Standard Products (ASSPs), System-on-Chip (SoCs), Complex Programmable Logic Devices (CPLDs), and so on.

[0128] The program code used to implement the methods of the present invention can be written in any combination of one or more programming languages. This program code can be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code can be executed entirely on the machine, partially on the machine, as a standalone software package partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0129] In the context of this invention, a machine-readable medium can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. Machine-readable media can include, but are not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0130] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for predicting the steady-state temperature of a three-phase multi-circuit tunnel cable core, characterized in that, The method includes the following steps: Step S1: Establish a steady-state thermal circuit model of a single-phase, single-circuit tunnel cable, and use the established model to solve for the steady-state temperature T of the cable core in a single phase, single circuit. c0 ; Step S2: Based on step S1, the steady-state temperature T of the cable core under three-phase single-circuit laying is calculated using a correction method. c0 '; Step S3: For single-phase four-circuit laying, the influence of mutual heating effect between loop cables on the core temperature is attributed to the mutual heating effect thermal resistance, and it is introduced into the steady-state thermal circuit model of single-phase single-circuit tunnel cable to form an improved thermal circuit model to predict the steady-state core temperature T of single-phase multi-circuit cable. c1 ; Step S4: Treat the three-phase multi-circuit cable as a combination of single-phase single-circuit, three-phase single-circuit, and single-phase multi-circuit, and use the T obtained in steps S1 to S3. c0 T c0 'and T c1 Predicting the core temperature T of a three-phase multi-circuit cable c .

2. The method for predicting the steady-state temperature of a three-phase multi-circuit tunnel cable core according to claim 1, characterized in that, The steady-state thermal circuit model of the single-phase single-circuit tunnel cable considers the complete flow and heat transfer process within the tunnel cable. In terms of flow, the model includes natural convection between the cable surface and the air inside the tunnel. In terms of heat transfer, the model includes conduction, convection, and radiation.

3. The method for predicting the steady-state temperature of a three-phase multi-circuit tunnel cable core according to claim 1, characterized in that, The steady-state thermal circuit model of the single-phase single-circuit tunnel cable includes multiple heat sources and thermal resistances. The heat sources include the cable core conductor loss when the cable is subjected to alternating current, and the thermal resistances include the thermal resistance of the cable body, the thermal resistance of the air layer inside the tunnel, the thermal resistance of the tunnel layer, and the thermal resistance of the soil layer. The thermal resistance of the air layer inside the tunnel is determined by the convective thermal resistance R. cov With radiation thermal resistance R rad Composed of parallel connections.

4. The method for predicting the steady-state temperature of a three-phase multi-circuit tunnel cable core according to claim 1, characterized in that, The process of step S2 includes: Step S2-1: Under a given cable load current I, calculate the single-phase, single-circuit cable core temperature T using finite element simulation software. c0 and the core temperature T of a three-phase single-circuit cable c0 ', and thus the cable core temperature correction factor C1 at this time is obtained: C1=T c0 ' / T c0 Step S2-2, at different currents I i For (i = 1, 2, ..., N), repeat step S2-1 above to obtain C under different currents. i , where N is the number of different currents; Steps S2-3, at different currents I i Lower cable core temperature correction factor C i Based on the value, the correction factor C is fitted as a function of the load current I: C = f(I) Step S2-4: Given the cable load current I, the core temperature T of the three-phase single-circuit cable is... c0 The solution can then be found: T c0 '=CT c0 Where T c0 The steady-state temperature of the single-phase, single-circuit cable core is obtained in step S1.

5. The method for predicting the steady-state temperature of a three-phase multi-circuit tunnel cable core according to claim 1, characterized in that, The improved thermal circuit model construction process in step S3 includes: Step S3-1: The loop cable with the core temperature to be determined is called the target cable, and the cables of the other three loops are called adjacent cables. The effect of the heating of the adjacent cables on the increase of the core temperature of the target cable is constructed as an additional thermal resistance R in the air layer thermal path of the target cable. m And called R m To determine the thermal resistance due to mutual heating effect, the finite element method was used to calculate the air temperature rise inside the tunnel under different working conditions, and then the value of R was determined. m value; Step S3-2: Change the current I of each adjacent loop cable individually. j All other circuit cables were unloaded, and the finite element method was used to calculate the I values ​​for different circuits. j Average temperature rise ΔT of air inside the lower tunnel aj and ΔT aj Fitted to I j Functions: ΔT aj =f j (I j ) Where j is the j-th neighboring loop, and if loop 1 is the target cable, then j = 2, 3, ..., n; Step S3-3: The increase in air temperature ΔT when current is applied to all adjacent circuits simultaneously. a It equals the sum of the increases in air temperature caused by each adjacent loop operating individually: Step S3-4: Apply current I to the target cable, calculate the cable loss Q according to IEC standards, and then determine the mutual heating effect R in the steady-state thermal circuit of the target cable. m Calculate using the following formula: R m =C2ΔT a / Q Where, ΔT a Q is the temperature rise of the air inside the tunnel caused by the heating of adjacent loops 2 to n; Q is the heat generated by loop 1 under current I; C2 is a correction factor. Step S3-5: Calculate the mutual heating effect thermal resistance R obtained in step S3-4. m Substitute the expression into the thermal circuit model constructed in step S1 to form an improved thermal circuit model.

6. The method for predicting the steady-state temperature of a three-phase multi-circuit tunnel cable core according to claim 5, characterized in that, In step S3, the steady-state temperature T of the cable core of the single-phase multi-circuit cable is predicted. c1 Specifically: when n loop currents I1~I are given n At that time, the cable loss Q is determined based on the target cable current, and ΔT is determined using step S3-3 based on the current of the adjacent cables. a The value is then used in step S3-4 to obtain the thermal resistance R of the mutual heating effect at this time. m Then, substituting this into the improved thermal circuit model, the steady-state temperature T of the cable core under single-phase four-circuit conditions is obtained by solving the improved thermal circuit model. c1 .

7. The method for predicting the steady-state temperature of a three-phase multi-circuit tunnel cable core according to claim 1, characterized in that, In step S4, the core temperature T of the three-phase multi-circuit cable is predicted. c The process includes: 1) Combine single-phase single-circuit cables into single-phase multi-circuit cables, with the core temperature determined by the steady-state core temperature T of the single-phase single-circuit cable. c0 The steady-state temperature T of the cable core when converted to a single-phase multi-circuit cable c1 T c1 Solved using an improved thermal circuit model; 2) In single-phase multi-circuit laying, each adjacent circuit of circuit 1 adds one phase, and the core temperature of circuit 1 is increased from T c1 Transform into T c1 +(T c1 -T c0 ); 3) Add one phase to each adjacent circuit of circuit 1. At this time, all adjacent circuits are complete three-phase circuits. The core temperature of circuit 1 is T c1 +(T c1 -T c0 ) becomes T c1 +2(T c1 -T c0 ); 4) Circuit 1 is changed from single-phase to three-phase, and the core temperature of Circuit 1 is changed from T c1 +2(T c1 -T c0 ) becomes C1[T c1 +2(T c1 -T c0 )], where C1 is the correction factor between single-phase and three-phase cables; Therefore, the core temperature T of loop 1 in a three-phase multi-loop circuit is... c The expression is as follows: T c = C1[T c1 + 2(T c1 - T c0 )], that is: T c = C1[T c0 + 3(T c1 - T c0 )].

8. The method for predicting the steady-state temperature of a three-phase multi-circuit tunnel cable core according to claim 3, characterized in that, The aforementioned convection thermal resistance R cov The calculation is as follows: Where A is the cable surface area; h(I) is the convective heat transfer coefficient of the cable surface, which is a function of the load current I.

9. The method for predicting the steady-state temperature of a three-phase multi-circuit tunnel cable core according to claim 3, characterized in that, The radiation thermal resistance R rad The calculation is as follows: Where π is the mathematical constant Pi, and T s and T t These are the average temperatures of the cable surface and the tunnel inner wall, respectively; D is the cable outer diameter; ε c Let σ be the surface emissivity of the cable, and σ be the blackbody radiation constant.

10. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1 to 9.

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