A method for obtaining transient temperature rise of a single cable in a trench considering nonlinear convection heat dissipation
By constructing a grooved single cable thermal circuit model that considers nonlinear convection heat dissipation, and estimating and correcting relevant parameters, the problem in the existing technology that it is difficult to quickly and accurately obtain the transient temperature rise of the cable is solved, and efficient and accurate transient temperature rise is achieved. Temperature rise calculation provides important support for power grid planning and cable resource utilization.
Patent Information
- Application Number
- CN202110214369.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2021-02-26
- Publication Date
- 2025-01-21
- Estimated Expiration
- 2041-02-26
AI Technical Summary
The prior art is difficult to quickly and accurately obtain the transient temperature rise of trench cables, especially under nonlinear convective heat dissipation conditions, resulting in low cable resource utilization efficiency and difficulty in grid planning and construction.
By constructing a grooved single cable thermal path model that considers nonlinear convection heat dissipation, the model parameters are estimated, and an iterative method is used to obtain the transient temperature rise, including the thermal resistance between the core and the sheath, the cable's own heat generation, and the equivalent heat capacity. Estimation and correction of parameters such as equivalent thermal resistance.
It achieves the rapid and accurate acquisition of the transient temperature rise of a single cable in a trench without relying on skin temperature measurement, overcomes the problems of poor timeliness of numerical calculation and poor reliability of real-time monitoring in the existing technology, and provides a solution for cable equipment. Actual operation control provides direct basis.
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Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of power cable operation detection, and in particular to a method for obtaining transient temperature rise of a single cable in a groove taking nonlinear convection heat dissipation into consideration. Background Art
[0002] Cables entering and exiting substations mostly use trenches. There is nonlinearity in the convective heat transfer and radiation heat transfer inside the trench, especially the lack of clear quantitative laws for convective heat dissipation. Therefore, the heating problem of trench cables is relatively complicated.
[0003] Due to the particularity of power cable operation, it is generally impossible to obtain the cable core temperature through direct measurement, especially the real-time transient temperature of the core. Generally, engineering formula method based on test results, numerical algorithm or indirect measurement method is used to grasp the core temperature. Among them, the empirical formula method is mainly used to calculate the steady-state temperature rise of typical laying, and the scope of application is insufficient. The heat dissipation inside the groove involves thermodynamics and fluid mechanics. Its numerical calculation method has a large amount of calculation and a long calculation time when simulating the actual temperature rise of cables under multiple working conditions, and it is impossible to obtain the temperature rise changes in time. The indirect measurement method first requires the installation of optical fiber temperature measurement or other devices to obtain the cable skin temperature, and then infer the core temperature. The reliability and economy are poor.
[0004] Therefore, constructing a convenient and fast method to predict the transient temperature rise of trench cable groups is of great significance for the full utilization of existing cable resources and power grid planning and construction. The rapid acquisition of the transient temperature rise of a single cable in the trench is the basis for the rapid calculation of the transient temperature rise of the trench cable group. Summary of the invention
[0005] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and to provide a method for obtaining the transient temperature rise of a single cable in a groove taking into account nonlinear convection heat dissipation.
[0006] The purpose of the present invention can be achieved by the following technical solutions:
[0007] A method for obtaining transient temperature rise of a single cable in a trench considering nonlinear convection heat dissipation comprises the following steps:
[0008] 1) Construct a thermal circuit model of a single cable in a trench considering nonlinear convection heat dissipation;
[0009] 2) Estimate the parameters in the thermal circuit model of a single cable in a trench;
[0010] 3) The thermal circuit model of a single cable in the trench is iterated after parameter estimation to finally obtain the transient temperature rise of the single cable in the trench.
[0011] In the step 1), the thermal circuit model of a single cable in the groove considering nonlinear convection heat dissipation is composed of the thermal resistance R1 between the core and the sheath, the first branch where the cable's own heat generation Q1 is located, the second branch where the cable core equivalent heat capacity C1 is located, the third branch where the cable sheath equivalent heat capacity C2 is located, the fourth branch where the cross-section equivalent heat capacity C4 and its balanced thermal resistance R2 are located, and the fifth branch where the equivalent thermal resistance R3 of the cable sheath to the groove environment is located. The thermal resistance R1 between the core and the sheath is located between the second branch and the third branch, the first branch and the second branch are connected in parallel with the core temperature and the groove environment temperature as a temperature reference point at both ends, and the third branch, the fourth branch and the fifth branch are connected in parallel with the sheath temperature and the groove environment temperature at both ends.
[0012] In the step 2), the constant parameters estimated in the thermal circuit model of a single cable in the groove include the thermal resistance R1 between the core and the sheath, the equivalent heat capacity C1 of the cable core, the equivalent heat capacity C2 of the cable sheath, the equivalent heat capacity C4 of the cross-section, and the balanced thermal resistance R2 of the equivalent heat capacity of the cross-section, and the variable parameter is the equivalent thermal resistance R3 of the cable sheath to the groove environment.
[0013] In the step 2), the thermal resistance R1 between the core and the outer skin is obtained by finite element calculation, and then:
[0014] R1=(T cor -T ski ) / Q cab
[0015] Among them, T cor is the core temperature, T ski is the skin temperature, Q cab For heat flow.
[0016] In the step 2), a genetic algorithm is used to solve the transient parameters according to the thermal circuit model of a single cable in a groove, namely, the equivalent thermal capacity C1 of the cable core, the equivalent thermal capacity C2 of the cable sheath, the equivalent thermal capacity C4 of the cross section, and the balanced thermal resistance R2 of the equivalent thermal capacity of the cross section.
[0017] The step 3) specifically comprises the following steps:
[0018] 31) According to the cable current I and the set initial core temperature Get the initial cable self-heating And set the initial value of the equivalent thermal resistance R3 of the cable sheath to the trench environment
[0019] 32) Based on the initial cable self-heating The initial heat flow is obtained by calculating the thermal path model of a single cable in the trench after parameter estimation. and the wire core temperature in the next step;
[0020] 33) For the kth iteration, according to the heat flow of the previous step Update the corresponding skin temperature And according to the heat flow in the previous step Corrected to obtain the equivalent thermal resistance of the cable sheath to the trench environment
[0021] 34) According to the core temperature of the k-th iteration and cable current I k Get the heat generated by the cable itself Combined with the modified equivalent thermal resistance of the cable sheath to the trench environment Calculate heat flow And repeat steps 32)-34) to finally obtain the transient temperature rise of a single cable in the trench.
[0022] In the step 31), the groove ambient temperature is used as the initial wire core temperature.
[0023] In the step 31), according to the cable current I and the set initial core temperature Get the initial cable self-heating The specific calculation expression is:
[0024] Q1=I·R·(1+αT cor )·β
[0025] Where R is the resistance of the cable at zero degrees Celsius, α is the cable temperature coefficient, and β is the conversion factor.
[0026] In the step 33), according to the heat flow of the previous step Combined with the characterization of the wire core temperature T cor , skin temperature T ski , Groove ambient temperature T amb With heat flow Q cab Update skin temperature The specific expression is:
[0027] T ski =[Q cab -r1·(power((T ski +273) / 100,4)-power((T amb +273) / 100,4))]·[p1+p2·power(T amb ,k1)+p3·power(T ski ,k2)]+T amb
[0028] Where r1 is the radiation heat dissipation coefficient, p1, p2, p3, k1, k2 are the average convection heat dissipation coefficients, and power(·) represents the power exponential calculation of the base.
[0029] In the step 33), the modified expression of the equivalent thermal resistance of the cable sheath to the groove environment is:
[0030]
[0031] Compared with the prior art, the present invention has the following advantages:
[0032] 1. The present invention establishes a rapid calculation model for transient temperature rise of a single cable in a groove, which takes into account nonlinear convection heat dissipation and does not rely on skin temperature measurement. It overcomes the shortcomings of poor timeliness of numerical calculation methods and poor reliability of real-time monitoring methods, and provides a direct basis for subsequent research on rapid algorithms for transient temperature rise of groove cable groups and even actual operation control of cable equipment.
[0033] 2. In order to adapt to the nonlinear heat dissipation characteristics of the trench cable to the adjacent trench environment, the present invention introduces the nonlinear thermal resistance R3 that characterizes the "skin temperature-heat generation" law into the transient temperature rise calculation model for the first time, and the calculation process is clear and unambiguous.
[0034] 3. The calculation model established in the present invention itself is basically irrelevant to the loss, and only reflects the thermal characteristics of the cross section. It has a clear physical meaning and provides a direct basis for subsequent analysis and improvement. BRIEF DESCRIPTION OF THE DRAWINGS
[0035] Figure 1 This is a single cable transient temperature rise calculation model.
[0036] Figure 2 It is a schematic diagram of the finite element calculation model for the temperature rise of a single cable in a groove of the present invention.
[0037] Figure 3 It is the temperature rise process of cable core and outer sheath.
[0038] Figure 4 Comparison of the temperature rise process of the cable core and sheath.
[0039] Figure 5 It is the change process of the equivalent thermal resistance R3 of the "skin-groove environment" during the cable temperature rise process.
[0040] Figure 6 To compare the temperature rise process of the cable core and sheath under verification working conditions.
[0041] Figure 7 To verify the change of equivalent thermal resistance R3 of "skin-groove environment" during cable temperature rise under working conditions. DETAILED DESCRIPTION
[0042] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.
[0043] Example:
[0044] The present invention provides a method for obtaining transient temperature rise of a single cable in a groove considering nonlinear convection heat dissipation, and the principle is as follows:
[0045] The heat generation of a single cable mainly depends on the cable loss and the thermal characteristics of the section. The former has a clear correspondence with the operating current and operating temperature and can be directly applied; while the latter mainly depends on the geometric parameters of the section and the physical parameters of each part. According to the analysis of heat transfer, the thermal resistance of the cable body is related to the specific structure of the cable and can be regarded as unchanged in the calculation; the radiation heat dissipation, radiation heat dissipation thermal resistance, and convection heat dissipation thermal resistance are related to factors such as ambient temperature and heat generation. The laws of the first two are known and can be obtained by determining the formula; for the latter, we will seek to express it in a certain mathematical form through mathematical modeling, so as to provide the possibility for rapid calculation. Therefore, the present invention takes this as the main idea to carry out work.
[0046] The temperature reference point of the calculation model proposed in the present invention is the groove ambient temperature, as follows Figure 1 shown.
[0047] exist Figure 1 In the figure, Q1 is the heat generated by the cable itself; C1 is the equivalent heat capacity of the cable core; C2 is the equivalent heat capacity of the cable sheath; C4 is the equivalent heat capacity of the cross section; R1 is the thermal resistance between the "core and the sheath", R2 is the balanced thermal resistance of the cross section equivalent heat capacity; R3 is the equivalent thermal resistance of the cable sheath to the groove environment, which is the parallel connection of the convection heat dissipation thermal resistance and the radiation heat dissipation thermal resistance.
[0048] The determination of this model does not depend on the heat generated by the cable itself or the current size, but is only related to the thermal properties of the materials surrounding the cable. Except for R3, such properties can be considered to be basically unchanged within the general operating temperature range. For a specific cross-section, R3 can be expressed in a certain mathematical form through mathematical modeling. Therefore, after the model is established, there is no need to repeat numerical calculations such as finite element when transforming the cable current, and satisfactory results can be obtained directly through simple iterations.
[0049] 1. Main steps of the present invention
[0050] 1.1 Finite element calculation model
[0051] This method uses finite element calculation, and other numerical calculation or experimental methods can also be used in practical applications. Figure 2 shown.
[0052] The calculation adopts the finite element method, the groove is selected as 1m*0.5m, the air is selected as the ideal gas information, the cable is selected as the non-uniform thermal conductivity, and the thermal conductivity of the copper conductor is selected as 380W / (m2 *k), the thermal conductivity of XLPE material is selected as 0.3W / (m 2 *k), the conductor diameter is 5cm, the insulation layer thickness is 2.5cm, the calculation condition is randomly selected as the ambient temperature 0-30 degrees, the body heat flow is randomly selected, the number of iterations is 500 steps, and the relaxation factor is 0.5.
[0053] 1.2 Thermal circuit model establishment
[0054] The parameters R1 and R3 in the model can be extracted through steady-state calculations, and other parameters can be obtained through transient calculation data.
[0055] At different ambient temperatures T amb 、Heat flow Q cab Under the condition, the core temperature T of 10 working conditions cor , skin temperature T ski The steady-state calculation results are shown in Table 1.
[0056] Table 1 Calculation results of trench cable
[0057] Working conditions <![CDATA[Q cab (W / m)]]> <![CDATA[T amb (℃)]]> <![CDATA[T cor (℃)]]> <![CDATA[T ski (℃)]]> 1 53.83 25.42 64.07 32.84 2 81.53 11.64 70.71 23.36 3 72.76 16.13 69.12 26.56 4 0.39 25.44 25.69 25.47 5 37.71 14.07 41.8 19.9 6 68.55 23.78 72.98 33.17 7 8.24 20.85 26.94 22.15 8 13.24 10.42 20.27 12.58 9 116.51 15.89 98.96 31.48 10 17.77 18.95 32.01 21.68
[0058] (1) Calculation of thermal resistance R1 between “core and outer skin”:
[0059] According to the data in Table 1, after averaging, we can get: R1=(T cor -T ski ) / Q cab =0.5785K*m / W.
[0060] (2) Fitting of the “skin temperature-heat generation” law (i.e., the equivalent thermal resistance R3 of the cable skin to the groove environment) The present invention compares a variety of fitting relationships and proposes a calculation model for the skin temperature of a single cable in a groove, as shown in formula (1).
[0061]
[0062] Among them, r1 is the radiation heat dissipation coefficient, and p1, p2, p3, k1, and k2 are the convection heat dissipation coefficient groups.
[0063] According to the data in Table 1, the parameters in formula (1) are estimated using the “Macquart method + general global optimization method”. The results are shown in Table 2. The skin temperature fitting results are shown in Table 3. The error statistics between the fitting results and the direct calculation are shown in Table 4. Statistics show that the above fitting is reasonable and effective.
[0064] Table 2 Parameter estimation results
[0065] parameter Best estimate parameter Best estimate p1 0.241246 k1 0.788691 p2 0.003093 k2 0.729797 p3 -0.00773 r1 1.597521
[0066] Table 3 Skin temperature Tski fitting results
[0067]
[0068] Table 4 Statistics of skin temperature Tski error
[0069] Statistics Minimum maximum Mean Mean square error Skin temperature error (K) -0.09 0.16 0.023 0.078
[0070] Substituting the parameters in Table 2 into formula (1), we can obtain the temperature T of a single cable core in the groove. cor , skin temperature T ski , Groove ambient temperature T amb and heat Q cab The quantitative law of the relationship between them is shown in formula (2).
[0071]
[0072] (3) Extract transient parameters such as cable core equivalent heat capacity C1, cable sheath equivalent heat capacity C2, cross-section equivalent heat capacity C4, and balanced thermal resistance R2 of cross-section equivalent heat capacity.
[0073] The calculation conditions are ambient temperature 10℃, "cable thermal load step excitation", heat generation 75W / m; step length 1000s, calculation time 300*1000s, single-step iteration number 250 steps, relaxation factor 0.5. The finite element calculation results are as follows: Figure 3 shown.
[0074] according to Figure 1 The transient model of a single groove is shown, and the transient parameters are solved by genetic algorithm: C1 is the equivalent heat capacity of the cable core, C2 is the equivalent heat capacity of the cable sheath, C4 is the equivalent heat capacity of the section, and R2 is the balanced thermal resistance of the equivalent heat capacity of the section. The above parameters reflect the thermal transition process of the groove section.
[0075] 1) Set parameter range
[0076] Take C1, C2, C4∈(0,100), R2∈(0,100), binary coding, the initial population size is 200, the maximum genetic generation is 100, the crossover probability is 0.75, and the mutation probability is 0.25.
[0077] 2) Set the fitness function
[0078] according to Figure 1 The transient temperature rise response of the line core of the model shown is m c (i) Transient temperature rise response of outer sheath m s (i), and Figure 3 The calculated transient temperature rise response of the line core is shown in T c (i) Transient temperature rise response of outer sheath T s (i), the deviation of the two sets of curves is used as the fitness function, as shown in formula (3).
[0079]
[0080] 3) Set convergence criteria
[0081] When the fitness function reaches the maximum genetic generation number, it is less than 300*0.3*0.3*2=54, which is considered to be converged.
[0082] 4) Application of R3 rule
[0083] a. Set the initial value of R3 to 1. It should be noted that due to the existence of C1, C2, and C4, the setting of the initial value of R3 does not affect subsequent calculations;
[0084] b. Utilization Figure 1 The model shown and the set heat flow are used to calculate the heat flow Q of the branch where R3 is located. cab =I R3 ;
[0085] c. Using equation (2) to update, we can get the skin temperature rise T relative to the groove ambient temperature. ski With the core temperature rise T cor ;
[0086] d. Correction R3 = T ski / Q cab ,right Figure 1 The model shown is subjected to parameter adjustment;
[0087] e. Repeat steps b to d until the transient process ends.
[0088] 5) Calculation results
[0089] The calculation results are: C1=47.47W*s / (K*m), C2=62.58W*s / (K*m), C4=6.632W*s / (K*m), R2=0.257K*m / W, and the corresponding fitness function fitness=35.32, which is less than the convergence criterion 54, and the calculation can be considered to have converged.
[0090] According to the parameters, use Figure 1 The model shown in the figure calculates the temperature rise of the cable core and the outer sheath, and directly calculates the results with ANSYS (such as Figure 3 Compared with Figure 4 The error statistics are shown in Table 5.
[0091] The equivalent thermal resistance R3 of the "skin-groove environment" changes during the cable temperature rise process as follows: Figure 5 As shown, it can be seen that the model proposed in the present invention can well reflect the influence of nonlinear heat dissipation during the temperature rise process.
[0092] 1.3 Application steps and verification of thermal circuit model
[0093] (1) Model application steps
[0094] 1) Use the estimated parameters to establish a thermal circuit model and set the initial value of R3 to 1;
[0095] 2) Using the thermal circuit model and the initial heat flux Q1 (calculated based on the set initial core temperature (ambient temperature) and cable current), calculate the core temperature rise T at this time cor And the heat flow Q of the branch where R3 is located cab =I R3 ;
[0096] 3) Using formula (2), calculate the skin temperature rise T relative to the groove ambient temperature ski ;
[0097] 4) Through the formula R3 = T ski / Q cab Fix R3;
[0098] 5) Correct the cable heat flow Q1 in the thermal circuit model according to the updated core temperature rise and real-time current;
[0099] 6) Repeat steps 2) to 5) until the transient process ends, and obtain the transient temperature rise relative to the ambient temperature.
[0100] (2) Verification conditions
[0101] like Figure 7 As shown in Table 6, the above model is applied to the working conditions shown in Table 6, the groove ambient temperature is 15℃, and compared with the finite element calculation, the temperature rise comparison between the cable core and the outer sheath is Figure 6 shown.
[0102] Table 6 Cable working conditions
[0103] Time (*1000s) Cable(*800A) 0-100 0.50 100-200 1.00 200-300 1.12 300-400 0.22 400-500 0.87 500-600 1.12
[0104] Table 7 Cable core and outer skin temperature rise process error statistics
[0105] Minimum Maximum Mean Std. Deviation Core error (K) -2.56 1.50 0.0294 0.48815 Skin error (K) -1.39 0.44 -0.1242 0.36247
Claims
1. A method for obtaining transient temperature rise of a single cable in a trench considering nonlinear convection heat dissipation, characterized in that: The following steps are involved: 1) Construct a thermal circuit model of a single cable in a trench considering nonlinear convection heat dissipation; 2) Estimate the parameters in the thermal circuit model of a single cable in a trench; 3) The thermal circuit model of a single cable in the trench is iterated using the estimated parameters to finally obtain the transient temperature rise of the single cable in the trench; In the step 1), the thermal circuit model of a single cable in the groove considering nonlinear convection heat dissipation is composed of the thermal resistance R1 between the core and the outer skin, the first branch where the cable's own heat generation Q1 is located, the second branch where the cable core equivalent heat capacity C1 is located, the third branch where the cable outer skin equivalent heat capacity C2 is located, the fourth branch where the cross-section equivalent heat capacity C4 and its balanced thermal resistance R2 are located, and the fifth branch where the equivalent thermal resistance R3 of the cable outer skin to the groove environment is located. The thermal resistance R1 between the core and the outer skin is located between the second branch and the third branch, the first branch and the second branch are connected in parallel with the core temperature and the groove environment temperature as a temperature reference point at both ends, and the third branch, the fourth branch and the fifth branch are connected in parallel with the outer skin temperature and the groove environment temperature at both ends; In the step 2), the constant parameters estimated in the thermal circuit model of the single cable in the groove include the thermal resistance R1 between the core and the sheath, the equivalent heat capacity C1 of the cable core, the equivalent heat capacity C2 of the cable sheath, the equivalent heat capacity C4 of the cross section, and the balanced thermal resistance R2 of the equivalent heat capacity of the cross section, and the variable parameter is the equivalent thermal resistance R3 of the cable sheath to the groove environment; The step 3) specifically comprises the following steps: 31) According to the cable current I and the set initial core temperature Get the initial cable self-heating And set the initial value of the equivalent thermal resistance R3 of the cable sheath to the trench environment 32) Based on the initial cable self-heating The initial heat flow is obtained by calculating the thermal path model of a single cable in the trench after parameter estimation. and the wire core temperature in the next step; 33) For the kth iteration, according to the heat flow of the previous step Update the corresponding skin temperature And according to the heat flow in the previous step Corrected to obtain the equivalent thermal resistance of the cable sheath to the trench environment 34) According to the core temperature of the k-th iteration and cable current I k Get the heat generated by the cable itself Combined with the modified equivalent thermal resistance of the cable sheath to the trench environment Calculate heat flow And repeat steps 32)-34) to finally obtain the transient temperature rise of a single cable in the trench.
2. According to the method for obtaining transient temperature rise of a single cable in a groove considering nonlinear convection heat dissipation according to claim 1, it is characterized in that: In the step 2), the thermal resistance R1 between the core and the outer skin is obtained by finite element calculation, and then: R1=(T cor -T ski ) / Q cab Among them, T cor is the core temperature, T ski is the skin temperature, Q cab For heat flow.
3. The method for obtaining transient temperature rise of a single cable in a groove considering nonlinear convection heat dissipation according to claim 1 is characterized in that: In the step 2), a genetic algorithm is used to solve the transient parameters according to the thermal circuit model of a single cable in a groove, namely, the equivalent thermal capacity C1 of the cable core, the equivalent thermal capacity C2 of the cable sheath, the equivalent thermal capacity C4 of the cross section, and the balanced thermal resistance R2 of the equivalent thermal capacity of the cross section.
4. The method for obtaining transient temperature rise of a single cable in a groove considering nonlinear convection heat dissipation according to claim 1 is characterized in that: In the step 31), the groove ambient temperature is used as the initial wire core temperature.
5. The method for obtaining transient temperature rise of a single cable in a groove considering nonlinear convection heat dissipation according to claim 4, characterized in that: In the step 31), according to the cable current I and the set initial core temperature Get the initial cable self-heating The specific calculation expression is: Q1=I·R·(1+αT cor )·β Where R is the resistance of the cable at zero degrees Celsius, α is the cable temperature coefficient, β is the conversion factor, T cor is the core temperature.
6. The method for obtaining transient temperature rise of a single cable in a groove considering nonlinear convection heat dissipation according to claim 1 is characterized in that: In the step 33), according to the heat flow of the previous step Combined with the characterization of the wire core temperature T cor , skin temperature T ski , Groove ambient temperature T amb With heat flow Q cab Update skin temperature The specific expression is: T ski =[Q cab -r1·(power((T ski +273) / 100,4)-power((T amb +273) / 100,4))]·[p1+p2·power(T amb ,k1)+p3·power(T ski ,k2)]+T amb Where r1 is the radiation heat dissipation coefficient, p1, p2, p3, k1, k2 are the average convection heat dissipation coefficients, and power(·) represents the power exponential calculation of the base.
7. The method for obtaining transient temperature rise of a single cable in a groove considering nonlinear convection heat dissipation according to claim 1, characterized in that: In the step 33), the modified expression of the equivalent thermal resistance of the cable sheath to the groove environment is: