Cable group fluctuation load lower section type selection method

Abstract

The invention relates to the technical field of power cables, and discloses a cable group fluctuation load lower section type selection method, which comprises the following steps of: calculating a temperature rise condition of a cable group based on a thermal time constant of a cable and an additional thermal time constant of the cable, and calculating a current-carrying capacity factor of the cable group based on the temperature rise condition of the cable group; and performing section type selection of the cables in the cable group according to the current-carrying capacity factor of the cable group. The problem that the thermal performance of the cable is difficult to accurately reflect in the prior art is solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power cable, in particular to a cross section selection method under fluctuating load of cable group. BACKGROUND

[0002] Power cable is an important part of new energy investment, accounting for 5% in photovoltaic power station investment, 5% in wind power plant investment and 12% in offshore wind power investment. It is a link of design optimization space in addition to equipment, construction and building structures in new energy power station investment. However, the research on cable thermal time constant is very limited at present, and most of them are obtained by fitting temperature curve through experiment. The thermal time constant of cable of different sizes and different laying conditions is different, and the thermal time constant of cable is independent of environmental temperature and only depends on the thermal resistance and heat capacity of cable. In addition, the ampacity is an important factor to be considered in the selection of power cable selection. According to the working condition, it can be divided into long-term continuous load ampacity and fluctuating load ampacity. Long-term continuous load ampacity refers to the ampacity of cable system when the conductor temperature does not exceed the long-term allowable maximum working temperature, the stable heat flow field is formed, and the steady state temperature distribution working condition is reached. According to different use conditions, the appropriate cross section area of cable conductor can be selected to improve the use efficiency of power cable and reduce the investment cost of cable.

[0003] The existing calculation of thermal time constant of cable is mainly for single core and three core single cable laying condition, while in common cable engineering, cable group laying condition is common. Compared with the simple modeling method of single cable, the cable group system is more complex, and the temperature rise of the cable during operation will affect each other.

[0004] At present, the calculation of transient ampacity of cable group mainly uses finite element method and simulation software for calculation, and there is no practical analytical model. This leads to a big gap in the theoretical analytical calculation method of transient ampacity of cable group. SUMMARY

[0005] In order to overcome the defects of the prior art, the present application provides a cross section selection method under fluctuating load of cable group, which solves the problem that the existing technology cannot accurately reflect the thermal performance of cable.

[0006] The technical scheme adopted by the present application to solve the above problems is: A cross section selection method under fluctuating load of cable group, which is based on the ampacity factor of cable group to select the cross section of cable in cable group.

[0007] As a preferred technical scheme, a cross section selection method under fluctuating load of cable group is provided, which is based on the temperature rise of cable group to calculate the ampacity factor of cable group, and then the cross section of cable in cable group is selected according to the ampacity factor of cable group.

[0008] As a preferred technical solution, a cable group fluctuation load cross section selection method is provided, the temperature rise of the cable group is calculated based on the thermal time constant of the cable itself and the additional thermal time constant of the cable, the ampacity factor of the cable group is calculated based on the temperature rise of the cable group, and then the cross section selection of the cable in the cable group is performed according to the ampacity factor of the cable group.

[0009] As a preferred technical solution, when the temperature rise of the cable group is obtained, the temperature rise calculation formula of the cable group is:

[0010] Among them, represents the temperature rise at time t, represents the ambient temperature, t represents time, n represents the number of cables, x represents the cable number, represents the n th cable to the x th cable temperature rise contribution, represents the x th cable additional thermal time constant.

[0011] Further, The calculation formula of is:

[0012] Among them, represents the maximum working temperature rise, .

[0013] Further, the calculation formula of the transient temperature rise of the cable conductor is: Δθ = Δθ

[0014]

[0015] Among them, Δθ represents the steady-state temperature rise of the cable, represents the cable conductor loss, represents the thermal resistance of the cable system containing external soil or air, represents the current lasting t time, represents the maximum current value in the entire current cycle, represents the maximum working temperature rise, represents t i the load of the cable between time t i+1 , represents the maximum load in the whole fluctuating load process, represents the time number, t i represents a certain time in the cycle, t i+1 represents the next time of a certain time in the cycle, represents the highest load value in the whole fluctuating load, represents i the temperature at the time, represents i+1 the temperature at the time, represents the thermal time constant of the cable itself.

[0016] Further,the calculation formula of the thermal time constant of the cable is:

[0017]

[0018] wherein, represents the temperature of the cable conductor after the cable conductor is continuously loaded for t time, represents a natural number, t represents time, represents the current passing through the cable, represents the resistance per unit length of the cable conductor.

[0019] Further, the calculation formula of the ampacity factor is:

[0020] wherein, represents the ampacity factor of the cable group, represents the maximum value of the cable temperature at all times, represents the maximum stable operating temperature of the cable conductor.

[0021] As a preferred technical solution, the calculation formula of the thermal time constant of the single-core cable is: When the single-core cable is laid in air:

[0022]

[0023]

[0024] When the single-core cable is laid in soil:

[0025]

[0026]

[0027] When the single-core cable is laid in the pipe:

[0028]

[0029]

[0030] wherein, represents the thermal time constant of the cable, represents the total thermal capacity of the cable, represents the total thermal resistance of the cable, represents the first equivalent thermal resistance inside the cable, represents the second equivalent thermal resistance inside the cable, represents the third equivalent thermal resistance inside the cable, represents the air thermal resistance, represents the first equivalent thermal capacity of the cable, represents the second equivalent thermal capacity of the cable, represents the third equivalent thermal capacity of the cable, represents the fourth equivalent thermal capacity of the cable, represents the first equivalent thermal resistance of the soil, represents the sum of the fourth equivalent thermal capacity of the cable and the first equivalent thermal resistance of the soil, represents the pipe thermal resistance, represents the pipe thermal capacity, represents the first equivalent thermal capacity of the soil.

[0031] As a preferred technical solution, the calculation formula of the thermal time constant of the three-core cable is: When the three-core cable is laid in the air:

[0032]

[0033]

[0034] When the three-core cable is laid in the soil:

[0035]

[0036]

[0037] When the three-core cable is laid in the pipe:

[0038]

[0039]

[0040] wherein, represents the thermal time constant of the cable, represents the total thermal capacity of the cable, represents the total thermal resistance of the cable, represents the first equivalent thermal resistance inside the cable, represents the second equivalent thermal resistance inside the cable, represents the third equivalent thermal resistance inside the cable, represents the air thermal resistance, represents the first equivalent thermal capacity of the cable, represents the second equivalent thermal capacity of the cable, represents the third equivalent thermal capacity of the cable, represents the fourth equivalent thermal capacity of the cable, represents the first equivalent thermal resistance of the soil, represents the sum of the fourth equivalent thermal capacity of the cable and the first equivalent thermal resistance of the soil, represents the pipe thermal resistance, represents the pipe thermal capacity, represents the first equivalent thermal capacity of the soil

[0041] As a preferred technical solution, Compared with the prior art, the present application has the following beneficial effects: (1) The system considers the thermal resistance and thermal capacity characteristics of the cable and the surrounding medium, and deduces a thermal time constant calculation model suitable for different laying conditions; the accuracy of the model is comprehensively verified through finite element simulation analysis and experimental method, which provides a reliable theoretical basis for further optimizing the cable thermal performance analysis; (2) The present application deeply discusses the influence mechanism of typical laying environments such as air and soil on the thermal time constant and current-carrying capacity of the cable, and comprehensively reveals the key influence of the laying environment on the thermal response characteristics and current-carrying capacity of the cable, which provides scientific guidance for optimizing the cable laying scheme in different application scenarios; (3) The present application improves the accuracy of the cable thermal time constant calculation model in the soil laying environment by layering optimization of the soil model, improves the accuracy of the thermal time constant calculation, helps to reasonably select the cable cross section, and provides scientific guidance for optimizing the cable laying scheme in different application scenarios, further improves the safety and operation efficiency of the cable system; (4) The application proposes a new method for calculating transient temperature rise under fluctuating load condition based on thermal time constant for single cable; through in-depth analysis of temperature rise curve of cable under fluctuating load condition, transient current-carrying capacity is deduced, and current-carrying capacity factor M is calculated, and the accuracy and feasibility of the thermal time constant method in calculating M value are verified through comparison with IEC method and simulation method; (5) The application proposes a calculation method for calculating current-carrying capacity factor of cable group based on mutual heat influence, through mutual heat influence analysis of cable group under different laying conditions, temperature rise of cable group under fluctuating load is obtained through calculation, and the calculation method of current-carrying capacity factor of cable group is improved. BRIEF DESCRIPTION OF DRAWINGS

[0042] Fig. 1 It is a typical first-order transient thermal circuit diagram; Fig. 2 It is a cable conductor temperature rise curve diagram with thermal time constant τ; Fig. 3 It is a single-core cable complete transient thermal circuit diagram; Fig. 4 It is a single-core cable simplified equivalent transient thermal circuit diagram; Fig. 5 It is an equivalent transient thermal circuit diagram of single-core cable in air; Fig. 6 It is an equivalent transient thermal circuit diagram of single-core cable laid in soil; Fig. 7 It is an equivalent transient thermal circuit diagram of single-core cable laid in pipe; Fig. 8 It is a three-core cable complete transient thermal circuit diagram; Fig. 9 It is a three-core cable primary simplified equivalent transient thermal circuit diagram; Fig. 10 It is a three-core cable secondary simplified equivalent transient thermal circuit diagram; Fig. 11 It is an equivalent transient thermal circuit diagram of three-core cable in air; Fig. 12 It is an equivalent transient thermal circuit diagram of three-core cable laid in soil; Fig. 13 It is an equivalent transient thermal circuit diagram of three-core cable laid in pipe. DETAILED DESCRIPTION

[0043] The application will be further described in detail below in combination with embodiments and drawings, but the embodiments of the application are not limited thereto.

[0044] Example 1 As Figs. 1 to 13The purpose of the present application is to provide a scientific basis for cable selection in new energy power stations by accurately calculating the transient current-carrying capacity of the cable, reduce resource waste, improve the efficiency of cable use, and contribute to cost savings and economic benefits for new energy projects.

[0045] The present application carries out optimization research on the cross-section of new energy power cables based on the transient current-carrying capacity of the cable, providing a calculation basis for cable engineering optimization in new energy projects. First, the theoretical basis for the thermal time constant of the cable is established. Second, the calculation results of the analytical method and the simulation method are verified through experimental data, and the accuracy and applicability of the three methods are compared and analyzed. Then, for different laying environments, cable models are constructed and finite element analysis is carried out to study the influence of laying conditions on the steady-state current-carrying capacity of the cable and optimize the cable laying design. Finally, based on the thermal time constant model, combined with the characteristics of fluctuating load, the dynamic change trend of the transient current-carrying capacity of the cable is calculated and evaluated.

[0046] The present application constructs an analytical model of the thermal time constant of the cable suitable for air, soil and buried pipe laying environments, and optimizes the soil model in the soil laying environment by layering to improve the accuracy of thermal time constant calculation. Then, by comparing the thermal time constants solved by the analytical method, the finite element simulation method and the experimental method, the correctness of the analytical model is verified.

[0047] The present application proposes a new method for calculating the transient temperature rise under fluctuating load based on the thermal time constant for single cable and cable group. By deeply analyzing the temperature rise curve of the cable under fluctuating load, the transient current-carrying capacity is derived, and the current-carrying factor M and mutual heat time constant table are calculated. It is helpful to reasonably select the cross-section of the cable, and also provides scientific guidance for optimizing the cable laying scheme in different application scenarios, further improving the safety and operation efficiency of the cable system.

[0048] The present application includes the following aspects: Establish a single-core cable thermal time constant calculation model based on the analytical calculation method; Establish a three-core cable thermal time constant calculation model based on the analytical calculation method; Based on the above model analysis, establish a current-carrying factor M calculation model under the thermal time constant method.

[0049] More specifically, as follows: Cable thermal time constant calculation based on analytical calculation method: Similar to the circuit principle, when the first-order resistance-capacitance series circuit is suddenly applied with excitation in the initial state, its transient response is generally solved by three elements method, namely initial state, steady-state response and time constant. According to the similarity relationship of physical quantities in thermal circuit and circuit, the transient thermal response of cable is analyzed by using the knowledge of current field and circuit. The transient thermal circuit of cable is similar to the RC series circuit in circuit. When the cable conductor passes through the current I, the heat is conducted from the conductor to each direction, and the thermal process can be equivalent to the series and parallel thermal circuit of the thermal resistance and thermal capacity of each layer of the cable body and the surrounding medium. If the equivalent transformation can be carried out, the cable thermal circuit will finally be equivalent to a total thermal resistance T and a total thermal capacity Q in series, as shown in Fig. 1 .

[0050] Fig. 1 In the middle for conductor heat flow, for t conductor temperature at time, ambient temperature. From the figure, the following thermal balance equation can be established:

[0051] Solving the thermal balance equation can obtain the following general solution of the equation:

[0052] According to the initial condition: (0) = θ 0, the particular solution of the equation can be obtained:

[0053] In the formula T Q is a quantity with time, called thermal time constant, expressed by τ , the expression of is drawn into a curve, as shown in Fig. 2

[0054] The physical meaning of thermal time constant is that after the cable passes through the current, the time used for the change amount of conductor temperature rise from zero to 63.2% of the total temperature rise amount. It reflects the change speed of cable conductor temperature rise, and is one of the characteristic parameters of cable. The thermal time constant of cable τ can be obtained by formula T Q .

[0055] 1 Analytical method for calculating the thermal time constant of single-core cable model: ​The body structure of single-core cable is considered in layers of conductor, insulation layer, semi-conductive layer, metal sheath and outer sheath, and the heat transfer characteristics of different materials are not the same. In the transient thermal circuit, the insulation layer thermal resistance, semi-conductive layer thermal resistance, outer sheath thermal resistance need to be considered; and the conductor heat capacity, insulation layer heat capacity, semi-conductive layer heat capacity, metal sheath heat capacity, outer sheath heat capacity, in addition to the conductor loss, metal sheath loss, the equivalent thermal circuit is as follows Fig. 3 .

[0056] Wherein: T i Insulation layer thermal resistance T j Semi-conductive layer thermal resistance T k Outer sheath thermal resistance Q c Conductor heat capacity Q i Insulation layer heat capacity Q j Semi-conductive layer heat capacity Q s Metal sheath heat capacity Q k Outer sheath heat capacity W c Conductor loss W s Metal sheath loss.

[0057] According to the thermal resistance calculation method in JB / T 10181.21 standard and the heat capacity calculation method in IEC-60287 standard, the general thermal resistance and heat capacity calculation formula of each layer in the cable is obtained, and the corresponding formula is as follows: (4) (5) Wherein: ρ Thermal resistance coefficient of corresponding material D i Outer diameter of corresponding layer D i-1 Outer diameter of inner layer of corresponding layer c Thermal characteristic coefficient of corresponding material.

[0058] Through the above calculation, the thermal resistance and thermal capacity of the corresponding layers inside the cable can be calculated according to the structural parameters of the cable, providing data for the subsequent equivalent thermal resistance and thermal capacity calculation.

[0059] According to the IEC-60853 proposal, the thermal capacity of these layers is distributed to the adjacent temperature nodes according to the distribution factor, and the equivalent transient thermal circuit of the single-core cable after the distribution factor distribution simplification is shown in Fig. 4 . Among them, the equivalent thermal resistance inside the cable is T A , T B 、T C , and the equivalent thermal capacity is Q A , Q B , Q C 、 Q D .

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066]

[0067] Among them

[0068]

[0069]

[0070] ( ) The thermal time constant calculation model of the single-core cable laid in the air: When the single-core cable is laid in the air, due to the strong flowability of the air medium, the thermal hysteresis effect is not obvious, so the influence of air thermal capacity on thermal time constant can be ignored. Therefore, here only the influence of air thermal resistance on thermal time constant is considered. The equivalent transient thermal circuit of the single-core cable laid in the air is shown inFig. 5 .

[0071] where: T air - air thermal resistance According to the empirical formula of dynamic air thermal resistance, the total thermal resistance T air is calculated and assigned. The calculation formula of the total thermal resistance T , total thermal capacity Q and cable thermal time constant τ in this case are as follows:

[0072] where

[0073]

[0074] Thermal time constant calculation model of single-core cable laid in soil: The existence of surrounding medium thermal resistance and thermal capacity will affect the thermal time constant of the cable. For single-core cable laid in soil, due to the complexity of the structure and thermal properties of the soil, it is difficult to establish its transient thermal circuit. In the steady-state thermal circuit, IEC60853-1 proposes to calculate the soil thermal resistance by mirror method. At the same time, the influence of heat dissipation of surrounding medium with a radiation radius of 4 times the laying depth is considered.

[0075] The division method of the four regions of the soil is as follows: the inner diameter of the first region of the soil is equal to the outer diameter of the cable, and the inner diameter of the fourth region is 4 times the laying depth. Then the entire soil region is divided into four concentric circular regions according to the thermal capacity ratio, i.e. the volume ratio is 1:4:16:64, so the outer diameters of the first to fourth regions of the soil are D 1 ～D 4 (where D 4=4 L ), then the calculation formula of the layered soil is as follows:

[0076]

[0077] In the transient thermal circuit, the thermal capacity of the soil is considered, in order to better reflect the conductor temperature rise of the cable, the soil within 4 times the laying range is subdivided, so the soil is divided into four regions, the thermal resistance and thermal capacity corresponding to the four regions are calculated respectively, and are represented as T 4,0 、 T 4,1 、 T 4,2 、 T 4,3With Q 4,0 , Q 4,1 , Q 4,2 , Q 4,3 .

[0078] The heat capacity of each layer of soil is separated to adjacent nodes according to the distribution ratio factor, and the redistribution calculation is performed for four regions. The equivalent thermal resistance of the four regions is respectively represented as T D,0 , T D,1 , T D,2 , T D,3 The equivalent heat capacity is respectively represented as Q D,0 , Q D,1 , Q D,2 , Q D,3 The transient thermal circuit of the cable laid in the soil is shown in Fig. 6 .

[0079]

[0080] After the soil is equivalently distributed, the heat capacity and thermal resistance calculation formula corresponding to different layers is as follows:

[0081] Wherein

[0082] Since the heat capacity of the soil is much larger than the total heat capacity of the cable body, and the thermal resistance of the second, third and fourth layers of the soil is very small relative to the cable body, it is considered that the temperature of the last three layers is consistent with the surrounding environment, that is, only the first layer of the soil heat capacity model is considered. The calculation formula of the thermal time constant τ of the cable laid in the soil is as follows:

[0083]

[0084]

[0085] Thermal time constant calculation model of single-core cable laid in pipe When the single-core cable is laid in the pipe, the external environment of the cable is air, pipe and soil in turn, so the equivalent transient thermal circuit of the cable and the external environment is as shown in Fig. 7 .

[0086] Wherein:T pipe — pipe thermal resistance Q pipe — pipe thermal capacity T pipe with Q pipe The two data are still calculated according to the corresponding layer calculation formula in formula (4) and (5). And the thermal resistance and thermal capacity of air and soil corresponding to the above-mentioned calculation method are the same.

[0087] Because the soil thermal capacity is much larger than the total thermal capacity of the single-core cable body laid in the pipe, and the thermal resistance of the second, third and fourth layers of the soil is very small relative to the cable body, it is considered that the last three layers of temperature are consistent with the surrounding environment, that is, only the first layer of the soil thermal capacity model is considered. The calculation formula of the total thermal resistance T , total thermal capacity Q and cable thermal time constant τ in this case is:

[0088]

[0089]

[0090] 2 Analytical method for calculating the thermal time constant of a three-core cable: The body of the three-core cable is layered according to the internal structure, and the heat transfer characteristics of different materials are not the same. In the transient thermal circuit, the thermal resistance of the insulation layer, the thermal resistance of the filling and inner protective layer, and the thermal resistance of the outer protective layer, and the thermal capacity of the conductor, the thermal capacity of the insulation layer, the thermal capacity of the metal shielding layer, the thermal capacity of the filling layer and the inner protective layer, the thermal capacity of the armored layer and the outer protective layer need to be considered. However, due to the irregular shape of the filling layer, it cannot be calculated using the conventional method for calculating thermal resistance, so the shape factor method is used to calculate the thermal resistance of the filling layer. In addition to thermal resistance and thermal capacity, conductor loss, insulation loss, metal shielding loss and armored loss also need to be considered in the calculation of the thermal time constant of the three-core cable. The equivalent transient thermal circuit is as Fig. 3 shown in the figure.

[0091] Among them: T i — thermal resistance of the insulation layer T t — thermal resistance of the filling and inner protective layer T k — thermal resistance of the outer protective layer Q c — thermal capacity of the conductor Q i— Insulation thermal capacity Q s — Metal shield thermal capacity Q t — Filler and inner semi-conductive layer thermal capacity Q l — Armoring layer thermal capacity Q k — Outer semi-conductive layer thermal capacity W c — Conductor loss W i — Insulation loss W s — Metal shield loss W l — Armoring loss The first thermal circuit model simplification, the distribution of the proportion of the factors of these layers of thermal capacity to adjacent temperature nodes, after the proportion of the factors of the distribution of the simplified as shown in Figure 1, the equivalent transient thermal circuit of three-core cable, wherein the first simplification of the equivalent thermal capacity is Fig. 9 1、 Q 2、 Q 3、 Q 4, Q W 1、 W 2、 W 3.

[0092] Again, the distribution of the proportion of the coefficient of the simplification, the use of equivalent loss calculation of the proportion of the coefficient, after the second equivalent processing, the cable internal equivalent thermal resistance is T A 、 T B 、 T C , the equivalent thermal capacity is Q A 、 Q B 、 Q C 、 Q D . As shown in Figure 2. Fig. 10

[0093] The equivalent transient thermal circuit of each thermal resistance and thermal capacity calculation formula is as follows: （3-31） ​​

[0094]

[0095]

[0096]

[0097]

[0098]

[0099]

[0100]

[0101]

[0102]

[0103] wherein

[0104]

[0105]

[0106]

[0107]

[0108] The thermal time constant calculation model of three-core cable in air laying: The equivalent transient thermal circuit of three-core cable in air laying condition is as follows Fig. 11 .

[0109] T air The external thermal resistance of cable in air laying is processed in the same way as single-core cable air laying, and the calculation formula of T , Q and the thermal time constant of cable τ is as follows:

[0110]

[0111]

[0112] The thermal time constant calculation model of three-core cable in soil laying: The equivalent transient thermal circuit of three-core cable in soil laying condition is as follows Fig. 12 .

[0113] Since the soil heat capacity is much larger than the total heat capacity of the cable body, and the thermal resistance of the last three layers of soil is very small relative to the cable body, it is considered that the temperature of the last three layers is consistent with the surrounding environment, that is, only the first layer of the soil heat capacity model is considered.

[0114] The calculation formula of the cable thermal time constant τ under this condition is:

[0115]

[0116]

[0117] Thermal time constant calculation model of three-core cable laid in the pipeline: The equivalent transient thermal circuit of three-core cable under the condition of buried pipe laying is as follows Fig. 13 .

[0118] Since the soil heat capacity is much larger than the total heat capacity of the cable body, and the thermal resistance of the last three layers of soil is very small relative to the cable body, it is considered that the temperature of the last three layers is consistent with the surrounding environment, that is, only the first layer of the soil heat capacity model is considered.

[0119] The calculation formula of the cable thermal time constant τ under this condition is:

[0120]

[0121]

[0122] 2. Cable current-carrying capacity factor calculation: When accurately calculating the current-carrying capacity of the cable, the effect of thermal time constant needs to be considered. Traditional current-carrying capacity calculation methods usually assume steady-state conditions, but in the case of load fluctuations, this assumption may result in large errors. After introducing the thermal time constant, a more realistic dynamic thermal model can be established. According to the load variation mode and time characteristics, the heat transfer and temperature fluctuations in the cable are analyzed in combination with the thermal time constant.

[0123] For example, in periodic load fluctuations, the thermal time constant affects the amplitude and phase of the cable temperature fluctuations. Ignoring this factor may lead to inaccurate estimation of the current-carrying capacity, which in turn affects the safety of the cable. Overestimating the current-carrying capacity can lead to overheating and damage, while underestimating it can result in resource waste.

[0124] Cable thermal time constant: According to the principle of thermal equilibrium, the constant load on the cable is I by solving the differential equation, the following equation can be obtained

[0125]

[0126] In the formula: R c — Unit length resistance of cable conductor τ — Thermal time constant of cable system θ 0 — Ambient temperature θ c — Temperature of cable conductor after t time after the cable conductor is loaded (current is passed) T — Thermal resistance of cable system containing external soil or air

[0127] The load current of the cable in operation is dynamically changing, and due to the effect of the internal thermal capacity of the cable, the temperature of the cable lags behind the change of the current. The thermal time constant τ represents the time required for the conductor temperature to rise from the initial value to 63.2% of the total temperature rise after the cable is powered on. It reflects the speed of temperature rise change of the cable in the environment such as soil, air, etc.

[0128] Transient temperature rise of cable: The transient temperature rise of the cable refers to the phenomenon that the temperature of the cable deviates from the normal operating value and rises in a short time when the cable is subjected to non-steady load (such as sudden overload or intermittent load). Assuming that the load of the cable changes in steps at t1, the calculation formula of the temperature of the cable conductor at t2 can be derived:

[0129] In the formula: θ 1 — Temperature of cable conductor before the load changes in steps; θ 2 — Temperature of cable conductor at t2 after the load changes in steps.

[0130] Based on the fact that the dielectric loss of the cable is negligible at 35 kV and below, the cable temperature rise calculation formula according to JB1018.11 can be simplified as follows.

[0131]

[0132] In the above formula, since Δθ The steady-state temperature rise that the cable conductor can reach when the load current is I The maximum temperature of the direct-buried cable is conservatively considered to be 90 (maximum stable working temperature of cable conductor) - 25 (ambient temperature) = 65 (temperature rise of cable conductor) ℃, and the maximum temperature of the cable in air is Δθ Δθ ​90 (maximum stable operating temperature of cable conductor) - 40 (ambient temperature) = 50 (temperature rise of cable conductor) °C; T1 ~ T4 Thermal resistance of cable conductor to each part of soil or air.

[0133] W c T The product of I2 and the square of the temperature rise of cable conductor is equal to the transient temperature rise of cable conductor when the current is I. Δθ It can be seen that I2 is proportional to the square of the temperature rise of cable conductor, and the highest temperature rise is obtained when the current is In. Δθ Therefore, for a direct-buried cable conductor, when a step current flows through it,

[0134]

[0135] In the formula: W n Load when the highest temperature rise of cable system occurs W (t) Load when the temperature rise of cable conductor is t i Load when the temperature rise of cable conductor is t i+1 Load of cable between time t1 and t2 For a continuously changing load, the load can be divided into different time intervals for calculation. The smaller the size and duration of the divided load, the more accurate the calculation.

[0136] Calculation of load-carrying capacity factor M under thermal time constant method: Since this method is calculated under the condition of ignoring medium loss, it is only applicable to cables below 35kV. In this report, only three-core cables are analyzed.

[0137] According to the provided load data, the temperature rise of this period is calculated to obtain the temperature situation in this period. The maximum value of all temperatures is taken as the temperature rise of the cable conductor θ max The M value is calculated, and the calculation formula is as follows:

[0138] 3. Calculation of additional thermal time constant of cable group M under mutual heating effect: In the study of the temperature rise of the cable group, it is found that although the temperature rise of the cable group is fast at the beginning, it is slow to reach the steady-state temperature rise of the cable group, and the concept of thermal time constant is not applicable in the cable group. Therefore, the temperature rise of two cables (one is powered and the other is not) is studied. The unpowered cable is placed near the powered cable, and its temperature rise is observed. It is found that it has a certain thermal time constant, which is caused by the thermal diffusion of the powered cable. This thermal time constant is called additional thermal time constant.​

[0139] For the temperature rise of any single cable in a cable group, besides the temperature rise caused by the cable's own heat generation, the mutual heat generated by the other cables also contributes to the temperature rise. The derating factor table for different numbers and spacings of cables in a cable group can be obtained from the relevant IEC-60287 standard. Furthermore, the transient temperature rise formula for a cable group shows that the square of the current carrying capacity I is related to the temperature rise. The temperature rise is directly proportional to the temperature rise of a cable in a cable group. When calculating the temperature rise of a particular cable in a cable group, the contribution of each of the other cables to that cable can be calculated by combining Table 1 and the transient temperature rise formula of the cable group.

[0140] The temperature rise of cables in a cable group is composed of the temperature rise of the cable itself and the temperature rise contributed by the mutual heat influence of surrounding cables. The temperature rise of the cable itself and the temperature rise contributed by surrounding cables require a certain amount of time. The temperature rise time of cables in the cable group is described by thermal time constant and additional thermal time constant.

[0141] For calculating the temperature rise of a specific cable in a cable group, we made the following assumptions: The steady-state temperature rise of the cable can be calculated using the following formula.

[0142] in: n Represents the number of cables. x Represents the xth cable; Representing the n root cable to the first x The contribution of the cable to temperature rise; Representing the n The additional heating time constant of the root cable; for The following calculation method is used: when n When =1, it is obvious x =1

[0143] when n When =2, i =1,2

[0144]

[0145] when n When =3, x =1,2,3

[0146]

[0147]

[0148] when n When =4, x =1,2,3,4

[0149]

[0150]

[0151]

[0152] when n When =5, x =1,2,3,4,5

[0153]

[0154]

[0155]

[0156]

[0157] when n = n hour, x =1,2, , n

[0158]

[0159]

[0160]

[0161]

[0162]

[0163] in: The value is the derating factor for a certain spacing. n The recommended derating factor is given based on the number of cables, as shown in Table 1: Table 1. Derating Factors

[0164] When calculating the temperature rise of cable groups under fluctuating loads, the transformation is performed according to Formula 6-6, as follows: whenn =1, the cable transient temperature rise calculation formula is as follows

[0165] When n =2, the cable group transient temperature rise calculation formula is as follows

[0166] Similarly, n = n When

[0167] That is, the cable group heat transfer time constant is known, the temperature rise curve can be calculated, and the ampacity factor M of the cable group under the analytical method can be obtained through the above-mentioned ampacity factor calculation method.

[0168] According to the analytical method of the cable group mentioned above, the cable group is calculated, the temperature rise curve of the cable group can be solved by using the analytical method under the condition that the heat transfer time constant between the cables is known, and the M value of the cable group is further obtained.

[0169] The application analyzes the heat generation characteristics and environmental characteristics of single cable (single core and three core) in air, direct burial, buried pipe and other laying scenes, applies the thermal circuit analysis method to construct a cable thermal time constant solving model, and obtains the cable thermal time constant calculation formula in multiple scenes through parameter equivalence.

[0170] The application considers the cable laying environmental characteristics and structural characteristics, builds a cable finite element simulation model, obtains the cable thermal time constant in different scenes by simulating the actual cable operation, and verifies the thermal circuit model; secondly, a typical laying scene is selected, the model accuracy is verified through actual cable heat test, and then the accurate calculation of the cable thermal time constant in multiple scenes is realized.

[0171] The application considers different laying forms of single cable and multiple cables, analyzes the heat conduction process of each layer in the cable, and calculates the heat source loss of the cable system.

[0172] As described above, the application can be well realized.

[0173] All features disclosed in this specification, and / or all methods or processes specified in this specification may be combined in any combination, and / or substituted for one another, form new claims, unless the disclosure or the claims expressly exclude combinations, alternatives, sub-combinations, additional steps, alternative steps, and / or optional steps.

[0174] The above descriptions are only the preferred embodiments of the present application, not intended to limit the present application in any form. Any simple modification, equivalent replacement and improvement of the above embodiments made according to the technical essence of the present application, within the spirit and principle of the present application, shall still fall into the protection scope of the technical solutions of the present application.

Claims

1. A method for cross-section sizing of a cable group under fluctuating load, characterized by, The cross section of the cable in the cable group is selected based on the ampacity factor of the cable group.

2. The method of claim 1, wherein, The cross section of the cable in the cable group is selected based on the ampacity factor of the cable group calculated based on the temperature rise of the cable group.

3. The method of claim 2, wherein, The cross section of the cable in the cable group is selected based on the ampacity factor of the cable group calculated based on the temperature rise of the cable group.

4. A method of cross-section sizing of a cable population under fluctuating load according to any one of claims 1 to 3, characterized in that, The temperature rise of the cable group is calculated by the following formula: wherein, represents the temperature rise at time t, denotes the ambient temperature, t represents time, n represents the number of cables, x represents the cable number, represents the first n root cable to the first x root cable temperature rise contribution, represents the first x root cable additional thermal time constant.

5. A method of sizing the cross-section of a cable group according to claim 4, characterized in that, The calculation formula is: wherein represents the maximum operating temperature rise, .

6. A method of sizing the cross-section of a cable group according to claim 5, characterized in that, The transient temperature rise of the cable conductor is calculated by the following formula: The ampacity factor is calculated by the following formula: wherein, The thermal time constant of the single-core cable is calculated by the following formula: represents the steady state temperature rise of the cable, represents the cable conductor losses, represents the thermal resistance of the cable system to the surrounding soil or air, represents the current, t for a time, represents the maximum current value over the current cycle, represents the maximum operating temperature rise, represents t i the time instant to t i+1 the load on the cable between time instants, represents the maximum load over the fluctuating load process, represents the time instant number, t i represents a time instant in the cycle, t i+1 represents the next time instant of a time instant in the cycle, represents the maximum load value over the fluctuating load, represents i the temperature at a time instant, represents i+1 the temperature at a time instant, represents the thermal time constant of the cable itself.

7. A method of sizing the cross-section of a cable group according to claim 6, characterized in that, The calculation formula of the cable thermal time constant is: wherein, represents the temperature of the cable conductor after the cable conductor has been loaded for a certain t time, represents a natural number, t represents time, represents the current through the cable, represents the resistance of the cable conductor per unit length.

8. A method of sizing the cross-section of a cable group according to claim 7, characterized in that, When the single-core cable is laid in the air: wherein, represents the ampacity factor of the cable group, represents the maximum value of the cable temperature at all times, represents the maximum steady state operating temperature of the cable conductor.

9. A method of cross-section sizing for a group of cables under fluctuating load according to claim 7 or 8, characterized in that, When the single-core cable is laid in the soil: When the single-core cable is laid in the pipe: The thermal time constant of the three-core cable is calculated by the following formula: When the three-core cable is laid in the air: wherein, represents the thermal time constant of the cable, represents the total thermal capacity of the cable, represents the total thermal resistance of the cable, represents the first equivalent thermal resistance inside the cable, represents the second equivalent thermal resistance inside the cable, represents the third equivalent thermal resistance inside the cable, represents the air thermal resistance, represents the first equivalent thermal capacity of the cable, represents the second equivalent thermal capacity of the cable, represents the third equivalent thermal capacity of the cable, represents the fourth equivalent thermal capacity of the cable, represents the first equivalent thermal resistance of the soil, represents the sum of the fourth equivalent thermal capacity of the cable and the first equivalent thermal resistance of the soil, represents the pipe thermal resistance, represents the pipe thermal capacity, represents the first equivalent thermal resistance of the soil.

10. A method of sizing the cross-section of a cable group under fluctuating load according to claim 7 or 8, characterized in that, When the three-core cable is laid in the soil: When the three-core cable is laid in the pipe: ​ ​ wherein, represents the thermal time constant of the cable, represents the total thermal capacity of the cable, represents the total thermal resistance of the cable, represents the first equivalent thermal resistance inside the cable, represents the second equivalent thermal resistance inside the cable, represents the third equivalent thermal resistance inside the cable, represents the air thermal resistance, represents the first equivalent thermal capacity of the cable, represents the second equivalent thermal capacity of the cable, represents the third equivalent thermal capacity of the cable, represents the fourth equivalent thermal capacity of the cable, represents the first equivalent thermal resistance of the soil, represents the sum of the fourth equivalent thermal capacity of the cable and the first equivalent thermal resistance of the soil, represents the pipe thermal resistance, represents the pipe thermal capacity, represents the first equivalent thermal capacity of the soil.

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